\r\n\tThis book aims to present an overview of the current status of nanofibers, fabrication and recent trends in the fabrication of nanofibers, and functional nanofibers and applications of nanofibers in various fields including environmental, bio-sensing, drug delivery, catalysis, and medical. The book hopes to provide a piece of up-to-date information about the mentioned topics and fundamental knowledge necessary for the advanced study in the field of nanofibers and their applications, making it interesting to research students, scientists, engineers, and material scientists.
",isbn:"978-1-80356-387-9",printIsbn:"978-1-80356-386-2",pdfIsbn:"978-1-80356-388-6",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,isSalesforceBook:!1,hash:"a255898117275990dffe83c75a9f815d",bookSignature:"Dr. Maaz Khan",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/11462.jpg",keywords:"Nanofiber, Nanofiber Fabrication, Functional Nanofiber, Nanofiber Application, Fiber Technology, Electrospinning, Drug Delivery, Fabrication Strategy, Commercialization, Polymer, Tissue Engineering, Catalysis",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 23rd 2022",dateEndSecondStepPublish:"April 26th 2022",dateEndThirdStepPublish:"June 25th 2022",dateEndFourthStepPublish:"September 13th 2022",dateEndFifthStepPublish:"November 12th 2022",remainingDaysToSecondStep:"24 days",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Dr. Maaz Khan is an expert in the field of Nanoscience and Nanotechnology with over 100 articles and 3,300 citations to his name.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"107765",title:"Dr.",name:"Maaz",middleName:null,surname:"Khan",slug:"maaz-khan",fullName:"Maaz Khan",profilePictureURL:"https://mts.intechopen.com/storage/users/107765/images/system/107765.png",biography:"Dr. Maaz Khan is working as Deputy Chief Scientist (Professor) at PINSTECH, Pakistan. He has done Ph.D. and post doctorate in the field of Material Science (Nanoscience). His research interests include fabrication of nanomaterials and their structural, optical, magnetic, and electrical characterizations. He has authored more than 100 research articles and published 10 books. Presently, he is the Editor-in-Chief of ‘Journal of Materials, Processing and Design\\' and \\'The Nucleus\\'. He is also the Executive Editor of \\'International Journal of Nano Studies and Technology\\'. 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1. Introduction
The analysis of the mechanical integrity of Light Water Nuclear Reactors has experienced a strong evolution in the two latest decades. Until the nineteen eighties, the structural design was practically based on static loads with amplifying factors to take dynamic effects into account, (see e. g. Laheyand Moody, 1993), and on wide safety margins. Even if an incipient methodology for studying earthquake effects already existed, it was only at the end of the nineties when a complete analysis about dynamic loads, caused by a steam line guillotine-break of a BWR, was carried out for the first time (Hermansson and Thorsson, 1997). This analysis, based on a three-dimensional Computational Fluid Dynamic (CFD) simulation of the break, revealed a discrepancy with former applied loads that had never been exposed in the past due to inappropriate experimental setup geometry (Tinoco, 2001). In addition, the analysis pointed out the importance of also studying the load frequencies. The complete issue is further discussed in Section 3.
Nonetheless, CFD has shown to be a much more versatile tool. Issues like checking the maximum temperature of the core shroud of the reactor, when the power of the reactor is uprated (Tinoco et al., 2008), or estimating the thermal loadings during different transient conditions when the Emergency Core Cooling System (ECCS) has been modified, (Tinoco et al., 2005), or studying the automatic boron injection during an Anticipated Transient Without Scram (ATWS),(Tinoco et al., 2010a), have all been settled by means of CFD simulations.
Even more significantly, a rather complete CFD model of the Downcomer, internal Main Recirculation Pumps (MRP) and Lower Plenum up to the Core Inlet, (Tinoco and Ahlinder, 2009), has shed some light concerning the thermal mixing in the different regions of the reactor and also about the appropriateness of using connected sub-models as constituting parts of a larger model. The complete matter of thermal mixing is discussed in detail in Section 4.
Last but not least, CFD has demonstrated that it can be used to establish the causes of component failure. Even if justified suspicions existed about the cause of two broken control rods and of a large number of rods with cracks at the twin reactors Oskarshamn 3 and Forsmark 3, no knowledge existed about the details of the failure process (Tinoco and Lindqvist, 2009). It was first when time dependent CFD simulations revealed the structure of the thermal mixing process in the control rod guide tube that the cause, thermal fatigue of the rods, was confirmed and understood (Tinoco and Lindqvist, 2009, Tinocoet al., 2010b, Angele et al., 2011). This subject, together with the general problem of conjugate heat transfer, is analysed in Section 5.
Firstly, this chapter intends to communicate an historical view of CFD applied to the analysis of the mechanical integrity of Light Water Nuclear Reactors. Secondly, the chapter examines and evaluates several methodologies and approaches corresponding to the present and future modelling in the field of thermal hydraulics related to this type of analysis.
2. The determination of loadings
Considering the devastating effect that uncontrolled loadings may have on life and property, this section will begin by evoking the history of pressure vessel advance. This road to progress is paved with disastrous accidents which, during the decade of the eighteen eighties, amounted in the USA to more than 2000 boiler explosions. The establishment of ASME in February 1880 was, according to legend, directly prompted by the need to solve the problem of unsafe boilers (Varrasi, 2005). But it was first after the explosion on March 20, 1905, of the boiler of the R. B. Grover & Company Shoe Factory in Brockton, Massachusetts, (see Fig. 1 below, USGenWeb, 2011, Ellenberger et al., 2004) that the real effort of developing rules and regulations for the construction of secure steam boilers speeded up, urged by the public opinion. During the subsequent years, many states legislated, without too much coordination, about what was considered suitable instructions and procedures, leading to inconsistency in the construction requirements. Finally, in the spring of 1915, the first ASME Rules for Construction of Stationary Boilers and For Allowable Working Pressures consisting of one book of 114 pages, known as the 1914 edition, was made available, and the path towards regulation uniformity commenced.
Figure 1.
View of the R. B. Grover & Company Shoe Factory before (left) and after (middle and right) the boiler explosion on March 20, 1905, that killed 58 persons and injured 117, (USGenWeb, 2011, Ellenberger et al., 2004).
Since then, the ASME Code has become both larger and more comprehensive, comprising today 28 books, with 12 books dedicated to the Construction and Inspection of Nuclear Power Plant Components. Fortunately, even the boiler explosion trend in the USA has radically changed since 1905, as Figure 2 below shows.
Figure 2.
Trend for boiler explosions in the USA (from Hill, 2008).
For nuclear applications, the complete ASME code is mandatory only in the USA. In the European Union, on the other hand, no coordination process has been agreed. The Pressure Equipment Directive, (EU, 1997), has been adopted by the European Parliament and the European Council for harmonizing the national laws of Member States to promote and facilitate trade and exchange between States. But in the nuclear field, the application limits of the Directive and the Nuclear Codes (possibly ASME) have to be agreed with the National Nuclear Regulatory Authorities.
2.1. Section III
The ASME Boiler and Pressure Vessel Code, Section III, Rules for Construction of Nuclear Power Plant Components, of which the last Edition is from 2010, (ASME, 2010), regulates the design and construction of nuclear facility components. This Section “provides requirements for the materials, design, fabrication, examination, testing, inspection, installation, certification, stamping, and overpressure protection of nuclear power plant components, and component and piping supports. Components include metal vessels and systems, pumps, valves, and core support structures.”
Section III comprises Divisions 1, 2 and 3 and the introductory Subsection NCA that specifies General Requirements for Divisions 1 and 2. Division 1 contains eight Subsections, namely NB, for Class 1 Components, NC, for class 2 Components, ND, for class 3 Components, NE, for class MC Components, NF, for Supports, NG, for Core Support Structures, NH, for Class 1 Components in Elevated Temperature Service, and Appendices, both mandatory and nonmandatory, including, inter alia, a listing of design and design analysis methods.
2.2. Categorisation of parts in code classes
The aforementioned Code classes are proposed for the categorisation of parts of a nuclear power system, in accordance with the level of importance related to their function in the safe operation of the plant. However, the Code does not provide guidance for classifying the different parts. Classification, which is the responsibility of the Owner, has to be achieved by applying system safety criteria to be found in engineering standards and/or requirements of the Nuclear Regulatory Authorities. For instance, Class 1 components are those that are part of the primary core cooling system, or components that are used in elevated temperature service, and are constructed in accordance with the rules of Subsection NB. Class 2 components are those that are part of various important-to-safety emergency core cooling systems, and are constructed in accordance with the rules of Subsection NC. Class 3 components are those that are part of the various systems needed for plant operation, and are constructed in accordance with the rules of Subsection ND. Class MC components are metal containment vessels constructed in conformity with the rules of Subsection NE. Class CS components are core support structures constructed in accordance with the rules of Subsection NG. Mandatory and/or nonmandatory modifications and/or extensions to these classes may be included by Nuclear Regulatory or other Authorities, (STUK, 2000, IAEA, 2010).
2.3. Mechanical integrity and design specifications
The requirements for mechanical integrity are based on Norms and aim at ensuring that nuclear components shall withstand pressure and other types of loadings without system break or leakage. The Class to which the component belongs to shall govern the choice of Norms that are used for the analysis of its mechanical integrity. Design Specifications for mechanical integrity shall indicate the Loadings and Loading Combinations that a mechanical component is submitted to and, at the same time, the acceptable level of the Loadings and Loading Combinations, i.e. Loading Limits.
Within the realm of the ASME Code, the introductory Subsection NCA covers “general requirements for manufacturers, fabricators, installers, designers, material manufacturers, material suppliers, and owners of nuclear power plants”, (ASME, 2010). Here, Subsection NCA-2142 imposes to the Owner or his designee the duty of “identify the Loadings and combinations of Loadings and establish the appropriate Design, Service, and Test Limits for each component or support”. For this purpose, Loadings are separated into Design, Service and Test Loadings, and their Limits correspond to the acceptable Loadings permitted in a structural analysis. General directions about the characterization of Design, Service and Test Limits may be found in Subsection NCA-2142.4.
In order to be able to determine the Loadings that a component or support is submitted to, the different operating conditions that may affect the component or support have to be defined. The selection should include Normal Operation, Abnormal Conditions and Accidents that the component or support shall successfully withstand. Also, to be able to estimate the Limits that the Loadings must conform to, each operation condition must be related to an occurrence probability, being a lower probability associated with higher acceptable Limits. This matter may be solved by an event classification such as that of ANSI/ANS (1983a) for PWR and ANSI/ANS (1983b) for BWR. Here, Plant Condition PC1 corresponds to normal operating conditions, PC2 to anticipated conditions (occurrence frequency of > 10-2 times/year), PC3 to abnormal operating conditions (occurrence frequency of 10-2 - 10-4 times/year), PC4 to postulated accidents (occurrence frequency of 10-4- 10-6 times/year) and PC5 to low probability accidents (occurrence frequency of 10-6 - 10-7 times/year).
2.4. Design loadings and limits
Subsection NCA-2142.1 indicates that the Design Loadings shall be specified by stipulating (a) the Design Pressure, (b) the Design Temperature and (c) the Design Mechanical Loads. External and internal Design Pressure shall be consistent with the maximum pressure difference between the inside and outside of the item, or between any two chambers of a combination unit. The Design Temperature shall be equal to or higher than the expected maximum thickness-mean metal temperature of the part considered. The Design Mechanical Loads “shall be selected so that when combined with the effects of Design Pressure, they produce the highest primary stresses of any coincident combination of loadings for which Level A Service Limits (see below about limits) are designated in the Design Specification”. Primary stresses are those arising from the imposed loading, not those developed by constraining the free displacement of the structural system. Primary stresses are necessary to satisfy the mechanical equilibrium of the system. The component or support shall be structurally analysed for the Loadings associated with Design Pressure, Design Temperature and Design Mechanical Loads where, in general, their possible cyclic or transient behaviour is not included.
Design Limits shall designate the limits for Design Loadings. The Limits for Design Loadings shall conform to the requisites given in the applicable Subsection of Section III, i.e. NB, NC, ND, NE, NF or NG. In the event of Loadings that are not structurally analysed, the Limits are set to the same level as Service Limits A (see below).
2.5. Service loadings and limits
From the defined operation conditions, the Service Loadings may now be derived. Service Loadings are all loadings that a component is subject to under predictable normal and abnormal operational conditions and postulated accidents that have to be included in the Design Specification. More specifically, Service Loadings are pressure, temperature loads, mechanical loads and their possible cyclic or transient behaviour (see e.g. Subsection NCA-2142.2). Related loadings shall be integrated in Service Loading Combinations which, together with the corresponding Plant Condition or assigned probability, shall be assessed against relevant Limits.
According to Subsection NCA-2142-3, Service Limits are divided into four levels, namely Service Limits A, B, C and D. Service Limit A corresponds to bounds that contain the safety margins and factors that are required for the component to completely fulfil the specified performance. Service Limit B corresponds to bounds that contain smaller safety margins and factors than Limit A, but that still ensure a component free from damage. Service Limits C and D correspond to bounds with even more reduced safety margins and factors that now may lead to permanent deformation and damage of the component, a situation requiring repair of the component. The last two Limit levels may not be suitable for pressure vessels since their mechanical integrity should not be jeopardised.
The Plant Conditions (operation conditions together with their corresponding occurrence probability) shall decide which Limit to be applied. This coupling shall be account for in the Safety Analysis of the system (see e.g. ANSI/ANS 51.1 or ANSI/ANS 52.1, Appendix 2).
In the evaluation of a component according to Section III, Subsections NB, NC, ND, NE, NF or NG, quantifying values corresponding to Service Limits A to D shall be assigned to the allowed stresses.
2.6. Test loadings and limits
Test Loadings correspond to all Loadings that a component is subjected to during the tests that the component has to undergo. In general, these correspond to pressure tests but, if other types of tests are required, these must be stated in the Design Specification (see Subsection NCA-2142.3).
Test Limits indicate bounds for the tests to be performed on a component. In the evaluation of a component according to Section III, Subsections NB, NC, ND, NE, NF or NG, quantifying values corresponding to the Test Limits shall be assigned to the allowed stresses.
2.7. Load combinations
The overall-categorized Loadings with their corresponding Limits comprise a part of the background necessary to accomplish a structural analysis. Its complementary part is constituted by Load Combinations, the definition of which is, according to NCA-2142, a responsibility of the Owner of the Nuclear Facility, or of his designee. The combination of already identified Loads has to consider the type of Load, i.e. static or dynamic, global or local. In addition, the combination has to determine if they are consecutive or simultaneous, i.e. pressure and temperature loads related to a Loss of Coolant Accident (LOCA). Also, the time history of each Load shall be taken into account in order to prevent an unlikely superposition of non-simultaneous peaks. Eventually, the occurrence probability of each load combination shall be assessed.
Consequently, Design Conditions may include not only static loads like Design Pressure (DP), Design Temperature (TD) and Dead Weight (DW) but also dynamic loads like those generated by, for instance, the opening/closing of one safety valve (GV/SRV(1)). In the combination notation, the number of valves involved is indicated within parenthesis. Also, the occurrence probability of the maximum load may be added as the inverse of the number of valve activations under which this maximum is achieved, for instance “≥ E-3”, meaning the maximum load in 1000 activations (see e.g. Table 1).
More specifically, the loadings due to Operational Transients and Postulated Accidents may, for instance, include the Operation Pressure (PO), the Operation Temperature (TO), temperature transient (TT), joint displacement of reactor nozzle (D/RPV), building displacement (DB), condensation-induced water hammer when starting the high pressure Emergency Core Cooling (HP-ECCS) system or the Feed Water System (WH/SC), water hammer by star/stop of a pump (WH/PT) and global vibration due to safety valve discharge (GV/SRV).
The loadings due to Postulated Accidents may also include water hammer caused by a pipe break external to the Containment (WH/PBO), reactor vibrations generated by internal pipe break in the Containment (PRVV/PBI), global vibrations due to condensation oscillations in the suppression pool (GV/CO) and global vibration by condensation-induced pressure pulses, chugging, in the suppression pool, (GV/CH). Finally, loads caused by other incidents may be those corresponding to global vibrations due to Safe-Shutdown Earthquake (GV/SSE).
In a linear structural analysis, the effect of a Load Combinations is evaluated by a simple linear superposition of the response of each normal mode, separately analysed, through the procedure referred to as modal analysis. In cases where the time dependent functions of Loads acting simultaneously are statistically independent of each other, an upper bound of the total response may be estimated by a method denoted Square Root of Sum of Squares (SRSS), and not by the very conservative linear sum of the maxima. If the structural analysis is non-linear, as in Zeng et al. (2011), modal analysis is no longer valid and Collapse-Load analysis, together with non-linear Transient analysis, is required.
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\tCombination\n\t\t\t
\n\t\t\t
\n\t\t\t\tSuperposition Rule\n\t\t\t
\n\t\t\t
PlantCondition
\n\t\t\t
Service LimitLevels
\n\t\t
\n\t\t
\n\t\t\t
A01
\n\t\t\t
PD + DW
\n\t\t\t
−
\n\t\t\t
Design
\n\t\t
\n\t\t
\n\t\t\t
A03
\n\t\t\t
PO + DW + TT + D/RPV + D/B
\n\t\t\t
PC1/PC2
\n\t\t\t
A/B
\n\t\t
\n\t\t
\n\t\t\t
A06
\n\t\t\t
PO + DW + GV/SRV(1)
\n\t\t\t
PC1
\n\t\t\t
Design, A
\n\t\t
\n\t\t
\n\t\t\t
A07a
\n\t\t\t
PO + DW + GV/SRV(12 ≥ E-3)
\n\t\t\t
PC2
\n\t\t\t
B
\n\t\t
\n\t\t
\n\t\t\t
A07b
\n\t\t\t
PO + DW + GV/SRV(12 ≥ E-8)
\n\t\t\t
PC4
\n\t\t\t
D
\n\t\t
\n\t\t
\n\t\t\t
A08a
\n\t\t\t
PO + DW + GV/SRV(12 ≥ E-2)
\n\t\t\t
PC3
\n\t\t\t
C
\n\t\t
\n\t\t
\n\t\t\t
A09a
\n\t\t\t
PO + DW + WH/SC
\n\t\t\t
PC2
\n\t\t\t
B
\n\t\t
\n\t\t
\n\t\t\t
A09b
\n\t\t\t
PO + DW + WH/SC
\n\t\t\t
PC3
\n\t\t\t
C
\n\t\t
\n\t\t
\n\t\t\t
A11
\n\t\t\t
PO + DW + WH/PBO
\n\t\t\t
PC4
\n\t\t\t
D
\n\t\t
\n\t\t
\n\t\t\t
A13
\n\t\t\t
PO + DW + [(GV/SVR(1))2 + (GV/CO)2]1/2\n\t\t\t
\n\t\t\t
PC4
\n\t\t\t
D
\n\t\t
\n\t\t
\n\t\t\t
A14
\n\t\t\t
PO + DW + [(GV/SVR(1))2 + (GV/CH)2]1/2\n\t\t\t
\n\t\t\t
PC4
\n\t\t\t
D
\n\t\t
\n\t\t
\n\t\t\t
A16
\n\t\t\t
PO + DW + [(GV/SVR(12 ≥ E-3))2 + (RPVV/PBI)2]1/2\n\t\t\t
\n\t\t\t
PC4
\n\t\t\t
D
\n\t\t
\n\t\t
\n\t\t\t
A17
\n\t\t\t
PO + DW + [(GV/SVR(12 ≥ E-2))2 + (GV/SSE)2]1/2\n\t\t\t
\n\t\t\t
PC5
\n\t\t\t
D
\n\t\t
\n\t
Table 1.
Design Specifications for the feed water system (System 415) of a BWR (Forsmark 1, Forsmarks Kraftgrupp, 2007).
As an example of Design Specifications for pressure- and force-bearing components, Table 1 shows the different Load Combinations corresponding to a part of the feed water system of an internal pump BWR corresponding to Unit 1 of Forsmark Nuclear Power Plant (NPP). In this table, some of the Load combinations appear to be identical but they actually differ in, for instance, the pressure and/or temperature limits. For the sake of simplicity, this information has not been included in the table. It might be of some interest to point out that the Case A17 corresponds to a combination of an earthquake from San Francisco, USA, and another from Sweden, since the spectra of these earthquakes differ in the frequency content. This Combination has a Plant Condition PC5 for the Swedish reality, for which a safe shutdown of the reactor must be guaranteed.
Forsmark is the youngest Swedish NPP that became operational in 1980 with Unit 1 and whose installed power was completed in 1985 with the start of Unit 3. This Unit and Unit 3 of Oskarshamn NPP were the last reactors to be built in Sweden. These two internal pump reactors were designed at the end of the nineteen sixties and beginning of seventies, when the first pocket calculators begun to invade the market. But these calculators were initially quite expensive (Hewlett-Packard’s HP-35 cost $395 in 1972 which corresponds today to more than $2000), forcing the structural analyses to the use of rather simplified rough models, such as columns and beams subjected mainly to static loads, computed by means of slide rules. Dynamical effects were considered using a quasi-static approach with adequate safety margins (see e.g. Lahey and Moody, 1993), constituting the only feasible and realistic conservative approach compatible with the existing algorithms and computer capacity of the time. Nevertheless, thanks to the increased knowledge in the physics of single- and multi-phase flows, to the development of numerical models for fluids and structures together with the massive computing power through parallelization and low-price processers, mechanical integrity analysis of Light Water Nuclear Reactors has, during the two last decades, experienced a strong progress.
As discussed above, a nuclear reactor is designed for normal steady-state operation, for normal changes such as start-up, shutdown, change in power level, etc., without going beyond the design limits. In addition, the design must manage expected abnormal conditions and postulated accidents. In this context and according to Lahey and Moody (1993), an accident “is defined as a single event, not reasonably expected during the course of plant operation, that has been hypothesized for analysis purposes or postulated from unlikely but possible situations and that has the potential to cause a release of an unacceptable amount of radioactive material”. Consequently, a break in the reactor coolant system has to be considered an accident whereas a fuel cladding tube damage is not.
Among postulated accidents, a group known as Anticipated Transients Without Scram (ATWS), has a preferential status due to the interest that it has attracted since the end of the nineteen seventies. It assumes the partial or total failure of the automatic control rod insertion (SCRAM). A total ATWS has a very low occurrence probability in the reactors of Forsmark NPP. The total of about 170 control rods is divided into independent scram groups, each served by a scram module and containing eight to ten control rods. A scram module consists of a high-pressure nitrogen tank connected by a scram valve to another tank containing water to be pressurized by the nitrogen, water that may act on piston tubes for accomplishing rapid insertion of control rods. It might be of some interest to point out that similar scram systems successfully stopped units 2, 3, 4 and 7 of the Kashiwazaki-Kariwa NPP in Japan at the beginning of the earthquake Chūetsu of July 16, 2007 (the remaining units 1, 5 and 6 and were not operational due to refuelling outage). Still, Forsmark’s Units have an independent system of boron injection for emergency stop of the reactors, which is automated for Units 1 and 2 but still manual for Unit 3. Although the automation of this system, which was a Regulatory compliance, is not associated with safety issues, can, nevertheless, lead to new thermal loads for the fuel and/or adjacent structures in the reactor core (Tinoco et al., 2010a). As mentioned above, it is the duty of the owner or designee of the nuclear facility to identify the Mechanical Loadings and/or their Combinations and establish appropriate Limits. It is therefore necessary to analyse the effects of boron injection, a topic to be discussed in somewhat more detail in Section 3 of this chapter.
The design basis accident of an external pump Boiling Water Reactor (BWR) consists of a two-ended instantaneous circumferential break on the suction side of one of the main recirculation lines, resulting in a discharge from both ends. In a BWR with internal pumps, this postulated accident is not possible since there are no main recirculation lines. For an internal pump BWR, there no longer exists a single design basis accident, but rather a series of accidents, whose consequences for safety and mechanical integrity are at least an order of magnitude smaller than the rupture of a main recirculation line. One of these accidents consists of the two-ended instantaneous circumferential break of a steam line, which produces the highest loads in the vessel and reactor internals. A similar break of a feedwater line will result in lower Loads due to damping two-phase effects, in this case mainly from rapid boiling, i.e. flashing. Therefore, a design basis accident to be analysed for an internal pump BWR is a steam line break that will be discussed in more detail in the following Section.
3. A steam line break
Until the mid-nineties, studies and analysis of the effects of a steam line break were mainly based on experiments such as those of The Marviken Full Scale Critical Flow Tests (1979) where the pressure vessel consisted of a cylindrical tank with no internal parts, filled only with steam. For this reason, the only pressure waves considered in the loading analyses were the alternating decompression and compression waves formed in the pipe segment coupled to the cylindrical tank, between the break section and the coupling section to the tank (see for example Laheyand Moody, 1993, pp. 498-501). Consequently, the Loads given by the standard ANSI/ANS-58.2-1988, (ANSI/ANS, 1988), contain a component due to pressure waves of slightly over 30% of the product of the initial pressure of the cylindrical tank times the area of the section break. That the presence of the concentric steam annulus between the reactor vessel and the core shroud has an important part in the process of decompression by supporting standing pressure waves, (Tinoco, 2001), has been understood after the CDF analysis to be briefly describe in what follows.
A three-dimensional numerical analysis of the rapid transient corresponding to the rupture of the steam line (Tinoco, 2002) started in the late nineties with the purpose of obtaining the time signal of the pressure inside the reactor pressure vessel and its internals, to be later used in a structural time history analysis. This work was motivated as a part of the structural analysis related to replacement of the core grid of Units 1 and 2 of Forsmark NPP from the original, fabricated by welded parts that had developed cracks in the welds, to a new manufactured in one piece.
Historically, the three-dimensional numerical simulation of the fast transient was one of the first successes in this area of thermal-hydraulics. This was due to several factors that allowed an analysis with relatively limited computational resources, namely a negligible effect of turbulence, single-phase treatment due to flashing delay and the lack of importance of friction allowing relatively coarse mesh (see Tinoco, 2002).
Figure 3.
(a) View of the reactor with water surface indicated by blue line, (b) Model of the steam dome, annulus and dryers (down to water surface) after steam line break: 9 ms (upper view), 20 ms (central view) and 100 ms (lower view), (c) Simplified FEM model of the reactor with containment building, (d) detailed FEM model of the reactor with core grid in red.
Figure 3 shows in (a) an image of the reactor with the water surface indicated by a blue line. In (b) this figure shows a sequence of views of the pressure on the inner surface of the numerical model CFD ("Computational Fluid Dynamics") model (Tinoco, 2002), containing the steam dome, the annular region of steam and steam dryers. The steam separators, located under the dryers were modelled together as a single barrel without details. The first view of the sequence corresponds to 9.2 ms after the break, where the decompression wave extends with a single front symmetrically with respect to the axis of the steam nozzle, on whose outer end the line break is assumed to be located. The second view corresponds to 20.2 ms after the break, showing a picture of a less ordered and more chaotic pressure field due to reflections with different parts of the complex geometry of the reactor vessel. The third view corresponds to 100 ms from the break, displaying a more simplified image of the pressure than in the previous view, due mainly to the general decompression of the reactor that has almost homogenised the dome pressure. Image (c) shows a general view of the low-resolution structural analysis FEM model, including the containment building. Image (d) shows a view of the high-resolution FEM model of the reactor.
A structural analysis was performed using both models because, due to the rupture of the steam line, there is an effect, external to the reactor vessel, on the reactor containment building, not considered in Tinoco (2002) since it only treats internal effects. The analysis was conducted using the method of direct time integration, (Hermansson and Thorsson, 1997). The time signals of the loads were applied to the structures and, as a result, response spectra were generated for the different structures. A response spectrum is a graph of the maximal response (displacement, velocity or acceleration) of a linear oscillatory system (elastic structure) forced to move by a vibrational excitation or pulse (shock). Figure 4 shows in (a) two time signals of load components in the direction of the axis of the steam nozzle with the line break, acting on a node located in the core grid. The lower value corresponds to that computed directly by the CFD model. The higher, amplified value takes into account the effect of the second end of the break, which is connected to the adjacent steam line (Hermansson and Thorsson, 1997). Due to this connection in pairs of the steam lines, the reactor vessel is also decompressed, with a certain delay, through the contiguous steam nozzle. In (b),Figure 4 shows the smoothed envelope spectra in the direction of the axis of the steam nozzle with the line break, corresponding to the same node. It might be of same interest to reiterate that the loads applied in this analysis are about twice the loads according to standard ANSI/ANS-58.2-1988, (ANSI/ANS,1988), due to an effect of resonance of pressure waves in the steam annulus (Tinoco, 2001).
Figure 4.
(a) Time signals of the acceleration of a node in the core grid in the direction of the axis of the steam nozzle with break: value calculated by CFD and amplified value. (b) Smoothed envelope spectra in in the direction of the axis of the steam nozzle with break for the same node in the core grid.
4. The problem of mixing
Mixing the same fluid with different properties like temperature or concentration, or with different phases like steam and water, or even different fluids, is a far from trivial industrial problem. The process involved in the operation of Light Water Reactors contains many situations where mixing is of crucial importance like the mixing of reactor water and feedwater in BRWs, the mixing needed to regulate boron concentration in PWRs, etc. Yet, a high degree of mixing between the originally rather segregated components may be a hard task or, depending on the space and time scales of the mixing process, a complete mixing may even be impossible without special mixing devices. For instance, specially designed spacers in the nuclear fuel are needed to enhance the turbulent heat transport, and mixers are used to avoid thermal fatigue due to temperature fluctuations when flows with different temperatures meet within a tee-junction.
All these situations relay on turbulent mixing that, according to Dimotakis (2005), “can be viewed as a three-stage process of entrainment, dispersion (or stirring), and diffusion, spanning the full spectrum of space-time scales of the flow”. The mixing level, or quality of mixing, may be estimated, according to Brodkey (1967), through two parameters. The first parameter is the scale of segregation that gives a measure of the size of the unmixed lumps of the original components, i.e. a measure of the spreading of one component within the other. A length scale or a volume scale, analogous to the integral scales of turbulence, may be defined based on the Eulerian autocorrelation function of the concentration. Since the scale of segregation provides a measure of the extent of the region over which concentrations are appreciably correlated, it constitutes a good assess of the large-scale (turbulence-controlled eddy break-up) process, but not of the small scale (diffusion-controlled) process. The second is the intensity of segregation, given by the one-point concentration variance normalised with its initial value. It constitutes a measure of the concentration difference between neighbouring lumps of fluid, i.e. it describes the effect of molecular diffusion on the mixing process.
But, according to Kukukova et al. (2009), a general, objective and complete definition of mixing, or of its opposite, segregation, needs a third parameter, or dimension, as the authors of the reference express it, namely the exposure or the potential to reduce segregation. This rate of change of segregation associated to a time scale of mixing, combines the strength of the interaction, in this case the turbulent diffusivity, the concentration gradients and the contact area between components. Therefore, good mixing characterized by a small scale of segregation and a low intensity of segregation may be achieved if the mixing process is contained within the exposure time scale, i.e. for adequately high exposure.
However, many design problems of light water reactors that have arisen during their operation, originate from overconfidence about the mixing properties of turbulence. A classic example is that of the mixing of feedwater and reactor water in the downcomer of a BWR, in connection with Hydrogen Water Chemistry (HWC) to mitigate Intergranular Stress Corrosion Cracking (IGSCC) of sensitized stainless steel. The injection of reducing hydrogen gas to the feedwater was intended for recombination with oxidizing radicals contained in the reactor water and produced by radiolysis, through a turbulence-induced, optimal mixing in the downcomer. Surprisingly, the recombination effect for Units 1 and 2 of Forsmark NPP was not in proportion to the amount of injected hydrogen and the only solution appeared to be a major increase in the addition rate of hydrogen. But, in 1992, a very primitive and rough CFD model of an octant (45º) of the downcomer (Hemström et al., 1992) indicated that the flow field and the mixing were rather complex and highly tree-dimensional, leaving the regions between feedwater spargers with practically no mixing, and that buoyancy ostensibly aggravated the mixing issue. The poor mixing in the downcomer of Units 1 and 2 of Forsmark NPP arose from the design of the core shroud cover that, radially and freely over its entire perimeter, directed the warmer reactor water coming from the steam separators into the downcomer. Owing to the limited azimuthal extent of the four feedwaterspargers, four vertical regions without direct injection of colder feedwater were established in the downcomer. Due to buoyancy combined with mass conservation, the colder and falling regions contracted azimuthally, making the warmer and slower regions to expand. Turbulence acted within the colder regions, tending rather effectively to achieve temperature homogeneity, and at the boundary areas between the warmer and colder regions. The transit time of the vertical flow in the downcomer was not long enough for turbulence to achieve a complete temperature homogenization of the recirculation water. In other words, the turbulent diffusivity, the temperature gradients and the contact surfaces between cold and warm water were not large enough to achieve a good mixing, i.e. the exposure was too low. The mixing was achieved further downstream in two main steps, namely by forcing cold and warm water to meet within the inlet pumps, at the bottom of the downcomer, and by rotating agitation within the remnant vortexes at the pump outlets, produced by the Main Recirculation Pumps (MRP). This mixing process is quite effective, leaving only less than 3 % difference in temperature (Tinoco and Ahlinder, 2009) but for HWC, this homogeneity comes too late in the process since radiation at the level of the core in the downcomer is needed for triggering recombination of oxygen with hydrogen.
Finally, the problem of poor mixing in the downcomer was significantly reduced by modifying the design of the core shroud cover. Cylindrical-vertical walls were placed at the edge of the cover in the azimuthal locations facing the regions between spargers in order to completely block the reactor water flow. Radial flow out of the cover was allowed only regions in front of the spargers. This design was first tested in a rather advanced CFD model (Ahlinder et al., 2007), used to investigate HWC. The results obtained showed a higher degree of recombination with the modified core shroud. However, the decisive factor in the recombination was the level of radiation absorbed by the water in the downcomer, indicating that an effective recombination might not be possible over the complete fuel cycle without a modified core design. For a couple of years ago, this shroud cover design was implemented in Units 1 and 2 of Forsmark NPP, as a step in the modernisation and improvement of the process and safety to cope with a programmed power uprate. HWC was not carried out due to the aforementioned core design issue but an improved mixing in the downcomer has other advantages like minimizing the risk of cavitation in the MRPs.
The most complete CFD model including for the first time rotating MRPs was developed in 2008 (Tinoco and Ahlinder, 2009) for studying thermal mixing in an internal pump BWR. Figure 5 shows in (a) once more the view of the reactor as a reference, and in (b) it shows a view of the geometry involved in the CFD model that is limited from above by the free water surface. The model includes the downcomer (the water annular region between the inner surface of the reactor and the outer surface of the core shroud), the MRPs (4 pumps for this half of the reactor) and the lower plenum with the guide tubes of the control rods which extend to the entrance of the core reactor. In (c) a MRP is shown in more detail and in (d) the lower plenum, also in more detail. The complete CFD model contains slightly more than 25 million cells to represent the included part of the reactor. The correct flow through the model is achieved by rotating the pumps to the adequate rotational speed for normal operation. The thermodynamic properties of water as a function of pressure and temperature have been included in the physical properties of the studied fluid, allowing with that the analysis of the mixing of warmer recirculation water with cooler feed water. The results indicate a substantial mixing at the lower plenum inlet, being the maximum difference in the temperature of water entering the reactor core of about 2.5 ºC (see Tinoco and Ahlinder, 2009). This model may be used in the future to analyse the mixing of boron injected to the reactor with the surrounding water, as suggested below.
Figure 5.
(a) View of the reactor; (b) Model of the Downcomer, MR Pumps and Lower Plenum limited from above by the free water surface; (c) Model of MR Pump with diffuser vanes; (d) Lower Plenum detail with control rod guide tubes.
Originally, this CFD model consisted of two separated sub-models linked by boundary conditions at a common surface constituted by the Lower Plenum Inlet, since this split was geometrically and computationally optimal. The Lower Plenum Inlet is constituted by cylindrical-rectangular openings located almost directly downstream of the MRP outlets equipped with diffuser vanes. Even if these diffuser vanes recover an important amount of the mechanical energy stored in the rotation of the flow imparted by the pump, a vortex is still formed with a significant downstream extension, being this vortex responsible for an appreciable part of the thermal mixing. The use of a surface, as outlet for the first sub-model and as inlet for the second sub-model, to transfer the information of the flow behaviour from one sub-model to the other is not adequate. The information corresponding to the different fields is correctly transferred but no information about the field tendencies, i.e. the different gradients, reaches the second sub-model. In this case, the further development of the vortices coming from the pumps is corrupted beyond the inlets of the second sub-model. The result is a rather strong underestimation of the thermal mixing, predicting temperature differences of the order of 10 %, (see Tinoco and Ahlinder, 2009), temperature differences that have never been detected by measurements or, indirectly, by contingent fuel damage. The analysis of the different turbulence parameters objectively endorses this difference in mixing, which leads to the only reasonable recommendation of using a larger and computationally heavier model but right from the point of view of the physics of the flow. Model separations in CFD simulations, similar to the one described above, will deliver proper results only if the different gradients associated with the flow are small or negligible, otherwise a finite, common, transition volume is needed. This type of coupling between two CFD models might be difficult to achieve in rather standard commercial codes.
By Regulatory compliance, the safety system for the injection of boron to achieve an emergency stop of the reactor in case of an ATWS is now automatically operated in Units 1 and 2. Due to the automation, the accidental or programmed injection of boron will be associated with a set of new cases of postulated accidents that have to be analysed. Since the injection of boron in these Units is done in only two points, closely and not symmetrically located in the upper downcomer, the probability of an inhomogeneous distribution of boron, especially at the entrance of the core, is very high, as a preliminary study using a reduced model containing only the downcomer indicates (Tinoco et al., 2010a). This situation may lead to rapid variations in space and time of the reactivity of the core that might result in local maxima of thermal power that could ultimately damage the fuel and/or adjacent structures. The CFD simulations of boron injection and its mixing with the reactor water have to be linked to three-dimensional simulations of the neutron kinetics of the reactor core in order to correctly capture the physics of these thermal power variations.
5. Heat transfer
Turbulent thermal mixing implies, of course, transfer of heat from the warmer component, or fluid, to the colder component, resulting in a tendency to temperature and enthalpy homogenization. But, depending on the geometry of the thermal system, the process towards homogenization may have a rather well defined composition that involves the system boundaries which, in general, correspond to solid structures. These structures interact thermally with the fluid or fluids involved in the thermal mixing process, being the composition of the process decisive for the behaviour of the structures. According to the viewpoint of this work, the composition of the thermal mixing process includes firstly the morphology of the turbulent flow involved, i.e. the flow geometry, the eddy structure, the presence of stable boundary layers, etc. Secondly, it includes the thermophysical properties of the fluid and the thermophysical and geometrical properties of the solid boundaries. Depending on the composition of the thermal mixing process, the solid boundaries may or may not be exposed to the problem of high-cycle thermal fatigue. Therefore, the composition of the thermal mixing process, as defined above, implies the analysis of the complete system, including the solid boundaries, i.e. the type of heat transfer which is denoted as conjugate heat transfer, with rather advanced requirements regarding comprehensive information of the turbulent flow involved. The aforementioned concepts discussed so far will be emphasized through a slightly different analysis of the paradigm of thermal mixing and fatigue, i.e. the tee-junction.
5.1. Thermal mixing in a tee-junction
This exemplar of thermal mixing has been and is still being extensively studied, both experimentally and numerically, as the work of Naik-Nimbalkar et al. (2010) confirms with a rather wide, but not absolutely comprehensive, review of the literature about the subject. Probably the review should be completed by mentioning the experimental work of Hosseini et al.(2008) about the classification of the branch jet flow and about the structure of the flow field (Hosseini et al., 2009). Also other publications not included in the aforementioned review, (Muramatsu, 2003, Ogawa et al., 2005, Westin et al., 2008, OECD/NEA, 2011), that are experimental or including an experimental part for validation of a numerical simulation, investigate the bulk flow structures of the mixing in a tee-junction. All the references mentioned in this Subsection, and many others not included due to lack of space, have, as the main motivation, the purpose of studying, understanding and eventually controlling the wall temperature fluctuations associated with thermal fatigue. Particularly the reference OECD/NEA (2011), which is a rather major effort to validate numerical simulations of the thermal mixing in a tee-junction, clearly proclaims: “In T-junctions, where hot and cold streams join and mix (though often not completely), significant temperature fluctuations can be created near the walls. The wall temperature fluctuations can cause cyclical thermal stresses which may induce fatigue cracking”. But none of these references presents temperature or velocity data of the wall near region, i.e. the boundary layers, or of temperature at the walls. Even worse, the solid walls are never involved in any measurements, although it is the propagation of temperature fluctuations from the surface and inside the solid that may lead to fatigue cracking.
The reason for the absence of this crucial part of the mixing matter may be the great difficulty in measuring very close to walls and within the walls. For instance, velocity measurements in a thin boundary layer with Lase Doppler Velocimetry (LDV) are biased by even small density differences in the fluid, and temperature measurements within the solid are intrusive, cannot be relocated and may lead to errors due to contact continuity. But, in situations when temperature may be considered as a passive scalar, i.e. relatively small temperature differences not affecting the flow, the velocity measurements may be carried out in isothermal conditions. Since measurements of this kind have been done in this and other situations, to be reported in what follows, the true reason for the absence of this type of measurements in the study of tee-junction flows may be lack of knowledge about how vital the information related to temperature fluctuations close to the wall and within the wall is for understanding and being able to estimate the risk for wall thermal fatigue in a specific case. Of course, the information about flow behaviour close to the wall is directly related to the behaviour of the flow in the bulk, but the physical properties of fluid and the physical and geometrical properties of the wall will also affect the near wall flow, as the next paragraphs of this Subsection will describe. In other words, the problem of turbulent thermal mixing in a tee-junction is a process with a well-defined composition that has to be solved in its wholeness, i.e. a conjugate heat transfer problem.
As the preceding discussion reveals, measurements of the temperature fluctuations due to heat transfer within the boundary layer of a fluid close a wall and/or within the solid wall are very scarce. The work of de Tilly et al., (2006), de Tilly and Sousa (2008a) and de Tilly and Sousa (2008b) deals with the development of a multi-thermocouple planar probe of dimensions of the order of 300 μm to measure the instantaneous values of the wall heat flux in a boundary layer. Preliminary results of the wall heat flux have been obtained for the boundary layer flow developing downstream of a two-dimensional tee-junction. Even if this device is very promising, some questions arise from these tests, namely how to check the accuracy of the measurements with an independent method, how to handle thinner boundary layers than the instrument and how to deal with three-dimensional flow. In any event, this novel concept deserves a positive and successful development as a significant contribution to a difficult but important subject.
The measurements reported by Mosyak et al. (2001) seem to move this discussion away from the trail of wall temperature fluctuations and the risk of fatigue cracking since this reference treats the subject of constant heat flux boundary condition in heat transfer from the solid walls of channel flow. However, the experimental data substantiate the analytically demonstrated fact (Polyakov, 1974) that temperature fluctuations near a wall differ for different combinations of fluid and solid in conjugate heat transfer problems. Also Direct Numerical Simulations (DNS) of conjugate heat transfer (Tiselj et al., 2001, Tiselj et al., 2004, Tiselj, 2011) corroborate this information, where the governing parameters of the fluid-solid combination are the wall thickness dw, the thermal activity ratio K=(ρ⋅cp⋅λ)f/(ρ⋅cp⋅λ)w and the ratio of thermal diffusivities G=αf/αw. Here, ρ is the density, cp the isobaric specific heat, λ the thermal conductivity and α=λ/(ρ⋅cp) the thermal diffusivity. The sub-indices f and w indicate respectively “fluid” and “wall”. Depending on the values of dw and K, two asymptotic limits of the conjugate turbulent heat transfer exist at the same Reynolds and Prandtl numbers and at the same wall heat flux. When K → 0 and dw> 0, the turbulent temperature fluctuations do not penetrate the wall and the wall temperature does not fluctuate. When K → ∞, dw is of no importance, the turbulent temperature fluctuations do penetrate the wall and the wall temperature does fluctuate. In a particular solid-fluid case with given K and dw, the wall temperature behaviour will be between these two limiting cases, as may be observed through the results of Tiselj et al. (2001), given in Figure 6.
The results displayed in Figure 6 are not completely general since they have been obtained for G=1, as Tiselj and Cizelj (2012) point out, while Pr≈0.9, K≈0.2 and G≈0.04 for water and stainless steel at the pressure and temperature conditions of a BWR. Nonetheless, the main conclusion of these results is that, despite the large spectrum of temperature fluctuation variations as functions of the aforementioned material and geometrical parameters, the heat transfer rate for the limiting case K = ∞ is only 1 % higher than that for the other limiting case K = 0. The reason for this coincidence is the fact that the heat transfer rate is associated with the mean temperature gradient, which is very similar in both cases. These are good news for the heat exchanger designers, but the large spectrum of temperature fluctuation variations is bad news for the nuclear and other designers responsible for the mechanical integrity of solid structures.
Figure 6.
Temperature fluctuations from Tiselj et al. (2001) with ASME permission. Upper view: RMS-values, Pr = 7, d++ = 20, (a) fluid; (b) solid. Middle view: RMS-values, Pr = 7, K = 1, (a) fluid; (b) solid. Lower view: RMS-values normalized with ideal RMS-value of K= ∞, (a) Pr = 0.71; (b) Pr = 7; dotted lines from Kasagi, N., Kuroda, A., and Hirata, M., (1989).
The value G=1 associated with the results of Tiselj et al. (2001) shown in Figure 6, implies that the scale y++ ≡ y+, d++ ≡ d+ since y++ =\n\t\t\t\t\tGy+, a scale used for the results of Figure 6. Tiselj and Cizelj (2012) mention that this scale has an uncertain meaning and should be abandoned. Also, smaller values than G=1 will probably lead to lower temperature fluctuations inside the wall, as the results of Tiselj and Cizelj (2012) indicate, but for Pr=0.01. According to Figure 6, an increase in the Prandtl number will further decrease, though moderately, the temperature fluctuations inside the wall. The conclusion of Tiselj and Cizelj (2012) is that, for the combination liquid sodium-stainless steel (K≈1,G≈10), the results indicate a relative high penetration of turbulent temperature fluctuations into the simulated heated wall.
The lower values of the parameters for the combination water-stainless steel of BWR suggest that the penetration of turbulent temperature fluctuations in walls will be rather low under the conditions investigated through DNS simulations of channel flow. But, in other circumstances such as tee-junctions or control rod stems, which will be discussed in the next Subsection, the temperature fluctuations seem to be large enough to cause damage through thermal fatigue. It seems apparent that further investigation is needed to elucidate the wall behaviour in cases where no stable boundary layers are built and large structures coming from the bulk flow may strongly interact thermally with the walls. A first step in this direction has been taken by van Haren (2011), where a DNS of a tee-junction has been carried out. Unfortunately, only very preliminary results have been reported since, due to high computer requirements, the run-time was not enough to obtain a statistically stationary and converged solution.
Hopefully, the preceding discussion has made clear that the problem of thermal fatigue induced by flow temperature fluctuations is a conjugate heat transfer problem, i.e. a heat transfer problem of the specific combination fluid-wall. More knowledge is needed to understand the aforementioned interaction between large structures generated in the bulk flow and the walls. This knowledge should be obtained primarily by experiments but further difficulties with temperature measurements should be added to those already mentioned, i.e. intrusive, non-relocatable and contact continuity problems. For instance, the specificity of the combination fluid-wall questions the use in an experimental facility of Plexiglas or other material than the precise of the prototype to be investigated. Even the conditions of the experiment should match those of the prototype since they affect the different material parameters that ultimate influence the thermal fluctuations. Intrusive measurements have to be done with material properties matching those already mentioned of the walls, not only thermal conductivity. For instance, at the FATHERINO 2 facility at CEA Cadarache, briefly described by Kuhn et al. (2010), a thin brass mock-up (“Skin of Fluid Mock-up”) has been developed to visualize, by infrared thermography, the mean and fluctuating temperature fields at the interface of the fluid and the wall. This mock-up may only have relevance as a case for validating numerical simulations, as it is used by Kuhn et al. (2010), but more knowledge is needed about the correct conditions, to be discussed below, for simulating the wall heat transfer, including the right distribution of temperature fluctuations within the wall.
Numerical simulations of conjugate heat transfer including temperature fluctuations inside the solid structure other than DNS have already been carried out using diverse approaches. The previously mentioned reference, Kuhn et al. (2010), uses a LES approach to resolve the flow and temperature fields inside the fluid for two cases, namely a thin-wall brass model and a thick-wall steel model. The results show relatively large differences between models in both the mean temperature fields and the distribution of temperature fluctuations inside the solids. This is attributed only to the heat conduction in the thicker wall, apparently both radial and axial, with no further analysis of other possible reasons, i.e. nothing is commented about the different combinations fluid-solid. From the numerical point of view several questions arise, firstly the fact that the same grid is used for the two walls. Secondly, y+ may be up to 5 in the mixing region when requirements in LES of channel flow, for less than 1 % difference in heat transfer rate with DNS results, are y+ = 0.5, x+ = 30 (streamwise) and z+ = 10 (spanwise), according to Carlsson and Veber (2010). In Kuhn et al. (2010) nothing is mentioned about the grid resolution in the streamwise and/or spanwise directions. However, a validation like that of Carlsson and Veber (2010) about the distribution of temperature fluctuations has not yet been carried out, a situation that sheds some doubts about the accuracy of the results obtained in Kuhn et al. (2010) and, for the rest, of the results obtained with any other methods different from DNS.
A brief and definitely incomplete review of other approaches reveals the use of LES with thermal wall functions (Châtelain et al., 2003). The results show that the temperature fluctuations in the vicinity of the wall and inside the wall can be highly underestimated a fact that is corroborated by Pasutto et al. (2006) and Jayaraju et al. (2010). Also some attempts have been done with the RANS approach, with varied results (Keshmiri, 2006, Tinoco and Lindqvist, 2009, Tinocoet al., 2010b, Craft et al., 2010), and with the more unconventional Lagrangian approach of Pozorski and Minier (2005). The majority of the numerical results discussed in this Subsection are waiting for an experimental validation, or numerical by DNS, in order to be able to establish the correct methodology to be used in future simulations for estimating the risk of thermal fatigue.
5.2. The control rod issue
Broken control rods and rods with cracks were found in the twin reactors Oskarshamn 3 and Forsmark 3 in the fall of 2008.As a part of an extensive damage investigation, time dependent CFD simulations of the flow and the heat transfer in the annular region formed by the guide tube and control rod stem were carried out with a model containing 9 million computational cells (Tinoco and Lindqvist, 2009). Due to limitations in time and computer resources, only a quadrant of the guide tube and control rod with an axial length of approximately 1 m was included in the model, as Figure 7 shows. Also an Unsteady RANS (URANS) approach with the SST k-ω model was chosen for handling turbulence.
Figure 7.
CAD view (left) and drawing of a part of the CFD model used inTinoco and Lindqvist (2009).
In this figure, where gravity is from right to left in the right view, the different mass flow rates per quadrant are indicated with their temperatures by arrows. The upper bypass inlet (right) divides its mass flow rate into two holes of14.6 mm in diameter, resulting in inlet velocities of about 10 m/s. The lower bypass inlet has only one hole of 8 mm in diameter that connects to an annular channel before the flow is delivered with relatively low velocity to the annular region between control rod stem and guide tube.
Figure 8.
Temperature sequence showing a large scale variation of the surface temperature of the control rod stem with a period of ~15 seconds (temperatures in K).
Figure 8 shows a typical time sequence, from left to right and in two rows, of the surface temperature of the control rod stem with a large scale variation with a frequency of approximately 0.07 Hz. Three horizontal planes are shown in the views, namely the upper plane corresponding to the lower bypass inlet, the middle plane corresponding approximately to the region of the break (10 cm below the lower bypass inlet) and the lower plane corresponding approximately to the end of the inlet region of the cold crud-cleaning flow (20 cm below the lower bypass inlet). These simulations together with metallurgical and structural analyses indicated that the cracks were initiated by thermal fatigue.
The results of the damage investigation were accepted by the Swedish Nuclear Regulatory Authorities for a reactor restart with new control rods. Meanwhile, further studies had to be accomplished to clarify some remaining matters. One of the contested issues concerned the validity and accuracy of the CFD simulations. Consequently, new CFD models, (Tinoco et al., 2010b), were developed in conformity with the guidelines of Casey and Wintergerste (2000) and Menter (2002), while the URANS approach with the SST k-ω model was preserved, and validation experiments were carried out. The largest CFD model contained 16.8 million cells because large effort was put into maintaining a value of y+~ 1 for the dynamic mesh resolution in the near wall region of the control rod stem at the level of the mixing area. Validation tests had indicated that a y+ close to 1 is a necessary condition to ensure sufficiently accurate heat transfer results (Tinoco et al., 2010b), but no control was done about the values of x+ and z+ since the results of Carlsson and Veber (2010) were at that time not known. Figure 9 shows the low y+ values for the grid at the stem wall in the mixing region indicated by the horizontal black line for different times of the simulation.
Figure 9.
Grid y+ adjacent to the control rod wall at different times of the simulation.
Figure 10 shows in the upper view a sequence of colour pictures representing the velocity magnitude, maximized to 1 m/s (red scale ≥ 1 m/s), in a vertical plane bisecting the quadrant and containing the region below the jets of the upper bypass inlet. The pictures are completely symmetric since the original data of the quadrant have been mirrored with respect to vertical axis. In this sequence, it is possible to observe many structures forming and moving downwards, towards the lower bypass inlet, in the annular region between the stem and the guide tube. In this view, the black line indicating the level of the stem weld corresponds to the level of plane 7 shown in the middle view.
The middle view depicts five time signals of the axial vertical velocity component of the fluid at radially 2 mm from the stem wall. The points are located in plane 7 (blue line in left reference picture) at 5 different azimuthal positions. The signals indicate large vertical intermittent movements downwards, with speeds of the order of 1 m/s and frequencies of 0.1-0.2 Hz which corroborate the impression given by the pictures of the upper view. This is the dynamical mechanism of the mixing responsible for the thermal fatigue of the control rod stems. This effect has been further confirmed by simulations of guide tubes without the upper bypass inlet, reported in Tinoco and Lindqvist (2009), where no such structures are present.
The lower view shows the thermal consequences of the above described dynamical process that transports large lumps of warm fluid downwards with relatively large velocities. The maxima of the temperature time signal correlate well with the minima of the axial vertical velocity component. The fact that the temperature signal (in blue) corresponds to only one single fluid point indicates that the lumps of warm fluid cover a large part of the annular gap modelled in the quadrant. This view also shows the temperature signal of two points located inside the solid, namely the first located radially at 0.5 mm from the stem outer wall (in green) and the second located radially at 2 mm from the wall (in red). In this graph, it is possible to observe that, compared to the fluid signal, both solid signals are damped, with high frequency variations filtered out. Also, the red signal is not always smaller than the green indicating switches in the direction of the heat flux.
Figure 10.
Upper view: velocity magnitude limited to 1 m/s (red ≥ 1 m/s). Middle view: time signal of axial vertical velocity component of the fluid in plane 7 (blue line in left reference picture) at 2 mm from the stem wall and for 5 different azimuthal positions. Lower view: temperature signal at three radial points at plane 7 with azimuthal angle of 45º.
However, the central question is still the quality of these simulations. Is a URANS simulation with good spatial and time resolutions enough to capture both the flow field and the heat transfer correctly? The author is tempted to answer with a “yes” but a more objective answer should be “probably”. If the resolutions are adequate, the URANS approach based on SST k-ω model seems to work properly for cases with high enough Reynolds numbers and turbulent flow containing large perturbations. Furthermore, the comparison with experiments shown in Figure 11 exhibits a rather good agreement for mean temperature and temperature fluctuation distributions along a vertical line 1 mm apart from the stem wall. Incidentally, the material properties in the experiment are those of the prototype. Unfortunately, no comparisons of the velocity and velocity fluctuation fields were done but it is difficult to think that the agreement in the temperature fields shown in Figure 11 may be achieved with a radically different velocity field to that of the experiments.
Figure 11.
Comparison with the steel model experimental data (see Angele et al., 2011); left: mean temperature; right: temperature fluctuations (rms-value).
Then, are the simulated temperature fluctuations inside the solid stem also correct? This question is more difficult to answer since no experimental validation has been carried out but indirect indications about some properties of these fluctuations have nonetheless been obtained. Some of these properties are the order of magnitude of the most energy-containing frequencies of the temperature fluctuations at stem wall and of the associated heat transfer coefficients. Structural analyses (see e.g. Forsmarks Kraftgrupp, 2009) using this range of frequencies, together with the large temperature amplitudes and velocities of the order of 1 m/s, show that this kind of heat transfer is associated with the initiation of cracks on the stem surface. Moreover, the analyses also show that the time scale of the crack development that resulted in broken control rod stems is consistent both with the geometry of the stem (hollow welded joining; see Tinoco and Lindqvist, 2009) and the thermal loadings arising from the heat transfer process described by the CFD simulations. In general, the results of the structural analyses based on the aforementioned CFD-simulated conditions are consistent with the damage picture obtained by inspection. Using more “conservative” conditions, e.g. higher heat transfer coefficients, leads to unrealistic short time scales of the damage.
Furthermore, the mathematical and physical consistency of the temperature field inside the stem has been demonstrated by solving of the Inverse Heat Conduction Problem (IHCP), (Taler et al., 2011). The IHCP is defined as the determination of the boundary conditions of the problem from transient temperature histories given at one or more interior locations. The IHCP is a so called ill-posed problem, i.e. any small change on the input data can result in a dramatic change of the solution. By giving CFD-computed time signals of the temperature at selected points inside the stem, the temperature signal and the heat flux at the surface of the stem were recovered with good accuracy. The question that remains is the correctness of the temperature fluctuations at the surface of the stem, i.e. the correctness of the thermal interaction between the solid surface and the near wall region of the fluid. A definite answer can only be obtained by experimental validation or DNS.
Summing up, further structural analyses based on the same CFD-computed conditions have led to a set of measures that have been taken and/or are being implemented. The crud-cleaning flow has been modified to deliver a flow with a temperature of up to 100 ºC instead of the original of 60 ºC. After turning, a control rod stem may acquire surface tensile residual stress which increases the risk of crack initiation. In order to counteract this undesirable effect, all control rod stems are now burnished since this procedure creates surface compressive residual stress that increases the resistance of the stem against damage, i.e. increased protection against crack initiation and crack growth. At locations of the core most exposed to high warm bypass flows, a better material, stainless steel XM-19, has been chosen for the stems of the control rods. Only 50 of the 169 control rods will keep stems of a somewhat poorer material, stainless steel 316L. In the fuel outage of year 2014, all control rods will be tested in order to detect the presence of cracks and, based on the existent experience at that time, a renewed test program will be decided. This set of measures has been conceived as a viable alternative to the very expensive option of eliminating the cause of the mixing problem by changing the design of the control rod guide tubes comprising a new location of the upper bypass inlet.
6. Conclusion
This chapter constitutes a partial view of CFD, both in the sense of limited and favouring, since, for instance, the examples concerning BWR applications are overrepresented and important subjects such as nuclear safety and two-phase flows are left aside. As a kind of defence, it may be argued that the methods used for BWRs are valid, in general, for PWRs and, probably with important modifications, for SuperCritical Water Reactors (SCWRs). As far as CFD in nuclear safety is concerned, the high interest and large amount of work in the subject from, among others, the European Commission, (European Commission, 2005), and the U.S. Department of Energy, Idaho National Laboratory, (Johnson et al., 2006), make and analysis and a review of the subject rather superfluous.
As pointed out by Tinoco et al. (2010c), two-phase flow simulations still have a relatively high degree of uncertainty and they have not reached the level of quality of single-phase simulations. The physics involved in two-phase phenomena is still not well understood, due mainly to the measuring difficulties entailed by the requirement of local knowledge of the processes needed in CFD. Consequently, the models available lack the distinctive prediction capability of CFD because they are usually based on information collected as relatively general correlations. A fundamental example is the experimental lack of knowledge about the modification by boiling of the detailed structure of a boundary layer at a wall. This deficiency leads to wrong predictions of flow resistance and void distribution in, for instance, pipe flow with boiling from the walls.
Another topic that has not been mentioned in this work is the field of acoustic perturbations in the reactor system, especially in the parts corresponding to pipe networks. The problem of flow-induced structural resonances has become more topical due to the increased interest in operating the reactors at uprated power output. The new components and/or the increased flow rates necessary for achieving the upgrade may lead to the generation of pressure waves that may excite structural vibration modes and increase the risk of mechanical fatigue. CFD may be used to analyse the pipe-network system if the geometry is realistically represented, the grid has a suitable resolution, the turbulence model is appropriate and, in the case of steam, compressibility is included (Lirvat et al., 2012). Post-processing of the generated data can provide information about the flow induced excitation modes, the source of the excitation frequencies/modes and possible standing pressure waves. In the past, attempts have been carried out to collect acoustic signals generated in complex systems like a nuclear reactor in order to detect possible deviations from normal operation of the different components. Any success has failed to turn up not due to the process of acquiring the data, which is relatively easy, but to the difficulties in interpreting the signal constituted by the superposition of broadcasted pressure waves from every component that may act as a source. In the future, CFD might help identifying the sources and describing how the different pressure waves propagate in the system. Perhaps, detecting the leakage of valves in complex systems like a nuclear reactor by means of acoustic signals may become possible.
As usual when trying to solve a problem, more questions than those initially asked arise during the solution process. The case of the control rod cracks in no exception and, as mentioned before, the apparent success of the URANS simulations with the SST k-ω model raises several questions, namely if this is the merit of the model, and at which Reynolds numbers the URANS approach begins to work, if the associate heat transfer, including temperature fluctuations, is correct, and with which resolutions in time and space, etc. All these questions should be investigated in the future since URANS may constitute a realistic alternative, especially at high Reynolds number, to the promising LES approach that still is too expensive for relatively large applications. Another alternative that has already been used with encouraging results, (Lindqvist, 2011), is Very Large Eddy Simulation (VLES) in the spirit of Speziale, (Speziale, 1998), an approach which has been further commented by Tinoco et al. (2010c).
Even if LES may be considered in many cases still too resource demanding, it is undeniably the approach of the near future provided that the computer development trend is maintained. However, conjugate heat transfer simulations of industrial applications, i.e. simulations at high Reynolds numbers, involved geometries and complex boundary conditions, appear to lack guidelines for ensuring acceptable quality with a suitable uncertainty. LES, as one of the simulation alternatives for these applications, seems to have taken a first step towards the definition of more complete rules for conjugate heat transfer simulations with the work of Carlsson and Veber (2010). Using a DNS data base for channel flow, (The University of Tokyo, 2012), mesh requirements for LES simulations of heat transfer are established, as functions of the Reynolds and Prandtl numbers. This work should be extended to conjugate heat transfer and temperature fluctuations in the solid by using the results of Tiselj et al.(2001), Tiselj et al. (2004), Tiselj (2011) and Tiselj and Cizelj (2012).
To conclude, this study has tried to show that the analysis of the mechanical integrity of light water reactors as a rather complex task, multidisciplinary and in continuous progress, evolving towards improved safety due to Regulatory demands, new and more advanced methods of analysis and taking advantage of the stably increasing available computer power. Additionally, this work has tried to describe, although incompletely and briefly, the historical progress of the currently accepted methodology and future prospects. Other types of analysis included in the existing methodology, which are not mentioned here due to space limitations, are, for example, studies of thermal loads in transients such as the loss of offsite power (Tinoco et al., 2005) or estimating the moderator tank maximum temperature due to gamma radiation and subcooled boiling heat transfer (Tinoco et al., 2008).
As it might have become apparent from this study, the FEM method for the analysis of structures is considered well established and sufficiently accurate, giving results that do not need verification or experimental validation. The case of three-dimensional numerical computations (CFD) applied to the thermal-hydraulics is very different, mainly due to turbulence, which still lacks an explanatory theory, and to the presence of two-phase flows where the knowledge about the physical processes involved is far from complete. Therefore, the results obtained using three-dimensional numerical computations require validation or at least verification, which is not always possible for complex systems such as nuclear reactors, an issue that has been discussed by Tinoco et al. (2010c).
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Introduction",level:"1"},{id:"sec_2",title:"2. The determination of loadings",level:"1"},{id:"sec_2_2",title:"2.1. Section III",level:"2"},{id:"sec_3_2",title:"2.2. Categorisation of parts in code classes",level:"2"},{id:"sec_4_2",title:"2.3. Mechanical integrity and design specifications",level:"2"},{id:"sec_5_2",title:"2.4. Design loadings and limits",level:"2"},{id:"sec_6_2",title:"2.5. Service loadings and limits",level:"2"},{id:"sec_7_2",title:"2.6. Test loadings and limits",level:"2"},{id:"sec_8_2",title:"2.7. Load combinations",level:"2"},{id:"sec_10",title:"3. A steam line break",level:"1"},{id:"sec_11",title:"4. The problem of mixing",level:"1"},{id:"sec_12",title:"5. Heat transfer",level:"1"},{id:"sec_12_2",title:"5.1. Thermal mixing in a tee-junction",level:"2"},{id:"sec_13_2",title:"5.2. The control rod issue",level:"2"},{id:"sec_15",title:"6. 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F., (1974). “Wall Effect of Temperature Fluctuations in the Viscous Sublayer”, TeplofizikaVysokihTemperatur, Vol. 12, pp. 328–337.'},{id:"B44",body:'Pozorski, J. and Minier, J.-P., (2005). ”Stochastic Modelling of Conjugate Heat Transfer in Near-Wall Turbulence”, Engineering Turbulence Modelling and Experiments 6, W. Rodi Editor, Elsevier, pp. 803-812.'},{id:"B45",body:'Speziale, C., (1998). “Turbulence Modeling for Time-Dependent RANS and VLES: A Review”, AIAA Journal, Vol. 36, No.2, pp.173-184.'},{id:"B46",body:'STUK, (2000). “Nuclear Power Plant Systems, Structures and Components and their Safety Classification”, Guide YVL 2.1, 26 June, 2000.'},{id:"B47",body:'Taler, J., Cebula, A., Marcinkiewicz, J. and Tinoco, H., (2011). “Heat Flux and Temperature Determination on the Control Rod Outer Surface”, 14th International Topical Meeting on Nuclear Reactor Thermalhydraulics, NURETH-14, Toronto, Ontario, Canada, September 25-30, 2011.'},{id:"B48",body:'The Marviken Full Scale Critical Flow Tests, (1979). “Summary Report, Joint Reactor Safety Experiments in the Marviken Power Station”, StudsvikEnergiteknik A.B., Nyköping, December 1979, Sweden.'},{id:"B49",body:'The University of Tokyo, (2012). Department of Mechanical Engineering, Turbulence and Heat Transfer Laboratory, http://www.thtlab.t.u-tokyo.ac.jp/.'},{id:"B50",body:'Tinoco, H., (2001). “A Standing Pressure Wave Hypothesis of Oscillating Forces Generated During a Steam-Line Break”, proceedings of the 9th International Conference on Nuclear Engineering (ICONE 9), Nice, France, April 8-12, 2001.'},{id:"B51",body:'Tinoco, H., (2002). “Three-Dimensional Modeling of a Steam-Line Break in a Boiling Water Reactor”, Nuclear Sci. and Eng., Vol. 140, pp. 152-164.'},{id:"B52",body:'Tinoco, H., Adolfsson, E., Baltyn, W. and Marcinkiewicz, J., (2005). “BWR ECCS – Thermal Loading Analysis of Internals Related to Spray System Removal”, proceedings of the 13th International Conference on Nuclear Engineering (ICONE 13), Beijing, China, May 16-20, 2005.'},{id:"B53",body:'Tinoco, H., Ahlinder, S. and Hedberg, P., (2008). “Estimate of Core Shroud Temperature by means of a CFD-Model of the Core Bypass”, proceedings of the 15th International Conference on Nuclear Engineering (ICONE 15), Nagoya, Japan, April 22-26 (2007) and Journal of Power and Energy Systems, Vol. 2, No. 2, pp. 775-789, 2008.'},{id:"B54",body:'Tinoco, H. and Lindqvist, H., (2009). “Thermal Mixing Instability of the Flow Inside a Control-Rod Guide Tube”, proceedings of the 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH 13), Kanazawa City, Ishikawa Prefecture, Japan, September 27-October 2, 2009.'},{id:"B55",body:'Tinoco, H. and Ahlinder, S., (2009). “Mixing Conditions in the Lower Plenum and Core Inlet of a BWR”, J. Eng. Gas Turbines & Power, Vol. 131, 062903-1 - 062903-12, November, 2009.'},{id:"B56",body:'Tinoco, H., Buchwald, P. and Frid, W., (2010a). “Numerical Simulation of Boron Injection in a BWR”, Nuclear Eng. Design, Vol. 240, Issue 2, February, 2010.'},{id:"B57",body:'Tinoco, H., Lindqvist, H., Odemark, Y., Högström, C.-M., Hemström, B. and Angele, K., (2010b). “Flow Mixing Inside a Control-Rod Guide Tube – Part I: CFD Simulations”, Proceedings of the 18th International Conference on Nuclear Engineering (ICONE 18), Xi’an, China, May 17-21, 2010.'},{id:"B58",body:'Tinoco, H., Lindqvist, H. and Frid, W., (2010c). “Numerical Simulation of Industrial Flows”, Numerical Simulations - Examples and Applications in Computational Fluid Dynamics, Lutz Angermann (Ed.), ISBN: 978-953-307-153-4, InTech, Available from: http://www.intechopen.com/books/numerical-simulations-examples-and-applications-in-computational-fluid-dynamics/numerical-simulation-of-industrial-flows.'},{id:"B59",body:'Tiselj, I., Bergant, R., Mavko, B., Bajsić, I. and Hetsroni, G., (2001). ”DNS of turbulent heat transfer in channel flow with heat conduction in the wall”, J. Heat Transfer – Transactions of ASME, Vol. 123 (5), pp. 849-857.'},{id:"B60",body:'Tiselj, I., Horvat, A., Mavko, B., Pogrebnyak, E., Mosyak, A. and Hetsroni, G., (2004). “Wall properties and heat transfer in near wall turbulent flow”, Numerical Heat Transfer A, Vol. 46, pp. 717-729.'},{id:"B61",body:'Tiselj, I. (2011). “DNS of Turbulent Channel Flow at ReT = 395, 590 and Pr = 0.01”, 14th International Topical Meeting on Nuclear Reactor Thermalhydraulics (NURETH-14), Toronto, Ontario, Canada, September 25-30, 2011.'},{id:"B62",body:'Tiselj, I. and Cizelj, L., (2012). “DNS of turbulent channel flow with conjugate heat transfer at Prandtl number 0.01”, Nuc. Eng. Design - in print.'},{id:"B63",body:'USGenWeb, (2011). “The R. B. Grover & Company Shoe Factory Boiler Explosion”, http://plymouthcolony.net/brockton/boiler.html.'},{id:"B64",body:'vanHaren, S. W. (2011). “Testing DNS capability of OpenFOAM and STAR-CCM+”, Master Thesis, University of Delft, September 15, 2011.'},{id:"B65",body:'Varrasi, J., (2005). “The True Harnessing of Steam”, Mechanical Eng. Mag., January 2005, New York, USA. '},{id:"B66",body:'Westin, J., \'t Mannetje, C., Alavyoon, F., Veber, P., Andersson, L., Andersson, U., Eriksson, J., Henriksson, M., & Andersson, C., (2008). “High-cycle thermal fatigue in mixing tees. Large-eddy simulations compared to a new validation experiment”, proceedings of the 16th International Conference on Nuclear Engineering (ICONE 18), Orlando, Florida, USA, May 11-15, 2008.'},{id:"B67",body:'Zeng, L., Jansson, L.G. and Dahlström, L., (2011). “Non-Linear Design Evaluation of Class 1-3 Nuclear Power Piping”, Nuclear Power - System Simulations and Operation, PavelTsvetkov (Ed.), ISBN: 978-953-307-506-8, InTech, Available from: http://www.intechopen.com/books/nuclear-power-system-simulations-and-operation/non-linear-design-evaluation-of-class-1-3-nuclear-power-piping.'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Hernan Tinoco",address:null,affiliation:'
Forsmarks Kraftgrupp AB, Sweden
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1. Introduction
Multiphase systems comprising of more than two phases are a common occurrence in the fields of chemical and bioprocess engineering. Such multiphase systems may be comprised of a gas phase, a liquid phase and a solid phase as is the case in froth flotation processes in the minerals sector [1, 2]. Alternatively, such multiphase systems may be comprised of a gas phase and two immiscible liquid phases as is often found in biological gas stripping [3] or biocatalysis [4]. Irrespective of the application field, a common expectation among such multiphase systems is that they are characterised by more complex hydrodynamics than two phase systems which are reasonably well understood [5, 6]. Similarly, mixing and mass transfer effects are expected to be more complex in such systems.
Given the above considerations, the design and analysis of multiphase systems requires the use of comprehensive frameworks that are capable of taking into account the various mechanisms of action that are at play. Computational Fluid Dynamics (CFD) has been proposed as one such framework since it is able to describe the hydrodynamics of multiphase systems based on fundamental equations of flows [7]. Furthermore, coupling of CFD simulations to sub-models of mass transfer, mixing or flotation can enable the description of these effects at finer resolutions than can be obtained based on empirical modelling. Thus, significant effort has been recently directed towards the development and application of CFD techniques to simulate multiphase systems comprising of two phase reactors [8, 9, 10] as well as those with more than two phases [2, 11, 12, 13].
This chapter builds upon recent work by presenting a discussion on the use of CFD in the design and analysis of gas–liquid–liquid reactors within the context of mass transfer. Key considerations informing the modelling approach have been discussed with their implementation illustrated by the review of recently modelled case studies [12, 13]. Furthermore, the successes and challenges attending the CFD-based modelling of gas–liquid–liquid reactors have been highlighted and on the basis of these, recommendations have been given on areas requiring further investigation. The chapter thus addresses itself to graduate students, academics and industrial practitioners interested in a comprehensive modelling framework for the design and analysis of gas–liquid–liquid reactors.
2. Considerations in gas–liquid–liquid systems
Gas–liquid–liquid reactors are a common occurrence in the bioprocess field (see Table 1). Such reactors tend to be comprised of one continuous liquid phase (primary liquid phase) and two dispersed phases (gas phase and secondary liquid phase) as illustrated in Figure 1. The departure of such reactors from traditional gas–liquid reactors is through the introduction of a secondary liquid phase within the system. The introduction of the latter modifies the system in a manner that impacts mass transfer and this can be seen by changes in the gas hold up, the bubble diameters and the overall volumetric mass transfer coefficients [4]. Underpinning these observable changes, however, are modifications to the fluid properties, mass transfer properties and pathways as well as the reactor hydrodynamics. A consideration of these modifications is necessary for appropriate modelling and as such a brief review on the same is presented herein. In-depth reviews are available elsewhere [4, 19, 20].
Figure 1.
Illustration of gas–liquid–liquid stirred tank reactor.
2.1 Changes in fluid properties
The introduction of a secondary liquid phase into a traditional gas–liquid reactor can result in a change of fluid properties. For example, the surface tension between the primary liquid phase and the gas phase can change depending on the degree of solubility of the secondary liquid phase in the primary liquid phase. To characterise this, surface tension values based on mutually saturated liquids have been reported in literature [16, 18]. Such values have generally been obtained by mixing the primary liquid phase with the additional liquid phases for long periods followed by a separation of the phases and surface tension measurements using a tensiometer [18]. Table 2 illustrates selected results from literature.
Saturated surface tension for various liquid–liquid combinations.
The results in Table 2 generally point to a decrease in the saturated surface tension (σsat) with addition of the secondary liquid phase. Furthermore, this change in surface tension has been observed to be greater when the secondary liquid phase is more soluble in the primary liquid phase [18]. As a decrease in the surface tension results in smaller gas bubbles, an enhancement in mass transfer can be expected. However, this is not always the case. For example, Kundu et al. [18] observed a negative impact on mass transfer upon the addition of toluene, anisole, decyl alcohol and 2-ethyl-1-hexanol despite a decrease in σsat (refer to Table 2). This points to the presence of additional factors that need to be taken into account for a proper description of mass transfer in such systems.
Two additional points need to be highlighted with regard to surface tension. First, discrepancies in the reported values of σsat exist as seen in Table 2. For example, Ngo & Schumpe [16] measured an insignificant change in σsat (71.8 mN/m) upon the addition of n-Heptane whereas Kundu et al. [18] measured a significant change (σsat = 65 mN/m). Such discrepancies point to a need for additional experimental measurements of σsat.
A second point to note is that researchers have also attempted to report on dynamic values of the surface tension [21]. This was achieved by preparation of a “stable” liquid–liquid dispersion followed by measurement of the surface tension [21]. The values obtained were in the range of 17–26 mN/m for an n-C10-C13 alkane cut mixed with water [21]. These values were lower than those reported in Table 2 and tended towards the surface tension values of pure alkanes (23.9 mN/m for n-Decane, 25.41 mN/m for n-Dodecane [18]). Consequently, it may be suggested that a degree of separation of the liquid–liquid dispersion occurred during surface tension measurements despite the best efforts of the researchers. In this case, the settled-out and less dense alkane phase would form an intervening layer between the gas phase and the dispersion.
Besides the above changes to the surface tension, the presence of a secondary liquid phase can lead to changes in effective fluid properties such as the effective density, the effective viscosity as well as the effective solubility. The pre-qualifying term, “effective”, is used in this case since such properties are defined based on a view of the liquid–liquid dispersion as a single pseudo-homogenous liquid. This view permits for a simplification of the 3-phase gas–liquid–liquid reactor to an effective 2-phase reactor. Consequently, correlations derived for traditional 2-phase reactors, such as Eq. (1) with an empirical basis and Eq. (2) with a theoretical basis [5], can be used as a starting point for the design of 3-phase reactors. In these equations, KLa represents the overall volumetric mass transfer coefficients in a 2-phase reactor whereas xg and dg respectively represent the gas hold up and the bubble diameters (see Eq. (3) and (4)). Other variables are as defined in the Nomenclature.
Effective fluid properties can be specified on the basis of simple mixing rules such as Eq. (5) for the effective density (ρeff). Such equations consider the contributions of the individual liquid phases based on their volumetric proportions (xi) but neglect non-ideal effects that may arise from molecular interactions, commonly found in homogeneous mixtures, which may lead to excess volumes. This notwithstanding, experimental evidence suggests that such equations are sufficient for the effective density [22] and the effective solubility (see next section). This may be due to the poor mutual solubility of liquid phases typically tested for gas–liquid–liquid reactor applications: the properties of the individual liquid phases remain unchanged by the presence of a second, immiscible phase and the bulk properties can be estimated by simple volume averaging.
ρeff=∑i=1nxiρiE5
With regard to effective viscosity (μeff), models of a more complicated form than that given in Eq. (5) are required. This is due to the need to account for the perturbation of fluid flow in the presence of droplets of the secondary liquid phase. Models varying in complexity have been proposed. For example, the Taylor model (see Eq. (6)) has been proposed for dilute dispersions of spherical droplets [23]. Additionally, models such as those given in Eq. (7) and (8) have been proposed for non-dilute dispersions where the hydrodynamic interactions among droplets need to be accounted for [23, 24]. Besides these, however, models have also been proposed to account for non-zero shear rates in the fluid which introduce effects such as droplet deformation [23, 25].
μeffμc=1+2.5xd0.4+μr1+μr;xd→0E6
μeffμc2μeffμc+5μr2+5μr1.5=exp2.5xd1−xd/xmE7
μeffμc2μeffμc+5μr2+5μr1.5=1−xdxm−2.5xmE8
In the equations above, μr refers to the ratio of viscosity of the secondary liquid phase (μd) to that of the primary liquid phase (μc). Variables xd and xm, on the other hand, refer to the volume fraction of the secondary liquid phase and the maximum packing limit of its droplets respectively.
2.2 Changes in mass transfer properties and pathways
Properties of interest affecting mass transfer include the solubility and diffusivity of a species within the liquid–liquid dispersion. Taking the liquid–liquid dispersion as a pseudo-homogenous liquid, effective properties have been defined. For example, it has been observed that the effective solubility of a species (Ceff∗) can be specified according to the volumetric proportions of the liquids involved, once again recognising that the presence of immiscible phases has a negligible effect on the solubilities associated with individual phases [22, 26]. This is illustrated in Eq. (9) below, with Ci∗ representing the solubility in liquid phase i and n representing the total number of liquid phases.
Ceff∗=∑i=1nxiCi∗E9
Given the application fields of gas–liquid–liquid reactors (such as biological gas stripping), the effective solubility is usually higher than the solubility of a species in the primary liquid phase (Ceff∗>Cc∗). This implies that a longer duration is required to saturate the liquid–liquid dispersion with a given species in comparison to the time required to saturate the pure primary liquid phase [27, 28]. Consequently, for a fixed mass transfer rate, lower values of the overall volumetric mass transfer coefficients can be obtained upon the addition of a secondary liquid phase [28, 29].
With regard to the molecular diffusion of a species, the effective diffusivity Deff has been defined as illustrated in Eq. (10) for dilute liquid–liquid dispersions [30]. This equation, being of a general nature, has also been used to describe the effective diffusivity of solid–liquid suspensions [31]. The variable Dr in this equation represents the diffusivity ratio whereas Dd and Dc represent the diffusivity of the species in the secondary and primary liquid phases respectively.
Deff=DcDr1+2xd+21−xdDr1−xd+2+xd;Dr=DdDcE10
It should be noted that the effective properties defined by Eqs. (9) and (10) can be, in a general sense, regarded as bulk properties. Appropriate as it may be to define them, a full description of mass transfer in a liquid–liquid dispersion also requires an examination of changes introduced by the secondary liquid phase at the mass-transfer interface. Tied to this are the questions whether the secondary liquid phase will be present at the interface and whether it is involved in active uptake of dissolving species at the interface. Indeed, the concept of a pseudo-homogenous liquid implies that the secondary liquid phase will be present, not only in the bulk of the primary liquid, but also at the interface. Furthermore, homogeneity implies that a similar distribution of the secondary liquid phase is found at the interface as is found in the bulk of the primary liquid phase. However, researchers have considered different possible configurations of the interface as illustrated in Figure 2. In this way, the requirement for homogeneity has been relaxed at the interface while being maintained in the bulk.
Figure 2.
Mass transfer interface illustrating possible configurations – (A) parallel mass transfer, (B) series mass transfer without shuttling and (C) series mass transfer with shuttling.
Assuming active uptake by the secondary liquid phase, different possible pathways of mass transfer have arisen. These have included, for example, parallel mass transfer and series mass transfer with or without the shuttling of the droplets of the secondary liquid phase [14, 30, 32, 33]. These various pathways have been associated with an enhancement in mass transfer besides that occurring due to changes discussed earlier (refer to Eq. (9) and (10)). A review of these pathways as well as their associated enhancement factors can be found in the work by Dumont & Delmas [19].
2.3 Changes in reactor hydrodynamics
The hydrodynamics of a reactor are taken to refer to the mean velocity field and the turbulence field within a reactor. These affect mass transfer in various ways. For example, the transport of gas bubbles within a reactor (and hence overall gas hold up) is dependent on the magnitude and orientation of the mean velocity field. Additionally, mass transfer at the interface between the gas bubbles and the liquid phase will depend on the prevailing local turbulence. Consequently, a change in the reactor hydrodynamics will lead to a change in the mass transfer.
The addition of a secondary liquid phase has been observed to change both the mean velocity field and the turbulence levels in stirred tank reactors [34, 35, 36]. Direct measurements of the velocity through techniques such as Particle Image Velocimetry [34, 36] and Laser Doppler Anemometry [35] have revealed that a secondary liquid phase can dampen the mean velocities [34, 35] while either increasing or decreasing the turbulence levels [34, 35, 36]. Further evidence in literature for a change in the hydrodynamics has been largely indirect – inferred from examining the change in, for example, mixing time upon addition of a secondary liquid phase [37, 38].
Two schools of thought have been postulated to explain the interaction of the secondary liquid phase with the hydrodynamics of a reactor. The first has been focused on the change in effective fluid properties. In this line of thinking, it has been suggested that a decrease in the effective density should lead to an increase in the velocities [34]. On the other hand, it has been suggested that an increase in the effective viscosity should have a dampening effect on both the mean velocities and the turbulence levels [34, 35].
The second school of thought, on the other hand, has been focused on the augmentation or dampening of turbulence by the droplets of the secondary liquid phase [34, 35]. Various mechanisms have been suggested in this regard although these are still the subject of active research [39, 40, 41, 42]. For example, whether a particle (solid, liquid or gas) augments or dampens turbulence has been traditionally associated with the size of the particle (dp) in relation to the integral (or large) scales of turbulence (l) [43]. Large particles dp/l>0.1 with characteristically large particle’s Reynolds numbers Rep>400 have generally been associated with turbulence augmentation through mechanisms such as vortex shedding in the wakes behind the particles [43, 44]. On the other hand, small particles dp/l<0.1 have generally been associated with a dampening of turbulent kinetic energy (TKE) that occurs as the particles are accelerated/dragged by the flow [39, 43].
It should be noted, however, that the above observations do not represent a fixed rule; exceptions have been observed. For example, it has been observed that particles of a size dp/l<0.1 can both augment and dampen turbulence depending on the flow’s Reynolds number [45]. Furthermore, it has been observed that turbulence can be augmented by particles of a size in the order of the Kolmogorov (smallest) scales of turbulence [46, 47, 48, 49, 50]. In the latter cases, however, the non-uniform modification of the spectrum of TKE by particles was considered with the augmentation of TKE observed to occur at the small scales of turbulence [46, 47, 48, 49, 50]. Mechanisms that were proposed for the turbulence augmentation included flow forcing due to the inertia [50] or buoyancy [49] of small particles that were well correlated with the fluctuating fluid flow.
3. Computational fluid dynamics for gas–liquid–liquid reactors
As illustrated in the previous sections, the introduction of a secondary liquid phase into a traditional gas–liquid reactor can result in a variety of changes. Consequently, the modelling of mass transfer in gas–liquid–liquid reactors requires a comprehensive modelling framework that can account for the different changes. An empirical approach, such as illustrated in Eq. (11) [51], may not suffice as the numerous effects introduced by the secondary liquid phase are reduced into a single term with an adjustable exponent requiring optimisation (compare to Eq. (1)). This is not an easily generalizable approach.
KLa′=Γ·PgVxνsy1−xdzE11
Computational Fluid Dynamics (CFD), on the other hand, offers a fundamental framework that can be built upon to incorporate as much level of detail (or physics) as necessary/desired. This is the case since CFD offers an approximate/numerical solution to the fundamental equations of flow governing a system/reactor [7, 52]. Consequently, the hydrodynamics of a reactor are resolved in space and time and such hydrodynamic data can be coupled to fundamental models of mass transfer so as to predict parameters of interest such as the overall volumetric mass transfer coefficient, KLa′.
As CFD-based approaches are inherently computationally intensive, a major constraint to such approaches is the computational resources available [7, 52]. Thus, a compromise has to be made between the level of physics to be captured and computational resources available [7]. For example, prior consideration must be given as to the level of resolution to be employed for the flow field. Similarly, an appropriate continuum description of the phases involved must be chosen a priori. Such compromises notwithstanding, a higher level of detail, accuracy and generality is still maintained with a CFD-based approach in comparison to empirical approaches. This will be illustrated in Section 4.
3.1 Modelling frameworks for hydrodynamics
As noted in the introduction to CFD above, several prior considerations have to be made with regard to the modelling approach. These considerations tend to give rise to different modelling frameworks or techniques. For example, as relates to the resolution of flow fields, it is possible to simulate the usually turbulent flow in a reactor at all length- and time-scales using Direct Numerical Simulations but the associated computational expense is prohibitive [53]. Therefore, filtering or averaging of the flow field is usually done [53]. Filtering techniques such as those used in Large Eddy Simulations offer an enhanced resolution of the flow field as compared to averaging techniques [53]. However, they are still considered computationally expensive and their use has been largely limited to single-phase reactors [53]. Averaging techniques such as those used to generate the Reynolds-Averaged Navier–Stokes (RANS) equations, on the other hand, lead to tractable simulations [53] and are a practical choice for the modelling of multiphase reactors.
With regard to the description of the phases, an Eulerian framework is typically used for the continuous phase (primary liquid phase) and it involves describing the flow based on a fixed observer position [54]. For the dispersed phases (gas and secondary liquid phase), on the other hand, either an Eulerian framework or a Lagrangian framework can be employed [54]. The Lagrangian framework involves the tracking of individual particles of the dispersed phase within the flow field of the continuous phase [54]. The particles either follow the flow field without interaction (one-way coupling) or interact with it thus modifying it (two-way coupling) [55].
The Lagrangian framework provides a greater degree of detail and as can be expected, it is costly to implement [54]. Consequently, an Eulerian framework for both the continuous and dispersed phases tends to provide a practical choice for modelling. An Eulerian description of both phases assumes that the phases involved can be treated as a continuum [56]. In this case, a phase indicator function is introduced into the governing equations of flow to account for the possible realisation of a phase i at a given position and a given time [56]. Averaging of the governing equations after decomposing the instantaneous flow field into its mean and fluctuating components results in Eq. (12) and (13) [57].
DDtαiρi=0E12
DDtαiρiVi¯=−αi∇p+∇·τ¯¯i+αiρig¯+∑j=1nR¯jiE13
In Eqs. (12) and (13), subscripts i and j represent individual phases whereas α represents the respective phase volume fraction. This volume fraction is based on the total volume of all phases as opposed to the total liquid volume (see variable x in earlier equations). The respective phases can be either the gas phase, the primary liquid phase or the secondary liquid phase. Alternatively, if the liquid–liquid dispersion is treated as a pseudo-homogenous liquid, then the subscripts would refer to either the gas phase or the pseudo-homogenous liquid.
Other variables in Eqs. (12) and (13) such as ρ and V¯ represent the density and the mean velocity of the respective phases whereas p represents the shared pressure field. Additionally, g¯ represents the gravitational acceleration while R¯ represents the interphase momentum exchange terms. These terms include the lift force, the drag force, the turbulent dispersion force and the added mass force among others [56].
There are two key points to note regarding the interphase momentum exchange terms. First, their significance varies with the set up being considered. For example, the drag force has been observed to be the most significant interphase exchange term in the bulk of a stirred tank reactor [58, 59]. On the other hand, terms such as the lift force have been observed to significantly affect the flow in a bubble column reactor [60]. Consequently, modelling can be simplified by only accounting for significant terms.
The second point to note touches on the various models that have been proposed to specify the interphase momentum exchange terms. Such models chiefly consider 2-phase interactions, that is, gas–liquid or liquid–liquid interactions [61, 62, 63]. Though such models have been improved upon to consider effects such as particle-particle interaction at high volume fractions of a single dispersed phase [61, 62, 63], there is still a need for appropriate models that specify the interphase exchange terms when more than two phases are present. To this end, work such as that by Baltussen et al. [64, 65] investigating the effective gas–liquid drag in the presence of an additional solid phase may provide direction.
Finally, τ¯¯ in Eq. (13) represents the stress tensor accounting for both viscous and turbulent (Reynolds’) stresses. The specification of the stress tensor is non-trivial due to the Reynolds’ stresses that need to be solved directly or modelled. A direct solution of the Reynolds’ stresses provides a greater amount of detail and is able to resolve complex features of the turbulence field such as anisotropy [53, 54]. However, the computational costs associated with this approach as well as reported solution difficulties favour the specification of the stress tensor using alternative simplified approaches [53, 54]. Modelling of the stress tensor using the Boussinesq hypothesis is one such alternative approach [53, 54]. In the latter, the Reynolds’ stresses are related to the gradients of the mean velocity with the eddy/turbulent viscosity (μt) arising as a proportionality constant (see Eq. (14)) [57].
The eddy viscosity can be modelled in various ways such as that illustrated in Eq. (15) [53, 57]. In this case, it is related to the turbulent kinetic energy (k) and its dissipation rate (ϵ), both of which need to be solved for. Various models have been proposed for these latter parameters (k and ϵ) such as the dispersed k–ϵ turbulence model, the mixture k–ϵ turbulence model and the per-phase k–ϵ turbulence model [57]. These models represent an extension of the single phase k–ϵ turbulence model to multiphase situations and their applicability depends on the expected/prevailing type of flow [57]. For example, the mixture k–ϵ model is recommended for stratified flow whereas the dispersed k–ϵ model is recommended where there is one clear continuous phase and the other phases are dispersed within it [57].
It should be noted that irrespective of the choice of turbulence model, one key point to consider is the interaction of the dispersed phases with the prevailing turbulence. As noted in Section 2.3, the dispersed phase can modify the prevailing turbulence and this needs to be captured. To this end, various models have been proposed in literature and these vary in complexity depending on the level of detail captured. Various authors have recently examined the sufficiency of these models and their work is recommended [66, 67, 68, 69, 70, 71].
3.2 Modelling frameworks for mass transfer
Similar to the modelling of hydrodynamics, the modelling of mass transfer involves the selection of appropriate frameworks prior to the actual simulation. The choice of a particular framework involves a compromise between the level of detail captured and computational cost involved. Furthermore, the choice of a modelling framework for mass transfer tends to be influenced by choices made during the modelling of the hydrodynamics. For example, the use of an Eulerian description of the phases together with averaged equations of flow offers a practical choice for the modelling of a reactor hydrodynamics. However, this approach involves a loss of specifics on the mass transfer interface thus necessitating the prescription of models to approximate the expected mass transfer behaviour. On the other hand, a Lagrangian tracking of particles coupled with interface tracking algorithms better resolves the mass transfer interface but is unfeasible for reactors with a large number of dispersed particles (droplets or bubbles). Consequently, the discussion below focuses on the modelling of mass transfer within the context of an Eulerian description of the phases and the modelling of hydrodynamics using averaged equations of flow.
Mass transfer in a gas–liquid–liquid reactor can be solved for by tracking the concentration of a species in each phase within the reactor. This results in three equations as given in Eqs. (16)–(18). In these equations, C represents the concentration of the species in the respective phase (subscripts g,c,d) whereas J¯ and S represent the diffusive flux and the interphase mass transfer source terms respectively. Closure models are required for the interphase mass transfer source terms depending on the expected mass transfer behaviour.
DDtαgCg=−∇·αgJ¯g−Sgc−SgdE16
DDtαcCc=−∇·αcJ¯c+Sgc−ScdE17
DDtαdCd=−∇·αdJ¯d+Sgd+ScdE18
In the most general case, mass transfer can be assumed to occur between the gas phase and both the primary and the secondary liquid phases (Sgc≠0,Sgd≠0). This would correspond to the case of parallel mass transfer as illustrated in Figure 2(A). Evidence for this mass transfer pathway has been provided based on observations of the formation by oil films on gas bubbles during “static” experiments [72]. The question arises, however, as to whether sufficient time for film formation occurs in a dynamic/agitated reactor [72, 73].
Series mass transfer is often taken to be the more probable mass transfer pathway in an agitated reactor (cases (B) or (C) in Figure 2 with Sgd=0) [34]. In addition, the formation of small droplets of the secondary liquid phase with a large interfacial area implies that mass transfer between the respective liquid phases is usually faster than that occurring between the gas phase and the primary liquid phase [72]. Thus, based on the timescale of mass transfer between the gas phase and the primary liquid phase, it may be assumed that equilibrium conditions exist between the respective liquid phases. Furthermore, one need only track the concentration of the species in two phases – the gas phase (Eq. (16)) and the primary liquid phase (Eq. (17) with Scd=0). With these simplifying assumptions, the only unknown left is the interphase source term between the gas phase and the primary liquid phase (Sgc). Gakingo et al. [13, 28] proposed definitions for Sgc that account for possible mass transfer pathways at the gas–liquid interface plus an apparent decrease in the overall volumetric mass transfer coefficients that occurs due to a larger total solubility of the species in the liquid–liquid dispersion (refer to Section 2.2). This illustrated in Eqs. (19)–(21) below [13, 28].
Sgc=KLa′Cc∗−CcE19
KLa′≈E′·Λ·Dcρcϵcμc0.25·6αgdgE20
E′=11−αd+αdmφE21
In the equations above, KLa′ represents the overall volumetric mass transfer coefficient in the presence of the secondary liquid phase. The latter has been expanded in Eq. (20) based on an eddy cell model [74] with Λ and E′ representing a constant and the enhancement factor respectively. The enhancement factor is given in Eq. (21) where m represents the solubility ratio (m=Cd∗/Cc∗) and the exponent φ varies between 0.5 and 1. A value of φ=1 represents the series mass transfer pathway without shuttling whereas a value of φ=0.5 represents the series mass transfer pathway with shuttling [13, 28]. Other variables are as previously defined.
4. Case studies
Few studies have reported on the CFD-based modelling of gas–liquid–liquid reactors. Two such studies are reviewed in this section with the one having focussed on the modelling of mixing time [12] while the other focussed on the modelling of mass transfer [13].
In the case studies of interest, stirred tank reactors were considered as illustrated in Table 3. In addition, the modelling in both cases was done based on an Eulerian description of the phases involved (refer to Eqs. (12) and (13)). There were certain similarities in the modelling and these included, for example, a consideration of drag force as the only interphase momentum exchange term. The latter was specified according to Eq. (22) [13] with different models for the drag coefficient (CD) employed as illustrated in Table 4. Constant sizes were also assumed for both the gas phase bubbles and the droplets of the secondary liquid phase and these were predicted by Eqs. (3) and (23) respectively [12, 13]. Finally, turbulence was modelled based on the dispersed k–ϵ model (see Eqs. (24) and (25)) though the use of the Reynolds stress model was additionally considered in one study [12].
The above similarities, notwithstanding, there were some notable differences between the two studies. For example, Gakingo et al. [13] tested two approaches in the modelling of the liquid–liquid dispersion. The first approach involved the treatment of the dispersion as a pseudo-homogenous liquid (herein referred to as the P-HOM approach) and the mixture properties were obtained from Eq. (5) for effective density or through experimental measurements for effective viscosity. The second approach, also used by Cheng et al. [12], involved a consideration of the heterogeneous nature of the dispersion and a modelling of each individual liquid phase (herein referred to as the HET approach). In this second approach, there was a need to specify models for turbulence modulation by the dispersed phases (Πkc in Eq. (24)) and different models were employed as illustrated in Table 4. Last but not least, mass transfer was considered in only one study [13] where the authors employed the previously reviewed frameworks, that is, Eqs. (16) and (17) with Sgd=0, Scd=0 and Eqs. (19)–(21). Further specifics on the implementation of the modelling approaches (meshing, boundary conditions and solver settings) can be found in the respective studies [12, 13].
Several key observations can be made from the reported modelling works [12, 13]. First, it was observed that the hydrodynamics of a gas–liquid–liquid stirred tank reactor were better captured based on the HET modelling approach as opposed to the P-HOM modelling approach [13]. The failure by the latter approach was attributed to the fact that the hydrodynamics in a turbulent stirred tank reactor are dominated by turbulence as opposed to the effective (mixture) viscosity. To this end, it was reported that the ratio of turbulence viscosity to mixture viscosity was in the order of O(10−100) based on the P-HOM modelling approach [13]. Consequently, a minimal change in the hydrodynamics was observed despite an almost 2-fold increase in the values of mixture viscosity [13]. This is illustrated through the minimal change in gas hold up trends shown in Figure 3.
Figure 3.
Gas hold up versus volume fraction of secondary liquid phase at 600 rpm. P-HOM refers to the pseudo-homogenous modelling approach whereas HET refers to the individual treatment of the liquid phases. Data from Gakingo et al. [13].
As pertains to the HET modelling approach, the better performance at capturing the hydrodynamics and hence gas hold up trends (see Figure 3) was attributed to the capture of turbulence modulation by droplets of the secondary liquid phase [13]. In particular, it was reported that there was an increase in the turbulence viscosity which served to dampen the mean velocity field (see Figure 4) thus reducing the effective drag and dispersion experienced by the gas bubbles [13]. Cheng et al. [12], on the other hand, did not make an explicit mention of changes in the turbulence viscosity. Rather, they hypothesised that their mixing time was reduced at low volume fractions of the secondary liquid phase due to an increase in turbulence caused by the droplets of the latter [12]. Furthermore, they hypothesised that an increase in mixing time at high volume fractions of the secondary liquid phase was due to a dampening of the turbulence arising from an increase in the effective viscosity [12]. This reference to notable changes due to the effective viscosity stands in contrast with the findings on the P-HOM modelling approach [13].
Figure 4.
Velocity contours based on the HET modelling approach on a mid-baffle plane at 600 rpm. Left – 0% alkane volume fraction (2-phase). Right −10% alkane volume fraction.
A recent study on a gas–liquid–solid reactor has reported similar gas hold up trends as those reported for the HET approach [75]. Furthermore, the modelling of such a reactor based on non-Newtonian models for the liquid–solid slurry has been observed to result in the formation of regions of localised fluid motion near the impeller (caverns) with stagnant fluid elsewhere in the tank [75, 76]. This corresponds to the reports of a dampened mean velocity field according to the HET approach as seen in Figure 4. Observations such as these suggest that the dampening of the mean velocity field may be a common feature in three-phase reactors. However, questions arise as to the appropriate manner of describing such effects. For example, the question may be posed as to whether liquid–liquid dispersions in stirred tanks should be treated based on non-Newtonian models with a yield stress and shear-thinning behaviour rather than equations of the type given in Section 2.1 (Eqs. (6)–(8)). It is to be noted that Eqs. (6)–(8) predict the effective viscosity of the dispersion assuming no non-Newtonian behaviour. Furthermore, the experimental effective viscosity values that were used for the P-HOM modelling approach were in close agreement with those predicted by these equations [13].
Further observations made in the case studies of interest touched on the trends of pumping capacity and power drawn by the impellers. It was observed that the pumping capacity of the impellers decreased at high volume fractions of the secondary liquid phase [12, 13]. This was attributed to a decrease in the mean velocity field as dissipated by an increasing turbulence viscosity [13]. As for the power drawn, both an increase and a decrease in the power was reported. The decrease in power, as noted by Cheng et al. [12], was attributed to a decrease in the effective density upon addition of the secondary liquid phase. On the other hand, Gakingo et al. [13] attributed a noted increase in power drawn to increased energy dissipation by the droplets of the secondary liquid phase. This latter effect was not reported by Cheng et al. [12] and this could have been due to the use of different models to capture turbulence modulation by the dispersed phases (see Table 4). Cheng et al. [12] used a model by Katoaoka et al. [77] which considers only the mean velocity differences Vi¯−Vc¯ in computing the work done by interfacial drag. Gakingo et al. [13], on the other hand, employed the model by Simonin et al. [57, 78, 79, 80] which considers not only the effects arising from mean velocity differences but also the effects arising from the fluctuating velocities of the dispersed phase particles. These latter effects were expected to become more significant than the former as the size of the dispersed phase particles decreased (Vi¯−Vc¯→0asdp→0) [68]. Consequently, it may be suggested that the use of the model by Simonin et al. [57, 78, 79, 80] was more appropriate as it is more comprehensive.
With regard to mass transfer, it was illustrated that potentially accurate predictions can be obtained by using the HET modelling approach for hydrodynamics and Eqs. (16), (17) and (19)–(21) for mass transfer with Sgd=Scd=0 (see Figure 5) [13]. These equations correspond to a case where the concentrations of a species in the two liquid phases are at equilibrium and no direct uptake by the secondary liquid phase occurs at the gas–liquid interface. Though this scenario implied the occurrence of either series mass transfer or series mass transfer with shuttling, minimal differences were reported based on a consideration of these two alternatives [13]. Thus, it may be suggested that mass transfer in gas–liquid–liquid reactors is less sensitive to the assumed configuration at the gas–liquid interface and more sensitive to other varying parameters such as the energy dissipation rate and the gas hold up. More evidence for or against this suggestion should, however, be provided based on a re-examination of mass transfer using a different set of modelling assumptions.
Figure 5.
Comparison of predicted versus experimental overall volumetric mass transfer coefficients at 600 rpm and varying alkane concentrations. Experimental measurements have been obtained by the pressure step method. Data from Gakingo et al. [13].
In conclusion, the usefulness of a CFD-based mass transfer model may be glimpsed from the amount of detail that it can generate. For example, spatial resolutions of variables of interest can be quickly generated as illustrated in Figure 6 to support the visualisation of changes made during in situ reactor design. This is indeed the chief advantage of a CFD-based approach over an empirical approach. However, before the full potential of the CFD-based approach can be realised, a number of areas will need improvement or further investigation. More on this is presented in the subsequent section.
Figure 6.
Contours of local KLa′ values predicted based on the HET modelling approach on a mid-baffle plane at 600 rpm. Left – 0% alkane volume fraction (2-phase). Right −10% alkane volume fraction.
5. Areas requiring further investigation
The results reviewed in the previous section illustrate that the addition of a secondary liquid phase can have a great impact on both the hydrodynamics and the mass transfer in a reactor. In particular, the results suggest that turbulence modulation by the secondary liquid phase is the key mechanism of action through which changes in a reactor occur. A CFD-based framework that is able to capture this mechanism of action has also been proposed and its potential has been illustrated. This notwithstanding, care ought to be taken in generalising the results obtained and the implications arising from them. This is because there still are a number of issues that need further investigation. Two such pertinent issues are highlighted below.
The first pertinent issue concerns the applicability of the obtained results to different reactors. It is the view of the authors that the results reported above should be taken as being particular to stirred tank reactors operating in the turbulent regime. This would be in line with existing experimental evidence for turbulence modulation by secondary liquid phases in turbulent stirred tank reactors [34, 35, 36, 37]. Different reactors, on the other hand, may have alternative mechanisms of action. For example, recent studies in a gas–liquid–liquid–solid bubble column reactor have illustrated that the addition of a secondary liquid phase did not significantly impact the hydrodynamics of the reactor [81, 82]. Rather, a greater impact on the hydrodynamics was observed for the solid phase and this depended on the type of the solid phase employed [81, 82]. Consequently, it may be suggested that a pseudo-homogenous treatment of the liquid–liquid dispersion would suffice for such a bubble column reactor contrary to what has been established in the case study above.
The second point worth investigation is the sensitivity of CFD-based results to the sub-models and simplifying assumptions employed. As noted in sections 3.1 and 3.2, quite a number of decisions have to be made prior to the actual simulations. Though these decisions are necessitated by a need to keep the simulations tractable, the quality of results obtained may be impacted. It is the view of the authors that particular attention should be given to the sub-models used to capture turbulence modulation. This is because of the seemingly large effects that turbulence modulation had on the results presented in the case study. To this end, it is recommended that comprehensive sets of experiments should be conducted on gas–liquid–liquid reactors and these should involve a concurrent measurement of the mass transfer and the hydrodynamics. Current literature is fragmented with authors who have investigated mass transfer not having measured the potential changes in the hydrodynamics and vice versa.
Acknowledgments
The authors would like to acknowledge Ayman A. Abufalgha for performing the surface tension measurements.
The first author would also like to acknowledge funding received from the DST-NRF Centre of Excellence in Catalysis (c*change) and the DAAD-AIMS In Region Scholarship Programme.
ratio of concentration of a species dissolved in secondary liquid phase to that dissolved in primary liquid phase at equilibrium.
n
Total number of phases.
νs
Superficial gas velocity (m/s).
xg
Volume fraction of gas phase based on total volume in a gas–liquid reactor.
xd
Volume fraction of secondary liquid phase based on total volume of un-gassed reactor.
xm
Maximum packing limit.
C
Dissolved concentration of a species (mol/m3).
C∗
Dissolved saturation concentration of a species (mol/m3).
CD
Drag coefficient.
CD,∞
Drag coefficient in the absence of turbulence.
D
Diffusivity of a species in a liquid phase (m2/s).
Dr
Diffusivity ratio
E′
Enhancement factor.
Eo
Eotvos number.
I¯¯
Identity tensor.
J¯
Total diffusive flux of a species.
Gk,c
Production of turbulent kinetic energy from mean velocity gradients.
KLa
Overall volumetric mass transfer coefficient in the absence of a secondary liquid phase (s−1).
KLa′
Overall volumetric mass transfer coefficient in the presence of a secondary liquid phase (s−1).
Kji
Interphase momentum exchange coefficient between phases i and j.
N
Impeller speed (rps).
Pg
Gassed power (W).
Re
Reynolds number.
St
Stokes number.
T
Impeller diameter (m).
V
Volume (m3).
V¯
Velocity vector (m/s).
V¯dr
Drift velocity (m/s).
α
Volume fraction based on total volume in a gassed reactor.
ϵ
Turbulent kinetic energy dissipation rate (m2/s3).
ρ
Density (kg/m3).
σ
Surface/interfacial tension (N/m).
τ¯¯
Stress tensor (Pa).
μ
Dynamic viscosity (Pa s).
μt
Turbulent viscosity (Pa s).
μr
Viscosity ratio.
λ
Kolmogorov length scale.
ζic
Covariance of fluctuating velocities between phase i and the continuous liquid phase (subscript c).
Πkc
Production (destruction) of turbulent kinetic energy by motion of dispersed particles.
Πϵc
Production (destruction) of turbulent kinetic energy dissipation rate by motion of dispersed particles.
x,y,z,φ
Exponents.
Γ,Λ,γ,Ω,Θ,Cμ
Constants.
σk,σϵ,C1ϵ,C2ϵ
C3ϵ,CAM
c
Continuous/primary liquid phase.
d
Secondary liquid phase.
g
Gas phase.
p
Dispersed particle (gas, liquid or solid).
i,j
Phases i,j.
cap
Spherical cap.
ell
Elliptical shape.
eff
Effective.
sph
Spherical shape.
sat
Saturated.
\n',keywords:"Gas–liquid–liquid reactors, stirred tanks, hydrodynamics, mass transfer, Computational Fluid Dynamics, predictive modelling",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/77792.pdf",chapterXML:"https://mts.intechopen.com/source/xml/77792.xml",downloadPdfUrl:"/chapter/pdf-download/77792",previewPdfUrl:"/chapter/pdf-preview/77792",totalDownloads:91,totalViews:0,totalCrossrefCites:0,dateSubmitted:"May 28th 2021",dateReviewed:"June 30th 2021",datePrePublished:"August 2nd 2021",datePublished:null,dateFinished:"August 2nd 2021",readingETA:"0",abstract:"Gas–liquid–liquid reactors are typically found in bioprocess setups such as those used in alkane biocatalysis and biological gas stripping. The departure of such reactors from traditional gas–liquid setups is by the introduction of a secondary (dispersed) liquid phase. The introduction of the latter results in complicated hydrodynamics as observed through measurements of velocity fields, turbulence levels and mixing times. Similarly, changes in mass transfer occur as observed through measurements of gas hold up, bubble diameters and the volumetric mass transfer coefficients. The design and analysis of such reactors thus requires the adoption of an approach that can comprehensively account for the various observed changes. This chapter proposes Computational Fluid Dynamics as an approach fit for this purpose. Key considerations, successes and challenges of this approach are highlighted and discussed based on a review of previously published case studies.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/77792",risUrl:"/chapter/ris/77792",signatures:"Godfrey Kabungo Gakingo and Tobias Muller Louw",book:{id:"10687",type:"book",title:"Energy Efficiency",subtitle:null,fullTitle:"Energy Efficiency",slug:null,publishedDate:null,bookSignature:"Dr. Muhammad Wakil Shahzad, Prof. Muhammad Sultan, Dr. Laurent Dala, Prof. Ben Bin Xu and Dr. Yinzhu Jiang",coverURL:"https://cdn.intechopen.com/books/images_new/10687.jpg",licenceType:"CC BY 3.0",editedByType:null,isbn:"978-1-83969-828-6",printIsbn:"978-1-83969-827-9",pdfIsbn:"978-1-83969-829-3",isAvailableForWebshopOrdering:!0,editors:[{id:"174208",title:"Dr.",name:"Muhammad Wakil",middleName:null,surname:"Shahzad",slug:"muhammad-wakil-shahzad",fullName:"Muhammad Wakil Shahzad"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Considerations in gas–liquid–liquid systems",level:"1"},{id:"sec_2_2",title:"2.1 Changes in fluid properties",level:"2"},{id:"sec_3_2",title:"2.2 Changes in mass transfer properties and pathways",level:"2"},{id:"sec_4_2",title:"2.3 Changes in reactor hydrodynamics",level:"2"},{id:"sec_6",title:"3. Computational fluid dynamics for gas–liquid–liquid reactors",level:"1"},{id:"sec_6_2",title:"3.1 Modelling frameworks for hydrodynamics",level:"2"},{id:"sec_7_2",title:"3.2 Modelling frameworks for mass transfer",level:"2"},{id:"sec_9",title:"4. Case studies",level:"1"},{id:"sec_10",title:"5. Areas requiring further investigation",level:"1"},{id:"sec_11",title:"Acknowledgments",level:"1"},{id:"sec_13",title:"Nomenclature",level:"1"}],chapterReferences:[{id:"B1",body:'Kasat GR, Pandit AB. Review on mixing characteristics in solid-liquid and solid-liquid-gas reactor vessels. Canadian Journal of Chemical Engineering. 2005;83:618–43. 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DOI: 10.1016/j.ijheatfluidflow.2008.12.005.'},{id:"B71",body:'Horender S, Hardalupas Y. Fluid-particle correlated motion and turbulent energy transfer in a two-dimensional particle-laden shear flow. Chemical Engineering Science. 2010;65:5075–91. DOI: 10.1016/j.ces.2010.05.033.'},{id:"B72",body:'Rols JL, Condoret JS, Fonade C, Goma G. Mechanism of enhanced oxygen transfer in fermentation using emulsified oxygen-vectors. Biotechnology and Bioengineering. February 20, 1990;35:427–35. DOI: 10.1002/bit.260350410.'},{id:"B73",body:'Mcmillan JD, Wang DIC. Mechanisms of oxygen transfer enhancement during submerged cultivation in perfluorochemical-in-water dispersions. Annals of the New York Academy of Sciences. 1990;589:283–300. DOI: 10.1111/j.1749-6632.1990.tb24253.x.'},{id:"B74",body:'Lamont J, Scott D. An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE Journal. 1970;16:513–9. DOI: 10.1002/aic.690160403.'},{id:"B75",body:'Shabalala NZP, Harris M, Leal Filho LS, Deglon DA. Effect of slurry rheology on gas dispersion in a pilot-scale mechanical flotation cell. Minerals Engineering. 2011;24:1448–53. DOI: 10.1016/j.mineng.2011.07.004.'},{id:"B76",body:'Bakker CW, Meyer CJ, Deglon DA. Numerical modelling of non-Newtonian slurry in a mechanical flotation cell. Minerals Engineering. 2009;22:944–50. DOI: 10.1016/j.mineng.2009.03.016.'},{id:"B77",body:'Kataoka I, Besnard DC, Serizawa A. Basic equation of turbulence and modeling of interfacial transfer terms in gas-liquid two-phase flow. Chemical Engineering Communications. November 1, 1992;118:221–36. DOI: 10.1080/00986449208936095.'},{id:"B78",body:'Viollet PL, Simonin O. Modelling dispersed two-phase flows: closure, validation and software development. Appl Mech Rev. June 1, 1994;47:80–4. DOI: 10.1115/1.3124445.'},{id:"B79",body:'Mudde RF, Simonin O. Two- and three-dimensional simulations of a bubble plume using a two-fluid model. Chemical Engineering Science. November 1, 1999;54:5061–9. DOI: 10.1016/S0009-2509(99)00234-1.'},{id:"B80",body:'Bel F’dhila R, Simonin O. Eulerian prediction of a turbulent bubbly flow downstream of a sudden pipe expansion. In: 6th Workshop on Two-Phase Flow Predictions; 1992; Erlangen, Germany: p. 264–73.'},{id:"B81",body:'Abufalgha AA, Clarke KG, Pott RWM. Characterisation of bubble diameter and gas hold-up in simulated hydrocarbon-based bioprocesses in a bubble column reactor. Biochemical Engineering Journal. 2020;158. DOI: 10.1016/j.bej.2020.107577.'},{id:"B82",body:'Abufalgha AA, Pott RWM, Cloete JC, Clarke KG. Gas–liquid interfacial area and its influence on oxygen transfer coefficients in a simulated hydrocarbon bioprocess in a bubble column reactor. Journal of Chemical Technology and Biotechnology. 2021;96:1096–106. DOI: 10.1002/jctb.6625.'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Godfrey Kabungo Gakingo",address:null,affiliation:'
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From 1985 to 1986, he was a Research Fellow in the Research Institute for Electronic Equipment, ZZU AD, Plovdiv, Bulgaria. In 1986, he joined the Department of Control Systems, Technical University of Sofia at the Plovdiv campus, where he is presently a Full Professor. He has held long-term visiting Professor/Scholar positions at various institutions in South Korea, Turkey, Mexico, Greece, Belgium, UK, and Germany. And he has coauthored one book and authored or coauthored more than 80 research papers in conference proceedings and journals. 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Aalborg University has Two Satellite Campuses, one in Copenhagen (Aalborg University Copenhagen) and the other in Esbjerg (Aalborg University Esbjerg).\n· He is a member of prestigious IEEE (Institute of Electrical and Electronics Engineers), and IAENG (International Association of Engineers) organizations. \n· He is the chief Editor of the Journal of Software Engineering.\n· He is the member of the Editorial Board of International Journal of Computer Science and Software Technology (IJCSST) and International Journal of Computer Engineering and Information Technology. \n· He is also the Editor of Communication in Computer and Information Science CCIS-20 by Springer.\n· Reviewer For Many Conferences\nHe is the lead person in making collaboration agreements between Aalborg University and many universities of Pakistan, for which the MOU’s (Memorandum of Understanding) have been signed.\nProfessor Akbar is working in Academia since 1990, he started his career as a Lab demonstrator/TA at the University of Sussex. After finishing his P. hD degree in 1992, he served in the Industry as a Scientific Officer and continued his academic career as a visiting scholar for a number of educational institutions. In 1996 he joined National University of Science & Technology Pakistan (NUST) as an Associate Professor; NUST is one of the top few universities in Pakistan. In 1999 he joined an International Company Lineo Inc, Canada as Manager Compiler Group, where he headed the group for developing Compiler Tool Chain and Porting of Operating Systems for the BLACKfin processor. The processor development was a joint venture by Intel and Analog Devices. In 2002 Lineo Inc., was taken over by another company, so he joined Aalborg University Denmark as an Assistant Professor.\nProfessor Akbar has truly a multi-disciplined career and he continued his legacy and making progress in many areas of his interests both in teaching and research. 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He was also invited to serve as an associate editor for special issues of the Journal of the American Water Resources Association. He has served as an editorial member for international journals such as Hydrology, Journal of Ecology & Natural Resources, and Hydro Science & Marine Engineering, among others. He has chaired or acted as a technical committee member for twenty-five international forums (conferences). Dr. Shang graduated from Tsinghua University, China, in 2010 with a Ph.D. in Engineering. Prior to that, he worked as a research fellow at Harvard University from 2008 to 2009. 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Dr. Santos also has experience as a professor of graduate courses. Graduated in Pharmacy, specialization in Cosmetology and Cosmeceuticals applied to aesthetics, specialization in Aesthetic and Cosmetic Health, and a doctorate in Pharmaceutical Nanotechnology. Teaching experience in Pharmacy and Aesthetics and Cosmetics courses. She works mainly on the following subjects: nanotechnology, cosmetology, pharmaceutical technology, aesthetics.",institutionString:"Universidade Federal de Juiz de Fora",institution:{name:"Universidade Federal de Juiz de Fora",country:{name:"Brazil"}}},{id:"219081",title:"Dr.",name:"Abdulsamed",middleName:null,surname:"Kükürt",slug:"abdulsamed-kukurt",fullName:"Abdulsamed Kükürt",position:null,profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRNVJQA4/Profile_Picture_2022-03-07T13:23:04.png",biography:"Dr. Kükürt graduated from Uludağ University in Turkey. He started his academic career as a Research Assistant in the Department of Biochemistry at Kafkas University. In 2019, he completed his Ph.D. program in the Department of Biochemistry at the Institute of Health Sciences. He is currently working at the Department of Biochemistry, Kafkas University. He has 27 published research articles in academic journals, 11 book chapters, and 37 papers. He took part in 10 academic projects. He served as a reviewer for many articles. He still serves as a member of the review board in many academic journals. His research interests include biochemistry, oxidative stress, reactive species, antioxidants, lipid peroxidation, inflammation, reproductive hormones, phenolic compounds, female infertility.",institutionString:"Kafkas University",institution:{name:"Kafkas University",country:{name:"Turkey"}}},{id:"178366",title:"Associate Prof.",name:"Volkan",middleName:null,surname:"Gelen",slug:"volkan-gelen",fullName:"Volkan Gelen",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/178366/images/system/178366.jpg",biography:"Volkan Gelen is a Physiology specialist who received his veterinary degree from Kafkas University in 2011. Between 2011-2015, he worked as an assistant at Atatürk University, Faculty of Veterinary Medicine, Department of Physiology. In 2016, he joined Kafkas University, Faculty of Veterinary Medicine, Department of Physiology as an assistant professor. Dr. Gelen has been engaged in various academic activities at Kafkas University since 2016. There he completed 5 projects and has 3 ongoing projects. He has 60 articles published in scientific journals and 20 poster presentations in scientific congresses. His research interests include physiology, endocrine system, cancer, diabetes, cardiovascular system diseases, and isolated organ bath system studies.",institutionString:"Kafkas University",institution:{name:"Kafkas University",country:{name:"Turkey"}}},{id:"418963",title:"Dr.",name:"Augustine Ododo",middleName:"Augustine",surname:"Osagie",slug:"augustine-ododo-osagie",fullName:"Augustine Ododo Osagie",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/418963/images/16900_n.jpg",biography:"Born into the family of Osagie, a prince of the Benin Kingdom. I am currently an academic in the Department of Medical Biochemistry, University of Benin. Part of the duties are to teach undergraduate students and conduct academic research.",institutionString:null,institution:{name:"University of Benin",country:{name:"Nigeria"}}},{id:"192992",title:"Prof.",name:"Shagufta",middleName:null,surname:"Perveen",slug:"shagufta-perveen",fullName:"Shagufta Perveen",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/192992/images/system/192992.png",biography:"Prof. Shagufta Perveen is a Distinguish Professor in the Department of Pharmacognosy, College of Pharmacy, King Saud University, Riyadh, Saudi Arabia. Dr. Perveen has acted as the principal investigator of major research projects funded by the research unit of King Saud University. She has more than ninety original research papers in peer-reviewed journals of international repute to her credit. She is a fellow member of the Royal Society of Chemistry UK and the American Chemical Society of the United States.",institutionString:"King Saud University",institution:{name:"King Saud University",country:{name:"Saudi Arabia"}}},{id:"49848",title:"Dr.",name:"Wen-Long",middleName:null,surname:"Hu",slug:"wen-long-hu",fullName:"Wen-Long Hu",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/49848/images/system/49848.jpg",biography:"Wen-Long Hu is Chief of the Division of Acupuncture, Department of Chinese Medicine at Kaohsiung Chang Gung Memorial Hospital, as well as an adjunct associate professor at Fooyin University and Kaohsiung Medical University. Wen-Long is President of Taiwan Traditional Chinese Medicine Medical Association. He has 28 years of experience in clinical practice in laser acupuncture therapy and 34 years in acupuncture. He is an invited speaker for lectures and workshops in laser acupuncture at many symposiums held by medical associations. He owns the patent for herbal preparation and producing, and for the supercritical fluid-treated needle. Dr. Hu has published three books, 12 book chapters, and more than 30 papers in reputed journals, besides serving as an editorial board member of repute.",institutionString:"Kaohsiung Chang Gung Memorial Hospital",institution:{name:"Kaohsiung Chang Gung Memorial Hospital",country:{name:"Taiwan"}}},{id:"298472",title:"Prof.",name:"Andrey V.",middleName:null,surname:"Grechko",slug:"andrey-v.-grechko",fullName:"Andrey V. Grechko",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/298472/images/system/298472.png",biography:"Andrey Vyacheslavovich Grechko, Ph.D., Professor, is a Corresponding Member of the Russian Academy of Sciences. He graduated from the Semashko Moscow Medical Institute (Semashko National Research Institute of Public Health) with a degree in Medicine (1998), the Clinical Department of Dermatovenerology (2000), and received a second higher education in Psychology (2009). Professor A.V. Grechko held the position of Сhief Physician of the Central Clinical Hospital in Moscow. He worked as a professor at the faculty and was engaged in scientific research at the Medical University. Starting in 2013, he has been the initiator of the creation of the Federal Scientific and Clinical Center for Intensive Care and Rehabilitology, Moscow, Russian Federation, where he also serves as Director since 2015. He has many years of experience in research and teaching in various fields of medicine, is an author/co-author of more than 200 scientific publications, 13 patents, 15 medical books/chapters, including Chapter in Book «Metabolomics», IntechOpen, 2020 «Metabolomic Discovery of Microbiota Dysfunction as the Cause of Pathology».",institutionString:"Federal Research and Clinical Center of Intensive Care Medicine and Rehabilitology",institution:null},{id:"199461",title:"Prof.",name:"Natalia V.",middleName:null,surname:"Beloborodova",slug:"natalia-v.-beloborodova",fullName:"Natalia V. Beloborodova",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/199461/images/system/199461.jpg",biography:'Natalia Vladimirovna Beloborodova was educated at the Pirogov Russian National Research Medical University, with a degree in pediatrics in 1980, a Ph.D. in 1987, and a specialization in Clinical Microbiology from First Moscow State Medical University in 2004. She has been a Professor since 1996. Currently, she is the Head of the Laboratory of Metabolism, a division of the Federal Research and Clinical Center of Intensive Care Medicine and Rehabilitology, Moscow, Russian Federation. N.V. Beloborodova has many years of clinical experience in the field of intensive care and surgery. She studies infectious complications and sepsis. She initiated a series of interdisciplinary clinical and experimental studies based on the concept of integrating human metabolism and its microbiota. Her scientific achievements are widely known: she is the recipient of the Marie E. Coates Award \\"Best lecturer-scientist\\" Gustafsson Fund, Karolinska Institutes, Stockholm, Sweden, and the International Sepsis Forum Award, Pasteur Institute, Paris, France (2014), etc. Professor N.V. Beloborodova wrote 210 papers, five books, 10 chapters and has edited four books.',institutionString:"Federal Research and Clinical Center of Intensive Care Medicine and Rehabilitology",institution:null},{id:"354260",title:"Ph.D.",name:"Tércio Elyan",middleName:"Azevedo",surname:"Azevedo Martins",slug:"tercio-elyan-azevedo-martins",fullName:"Tércio Elyan Azevedo Martins",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/354260/images/16241_n.jpg",biography:"Graduated in Pharmacy from the Federal University of Ceará with the modality in Industrial Pharmacy, Specialist in Production and Control of Medicines from the University of São Paulo (USP), Master in Pharmaceuticals and Medicines from the University of São Paulo (USP) and Doctor of Science in the program of Pharmaceuticals and Medicines by the University of São Paulo. Professor at Universidade Paulista (UNIP) in the areas of chemistry, cosmetology and trichology. Assistant Coordinator of the Higher Course in Aesthetic and Cosmetic Technology at Universidade Paulista Campus Chácara Santo Antônio. Experience in the Pharmacy area, with emphasis on Pharmacotechnics, Pharmaceutical Technology, Research and Development of Cosmetics, acting mainly on topics such as cosmetology, antioxidant activity, aesthetics, photoprotection, cyclodextrin and thermal analysis.",institutionString:null,institution:{name:"University of Sao Paulo",country:{name:"Brazil"}}},{id:"334285",title:"Ph.D. Student",name:"Sameer",middleName:"Kumar",surname:"Jagirdar",slug:"sameer-jagirdar",fullName:"Sameer Jagirdar",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/334285/images/14691_n.jpg",biography:"I\\'m a graduate student at the center for biosystems science and engineering at the Indian Institute of Science, Bangalore, India. I am interested in studying host-pathogen interactions at the biomaterial interface.",institutionString:null,institution:{name:"Indian Institute of Science Bangalore",country:{name:"India"}}},{id:"329795",title:"Dr.",name:"Mohd Aftab",middleName:"Aftab",surname:"Siddiqui",slug:"mohd-aftab-siddiqui",fullName:"Mohd Aftab Siddiqui",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/329795/images/15648_n.jpg",biography:"Dr. Mohd Aftab Siddiqui is currently working as Assistant Professor in the Faculty of Pharmacy, Integral University, Lucknow for the last 6 years. He has completed his Doctor in Philosophy (Pharmacology) in 2020 from Integral University, Lucknow. He completed his Bachelor in Pharmacy in 2013 and Master in Pharmacy (Pharmacology) in 2015 from Integral University, Lucknow. He is the gold medalist in Bachelor and Master degree. He qualified GPAT -2013, GPAT -2014, and GPAT 2015. His area of research is Pharmacological screening of herbal drugs/ natural products in liver and cardiac diseases. He has guided many M. Pharm. research projects. He has many national and international publications.",institutionString:"Integral University",institution:null},{id:"255360",title:"Dr.",name:"Usama",middleName:null,surname:"Ahmad",slug:"usama-ahmad",fullName:"Usama Ahmad",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/255360/images/system/255360.png",biography:"Dr. Usama Ahmad holds a specialization in Pharmaceutics from Amity University, Lucknow, India. He received his Ph.D. degree from Integral University. Currently, he’s working as an Assistant Professor of Pharmaceutics in the Faculty of Pharmacy, Integral University. From 2013 to 2014 he worked on a research project funded by SERB-DST, Government of India. He has a rich publication record with more than 32 original articles published in reputed journals, 3 edited books, 5 book chapters, and a number of scientific articles published in ‘Ingredients South Asia Magazine’ and ‘QualPharma Magazine’. He is a member of the American Association for Cancer Research, International Association for the Study of Lung Cancer, and the British Society for Nanomedicine. Dr. Ahmad’s research focus is on the development of nanoformulations to facilitate the delivery of drugs that aim to provide practical solutions to current healthcare problems.",institutionString:"Integral University",institution:{name:"Integral University",country:{name:"India"}}},{id:"30568",title:"Prof.",name:"Madhu",middleName:null,surname:"Khullar",slug:"madhu-khullar",fullName:"Madhu Khullar",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/30568/images/system/30568.jpg",biography:"Dr. Madhu Khullar is a Professor of Experimental Medicine and Biotechnology at the Post Graduate Institute of Medical Education and Research, Chandigarh, India. She completed her Post Doctorate in hypertension research at the Henry Ford Hospital, Detroit, USA in 1985. She is an editor and reviewer of several international journals, and a fellow and member of several cardiovascular research societies. Dr. Khullar has a keen research interest in genetics of hypertension, and is currently studying pharmacogenetics of hypertension.",institutionString:"Post Graduate Institute of Medical Education and Research",institution:{name:"Post Graduate Institute of Medical Education and Research",country:{name:"India"}}},{id:"223233",title:"Prof.",name:"Xianquan",middleName:null,surname:"Zhan",slug:"xianquan-zhan",fullName:"Xianquan Zhan",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/223233/images/system/223233.png",biography:"Xianquan Zhan received his MD and Ph.D. in Preventive Medicine at West China University of Medical Sciences. He received his post-doctoral training in oncology and cancer proteomics at the Central South University, China, and the University of Tennessee Health Science Center (UTHSC), USA. He worked at UTHSC and the Cleveland Clinic in 2001–2012 and achieved the rank of associate professor at UTHSC. Currently, he is a full professor at Central South University and Shandong First Medical University, and an advisor to MS/PhD students and postdoctoral fellows. He is also a fellow of the Royal Society of Medicine and European Association for Predictive Preventive Personalized Medicine (EPMA), a national representative of EPMA, and a member of the American Society of Clinical Oncology (ASCO) and the American Association for the Advancement of Sciences (AAAS). He is also the editor in chief of International Journal of Chronic Diseases & Therapy, an associate editor of EPMA Journal, Frontiers in Endocrinology, and BMC Medical Genomics, and a guest editor of Mass Spectrometry Reviews, Frontiers in Endocrinology, EPMA Journal, and Oxidative Medicine and Cellular Longevity. He has published more than 148 articles, 28 book chapters, 6 books, and 2 US patents in the field of clinical proteomics and biomarkers.",institutionString:"Shandong First Medical University",institution:{name:"Affiliated Hospital of Shandong Academy of Medical Sciences",country:{name:"China"}}},{id:"297507",title:"Dr.",name:"Charles",middleName:"Elias",surname:"Assmann",slug:"charles-assmann",fullName:"Charles Assmann",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/297507/images/system/297507.jpg",biography:"Charles Elias Assmann is a biologist from Federal University of Santa Maria (UFSM, Brazil), who spent some time abroad at the Ludwig-Maximilians-Universität München (LMU, Germany). He has Masters Degree in Biochemistry (UFSM), and is currently a PhD student at Biochemistry at the Department of Biochemistry and Molecular Biology of the UFSM. His areas of expertise include: Biochemistry, Molecular Biology, Enzymology, Genetics and Toxicology. He is currently working on the following subjects: Aluminium toxicity, Neuroinflammation, Oxidative stress and Purinergic system. Since 2011 he has presented more than 80 abstracts in scientific proceedings of national and international meetings. Since 2014, he has published more than 20 peer reviewed papers (including 4 reviews, 3 in Portuguese) and 2 book chapters. He has also been a reviewer of international journals and ad hoc reviewer of scientific committees from Brazilian Universities.",institutionString:"Universidade Federal de Santa Maria",institution:{name:"Universidade Federal de Santa Maria",country:{name:"Brazil"}}},{id:"217850",title:"Dr.",name:"Margarete Dulce",middleName:null,surname:"Bagatini",slug:"margarete-dulce-bagatini",fullName:"Margarete Dulce Bagatini",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/217850/images/system/217850.jpeg",biography:"Dr. Margarete Dulce Bagatini is an associate professor at the Federal University of Fronteira Sul/Brazil. She has a degree in Pharmacy and a PhD in Biological Sciences: Toxicological Biochemistry. She is a member of the UFFS Research Advisory Committee\nand a member of the Biovitta Research Institute. She is currently:\nthe leader of the research group: Biological and Clinical Studies\nin Human Pathologies, professor of postgraduate program in\nBiochemistry at UFSC and postgraduate program in Science and Food Technology at\nUFFS. She has experience in the area of pharmacy and clinical analysis, acting mainly\non the following topics: oxidative stress, the purinergic system and human pathologies, being a reviewer of several international journals and books.",institutionString:"Universidade Federal da Fronteira Sul",institution:{name:"Universidade Federal da Fronteira Sul",country:{name:"Brazil"}}},{id:"226275",title:"Ph.D.",name:"Metin",middleName:null,surname:"Budak",slug:"metin-budak",fullName:"Metin Budak",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/226275/images/system/226275.jfif",biography:"Metin Budak, MSc, PhD is an Assistant Professor at Trakya University, Faculty of Medicine. He has been Head of the Molecular Research Lab at Prof. Mirko Tos Ear and Hearing Research Center since 2018. His specializations are biophysics, epigenetics, genetics, and methylation mechanisms. He has published around 25 peer-reviewed papers, 2 book chapters, and 28 abstracts. He is a member of the Clinical Research Ethics Committee and Quantification and Consideration Committee of Medicine Faculty. His research area is the role of methylation during gene transcription, chromatin packages DNA within the cell and DNA repair, replication, recombination, and gene transcription. His research focuses on how the cell overcomes chromatin structure and methylation to allow access to the underlying DNA and enable normal cellular function.",institutionString:"Trakya University",institution:{name:"Trakya University",country:{name:"Turkey"}}},{id:"243049",title:"Dr.",name:"Anca",middleName:null,surname:"Pantea Stoian",slug:"anca-pantea-stoian",fullName:"Anca Pantea Stoian",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/243049/images/system/243049.jpg",biography:"Anca Pantea Stoian is a specialist in diabetes, nutrition, and metabolic diseases as well as health food hygiene. She also has competency in general ultrasonography.\n\nShe is an associate professor in the Diabetes, Nutrition and Metabolic Diseases Department, Carol Davila University of Medicine and Pharmacy, Bucharest, Romania. She has been chief of the Hygiene Department, Faculty of Dentistry, at the same university since 2019. Her interests include micro and macrovascular complications in diabetes and new therapies. Her research activities focus on nutritional intervention in chronic pathology, as well as cardio-renal-metabolic risk assessment, and diabetes in cancer. She is currently engaged in developing new therapies and technological tools for screening, prevention, and patient education in diabetes. \n\nShe is a member of the European Association for the Study of Diabetes, Cardiometabolic Academy, CEDA, Romanian Society of Diabetes, Nutrition and Metabolic Diseases, Romanian Diabetes Federation, and Association for Renal Metabolic and Nutrition studies. She has authored or co-authored 160 papers in national and international peer-reviewed journals.",institutionString:null,institution:{name:"Carol Davila University of Medicine and Pharmacy",country:{name:"Romania"}}},{id:"279792",title:"Dr.",name:"João",middleName:null,surname:"Cotas",slug:"joao-cotas",fullName:"João Cotas",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/279792/images/system/279792.jpg",biography:"Graduate and master in Biology from the University of Coimbra.\n\nI am a research fellow at the Macroalgae Laboratory Unit, in the MARE-UC – Marine and Environmental Sciences Centre of the University of Coimbra. My principal function is the collection, extraction and purification of macroalgae compounds, chemical and bioactive characterization of the compounds and algae extracts and development of new methodologies in marine biotechnology area. \nI am associated in two projects: one consists on discovery of natural compounds for oncobiology. The other project is the about the natural compounds/products for agricultural area.\n\nPublications:\nCotas, J.; Figueirinha, A.; Pereira, L.; Batista, T. 2018. An analysis of the effects of salinity on Fucus ceranoides (Ochrophyta, Phaeophyceae), in the Mondego River (Portugal). Journal of Oceanology and Limnology. in press. DOI: 10.1007/s00343-019-8111-3",institutionString:"Faculty of Sciences and Technology of University of Coimbra",institution:null},{id:"279788",title:"Dr.",name:"Leonel",middleName:null,surname:"Pereira",slug:"leonel-pereira",fullName:"Leonel Pereira",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/279788/images/system/279788.jpg",biography:"Leonel Pereira has an undergraduate degree in Biology, a Ph.D. in Biology (specialty in Cell Biology), and a Habilitation degree in Biosciences (specialization in Biotechnology) from the Faculty of Science and Technology, University of Coimbra, Portugal, where he is currently a professor. In addition to teaching at this university, he is an integrated researcher at the Marine and Environmental Sciences Center (MARE), Portugal. His interests include marine biodiversity (algae), marine biotechnology (algae bioactive compounds), and marine ecology (environmental assessment). Since 2008, he has been the author and editor of the electronic publication MACOI – Portuguese Seaweeds Website (www.seaweeds.uc.pt). He is also a member of the editorial boards of several scientific journals. Dr. Pereira has edited or authored more than 20 books, 100 journal articles, and 45 book chapters. He has given more than 100 lectures and oral communications at various national and international scientific events. He is the coordinator of several national and international research projects. In 1998, he received the Francisco de Holanda Award (Honorable Mention) and, more recently, the Mar Rei D. Carlos award (18th edition). He is also a winner of the 2016 CHOICE Award for an outstanding academic title for his book Edible Seaweeds of the World. In 2020, Dr. Pereira received an Honorable Mention for the Impact of International Publications from the Web of Science",institutionString:"University of Coimbra",institution:{name:"University of Coimbra",country:{name:"Portugal"}}},{id:"61946",title:"Dr.",name:"Carol",middleName:null,surname:"Bernstein",slug:"carol-bernstein",fullName:"Carol Bernstein",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/61946/images/system/61946.jpg",biography:"Carol Bernstein received her PhD in Genetics from the University of California (Davis). She was a faculty member at the University of Arizona College of Medicine for 43 years, retiring in 2011. Her research interests focus on DNA damage and its underlying role in sex, aging and in the early steps of initiation and progression to cancer. In her research, she had used organisms including bacteriophage T4, Neurospora crassa, Schizosaccharomyces pombe and mice, as well as human cells and tissues. She authored or co-authored more than 140 scientific publications, including articles in major peer reviewed journals, book chapters, invited reviews and one book.",institutionString:"University of Arizona",institution:{name:"University of Arizona",country:{name:"United States of America"}}},{id:"182258",title:"Dr.",name:"Ademar",middleName:"Pereira",surname:"Serra",slug:"ademar-serra",fullName:"Ademar Serra",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/182258/images/system/182258.jpeg",biography:"Dr. Serra studied Agronomy on Universidade Federal de Mato Grosso do Sul (UFMS) (2005). He received master degree in Agronomy, Crop Science (Soil fertility and plant nutrition) (2007) by Universidade Federal da Grande Dourados (UFGD), and PhD in agronomy (Soil fertility and plant nutrition) (2011) from Universidade Federal da Grande Dourados / Escola Superior de Agricultura Luiz de Queiroz (UFGD/ESALQ-USP). Dr. Serra is currently working at Brazilian Agricultural Research Corporation (EMBRAPA). His research focus is on mineral nutrition of plants, crop science and soil science. Dr. Serra\\'s current projects are soil organic matter, soil phosphorus fractions, compositional nutrient diagnosis (CND) and isometric log ratio (ilr) transformation in compositional data analysis.",institutionString:"Brazilian Agricultural Research Corporation",institution:{name:"Brazilian Agricultural Research Corporation",country:{name:"Brazil"}}}]}},subseries:{item:{id:"26",type:"subseries",title:"Machine Learning and Data Mining",keywords:"Intelligent Systems, Machine Learning, Data Science, Data Mining, Artificial Intelligence",scope:"The scope of machine learning and data mining is immense and is growing every day. It has become a massive part of our daily lives, making predictions based on experience, making this a fascinating area that solves problems that otherwise would not be possible or easy to solve. This topic aims to encompass algorithms that learn from experience (supervised and unsupervised), improve their performance over time and enable machines to make data-driven decisions. It is not limited to any particular applications, but contributions are encouraged from all disciplines.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/26.jpg",hasOnlineFirst:!0,hasPublishedBooks:!0,annualVolume:11422,editor:{id:"24555",title:"Dr.",name:"Marco Antonio",middleName:null,surname:"Aceves Fernandez",slug:"marco-antonio-aceves-fernandez",fullName:"Marco Antonio Aceves Fernandez",profilePictureURL:"https://mts.intechopen.com/storage/users/24555/images/system/24555.jpg",biography:"Dr. Marco Antonio Aceves Fernandez obtained his B.Sc. (Eng.) in Telematics from the Universidad de Colima, Mexico. He obtained both his M.Sc. and Ph.D. from the University of Liverpool, England, in the field of Intelligent Systems. He is a full professor at the Universidad Autonoma de Queretaro, Mexico, and a member of the National System of Researchers (SNI) since 2009. Dr. Aceves Fernandez has published more than 80 research papers as well as a number of book chapters and congress papers. He has contributed in more than 20 funded research projects, both academic and industrial, in the area of artificial intelligence, ranging from environmental, biomedical, automotive, aviation, consumer, and robotics to other applications. He is also a honorary president at the National Association of Embedded Systems (AMESE), a senior member of the IEEE, and a board member of many institutions. 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