Summary of experimental test matrix to investigate the effect of working fluid charge [6].
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Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
\n\nThis achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
\n\nWe are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
\n\nThank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
\n\n\n\n\n'}],latestNews:[{slug:"intechopen-partners-with-ehs-for-digital-advertising-representation-20210416",title:"IntechOpen Partners with EHS for Digital Advertising Representation"},{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"}]},book:{item:{type:"book",id:"2241",leadTitle:null,fullTitle:"Biomedical Engineering - From Theory to Applications",title:"Biomedical Engineering",subtitle:"From Theory to Applications",reviewType:"peer-reviewed",abstract:"In all different areas in biomedical engineering, the ultimate objectives in research and education are to improve the quality life, reduce the impact of disease on the everyday life of individuals, and provide an appropriate infrastructure to promote and enhance the interaction of biomedical engineering researchers. 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\r\n\tIn textbooks and manuals, diplomacy is often defined as "the science of foreign relations" and "the art of negotiation." This certainly makes a lot of sense. A balanced analysis of the global situation and the correct consideration of the balance of power in the international arena are essential for the development of truly scientific, deeply grounded recommendations in the field of foreign policy. It is necessary to carefully study historical trends, fully take into account the different directions and trends in international relations, to be able to seek and attract allies to desired side, to achieve the isolation of the most aggressive and hostile circles. One can really expect success only if diplomacy acts in principle and, at the same time, pragmatically and flexibly, avoids dogmatism and sectarianism, and is not afraid of compromises that ultimately benefit national interests. Hence, the importance of mastering a number of sciences: history of individual countries and international relations, international law, complex sciences related to the study of the world economy and the economies of individual countries, comparative political science and law, philosophy, psychology, and etc. In short, diplomacy should rely on the laws of social life and consider the findings of the relevant sciences.
\r\n\r\n\tThis book intends to provide the reader with a comprehensive understanding of the real essence of public diplomacy. Public diplomacy and related concepts such as ""strategic communication"" and ""national branding"" are a part of increasingly common public administration practices. It also represents an area of research with significant growth potential. The nation states have in various contexts recognized the need to communicate with foreign communities and to develop networks through various forms of interaction, including international communication, exchange programmes and cultural diplomacy. As a result, public diplomacy has become an effective tool of purposeful communication with the foreign public to promote short-term political goals, to develop long-term relations, and to address pressing issues of transnational politics. Nevertheless, there are big problems that lie behind the popularization of modern public diplomacy initiatives which will also be discussed in the book.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"ca82945156946b18f4e457ce91ac6643",bookSignature:"Dr. Galina V. Timofeeva and Ms. Alexandra Baranova",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8535.jpg",keywords:"Diplomatic Service, Cultural Diplomacy, Negotiation, Tools, Mechanisms, Actors, Official Diplomacy, Digital Diplomacy, Conflict Resolution, Intergovernmental Organizations, Cooperation",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 13th 2019",dateEndSecondStepPublish:"March 27th 2020",dateEndThirdStepPublish:"May 26th 2020",dateEndFourthStepPublish:"August 14th 2020",dateEndFifthStepPublish:"October 13th 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"311522",title:"Dr.",name:"Galina",middleName:"V.",surname:"Timofeeva",slug:"galina-timofeeva",fullName:"Galina Timofeeva",profilePictureURL:"https://mts.intechopen.com/storage/users/311522/images/system/311522.jpg",biography:"Galina V. Timofeeva, PhD is a Professor at the Department of Economics and Public Diplomacy at the Institute of Public Service and Management of the Russian Presidential Academy of National Economy and Public Administration (RANEPA). Professor Timofeeva is an expert of the Higher Attestation Commission of the Ministry of Education and Science of the Russian Federation. She is also an expert and a scientific editor of the strategy of socio-economic development of the Republic of Abkhazia-2025, as well as the specialist at the Russian Foundation for Basic Research.",institutionString:"Russian Presidential Academy of National Economy and Public Administration",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Russian Presidential Academy of National Economy and Public Administration",institutionURL:null,country:{name:"Russia"}}}],coeditorOne:{id:"312195",title:"Ms.",name:"Alexandra",middleName:null,surname:"Baranova",slug:"alexandra-baranova",fullName:"Alexandra Baranova",profilePictureURL:"https://mts.intechopen.com/storage/users/no_image.jpg",biography:"Dr. Alexandra Baranova is a lecturer at the Russian Academy of National Economy and Public Administration. Her scientific interests include linguistic tools of public diplomacy, as well as the role of mass media in diplomatic processes.",institutionString:"Russian Presidential Academy of National Economy and Public Administration",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Russian Presidential Academy of National Economy and Public Administration",institutionURL:null,country:{name:"Russia"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"23",title:"Social Sciences",slug:"social-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"247041",firstName:"Dolores",lastName:"Kuzelj",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/247041/images/7108_n.jpg",email:"dolores@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Despite this, it is not always easy to diagnose it, even for experienced surgeons. Acute appendicitis should be suspected in any patient with abdominal pain, and its correct diagnosis in many cases depends on the completeness of anamnestic data.
\nThere are no other diseases that have such a variety of symptoms as acute appendicitis. At the same time, if gangrene develops, it may be asymptomatic until complications occur. And who among the surgeons have not ever observed the typical classic symptom complex and at the same time the absence of visual morphological changes in the appendix, after removal of which the patient felt better in the next few hours after the operation? In short, atypical acute appendicitis is more frequent than its classical manifestations.
\nAs a rule, the main sign of acute appendicitis is abdominal pain, which makes a patient visit the doctor. It should be emphasized that the pain does not always occur in the right iliac fossa being the most typical position of the appendix. It may be in the epigastric region or migrate throughout the abdomen without any specific localization. In the initial period, pain is not intense, dull, and only occasionally may be cramping. After 2–3 h from the onset of the disease, they gradually increase and move to the right iliac region where the appendix is localized. This pain displacement is characteristic of acute appendicitis onset and is known as Kocher-Volkovich sign. This sign results from the initial pain signals being transferred through the midgut visceral innervation. When the parietal peritoneum starts being involved in the inflammatory process, the pain acquires more certain localization.
\nOften patients mistakenly associate the presence of abdominal pain with an unhealthy diet or believe that they have got poisoned, especially since the disease is accompanied by loss of appetite, nausea, and one- or two-time reflexive vomiting from the very beginning. Sometimes patients try to induce vomiting artificially or pump the stomach. Murphy, in 1904, first described vomiting and migration of colicky central abdominal pain to the right iliac fossa.
\nCope described constipation in patients and their expectations of pain relief after defecation, which does not happen. Urination problems are rare.
\nA simple visual examination in the first few hours shows the doctor that the patient’s condition is not worsened much. He is comparatively calm, moves actively, and sometimes holds on to his right side. Pulse rate typically increases and does not correspond to body temperature, which often remains normal and rises as destructive changes develop in the appendix.
\nFurther examination is supposed to reveal three signs that characterize acute appendicitis: tenderness, muscular contraction, and skin hyperesthesia (Dieulafoy triad). Abdominal tenderness is the most typical sign of acute appendicitis. Visually, the movements of the right iliac region moderately lag during breathing. An attempt to take a deep breath, draw in a stomach, or make a cough causes an intensification of pain.
\nPalpation of the abdomen should be started from the left side, away from the pain area. Caressing counter-clockwise movements should gradually approach the right iliac region, where the patient may suddenly feel a sharp and intolerable pain. In some cases, its epicenter is McBurney’s point, which was described by the author as follows: “…exactly between an inch and half and two inches from the anterior spinous process of the ileum on a straight line drawn from that process to the umbilicus” [1]. This point was assumed to match with the location of the inflamed appendix irritating the abdominal peritoneum over the T11 and T12 dermatome segment. Opposed to McBurney’s original description, most textbooks mistakenly define the point as being one-third of the line from the anterior superior iliac spine to the umbilicus. Meanwhile, Lanz believed that “the McBurney’s point has nothing to do with the origin of the vermiform appendix” and suggested its own localization that is on the line between the two anterosuperior iliac spines one-third of the distance from the right spine [2].
\nIn general, the projection of pain need not necessarily correspond to the Lanz or McBurney’s point. Occasionally, pain is noted on the middle line under the umbilicus or above the pubic region. Less often it is found anteriorly or posteriorly in the right- or left hypochondrium. In the absence of pain in the surveyed areas, it is advised to turn a patient on the left side and palpate over the iliac crest and along its entire length. If a negative result is obtained, rectal examination should be started. Pain in the Douglas pouch is an excellent sign. It often combines with pain in the right iliac region but is often found singly.
\nAbdominal wall muscle contraction or defense (muscular protection) is the most important of the signs revealed on careful examination. According to Mondor, there is no other sign which allowed doctors to save more lives than this one. When palpating an abdomen, which is not swollen and rigid but does not participate in respiratory movements, it is necessary to attempt to find the reaction of the abdominal wall in the form of muscular contraction. In acute appendicitis, it is usually localized in the right iliac region. Skin hypersthesia appears in most cases of local or diffuse peritonitis [3].
\nIn addition, there are many symptoms and signs that can be associated with appendicitis, depending on the location of the inflamed vermiform appendix, for example: Dunphy’s sign (coughing intensifies pain in right lower quadrant), obturator sign (hip flexion and internal rotation increases pain), psoas sign (right hip passive extension increases pain in a patient lying on the left side), Rovsing’s sign (palpation in the left lower quadrant intensifies pain in the right lower quadrant), etc. At the same time, most of them are not specific and their importance increases significantly when they are evaluated together with laboratory signs [4].
\nChanges in laboratory parameters in acute appendicitis include leukocytosis with left shift and increased inflammatory markers such as C-reactive protein and erythrocyte sedimentation rate. As with the clinical symptoms and signs, each particular laboratory value hardly indicates the presence of acute appendicitis. However, combinations of clinical and laboratory data or aggregate of various laboratory values are more reliable. For example, it was determined that high rates of laboratory inflammatory markers such as white blood cell and granulocyte counts and C-reactive protein level were comparatively strong predictors of perforated appendicitis, whereas low values testified to its absence [5].
\nThere are several clinical scoring systems that are used to diagnose acute appendicitis. In 1986, Alfredo Alvarado developed his score, also called MANTRELS based on the mnemonic for remembering the combination of eight signs and symptoms: migration (1), anorexia-acetone (1), nausea-vomiting (1), tenderness in right lower quadrant (2), rebound pain (1), elevation of temperature (1), leukocytosis (2), shift to the left (1). Each indicator is assigned 1–2 points, which are then summed. If the sum of points equals numbers from 0 to 4, acute appendicitis is unlikely. The score of 5 or 6 means that acute appendicitis should be suspected and observation is necessary. The score of 7 and 8 signifies that the diagnosis is probable. Acute appendicitis is very likely if the score is 9 or 10 [6]. Currently, there have been developed the modified versions of the Alvarado scale, such as the Pediatric Appendicitis Score, described in 2002 by Samuel [7] and other scores such as the Eskelinen, Ohhmann, RIPASA scores [8], etc. Generally, these clinical scoring systems are more informative than specific symptoms or signs alone. Still, they are not capable of predicting appendicitis with sufficient probability and therefore should not be used alone to diagnose it. They have been applied to define the necessity for radiological tests or as a guide for planning clinical management.
\nRadiological imaging is used more and more to evaluate abdominal pain and diagnose acute appendicitis. On one hand, imaging may be useful in the examination of patients with abdominal pain for establishing or excluding other diagnoses or for averting unnecessary surgery. On the other hand, imaging could possibly delay operation, and in the case of computed tomography (CT), radiologic imaging exposes patients to the risks of ionizing radiation. Abdominal ultrasound (US) is less and less used to diagnose acute appendicitis. It was designated that US sensitivity and specificity in this disease do not exceed those of physical examination or approved clinical scores such as the Alvarado score [9]. The noninvasive gold standard for acute appendicitis remains CT with contrast medium. It was proved that preoperative CT reduced the number of negative appendectomies but increased waiting time for surgery, although perforation rate was not elevated [10]. Magnetic resonance imaging (MRI) is a promising technique because of its high diagnostic accuracy and avoidance of ionizing radiation and intravenous contrast medium [11].
\nAppendectomy is one of the most common surgical procedures performed worldwide. Since the late 1880s, open appendectomy has been accepted as the standard for the treatment of acute appendicitis and has saved many lives since then. In Europe, it was promoted by the thesis of Charles Krafft “Essay on the need for surgical treatment of perityphlitis and purulent perforated appendicitis” (1888), while in America there were the works of Charles McBurney, in particular, “Experience with early operative interference in cases of disease of the vermiform appendix” (1889) [12].
\nTreatment of uncomplicated acute appendicitis without surgery is principally unstudied, although it often resolves spontaneously or with antibiotic therapy. Few studies state that it has the outcomes comparable to those of appendectomy [13].
\nThe widespread use of CT for the diagnosis of appendicitis led to interesting observations regarding the possibility of spontaneously resolved acute appendicitis. It was shown that the inclusion of the CT result in the Alvarado score increases the frequency of appendectomy. When classified as having a low likelihood of appendicitis (Alvarado score ≤ 4), patients who underwent a CT scan had an appendectomy rate of 48%. In contrast, those with an Alvarado score ≤ 4 who did not undergo a CT scan had an appendectomy rate of only 12% [14].
\nIn another study, diagnostic laparoscopy was used instead of CT scan in the management of patients with nonspecific abdominal pain. Patients were randomized to either (1) diagnostic laparoscopy or (2) nonoperative management (with operative intervention if peritonitis developed). The appendectomy rate was 39% for those randomized to diagnostic laparoscopy and 13% for those managed nonoperatively [15].
\nIn a number of studies, the incidence of acute uncomplicated appendicitis correlated strongly to the incidence of normal appendix removal and inversely correlated to diagnostic accuracy. Due to this, the authors reasoned that the observed incidence of uncomplicated appendicitis was influenced by the willingness to perform appendectomy in cases of presumed appendicitis. A high rate of appendectomy in such situations increases the proportion of confirmed cases probably by adding instances of self-limited inflammation that would escape detection in other circumstances [16]. This indirect evidence indicates that uncomplicated acute appendicitis can initially be treated without resorting to surgery. The safety of the initial non-surgical treatment of uncomplicated appendicitis was further confirmed, and it was shown that successful appendectomy can be avoided in almost all patients for the first 24 h with antibiotic therapy [17].
\nA large, population-based study using the American College of Surgeons National Surgical Quality Improvement Program database supports this semi-elective strategy, suggesting that appendectomy may be delayed up to 24–48 h without a significant increase in adverse outcome. In that study, there was no difference in the complication rate for those undergoing appendectomy within 1 day of admission. However, complication rate doubled if waiting time for surgery was delayed more than 48 h [18]. Contrary to the studies supporting a safe delay of appendectomy, there have been investigations demonstrating negative outcomes of even 6–12 h delays in surgery [19]. A recent study from the UK found no increased rate of complicated appendicitis when appendectomy was performed within 48 h [20].
\nAcute appendicitis is one of the most common surgical diseases in children. It occurs in all age groups, but rarely in infants. The associated lethality is 0.1–1% with prevalence in young children. Death in infants and neonates happens because of: (1) the failure to identify the disease because of its clinical presentation, which is similar to other common conditions in this age group, and (2) the inability of a younger patient to tell about abdominal pain or the absence of systemic symptoms, such as fever. At the time of the diagnosis, the percentage of perforated appendicitis has been up to 30% [21]. The percentage of perforation has been stated as high as 80–100% for children younger than 3 years, compared with 10–20% in 10–17-year-old children [22].
\nIn general, the strategy of diagnosis and treatment of acute appendicitis in children does not differ much from adults. Problems in the treatment of acute appendicitis are mostly the same in adults and children. Important concerns about the diagnosis, surgical technique, and antibiotic therapy remain uncertain for all patients. There are specific considerations for a pediatric appendectomy that remain questionable. They include the growing use of single-incision or single-port laparoscopic appendectomy and the primary nonoperative management of acute appendicitis with or without following appendectomy [23].
\nAcute appendicitis, being one of the most common diseases in emergency abdominal surgery, is a problem that still creates diagnostic difficulties. Although clinical studies alone cannot be sufficient to diagnose appendicitis, the importance of careful anamnesis and physical examination should not be underestimated. If extra tests are necessary, their risks and opportunities should be considered along with the possibility that such tests will change the management. Progress in imaging and computer decision support hold promise for the future, but additional study is needed to guarantee the accuracy, efficiency, and cost-effectiveness of novel diagnostic approaches for acute appendicitis.
\nThe available data concerning nonoperative management of acute appendicitis is discrepant. Pathologic confirmation of appendicitis is one of the difficulties in performing a well-planned randomized clinical trial of nonoperative versus operative therapy for acute appendicitis. Successful antibiotic therapy for “suspected” appendicitis may cause doubts about the diagnosis. On the other hand, there are patients who undergo a negative appendectomy and surgical risks, which is a valid concern.
\nIn spite of the fact that acute appendicitis is widespread, optimal diagnostics and management of it remain uncertain. This problem may be solved by conducting large multicenter randomized trials.
\nOrganic Rankine cycle (ORC) systems are widely acknowledged as one of the most suitable technologies for harvesting medium- to low-grade heat sources (i.e., below 300°C) from both renewable sources (e.g., geothermal and solar) and waste heat [1]. Nowadays, the total power capacity installed worldwide is estimated to be above 2.7 GWe, as reported by Tartière et al. in the ORC World Map [2, 3]. Furthermore, there has been a continuous increase in research activity related to ORC-based power systems over the last decades that has demonstrated the value of this technology and its potential to improve energy sustainability [4].
\nGenerally, ORCs are designed and optimized for steady-state operating conditions, unless mobile applications are considered. However, in the vast majority of stationary applications (e.g., solar thermal power, geothermal, waste heat recovery, and combined heat and power), the heat source and heat sink conditions are subjected to fluctuations and the ORC systems often operate at part-load or off-design conditions. To this end, numerical and experimental studies on off-design ORC performance have been published in the scientific literature, as outlined by Dickes et al. [5]. Similar to vapor compression systems, ORC performance is sensitive to working fluid charge and an incorrect charge level affects the system performance, especially under part-load conditions. Yet, very limited work can be found on the impact of working fluid charge on off-design operations. In fact, besides the research conducted by the Authors [6, 7, 8], only two additional studies could be found in the literature. Liu et al. [9] discussed the effect of different working fluid charge masses on the system performance. Experimental and numerical analyses were carried out to identify the optimal working fluid charge. Pan et al. [10] analyzed the impact of the working fluid charge on the length distribution of the different zones in the heat exchangers under several operating conditions. Furthermore, different void fraction models and heat transfer correlations were compared to assess their impact on the working fluid mass estimations in the heat exchangers.
\nThe present chapter discusses the relationship between working fluid charge and performance in ORC systems under different operating conditions. Furthermore, the fundamentals of deterministic numerical methods to account for working fluid charge in ORC simulations are also described.
\nA general sub-critical ORC with an internal heat exchanger (or regenerator), as shown in Figure 1, is considered as an example to understand the effect of working fluid charge. Although this chapter focuses on sub-critical ORC systems, the principles and the methodologies discussed hereafter can be extended to transcritical cycles and other cycle configurations [11]. By referring to Figure 1, the system consists of three heat exchangers (e.g., brazed plate heat exchangers), a pump (either centrifugal or volumetric type), a positive displacement expander (e.g., scroll type), a liquid receiver (or buffer tank), and line sets (or pipelines) between each component. Depending on the type of expander (e.g., single- and twin-screw, swash plate, or scroll), a dedicated oil-injection loop with an additional pump may be present in the system (see Figure 1). An oil separator is typically installed after the expander to avoid accumulation of the lubricant oil inside the heat exchangers, where hot spots may occur.
\nGeneral schematic of a regenerative organic Rankine cycle system. An independent lubricant oil loop is also included for completeness. Typical location of the sensors is also shown.
The operation of a sub-critical ORC encompasses several aspects that are common to refrigeration systems, such as the control of the subcooling at the condenser outlet and the degree of superheating at the evaporator outlet, single- and two-phase heat transfer in the heat exchangers, as well as working fluid leaks. The amount of working fluid charged into the system has a direct effect on the performance, the flexibility, as well as on the operational costs of the unit. The costs associated with the working fluid and possible working fluid losses due to leaks can be significant, especially in large-scale systems (up to 10% of the plant cost) [12].
\nWith respect to the system behavior, when the operating conditions shift from design to off-design, the working fluid charge migrates within the system, altering the transition between single-to two-phase heat transfer regimes inside the heat exchangers. If the system is over-charged, typically the length (or, equivalently, the spatial fraction) of the subcooled zone in the evaporator increases, reducing both the capacity and degree of superheating. However, if the system is under-charged, one of the drawbacks is the decrease of subcooling at the condenser outlet, which may cause the pump to cavitate [13]. Additionally, a liquid receiver can be installed before the pump, as shown in Figure 1, in order to compensate for charge migration during off-design conditions, especially in large scale ORC systems. Nevertheless, a non-proper charge level may completely empty or flood the liquid receiver.
\nThe estimation of the optimum charge level is particularly challenging when additional aspects of the normal ORC operation are considered. In particular, lubricant oil may be pre-mixed with the working fluid to ensure the correct functioning of positive displacement expanders. In other cases, oil-separators are utilized to separate the working fluid from the lubricant oil at the expander outlet. However, oil entrainment in the vapor and oil solubility affect the distribution of charge in the system. Furthermore, non-condensable gases can also be present inside the system, which can impact the operation of the ORCs by altering the condensing pressure [14].
\nBased on the aforementioned reasoning, appropriate numerical methodologies are required to predict the performance of the system and to account for the total working fluid charge in a deterministic way such that the system model resembles the actual behavior of the system. Experimental results are also necessary to validate such numerical methods and to conduct additional analyses. Therefore, in the following sections, the state-of-the-art numerical methods utilized to simulate ORC systems are described and their limitations are also highlighted.
\nModeling of ORC systems is typically performed for steady-state conditions using purely thermodynamic considerations. Assumptions are made regarding the minimum temperature difference (i.e., the pinch point) between the working fluid and the heat source and heat sink fluids. The degrees of subcooling at the pump inlet and superheat at the expander inlet are set, as well as the condensing and evaporating temperatures. Constant values of isentropic efficiency for the pump and expander are often assumed. Then, the cycle is solved by computing the enthalpy of the working fluid at each state point and assuming the pump and expander to be adiabatic. This type of simplified model works well as an initial working fluid screening tool and to broadly assess cycle performance trends. However, in such a model, the physical characteristics of the system components are not taken into account. It follows that a more detailed model is necessary to study the behavior of a real ORC system in off-design conditions. Such a detailed model also typically estimates the steady-state response of the system, although dynamic models have been constructed from similar considerations [15]. For the scope of this chapter, the following discussions will be limited to steady-state modeling.
\nDetailed off-design models of ORC systems are built by connecting together different sub-models for each component of the system and are implicitly solved by driving to zero a number of residuals to ensure that the solution is within a physical domain. Such detailed models are based upon the extensive literature available for vapor compression cooling and heat pumping systems [16, 17]. A recent overview of off-design steady-state performance studies and modeling applied to ORC systems can be found in [8].
\nGenerally, an ORC system model can be regarded as mechanistic if the inputs and the known parameters are similar to those an ORC operator would know in practice. The model then uses physical principles and empirical or semi-empirical component models to simulate system performance given these parameters, inputs and boundary conditions. An ORC system model requires knowledge of the pump and expander displacements, the heat exchangers geometry, and the total system volume. Such a model receives as inputs the working fluid type, the inlet temperature and mass flow rate of the source and sink fluids, the rotational speeds of the pump and expander, and the condenser exit subcooling or the total working fluid charge in the system. A truly mechanistic model is charge-sensitive, meaning the total refrigerant charge is known, but the condenser exit subcooling is determined by the ORC operation [5]. In fact, if the condenser exit subcooling is fixed within the simulation, an assumption is made regarding the system state, which is not known in a real system. Outputs of the model include rotating equipment efficiency, system efficiency, heat transfer rates, condensing and evaporating temperatures, and net power production. In addition, a Second Law analysis can also be applied to estimate the system irreversibilities [18].
\nA detailed ORC model such as the one described above can give information about off-design performance, working fluid charge sensitivity, migration of charge between operating points, pressure drops, and the impact of working fluid transport properties on the heat transfer processes. Although, it only applies to the exact system being modeled, it provides a general framework (see for example
While constructing a charge-sensitive model, a number of challenges, both numerical and thermophysical, need to be considered:
Since the entire ORC model is obtained by connecting several sub-models representing the system components and a number of residuals are necessary to ensure a physically-meaningful solution, a robust solution scheme is required to perform charge-sensitive simulations with reasonable computational efforts.
Due to the presence of multiple heat transfer mechanisms, pressure drops, and flow regimes inside the heat exchangers, it is important to properly identify the convective heat transfer coefficients in multi-zone heat exchangers and understand how the working fluid charge can improve the reliability of estimating such coefficients.
The charge estimation inside the heat exchangers relies on the proper knowledge of spatial fraction occupied by each zone (i.e., single-phase liquid or vapor, two-phase) as well as the estimation of the working fluid density. In the case of single-phase zones, such calculation is straightforward. However, in the case of two-phase zones, the density depends on the pressure, temperature, quality, and flow regime through the void fraction. Void fraction models directly impact the charge estimation.
Presence of a liquid receiver in the system.
Difficulties in accounting all the system volumes (e.g., valves, sight glasses, filters, sensors, and line sets).
Estimation of working fluid dissolved in lubricant oil.
Correctness of the model in predicting the total working fluid charge with different working fluids.
Uncertainties associated with the exact amount of working fluid charge present in the actual system.
In order to address the majority of these modeling aspects, general guidelines for developing charge-sensitive models are discussed in the following section. Among these aspects, heat transfer correlations and the length of each zone inside the heat exchangers account for the majority of the inaccuracy in charge estimations. However, it will be shown in Section 4.3 that the solubility of working fluid in oil can also be significant. A charge tuning scheme can be applied to improve the accuracy of charge estimation, as outlined in Section 3.3. Experimental results from a test case will be used to address the last three bullet points in Section 4.
\nAs aforementioned, the individual components are properly arranged to form the overall cycle model. By referring to the ORC schematic of Figure 1, two general approaches can be identified to assemble the cycle models, which are shown as block diagrams in Figures 2 and 3, respectively. By looking at the two diagrams, it appears evident that the major cycle components, that is, heat exchangers, pump and expander, are arranged in the same fashion. The major difference is the approach adopted to account for the line sets connecting the active components and, therefore, the associated pressure drops and heat losses. The approach shown in Figure 2 retains the physical description of the cycle with the line set sub-models placed between two consecutive cycle components. It follows that an accurate description of each line set, including internal and external diameters as well as equivalent length, is required. Whereas, in the block diagram of Figure 3, the line set losses are lumped into two single artificial components representing high- and low-pressure sides of the systems. These lumped components are placed at the outlet of the evaporator and the condenser, respectively.
\nBlock diagram showing how the individual component models are arranged to form the overall ORC model. Variables are updated as they pass through each component (adapted from [
Block diagram showing the solver architecture of the charge-sensitive ORC model proposed by Dickes et al. [
Each block diagram also determines the required initial guess values and the residual to be driven to zero to solve the system. In particular, in the case of the block diagram of Figure 2, the five initial guesses are the pump inlet specific enthalpy (\n
The fifth residual is associated with the total system charge, which is estimated by summing all the charge contributions:
\nwhere the mass of working fluid for each component is given by \n
In the case of the block diagram of Figure 3, the model iterates on the evaporator outlet specific enthalpy (\n
where the total working fluid charge is calculated by employing an analogous expression to that one appearing in Eq. (2).
\nIn both solution schemes, the resulting problem to be solved is multi-dimensional, leading to possible convergence issues when the charge is imposed. To increase the robustness of the model, a multi-stage solver can be employed to run the simulations. Dickes et al. [8] described these ad-hoc solvers in detail. The thermophysical properties of the working fluid can be retrieved either from CoolProp [20] or REFPROP [21].
\nIn order to simulate the entire cycle, different sub-models are required to characterize each of the components. In the context of charge-sensitive modeling, the heat exchangers typically have the largest volumes in the system and are subjected to varying flow regimes, as outlined in Section 3.3. However, pump, expander, liquid receiver, and line sets also require proper modeling. Particular emphasis is given to estimate the working fluid charge in each of these components. For an extensive description and examples of these models, the reader is invited to referred to [5, 6, 7, 8, 19].
\nAs a general overview, the rotating equipment is modeled by using one or more of the following approaches: (i) a performance map based on experimental data (black box models); (ii) physics-based models with empirically determined parameters (gray box models); (iii) entirely physics-based models (white box models). Semi-empirical models are usually preferred as a compromise between physical-characteristics (e.g., under- over-expansion/compression, pressure drops, heat transfer and mechanical losses) and computational cost. Regarding the charge estimation of rotating equipment, the mass of working fluid is computed by knowing the internal volume of the machine and by computing an average density. This simplified approach is usually reasonable given the relatively small internal volumes of pumps and expanders compared to heat exchangers and other volumes of the system. However, especially in the case of oil lubricated positive displacement expanders, high pressures and temperatures may lead to dissolved refrigerant in the oil that could be accounted for using solubility data of the refrigerant-oil mixture [16, 22, 23].
\nA liquid receiver (or buffer tank) can be installed in an ORC system at the condenser outlet. Under normal operating conditions, the liquid receiver ensures a saturated liquid at the condenser outlet and serves as a mass damping device during off-design conditions. In most cases, the liquid receiver is modeled by neglecting heat losses to the environment as well as potential hydrostatic effects due to the height of liquid (i.e., the pressure is considered to be uniform inside the liquid receiver). Nevertheless, it is not straightforward to predict the mass of liquid stored inside the tank at any operating condition with a steady-state model. In an experimental setup, a level sensor could be used to monitor the liquid level inside the tank. However, in commercial ORC systems, this may not be a viable option. Recently, Dickes et al. [8] proposed a liquid receiver model by introducing four hypotheses that resulted in the following constraints for calculating the mass of working fluid inside the liquid receiver:
\nwhere \n
The line sets (or pipelines) connect the different system components and carry the working fluid. The line sets consist of piping, valves, fittings, sight glasses, filters and other elements and are also associated with pressure drops and heat losses. As mentioned at the beginning of this section, two different modeling approaches can be employed to estimate the working fluid charge carried by the line sets as well as the thermodynamic states at inlet and outlet of each line set. By referring to Figure 2, a total of six line sets is considered. In particular, each line set can carry single-phase or two-phase working fluid and they are modeled as an equivalent tube having inner and outer diameters. An equivalent length that accounts for straight sections (\n
where \n
The heat losses though the line sets to the surroundings can be calculated with the effectiveness-NTU method [17], as given in Eq. (7), where \n
A more simplified approach is proposed in Figure 3, where the line sets and associated losses are lumped in the high- and the low-pressure lines by using single fictitious components placed at the outlet of the evaporator and the condenser, respectively. The pressure losses are computed as a linear function of the working fluid kinetic energy with two coefficients to be calibrated using experimental data. That is:
\nThe ambient losses are modeled by introducing an overall heat transfer coefficient of the line set (\n
The working fluid charge of each line set is calculated in a manner that is similar to the approach that will be presented for each zone of the heat exchangers (see Section 3.3). In the case of single-phase working fluid, the mass of working fluid is calculated as
\nwhere \n
An ORC system operates between a heat source and heat sink by using heat exchangers (HEX) for the heat input and rejection processes, respectively. The working fluid undergoes phase changes in both evaporator and condenser and different phases co-exist during these processes. An internal heat exchanger (or regenerator) can be present in the system to improve the cycle thermal efficiency [11]. The heat exchangers account for the majority of the volume in an ORC system and therefore, it is particularly important to have reliable models to predict the heat transfer rate, zone lengths, and working fluid charge.
\nTo predict the different zones inside an HEX, three different numerical methods can be used: moving-boundary [7, 8], finite-volume (or discretized) [16], and hybrid approach [26]. The main advantage of moving-boundary models is their fast computation time and good accuracy. Finite-volume models provide greater spatial resolution but can be computationally expensive. Hybrid models represent a compromise between the former methods. By considering the moving-boundary model as an example, the heat exchanger can be divided in multiple zones, as shown in Figure 4. Each zone is characterized by a heat transfer coefficient and heat transfer area through which a certain heat transfer process occurs. By knowing the inlet conditions of both streams, the effective heat transfer rate between the hot and cold streams is calculated by enforcing that the total surface area occupied by the different zones is equal to the geometrical surface area of the heat exchanger [8]. It follows that the total working fluid mass inside the heat exchanger (\n
where \n
Schematic of counterflow HEX model simulated by moving boundary method showing phase boundaries (solid lines) and zone boundaries (dashed lines).
Various heat exchanger types are employed in ORC systems (e.g., brazed plate heat exchangers, fin and tubes, shell and tubes, etc.) and a number of state-of-the-art heat transfer correlations are available in the literature that are used to predict the convective heat transfer coefficients in each zone. However, these correlations are often purely empirical and calibrated to fit experimental data and multiple correlations may be available for the same type of heat exchanger and working fluid. Furthermore, these correlations are typically derived for refrigeration systems, which present different operating conditions than ORCs. It follows that such correlations are likely to over-predict or under-predict the actual heat transfer coefficient within a certain zone, even though the overall predictions of the heat transfer rate may be reasonable. Nevertheless, errors in predictions of heat transfer within individual zones can lead to significant errors in charge estimations [8]. To improve the accuracy in predicting the heat transfer coefficients in the different zones, empirical parameters of these correlations should be fitted with experimental results by using identification methods [8].
\nThe accuracy of the heat transfer predictions alone does not ensure the correctness of the charge estimation. In fact, as already indicated in Eq. (14), under two-phase conditions, the density is a function of the thermodynamic conditions as well as the flow pattern characterizing each phase. The void fraction, \n
To be further noted is that the void fraction \n
Working fluid charge predictions for different void fraction models as well as three adjusting methods to tune the convective heat transfer correlations [
The study considered a total of 360 charge-sensitive simulations including 40 experimental data points, 4 tuning methods, 5 void fraction correlations, and 72 heat exchanger models. It was concluded that the total working fluid charge estimation is mainly affected by the adjusting (or tuning) method applied to the convective heat transfer coefficient rather than the void fraction model. However, a trade-off between the two aspects exists since higher accuracy in the thermal performance predictions led to a large scatter of the charge inventory predictions.
\nIn Section 3, the numerical aspects to be considered while developing a charge-sensitive ORC model have been discussed. However, in order to understand the usefulness of the model in predicting a real ORC behavior, it is necessary to consider experimental data. To this end, in the following sub-sections, several aspects related to analyzing different charge levels using both experimental and charge-sensitive model results are presented.
\nSteady-state operation of an ORC system can be detected by adopting for example the conditions proposed by Woodland et al. [15]. Alternatively, the methodology described by Dickes et al. [5] could also be employed. Due to the fact that experimental data is subject to different uncertainties, possible errors or sensor malfunction, a post-treatment data can be performed to identify possible outliers by using the open-source
Uncertainty propagation from the measured system properties to the calculated quantities is usually performed according to the method described by Figliola and Beasley [29]. In particular, it is important to discuss the uncertainties associated with the total system charges, which are often not thoroughly accounted for when reporting experimental results of ORC systems. In general, there are several sources of uncertainty in the measurement of the total system charge, such as inaccuracy of the scale used to weight the supply cylinder, leakage of working fluid from the system during operation, small portions of working fluid occupying charging hoses, small losses in system charge due to purging of charging hoses, stacked uncertainties due to the summing of several incremental charging steps. In experimental test rigs, the uncertainty due to purging of system charging hoses can be eliminated by leaving all charging hoses connected and full of working fluid during all tests and incremental charge conditions. Leakage of working fluid from the system during operation can be neglected after ensuring that repeated tests at the same conditions, but several days apart, yield approximately the same condenser subcooling. The main sources of uncertainty in the working fluid charge level are the inaccuracy of the scale and the stacked uncertainties due to several incremental steps in adding or subtracting charge. As an example, if a scale has a known resolution of ±0.005 kg, and a measurement uncertainty of ten times the resolution or ± 0.045 kg is conservatively assumed, the uncertainty of the total system charge (\n
As reported by Woodland [6], given a system charge of 18.1 kg, the relative uncertainty in system charge assuming a maximum of 8 charge steps is still less than 1%. Therefore, a high degree of confidence can be placed on the measured system charge level. More challenging is determining the actual charge inside the heat exchangers, which would require active measurements of their weight during operation.
\nIn the case of a zeotropic mixture, for example, R134a-R245fa (0.625–0.375), uncertainty in the charge level of each component of the binary mixture results in some uncertainties in the concentration of the mixture, which is an important parameter in computing the thermophysical properties of the mixture. However, even with the conservative estimate on the charge uncertainty previously mentioned, the resulting relative uncertainty in the concentration is
To conduct a working fluid charge study, it is desired to explore a wide range of working conditions, different working fluids, and several charge levels. In the current available literature, only the study published by Woodland [6] meets all of these criteria, and, therefore, it is used hereafter as an example. In particular, three working fluids were chosen to investigate low grade waste heat recovery by means of an ORC: R134a, R245fa, and the zeotropic mixture R134a-R245fa (0.625–0.375). In addition, two heat source temperatures, and several charge levels of the working fluids were considered. The range of conditions tested experimentally for each working fluid is summarized in Table 1. A complete description of the ORC system can be found in [6] and its schematic is shown in Figure 1. The effect of the working fluid charge on the ORC system performance is shown in Figure 6, where the Second Law efficiency, defined as the ratio of the system net power to the total exergy rate available, is plotted as a function of the subcooling level for different operating conditions. It can be seen that for a given working fluid and heat source inlet temperature, there exists an optimum charge level that maximizes the Second Law efficiency (i.e., power output) of the system. Furthermore, for each working fluid, the efficiency tends to be higher at lower subcooling due to lower condensing pressures dictated by lower fluid charge.
\nWorking fluid | \nCharge [kg] | \nSource temperature [°C] | \nExpander speed range [rpm] | \nPump speed range [rpm] | \n
---|---|---|---|---|
R134a | \n18.1 | \n80, 100 | \n2800–3000 | \n1000 | \n
20.4 | \n80, 100 | \n1200–3000 | \n1000 | \n|
22.7 | \n100 | \n1500–2300 | \n1000 | \n|
R245fa | \n27.4 | \n80, 100 | \n1000–2000 | \n300–500 | \n
29.5 | \n80, 100 | \n1000–2000 | \n300–500 | \n|
31.8 | \n80, 100 | \n1000–2000 | \n300–500 | \n|
R134a-R245fa (0.625–0.375) | \n24.9 | \n80, 100 | \n1000–1500 | \n500–1000 | \n
27.2 | \n80, 100 | \n1000–2500 | \n500–1000 | \n|
29.5 | \n80, 100 | \n1000–2200 | \n500–1000 | \n
Summary of experimental test matrix to investigate the effect of working fluid charge [6].
Measured second law efficiency versus condenser exit subcooling for each working fluid. The contour shows the working fluid charge and the size of the markers is proportional to the expander rotational speed (data from [
One of the main purposes of a charge-sensitive model is to predict the total charge of a certain ORC system for which it has been developed and its behavior (e.g., evaporating and condensing temperatures, subcooling and superheating). This needs to hold true also under the circumstances that the system is under-charged or over-charged as well as if the working fluid is changed, that is, drop-in replacement. To this end, the same ORC system considered in Section 4.2 is used as an example [6]. The charge-sensitive model is employed to simulate three different working fluids (i.e., R134a, R245fa, and R134a-R245fa (0.635–0.375)) at three different charge levels, without any tuning. The untuned model prediction of the system charge versus the measured charge for all the test points is shown in Figure 7. It can be seen that even without tuning, the model predictions are reasonably accurate due to the fact that the heat exchanger volumes as well as the liquid line sets have been accounted for. These liquid volumes remain constant across all experimental tests and therefore set the baseline charge level of the system. However, the model does not predict the variability in charge well for all cases. For R134a, the trend in system charge is captured well, but with increased underprediction of the charge at higher charge levels. For R245fa, the trend is not captured well. A general increase is observed, but the underprediction is significant. For the zeotropic mixture, no trend is visible at all in the charge prediction. Variability in the predicted charge is due to the changing liquid lengths in the heat exchangers, the void fraction of two-phase flow, and the solubility of the working fluid in the lubricant oil. In particular, if the boundary conditions of the ORC are fixed then an increase in the working fluid charge in the system leads to a decrease in the two-phase zone in the condenser (resp. subcooled zone), as shown in Figure 8(a). If the void fraction model and the heat transfer coefficient of the two-phase zone are not estimated correctly, the charge of the subcooled region can be largely under predicted due to the rapid increase in liquid level inside the condenser, as shown in Figure 8(b). Solubility of the working fluid in the oil was not considered in the model. However, it can have a significant impact on prediction of the total system charge. In fact, if an oil separator is present in the ORC system, the working fluid dissolved in the lubricant oil could be up to 10% of the total charge depending on the solubility of the working fluid-lubricant oil mixture [6].
\nParity plot showing the ability of the charge-sensitive model to predict the total working fluid charge without any charge tuning.
As shown in Figure 8, the estimation of working fluid charge in system modeling is usually biased due to inaccurate estimation of system volumes, ambiguous flow patterns under two-phase flow conditions, solubility of working fluid in the lubricant oil, etc. A charge-tuning scheme can be used to eliminate the bias. Although such methods have been widely used for vapor compression heat pumping cycles [16, 17], they have not been employed in charge-sensitive ORC system modeling. An empirical two-point charge tuning equation that incorporates a linear function of the length of the subcooled section in the condenser (\n
where \n
Heat exchanger length fraction (a) and breakdown of component charge (b) versus condenser exit subcooling when the total charge is imposed as model input. Pump speed = 1000 rpm, expander speed = 2000 rpm, source temperature = 100°C, source and sink fluid flow rates are 0.45 and 1 kg/s, respectively. The charge calculation is untuned.
In this chapter, the effects of the total working fluid charge on the performance and operation of an ORC system have been discussed. In particular, both numerical and experimental have been used to demonstrate the importance of considering the charge inventory when analyzing off-design conditions of the ORC system. Under-charging or over-charging the system has a direct effect on the spatial distribution of the different zones inside the heat exchangers. Additional aspects such as oil solubility can also have non-negligible impact on the system performance. A detailed mechanistic model of the ORC allows identification of optimal charge level. However, charge-tuning is always required to account for inaccuracies and uncertainties associated with the modeling assumptions. In fact, two-phase heat transfer correlations and void fraction models directly affect the charge inventory estimations. The analysis of the charge inventory of ORC systems is also particularly important when considering drop-in replacements such as HFOs and their blends. The size of the heat exchangers as well as the piping system require an optimal working fluid charge to ensure proper behavior of the ORC at both design and off-design conditions.
\nThe Authors declare no conflict of interest.
A | area, [m2] |
c | tuning coefficient, [−] |
C | regression coefficient, [−] |
h | specific enthalpy, [kJ/kg] |
m | mass, [kg] |
N | rotational speed, [rpm] |
Nu | Nusselt number, [−] |
p | pressure, [Pa] |
\n\n\nQ\n\n\n | heat transfer rate, [W] |
Subscripts | |
calc | calculated |
cond | condenser |
evap | evaporator |
ex | exit |
exp. | expander |
R | Thermal resistance, [K/W] |
Re | Reynolds number, [−] |
T | temperature, [K] |
UA | heat conductance, [W/K] |
V | volume, [m3] |
x | quality, [−] |
\n\n\nα\n\n\n | void fraction, [−] |
\n\n\nρ\n\n\n | density, [kg/m3] |
meas | measured |
sc | subcooled |
su | supply |
wf | working fluid |
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