Specific thermal conductivity for different materials [5, 6].
\r\n\tThe planning and technology of the tunnel and underground structures is an important issue for building of the structure. Depending on the particulars of each project location and the construction time available, the adopted construction methods have an important influence on the success of the project. Traditional and novel methods are underlined with the focus on reliable and cost effective technology.
\r\n\tOnce built, the tunnel needs to guarantee comfort to the users and reduce the risks of accident. The equipment is important to obtain adequate visibility and reduced concentration of contaminants. For these purposes, an adequate lighting system and ventilation system are necessary. Ventilation is also crucial in the case of emergency conditions, as it used to control fire development and smoke propagation. Operational and safety systems are to be analysed to fulfill the all the operational and emergency needs. The book investigates the relevant topics in these regards as the crucial point of tunnel exploitation.
\r\n\tThe aim of the book in focused also on the aspect of the optimised maintenance strategy of tunnels that bases on a systematic condition assessment through the investigations. Operation and maintenance works in tunnels have an adverse effect on the traffic, hence it is essential to plan operation and maintenance works rationally and effectively as the maintenance have to minimise the impact on the daily traffic and to ensure cost effectiveness at all times.
Coherence is an important property of a light beam, which has been investigated widely in the past few decades [1]. Coherence can be regarded as a consequence of correlations between the components of the fluctuating electric field at two or more points. Light beam with low coherence is called partially coherent beam, and such beam has an advantage over a coherent beam in many applications, such as optical imaging [2–4], optical trapping [5, 6], free‐space optical communications [7, 8], laser radar systems [9, 10] and remote sensing [11]. Before 2000, most literatures on partially coherent beam were focused on the conventional partially coherent beam named Gaussian Schell‐model (GSM) beam [12–16], whose intensity and degree of coherence satisfy Gaussian distributions. Since 2000, partially coherent beams with prescribed phase, state of polarization and degree of coherence were investigated widely due to their extraordinary properties and potential applications [17–31].
\nPhase is another important property of a light beam, which is characterized by the wavefront on propagation. Conventional Gaussian beam carries customary quadratic phase with spherical wavefront. Vortex beam, such as Laguerre‐Gaussian beam, carries a vortex phase with helical wavefront. The intensity in the vortex beam center is zero while the phase is undefined, and this point is called phase singularity. In 1992, Allen et al. found that the vortex beam carries an orbital angular momentum (OAM) of \n
Vortex beam with low coherence is called partially coherent vortex beam, which was first proposed by Gori et al. [43]. Later, various partially coherent vortex beams were introduced [44–54]. Partially coherent vortex beam differs in many aspects from a coherent vortex beam, and it exhibits some unique interesting properties, for example, correlation singularities (i.e., ring dislocations) exist in its correlation function (i.e., cross‐spectral density or degree of coherence) [47, 55–59]. Here the correlation singularity is defined as the point where the value of the cross‐spectral density or degree of coherence equal zero, while the corresponding phase is undefined. Recently, more and more attention is being paid to partially coherent vortex beams [60–73], more interesting and useful results are being revealed. In this chapter, we will introduce recent theoretical and experimental developments on partially coherent vortex beams.
\nThere are different types of partially coherent vortex beams, such as partially coherent beam with helicoidal modes [43], partially coherent vortex beam with a separable phase [44, 45], Gaussian Schell‐model vortex (GSMV) beam [46], partially coherent LG0l\n beam [47, 48], partially coherent LG\npl\n beam [49], partially coherent Bessel‐Gaussian beam [50], special correlated partially coherent vortex beam [51, 52] and vector partially coherent vortex beam [53, 54]. Here we only introduce some models which can be realized in experiment easily.
\nA scalar partially coherent beam can be characterized by the cross‐spectral density (CSD) in the space‐frequency domain or mutual intensity in the space‐time domain [1]. For a GSMV beam, its CSD in the source plane is expressed as follows [46]:
where \n
The CSD of a partially coherent LG\npl\n beam in the source plane is expressed as follows [49]:
where \n
As a typical kind of special correlated partially coherent vortex beam, the CSD of a Laguerre‐Gaussian correlated Schell‐model vortex (LGCSMV) beam in the source plane is expressed as [51]:
When n = 0, Eq. (3) reduces to the CSD of a GSMV beam.
\nA vector partially coherent beam can be characterized by the CSD matrix in space‐frequency domain or the beam coherence‐polarization matrix in the space‐time domain [17]. The elements of the CSD matrix of a vector partially coherent vortex beam with uniform state of polarization named electromagnetic Gaussian Schell‐model vortex (EGSMV) beam in the source plane are given as [53]:
where Ax\n and Ay\n are the amplitudes of x and y components of the electric field, respectively. \n
The elements of the CSD matrix of a vector partially coherent vortex beam with non‐uniform state of polarization named radially polarized partially coherent vortex beam in the source plane are expressed as [54]:
with
Propagation of a partially coherent vortex beam in free space can be studied with the help of the well‐known Huygens‐Fresnel integral, and propagation of a partially coherent vortex beam through a paraxial ABCD optical can be studied with the help of the following generalized Collins formula [74]:
where \n
Propagation of a partially coherent vortex beam through turbulent atmosphere can be studied with the help of the following generalized Huygens‐Fresnel integral [75]
Here \n
The average intensity and the degree of coherence of a partially coherent vortex beam in the receiver plane are obtained as:
Coherent vortex beam displays dark hollow beam profile in the source plane or on propagation in free space. For a partially coherent vortex beam, it also displays dark hollow beam profile in the source plane, while its beam profile varies on propagation due to the degradation caused by the source spatial coherence, and one can shape the beam spot of a partially coherent vortex beam in the focal plane through varying the initial coherence width, for example, the beam profile of the focused beam spot gradually transforms from a dark hollow beam profile to a flat‐topped beam profile and finally to a Gaussian beam profile when the coherence width gradually decreases (see \nFigure 1\n). Furthermore, when the initial coherence width is fixed, one also can shape the beam spot of a partially coherent vortex beam through varying its initial topological charge because the topological charge plays a role of anti‐degradation caused by the coherence [46].
\nAverage intensity of a partially coherent LG0l\n beam with l = 2 in the focal plane for different values of the initial coherence width \n\n\n\nδ\n0\n\n\n\n.
For a vector partially coherent beam with nonuniform state of polarization (i.e., radially polarized partially coherent beam), it is known that such beam always displays radial polarization on propagation (see \nFigure 2(a1)\n–\n(e1)\n) although its degree of polarization varies. For a radially polarized partially coherent vortex beam, one finds from [54] that the vortex phase induces changes of not only the degree of polarization but also the state of polarization (see \nFigure 2(a2)\n–\n(e2)\n and \n(a3)\n–\n(e3)\n) besides rotation of the beam spot, that is, radial polarization disappears and elliptical polarization appears on propagation. The state of polarization displays left‐handed elliptical polarization around the beam center and right‐handed elliptical polarization outside of the beam center for l > 0, and the handedness of the polarization ellipse is reversed for l < 0. Furthermore, the polarization ellipse rotates clockwise for l > 0 and anti‐clockwise for l < 0 on propagation. Thus, modulating the magnitude and sign of the topological charge of the vortex phase provides a convenient way for modulating the polarization properties of a vector partially coherent vortex beam. What is more, the phenomenon of vortex phase‐induced changes of the state of polarization of a radially polarized partially coherent beam may be used to detect a phase object.
\nChanges of the state of polarization of a focused radially polarized partially coherent vortex beam on propagation for different values of the topological charge l.
Coherent vortex beam carries phase singularity in the source plane and on propagation. Phase singularity is defined as the point where the intensity is zero while the phase is undefined. When the spatial coherence of a vortex beam is reduced, the dark hollow beam profile disappears on propagation due to the degradation caused by the coherence (see \nFigure 3(a)\n–\n(c)\n). Thus, a partially coherent vortex beam does not carry phase singularity on propagation, while an interesting correlation singularity named ring dislocation appears (see \nFigure 3(d)\n–\n(f)\n). Here the correlation singularity is defined as the point where the amplitude of the cross‐spectral density \n
Far‐field intensity distribution and corresponding amplitude and phase distribution of the correlation function of a partially coherent LG0l\n beam.
The study of optical beam propagation in turbulent atmosphere is a venerable subject. It is known that the turbulence induces scintillation (i.e., intensity fluctuations), beam wander and deformation of laser beam, which impedes the applications of free‐space optical communications, optical imaging and remote sensing. Propagation properties of a partially coherent beam in turbulent atmosphere have been investigated in detail in the past few decades, and it was found that a GSM beam has an advantage over a coherent Gaussian beam for reducing turbulence‐induced scintillation and degradation [7, 8]. The scintillation index of a beam in turbulent atmosphere is defined as follows:
where \n
Is it possible to further reduce turbulence‐induced scintillation compared to GSM beam? Recently, propagation properties of a partially coherent vortex beam in turbulent atmosphere have been investigated both theoretically and experimentally [60–62]. It was shown in [62] that a GSMV beam has an advantage over a GSM beam for further reducing turbulence‐induced scintillation (see \nFigure 4\n). From \nFigure 4\n, one sees that the scintillation index of a GSMV beam or a GSM beam decreases with the decrease of initial coherence width \n
Experimental results of the scintillation index of a GSM or GSMV beam (l = 1, 2) at the centroid versus the initial coherence width after propagating through thermal turbulence.
Up to now, many different methods have been developed to generate a coherent vortex beam, such as spiral phase plate [76], transverse mode selection [77], holographic grating [78], spatial light modulator [79], helical optical fiber [80] and uniaxial crystal [81], while only few papers were devoted to generation of partially coherent vortex beams [46–48, 51, 53, 54, 73].
\nOne can generate a GSMV beam in experiment with the help of a rotating ground‐glass disk, Gaussian amplitude filter and a spiral phase plate [46]. As shown in \nFigure 5\n, a focused laser beam generated by a He‐Ne laser is reflected by a mirror and then illuminates a RGGD, producing a partially coherent beam with Gaussian statistics. The thin lens L2 is used to collimate the transmitted light, and the GAF is used to transform the intensity of the transmitted light into a Gaussian profile. The transmitted light behind the GAF is a GSM beam. The coherence width of the GSM beam is determined by the focused beam spot size on the RGGD, which is controlled by the varying the distance between lens L1 and RGGD. After passing through a SPP located just behind the GAF, the GSM beam becomes a GSMV beam. It is true that the beam spot of the generated GSMV beam in the focal plane is shaped by varying its coherence width (see \nFigure 6\n).
\nExperimental setup for generating a GSMV beam. L1, L2, thin lenses; M, mirror; RGGD, rotating ground‐glass disk; GAF, Gaussian amplitude filter; SPP, spiral phase plate.
Experimental results of the focused intensity distribution and the corresponding cross line (dotted curve) of the generated GSMV beam for three different coherence widths. The solid curves are calculated by theoretical formulae.
One can generate a partially coherent LG\npl\n beam in experiment with the help of a rotating ground‐glass disk, Gaussian amplitude filter and a SLM [48]. As shown in \nFigure 7\n, the RGGD and GAF are used to generate a GSM beam. The generated GSM beam goes toward a spatial light modulator (SLM), which acts as a grating with fork pattern designed by the method of computer‐generated holograms. The first‐order diffraction pattern of the beam reflected from the SLM is regarded as a partially coherent LG\npl\n beam and is selected out by a circular aperture.
\nExperimental setup for generating a partially coherent LG\npl\n beam. L1, L2, L3, thin lenses; RGGD, rotating ground‐glass disk; GAF, Gaussian amplitude filter; SLM, spatial light modulator; CA, circular aperture; BPA, beam profile analyzer.
\n\nFigure 8\n shows the experimental setup for generating a LGCSMV beam [25]. A beam emitted from the He‐Ne laser passes through a beam expander, and then it goes toward a SLM. The first order of the beam from the SLM is a dark hollow beam and is selected out by a circular aperture. The generated dark hollow beam illuminates a RGGD, producing an incoherent beam with dark hollow beam profile. After passing through free space with length f\n2, the thin lens L2, and the GAF, the generated incoherent dark hollow beam becomes a LGCSM beam. After passing through a SPP, the generated LGCSM beam becomes a LGCSMV beam. Due to the influence of the special correlation function, the LGCSMV beam exhibits interesting focusing properties, for example, the focused beam spot displays dark hollow beam profile when the coherence width is very large or very small, and displays flat‐topped beam profile of Gaussian beam profile when the coherence width takes a middle value (see \nFigure 9\n), which are much different from the focusing properties of the conventional partially coherent vortex beam (see \nFigures 1\n and \n6\n).
\nExperimental setup for generating a LGCSMV beam. BE, beam expander; SLM, spatial light modulator; CA, circular aperture; L1, L2, L3, thin lenses; RGGD, rotating ground‐glass disk; GAF, Gaussian amplitude filter; SPP, spiral phase plate; BPA, beam profile analyzer.
Experimental results of the intensity distribution and the corresponding cross line of the generated LGCSM vortex beam in the focal plane for different values of the coherence width. The solid curve denotes the theoretical results.
In a similar way, experimental generation of an EGSMV beam and a radially polarized partially coherent vortex beam were reported in [53, 54], respectively. It was shown that the vortex phase induces not only the rotation of the beam spot, but also the changes of the beam shape, the degree of polarization and the state of polarization. Furthermore, it was revealed that the vortex phase plays a role of resisting the coherence‐induced degradation of the intensity distribution and the coherence‐induced depolarization.
\nMore recently, a new experimental technique is developed in [81] to generate partially coherent vortex beams with arbitrary azimuthal index using only a spatial light modulator (see \nFigure 10\n). This technique is based on digitally simulating the intrinsic randomness of broadband light passing through a spiral phase plate, and it provides control over the transverse coherence length, which will be useful for study of vector singularities in partially coherent fields or in the fields of optical communications and imaging systems where coherence plays a key role.
\nExperimental setup for digital generation of partially coherent vortex beam. HeNe Laser; BE: beam expander; L1–L2: lenses; D: iris diaphragm; SLM: spatial light modulator; BS: beam splitter; DP: Dove prism; M1–M3: mirrors; CMOS: camera.
It is known that a vortex beam carries an OAM of \n
For a coherent vortex beam, it is known from [88] that the number of dark rings in the Fourier transform of the intensity of a coherent vortex beam equals to the magnitude of the topological charge, thus one can determine the magnitude of the topological charge once we obtain the information of the intensity of a vortex beam. With the decrease of initial coherence width, the hollow profile of the intensity distribution of a vortex beam in the focal plane or in the far field disappears gradually and finally becomes a Gaussian beam profile (see \nFigure 11(a‐1)\n–\n(a‐4)\n), and the dark rings of the Fourier transform of the intensity distribution disappear (see \nFigure 11(b‐1)\n–\n(b‐4)\n). Then how to determine the topological charge of a partially coherent vortex beam? It is shown in [47] that the correlation function of a partially coherent vortex beam (i.e., partially coherent LG\n0l\n beam) displays correlation singularity (i.e., ring dislocation) in the far field. Here the correlation function denotes the cross‐spectral density \n
(a‐1)–(a‐4) Intensity distribution and (b‐1)–(b‐4) the corresponding Fourier transform of a partially coherent LG0l\n beam with l = 3 in the focal plane for different state of coherence.
Distribution of the modulus of the degree of coherence of a partially coherent LG0l\n beam with different values of the topological charge l in the focal plane for different state of coherence.
Experimental results of the distribution of the modulus of the degree of coherence of a partially coherent LGpl\n beam in the focal plane for different values of p and l.
Abovementioned literatures are confined to measure the magnitude of the topological charge of a partially coherent vortex beam. In fact, the sign of the topological charge of vortex phase also plays an important role in practical applications, for example, the sign of the vortex phase provides an additional degree of freedom for optical storage and communication [89, 90]. Recently, a simple method for simultaneous determination of the sign and the magnitude of the topological charge of a partially coherent LG0l\n beam was proposed. This method is based on the measurement of the modulus of the degree of coherence of a partially coherent LG0l\n beam after propagating through a couple of cylindrical lenses (see \nFigure 14\n). It was found that the distribution of the modulus of the degree of coherence becomes anisotropic, and it rotates anti‐clockwise (or clockwise) during propagation when the sign of the topological charge is positive (or negative), furthermore, the modulus of the degree of coherence displays fringes distribution within certain propagation distances and the number of the bring fringes equals to 2|l|+1 (see \nFigure 15\n). One can extend this method to determine the sign and the magnitude of the topological charge of a partially coherent LGpl\n beam based on the measurement of the double‐correlation function.
\nExperimental setup for determining the magnitude and the sign of the topological charge. NDF, neutral‐density filter; BE, beam expander; RM, reflecting mirror; L1, L2, thin lenses; RGGD, rotating ground‐glass disk; GAF, Gaussian amplitude filter; SLM, spatial light modulator; CA, circular aperture; CL1, CL2, cylindrical lenses; BPA, beam profile analyzer.
Distribution of the modulus of the degree of coherence of a partially coherent LG0l\n beam after passing through a couple of cylindrical lenses at different propagation distances with l = 2 and \n\n\n\nδ\n0\n\n=\n0.04\nmm\n\n\n.
Due to their extraordinary propagation properties, partially coherent vortex beams are useful in many applications, such as material processing, optical trapping, free‐space optical communications and optical imaging.
\nIt was shown in [46] that one can shape the beam profile of a focused partially coherent vortex beam through varying its initial spatial coherence width, and one can obtain flat‐topped beam profile, dark hollow beam profile and Gaussian beam profile in the focal plane. The formed flat‐topped beam profile is useful in material processing [91], and in trapping a Rayleigh particle whose refractive index is larger than that of the ambient [92], and the formed dark hollow beam profile is useful in trapping a Rayleigh particle whose refractive index is smaller than that of the ambient [72].
\nIt is known that atmosphere turbulence induces scintillation of laser beam, which impedes the application of free‐space optical communications. It was shown in [93] that partially coherent beam can be used to reduce turbulence‐induced scintillation, and is useful in free‐space optical communications [7, 8]. In [62], it was demonstrated experimentally a partially coherent vortex beam has an advantage over a partially coherent beam without vortex phase for reducing turbulence‐induced scintillation, thus is expect to be useful in free‐space optical communication.
\nFinally, we know that both partially coherent beam and vortex beam are useful in super‐resolution imaging [94, 95], one may expect that partially coherent vortex beam has an advantage over partially coherent beam and vortex beam in super‐resolution imaging. What is more, partially coherent vortex beam carries correlation singularities, and one may apply correlation singularities for information encoding, transfer and decoding.
\nWe have presented on a review on recent theoretical and experimental developments on partially coherent vortex beam. The theoretical models, propagation properties, and generation methods for various partially coherent vortex beams have been illustrated in detail. Partially coherent vortex beams display many unique and interesting properties, and are useful in some applications, such as material processing, optical trapping, free‐space optical communications and optical imaging. We believe this field will grow further and expand rapidly, and more and more interesting results and potential applications will be revealed.
\nThis work is supported by the National Natural Science Fund for Distinguished Young Scholar under Grant no. 11525418, the National Natural Science Foundation of China under Grant no. 11404234 and 11274005, and the Project of the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.
\nHeat exchangers are used to transfer heat energy from one to another medium without intermixing them. There are different types available like plate, bundled tube or rotary heat exchangers. Figure 1 shows an example of a conventional plate heat exchanger.
Setup of a conventional plate heat exchanger [1].
In addition, heat exchangers also differ in their working principle (counterflow, direct flow, or cross flow) and can consist of differently shaped plates or tubes with, for example, smooth, buckled, or rippled surfaces. A typical wall thickness reaches from 0.4 to 2.5 mm and is mainly designed to withstand blockage, corrosion, active pressure, or abrasive media. Such heat exchangers are very cost-effective.
In conventional heat exchangers, a lot of restrictions and disadvantages exist, concerning the realizable geometry, the operating temperature, as well as the manufacturing costs:
Heat exchanger manufactured by the combination of different planar parts is limited in the realizable design and compactness (the ratio between heat exchanging surface and total volume).
The assembly of the different parts can result in assembly failures.
The realization of mechanical and fluidic interfaces is very challenging (often, the cross-flow principle is realized instead of the superiorly counterflow principle because of the feeding system for the different fluid channels).
The joining of the different parts is often realized by brazing. But the brazing material limits the operating temperature, and the brazing process can result in leakage.
Because of the used standardized geometries for the parts as well as the whole heat exchanger components, their outer geometry can hardly be individualized. Furthermore, no adjustment of the outer geometry on the shape of the surrounding system can be realized.
Some examples for ceramic-based heat exchangers for high temperature or high corrosive or abrasion applications exist, but their design is limited because of the ceramic shaping and finishing technologies. Furthermore, the operation temperature is limited because of the needed joining additives (e.g., solders or brazes) for the different ceramic parts.
Additive manufacturing (AM) is a new class of manufacturing technologies, which has been developed for polymers, metals, and ceramics during the last three decades and keeps evolving. Based on computer-aided design (CAD) files in 3D, typically a layer-wise manufacturing process follows, which allows the realization of component designs as well as inner and outer geometries which were previously regarded as not producible. Concerning the manufacturing of heat exchanger, AM technologies open the door to overcome all of the restrictions mentioned above:
The manufacturing of the heat exchanger as one component with integrated mechanical and fluidic interfaces becomes possible.
No joining steps are needed, and the same properties are available in the whole component.
Very complex designs can be realized, and the ratio between the heat exchanging surfaces to the total volume of the heat exchanger can be increased significantly. The increased performance allows the miniaturization of the heat exchanger.
The adjustment of the outer geometry becomes possible, and the required volume for the implementation of heat exchanger and the surrounding system can be decreased.
AM of ceramics opens the door for complex heat exchangers for demanding applications concerning operation temperature, abrasion, or corrosion.
Thus, heat exchangers seem to be very interesting for AM while prices are falling especially for AM of metal components [3]. Also, an integrated manufacturing process for heat exchangers seems to be positive on their pressure resistance and against leakage. Today, only a few designs are described or commercially available. EOS and 3TRPD have designed a heat exchanger, which was manufactured with laser beam melting (Figure 2). Unfortunately, they have not published any performance data for comparison.
Additively manufactured heat exchanger by EOS and 3TRPD [2].
Furthermore, at Fraunhofer IFAM, a counterflow heat exchanger was developed to improve the efficiency of a micro-gas turbine system (Figure 3). In this case study, the hot exhaust gas should heat up the inflowing cold air to improve the overall combustion efficiency of the system. The heat exchanger was particularly designed for laser beam melting, so there was no conventional way to manufacture the part. The heat exchanger combines 18 layers of channels in the limited design space. Furthermore, the complex inner channels were designed in a wave shape combined with a very small spacing to each other in order to maximize the surface for heat transfer (Figure 3). With the special design for laser beam melting, it was possible to reduce the required time and costs for postprocessing. It was only necessary to machine the inlet and outlet at the side toward the build platform after the LBM process [C4].
Counterflow heat exchanger manufactured by LBM; left: manufactured component [4]; right: rendering of complex internal structure inside the heat exchanger [4].
But still, a lot of challenges exist, which have to be overcome, to allow the AM of high-performance heat exchanger.
Design stage:
designing and dimensioning of the heat exchanger;
generation of the CAD files;
modeling and simulation of the fluid flow and heat flux;
providing software tools for the different tasks, coupling, and automatization of all tasks.
Manufacturing stage:
enhancement of the material portfolios for the different AM technologies;
increasing productivity (higher building speed, larger building space with more components manufactured simultaneously, less reject rate) will result in decreasing manufacturing costs.
To overcome the current restrictions, we are working on all links of the process chain. In this chapter, we want to introduce different AM technologies for metals (Laser beam Melting—LBM) and ceramics (Fused Filament Fabrication—FFF and Lithography-based Ceramic Manufacturing—LCM) as well as two different approaches for designing and creating the CAD files, one based on conventional software tools and one based on mathematical algorithms. In addition, the specification of the operation conditions of a solid oxide fuel cell system with an operation temperature of 850°C and higher will exemplarily illustrate the requirements for heat exchangers suitable for high-temperature applications and will justify the need for AM of high-temperature materials like ceramics.
For additively manufactured heat exchangers, a high heat exchange capacity is essential. It is represented by the heat flow, which can be calculated from the thermal conductivity
Material | Thermal conductivity |
---|---|
Silver | 429 |
Copper | 401 |
Aluminum | 237 |
High alloyed steel | ∼20 |
Low alloyed steel | ∼30 |
Usually, the temperature gradient
In this work, principle insights into the design of structures with a high heat exchange capability and coincident low pressure drop shall be given. Therefore, simulation of the flow is inevitable, and the structures were designed using CAD tools. The aim is to obtain a structure, which can be individualized at its outer geometry and optimizes the flow problems inside of the structure.
On the basis of the constraints explained before, basic sketches were developed and compared on its contour length of all the channels that will be involved in the heat transfer. To enhance the performance of the heat exchanger, the aim is to maximize the surface for the heat transfer. Therefore, the contour length of the channels is maximized in each evolution of the sketches by retaining the hydraulic diameter. Basic sketches were made and afterwards extruded in height with a helical-shaped structure for generating a longer streamline and for maximizing the heat transfer area. All in all, seven basic sketches were defined with nine resulting structures, as shown in Figure 4. Structures 1 and 2 show a simple geometry, which could also be produced with conventional manufacturing processes. Structures 3–5 are very complicated in terms of connecting geometries. Structures 6.1 and 6.2 are highly optimized for production with straight walls which can be efficiently produced with LBM with special slicer options. At last, structures 7.1 and 7.2 are optimized for production and fluid flow by using special slicer options and not having sharp edges like structures 6.1 and 6.2 which lead to a higher pressure drop.
Different designs of inner structures for heat transfer.
A comparison of the geometrical and heat flow characteristics of these structures is given in Table 2. Also, the structures show a surface roughness as build. This roughness is assumed to be the same value for all side surfaces since they are all in the same build direction (same as the orientation of the pictures).
Compactness | Heat flow | Performance per volume | Pressure drop [Pa] | |
---|---|---|---|---|
1 | 267 | 270 | 38.20 | 0.05 |
2 | 243 | 170 | 24.05 | 0.06 |
3 | 664 | 200 | 28.29 | 0.06 |
4 | 651 | 350 | 49.51 | 0.50 |
5 | 1576 | 420 | 59.42 | 0.15 |
6.1 | 1471 | 520 | 65.47 | 0.10 |
6.2 | 1711 | 550 | 80.54 | 0.20 |
7.1 | 1264 | 750 | 50.71 | 0.10 |
7.2 | 1246 | 900 | 60.86 | 0.10 |
Simulation results for the different designed structures (compactness, heat flow, performance per volume and pressure drop; possible choice highlighted).
As stated above, connecting structures for fluid guidance inside the heat exchanging structure are important, but rather complex and difficult to design. As a first attempt for structures 5 and 6.2, connecting structures are shown in Figure 5, which were derived from biomimetic role models like fennel.
Exemplary connecting structures for designed structures 5 and 6.2.
To avoid such a complexity of the connecting structures and at the same time to enable the engineer to model them economically, a new approach was chosen. The design process now starts with the connecting structures, and the inner geometry is optimized afterwards. The design ideas were adopted from nature, too. Some possible basic structures are shown in Figure 6. The purpose of these structures is to transform a round connector with a 6-mm diameter to any amount of complex-shaped inner structures like tubes. In addition, the flow has to be equally distributed in all inner tubes, and heat transfer should also start within the connecting structure to minimize losses. Certainly, manufacturability has to be guaranteed as well by allowing a minimum angle of 45° to the building plane. For the same reason, gaps inside the structures have to be avoided, and the connecting structures have to be as narrow as possible.
Sampled possible structures for connecting geometries adopted from nature.
It is obvious that from these connecting structures, such immersed structures like those shown in Figure 4 (structures 6 and 7) cannot be accessed. This means that ideally nestable inner structures are preferred, which can be enveloped with one larger outer channel to gain a tube-in-tube-like design known from conventional heat exchangers.
Designing the inner structures, which are applicable to the previous connecting structures, is the next step. The profile shape may not be too complex due to terms of a steady connection to connecting structures. Furthermore, analytical calculation cannot be used for dimensioning these structures since they should all have the same hydraulic diameter. Therefore, fluid simulation was used for dimensioning. To validate these findings, experimental parameter evaluation should be conducted in further investigations. In Figure 7, some possible designed inner structures are compared. Herein, the lowest pressure drop per performance as indicating value was used to choose the optimal inner structure. These profiles are based on mathematical algorithms after Sierpinski (left profile) and Hilpert (right profile).
Comparison between inner structures with the same hydraulic diameter and optimal designs selected using fluid simulation.
Furthermore, the heat exchanging volume has to be filled with the inner structures using optimal arrangement options to fill the volume using curves, planes, or lines.
For combining the presented structures to a whole heat exchanger, a connecting structure has to be chosen and specified. In Figure 8, the possible structures emerged from biomimetic structures of Figure 3 are preselected in terms of producibility, compactness, and capability. The final selection was done by simulating the connecting structures with CFD using Ansys CFX to gain a uniform flow distribution over all profiles and minimum losses in flow distribution.
Selection of an optimal connecting structure.
Finally, three different complete heat exchanging structures were designed for comparison and to gain an optimal structure. The structures were combined to a whole exchanger geometry, and the capability of the models was simulated as shown in Figure 9.
Whole heat exchanger structures and flow in inner and outer channels.
As depicted, a uniform flow distribution can be achieved in the inner flow. The outer flow, however, shows a highly turbulent and uneven distribution especially in designs 2 and 3, leading to a high pressure drop. The obtained values from these structures are depicted in Table 3. The different values for design no. 1 are based on different lengths of the inner structure (50, 100, and 150 mm).
1 | 2 | 3 | |
---|---|---|---|
Compactness [m2/m3] | 736–1291–1348 | 735 | 1161 |
Heat flow | 3465–6202–9372 | 4482 | 6985 |
Capacity per volume | 376–435–421 | 139 | 272 |
Pressure drop | 1.87–1.95–2.50 | 5.49 | 0.97 (inner), 2.58 (outer) |
Calculated values for designed heat exchangers (outstanding values highlighted).
It can be seen that the compactness is highly dependent on the length of the structure (design no. 1) because the influence of connecting structures decreases with an increasing length. With this example, a good scalability with different performances can be achieved, especially in terms of individualization. All in all, individualized and complex-shaped heat exchanging structures can be obtained for optimized production with additive manufacturing. But still, optimization has to be done to increase the performance and to lower the pressure drop. Also, experimental validation of the simulation has to be carried out even since the convergence in simulation was not satisfying.
In the following section, a new approach to generate efficient design structures for heat exchangers is presented. This new approach is one of the main topics of the instaf project.
Fractal macrostructures are used to generate a large inner surface, which implicates a better energy transfer between the heat-exchanging fluids. The creation of microstructures with roughness (with respect to the process-based roughness of AM), induced by partial Brownian motions, leads to turbulences. This raises the performance even more.
Two irreconcilable goals define the design scope. On the one hand, the surface for heat exchanging should be maximal and the fluids should remain in the heat exchanger as long as possible. But on the other hand, the restrictions concerning the manufacturing process (e.g., minimal wall thickness, resolution, waiver of support structures, etc.) and the operation as heat exchanger (e.g., pressure drop, mechanical strength, etc.) have to be considered as well.
To generate a maximum heat exchange surface, the so-called fractals were studied. Fractals are inspired by nature and are a branch of research essentially introduced to mathematics by Benoit Mandelbrot [7]. Stochastic fractals can be found in lung alveoli and other breathing organs or in the capillaries in the fin of whales with a heat- and energy-saving component.
For the design of the macrostructures, our special focus lies on the construction of space-filling curves, which belong to the group of FASS curves. The acronym FASS stands for space-filling, self-avoiding, simple, and self-similar. This class of curves traverses every vertex of a polygonal grid so that every point is reached once. Because they are not allowed to cut themselves, they separate to areas perfectly and are therefore well suited for the construction of heat exchangers.
A Lindenmayer system (L-system) was used to generate the curves. An L-system is a way to describe a repetitive structure with a small number of rules. It is a character-based rewriting system, which consists of constants. These are representing draw commands and variables, which are replaced in every iteration step through a replacement rule. In Figure 10, the system is visualized by means of the Hilbert curve with the variables X, Y, the constants F (straight line), −(clockwise rotation), and +(counterclockwise rotation) with a starting value of X. The rules are X → +YF − XFX − FY+ and Y → −XF + YFY + FX−.
A visualization of the Lindenmayer-code demonstrated by means of the Hilbert Curve.
A process was developed to generate a large number of different curves with a small number of basic motifs considering only 2 × 2- and 3 × 3 grids in order to investigate the best properties. There are four ways to traverse through these grids, which leads to seven basic motifs, paying attention to reflection. Every motif can also be used as a mapping structure. Therefore, it represents the connecting pieces of the following iteration step. Figure 11 shows a curve where the basic motif of a Peano curve (represented by the purple lines) and the mapping structure of the Hilbert curve (represented by the green lines) are combined. The ratio of curve length to the surface area or in higher dimension from surface to volume is always the same for the same grid size. Therefore, the criteria of evaluation are turbulences in flow and the velocity of the fluids so as the basic conditions of the used AM technology.
One possible combination of the motifs.
To construct a three-dimensional structure, successive iteration steps of a curve were placed in a predefined distance. They were combined with an NURBS-based (non-uniform rational basic spline) surface. The surface is lofted over the curves and defines a closed structure in combination with the outer skin. Figure 12 illustrates the process for the first four iteration steps of a Peano curve. Since separate areas should always be consistent, the offset must be adjusted. As the curve gets longer in each iteration step, the selected offset also decreases. Figure 13 demonstrates the result, visualizing one of the two separate liquids.
The first four iteration steps of the Peano curve. They lead to a feeding structure for which we combined the four layers with an NURBS-based surface.
Rendering of the dispersion of one fluid in a feeding structure designed with a Peano curve down to the fourth iteration step.
In the illustrated structure, the thickness of the partition wall decreases from 4.5 to 0.2 mm, which corresponds to a factor of 22.5. The length of the partition wall increases in the same range, simultaneously. In addition, the extrusion of the final geometry results in a heat exchanger with a compactness of about 3000 m2/m3, which can be operated as a counterflow heat exchanger. The structure was created using the CAD software Rhinoceros 3D. In Figure 13, some renderings of the fluid paths are shown.
Another structure for a heat exchanger is presented in Figure 14. In this case, a curve was chosen, which can be closed. It can be used without an outer wrapping, and this is why it could also be used as an immersion heater. For a better view into the internal structure, it is presented cut open. The outer structure could be represented by a cuboid. The curves are constructed with the end points of the elements as control points. This makes the curves even longer and smoothens them evenly.
Alternative structure as a concept for a heat exchanger. From left to right: a 5/8 cutout to show the inner structure; the whole component (lying); the curves used for designing the structure.
The LBM process has a lot of different specific names such as LaserCUSING®, selective laser melting (SLM®), direct metal laser sintering (DMLS®), and direct metal printing, to name only a few. All of these names describe the powder bed-based laser process, where a part is manufactured by means of thin layers of a powder material, which are applied by a scraper and molten selectively by laser energy.
The digital process chain begins with the 3D CAD file (*.stl) of the part, which has to be manufactured. This file is transferred to a software program where the support generation and the positioning in the building chamber of the machine are done. Afterwards, the so-called build job is sliced into layers of 20–100 μm, dependent on the material and the laser parameters and carried over to the machine [8]. A principle schematic of an LBM machine is shown in Figure 15.
A principle schematic of an LBM machine.
To avoid oxidation, the process itself as well as the preparation and postprocessing of the powder has to be done under inert gas atmosphere. Overhanging structures have to be supported by supporting structures which have to be produced as well for stabilizing the model and to improve the dissipation of heat below these geometries [9].
The process is suitable for producing individual and highly complex parts and hollow structures such as topology-optimized components as shown in Figure 16. Also, very fine structures like lattice structures can be produced, which is also depicted therein.
Complexly designed skateboard trunk manufactured with LBM.
After the manufacturing process, the part is separated from the build platform, and the support structure is removed. To adjust the mechanical properties of the part, a heat treatment can be applied. Other conventional methods like machining or polishing can be utilized to achieve a better surface quality, dependent on the requirements.
Depending on slicing and scanning strategy, the quality of manufactured parts can widely vary, concerning cracks, pores, residual stresses, distortions, tightness, and fatigue properties. However, LBM processes are becoming relevant in series and tool production, while the reliability of such manufacturing technologies and the resulting component quality are of high importance [10].
At Fraunhofer IWU, a counterflow heat exchanger was specially developed for the LBM process with the focus on a low pressure drop, flexible, as well as compact design (Figure 17). To reduce the pressure drop and validate the best version, a fluid analysis was executed on each design. To get a maximum heat transfer and integrated insulation to the outer atmosphere, the cold channel is wrapped around the hot channel within the heat exchanger (heat exchange surface/volume: 405 m2/m3; performance: 36.2 W/cm3). Also, the wall between the cold and the hot channel system is reduced to a minimum of 0.8 mm to enhance the heat transfer. As a result of the special design for the laser beam melting process, no support structure and postprocessing were needed to manufacture the heat exchanger. The pressure drop (0.20 bar) as well as heat flow (1.3 kW) of the final design was calculated with flow simulations using Ansys CFX. The propagated heat exchanger shows one imperfection since it produces a thermal short circuit in the area of the connection geometries.
A counterflow heat exchanger with a low pressure drop and compact, flexible design.
The next step will be to avoid the thermal short circuit and to implement the designs described before within the metal heat exchanger in consideration of the general conditions of LBM.
The research and development of new technologies is sometimes limited by the availability of commercial peripheral components. These new technologies change the requirements on state-of-the-art products.
One of those new technologies is the fuel cell. A fuel cell has the benefit of directly converting chemical energy to electrical power without the conventional process steps in between. This reduces the losses on the whole conversion path. Fuel cells are available in various types with different characteristics (Figure 5). The low-temperature fuel cells are mostly used for portable or mobile applications because of the high power density, for example, as a battery charger for mobile devices. High-temperature fuel cells are typically used for stationary applications like power and heat supply for households and facilities [11].
Most of the low-temperature fuel cells like the PEFC (polymer electrolyte fuel cell) need pure hydrogen or at least “clean” fuel. Not allowed substances like carbon monoxide have to be filtered before operation. The high-temperature solid oxide fuel cell (SOFC) is designed to generate electrical and/or thermal power with a high efficiency based on the usage of worldwide available fuels such as natural gas and LPG (liquefied petroleum gas). These fuels are reformed to a gas mixture of hydrogen and carbon monoxide directly inside the SOFC System. In contrast to most of the common fuel cells, an SOFC can also generate electrical power by carbon monoxide conversion (Figure 18).
An overview of fuel cell technologies, including temperatures, reactions, and allowed and not allowed chemical components.
In order to achieve this high efficiency, high temperatures are necessary. The standard operation temperature of an SOFC is above 700°C. As mentioned before, these systems have different gas processing steps included [12], which is illustrated in Figure 19 as well:
the reforming process (REF),
the conversion of hydrogen and carbon monoxide to water and carbon dioxide inside the fuel cell itself, and
furthermore, a postprocessing step typically called tail gas oxidation (TOX).
An overview of SOFC system with integrated components.
The fuel cell itself cannot convert 100% of the fuel for various reasons, which will not be further explained in this context but are discussed in [13]. The rest of the fuel has to be oxidized in order to avoid emission of hydrogen and carbon monoxide. This kind of reaction leads to temperatures of 900°C and higher.
The different reactors REF and SOFC have different requirements on heat treatment. The REF needs heat for a high efficiency. The SOFC receives the reaction products of the REF with a temperature of approx. 800°C on the anode side. On the cathode side, typically air is used. In order to avoid thermal stress and to realize the necessary operating temperature of the SOFC, this air has to be preheated.
The realization of the heat treatment requires a rather complex packaging of all components. This packaging is realized in the HotBox. The efficiency of all steps is based on a minimum of losses inside the system. Therefore, an adapted heat exchange from TOX to air and an overall packaging for optimal heat management are necessary.
Commercial heat exchangers are not aware of these requirements. The used materials and/or joining technologies cannot handle this high temperature, and due to the standard design on commercial heat exchangers, especially plate heat exchangers, the integration of such components inside the HotBox is complicated and space-consuming.
In order to achieve the highest possible efficiency of such systems, heat exchangers that combine an adaptable design with high-temperature resistance are indispensable.
Fused filament fabrication (FFF) is a thermoplastic AM technology which bases on nearly endless filaments which are used as a semi-finished products and which are melted and deposited under a heated nozzle. To generate ceramic components, particle-filled filaments are used to manufacture the so-called green bodies additively [14]. These green bodies have to be debinded, to remove all organic materials, and sintered to densify the microstructure and to achieve the typical ceramic properties. The benefits of this AM technology are the high productivity and the large building space of the available devices. The existing challenges of FFF of ceramic components are the development of highly particle-filled filaments and the defect-free debinding and sintering of the components [14].
SiC filaments were developed to allow the AM of large volume SiC heat exchanger, which can be used for operation temperatures of 1000°C and higher. Figure 20 shows some ceramic test components and demonstrators manufactured by FFF.
Different ceramic demonstrators additively manufactured by FFF; left: SiC (green state); right: various ceramics (sintered state).
The next steps will be the investigation of FFF with SiC filaments concerning the realizable geometries and the tightness of the sintered structures.
The LCM technology was developed and commercialized by Lithoz GmbH, Austria [15]. As a special kind of stereolithography, free radical polymerization of the binder system takes place with light of a defined wavelength, causing the suspension to solidify. Via a DLP module, the suspension is selectively irradiated with a blue light, whereby all areas to be cross-linked on a given plane are exposed at the same time. The ceramic particles dispersed in the suspensions are fixed in the solid polymer matrix (green body). A final debinding and sintering step is necessary for this AM technologies for ceramics, as well [16].
The LCM technology impresses with a very high resolution (wall thickness down to 100 μm possible) [16] and very good surface properties (Ra < 1 μm) of the sintered components. The challenges are the small building area ((76 ×43 × 150) mm3) and the low productivity, both resulting in relatively high manufacturing costs as well as the cleaning and the debinding process for the green components [17].
Both FASS structures which were described before were additively manufactured via LCM technology and Al2O3 suspension of Lithoz. The sintering occurred at 1650°C which allows operation temperatures of significantly more than 1000°C. Figure 21 shows the feeding structure at the sintered state (left) and the alternative heat exchanger structure (green state).
The FASS structures as ceramic component in the sintered (left; 35 × 35 × 35 mm3) or green state (right), additively manufactured via LCM technology.
The rapid development of AM technologies enables a radical paradigm shift in the construction of heat exchangers. In place of a layout limited to the use of planar or tubular starting materials, heat exchangers can now be optimized, reflecting their function and application in a particular environment. The investigations show the potential of the technologies concerning increasing heat exchanging surface and compactness as well as the designing of the fluidic systems. The AM of ceramics will pave the way to realize heat exchanger for operation temperatures highly above 1000°C.
The new approach for designing can also be used for bent structures. They provide more potential than the straight heat exchangers and open a wider field of possible technical applications. A possible, curved geometry is shown in Figure 22.
A computer-aided designed curved heat exchanger. Its geometry bases on FASS.
To increase the inner surface even more, rough surfaces, which induce beneficial turbulences, can be generated by modeling partial Brownian motion.
The authors would like to thank the German Federal Ministry of Education and Research (BMBF) for funding the project “FunGeoS“ within the Framework Concept Zwanzig20— partnership for innovation” in the consortium AGENT-3D (fund number 03ZZ0208A) as well as European Union which funded parts of this work under the European Union’s Horizon 2020 Research and Innovation Programme (“CerAMfacturing,” Grant Agreement No 678503). Other parts of this chapter are based on results from instaf, a research project in the European network IraSME, which is carried out by partners in Austria and Germany. It is funded by the Federal Ministry for Economical Affairs and Energy (BMWi) on the basis of a decision of the German Bundestag.
There are no conflicts of interest and nothing else to declare.
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