THEORETICAL PROOF OF CONCEPT OF AN OPTIMAL SOLAR RECEIVER TO PRODUCE LOW-TEMPERATURE (-40 C) COOLING USING A THERMOACOUSTIC TRI-THERMAL MACHINE

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1 THEORETICAL PROOF OF CONCEPT OF AN OPTIMAL SOLAR RECEIVER TO PRODUCE LOW-TEMPERATURE (-40 C) COOLING USING A THERMOACOUSTIC TRI-THERMAL MACHINE S. Cordillet 1, P. Duthil 2, F. Nepveu 3, T. Le Pollès 4, G. Olalde 3, A. Salome 3 and J-P. Thermeau 2 1 Ph.D student, Université de Paris Sud (PXI), Orsay / IPNO-IN2P3-CNRS, BP1, ORSAY cedex, and PROMES-CNRS, 7 rue du Four Solaire, ODEILLO (France), +33 (0) , sophie.cordillet@promes.cnrs.fr. 2 IPNO-IN2P3-CNRS, BP1, ORSAY cedex (France) 3 PROMES-CNRS, 7 rue du Four Solaire, ODEILLO (France) 4 Hekyom, 2 rue Jean Rostand, ORSAY (France) Abstract The innovative part of this project is to develop a thermoacoustic refrigeration system driven by concentrated solar energy. Solar thermoacoustic refrigeration offers three significant advantages: first, the possibility to easily reach a large range of low temperatures, second, the absence of moving parts, which is conducive of high reliability, and finally a low environmental impact. A few preliminary investigations have described the concept of the solar-powered thermoacoustic prime mover, but not on a kw production scale. It is considered here that 1.5 kw of cooling power is a challenging proof of concept, considering the overall targeted performance (40% of the ideal Carnot s efficiency) for the combination of the thermoacoustic prime-mover and the heat pump. The solar receiver s purpose is to induce mechanical power production by producing an efficient energy transfer from the solar concentrator to the oscillating working pressurized gas within the thermoacoustic prime mover. Acoustic waves are indeed the power carrier, as they travel from this prime mover to the thermoacoustic refrigerator. Since acoustic waves are very sensitive to external perturbations (e.g., spatial or temporal changes in the temperature of the hot heat exchanger), the goal of this study is to investigate ways to maintain both the temperature and the power transferred to the gas as constant as possible over space and time. This paper focuses on the steady-state spatial homogeneity, using a series of appropriate models. Preliminary design considerations are offered for the jot heat exchanger and its optimal location within the solar cavity. Keywords: solar receiver, solar refrigeration, thermoacoustics, spatial temperature homogeneity, concentration 1. Introduction In the current global warming context, the refrigeration industry is one of the most constrained by the Kyoto protocol. Considering that cooling demand increases with the intensity of solar radiation, solar refrigeration has been looked upon as a possible solution to reduce greenhouse gases. In thermoacoustic systems, the direct conversion from solar energy to mechanical energy is done without any moving component, which makes the process simple and reliable. Moreover, the working fluid that is used to develop the acoustic motion is usually a noble gas, such as helium, with no environment hazard. It is also a carbon-free process with virtually no energy costs as long as the sun is not obscured. Thermoacoustic systems are relatively new, and so far have been used for a few specific applications only, like space refrigeration at low temperatures. It is a tri-thermal machine : the refrigerator is at the cold temperature, solar source powered at a high temperature the prime mover and both exhaust the heat at ambient. Current thermoacoustic systems on the market are powered by electricity. Preliminary investigations (reviewed below) have suggested that thermoacoustic refrigeration machines could be operated

2 by a renewable energy source, such as solar. A solar-driven thermoacoustic device constitutes an alternative to systems based on absorption, adsorption or vapor compression cycles in the solar thermal field. Moreover, thermoacoustic systems are not limited by a specific working temperature (their range is large, from ambient to cryogenic temperatures) and are potentially more efficient than conventional systems. A few small-scale experimental solar thermoacoustic systems have been described in the literature. For instance, Chen [1] constructed the first solar-powered thermoacoustic cooler a decade ago. A parabolic dish collector heated it. However, the cooler just achieved a 1.5 C temperature drop due to gas leakage and thermal losses. Adeff and Hofler [2] experimentally studied a thermoacoustic refrigerator that was powered by solar radiation concentrated with a Fresnel lens. The refrigerator produced 2.5 W of cooling power, with the cold temperature reaching 5 C and a temperature drop of 18 C. Considering the current intensive development in concentrating solar power devices able to deliver cost-effective and scalable power in the multi-kw range at high temperatures, it now appears logical to combine a solar concentrator and a thermoacoustic device for cooling production on a kw scale. The whole project, whose initial phase is reported here, is supported by the ANR (French National Research Agency). It is conducted jointly by three research laboratories: PROMES-CNRS for the solar study, IPNO for the thermoacoustic and integration studies, LaTEP for the transient modeling of the global system and cold storage, and by an industrial partner specialized in thermoacoustics, HEKYOM. The goal of the work described here is to model, for steady-state conditions, a solar receiver capable of transmitting a power of 4.4 kw to pressurized helium at 50 bar, and with a targeted outlet temperature of 1000 K. The solar receiver consists of a heat exchanger placed inside a cavity irradiated by concentrated solar energy. A high temperature of about 1000 K is necessary for the thermoacoustic prime-mover to reach a sufficiently high efficiency. The principle of this system is as follows (Fig. 1): Solar radiation is collected by a parabolic dish (1) and focused onto a hot heat exchanger (2) inside a cavity (3). The gas, which circulates inside the hot heat-exchanger tubes, absorbs a power of about 4.4 kw. When the thermoacoustic prime mover reaches a sufficient temperature ( 1000 K), it generates a traveling wave with large acoustic power. This power is then used into a thermoacoustic refrigerator to pump heat from the cold heat-exchanger. Fig. 1: Solar thermoacoustic system For thermoacoustic prime movers currently manufactured, an electric resistance surrounds the hot heat exchanger and allows very good temperature homogeneity. For the present research, the hot heat exchanger has to be adapted to a solar source. The main difficulty here is to design an absorber with an ideally homogeneous spatial distribution of temperature, even though the distribution of the concentrated solar power that is incident in the cavity has a Gaussian-like shape. The latter spatial distribution limits the overall thermal performances of the absorber and may introduce high mechanical stresses. A detailed theoretical study is needed to optimize the prototype s dimensions. Otherwise, the thermal spatial variations may alter the performances of the thermoacoustic system. Therefore, any prospective change in the design of an existing and working thermoacoustic prime mover is a delicate proposal. This explains why

3 an existing design of the thermoacoustic system is considered here, thus placing strong geometric constraints on the solar receiver. 2. System modelling The development of accurate simulation tools allows the evaluation of the system s thermal behavior in relation to specific physical and geometrical parameters, and also in relation to a spatially non-uniform power source. This simulation method provides a way to optimize geometries and materials as a function of the targeted system performance. To reduce the detrimental effects of spatial inhomogeneity in the solar source, three research topics are being explored simultaneously: - adapting the parabolic dish design to obtain a homogeneous flux profile; - optimizing both the absorber position relative to the dish s focal plane and the cavity s shape (to limit thermal losses and homogenize temperatures around the receiver); - optimizing the heat exchanger s architecture (dimensions and geometry) and the materials of the absorber to homogenize its spatial temperature distribution and maximize the power transferred to the gas. The development of the necessary models needed to accomplish these tasks is described in what follows Flux map modeling The thermoacoustic system is designed to produce 1.5 kw of cooling power at -40 C. For this power target, the gas must acoustically transfer 4.4 kw (as mentioned previously), thus requiring a solar power input between 5 and 10 kw onto the receiver. However, the parabolic dish currently available for this experiment is largely oversized, since it delivers 50 kw of concentrated solar energy, with a peak flux of 9.5 MW/m 2. The power at the focus must therefore be considerably reduced. This can be achieved by installing a flux modulator between the concentrator and the receiver and by selecting the most appropriate absorber location relative to the focal plane. The concentrated solar radiation delivered by the concentrator is simulated with SOLTRACE, a raytracing model developed by the National Renewable Energy Laboratory (NREL). It is used to model interactions between solar radiation and optical systems, and then analyze the latter s performance. A detailed measurement campaign on the 50-kW solar concentrator [3] led to its simulation using an optical model composed of 4400 parabolic elements [4], and in which macroscopic optical errors (distortion of element, error of normal vector ) were associated to each element. This optical model provides satisfying results: the modeled flux peaks are 5% lower than the measured peaks, and the modeled power peaks are 1% lower than the measured values [3]. SOLTRACE is run specifically here to generate a map of the solar flux distribution on the absorber plan (as shown in Fig. 2). It allows for comparisons between various possible ways to reduce the useful concentrator area and to evaluate its impact on the intensity, geometry and homogeneity of the heat flux distribution in the focal plane. Fig. 2: Example of a solar flux map (12 cm behind the focal plane, mirror reflectance 94%)

4 2.2. Cavity modeling To characterize the thermal behavior of the solar receiver, the heat transfer processes (by radiation, conduction and convection) that take place inside and outside of the cavity, or around the hot heat exchanger, are considered in a detailed specific model that has been developed in the MATLAB environment. This model takes into account the cavity s geometry (circular aperture diameter and internal cavity diameter), the hot heat exchanger dimensions, as well as its position relative to the focal plane. The cavity is modelled as a cylindrical shape having a circular aperture (cf. Fig. 3). Internal surfaces are considered opaque, grey and diffuse for both reflection and emission. Through successive model iterations, the cavity s geometrical constraints have been optimized to increase the system s performance (i.e., to obtain the most homogeneous flux on the absorber s top surface, while generating sufficient transmitted power and only minimal thermal losses). Fig. 3: The cavity design The results of this optimization study show that a heat exchanger s surface smaller than 16x16 cm does not intercept the whole concentrated solar energy transmitted by the concentrator/flux modulator assembly. For instance, a 5x8 cm absorber intercepts only 61% of the incoming power at the optimal position, without taking into account thermal losses. In contrast, a 16x16 cm absorber, placed behind the focal plane, can absorb 90% of the total incident power (still without considering thermal losses). In the latter case, the main source of losses is thermal emission from the hot heat exchanger, which is at high temperature. Its optimal position is found at 10 cm behind the focal plane. This position actually offers two main advantages: - the cavity s aperture can be placed right in the focal plane and can therefore have a small diameter, which effectively reduces the thermal emission losses of the absorber (in the cavity) through it. The graph in Fig.4 presents, for four surface absorber temperatures (from 1000 K to 1300 K in 100 K increments), the global thermal efficiency of two different cases: a 16x16 cm absorber without any cavity; and the same absorber surrounded by an optimized cavity. The cavity can reduce losses up to 20% in the 1000 K case. Fig. 4: Thermal efficiency of the solar absorber as a function of distance from the focal plane, with or without a cavity around it.

5 - the peak flux on the absorber can be reduced: at a distance 15 cm behind the focal plane, a 16x16 cm absorber gets 83.4% of the total incident energy, while the power flux peaks at only 820 kw m - ², compared with 4450 kw m - ² at the focal plane. It is concluded that the optimal absorber location just defined offers a more homogeneous flux, since it can effectively avoid hot spots, which otherwise could impact the heat exchanger core homogeneity and induce thermo-mechanical stress. Moreover, according to this model, the highest efficiency of the solar energy transfer to the absorber is 70% Solar heat exchanger modeling The geometry of the solar heat exchanger is simulated as a parallelepiped box with internal layers of parallel tubes. The thermal model is constructed by porting the COMSOL code into MATLAB. COMSOL is a finite element analysis solver that can simulate coupled phenomena [5]. This powerful computational tool is used to analyze the heat transfer processes (by radiation, convection and conduction) inside and around the absorber. It is assumed that the exchanger s top surface is irradiated by a Gaussian power density distribution given by the flux map model (from Section 1.1) at the optimized distance to the focal plane defined by the cavity study (Section 1.2). To predict the heat transfer coefficient, which depends on both the pressurized gas and the acoustic wave characteristics, a thermoacoustic analysis of the acoustic field has been carried out by HEKYOM. From the numerical value thus found for this coefficient, 7 kw m -2 K -1, it has been evaluated that the optimal total number of tubes should be 100, each having an internal diameter of 3 mm and a length of 230 mm. With this arrangement, the acceptable range of concentrated solar flux on the absorber is between 125 and 450 kw m -2. The thermoacoustic dimensional specifications further require that the tubes must be placed in different layers to gain compactness and to fit the absorber (and its cavity) within the highefficiency solar area, i.e., the area irradiated at a distance of 10 cm from the focal plane (Section 1.3). A large number of simulations have been conducted to reduce the number of a priori geometric possibilities and to look for the best 2D geometrical distribution of the tubes. In turn, this arrangement would create the most efficient solid-gas heat transfer with an acceptable 2D temperature field: a difference between the highest and the lowest temperatures of 40 K inside the exchanger s core, and a difference of 10 K at any tube s internal surface. 3. Results 3.1. Silver /Inconel absorber To homogenize the absorber temperature and, consequently, to reduce thermal stresses, the first step is to use silver in the absorber to benefit from its high thermal conductivity. This should also reduce the scatter in the helium temperatures throughout the successive tube layers. To evaluate the performance of such an arrangement, the thermal behavior of an exchanger consisting of a filling material with high thermal conductivity (silver in this case) and of Inconel tubes (which must resist the high gas pressure) was compared to what would be obtained with an absorber entirely made of Inconel. The results of these simulations show that the silver/inconel absorber successfully reduces the temperature inhomogeneity by almost 95%, and that the thickness of the Inconel tubes has no notable influence, as long as it is less than 0.3 mm Geometrical distribution of the tubes Different configurations, obtained by increasing the number of layers, N, and the number of tubes in each layer, have been considered. For each configuration, the effect of varying the distance between the tubes has been studied. The goal is to optimize the absorber s temperature homogeneity based on the difference between the highest and the lowest temperatures ( Tsol) and to achieve the required gas temperature of 1000 K, based on the internal temperature reached by the tubes (Tmax).

6 The number of tubes per layer and their spatial distribution is modeled as follows. A parameter, q, is defined to represent the number of additional tubes from a layer to the next one: if q = 0, each layer has the same number of tubes; if q > 0, the number of tubes increases from the top layer to the bottom layer; if q < 0, the number of tubes decreases from the top layer to the bottom layer. The number of tubes for the first (or the last) layer is m 1 = 1 2 [2M tube,total N (N 1)q] (1) Thus, the numbers of tubes for all other layers are: m = m 1 q (2) i i + The results of these simulations appear in Figs. 5 and 6. They show that, for a solar heat exchanger placed 10 cm behind the focal plane, the optimal configuration consists of 3 layers of tubes, with a total thickness of about 2 cm. The best distances between the tubes are 0.5 and 2 mm along width and thickness, respectively. The former dimension is linked to the irradiated solar area dimensions, whereas the latter allows the best heat radial diffusion into the absorber core. Figure 7 shows the simulated temperature field for the optimized hot heat exchanger. It is found that the temperature field varies from a minimum of 1035 K around the edges of the heat exchanger to 1070 K around its center. Such a spatial gradient of 35 K is relatively low, but can still impair the performance of the thermoacoustic system. Further steps to improve the current preliminary design of the system are therefore desirable, and are outlined in the next section.

7 Fig. 5: Effect on the temperature field within the absorber of the number of layers (N) and the number of tubes in a layer. Fig. 6: Effect on the temperature field of the longitudinal (ex) and vertical (ey) distances between tubes Fig. 7: Result of simulations of the temperature field (in K) for a receiver with optimal dimensions

8 4. Further research To reduce temperature inhomogeneities, it is anticipated that the prototype absorber will have a curved shape. This will better fit the Gaussian distribution of the concentrated solar energy than a planar shape. Furthermore, the absorber will be advantageously covered with an Inconel layer. This intends to protect the silver plate against oxidation and to provide higher mechanical resistance. Such variations from the simpler initial design will need to be modeled and optimized. Absorber Further theoretical research will be devoted to the study of the heat transfer through the receiver under transient conditions. This is needed to evaluate the impact of any intermittent effect caused by rapid solar flux variations, due for instance to partial cloudiness. The computational tools developed for the present work will still be useful to evaluate these transient effects. An experimental study of this solar thermoacoustic pilot system is planned to start during the summer of The objectives of this experiment will be threefold: study and qualify the main sub-systems (solar cavity, solar absorber, thermoacoustic heat pump, cooling loop ), as well as the whole system, under different operational conditions; better understand the physical phenomena in the thermoacoustic prime mover; and validate the calculation tools developed during this project. Fig. 8: Solar heat exchanger into the thermoacoustic motor If, as anticipated, the calculation tools presented here are validated during the future experimental study, a new generation of thermoacoustic refrigeration systems of larger capacity (in the kw range) could be developed relatively easily. Acknowledgements This study as well as first author s doctoral studies has been made possible by the financial support of ANR, which is gracefully acknowledged. The authors also thank Dr. C. GUEYMARD for his help with the manuscript. References [1] R-L. CHEN, Design, Construction, and Measurement of a Larger Solar Powered Thermoacoustic Cooler, Pennsylvania State University, [2] J. A. ADEFF, T. J. HOFLER, Design and construction of a solar-powered, thermoacoustically driven, thermoacoustic refrigerator, in: Acoustical Society of America 139th Meeting Press Release, Melville, New York, April 26, [3] W. REINALTER, S.UMLER, P. HELLER, T. RAUCH, J-M GINESTE, A. FERRIERE, F. NEPVEU, Detailed performance analysis of the 10kW CNRS-PROMES Dish/Stirling system, Proc. 13 th Solar PACES International Symposium, Seville, Spain, [4] F. NEPVEU, Production décentralisée d électricité et de chaleur par système Parabole/Stirling : Application au système EURODISH, Thèse de Doctorat, Université de Perpignan, November 28, [5] COMSOL,