Thermal Analysis of a Compressor for Application to Compressed Air Energy Storage. 111 Church St. S.E. Minneapolis, MN, 55455, USA

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1 Proceedings of IWHT2013 2nd International Workshop on Heat Transfer Advances for Energy Conservation and Pollution Control October 18-21, 2013, Xi an, China IWHT Thermal Analysis of a Compressor for Application to Compressed Air Energy Storage C. Zhang 1, B. Yan 1, J. Wieberdink 1, P. Y. Li 1, J. D. Van de Ven 1, E Loth 2, T. W. Simon* 1 1 Mechanical Engineering Department, University of Minnesota, 111 Church St. S.E. Minneapolis, MN, 55455, USA 2 Mechanical and Aerospace Engineering Department, University of Virginia, 122 Engineer s Way P.O. Box , Charlottesville, VA 22904, USA (*Corresponding Author: tsimon@me.umn.edu) Abstract In this paper, the topic of Compressed Air Energy Storage (CAES) is discussed and a program in which it is being applied to a wind turbine system for leveling power supplied to the grid is described. Noted is the importance of heat transfer in the design of the compressor and its effect on performance. Presented is a design for minimizing the temperature rise in the compressor during compression. The design requires modeling regenerative heat transfer from the compressed air to solid material inserted in the compression space. Modeling requires characterizing pressure drop through the porous insert, interfacial heat transfer between solid and fluid in the matrix, and thermal dispersion within the porous regions. Computation and experimentation are applied for developing correlations for such terms. Two types of porous media are applied, interrupted plates and open-cell metal foams. Cases with foam inserts are computed and the results are discussed. Discovered in the results are some complex secondary flow features in spaces above the porous inserts. Keywords: Energy storage, Compressor, Wind turbine, Heat transfer, Porous media 1. Introduction 1.1. Motivation This paper presents thermal analyses on a liquid piston driven compressor used for Compressed Air Energy Storage (CAES). The CAES system stores energy as high-pressure air, to retrieve it later in a liquid piston expander. Compression leads to a tendency for temperature rise in a compressible gas. This paper discusses techniques for minimizing that temperature rise. Absorbing heat from air during compression to reduce its temperature rise is important for improving compression efficiency. As the air temperature rises, part of the input work is being converted into internal energy rise that is wasted during the storage period as the compressed air cools toward the ambient temperature. Referring to the P-V diagram in Fig.1, one sees that the work input is represented by the integral of the area under the P-V curve. For the same pressure compression ratio, an isothermal process always requires smaller work input because the cooling process and the work required to maintain reservoir pressure during cooling are missing. Therefore, nearisothermal compression is important for reducing work input and enhancing efficiency for CAES systems Background on wind turbines and energy storage Our desire is that the CAES system is integrated into a wind power field. The benefit of integrating energy storage into a wind power array is that fluctuations in wind power input can be smoothed over time and electric power generation equipment can be sized commensurate with a supply power that is nearer the average wind power of the day. The alternative is sizing for peak power or throttling back the wind turbine when the wind is strong. Use of storage techniques for wind power is discussed in reference [1]. Various scenarios with and without storage were considered. In one, wind generation capacity in 2050 was 302GW without storage and 351GW with storage. Further, they concluded that CAES is more economical than hydroelectric pump storage (HPS) or batteries. 1

2 Fig. 1. Schematic of isothermal compression vs. non-isothermal compression From a report written by the US Offshore Wind Collaborative [2], we read that the total amount of US offshore wind energy capacity is almost equal to the current total installed capacity. Noting that most electricity-demanding regions are on the coasts, the report highlights the significant potential for offshore wind generation. It urges establishment of opportunities to coordinate technological, economic, and environmental advances, along with the chance to build public trust and investor confidence in the potential that offshore wind energy holds for the nation. Toward that goal, implementing CAES allows efficient use of offshore equipment and reduction of transmission line capacity. Traditional CAES systems store the compressed air in underground caverns and often marry this with combustion plants by using the compressed air as oxidant for burning in combustion turbines [3]. More recent advancements include using multi-stage compressors with inter-cooling between stages and multi-stage expansion turbines, with reheat [4]. The advantages of using near-isothermal compression and expansion to improve efficiency in the CAES systems were demonstrated in reference [3]. Herein, near-isothermal compression and expansion is by using regenerative heat exchange with elements within the compressor/expander volumes. A traditional reservoir for CAES, an accumulator, is a volume into which air is compressed. Energy is released by expanding that air to derive work until the accumulator-toambient pressure difference has decreased to the point at which further expansion is not practical. Then, power and energy density of the expanding air are small. If used in a hydraulic system, the air is compressed by displacing it with a pumped liquid and work derived from that compressed air drives the liquid through a hydraulic motor, as shown in Fig. 2(a). In the present system, we employ the open accumulator concept proposed in [5] and shown in Fig. 2(b). In this system, gas is exhausted to the atmosphere during expansion, reversing during compression. Compression is with pumped liquid and air and expansion is with a liquid motor and an air expander. It is operated at a constant accumulator pressure; the maximum design pressure. Thus, with the open accumulator, the energy storage density per unit volume of air is always high since the low-power, low-accumulator-pressure situation in the closed accumulator is avoided. An added benefit is a dramatic reduction in accumulator pressure oscillation cycles and improved fatigue performance. (a) Conventional closed accumulator configuration [5] (b) The open accumulator concept [5] Fig. 2. Closed and open accumulators Though not necessary for the open accumulator CAES to be successful, our design is proposed to be used in a fluid power wind turbine system. In such as system, we use hydraulic equipment for power conversion and transmission, as shown in Fig. 3. It employs hydraulic circuits, a hydraulic drive pump, hydraulic pumps and motors, open accumulators, and liquidpiston air compressors. Advantages include having a hydraulic pump in the nacelle at the top of the tower, rather than a heavy transmission and generator assembly and having much of the equipment, including the generator, at ground (or sea) level, allowing easier access for assembly and maintenance. When electricity demand is small, the system operates in storage mode in which the excess shaft power from the wind turbine is transferred to hydraulic power in the drive pump and the hydraulic power is transmitted through the hydraulic circuit to the hydraulic transformers, which are a series of specialized hydraulic pumps and valves to pump the liquid into the liquidpiston chamber to compress air. During this mode, compressed air is stored in the open accumulator. When the electricity demand is larger than the direct supply from the wind turbine, the unit switches to the generation mode in which air is withdrawn from the open accumulator and expanded in the liquid piston chamber to derive shaft power for the generator. Key to success of the system is efficient compression and expansion of air in the compressor/expander. As noted, this must be done under near isothermal conditions. Thus, the present paper will concentrate on the thermal design of the compressor/expander and the analysis on which it is based. This paper focuses on compression and expansion with a liquid 2

3 piston. The term liquid piston is applied because the gas compression is done with a liquid-gas interface rather than a solid piston. It will be shown that having a liquid piston design for the compressor is a major step in having an efficient compressor/expander. In the liquid-piston compressor, liquid (water in the present study) is pumped into the compression chamber from below. It is found in [6] that liquid-piston compressors have an advantage over solid pistons in terms of efficiency and reduced power consumption [6]. Further, for the purpose of cooling, insertion of solid material into the chamber is possible with liquid-piston compressors as liquid can flow through the open portions of the matrix. Cooling of the compressed air could also be effected by spraying drops into the air space and allowing them to be heated by the compressed air. Having a liquid piston is beneficial to spray cooling for the residue of the spray falls to join the piston liquid. Though spray cooling is effective and is being pursued by our group, this paper will focus on the method of inserting heat-absorbing solids into the compression chamber. Since thermal storage to the porous material in the compressor volume is so important to success, the remainder of the paper will be dedicated to modeling that process in preparation for design of the compressor. Fig. 3. Schematic of CAES system for offshore wind energy storage and generation [7] Nomenclature Area per unit volume of porous medium ( Cross-sectional area ( ) Half plate distance ( ) Coefficient for the Forchheimer term ( ) Constant-pressure specific heat (J/kgK) Specific heat for solid (J/kgK) Constant-volume specific heat (J/kgK) Hydraulic diameter ( ) Characteristic diameter ( ) Characteristic length based on filament dia. ( ) Filament diameter ( ) Mean pore diameter ( ) Storage energy (J) Gravitational acceleration (m/s 2 ) Surface heat transfer coefficient (W/m 2 K) Volumetric heat transfer coefficient (W/m 3 K) Permeability (m 2 ) Thermal conductivity (W/mK) Dispersion conductivity (W/mK) Chamber length ( ) Length of the upper region without insert ( ) Length of the insert region ( ) Plate length ( ) Total mass of air (kg) Polytropic exponent Nusselt number Bulk pressure (Pa) Supplied hydraulic pressure (Pa) Peclet number Area averaged wall heat flux Local pressure (Pa) Final air pressure (Pa) Prandtl number Radius of chamber ( ) Reynolds number based on Radial coordinate Ideal gas constant (J/kgK) Reynolds number based on characteristic length Momentum source term (Pa/m) Local air temperature (K) Initial temperature; wall temperature (K) Average air temperature in the chamber (K) Local solid temperature (K) Average temperature of solid in the chamber (K) Final averaged air temperature (K) Plate thickness ( ) Time (s) Liquid piston velocity (m/s) Instantaneous volume of chamber (m 3 ) Work input (J) Axial coordinate Greek Symbols Volume fraction Porosity Compression efficiency Dynamic viscosity (Ns/m 2 ) Density (kg/m 3 ) Final pressure compression ratio Subscripts Initial value of variable Air phase 3

4 Water phase Based on filament diameter Darcian Fluid phase Averaged on the REV Solid Local streamwise direction Local cross-stream direction Superscripts Dimensionless variable 1.3. Analysis on heat transfer and compression efficiency The effect of heat transfer on compression efficiency will be shown quantitatively through a simple thermodynamic analysis. The compression efficiency CAES is defined as the ratio of storage energy to work input [9, 10]. The storage energy is defined as the amount of work extraction from compressed air as it is isothermally expanded to atmospheric pressure. Compression of air is completed in two steps: compress the air from atmospheric pressure to a high pressure, typically resulting in temperature increase, and allow the air to cool while compressing at the storage pressure so that the work potential (storage energy) is maintained as volume decreases. Work of the latter stage is identified as cooling work. The total work input is the sum of the work done in the two steps. It is given by, (1) (2) The compression efficiency is given by the ratio of the storage energy to the total work input, It is shown that the compression process can be characterized as a polytropic process [10], where the polytropic exponent,, shows the effect of heat transfer; represents isothermal compression and for air represents adiabatic compression, with no heat transfer. Substituting Eq. (4) into Eq. (3), and writing in terms of dimensionless pressure and volume based on their initial values, Equation (5) shows that the compression efficiency is dependent * on the pressure compression ratio, p and heat transfer, given by n. Figure 4 shows that for the same pressure compression ratio, decreasing, which means enhancing heat transfer from the compressed air, significantly improves efficiency. (3) (4) (5) Fig. 4. Effects of heat transfer on compression efficiency with different pressure compression ratios. 2. Heat transfer to the porous inserts 2.1. Introduction Porous media can be inserted into the liquid-piston compression chamber so that the solid can absorb thermal energy from the air as it heats during compression. Because solid has much higher thermal capacity than air, the solid can absorb thermal energy from the air, while its temperature rises only a small fraction of the temperature drop of the air. The present study will introduce two kinds of porous inserts, an interrupted-plate insert and an open-cell metal foam (Fig. 5). The interrupted-plate insert consists of an array of plates oriented in a staggered fashion so that a new thermal boundary layer develops on each successive plate in the streamwise direction. The metal foam has very thin filament features that enhance mixing of the flow. Both have large heat transfer surface area to volume ratios. A zero-dimensional (Zero-D) numerical model has been developed [11] that can give quick solutions for the transient change of the gas bulk temperature and pressure during compression of air in a chamber having porous inserts. Applying the first law of thermodynamics to the air, Since air follows the ideal gas law and, in this case, the liquid piston volume flow rate is constant, Eq. (6) can be written, ( ) Energy conservation for the solid gives, (6) (7) (8) Equations (7) and (8) are the governing equations of the Zero-D model. 4

5 Fig. 6. Schematic of an REV of the exchanger [11] (a) A sketch of the interrupted (b) Metal foam inserts [12] plate insert [11] Fig. 5. Porous inserts used in the liquid piston compressor Important fluid and thermal characteristics of the porous inserts that must be included are the flow resistance and resulting pressure drop, the heat transfer coefficient between the solid material and surrounding air, and thermal dispersion. Next, these terms will be presented for the two types of porous inserts discussed in this paper Interrupted plate Shape analysis Because details of the shape of the interrupted-plate insert are known, CFD simulations on a Representative Elementary Volume (REV) of the interrupted-plate can be done. These CFD analyses are used to obtain the pressure drop and interfacial heat transfer relationships for flow with various velocities through the matrix. The REV is the minimum representative, repeating geometric feature of the porous medium. Its geometry for the interrupted plate insert is shown in Fig. 6. Three geometric dimensions are important: the plate length,, the plate distance,, and the plate thickness,. A study was conducted to quantify the effects of the shape parameters on heat transfer and compression efficiency [11]. Twenty-seven different shapes were analyzed. For each shape, two flow conditions were studied: and, where is defined as, (9) The CFD results show that smaller dimensional features are beneficial for effecting higher surface heat transfer rates. The fluid temperature distribution and the wall heat flux of the case with the smallest geometry features among all the cases studied are shown in Fig. 7. The maximum local heat flux is found at the edges of the frontal areas. The figure shows that the flow is effectively cooled by the solid surfaces. The hottest spot of the flow is in the fluid region at the core of the REV. Fig. 7.Temperature and wall heat flux [11] ( ) A heat transfer correlation based on the hydraulic diameter is developed [11]. The Reynolds number and Nusselt number based on hydraulic diameters are: (10) (11) The flow is presumed to be in the same direction as the axis (Fig. 6). Periodic momentum and thermal boundary conditions are used on the entry and exit surfaces of the REV model such that the flow being simulated is representative of a fullydeveloped flow through a central region of the porous matrix. The solid surfaces are maintained at a uniform and constant temperature in the REV simulations. Pressure drop and interfacial heat transfer correlations for use in the compressor analysis are extracted from the results of these simulations. where, The heat transfer correlation is given by [11]: (12) (13) (14) It is plotted with the data from the various CFD runs in Fig. 8. 5

6 Fig. 8. Dimensionless numbers based on hydraulic diameter,, computed from CFD runs on the REV with various values of the three dimensions and various flow velocities [11] Equation (14), developed based on different geometries given in terms of plate length,, plate distance,, plate thickness,, but generalized in terms of hydraulic diameter is used in the compressor analysis to assess the compression efficiency for different interrupted-plate inserts. The compression efficiency is defined by Eq. (3). In order to calculate the efficiency, the pressure vs. volume trajectory during compression in a compressor volume containing the interrupted-plate insert must be obtained. This can be evaluated using the Zero-D compression model given by Eqns. (7) and (8). The interfacial heat transfer coefficient that couples Eqns. (7) and (8) can be obtained from the Nusselt number correlation: (15) In addition, since the interrupted-plate has a flow resistance, this must be included in the calculation of compression efficiency. Thus, a pressure drop term must be added to the work in Eq. (3) to account for pressure drop work to the liquid of the piston. At any time, this pressure drop is computed in terms of the length of the porous section through which liquid passes, : (16) where, and are obtained from CFD simulations. The results of this analysis show that, in general, decreasing the separation distance between plates in the interrupted plate insert leads to improved efficiency. For a given plate separation distance, decreasing the plate length improves efficiency, as shown from a simple boundary layer development analysis. The results are given in Fig. 9 (from [11]) Heat transfer and pressure drop for a fixed shape Analyses in this section are focused on an interrupted-plate insert with the following shape parameters:,,. Simulations are done at eleven different Reynolds numbers,, ranging from 0.67 to Three different runs are computed at while varying the density of the air flow and the mass flow rate. Each is a single CFD run. Commercial CFD Software ANSYS FLUENT is used and the model is used for turbulence closure. The REV models have periodic momentum and thermal boundary conditions. The formulation and boundary conditions are the same as those discussed in [11]. The number of computational cells varies with Reynolds number; specifically: 169,632 for, 588,816 for, 1,357,056 for, and 2,024,352 for. These grid cells have been verified by gridindependence studies. From the CFD simulations, heat transfer coefficients and pressure drop terms are obtained. The area-averaged surface heat transfer coefficient depends on both flow velocity and density, as shown in Fig. 10. The Reynolds numbers and Nusselt numbers given by Eqns. (10) and (11) are calculated and plotted in Fig. 11. The data are fit using a least-square method to yield the following correlation: (17) The pressure drop terms also can be determined from CFD simulations. The pressure drop, written as a momentum source term, is given by the following governing equation: (18) From the CFD results, the permeability, K, as well as the Forchheimer coefficient,, are computed:, Thermal dispersion analysis for a fixed shape When volume averaging is applied to the energy equation, a thermal dispersion term appears. It is associated with spatial variations of velocity and temperature within the pores of the matrix. It is anisotropic in that a value found for streamwise dispersion is different than a value found for cross-stream dispersion. In this section, the streamwise thermal dispersion term for x-direction flow (see Fig. 6) is calculated based on CFD runs on the REV model for the interrupted plate insert and, and. The term is: (19) The streamwise thermal dispersion term is modeled using the dispersion conductivity,, (20) Cross-stream dispersion is computed similarly, but the velocity component for transport is normal to the streamline. The dispersion conductivity is normalized based on the air conductivity and plotted against the Peclet number. The results are shown in Fig. 12. The Peclet number dependency is expected since dispersion transport is by mechanisms that are velocity dependent. One of the dispersion mechanisms is, by nature, similar to eddy transport in turbulent flow. For porous media, the eddies are within the pores and scale on pore size. 6

7 (a) Fig. 11. Heat transfer correlation for the interrupted-plate:,, (b) Fig.12. Streamwise dispersion conductivity for x-direction flow (c) Fig.9. Compression efficiency of different interrupted-plate insert shapes; pressure compression ratio=10, [11] Pressure drop values for the metal foams have been measured in [12]. The setup is shown in Fig. 13 (a). Air flow is driven by a fan, as shown. The flow rate of air is adjusted by a manual valve. A Sierra TopTrack 822S flowmeter is used to measure the volumetric flow rate. The pressure drop, due to the metal foam insert, is measured using a micro-manometer and the pressure tap shown. The micro-manometer has an uncertainty of 0.125Pa. The uncertainty of the measured Darcian velocity is 1.5%. The results are shown in Fig. 13 (b). The pressure drop is a momentum sink term in the momentum equation. It can be modeled using the form of Eq. (18). The results from the measurements lead to the coefficients: 10PPI metal foam:, 40PPI metal foam:, Fig. 10. Area-averaged surface heat transfer coefficient 2.3. Porous metal foam The fine-scale geometry of the metal foam is randomly variable (over a feature size range) and essentially unknown to the numerical modeler. Computing the pressure drop, heat transfer and dispersion terms for representative, repeated geometries and combining them statistically would be approximate and tedious. Thus, we have chosen to determine the pressure drop and interfacial heat transfer terms through experiments and simulation. The dispersion term for the foam matrix is discussed later. The indicator PPI refers to the nominal number of pores per inch, a frequently-used descriptor of these foams. We used two foams in this study, as noted above and in Fig. 5(b). The following discusses how the porous foam interfacial heat transfer Nusselt was determined from compression experiments. First, the experiment is described. A schematic of the experimental setup is shown in Fig. 14. Water is circulated in the clockwise direction of the figure. A relief valve is installed between the pump and the remainder of the system to limit pressure to a maximum of 11 atm. (165 psia). The volume of water that enters the compression chamber is measured continuously using an Omega FTB-1412 turbine flow meter. 7

8 The upstream pressure is maintained approximately constant by the control valve. Downstream of the control valve is the compression chamber, a polycarbonate cylinder with length 353 mm and internal diameter 50.8 mm. A 16-bit analog input board is used to communicate with the lab controller using MATLAB/Simulink. The sampling frequency is 4kHz. Two experimental runs each are conducted with 10PPI and 40PPI metal foam inserts. Instantaneous values of volume and pressure are computed from the data and instantaneous gas-volumeaverage temperatures are calculated using the ideal gas law. Fig.14. Schematic of the experimental setup used to select the optimum open-cell metal foam heat transfer correlation [12] (a) Schematic of the experimental setup (a) 10PPI metal foam insert (b) Results of pressure drop measurements Fig. 13. Pressure drop from the experiments [12] The experimental runs were simulated using the Zero-D model (Eqns. (7) and (8)) by substituting different heat transfer correlations found from the literature. The experimental data are shown in Fig. 15 (taken from [12]). By comparison to these data, a modified version of the Kamiuto heat transfer correlation was selected as the most suitable heat transfer model for these metal foams, as discussed in [12]: (21) where is the Darcian velocity, the velocity that the fluid would have in the absence of the solid Simulations of a compressor filled with metal foam Simulations of liquid piston compression with inserted metal foam matrices were conducted [12]. Numerical modeling of the problem combines Volume of Fluid (VOF) and twoenergy equations, one for the fluid and a second for the solid. Thus, we solve for energy transport in the fluid and solid phases and couple the two through the interfacial heat transfer correlation. The VOF method tracks the instantaneous location of the water/air interface in the compression chamber. Let subscripts 1 and 2 represent air and water, respectively. The continuity equations for air and water are: (b) 40PPI metal foam insert Fig. 15. Comparison of experimental results to the Zero-D model solutions obtained by using different heat transfer correlations (Variables are non-dimensionalized by their initial values). [12]. Correlations: Fu et al. [14], Kamiuto and Yee, [13], Kuwahara et al. [15], Nakayama et al. [15], Wakao and Kaguei [16], and Zukauskas [17]. (22) and (23) Momentum and energy equations are solved for the immiscible fluid mixture, (24) where (25) 8

9 The stress tensor,, is based on viscosity of the mixture of air and water in nodes that contain the liquid-gas interface, (26) The momentum sink term, is given by Eq. (18). The energy equation for the fluid is, ( ) where and The energy equation for the solid is ( ) (27) (28) (29) (30) Next, CFD simulations are conducted using the commercial software ANSYS FLUENT and its VOF solver using userdefined-function scripts to include changes in the governing equations for two-energy equation (solid and fluid) modeling of the porous medium. Results (taken from [12]) show that when the entire length of the chamber is occupied by metal foam insert, the velocity streamlines are smooth (see Fig. 16). But, when only a portion of the chamber is occupied by the porous insert, flow is stable in the porous insert region but vortices develop in regions outside the porous insert. A study of the computed flow field indicates that optimization of the distribution of porous inserts in the chamber may be done to achieve minimal temperature rise of air during compression and best compression efficiency. This optimization study is ongoing. (a) 10PPI metal foamfulllyinserted in the chamber,, (b) 10PPI metal foampartiallyinserted in the chamber,, Fig. 16. CFD simulations on the chamber with metal foam insert (note that up is to the right in this figure) 2.5. Adding thermal dispersion In this section, a CFD simulation of one of the faster compression cases in [12] is conducted, but thermal dispersion is added. The chamber is fully occupied by the 10 PPI foam. The chamber length and radius are, respectively: m and m. The foam characteristic diameter,. The compression speed and total compression time are: m/s and 1.3 s. The continuity, momentum, and energy equations for the solid phase are given by Eqns. (22) through (24) and (30). The energy equation for the fluid mixture is given by: ( ) ( ) (31) The thermal dispersion term is modeled as, (32) 9

10 Kuwahara and Nakayama [18] proposed a thermal dispersion model for 2-D cross flow over small square rods: (33) (34) gradients in the flow for that case and the resulting higher heat transfer. Thermal dispersion has an influence on the bulk temperature when temperatures and temperature gradients rise to the point where dispersion becomes significant. The flow fields at two times during compression are shown in Fig. 18. The warmer region is in the upper portion of the chamber in which the velocities, heat transfer coefficients and thermal dispersion coefficients are low. (35) (36) where is the local streamwise direction and is the local cross-streamwise direction. In this example, this model is implemented in Eqns. (31) and (32) for the CFD simulation. The bulk temperature rise of the air is computed and compared to a simulation of the same case but without thermal dispersion (Fig. 17). Results of both cases show that, though the compression time is very short and isentropic compression would lead to a temperature of 575K, the insert is effective in suppressing the temperature rise. Further, they show that during the latter period of compression, the calculated temperature of the case with dispersion is less. This is due to larger thermal Fig. 17. Bulk temperature of air Fig. 18. Temperature field and velocity streamline (note that up is to the right in this figure) 3. Conclusions A compressed air energy storage system designed for use in wind turbine plants was introduced and the importance of thermal control during compression and expansion was emphasized. A compressor design was proposed and models for its analysis were presented. Noted in modeling was a need for sub-models to characterize pressure drop in the porous insert, heat transfer from fluid to solid phases of the insert and thermal dispersion within the insert. Such models were presented for two candidate inserts, one based on interrupted plates and another based upon metal foams. The models came from detailed computation of a representative elementary volume, in the case of the interrupted plate, and from experiments, in the case of the foam. Computational results using these models for the foam insert case were presented. The inserts are very effective in suppressing temperature rise. Computed results that compare a case with a completely-filled chamber and a case having the insert partially filling the chamber show that the insert stabilizes the flow where present; but, beyond the insert, there is a tendency for development of secondary flows. A study in which dispersion was added to the analysis showed that its effect is small and in the direction of reducing the maximum average temperature reached during compression. Dispersion weakens temperature gradients in the fluid, increasing near-wall gradients, and heat transfer to the walls. Acknowledgments This work is supported by the National Science Foundation under grant NSF-EFRI # and University of Minnesota, Institute for Renewable Energy and Environment (IREE) under grant: RS The authors thank also the Minnesota SuperComputing Institute for the computational resources used in this work. 10

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