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Metal Foams as Novel Compact High Performance Heat Exchangers Transport Phenomena in Emerging Technologies Doctoral Level Research Projects Contact: Professor Dimos Poulikakos |
1 Introduction
Current trends in the development of electronics require large amounts of heat to be developed for electronic components to meet their high performance demands. Complicating this issue is the miniaturization of componentry. The loss of surface area from which heat can be dissipated exponentially increases the heat flux required to maintain operating temperatures within reasonable material limits. A fitting example of this type of componentry is the insulated gate bipolar transistor, know as the IGBT for short. An individual IGBT measures 0.8 cm2, but conducts up to 12 amperes of current while simultaneously dissipating up to 100 Watts of heat to maintain a reasonable operating temperature. The individual IGBT chips are typically assembled in a module consisting of three IGBT chips. These modules are then assembled into a larger array consisting of eight modules. The relatively close proximity of each module and each individual IGBT chip inside the module results in a large package with substantial heat dissipation requirements. Current heat exchanger designs rely on high volumetric coolant flow rates to keep the temperature of the coolant in the heat exchanger low, thereby maintaining a large temperature difference between the coolant and the heat generating component. This large temperature difference compensates the relatively high thermal resistance between the coolant and the simple straight-flow heat exchanger assembly. Reducing the thermal resistance between the coolant flow and the heat exchanger assembly would allow smaller pumps to be used, thereby saving on initial and operational costs. Improvements in the performance of the heat exchangers without altering the coolant can take shape by increasing the following design factors:
effective convection surface area
thermal conductivity of the construction material
level of the coolant mixing inside the heat exchanger Realizing the improvements listed above in a single heat exchanger design can be a daunting task. Recently, however, a substance has been designed and manufactured which could possibly accomplish all three of the above listed factors while still being cost-effective. This material is open cell metal foam. Metal foams are can be viewed as well designed heat exchangers through their complex form designed by nature. Foam is created by a surface energy minimization process which simultaneously balances the pressure between the individual gas cells, the pressure in the liquid borders between the cells, the surface tension of the liquid, and gravity-induced foam drainage.
2 Metal Foams
A foam is the resulting two-phase combination created by dispersing a gas through a liquid without completely dissolving the gas, which is very similar to a general combination of two immiscible liquids called an emulsion. However, in contrast to an emulsion, a foam must have a gas phase. The gas phase then further defines the foam separately from that of emulsion by the foam’s well-defined cellular structure its associated porosity. All foams are manufactured by some process which distributes a gas through a liquid in order to obtain this well-defined structure. There are numerous types of foam manufacturing, but they derive from one of these basic four methods [1]:
blowing gas through a nozzle in a liquid
blowing gas through a porous plug (sparging)
the nucleation of gas bubbles in a supersaturated solution
mechanical agitation of a liquid while in contact with a gas Depending upon the particular open cell metal foam configuration, the specific surface area of an open cell metal foam varies between approximately 500 m2/m3 to over 10,000 m2/m3 in compressed form [2]. The metal matrix can be manufactured from a solid with a high thermal conductivity, such as an aluminum alloy (ks ~ 200 W·m-1·K-1) or a copper alloy (ks ~ 400 W·m-1·K-1). Merely by its presence in a static fluid, this solid phase dramatically increases the overall thermal conductivity of the fluid-solid system by more than the most general of all volume averaged thermal conductivity equations, which does not consider the geometry of the solid [3].
![Figure 1: A heat exchanger manufactured from a compressed aluminum foam.](https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fwww.ltnt.ethz.ch%2Fimg%2Fimage001.png) |
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Figure 1: A heat exchanger manufactured from a compressed aluminum foam.
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3 Heat Transfer Experiments
Open cell metal foam heat exchangers as depicted in Figure 1 of varying porosities and compression ratios were tested for their performance as heat exchangers. This included both the hydraulic as well as the thermal characteristics. The hydraulic characteristics included the permeability and the form coefficient as explained in [4] and [5]. A detailed summary of the hydraulic testing procedure can be found in [4]. The heat transfer analysis of the foams include the standard convection coefficient and corresponding Nusselt number. The ultimate presentation of the results is the comparison of a these open cell metal foam heat exchangers against commercially available heat exchangers. Below is a diagram of a the pumping power vs. the thermal resistance for the open cell metal foams and the commercially available heat exchangers [6]. The foams are labeled by “95-02” where the first two digits signify the precompression foam porosity and the second two digits give the compression factor of the foam. Foam 95-02 was 95% porous before compression and then compressed by a factor of two. Ideally, the most efficiently working heat exchanger approaches the origin of the plot with a required pumping power of zero with zero thermal resistance. Since this is not possible in reality, the best heat exchangers are those that approach the origin. All the foams with the exception of foam 95-08 generated thermal resistances that were approximately half of those produced by the commercially available heat exchanger configurations, showing their improvement in efficiency through their optimal heat exchanger design.
![Figure 2: Plot of the required pumping power vs. the thermal resistance of the metal foam heat exchangers and several commercially available heat exchanger configurations.](https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fwww.ltnt.ethz.ch%2Fimg%2Fimage004.jpg) |
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Figure 2: Plot of the required pumping power vs. the thermal resistance of the metal foam heat exchangers and several commercially available heat exchanger configurations.
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4 Numerical Simulations Introduction
There have been several approaches taken to model the fluid flow through porous media, both analytical or numerical. These models progressed beginning with regularly packed beds of spheres, then to more porous fibrous media, and finally to open cell metal foams. Modeling the fluid flow through the foam is significantly more difficult than solving the flow through packed beds of spheres due to the foam’s more intricate geometry and the higher porosity of the foam. Both of these factors may contribute to more complex flow patterns within the medium. However, many of the existing analytical and numerical models based on flow through granular media have been adapted to describe the fluid flow and the heat transfer within open cell metal foams with limited success. These issues can be overcome by taking a new approach to viewing the highly porous open cell metal foam medium and attempting to recreate the geometry by defining a representative elementary volume (REV) that captures the intricate details of the foam structure (Figure 3). Applying periodic boundary conditions over the surfaces of the periodic cell unit recreates the existence of an infinitely large foam matrix, thus allowing the pressure drop over a much larger foam matrix to be accurately solved with a grid of limited size. The only difficulty is creating a fitting boundary condition over the inlet-outlet pair. The flow velocity between the inlet and outlet boundaries must remain identical, but at the same time, a flow-driving component must be applied. This is quite often done by writing the solver to include a uniform pressure drop from one point on the inlet boundary to the its corresponding point on the outlet boundary [7]. However, using CFD-ACE, it becomes much simpler by defining a pseudo-periodic boundary condition over the inlet-outlet pair which forces a set volumetric flow rate through the inlet.
![Figure 3: Close-up of a single cell in an uncompressed open cell metal foam.](https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fwww.ltnt.ethz.ch%2Fimg%2Fimage006.jpg) |
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Figure 3: Close-up of a single cell in an uncompressed open cell metal foam.
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5 Periodic Cell Structure Reproduction
After deciding to take the approach of a detailed cell reproduction, the next step is recreating what is to be considered the most representative cell structure of an open cell metal foam. Because the open cell metal foams that were used in the experiments were manufactured following the DUOCEL [2] production process, the structure of the foam takes on the shape of a foamed polymer (Figure 3), and not a molten metal that generates a closed cell foam which lacks an easily distinguishable cell geometry [1]. The polymer foam in the DUOCEL production process takes on a surface tension dominated shape. This simplifies the cell modeling process when a surface minimization program is used, such as Surface Evolver [8, 9]. Through the use of Surface Evolver, the numerically optimized ideal periodic shape of a foam can be modeled and then meshed for importation into a flow solver with periodic boundary conditions and a prescribed volumetric flow rate in the longitudinal direction. The pressure drop from the flow simulations can then be compared to the pressure drop data obtained from the flow experiments that were performed on the uncompressed foam blocks as reported in [4] as a validity check on the numerical approach.
![Figure 4: The idealized foam structure through which the flow is solved using CFD-ACE with periodic boundary conditions and a flow-driving volumetric flow rate in the main flow direction.](https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fwww.ltnt.ethz.ch%2Fimg%2Fimage008.jpg) |
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Figure 4: The idealized foam structure through which the flow is solved using CFD-ACE with periodic boundary conditions and a flow-driving volumetric flow rate in the main flow direction.
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6 Solution Procedure
The previously shown structure was gridded to varying degrees of refinement and these grids were imported into an unstructured grid flow solver to solve the flow field. The unstructured flow solver implemented was CFD-ACE, which is licensed and distributed by CFDRC of Huntsville, U.S.A. The steady flow through each of the grids was first solved by using an upwind scheme with an algebraic multi-grid solver and a convergence criterion of 1 ´ 10-8 to provide an initial condition for the central solving scheme, which was used for a more accurate solution of the flow field in the reported results. The grids were scaled so that the average diameter of the cells corresponded to that of the 40 PPI foam that was tested in [4] which was 2.3 mm. The flow rate for the initial tests was set in the periodic boundary subroutine over the inlet and exit to target an average flow velocity of 0.075 m/s, which corresponded to volumetric flow rate of 1.587 ´ 10-6 m3/s or, with water as the working fluid, a mass flow rate of 0.001582 kg/s.
7 Flow Visualization
The following two figures show some visualization of one of the grids with the lowest test flow rate of 1.5870 x 10‑6 m3/s. Note the complexity of the flow pattern even with a low flow velocity in Figure 5. Also, the accuracy of the longitudinal velocity of the pseudo-periodic boundary condition over the inlet-outlet pair is shown in Figure 6.
![Figure 5: A snapshot of the fluid flow trace lines through the flow domain. The color gradient on the surface of the cell represents the static pressure on the surface of the cell.](https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fwww.ltnt.ethz.ch%2Fimg%2Fimage010.jpg) |
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Figure 5: A snapshot of the fluid flow trace lines through the flow domain. The color gradient on the surface of the cell represents the static pressure on the surface of the cell.
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![Figure 6: Color maps of the longitudinal velocity component over the inlet-outlet pair. Note the accuracy of the pseudo-periodic boundary condition with a prescribed volumetric flow rate.](https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fwww.ltnt.ethz.ch%2Fimg%2Fimage012.jpg) |
![](https://img1.daumcdn.net/relay/cafe/original/?fname=http%3A%2F%2Fwww.ltnt.ethz.ch%2Fpix%2Fblank.gif) |
Figure 6: Color maps of the longitudinal velocity component over the inlet-outlet pair. Note the accuracy of the pseudo-periodic boundary condition with a prescribed volumetric flow rate.
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8 Conclusion
From this work using CFD-ACE to model the flow through a representative volume of a periodic lattice structure of an open cell metal foam, the implementation of the pseudo-periodic boundary condition generated results which compared well to the pressure drop measurements attained in experiments on open cell metal foam blocks of similar configurations in a range of flow velocities. It was also shown that the pseudo-periodic inlet-outlet boundary condition with a set volumetric flow rate works very well at emulating a periodic boundary condition.
9 Bibliography
- Baumeister, J., 1997, "Überblick: Verfahren zur Herstellung von Metallschäumen," presented at Symposium Metallschäume, J. Banhart, Metall Innovation Technologie MIT, Bremen, Germany, pp. 3-14.
- ERG, 1999, Duocel Aluminum Foam Data Sheet., ERG Material and Aerospace, Oakland.
- Boomsma, K. and Poulikakos, D., 2001, "On the effective thermal conductivity of a three-dimensionally structured fluid-saturated metal foam," International Journal of Heat and Mass Transfer, 44, pp. 827-836..
- Boomsma, K. and Poulikakos, D., 2002, "The Effects of Compression and Pore Size Variations on the Liquid Flow Characteristics of Metal Foams," Journal of Fluids Engineering-Transactions of the Asme, 124, pp. 263-272..
- Lage, J. L., 1998, "The Fundamental Theory of Flow Through Permeable Media from Darcy to Turbulence," in Transport Phenomena in Porous Media, D. B. Ingham and I. Pop, Eds., Elsevier Science, Ltd., Oxford, pp. 1-30..
- Boomsma, K., Poulikakos, D., and Zwick, F., in press, "Metal Foams as Compact Heat Exchangers," Mechanics of Materials..
- Patankar, S. V., Liu, C. H., and Sparrow, E. M., 1977, "Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area," Journal of Heat Transfer-Transactions of the ASME, 99, pp. 180-186..
- Brakke, K., 1992, "The Surface Evolver," Experimental Mathematics, 1, pp. 141-165..
- Phelan, R., Weaire, D., Peters, E. A. J. F., and Verbist, G., 1996, "The conductivity of a foam," Journal of Physics: Condensed Matter, 8, pp. L475-L482.
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