Cellular materials have found very wide spread application for thermal insulation. The best thermal insulators are made from polymers (with intrinsic low thermal conductivity) that are foamed in the liquid state to create closed cell foams of very low density. Most of these materials on their own are not strong, but if they are used as the core of a sandwich panel or injected into the spaces within a hollow load supporting structure, they can enable structures that support stresses (like the wall or roof of a house) to also have a very high thermal resistance. They are therefore examples of bi-functional structures.
Open cell foams, and especially lattice-type cellular structures made from intrinsically high thermal conductivity materials such as copper and aluminum offer a different means of thermal management. Figure 1 shows an example of a bi-functional heat exchanger that also supports bending loads. In this example the faces and the core of the sandwich are made of a material with high thermal conductivity. Heat incident on one of the faces is conducted into the core, Figure 2, where it spreads into many trusses. A coolant that flows through the core is then in contact with a very high surface area of heated truss material and this very efficiently transfers (convects) heat from the core to the coolant providing a means for heat removal from the heated face.
Figure 1: Example of a multifunctional heat exchanger that uses an open cellular core sandwich panel for both bending stress support and thermal dissipation
Figure 2: Schematic illustrations of some of the heat transfer mechanisms active in metallic sandwich panels with cellular cores.
Advances by our group in the manufacture of cellular metals now enables great design flexibility. Figure 3 shows a simple example of a copper lattice core used in a heat exchanger. The square and diamond lattices have similar surface areas that would be in contact with a cooling flow, but the top (and bottom) surfaces in contact with the faces through which heat must flow are very different. As a result, the rate of heat transfer into the core can be adjusted (even along the length of the structure). In some applications the pressure needed to pump a coolant through the core drives design more than the thermal flux to be dissipated. Figure 4 shows a sandwich whose core has very low pressure drops for flows that travel in the channels between the trusses (in directions parallel to the square edges of the panel).
Figure 3: Photographs of high thermal conductivity copper cellular structures with (a) square and (b) diamond cell topologies. Note that the area of heat transfer from face sheet to core and the surface area exposed to a cooling flow can be manipulated by cell topology design.
Figure 4: Example of a an aluminum sandwich panel heat exchanger with a pyramidal lattice core.
These cellular concepts can compete with other state of the art designs for heat exchange. Figure 5 plots the Nusselt number (a measure of for the heat exchange core against the Reynolds number of a flow that cools it. The Nusselt number characterizes the ratio of convective to conductive heat transfer across a surface. A high Nusselt number is therefore indicative of efficient transfer of heat from the cellular structure to the coolant. Cellular metals like those shown in figures 3 and 4 are very good at heat transfer. If the pumping power needed to drive the coolant through the structure is as important to a design as the heat transfer, we can divide the Nusselt number by the friction factor, f, of the structure. This is plotted, again against Reynolds number (that is flow velocity) for a variety of heat exchange media in Figure 6. Cellular metals are now not quite as good as louvered fins or just empty channels, but they offer structural load support which these other concepts do not. They may even offer energy absorption opportunities during an impact so the same mass of material could simultaneously serve three purposes - heat exchange, stress support and impact protection – a true multifunctional material.
Figure 5: Comparison of the Nusselt number (a measure of heat transfer) as a function of coolant flow velocity (indicated by the Reynolds number) for vaarious heat exchange concepts.
Figure 6: A comparison of the Nusselt number divided by friction factor (merit index) for various heat exchange concepts. Pyramidal lattice heat exchangers have both a high figure of merit for heat exchange and excellent stress support.
A related multifunctional thermal management structure is shown in Figure 7. In this case a low thermal conductivity metallic (say stainless steel) sandwich panel with a low relative density pyramidal lattice core is filled with a polymer foam insulator. These panels offer high bending resistance, excellent thermal resistance and super corrosion resistance.
Figure 7: Example of a stainless steel lattice core sandwich structure with excellent bending resistance
In some engineering applications very high thermal fluxes are locally applied to a structure. This can cause serious thermomechanical problems as well as the usual concern about thermal degradation of the hot spot. Examples include the impingement of jet engine exhaust plumes on structures or the leading edge of hypersonic vehicles (or leading edges on of reentry protection systems on space craft). Our group has explored novel approaches for solving such problems and again, they exploit our understanding of materials, the opportunities presented by cellular concepts and knowledge of the physics of heat and mass transport. A basic concept is shown in Figure 8. Here we have created a sandwich panel from an aluminum alloy that has a crucifix core (a form of truncated square honeycomb structure) with excellent out of plane compressive strength yet facilitates complete fluid communication inside the panel, Figure 8(a). We then coat all the interior surfaces with nickel foam that serves as a wicking material, Figure 8(b), and seal up the sides of the plate structure. We then partially evacuate the interior of the panel and fill the empty spaces in the nickel foam with a working fluid to convert the panel into a heat plate.
Figure 8:Multifunctional heat plate where the crucifix (truncated square honeycomb) core is covered with a metal foam wick enabling the interior of the structure to function as a heat plate.
Heat plates (or pipes) work by converting a local thermal flux into vaporized working fluid. The increased gas pressure above the region of evaporation then drives a fast (sometimes sonic velocity) flow to a cooler area of the structure where it condenses releasing the latent heat of evaporation. The new liquid is then drawn by capillarity through the wick to replenish the material evaporated. This closed system is able to transport very high thermal fluxes and quickly get the heat from a localized hot spot to the rest of the structure so that it isothermalizes. The performance of the system is strongly influenced by the working fluid. Figure 9 shows the temperature dependence of a figure of merit (defined in the figure caption) of several working fluids. Water is good for near ambient temperature applications while sodium and other liquid alkali metals are best for high temperature applications. Water was used in the panel shown in Figure 9 and to avoid its reaction with aluminum (to form noncondensable hydrogen) we had first coated the inside of the aluminum structure with electroless nickel.
Figure 9: Heat pipe working fluid figures of merit = σ1Lρ1μ1where σ1is the surface tension, L is the latent heat of vaporization, ρ1 is the liquids density and μ1 the liquids viscosity.
Figure 10 shows the back surface of two 60 cm x 60 cm panels that were locally heated at the center of their front faces (by a propane torch). It can be seen that the heat plate never reached the high temperature of the solid aluminum panel and the temperature was much more uniform eliminating the thermal gradients that would damage the material over time. Our group tries to understand the fundamental heat transport phenomena active within these structures, and combines this with clever fabrication concepts to design novel thermal management solutions.
Figure 10: Thermal images of the rear of 60 cm x 60 cm x 2.5 cm plates subjected to an intense thermal source at the center of the front face. (a) A solid aluminum plate. (b) the heat plate shown in figure 8 using water for the working fluid. Note how the hot spot has been eliminated in the heat plate.
Sometimes we work on large scale challenges. A good example is the jet blast deflector shown in Figure 11. This structure is 14 feet high and about 36 feet wide. Aircraft drive over the panels when they are stowed (flat) on a surface. They then rise to an angle of 50° and deflect the exhaust plume of a jet engine upwards so structures (or people) behind the engine are not harmed. Such panels need to deflect the jet plume, dissipate the heat (so they next plane that crosses does so safely) and is sufficiently strong that it can support the weight of an aircraft. The novel concept shown in Figure 11 uses heat plates to spread the heat uniformly and a cool air flow through the interior of the panels to dissipate the thermal energy of the impinging plume. It is configured as a sandwich panel with very high bending resistance. A clever feature of this design is the use of a mixer (or ejector) plate to use the jet plumes momentum to increase the air flow through the interior of the panel. Figure 12 shows how the ejector works to help draw air up through the interior of the structure. Figure 13 shows a photograph of a 6 foot wide module just prior to (successful) testing with a jet engine at Virginia Tech.
Figure 11: Schematic illustration of a jet blast deflector that exploits multifunctional heat exchanger concepts developed by our group. The front and back faces and the webs of the core are heat plates. The deployable mixer plate is an ejector. It induces cooling air to flow up through the core of the sandwich structure.
Figure 12: Schematic illustration of the mixer used in the multifunctional jet blast deflector. The air flow over the top of the panel “pulls” air through the heat exchanger core.
Figure 13: Photograph of a 18 ft x 10.5 ft test stand with central (6 ft wide) heat plate jet blast deflector prior to engine testing.
Heat plates do not have to be flat. They can be folded to create a leading edge thermal protection structure! An example is shown in Figure 14 and some photographs of assembled panels are shown in Figure 15. The leading edges of hypersonic vehicles, especially those that fly at low altitude, must cope with some of the highest thermal fluxes encountered in engineering structures. These heat plate structures appear to provide a promising approach to a robust thermal management technology; one that might not fail when impacted by ice during lower speed flight as sadly happened with one of the space shuttles.
Figure 14: An example of a heat plate leading edge for a hypersonic vehicle. Our most recent designs use nickel base super alloy cases, nickel foam wicks and liquid sodium for the working fluid and protect leading edge structures at speeds in excess of Mach 5 at low altitude.
Figure 15: Photograph of some of our (partially evacuated) leading edge heat plate structures.
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Thermal Hydraulic Performance of Sanwich Structures with Wire Mesh Core and Embedded Heat Pipes, T. Tian, T.J. Lu, H.P. Hopson, D.T. Queheillalt, H.N.G. Wadley, 13th International Heat Pipe Conference, Shanghai, China 2004.
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Thermal Response of a Flat Heat Pipe Sandwich Structure to a Localized Heat Flux, G. Carbajal, C.B. Sobhan, G.P. Peterson, D.T. Queheillalt, H.N.G. Wadley, International Journal of Heat Mass Transfer, 49, p. 4070-4081, 2006.
A Magnetohydrodynamic Power Panel for Space Re-Entry Vehicles, Craig Steeves, Haydn N.G. Wadley, Richard B. Miles, Anthony G. Evans, Journal of Applied Mechanics, 74, p. 5195-5207, 2007.
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A Quasi 3D Analysis of the Thermal Performance of a Flat Heat Pipe, G. Carbajal, C.B. Sobhan, G.P. "Bud" Peterson, D.T. Queheillalt, Haydn N.G. Wadley, International Journal of Heat and Mass Transfer, 50, p. 4286-4296, 2007.
Metallic Structural Heat Pipes as Sharp Leading Edges for MACH 7 Vehicles, Craig A. Steeves, Lorenzo Valdevit, Hossein Haj-Hariri, Ming Y. He, Scott Kasen, Haydn N.G. Wadley, ASM Proceedings of IMECE, 2007.
A Multifunctional Heat Pipe Sandwich Panel Structure, Douglas T. Queheillalt, Gerado Carbajal, G.P. Peterson, Haydn N.G. Wadley, Journal of Heat Mass Transfer, 51, p. 312-326, 2008.
Feasibility of Metallic Structual Heat Pipes as Sharp Leading Edges for Hypersonic Vehicles, Craig A. Steeves, Ming Y. He, Scott D. Kasen, Lorenzo Valdevit, Haydn N.G. Wadley, Anthony G. Evans, Journal of Applied Mechanics, 76, p. 031014-1 - 031014-9, 2009.
Multi-Scale Pore Morphology in Vapor Deposited Yttria-Stabilized Zirconia Coatings, D.D. Hass, H. Zhao, T. Dobbins, A.J. Allen, A.J. Slifka, H.N.G. Wadley, Materials Science and Engineering A, 527, p. 6270-6282, 2010.