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Analysis on the heat transfer characteristics of a micro-channel type porous-sheets Stirling regenerator
Author: Li Zhigang | Print | Close | Text Size: A A A | 2016-10-29

To avoid the high flow frictional loss associated with conventional wire mesh Stirling regenerators, a micro-channel type stacked porous-sheets Stirling regenerator is investigated. An analytical solution is derived for the transient heat transfer characteristics of the fully developed reciprocating laminar flow under prescribed wall temperature profiles. The complex Nusselt number (Nu) is expressed as a function of kinetic Reynolds number (Rew) and Prandtl number (Pr). At low Reu of less than 10, the real part of Nu has an almost constant value of 6.0, approximately equal to the known real-valued Nu for the fully developed unidirectional laminar flow under constant wall heat flux, while the imaginary part is negligible, thus “scaling effect” can be utilized to enhance heat transfer. At higher Rew, both the real and imaginary parts of Nu increase with the increase of Rew and Pr, and the phase shift between the temperature difference and the heat flux gradually increases and approaches 45°. Approximate analytical solutions are also deduced for the entrance region from the integral boundary layer equations in both cases of “Thermally developing flow” and “Simultaneously developing flow”. The heat transfer is enhanced in the entrance region and the local Nu in the flow direction approaches the corresponding values of fully developed flow. The analytical results are confirmed by dynamic mesh CFD results, and the obtained Nu~ Rew data and patterns generally agree with available analytical and experimental data from published literatures. Application of the analytical results to the design and optimization of Stirling regenerator are also shown.

The regenerator is stacked by hundreds of porous, stainless steel sheets fabricated through an etching process, each having hundreds of through holes, as shown in Fig. 1, the holes of all sheets being aligned with each other and inserted into a cylindrical container, so as to form hundreds of micro-channel flow passages for the internal reciprocating working gas. One of the flow channels including the entrance region is illustrated in Fig. 2. The axial continuity of the solid matrix is interrupted by the intermediate clearance between adjacent sheets while maintaining the flow smoothness, which is intended to effectively increase the longitudinal contact resistance, and thus to reduce the axial heat conduction loss. The cross section of the flow channel is assumed as circular for the ease of analysis.

In this work, the heat transfer characteristics of the reciprocating laminar flow in a micro-channel type porous-sheets Stirling regenerator including the entrance effects are analytically or quasi-analytically investigated to facilitate the efficient design and optimization of Stirling engines, from which the following major conclusions can be drawn.

(1) For fully developed reciprocating laminar flow,    is expressed as a function of Rew and Pr. At low Rew of less than 10, Real [  ] and has an almost constant value of 6.0, approximately equal to the known real-valued Nu for the fully developed unidirectional laminar flow under constant wall heat flux, while Imag [  ] is negligible, thus “scaling effect” can be utilized to enhance heat transfer. At higher Rew, both Real [  ] and Imag [  ] increase with the increase of Rew and Pr, and the phase shift between the fluid-wall temperature difference and the wall heat flux gradually increases and approaches 45°.

(2) Heat transfer is enhanced in the entrance region, and Nux axially approaches the constant value of the fully developed flow. Compared to the “Thermally developing flow”, the “Simultaneously developing flow” has much thinner thermal boundary layer, higher Nux and longer thermal entrance length.

(3) The analytical solutions generally agree with the dynamic mesh CFD results, and the obtained Nu~ Rew data and patterns generally agree with available analytical and experimental data from published literatures.

The results have been published on INTERNATIONAL JOURNAL OF THERMAL SCIENCES Volume:94 Pages:37-49.

 
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