New Regenerator Design For Cryocoolers

Transcription

1 New Regenerator Design For Cryocoolers I. Rühlich and H. Quack Technische Universität Dresden, Lehrstuhl für Kälte- und Kryotechnik, D Dresden, Germany The comparison of different heat transfer surfaces shows a large potential to improve regenerators, concerning their ratio between pressure drop and heat transfer. With the use of computational fluid dynamics (CFD), shapes and arrangements of matrix elements were investigated systematically. The optimum geometry consists of slim elements in flow direction in a staggered overlapping arrangement. Such regenerators could provide equal thermal performance as stacked screens with up to five times lower pressure drop. INTRODUCTION The efficiency of regenerative cryocoolers depends to a large degree on the performance of the regenerator. Besides the heat capacity of the matrix, this performance is particularly determined by the heat transfer between the fluid and the matrix and by the pressure drop of the flow. In previous work, large differences between the heat transfer to pressure drop ratio for various heat transfer surfaces were recognized [1]. Recently we have published results of systematic investigations on the ideal inner regenerator geometry concerning this ratio [2]. To describe the suitability of a geometrical configuration for use as a regenerator, the ratio NPH/NTU (number of pressure heads pressure drop per number of transfer units) is proposed: When taking the mean velocity U m in main flow direction within the matrix as the characteristic velocity to calculate the Reynolds number Re and to determine the friction factor f, one can compare geometries with different porosities on an equal basis. This is advantageous for an investigation dealing with regenerators. The ratio NPH/NPH for several heat transfer surfaces is shown in Fig. 1. The "single plate" and "parallel plates" lines determine the "best possible" limits, against which all other geometries can be evaluated. The curves show a very small dependence on the Reynolds-number. A rise of the curves on smaller Reynolds numbers is due to longitudinal conduction effects. Longitudinal conduction has actually been neglected in the theoretically calculated values for single plate and parallel plates in Fig. 1. The rise of the curves to higher Reynolds numbers indicates flow separation or the onset of turbulence. When inspecting Fig. 1 one.

2 sees the large difference between the smooth surfaces with values for NPH/NTU below 3.5 and the flow across rods, screens or spheres all having NPH/NTU values above 6. As a result of the numerical simulations, the two main influence parameters of the inner geometry of the regenerator on the ratio of pressure drop to heat transfer were found. These are on one side the "slimness" (thickness to length ratio) of the single elements and on the other side the ratio of the average free flow area to the minimum free flow area, which is determined by the way the elements are arranged. Fig. 1 NPH/NTU vs. Re for Pr = 0.7 IMPROVED REGENERATOR DESIGN The optimum geometry consists of slim elements in flow direction in a staggered overlapping arrangement (Fig. 2). The lenticular shaped elements have a slimness of 0.3 and they are arranged with a flow area ratio A m /A min = This means that the fluid flow undergoes hardly any acceleration or deceleration. In addition the fluid meets regularly new leading edges with very good local heat transfer. On the back side of the element the boundary layer is still quite thin, because the following row of elements is preventing a separation of the flow. So there is still reasonably good heat transfer even at the back side

3 of the element. The result is a ratio of NPH/NTU of about 2.4 at Re = 500, which is nearly as good as the parallel plate arrangement. This value includes already the longitudinal conduction in the matrix elements and the fluid. Fig. 2 New Regenerator Geometry From numerically calculated velocity and temperature fields, values for f, Nu and the ratio NPH/NTU can be evaluated for the new proposed regenerator geometry. These data are compared with the respective values for parallel plates and stacked screens in Fig. 3 in Fig. 4. Fig. 3 Nu, f*re vs. Re

4 Fig. 4 NPH / NTU vs. Re INFLUENCE ON CRYOCOOLER PERFORMANCE To evaluate the potential improvement for an existing cryocooler when using the new inner geometry, the following calculations have been done for the "Jena Four Valve Pulse Tube" [3]. For steady-state flow the regenerator was subdivided into 4 regions with individual temperatures. From the appropriate fluid properties and a given mass flow rate, heat transfer, pressure drop and matrix temperature swing have been calculated. In the following table, the results for conventional screens and the new regenerator design (shape as in Fig. 2, performance data as in Fig. 3) are shown. The regenerator dimensions are: 32mm outer diameter, 16mm inner diameter and a length of 226mm. Low temperatures T C = 80K, ambient temperature T W = 300K. As the machine is running at about 4Hz only, no corrections are used in the pressure drop and heat transfer correlation to consider the oscillating flow conditions. Table 1 Comparison of Regenerator Performance in a Four Valve Pulse Tube mass flow rate g/s screens 150 mesh New Regenerator New Regenerator Porosity Heat transfer Surface m² Hydraulic Diameter mm

5 Regenerator Mass g Reynolds number (warm end) overall NTU Matrix Temperature Swing (cold end) K Temperature Diff. Wall-Fluid (cold end) K overall Pressure Drop at 12 bar bar NPH NPH / NTU friction factor f (warm end) Colburn modulus j (warm end) In the first case the results for the same mass flow rate like that one for the stacked screen regenerator are shown. The reduced pressure drop would lead to substantially larger p-vwork. In the second case, the mass flow rate can be increased by about 73% to produce the same pressure drop as that for the flow through the screens. Thus the refrigerator could be operated with a higher frequency and thus capacity. Similar calculations can be done for different kinds of regenerative cryocoolers with similar results. CONCLUSIONS Numerical simulations have shown, that there are inner regenerator geometries with an improved pressure drop to heat transfer ratio compared with stacked screens. The usage of such type of regenerators can substantially increase the performance and/or capacity of cryocoolers. ACKNOLEDGMENT Financial support by a BMBF grant (13N6619/0) is gratefully acknowledged. NOMENCLATURE A area m 2 NTU number of transfer units - c p specific heat J/(kgK) Nu Nusselt number - D h hydraulic diameter m p pressure Pa f fanning friction factor - Pr Prandtl number - j Colburn modulus& - Re Reynolds number - L length in flow direction m U velocity component in m/s mass flow rate kg/s main flow direction

6 NPH number of pressure heads - REFERENCES [1] Radebaugh, R., Louie, B., Proceedings of the Third Cryocooler Conference, NBS Special Publication 698, Washington DC, 1985 [2] Ruehlich, I. and Quack, H.; Investigations on Regenerative Heat Exchangers, to be published in the ICC 10 proceedings [3] Thuerk, M. et. al., Intrinsic Behavior of a Four Valve Pulse Tube, Proc. ICEC 16, Elsevier Science, New York, 1997, S. 259 ff.