Numerical correlation for the pressure drop in Stirling engine heat exchangers

New correlation equations, to be valid for the pressure drop and heat exchange calculation under the developing transitional reciprocating flow encountered in Stirling heat exchangers are numerically derived. Reynolds-Averaged Navier–Stokes (RANS) equations based turbulence models are used to analyse laminar to turbulent reciprocating flow, focussing on the onset of turbulence and transitional reciprocating flow regime. The relative performance of four turbulence models in more accurately capturing the characteristics of the flow of interest is assessed in relation to overcoming the problems identified in previous numerical studies. The simulation results are compared with published and well-known experimental data for reciprocating pipe flows, indicating that the effects of the turbulence anisotropy need to be taken into account in order to accurately predict the laminar to turbulent transition. The anisotropic Reynolds stress turbulence model is selected as a best choice among the tested turbulence models for analysis of this transitory phenomenon based on the comparative qualitative and quantitative results. This model is used to evaluate the heat transfer and pressure drop and propose new correlations considering the working and dimensional characteristics of Stirling heat exchangers: 100 ≤ Reω ≤ 600, A0 ≤ 600, βcri > 761 and 40 ≤ L/D ≤ 120. These correlation equations reduce the unsteady 2D behaviour in reciprocating pipe flow into a manageable form that can be incorporated into Stirling engine performance codes. It is believed that the validated numerical model can be used with confidence for studying the transitional reciprocating flow and the obtained correlations, can be applied as a cost effective solution for the development of Stirling engine heat exchangers.