Low Reynolds number kappa-epsilon and empirical transition models for oscillatory pipe flow and heat transfer
Stirling engine heat exchangers are shell-and-tube type with oscillatory flow (zero-mean velocity) for the inner fluid. This heat transfer process involves laminar-transition turbulent flow motions under oscillatory flow conditions. A low Reynolds number kappa-epsilon model, (Lam-Bremhorst form), was utilized in the present study to simulate fluid flow and heat transfer in a circular tube. An empirical transition model was used to activate the low Reynolds number k-e model at the appropriate time within the cycle for a given axial location within the tube. The computational results were compared with experimental flow and heat transfer data for: (1) velocity profiles, (2) kinetic energy of turbulence, (3) skin friction factor, (4) temperature profiles, and (5) wall heat flux. The experimental data were obtained for flow in a tube (38 mm diameter and 60 diameter long), with the maximum Reynolds number based on velocity being Re(sub max) = 11840, a dimensionless frequency (Valensi number) of Va = 80.2, at three axial locations X/D = 16, 30 and 44. The agreement between the computations and the experiment is excellent in the laminar portion of the cycle and good in the turbulent portion. Moreover, the location of transition was predicted accurately. The Low Reynolds Number kappa-epsilon model, together with an empirical transition model, is proposed herein to generate the wall heat flux values at different operating parameters than the experimental conditions. Those computational data can be used for testing the much simpler and less accurate one dimensional models utilized in 1-D Stirling Engine design codes.