Conjugate heat transfer analysis of rectangular cooling channels using modeled and direct numerical simulation of turbulence

We carry out a computational study of conjugate heat transfer in rectangular cooling channels typical of liquid propellant rocket engines, with the goal of establishing the predictive capability of Reynolds averaged Navier-Stokes (RANS) solvers. A classical Spalart-Allmaras RANS solver is here used, which is iteratively coupled with a Fourier solver which solves for conduction within the duct walls. Comparison is made with the reference solutions of the same problem obtained with a direct numerical simulation (DNS) approach, which allows to describe the full features of flow and heat evolution in the channel. Numerical simulations are carried out for different values of the fluid-solid thermal conductivity ratio to bring out conjugate heat transfer effects. Finite conductivity of the solid is found to imply reduced thermal efficiency of the overall system as a result of both increased thermal resistance, and asymmetric heat loading on the fluid. We find that, despite the absence of the secondary motions, the RANS/Fourier solver can accurately estimate the pressure drop. Differences in the prediction of thermal effects are generally larger. However, the wall temperature distributions are predicted by RANS with reasonable accuracy, and discrepancy in the overall heat transfer coefficient is no larger than 10%.