CFD simulations of flow in LREs rectangular cooling channels

In the design of liquid propellant rocket engines, the regenerative cooling of the thrust chamber represents one of the most challenging issues. In this respect, the importance of numerical prediction of pressure losses and wall temperatures is crucial. Among the flow models used as a support in the engine design phase, Reynolds-Averaged Navier-Stokes (RANS) equation solvers play an important role, since they represent a fast tool to reproduce turbulent flow phenomena. However, flow in liquid rocket engine cooling channels is characterized by complex and coupled phenomena. In particular, cooling channels typically exhibit rectangular cross section. This leads to the presence of secondary motions that have an influence on both skin friction and heat transfer. RANS turbulence closure models based on the linear eddy-viscosity ansatz are not able to predict secondary eddies, thus inhibiting additional momentum and heat transfer from the duct center toward the corners. In this work, quadratic constitutive relations (QCR) have been implemented in an in-house RANS solver equipped with the Spalart-Allmaras turbulence model. These relations add a nonlinear term to the linear Reynolds stress tensor in order to improve the eddy-viscosity approximation and the accuracy of RANS solvers. In particular, the effect of QCR on skin friction and heat transfer is investigated through a comparison with direct numerical simulations (DNS) of square and rectangular ducts.