We propose to carry out a synergistic 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 will be used as a first attempt, which will be iteratively coupled with a Fourier solver to account for thermal conduction within the duct walls. Comparison will made with reference solutions of the same problem obtained with direct numerical simulation (DNS) , which allows to describe the full features of flow and heat evolution in the channel. Numerical simulations will be carried out for different values of the fluid-solid thermal conductivity ratio to bring out conjugate heat transfer effects. Finite conductivity of the solid implies reduced thermal efficiency of the overall system as a result of both increased thermal resistance, and asymmetric heat loading on the fluid. Preliminary simulations carried out with the Spalart-Allmaras model have shown 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, amounting to underestimation of the overall heat transfer coefficient by about 10%. Additional turbulence models based on nonlinear constitutive relationships will be considered in the present project which are capable of correctly accounting for secondary motions, and modifications will be pursued to achieve accurate prediction of heat exchanges. Improvement of RANS model predictive capabilities would provide large competitive advantage to the national and European launch vehicle industry.
To the applicants' knowledge, there are no systematic quantitative studies on the capability of RANS models to accurately predict the heat transfer rate in CHT problems. Availability of targeted high-fidelity DNS to be carried out in the present project could provide a major achievement in this respect, from a dual perspective. First, the DNS setup will be new in its own sake, hence the results could be used to improve knowledge of the underlying flow physics. Furthermore, the DNS solutions will be used as a reference database for subsequent benchmark and optimization of RANS models.
The eventual goal of the project is to develop accurate and reliable predictive tools for the industrial design of cooling systems based on the RANS-Fourier approach. Given the shortcoming of traditional RANS models based on the linear eddy viscosity ansatz, we are going to explore modifications based on more elaborate, nonlinear closures such as the QRC model (Spalart 2000), or data-driven closures (Duraisamy 2019).
The expected impact would in aerospace propulsion would be huge, as heat transfer prediction techniques used in the design practice are based on semi-empirical correlations originally developed for flow in circular pipes, in the absence of CHT effects, whose error bar can be as large as 10%, or more. Restricting the error bar to less than, say, 1% would allow for the design of substantially lighter engines, and it would improve the overall propulsive efficiency, with incurred competitive gain in terms of cost reduction in launch vehicles.