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Abstract

In the light of the energetic challenges faced by aeronautical engine manufacturers, a better understanding of the flows governing their gas turbines is required. Numerical simulations through Large-Eddy Simulation (LES) approach is well suited to this quest for innovation. However, its computational cost is prohibitive in the case of boundary layers at Reynolds numbers encountered in aeronautics. One way to tackle this limitation is to use a WMLES (Wall-Modeled LES) approach: near-wall turbulence is modeled thanks to a wall-model. Nonetheless, this approach is still an open issue for industrials flows. Therefore, a new suited wall-model is developed in this study: the iWMLES (integral WMLES). It is analogous to the von Kármán-Pohlhausen integral method for laminar flows: the velocity and temperature profiles are parameterized, and unknown coefficients are determined by matching boundary conditions obeying the integral boundary layer equations. It allows compressibility, temperature and pressure gradient effects to be taken into account at a low computational cost. Parameterized profiles are based on the usual logarithmic wall functions with corrective terms to extend their range of applicability. Instead of solving a set of differential equations as standard numerical wall-models, a simple linear system is solved. The proposed wall-model is implemented in a finite-volume cell-centered structured grid solver and assessed on academic flows. First, adiabatic and isothermal plane channel flows at several friction Reynolds and Mach numbers are simulated. In all cases, mean profiles, wall fluxes, and turbulent fluctuations are in agreement with Direct Numerical Simulation (DNS) data. Especially, the supersonic flow cases show that the iWMLES has a wider domain of validity than standard wall-models. Second, an experimental boundary layer under adverse pressure gradient is considered. The iWMLES is shown to predict correctly the one-point turbulence statistics. Finally, the iWMLES is applied to an axial compressor stage, demonstrating its robustness, and results are compared with wall-resolved LES data.            

Jury