Abstract

Abstract

Abstract

In this work, a discontinuous Galerkin scheme is employed to perform large-eddy simulations of supersonic jet flows. A total of four simulations are performed with different meshes and order of accuracy to identify the resolution requirements to reproduce the physical characteristics from experiments. The number of degrees of freedom from the simulations varies from 50 × 106to 400 × 106. The results indicate that by increasing the resolution of simulation, in general, the results got closer to experimental data. The comparison of velocity distribution in the jet centerline and lipline from the simulation with 400 × 106with experimental shows that important characteristics of the flow are represented. The study investigated a procedure of using lower-order simulations to initialize high-order simulations to reduce the total computational cost of the calculation. This strategy is successful and allows the performance of high-order simulations with only 6% more computational effort than a second-order simulation with the same number of degrees of freedom.

Abstract

Reynolds-Averaged Navier-Stokes (RANS) simulations are inaccurate in predicting complex flow features (ex: separation regions), and therefore deriving an optimised shape using the RANS-adjoint framework does not yield a truly optimal geometry. With the purpose of obtaining accurate sensitivity to objective function of interest, we improve the RANS flowfield using the strategy of Singh et al. [1]. This involves multiplying a corrective factor to the production term in the Spalart-Allmaras (SA) turbulence model equation and solving the inverse problem to determine the appropriate field, which enables the RANS solution to match the high-fidelity data.The geometry of our interest is the U-Bend which is widely studied in literature in the context of gas turbine cooling, and which is known to be a challenging case for RANS simulations to reproduce. We use the mean flowfield from a large-eddy simulation of the U-Bend geometry as the high-fidelity data to which the RANS flowfield is fit using the strategy outlined above. We observe a clear improvement in the RANS flowfield by optimising for the field, the objective function to be minimized being L2-norm of the mean velocity difference between RANS and LES. We further show that adding an additional corrective factor () to the destruction term in the SA turbulence equation and simultaneously optimising for the field alongside the field results in a better match of the RANS flowfield with the corresponding LES flowfield. We also show that surface sensitivity map for the improved LES-aided flowfield varies significantly in comparison to the baseline SA-based flowfield for an objective function of interest, the total pressure loss in the U-Bend.