Providing adjoint optimized GEKO model coefficients for film cooling predictions of trench designs.

Published: 23 February 2023| Version 1 | DOI: 10.17632/5f7xcv8dgv.1
Lukas Fischer,


The data represent coefficients for the Generalized k-omega (GEKO) turbulence model used to solve the Reynolds-averaged Navier-Stokes equations (RANS) of wall-bounded film cooling flows involving the trench design. This model, with these coefficients, can be applied in Computational Fluid Dynamics (CFD) simulations using the commercial solver Ansys Fluent (version 2022 R1 or higher). The coefficients were tuned to match the 3D temperature field (temporal-averaged) of a Large Eddy Simulation (LES). The CFD case simulated for the RANS and LES was based on an optimized trench design by Peter Schreivogel at a momentum ratio of I=1 and a density ratio of 2. The LES and resulting RANS solution predicted the experimental results of Peter Schreivogel's optimized trench design and the transverse trench at I=1. At I=8, the tuned GEKO model still led to a better prediction than the standard model, but it was not as accurate as at I=1.


Steps to reproduce

We chose the experimental case of Peter Schreivogel's trench (I = 1 and a density ratio = 2) to later compare the results of the RANS and LES simulations. Thus, set the appropriate boundary conditions and prepare the numerical domain. The mesh should resolve the wall. Perform a mesh study using the standard GEKO model with second order schemes, pseudo time stepping, high order term relaxation and the warped-face gradient correction. Next, Use the Wall-Adapting Local Eddy-Viscosity (WALE) model with default settings (e.g. Prandtl number of 0.85) and second order schemes to run an LES simulation, applying the second order bounded scheme for the momentum equation and temporal discretization. Five through flows for initialization and three through flows for time averaging should be performed with a constant time step of 1e-6s. Ensure that the Pope criteria is over 80% in the domain. Then, perform GEKO model tuning by optimizing all four tunable coefficients, including the blending function. The optimization procedure should be done with the discrete adjoint solver of Ansys Fluent 2022 R1 (use newer version if possible), using the same equations as for the flow solver. The partially coupled adjoint solver should be chosen, and the equations of the adjoint solver should be discretized with first order upwind schemes due to stability issues. The Green-Gauss Cell based method was chosen for the gradient scheme (since Green-Gauss Node based was not available in Ansys Fluent 2022 R1) for an unstructured mesh with tetrahedral cells. Use an iterate AMG approach with the blended stabilization scheme to handle instabilities during the solving process. First, perform 300 iterations of the Dissipation scheme, then 60 iterations of the residual minimization scheme with 120 modes, 30 recycled modes, and 3 AMG iterations. Repeat this routine until the residuals reach the specified threshold (1e-4). The optimization of the GEKO turbulence model may take up to 30 hours on 336 CPU-cores. To optimize the turbulence model parameters, use online mode to train a Neural Network during each flow iteration (up to 1000 iterations with a pseudo time step size of 1e-4s). Use Softsign as the activation function and a default topology with three hidden layers consisting of 24, 16, and 8 nodes for the first, second, and third layer. Select six flow input features: Non-equilibrium parameter, 2nd - 5th invariant, and the length ratio. Choose default design limits to adjust each GEKO coefficient within a certain threshold.


Universitat der Bundeswehr Munchen


Computational Fluid Dynamics, Turbulence, Computational Heat Transfer, Neural Network