Methodology for Scale-Resolving Simulation of Unsteady Effects in Turbomachines

Alexey P. Duben; Viacheslav A.  Sapozhnikov

doi:10.14529/jsfi250107

Authors

Alexey P. Duben Keldysh Institute of Applied Mathematics, RAS, Moscow, Russian Federation https://orcid.org/0000-0002-2280-4400
Viacheslav A. Sapozhnikov Keldysh Institute of Applied Mathematics, RAS, Moscow, Russian Federation https://orcid.org/0009-0004-6285-9125

DOI:

https://doi.org/10.14529/jsfi250107

Keywords:

turbulent flows, non-linear harmonics method, scale-resolving simulation, hybrid RANS-LES approach, IDDES, CPU GPU, MPI OpenMP OpenCL, synthetic turbulence

Abstract

Methodology for studying effects associated with periodic unsteady impact of neighbouring rows in turbomachines is presented. The two-stage procedure of an investigation is as follows: simulation using an approach based on solving the Reynolds-averaged Navier–Stokes equations (RANS) of an entire turbomachine at the first stage and scale-resolving simulation (SRS) of a particular row at the second. The methodology exploits the following methods and technologies, which are implemented in the NOISEtte computational algorithm: the nonlinear harmonics method as a RANS approach to obtain unsteady inflow parameters for SRS; the hybrid Improved Delayed Detached Eddy Simulation approach for SRS of the row under detailed study. SRS considers using the dynamic synthetic turbulence generator in a form of volumetric source terms (VSTG) to reproduce unsteady periodic turbulent perturbations. A dynamic version of the VSTG, the parameters of which depend on the flow upstream the source region, is formulated. Details of the parallel heterogeneous implementation of the dynamic VSTG are discussed. To demonstrate the applicability of the presented methodology, a simulation of non-stationary effects in a cascade of T106 low-pressure turbine blades was performed.

References

NASA Turbulence Modeling Resource. 2DML: 2D Mixing Layer Validation Case. https://turbmodels.larc.nasa.gov/delvilleshear_val.html

Abalakin, I.V., Bakhvalov, P.A., Bobkov, V.G., et al.: NOISEtte CFD&CAA Supercomputer Code for Research and Applications. Supercomputing Frontiers and Innovations 11(2), 78–101 (Aug 2024). https://doi.org/10.14529/jsfi240206

Abalakin I., Bakhvalov P., Kozubskaya, T.: Edge-based reconstruction schemes for unstructured tetrahedral meshes. International Journal for Numerical Methods in Fluids 81, 331–356 (2016). https://doi.org/10.1002/fld.4187

Bakhvalov, P.A., Surnachev, M.D.: Method of averaged element splittings for diffusion terms discretization in vertex-centered framework. Journal of Computational Physics 450, 110819 (Feb 2022). https://doi.org/10.1016/j.jcp.2021.110819

Burgos, M.A., Contreras, J., Corral, R.: Efficient edge-based rotor/stator interaction method. AIAA Journal 49(1), 19–31 (Jan 2011). https://doi.org/10.2514/1.44512

Delville, J., Bellin, S., Garem, J.H., Bonnet, J.P.: Analysis of Structures in a Turbulent, Plane Mixing Layer by Use of a Pseudo Flow Visualization Method Based on Hot-Wire Anemometry, pp. 251–256. Springer Berlin Heidelberg (1989). https://doi.org/10.1007/978-3-642-83822-4_38

Duben, A.P., Zagitov, R.A., Shuvaev, N.V.: Nonlinear harmonics method for supercomputer simulations of fluid dynamics in turbomachines with higher accuracy on unstructured meshes. Lobachevskii Journal of Mathematics 45(7), 3007–3016 (Jul 2024). https://doi.org/10.1134/s1995080224603916

Duben, A., Gorobets, A.: Scale-resolving simulation of a low-pressure turbine on hybrid supercomputers. Computers & Fluids 265, 105984 (Oct 2023). https://doi.org/10.1016/j.compfluid.2023.105984

Duben, A., Gorobets, A., Soukov, S., et al.: Supercomputer Simulations of Turbomachinery Problems with Higher Accuracy on Unstructured Meshes, pp. 356–367. Springer International Publishing (2022). https://doi.org/10.1007/978-3-031-22941-1_26

Duben, A., Zagitov, R., Shuvaev, N., Marakueva, O.: Towards anAdaptation of the Nonlinear Harmonics Method Realized in an Unstructured Flow Solver for Simulation of Turbomachinery Problems on Supercomputers, pp. 253–266. Springer Nature Switzerland (2025). https://doi.org/10.1007/978-3-031-78459-0_19

Fiore, M., Gojon, R., S´aez-Mischlich, G., Gressier, J.: LES of the T106 low-pressure turbine: Spectral proper orthogonal decomposition of the flow based on a fluctuating energy norm. Computers & Fluids 252, 105761 (Feb 2023). https://doi.org/10.1016/j.compfluid.2022.105761

Gorobets, A.: Adapting a Scientific CFD Code to Industrial Applications on Hybrid Supercomputers. Supercomputing Frontiers and Innovations 9(4), 49–54 (Nov 2022). https://doi.org/10.14529/jsfi220405

Gorobets, A., Bakhvalov, P.: Heterogeneous CPU+GPU parallelization for high-accuracy scale-resolving simulations of compressible turbulent flows on hybrid supercomputers. Computer Physics Communications 271, 108231 (Dec 2022). https://doi.org/10.1016/j.cpc.2021.108231

Guseva, E.K., Garbaruk, A.V., Strelets, M.K.: Assessment of Delayed DES and Improved Delayed DES Combined with a Shear-Layer-Adapted Subgrid Length-Scale in Separated Flows. Flow, Turbulence and Combustion 98, 481–502 (2017). https://doi.org/10.1007/s10494-016-9769-7

Hu, S., Zhou, C., Xia, Z., Chen, S.: Large Eddy Simulation and CDNS Investigation of T106C Low-Pressure Turbine. Journal of Fluids Engineering 140(1) (Oct 2017). https://doi.org/10.1115/1.4037489

Magomedov, A.R., Gorobets, A.V.: Heterogeneous Implementation of Preconditioners Based on Gauss-Seidel Method for Sparse Block Matrices. Computational Mathematics and Modeling 33(4), 438–442 (Oct 2022). https://doi.org/10.1007/s10598-023-09585-2

Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32(8), 1598–1605 (Aug 1994). https://doi.org/10.2514/3.12149

Michelassi, V., Wissink, J., Rodi, W.: Analysis of DNS and LES of Flow in a Low Pressure Turbine Cascade with Incoming Wakes and Comparison with Experiments. Flow, Turbulence and Combustion 69, 295–329 (2002). https://doi.org/10.1023/a:1027334303200

Mockett, C., Fuchs, M., Garbaruk, A., et al.: Two non-zonal approaches to accelerate RANS to LES transition of free shear layers in DES. In: Progress in Hybrid RANS-LES Modelling, pp. 187–201. Springer International Publishing (2015). https://doi.org/10.1007/978-3-319-15141-0_15

Saad, Y.: Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics, Philadelphia (2003)

Sandberg, R.D., Michelassi, V.: The current state of high-fidelity simulations for main gas path turbomachinery components and their industrial impact. Flow, Turbulence and Combustion 102(4), 797–848 (Feb 2019). https://doi.org/10.1007/s10494-019-00013-3

Sandberg, R.D., Michelassi, V., Pichler, R., et al.: Compressible Direct Numerical Simulation of Low-Pressure Turbines–Part I: Methodology. Journal of Turbomachinery 137(5) (May 2015). https://doi.org/10.1115/1.4028731

Shorstov, V.A.: Possibilities and Restrictions on the Use of the Zonal RANS-IDDES Approach to Calculate Fan Noise. Mathematical Models and Computer Simulations 15(2), 265–276 (Apr 2023). https://doi.org/10.1134/s2070048223020163

Shur, M., Strelets, M., Travin, A., et al.: Improved Embedded Approaches. Notes on Numerical Fluid Mechanics and Multidisciplinary Design 134, 65–69 (2017). https://doi.org/10.1007/978-3-319-52995-0_3

Shur, M.L., Spalart, P.R., Strelets, M.K., Travin, A.K.: Synthetic Turbulence Generators for RANS-LES Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems. Flow, Turbulence and Combustion 93, 63–92 (2014). https://doi.org/10.1007/s10494-014-9534-8

Shur, M.L., Spalart, P.R., Strelets, M.K., Travin, A.K.: An enhanced version of DES with rapid transition from RANS to LES in separated flows. Flow, Turbulence and Combustion 95(4), 709–737 (2015). https://doi.org/10.1007/s10494-015-9618-0

Stadtm¨uller, P.: Investigation of wake-induced transition on the LPturbine cascade T106AEIZ. Tech. Rep. Fo 136/11, Version 1.1, DFG-Verbundproject (2002)

Suzuki, T., Spalart, P.R., Shur, M.L., et al.: Unsteady simulations of a fan/outlet-guidevane system: Broadband-noise computation. AIAA Journal 57(12), 5168–5181 (Dec 2019). https://doi.org/10.2514/1.j058177

Tyacke, J., Vadlamani, N.R., Trojak, W., et al.: Turbomachinery simulation challenges and the future. Progress in Aerospace Sciences 110, 100554 (Oct 2019). https://doi.org/10.1016/j.paerosci.2019.100554

Voevodin, V., Antonov, A., Nikitenko, D., et al.: Supercomputer Lomonosov-2: Large scale, deep monitoring and fine analytics for the user community. Supercomput. Front. Innov. 6(2), 4–11 (2019). https://doi.org/10.14529/jsfi190201

Voroshnin, D.V., Marakueva, O.V., Muraveiko, A.S.: Modeling unsteady phenomena in an axial compressor. Mathematical Models and Computer Simulations 12(3), 413–421 (May 2020). https://doi.org/10.1134/s2070048220030187

Wu, X., Durbin, P.A.: Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage. Journal of Fluid Mechanics 446, 199–228 (Oct 2001). https://doi.org/10.1017/s0022112001005717