Pierre Brenner

Development of Numerical Schemes for Hybrid Turbulence Modelling in an Industrial CFD Solver

Many turbulent flows are dominated by large turbulent structures caused by massive boundary layer separation, i.e : bluff body flows past launchers and missiles, cars, turbomachines. These flows represent a challenge for numerical simulation methods since models based on Reynolds averaged equations (URANS) are not able to give an accurate representation of unsteady turbulent structures. On the other hand, Large Eddy Simulation (LES) is generally too expensive for an industrial use. In the attempt to find a compromise between computation cost and accuracy, it becomes useful to consider hybrid approaches between RANS and LES modelling. The aim of such simulations is to resolve only that portion of the turbulent spectrum responsible for the aerodynamics forces acting on an immersed body, and to model the rest. A lot of simulation strategies hybrid exist (for example SAS, PANS, PITM, ZDES..) but exploring them is beyond the scope of this paper. Here we focuse instead on the impact of the numerical properties of the resolution scheme on hybrid RANS/LES simulations and investigate a simple but effective strategy to improve numerical accuracy of the solver for a given mesh resolution.

Automatic Hybrid RANS/LES Strategy for Industrial CFD

An automatic HRL (Hybrid RANS/LES) strategy is investigated in FLUSEPA, a finite-volume solver developed by Airbus Defense and Space. A HRL turbulence model is coupled to a high-order hybrid numerical approximation method. Concerning the turbulence model, the well-known \(k-\varepsilon \) two equations RANS turbulence model is sensitized to the grid as suggested by Perot and Gadebusch (Phy Fluids 19:1–11, 2007). Concerning the numerical strategy, a third-order accurate upwind approximation method is locally re-centered in vortex dominated regions to achieve non-dissipative fourth-order accuracy. Results are presented for a 2D backward facing step and an an axisymmetry backward facing step, which represent good prototypes of after body flows.

Multiple-correction hybrid k-exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids

Abstract A Godunovs type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries.

Assessment of automatic Hybrid RANS/LES Models for Industrial CFD

The objective of this paper is to assess and compare several self-adapting hybrid RANS/LES models for a backward facing step flow, in conjunction with a high-order finite volume numerical scheme well suited for scale-resolving simulations. The most promising model is then applied to an axisymmetric backward facing step, representative of the base flow behind a launcher. Present computations provide a satisfactory representation of the characteristic flow frequencies. Finally, the proposed methodology is applied to the computation of the flow behind the Ariane 5 space launcher to demonstrate its applicability to complex flow configurations of industrial interest.

Hybrid RANS/LES Simulation of a Space Launcher Using a High Order Finite Volume Scheme and Grid Intersections Technique

In this study, we apply a numerical strategy, based on high-accurate finite volume numerical schemes and advanced turbulence models, to calculate the mean and fluctuating pressure in the recirculation zone of a mock up of the Ariane 5 space launcher, which is one of our advanced validation test cases for the FLUSEPA solver, developed by Airbus Safran Launchers.

High-Order Hybrid RANS/LES Strategy for Industrial Applications

Turbulent flows of industrial interest are often dominated by large turbulent structures. A typical example is provided by launcher base flows, combining one or more extended and interacting separated regions with strong compressibility effects. Such flow features represent a challenge for CFD simulations, since, on the one hand, well established Reynolds-Averaged-Navier-Stokes (RANS) solvers cannot represent such highly unsteady and three-dimensional large scales and, on the other hand, Large Eddy Simulation (LES) approaches remain too expensive for routine production use in industry.

Toward an improved wall treatment for multiple-correction k-exact schemes

Improved wall boundary treatments are investigated for a family of high-order Godunovtype finite volume schemes based on k-exact polynomial reconstructions in each cell of the primitive variables, via a successive corrections procedure. We focus more particularly on the 1-exact and 2-exact schemes which offer a good trade-off between accuracy and computational efficiency. In both cases, the reconstruction stencil needs to be extended to the boundaries. Additionally, information about wall curvature has to be taken into account, which is done by using a surface model based on bicubic Bezier patches for the walls. The performance of the proposed models is presented for two compressible cases, namely the inviscid flow past a Gaussian bump and the viscous axisymmetric Couette flow.

Design and Analysis of a Task-based Parallelization over a Runtime System of an Explicit Finite-Volume CFD Code with Adaptive Time Stepping

Abstract FLUSEPA (registered trademark in France No. 134009261) is an advanced simulation tool which performs a large panel of aerodynamic studies. It is the unstructured finite-volume solver developed by Airbus Safran Launchers company to calculate compressible, multidimensional, unsteady, viscous and reactive flows around bodies in relative motion. The time integration in FLUSEPA is done using an explicit temporal adaptive method. The current production version of the code is based on MPI and OpenMP. This implementation leads to important synchronizations that must be reduced. To tackle this problem, we present the study of a task-based parallelization of the aerodynamic solver of FLUSEPA using the runtime system StarPU and combining up to three levels of parallelism. We validate our solution by the simulation (using a finite-volume mesh with 80 million cells) of a take-off blast wave propagation for Ariane 5 launcher.

High Order Finite Volume Scheme and Conservative Grid Overlapping Technique for Complex Industrial Applications

The numerical foundation of the CFD solver FLUSEPA (French trademark N. 13400926) is presented. It is a Godunov’s type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around 3D complex geometries and general non-Cartesian grids. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along curved cell faces. Then, a re-centering process is used to reduce as far as possible numerical diffusion. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors (cells which have common faces) of the mesh cells. To address complex geometries, a conservative grid intersection technique is used. Compressible numerical test cases are investigated to demonstrate the accuracy and the robustness of the presented numerical scheme, then, supersonic RANS/LES computations around the Ariane 5 space launcher are presented to shows the capability of the scheme to predict flows with shocks, vortical structures and complex geometries.

Hybrid RANS/LES Simulation of a Supersonic Coaxial He/Air Jet Experiment at Various Turbulent Lewis Numbers

In this article, the unstructured, high order finite-volume CFD solver FLUSEPA, developed by Airbus Safran Launchers, is used to simulate a supersonic coaxial Helium/Air mixing experiment. The aim is to assess the ability of the code to accurately represent mixing in compressible flows and to create a reference case in order to test a future hybrid RANS/LES (HRL) model with variable turbulent Prandtl and Schmidt numbers. Both RANS and HRL simulations are performed and the impact of Lewis number on the results is studied. Fine and coarse meshes are used to see the influence of spatial resolution on modeled and resolved scales. General good agreement is obtained for both RANS and HRL simulations. Predictably, the choice of Lewis numbers has almost no impact on the time-averaged fields of the fine HRL simulation. Its role is more significant on the coarse mesh and the steady RANS simulations.