Turbulent flow computations on 3D unstructured grids (original) (raw)
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High-Reynolds Number Viscous Flow Computations Using an Unstructured-Grid Method
Journal of Aircraft, 2005
An unstructured grid method is presented to compute three-dimensional compressible turbulent flows for complex geometries. The Navier-Stokes equations along with the one equation turbulence model of Spalart-Allmaras are solved using a parallel, matrix-free implicit method on unstructured tetrahedral grids. The developed method has been used to predict drags in the transonic regime for both DLR-F4 and DLR-F6 configurations to assess the accuracy and efficiency of the method. The results obtained are in good agreement with experimental data, indicating that the present method provides an accurate, efficient, and robust algorithm for computing turbulent flows for complex geometries on unstructured grids.
1996
A method is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered finite-volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.
34th Aerospace Sciences Meeting and Exhibit, 1996
An implicit algorithm is developed for the 2D compressible Favre-averaged Navier-Stokes equations. It incorporates the standard k-epsilon turbulence model of Launder and Spalding (1974) and the low-Reynolds-number correction of Chien (1982). The equations are solved using an unstructured grid of triangles with the flow variables stored at the centroids of the cells. The inviscid fluxes are obtained from Roe's flux difference split method. Linear reconstruction of the flow variables to the cell faces provides second-order spatial accuracy. Turbulent and viscous stresses as well as heat transfer are obtained from a discrete representation of Gauss's theorem. Interpolation of the flow variables to the nodes is achieved using a second-order-accurate method. Temporal discretization employs Euler, trapezoidal, or three-point backward differencing. An incomplete LU factorization of the Jacobian matrix is implemented as a preconditioning method. Results are presented for a supersonic turbulent mixing layer, a supersonic laminar compression corner, and a supersonic turbulent compression corner. (Author)
Turbulence Model Assessment in Compressible Flows around Complex Geometries with Unstructured Grids
Fluids, 2019
One of the key factors in simulating realistic wall-bounded flows at high Reynolds numbers is the selection of an appropriate turbulence model for the steady Reynolds Averaged Navier-Stokes equations (RANS) equations. In this investigation, the performance of several turbulence models was explored for the simulation of steady, compressible, turbulent flow on complex geometries (concave and convex surface curvatures) and unstructured grids. The turbulence models considered were the Spalart-Allmaras model, the Wilcox k-ω model and the Menter shear stress transport (SST) model. The FLITE3D flow solver was employed, which utilizes a stabilized finite volume method with discontinuity capturing. A numerical benchmarking of the different models was performed for classical Computational Fluid Dynamic (CFD) cases, such as supersonic flow over an isothermal flat plate, transonic flow over the RAE2822 airfoil, the ONERA M6 wing and a generic F15 aircraft configuration. Validation was performed by means of available experimental data from the literature as well as high spatial/temporal resolution Direct Numerical Simulation (DNS). For attached or mildly separated flows, the performance of all turbulence models was consistent. However, the contrary was observed in separated flows with recirculation zones. Particularly, the Menter SST model showed the best compromise between accurately describing the physics of the flow and numerical stability.
Adaptive unstructured grid generation for engineering computation of aerodynamic flows
Mathematics and Computers in Simulation, 2008
A unified framework is presented for automatic unstructured grid generation and grid flow adaptation. The method can simultaneously refine and coarsen the grid cells, a capability that is heavily required in transient flow problems. The proposed method includes a Cartesian grid generation approach in the first stage that enables an automatic field discretization without need to explicitly define the surface grid. The Cartesian grid cells are then subdivided in such a way that prevents the existence of hanging nodes. This allows the application of efficient fully unstructured flow solvers. The capabilities of the method are demonstrated by flow computation around a maneuver wing-flap geometry (SKF 1.1) at transonic flow conditions. An explicit finite volume cell-centered scheme is used for numerical solution of compressible inviscid flow equations. Results show the efficiency and applicability of the method.
A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow
Computational Mechanics, 2003
A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation. The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest.
The finite volume method with exact two-phase Riemann problems (FIVER) is a two-faceted computational method for compressible multi-material (fluid–fluid, fluid–structure, and multi-fluid–structure) problems characterized by large density jumps, and/or highly nonlinear structural motions and deformations. For compressible multi-phase flow problems, FIVER is a Godunov-type discretization scheme characterized by the construction and solution at the material interfaces of local, exact, two-phase Riemann problems. For compressible fluid–structure interaction (FSI) problems, it is an embedded boundary method for computational fluid dynamics (CFD) capable of handling large structural deformations and topological changes. Originally developed for inviscid multi-material computations on nonbody-fitted structured and unstructured grids, FIVER is extended in this paper to laminar and turbulent viscous flow and FSI problems. To this effect, it is equipped with carefully designed extrapolation schemes for populating the ghost fluid values needed for the construction, in the vicinity of the fluid–structure interface, of second-order spatial approximations of the viscous fluxes and source terms associated with Reynolds averaged Navier–Stokes (RANS)-based turbulence models and large eddy simulation (LES). Two support algorithms, which pertain to the application of any embedded boundary method for CFD to the robust, accurate, and fast solution of FSI problems, are also presented in this paper. The first one focuses on the fast computation of the time-dependent distance to the wall because it is required by many RANS-based turbulence models. The second algorithm addresses the robust and accurate computation of the flow-induced forces and moments on embedded discrete surfaces, and their finite element representations when these surfaces are flexible. Equipped with these two auxiliary algorithms, the extension of FIVER to viscous flow and FSI problems is first verified with the LES of a turbulent flow past an immobile prolate spheroid, and the computation of a series of unsteady laminar flows past two counter-rotating cylinders. Then, its potential for the solution of complex, turbulent, and flexible FSI problems is also demonstrated with the simulation, using the Spalart–Allmaras turbulence model, of the vertical tail buffeting of an F/A-18 aircraft configuration and the comparison of the obtained numerical results with flight test data.
An automatic unstructured grid generation method for viscous flow simulations
High aspect-ratio grids are required for accurate solution of boundary layer and wake flow. An approach for the efficient generation of isotropic and stretched viscous unstructured grids is introduced in this paper. The proposed grid generation algorithm starts with a very coarse initial grid. In far field regions, isotropic cells of excellent quality are produced using a combination of point insertion and cell subdivision techniques. Simultaneously, a directional grid refinement strategy is used to construct highly stretched triangular cells in viscous dominated regions. First, anisotropic unstructured grids are produced in the stream-wise direction. Then, cells close to the solid surface are refined to highly stretched layer of triangles suitable for boundary layer region. The accuracy of the current grid generation approach is assessed by laminar and turbulent compressible flow solutions around NACA0012, RAE2822, and NHLP multi-element airfoils. Numerical flow simulation results are compared with published data. Comparisons point to accuracy of the proposed unstructured viscous grid generation procedure.
A Navier-Stokes Solver for Compressible Turbulent Flows on Quadtree and Octree Based Cartesian Grids
Journal of Applied Fluid Mechanics
Cartesian grids represent a special extent in unstructured grid literature. They employ chiefly created algorithms to produce automatic meshing while simulating flows around complex geometries without considering shape of the bodies. In this article, firstly, it is intended to produce regionally developed Cartesian meshes for two dimensional and three dimensional, disordered geometries to provide solutions hierarchically. Secondly, accurate results for turbulent flows are developed by finite volume solver (GeULER-NaTURe) with both geometric and solution adaptations. As a result, a "hands-off" flow solver based on Cartesian grids as the preprocessor is performed using object-oriented programming. Spalart-Allmaras turbulence model added Reynolds Averaged Navier Stokes equations are solved for the flows around airfoils and wings. The solutions are validated and verified by one two dimensional and one three dimensional turbulent flow common test cases in literature. Both case studies disclose the efficaciousness of the developed codes and qualify in convergence and accuracy.