Nationaal Lucht- en Ruimtevaartlaboratorium National Aerospace Laboratory NLR NLR TP 96323 A robust multi-block Navier-Stokes flow solver for industrial applications. J.C. Kok, J.W. Boerstoel, A. Kassies, S.P. Spekreijse DOCUMENT CONTROL SHEET ORIGINATOR'S REF. SECURITY CLASS. NLR TP 96323 U Unclassified ORIGINATOR National Aerospace Laboratory NLR, Amsterdam, The Netherlands TITLE A robust multi-block Navier-Stokes flow solver for industrial applications. PRESENTED AT third ECCOMAS Computational Fluid Dynamics Conference, Paris, September 1996. AUTHORS DATE pp ref J.C. Kok, J.W. Boerstoel, A. Kassies, S.P. 960503 11 29 Spekreijse DESCRIPTORS Algorithms Navier-Stokes equation Body-wing configurations Pressure distribution Computational fluid dynamics Robustness (mathematics) Convergence Run time (computers) Grid generation (mathematics) Three dimensional flow Jacobi matrix method Turbulence models Multiblock grids ABSTRACT This paper presents a robust multi-block flow solver for the thin-layer Reynolds-averaged Navier-Stokes equations, that is currently being used for industrial applications. A modification of a matrix dissipation scheme has been developed, that improves the numerical accuracy of Navier-Stokes boundary-layer computations, while maintaining the robustness of the scalar artificial dissipation scheme with regard to shock capturing. An improved method is presented to define the turbulence length scales in the Baldwin-Lomax and Johnson-King turbulence models. The flow solver allows for multi-block grid which are of C -continuous at block interfaces or even only partly continuous, thus simplifying the grid generation task. It is stressed that, for industrial applications, not only a (multi-block) flow solver, but a complete flow-simulation system must be available, including efficient and robust methods for aerodynamic geometry processing, grid generation, and postprocessing. Results are presented which show the applicability of the flow-simulation system for industrial purposes. TP 96323 A Robust Multi-Block Navier-Stokes Flow Solver for Industrial Applications J.C. Kok ,1 J.W. Boerstoel, A. Kassies, S.P. Spekreijse Abstract. This paper presents a robust multi-block ¯ow for aerodynamic geometry processing, grid generation, ¯ow solver for the thin-layer Reynolds-averaged Navier-Stokes visualization, and postprocessing. Only then numerically ac- equations, that is currently being used for industrial applica- curate computation results can be ef®ciently produced at ac- tions. A modi®cation of a matrix dissipation scheme has been ceptable investments in man hour and computer costs, and developed, that improves the numerical accuracy of Navier- low turn-around times may be realized. Stokes boundary-layer computations, while maintaining the In order to provide this full CFD functionality, in the robustness of the scalar arti®cial dissipation scheme with re- ENFLOWsystem, the following tools are available (see ®gure gard to shock capturing. An improved method is presented to 1): de®ne the turbulence length scales in the Baldwin-Lomax and Johnson-King turbulence models. The ¯ow solver allows for the domain modeller ENDOMO, for the subdivision of multi-block grids which are only C0-continuous at block in- ¯ow domains around complex con®gurations into simple terfaces or even only partly continuous, thus simplifying the subdomains called blocks (block decomposition), grid generation task. It is stressed that, for industrial appli- the grid generator ENGRID, for the generation of grids in cations, not only a (multi-block) ¯ow solver, but a complete edges and faces of blocks, and in the blocks themselves, ¯ow-simulation system must be available, including ef®cient using algebraic and elliptic methods [24, 25], and robust methods for aerodynamic geometry processing, the ¯ow solver ENSOLV, for the solution of the Euler and grid generation, and postprocessing. Results are presented the thin-layer Navier-Stokes equations in arbitrary multi- which show the applicability of the ¯ow-simulation system block domains, for industrial purposes. the grid adaptor ENADAP, currently being implemented, for the adaption of grids through grid-point movement, in order to improve the accuracy of computational results 1 INTRODUCTION [8, 9], and In the past 10 years, progress in computational algorithms, several ¯ow visualization codes. numerical grid generation, and computing power has made it Recently,the ENFLOW system has been used by industry as a possible to solve the Navier-Stokes equations for ¯ows around major ¯ow-analysis tool for CFD analysis of wing-body con- complex con®gurations of engineering interest. In particular, ®gurations, and for the aerodynamic integration of propulsion it has become feasible to compute compressible, turbulent systems with transport-type aircraft. ¯ows around complete aircraft including the aerodynamic ef- The total turn-around time of the ¯ow simulation for a new fects of propulsion systems.In order for industry to apply such complete aircraft con®guration, including the construction of numerical simulations in a routine fashion, speci®cally during a high-quality, Navier-Stokes multi-block grid, is today of the design process of aircraft, it is important that the employed the order of three weeks. However, frequently a total turn- means for ¯ow computations, including grid generation, are around time of one or a few days may be realized, speci®cally robust and ef®cient from industry point of view. when computations have to be performed for a well-known At NLR a Navier-Stokes ¯ow-simulation system, called topology, or after a moderate geometry modi®cation, which ENFLOW, based on multi-block structured grids has been de- often occurs during aerodynamicdesign processes.The actual veloped [5]. This is a collection of CFD (Computational Fluid ¯ow computation needs only a computation time of three to Dynamics) programs for the computation of ¯ows around ®ve hours (for 1 to 2 million grid cells) on the NLR NEC complex aerospacecon®gurationsbasedon the Navier-Stokes SX3 supercomputer. These ®gures concerning turn-around equations. In order for such a system to be useful for industry, times should be contrasted with those of about ®ve to seven it should have full CFD functionality, thus including programs years ago, when multi-block grid generation around complex 1 National Aerospace Laboratory NLR, P.O. Box 90502, 1006 BM con®gurations starting from scratch required three to six man Amsterdam, the Netherlands months [4]. c 1996 ECCOMAS 96. Published in 1996 by John Wiley & Sons, Ltd. TP 96323 aerodynamic and Fourier for the viscous contributions, and the Boussinesq input geometry hypothesis for the Reynolds stresses, while maintaining only the derivatives in the direction, EULER / NAVIER-STOKES FLOW CALCULATION SYSTEM @~ @~ r u 1 u = kr k + r ~ tot (5), @ kr k geometric modelling block decomposition multi-block @ 3 for CFD work of 3D flow domain grid generation ICEM-CFD codes ENDOMO code ENGRID code @ T kr k Q = ktot , (6) @ with the temperature T given by the perfect gas law, T = grid flow graphical adaption computation visualization ( ) p= R . The total viscosity tot, and the total conductivity ktot ENADAP code ENSOLV code various codes are given by = + tot t, (7) ENFLOW t + ktot = Cp , (8) results of Pr Prt flow calculation with the laminar viscosity given by the Sutherland law, Figure 1. The ENFLOW system and the eddy-viscosity t given by the Baldwin-Lomax (BL) [3], the Cebeci-Smith (CS) [6], or the Johnson-King (JK) The following sections will give a description of the ¯ow turbulence model [16, 13]. solver ENSOLV, and present computational results obtained with the complete ¯ow-simulation system ENFLOW. 3 NUMERICAL MODEL 2 CONTINUOUS MODEL 3.1 Standard scheme [ 1) Consider as independentvariables the time t 2 0, ,andthe The standard numerical scheme used in ENSOLV consists T 3 =( ) ~ 2 Cartesian coordinates ~x x,y,z with x D R ,where of the schemes developed by Jameson [12, 11] and Mar- Dis the ¯ow domain. The ¯ow domain is divided in a set of tinelli [18], which may be considered proven technology (e.g. non-overlapping blocks, and each block may be described by references [19, 21, 26]). The continuous equations (1) are T3 ~ =() 2[ ] a curvilinear coordinate system ,,0,1 .Let discretized in space by a cell-centred ®nite-volume scheme: the basic dependentvariables be the density , the momentum dUi,j,k = ~ vector u, and the total energy per unit volume E. Assuming R , (9) dt i,j,k the -direction to be the normal direction in thin boundary c a d ( )= layers or wakes, the thin-layer Reynolds-averaged Navier- Ri,j,k = Di,j,k Di,j,k Di,j,k Vi,j,k, (10) Stokes equations may be written as ) with Vi,j,k the cell volume, and with the indices (i,j,k indicat- c c c d ing cell centres, corresponding to the curvilinear coordinates @ @ @ @ @ F F F F U c + + + = ) J , (1) ( , , , respectively.The convective ¯ux balanceD , the arti- @ @ @ @ @ t ®cial dissipative ¯ux balance Da, and the physical dissipative d ~ = ( ~ = ) with J det dx d , and with U the ¯ow-state vector given ¯ux balance D each consist of the summation of the corre- ) by sponding ¯uxes across the six faces of the grid cell (i,j,k .The ! convective and physical dissipative ¯uxes at a cell face are ~ ~ U = u . (2) given by equation (3), with A taken equal to the cell-face area E vector, with ¯ow variables located at the cell face de®ned by c simple averaging of the cell-centre values, and with ®rst-order The convective ¯ux vector F and the dissipative ¯ux vector d derivatives de®ned by central differencing in computational F are given by space. 0 1 ! In the standard scheme, the scalar arti®cial dissipation of uA 0 c d ~ A @ Jameson [12] is used, which is de®ned by a blending of ~ ~ = = k k ~ + F uuA p A ,F A , (3) second-order differences to obtain physically acceptable rep- ~ ~ + ) ( E p uA u Q resentations of shock waves and fourth-order differences to ~ ~ damp high-frequency modes.