1、Oil & Gas Science and Technology Rev. IFP, Vol. 64 (2009), No. 3, pp. 309-335 Copyright 2009, Institut franais du ptroleDOI: 10.2516/ogst/2009016IFP-C3D: an Unstructured Parallel Solverfor Reactive Compressible Gas Flow with SprayJ. Bohbot, N. Gillet and A. BenkenidaInstitutfranaisdu ptrole, IFP, 1-

2、4 avenuede Bois-Prau, 92852 Rueil-Malmaison Cedex- France e-mail: julien.bohbotifp.fr - nicolas.gilletifp.fr - adlene.benkenidaifp.frRsum Un code parallle non structur pour la rsolution des quations compressibles ractives avec spray Le code IFP-C3D ddi la simulation de chambre de combustion de moteu

3、r combustion interne est prsent dans cet article. IFP-C3D est un code parallle utilisant un formalisme non structur et des grilles hexadriques. Il rsout les quations de Navier-Stokes compressibles formules dans le formalisme ALE et en utilisant la mthode dintgration spatiale des volumes finis sur gr

4、ille dca - le. Larchitecture du code et les quations implantes sont rsolument multi-physiques afin de prendre en compte lensemble des phnomnes physiques prsents dans les moteurs. La prsence de parties mobiles telles que les soupapes dadmission et dchappement et le mouvement des pistons ncessitent de

5、s algorithmes originaux, tels que linterpolation (remapping) entre diffrents maillages afin de changer rgulirement de maillage en cours de simulation, et des mthodes sophistiques de mouvement de maillage bases sur une interpolation temporelle conditionne par un maillage cible. Linjection de carburan

6、t liquide est modlise par une approche stochastique Lagrangienne ainsi que la formation de film liquide. Les modles physiques originaux dvelopps par lIFP pour modliser la com- bustion essence et Diesel tels que les modles ECFM et ECFM3Z, lallumage par auto-inflammation (modle TKI) et par bougies dal

7、lumage (modle AKTIM) et linjection liquide permettent la simulation de toutes les configurations moteurs comme les moteurs Diesel combustion non conventionnelle de type homogne ( HCCI) mais aussi les moteur hydrogne injection directe. La simulation de configurations 3D ncessite lutilisation de super

8、calculateurs afin de rendre compatibles les temps de retour des calculs avec les exigences industrielles. Le code IFP-C3D a t paralllis en utilisant la librairie MPI permettant de distribuer le calcul sur un grand nombre de processeurs, ce qui permet de profiter de la gnralisation des supercalculate

9、urs de type Clusters composs de plus de 1000 processeurs et de rduire considrablement les temps de retour des simulations 3D.Abstract IFP-C3D: an Unstructured Parallel Solver for Reactive Compressible Gas Flow with Spray IFP-C3D, a hexahedral unstructured parallel solver dedicated to multiphysics ca

10、lculation, is being developed at IFP to compute the compressible combustion in internal engines. IFP-C3D uses an unstructured formalism, the finite volume method on staggered grids, time splitting, SIMPLE loop, sub-cycled advection, turbulent and Lagrangian spray and a liquid film model. Original al

11、gorithms and models such as the conditional temporal interpolation methodology for moving grids, the remapping algorithm for transferring quantities on different meshes during the computation enable IFP-C3D to deal with complex moving geometries with large volume deformation induced by all moving ge

12、ometrical parts (intake/exhaust valve, piston). The Van Leer and Superbee slop limiters are used for advective fluxes and the wall law for the heat transfer model. Physical models developed at IFP for combustion (ECFM gaso- line combustion model and ECFM3Z for Diesel combustion model), for ignition

13、(TKI forDos s ierSimulation Tools for Powertrain Design and ControlOutils de simulation pour la conception et le contrle du groupe motopropulseur310Oil & Gas Science and Technology Rev. IFP, Vol. 64 (2009), No. 3auto-ignition and AKTIM for spark plug ignition) and for spray modelling enable the simu

14、lation of a large variety of innovative engine configurations from non-conventional Diesel engines using for instance HCCI combustion mode, to direct injection hydrogen internal combustion engines. Large super-scalar machines up to 1 000 processors are being widely used and IFP-C3D has been optimize

15、d for running on these Cluster machines. IFP-C3D is parallelized using the Message Passing Interface (MPI) library to distribute calculation over a large number of processors. Moreover, IFP-C3D uses an optimized linear algebraic library to solve linear matrix systems and the METIS partitionner libra

16、ry to distribute the computational load equally for all meshes used during the calculation and in particular during the remap stage when new meshes are loaded. Numerical results and timing are presented to demonstrate the computational efficiency of thecode.Other CFD codes are also available to simu

17、late internal com- bustion engine as AVLs code Fire, CD-Adapcos code StarCD capable of simulating engineering problems that involve turbulence, combustion, heat transfer, reacting flows and multiphase physics. Since 2004, an open sourceINTRODUCTIONUnderstanding and developing new engine concepts req

18、uires more and more help from 3D CFD and combustion model- ling. Nevertheless, grid generation and computation time remain expensive and time consuming. For years, efforts have been directed toward making these key points easier and faster, and it seems that unstructured grids running on parallel co

19、mputers are efficient (Heel et al., 1998; ORourke et al., 1999; Tatschl et al., 2001). Since the introduction of the original KIVA in 1985, KIVA programs have become by far the most widely used CFD (Computational Fluid Dynamics) programs for multidimensional combustion mod- elling. At IFP, for many

20、years, a modified version of KIVA- II (Amsden et al., 1989), called KMB (Habchi and Torres, 1992), has been developed and used. Based on structured multi-blocks formalism, it can model multi-valve engines of the last generation. Even if KMB is adapted to engine calcu- lations, there are strong const

21、raints like the time taken by structured grid generation or the exclusive use of very expen- sive vector computers. Also, bad shaped cells and corner cells in complex geometry limit the numerical accuracy and highly increase the CPU time. Since 1992, KIVA-3 (Amsden et al., 1992), removed the handica

22、p by the use of a block- structured mesh that entirely eliminated the need to create regions of unused cells. In addition, the use of indirect addressing for neighbor connectivity allowed data storage arrays to be sorted, which minimized the length of vector loops and eliminated testing on cell and

23、vertex flags. Further, tailored boundary condition data was carried in tables that allowed KIVA-3 to sweep in shorter vectors over only those vertices or cells involved. A distributed-memory implemen- tation release of KIVA-3 has been developed in 1999 (Aytegin et al., 1999). This distributed-memory

24、 implementa- tion of the KIVA-3 code based on one-dimensional domain decomposition was successfully developed and tested. All of the essential features of KIVA-3 excluding chemical reac- tions, spray dynamics, and piston movement have been paral- lelized. KIVA-3V (Amsden et al., 1997), can model any

25、 number of vertical or canted valves in the cylinder head of an Internal Combustion (IC) engine. The valves are treated as solid objects that move through the mesh using the familiar “snapper” technique used for piston motion in KIVA-3.ComputationalFluidDynamics(CFD)toolboxOpenFOAM (Open Field Opera

26、tion and Manipulation) isavailable to simulate anything from complex fluid flows involving chemical reactions, turbulence and heat transfer. OpenFOAM uses finite volume to solve systems of partial differential equations ascribed on any 3D unstructured mesh of polyhedral cells. The fluid flow solvers

27、 are developed within a robust, implicit, pressure-velocity, iterative solution framework, although alternative techniques are applied to other continuum mechanics solvers.IFP have developed over the past few years a new parallel unstructured code devoted to internal CFD with spray and combustion mo

28、delling. This code named “IFP-C3D” is entirely dedicated to the simulation of compressible reactive flows with combustion and sprays. Moving-mesh strategies are integrated with all physical models needed to simulate internal combustion engines. Original moving-mesh func- tionnality make it easier to

29、 use the code for complex moving geometries with intake/exhaust valves and also to add or remove geometrical parts during the calculation. Extensive use of the remeshing method reduces the CPU time and increases the accuracy of the simulations. Furthermore, IFP- C3D provides an unstructured internal

30、 automatic mesher that enables a three dimensional wedge mesh to be created with periodic boundary conditions to avoid, for basic geometries, the use of an external software mesher. IFP-C3D code is fully parallelized for shared and distributed memory com- puter and uses optimised parallel mathematic

31、al libraries for linear algebraic system calculations. This code also used CGNS standard format for Input/Output data to facilitate the exchange of data between sites and applications and help to stabilise the archiving of aerodynamic data. The data are stored in a compact, binary format and are acc

32、essible through a complete and extendable library of functions. Moreover, the HDF5 extension of the CGNS format provides a parallel I/O system that gives it high potential for the treatment of large I/O data.J Bohbot et al. / IFP-C3D: an Unstructured Parallel Solver for Reactive Compressible Gas Flo

33、w with Spray311If the turbulence model is used (Aturb is equal to 1), the two additional transport equations for the turbulent kinetic energy k and the dissipation rate e have to be solved:1 GOVERNING EQUATIONSIFP-C3D solves the conservation equations of mass, mass species, momentum energy and the k

34、-e turbulence equationsV- rare also used in the code to model tracers of real species or to add tracers for physical modelling. Fictive species satisfied the conservation equation of mass and momentum but are not taken into account for conservation of energy.Dt3VV(5)+ .( m k )dV + WSpray dV - re dVP

35、rkVVVIf we note, r the density,Sprayrthe density sprayre u dV + .( m e)dVV DDtre dV =- ( c 2- c )(including the liquid film evaporation part) source term V the volume and D the total derivative of time, the conservationDtof mass is expressed as:133PreVV(6)e+ c s : u + c W Spray - c re dV 1S2kVwhere

36、the turbulent constant Pre, Prk, c1, c2, c3, and cS are constants whose values have been determined from experi- ments or results. In addition to the k-e standard turbulence model, IFP-C3D also provides the RNG k-e turbulent model. DDtrdV =(1)rSpray dVVVIf we note FSpray the rate of momentum gain pe

37、r unit of volume due to the spray, u the velocity vector, p the pressure and s the viscous stress tensor and k the turbulent kinetic energy, the conservation of momentum can be written as:2 NUMERICAL IMPLEMENTATIONru dV = - 1 p dV - Aturb D Dt2 rk dV2.1 Unstructured Grid and Connectivity Aspecta23VV

38、V(2)The unstructured formalism reduces constraints during the grid process generation and avoids the difficult numerical processing of cells located at the corner of two blocks present in the structured multiblock formalism. With unstructured grids, cells have a better shape and local refinement of

39、zones where the gradients are suspected to be high is less expen- sive. With hexahedral grids, gradient calculations are accu- rate and moving algorithms may maintain a good grid quality when the geometry is moving.Because of the unstructured approach, the connectivity (node, cell and face) must be

40、computed and registered. Nodes can have any number of neighbours, while hexahedron have 6 neighbours respectively to its 6 faces. Sorting cells and nodes indexes for a given face give the unstructured grids and mesh descriptors and connectivity has to be defined. The staggered hexahedral description

41、 with cell-centred scalar and node-centered vectors is used. The topological element “face” is widely used in the solver. This element can be linked easily to hexahedrons and nodes. It is defined by one or two hexahedrons (fluid or boundary faces) and 4 nodes, nodes 1 to 4 in Figure 1. Sorting cells

42、 and nodes indexes for a given face can give the orientation that we need for solving the transport equations. The 8 sorted border nodes, node 5 to 12 in Figure 1, are also registered and used for rising numeri- cal accuracy in convection terms.Because of the unstructured approach, the connectivity

43、(node, cell and face) must be all computed and registered. Nodes can have any number of neighbours, while a hexahedron can only have 6 respectively to its 6 faces.+ s dV + FSpray dVVVwith:o =m u +u + l uIT(3)(m and l are the first and second coefficients of viscosity.Aturb is equal to 1 for turbulen

44、t flows and 0for laminar flows.The internal energy equation is:DDt rE dV = - p u dV + (1- Aturb ) s : u dVV- Q dV +VV(4)ChemdVVV+ Spray dV + Aturb re dVVVwhere E is the specific internal energy. The heat flux vector Q is the sum of contributions due to the enthalpy diffusion and to the heat conducti

45、on.( r )Q = -K T - rD h riii =1, Nwith N equal to the number of chemical species, K the thermal conductivity and D the gas mass diffusion coefficient.312Oil & Gas Science and Technology Rev. IFP, Vol. 64 (2009), No. 3connectivity matrix of cells and faces. Several renumbering algorithms have been te

46、sted, among them the “Reverse Cuthill McKee” (Cuthill E.H. et al., 1969), Sloan (Sloan, 1986), Gibbs-King and Gibbs-Poole-Stockmeyer (Lewis, 1982). Table 1 shows results on an engine configuration grid which contains approximately 60 000 elements. The Gibbs- King algorithm gives the best reducing fa

47、ctor of the band- width and envelope size.Figure 2 shows the original and renumbered connectivity matrices using the Gibbs King algorithm of an Port Fuel Injection engine test case. CPU time results are reported in Table 1. When the grid is ordered in a random way (automatic unstructured grid genera

48、tor), the renumbering method makes the code faster by about 40%. Of course, the CPU reduction rate depends on the memory architecture of the computer.Node 11Node 3Node 7Cell 2Cell 1Node 12Node 4Normal at faceNode 8Node 10Node 2Node 6Node 9Node 1Node 5Figure 1Unstructured grid and connectivity.2.2 Nu

49、merical Scheme and Code ArchitectureThe performance of unstructured grid codes on the work- station and distributed memory parallel computers is substan- tially affected by the efficiency of the memory hierarchy. This efficiency depends on the order of computation and of the numbering of the grid gi

50、ven by the connectivity calcula- tion. To improve the efficiency of the code IFP-C3D, renum- bering methods are used to reduce the bandwith and enve- lope size of the connectivity matrix. There are various algorithms that renumber unstructured grids. The main idea behind renumbering for improving ca

51、che performance is to place neighbouring members (cell centers, faces) of a set close together in memory. The bandwidth reduction family of renumbering methods that place non-zero elements of a sparse matrix close to the main diagonal can be used for renumbering unstructured grids when they are appl

52、ied on theThe conservation equations previously presented have to be solved using the Arbitrary Lagrangian Eulerian formalism to take into account the effect of the moving geometric parts and of the large volume variation. IFP-C3D uses the time- splitting method to split the physical time-step into

53、three stages. The time-splitting begins with the source terms (stage A), then follows a full implicit Lagrangian stage (stage B), and finally a sub-cycled explicit Eulerian phase (stage C). SI units are used in IFP-C3D.In Stage A, source terms of the chemical reactions on gas (auto-ignition, combust

54、ion, post-oxydation, chemical equilib- rium, etc.) of the Lagrangian fuel injection (spray, liquid film) and of the spark ignition (AKTIM model) are calcu- lated and added to the conservation equations.0020 00020 00040 00040 00060 000060 000020 00040 00060 00020 00040 00060 000Figure 2Original and r

55、enumbered connectivity matrix using the Gibbs King algorithm.J Bohbot et al. / IFP-C3D: an Unstructured Parallel Solver for Reactive Compressible Gas Flow with Spray313TABLE 1Renumbering method comparisonIn the second stage, Stage B (Lagrangian stage), the original Semi-Implicit method introduced by

56、 Patankar (1980) is retained in its fully implicit version. The coupled implicit equations (momentum, temperature and pressure) are solved with the SIMPLE algorithm. The SIMPLE method consists of an iteration on the coupled equations until the maximum number of iterations is reached or if the conver

57、gence criterion on the initial pressure is reached. The pressure equation is solved using the BiCGSTAB iterative method with ILU pre- conditioning. The temperature and velocity equations are solved using the residual conjugate gradient with Jacobi pre- conditioning. When the SIMPLE algorithm has converged, the diffusion terms of the turbulent equation are solved. The use of the ILU preconditioning and of the BiCGSTAB method for the pressure solver gives a better rate of conver- gence of the SIMPLE algorithm to avoid small pressure oscillatio