Proceedings from FOI Workshop on Computational Fluid Dynamics

FOI-R--0456--SE Mars 2002 ISSN 1650-1942 Lägesrapport Christer Fureby, Peter Eliasson (Eds.) Proceedings from FOI Workshop on Computational Fluid Dynamics Weapons and Protection SE-147 25 TUMBA

SWEDISH DEFENCE RESEARCH AGENCY Weapons and Protection SE-147 25 Tumba Aeronautics SE-172 90 Stockholm FOI-R--0456--SE Mars 2002 ISSN 1650-1942 Lägesrapport Christer Fureby, Peter Eliasson (Eds.) Proceedings from FOI Workshop on Computational Fluid Dynamics

Issuing organization Report number, ISRN Report type FOI Swedish Defence Research Agency FOI-R--0456--SE Status report Weapons and Protection SE-147 25 Tumba Aeronautics Research area code 987, 3 Month year Project no. SE-172 90 Stockholm March 2002 I235 / I807 Customers code 5, 3 Sub area code?, 31 Author/s (editor/s) Project manager Christer Fureby Christer Fureby, Peter Eliasson Peter Eliasson Approved by (Eds.) Report title Proceedings from FOI Workshop on Computational Fluid Dynamics Scientifically and technically responsible Christer Fureby, Peter Eliasson Abstract (not more than 200 words) This report is the result of a workshop on Computational Fluid Dynamics, held at FOI Ursvik, 2001-10-30 with participation from Computational Aerodynamics at the Aeronautics Division and Computational Physics at the Weapons & Protection Division. The workshop indicates that FOI is active in a very wide range of activities within the field of Computational Fluid Dynamics, ranging from basic research on numerical methods and turbulence to real-world problem solving relevant to the Swedish defence and the Swedish defence industry. The current state-of-the-art at FOI holds strong promises for the future, and synergistic effects can be achived by collaboration in new projects utilizing the respective competences of the two groups. Keywords workshop, computational fluid dynamics, turbulrnce modelling, combustion, solid-fluid interactions, electrodynamics, aeroacoustics, IR-calculations, cavitation Further bibliographic information Language English ISSN 1650-1942 Pages 240 p. Price acc. to pricelist Security classification 2

Utgivare Rapportnummer, ISRN Klassificering Totalförsvarets Forskningsinstitut - FOI FOI-R--0456--SE Lägesrapport Vapen och skydd 147 25 Tumba Flygteknik Forskningsområde 987, 7 Månad, år Projektnummer 172 90 Stockholm Mars 2002 I235 / I807 Verksamhetsgren 5, 3 Delområde?, 31 Författare/redaktör Projektledare Christer Fureby Christer Fureby, Peter Eliasson Peter Eliasson Godkänd av (Eds.) Tekniskt och/eller vetenskapligt ansvarig Christer Fureby, Peter Eliasson Rapportens titel (i översättning) Proceedings from FOI Workshop om numerisk strömningsmekanik Sammanfattning (högst 200 ord) Föreliggande rapport är resultatet av en workshop in numerisk strömningsmekanik som höls I Ursvik 2001-10-30 med deltagande från Beräkningsaerodynamik vid avdelningen för Flygteknik och Beräk-ningsfysik vid avdelningen för Vapen och skydd. Workshopen visade att FOI har en bred verksamhet inom området numerisk strömningsmekanik, från grundläggande forskning om numeriska metoder och turbulens till praktisk problemlösning som är relavant för Totalförsvaret och försvarsindustrin i Sverige. I dagsläget visar FOI goda framtidsutsikter och synergieffekter kan uppnås genom samverkan i nya projekt som tillvaratar gruppernas respektive kompetenser. Nyckelord Workshop, numerisk strömningsmekanik, turbulrnsmodelering, förbränning, solid-fluidinteraktioner, elektrodynamik, numerisk analys, aeroakustik, IR-beräkningar, kavitation Övriga bibliografiska uppgifter Språk engelska ISSN 1650-1942 Antal sidor: 240 s. Distribution enligt missiv Pris: Enligt prislista Sekretess 3

Contents Introduction (C. Fureby & P. Eliasson) Introduction to FOI/ FFA s CFD software (P. Eliasson) Grid generation software (L. Thysell) Introduction to FOAM, FOI/ VS s CFD software (C. Fureby) Flow problems involving moving boundaries and interfaces (E. Lillberg, L. Olovsson) Turbulence modeling in RANS and LES (C. Fureby, L. Persson & U. Svennberg) Turbulence modeling (S. Wallin) Transition prediction (A. Hanifi) Optimal design and control (M. Berggren) High speed turbulent combustion (C. Fureby) Solid rocket propellant combustion and launch technology (M. Berglund) The pulse detonation engine (J. Tegnér) Ram jet robot calculations (M. Tormalm) Conceptual study of a supersonic heavy, low observable missile (J. Johansson) Numerical analysis (J. Nordström) Aeroacoustics (G. Efraimsson) The interaction between a lightning flash and an aircraft in flight (A. Larsson) IR calculations (M. Andersson) Low speed applications (S. Peng) Tip vortex cavitation modeling (N. Wikström) Underwater vehicle hydrodynamics (N. Alin) Surface ship hydrodynamics (E. Lillberg & U. Svennberg) 5 8 27 32 39 51 60 76 89 96 106 113 123 128 141 182 188 196 201 215 228 239 4

Introduction The main aim of the FOI Workshop on Computational Fluid Dynamics, held at FOI Ursvik, 2001-10-30 was to bring researchers together from Computational Aerodynamics at the Aeronautics Division in Bromma and from Computational Physics, Dept. of Warheads and Propulsion, Weapons & Protection Division at the Grindsjön Research Center. This joint initiative was an opportunity for the two groups to identify each other's current research areas as well as areas of mutual interest for the future, in order to coordinate their activities and facilitate the integration process between old FFA and old FOA. The workshop indicates that FOI is active in a very wide range of activities within the field of Computational Fluid Dynamics, ranging from basic research on numerical methods, turbulence and turbulence modeling to real-world problems relevant to the Swedish defence and the Swedish defence industry. In many of these areas the research at FOI is of high international quality which is corroborated by the large number of national and international collaborations shared by the two groups. The current state-of-the-art at FOI holds strong promises for the future, and synergistic effects can be achived by collaboration in new projects utilizing the respective competences of the two groups. These proceedings consist of a collection of slides presented at the workshop. Further information regarding specific research topics is available from the individual researchers. Christer Fureby Peter Eliasson 5

FOI Workshop on Computational Fluid Dynamics 2001-10-3 0 Beräkningsaerodynamik (Flygteknik) Beräkningsfysik (Vapen och Skydd) FOI Ursvik, Konferensrum Frej 6

Introduction to FOI/FFA s CFD software (P.Eliasson) Grid generation software (L.Thysell) Introduction to FOAM, FOI/VS s CFD software (C. Fureby) Aeroelastic activities ( J. Smith) Flow problems involving moving boundaries and interfaces (E.Lillberg) Turbulence modeling in RANS and LES (C.Fureby, L.Persson & U.Svennberg) Turbulence modeling (S.Wallin) Transition prediction (A.Hanifi) Optimal design and control (M.Berggren) High speed turbulent combustion (C.Fureby) The pulse detonation engine (J.Tegnér) Applied aerodynamics (O.Hamnér) Ram jet robot calculations (M.Tormalm) Conceptual study of a supersonic heavy, low observable missile (J.Johansson) Numerical analysis (J.Nordström) Aeroacoustics (G.Efraimsson) The interaction between a lightning flash and an aircraft in flight (A.Larsson) IR calculations (M.Andersson) Low speed applications (S.Peng) Tip vortex cavitation modeling (N.Wikström) Underwater vehicle hydrodynamics (N.Alin) Surface ship hydrodynamics (E.Lillberg & U.Svennberg) 7 Solid rocket propellant combustion and launch technology (M.Berglund)

Introduction to FOI/FFA s CFD software P. Eliasson 8

Euranus Euranus : European Numerical Aerodynamic Simulator, developed at FFA and VUB, developed for ESA 3D RANS compressible Navier-stokes cell centred finite-volume solver for structured multiblock grids Steady state solver/time accurate solver with/without moving grids Convergence acceleration like multigrid and implicit residual smoothing Originally designed for high-speed flows, contains thermally perfect gas models, equilibrium chemistry, chemical and thermal non-equilibrium models Several turbulence models Rotating frame of reference, block-wise Large variety of numerical models and b.c. for external/internal flows Sequential/parallel (PVM) 9

Turbulence models Baldwin-Lomax turbulence model (algebraic) Spalart Almaras turbulence model (one equation) k-ε turbulence model, near wall treatment by Chien (two equations) k-ω turbulence model (two equations) Wilcox standard model Wilcox low-reynolds model BSL model by Menter SST model by Menter Explicit Algebraic Reynolds Stress Models (two equations) New model by Wallin & Johansson Model by Gatski & Speziale; Shih Zhu & Lamley Linear model RANS/LES based on Spalart Almaras LES, dynamic SGS model Transition may be imposed along grid lines (by requiring P=0) 10

Additional options Spatial discretizations, 2nd order accurate Central discretization with artificial dissipation Upwind schemes with TVD limiters Boundary conditions Characteristic b.c., inlet and outlet b.c., spec. fields on boundary... Wall (viscous or Euler) Connectivity, periodicity, translation, rotation,... Non-matching boundary conditions Preconditioning for low Mach numbers Gas options Calorically perfect gas Thermally perfect gas Equilibrium thermo chemistry Chemical and thermo chemical non-equilibrium 11

Steady state solver FAS multigrid Saw-tooth, V-, or W-cycles Simplification on coarser grids Full multigrid Different transfer operators between coarse/fine grids Simplification on coarser grids N-stage explicit Runge-Kutta scheme as smoother Implicit residual smoothing Constant or variable coefficients, explicit contribution Usually gives a doubling of possible CFL number Point implicit treatment of turbulent and chemical source terms 12

Unsteady Solver Explicit 4th order Runge-Kutta Implicit 2nd order backward difference with explicit pseudo time iteration 1.5 ( qv ) n + 1 2 qv ( ) n + 0.5 qv t ( ) n 1 ------------------------------------------------------------------------------------------- + Rq ( n + 1 ) = 0 V n + 1 dq * + R * ( q * ) = 0 R * ( q * ) d τ = 1.5V n + 1 ---------------------- q * Rq ( * ) t 2 ( qv ) n 0.5 qv ( ) n 1 Typically: 10-20 multigrid cycles for about 3 orders of residual reduction Moving grids Grid movement from analytical expressions or perturbation grids GCL Block wise rotation/steady blocks Aeroelastic computations with linear eigenmodes as input perturbation grids Manoeuvres, e.g. acceleration + t + + ----------------------------------------------------------- dq * 0 q * q n + 1 dτ 13

Non-matching boundary conditions Non-matching options available, matched grids with grid discontinuity normal to the boundary. Useful for local refinement or rotating - non-rotating calculations The same grid topology in the two non-matching blocks No topology requirement (more expensive) Example, propeller-wing calculation AIAA-98-0371 y 0.3 sliding interface block boundaries block boundaries 0.0 wing -0.3 propeller 0.0 0.4 0.6 x 2.2 [m][ Pressure variation in time 300. Steady,fine Steady,coarse Time acc. Time acc.+wing 100. -100. 0.00 0.40 0.80 14

JAS at transonic conditions Mach number distribution JAS computation 15

3D delta wing with oscillating flap wing mounting shaft X 2 X 3 X 4 X 1 30%b pressure transducers 29 31 45%b pressure transducers 1 28 291.0 X 5 X n = accelerometer no n b=401.9 X 6 Dimensions in mm X 9 X 7 X 10 X 8 55 o delta wing Pressure measurements at FFA T1500 Euler calculations at SAAB Navier-Stokes computations at FFA 16

Unsteady Euler results Unsteady Cp-distribution Computations-Experiments 45.0% 45.0% 25.00 25.00 M = 0.94, α = 0, δ mean = 0 f = 48 Hz Real: in-phase Imaginary: out-of-phase 0.00 0.00 0.00 0.50 1.00 0.00 0.50 1.00 (damping) Re - C p Im - C p References: 45.0% 45.0% -25.00-25.00 25.00 25.00 AIAA-96-2417 f = 75 Hz ECCOMAS 1996, pp.478-484 0.00 0.00 0.00 0.50 1.00 0.00 0.50 1.00 17

-1.50-1.00-0.50 Cp 0.00 0.50 1.00 RAE2822 Case 10 std_k-w_f SST_k-w_f WJ_k-w_f expr 0.00 0.20 0.40 0.60 0.80 1.00 x/c Mach 0.754, a.o.a = 2.57, Re=6.2 10 6, C-mesh 273*81 18

European Cooperation Ongoing European projects (5th F.W) Eurolift - high lift project, industrially oriented HiAer - high lift research oriented Helix - high lift, new concepts Hyltec - Laminar flow technologies ALTA - Laminar flow technologies Aeroshape - shape optimization TurboNoiseCFD - Aero acoustics in jet engines Taurus - Aero elasticity Project starting 2002 FloMania - turbulence modelling KnowBlade - wind turbine project 19

System for computations on unstructured grids CAD Patch Grid Solver Postproc. EDGE Ensight generator TRITET generation SPIDER Adaption TRITET 20 SPIDER - in-house program for creation of patched surface patches from IGES files TRITET - Surface and volume generator. Includes also adaption modules EDGE - Flow solver Post processing: commercial tools, programs for simpler plotting exists

Hybrid grid generation TRITET Generation of unstructured grids 2D - triangles and quadrilaterals 3D - prisms (varying # layers), pyramids (transitional) and tetrahedra Grid adaptation (remeshing) embedded in Tritet Grid adaption uses original surface descr. Common file format with Edge solver Ongoing development of Tritet Moving grids with retained topology Local adaptation based on h-refinement Local remeshing 21

Overview EDGE solver EDGE solver based on: Finite volume, node centred, hybrid grids - arbitrary elements, agglomeration multigrid Preprocessor - Generates dual grid - Agglomerates coarser grids - Blocking for parallel computations Flow solver - Reads preprocessed grid containing node and edge data - Makes the flow computation Help programs - Sets boundary condition - Lists contents of files - Exports to different file formats - Plot programs - etc... Example of different element types 2D 3D Dual and primary grids Edge info. to flow solver N 2 S N 1 22

EDGE flow solver code characteristics Code in FORTRAN 90 Data stored in linked list - stored data may be retrieved everywhere Dynamic memory allocation Recursion, derived types, structures... Similarities with EURANUS EURANUS uses the same data structure in Fortran 77 Same name of routine names... FFA file format General file format in common with EURANUS Strategy to extend and implement most promising options in EURANUS to EDGE 23

Status of Edge Included and validated features of Edge (2001-10-29) Euler and NS, laminar and RANS Explicit, steady state, residual smoothing Agglomeration multigrid Central spatial discretization with artificial viscosity, 2nd order upwind scheme Rotation in a rotating frame of reference Turbulence: Wilcox k-ω and Explicit Algebraic Reynolds stress model (EARSM) Block partitioning with message passing using MPI Unsteady dual time stepping Preconditioning for low Mach numbers (Choi & Merkle) GUI 24

Validation of Edge Total pressure loss, RAE2822 airfoil. M=0.5, α = 2.8 3 structured grids, 545*97, 273*49, 137*25 6.0 1st order slope 2nd order slope EDGE, upw., trian. EDGE, upw., quads 2.0 log(error) EDGE, central, quads. EDGE, central, triangles Structured grid, quadrilaterals and triangles by triangulation -2.0-6.0 0.0 1.0 2.0 log(size) Euranus 25

M6-wing: Structured - unstructured 1.20 Transonic flow on M6-wing, M=0.84, α=3.06, Re=11*10 6 Cp distribution: Structured surface grid Unstructured surface grid 0.40 1.2 Mpoints 0.9 Mpoints -Cp y/c=44% 26 1.20 0.40 -Cp y/c=90% -0.40

Grid Generation Software L. Tysell 27

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FOAM Field Operation And Manipulation Christer Fureby Totalförsvarets Forskningsinstitut, FOI Vapen & Skydd Grindsjöns forskningscentrum 32

History 1989 Henry got tired of FORTRAN and started to play around with OOP and particularly C++ 1990-93 Intense development of the core of FOAM (Hrvoje & Dave) skeletal classes for field manipulation + numerics 1994 Gavin joins the group at IC and starts adding more physics 1995 Christer & Onno join the group at IC, further physics, turbulence, combustion, electromagnetics publications 1995-98 FOAM grows into a full-bodied CCM package (group of 5-7 people) 1999 Academic research code Commercial code? 2000 Foundation of Nabla Ltd. 2001- Marketing of FOAM on LINUX PC s as a package solution to CFD Contact: Nabla Ltd. e-mail H.Weller@nabla.co.uk Weller H.G., Tabor G., Jasak H. & Fureby C.; 1997, A Tensorial Approach to CFD using Object Oriented Techniques, Comp. in Physics, 12, p 629. 33

Overall Structure foam applications run src tutorials lib make cfd cases MeshTools sgi64 financial cfdtools LINUX stress foam fields boundaryfield util matrices fvmatrix meshes ldumatrix methods fvc thermophysical fvm dimensionset Platforms: UNIX, UNICOS: SUN, IBM, CRAY, SGI, HP, DEC LINUX PC Parallelization: pvm and mpi 34

Discretization and Numerics The NSE can be discretized as f ( v d A) f = 0 m n+ i β i t C D n+ i n+ i i = 0 ( αi( v) P + δ V f[ Ff + Ff ] ) = βi( p) P t P C where Ff = Ffvf Ff( lvp + ( 1 l) vn D F ν d A ( v v )/ d for CD. In other words, + 2 + 2 a v = H( v) ( p) and n P P f f N P 1 + 2 [( a ) da ]( p) = [( H( v)/ a ) da ] n P f f f 1 + 2 F [( H( v)/ a ) ( a ) ( p) ] da n f p f P f f Equations are solved in sequence using a PISO-type loop n P f f p f f for(runtime++;!runtime.end(); runtime++) { Info << "Time = "<<runtime.curtime() nl<<endl; } fvm Ueqn ( fvm::ddt(u)+fvm::div(phi,u,scheme) -fvm::laplacian(nu,u) ); solve(ueqn == -fvc::grad(p)); // --- PISO loop for (int corr=0; corr<ncorr; corr++) { phi=interp(ueqn.h()/ueqn.a())&mesh.areas(); } P da fvm peqn ( fvm::laplacian(1.0/ueqn.a(),p)==fvc::div(phi) ); peqn.solve(); phi-=peqn.flux(); U=(Ueqn.H()-fvc::grad(p))/Ueqn.A(); U.correctBoundaryConditions(); d f N 35

Equation Discretization The discretized equations can be compactly expressed by [A]{x}={y} { } geometricfield<type> [A] fvmatrix<type> Basic mesh description fvmatrix<type> geometricfield<type> volfield<type> surfacefield<type> pointfield<type> fvm (implicit) fvc (explicit) geometricfield<type> volfield<type> surfacefield<type> pointfield<type> metric information fvmesh Points Faces Cells pointfield facelist celllist internal boundary Boundary patchlist Additional features syntax that closely mimics the notation of written mathematics (+, symm, pow, &) written in C++ automatic dimension checking tensor mathematics (scalar, vector, tensor, tensorthird) all trancidental functions available 36

Parallelization Strategies Parallelisation of FOAM is via domain decomposition i.e. the domain is split up into sub-domains, one for each processor, and a copy of the code run on each domain. processor patch decomposepar The processor patch class caters for the inter-processer information within the solver. On decomposition, internal boundaries within the complete mesh are given processor patches which know about the inter-processor topology, and which hide the interprocessor calls (pvm or SHMEM). since the interprocessor communication is at the level of the field classes, any geometric field will automatically parallelise. 37

High-Level Language Codes a short selection Basic CFD codes icofoam incompressible laminar flow code for Newtonian and Non-newtonian fluids potential Foam potential flow code turbfoam incompressible turbulent flow code (algebraic, 2 eqn, & Reynolds stress) Compressible Flow sonicfoam compressible transsonic/supersonic laminar gas flow code sonicturbfoam compressible transsonic/supersonic turbulent gas flow code Heat Transfer chtfoam incompressible code with conjugate heat transfer DNS and LES codes dnsfoam direct numerical simulation code oodles incompressible large eddy simulation code sonicoodles compressible large eddy simulation code Combustion Xoodles compressible turbulent combustion code using the FW-model reactingoodles compressible turbulent combustion code a range of combustion models Electromagnetics Finance Stress Analysis 38

Moving Boundary and Interface Methods for Computational Fluid and Solid Mechanics Eric Lillberg och Lars Olovsson The Swedish Defence Research Agency, FOI Weapons and Protection Division Eric Lillberg, Computational Physics FOI Defence Research Agency 39

Moving Boundary and Interface Problems in Fluid Mechanics Many physical phenomena of interest must contend with moving boundaries and interfaces, e.g. free surface flows, penetration mechanics, flow induced vibrations, bodies with relative motion. Different methods needed to solve different problems. Fluid/solid, fluid/fluid and solid/solid interactions leads to highly coupled, nonlinear systems. LES is suitable for the transient non-linear coupling between fluid and structure where time accuracy is important. Several numerical solutions have been found to such problems, and this leads one to believe that the problems are well posed. Floryan and Rasmussen, Numerical methods for viscous flows, Appl. Mech Rev vol 42, no 12, Dec 1989 Eric Lillberg, Computational Physics FOI Defence Research Agency 40

Interface Representations Lagragian methods (a) Maintain the interface as a discontinuity and explicitly track its evolution. The grid is configured to conform to the shape of the interface and adapts continually to it. Eulerian methods (b) Employs a fixed grid. The interface is reconstructed from the properties of appropriate field variables such as fluid fractions or a level-set Eric Lillberg, Computational Physics FOI Defence Research Agency 41

General methods at hand ALE - Arbitrary Lagrangian-Eulerian + Explicit tracking of the interface Transformation methods + Boundary conditions - Complex geometries - Breakups/Mergers - Large deformations Volume of Fluid + Any geometry Volume of Solid + Complex interfacial behavior Cut-Cell Techniques + Large deformations Virtual Boundary methods - Interface not explicitly defined Level-Set methods - Complex boundary conditions - Interface reconstruction Over Set Grid Methods + Multiple geometries with relative motion Eric Lillberg, Computational Physics FOI Defence Research Agency 42

VOF Methods for Fluid Interfaces Bubble dynamics as an example of interface capturing for large, general deformations, using a Volume of Fluid (VOF) method div v = 0 t t ( ρ v ) + div( ρ v ( α ) + div( α v ) = v ) = grad p + div S + ρ g + f 0 ρ = αρ (, µ 1 + 1 α ) ρ 2 µ = αµ 1 + (1 α ) f = σ div(grad α / grad α ) grad α 2 Eric Lillberg, Computational Physics FOI Defence Research Agency 43

ALE Methods for Fluid/Structure Interaction Grid moves with the geometry while the N-S equations are solved in a fixed grid approach compensated for the mesh-motion fluxes U. Suitable for accurate fluid/structure interaction problems with limited deformations. Geometric conservation. div( t ( v v ) + U ) = div(( 0 v U ) = + v ) grad p div S Eric Lillberg, Computational Physics FOI Defence Research Agency 44

Några ord om penaltybaserad Euler-Lagrangekoppling Lars Olovsson The Swedish Defence Research Agency, FOI Weapons and Protection Division 45

Varför Euler-Lagrangekoppling? Det är ofta lämpligt att beskriva en del av en modell med en Lagrangeformulering och en del med en Eulerformulering. En kopplingsalgorithm krävs för kommunikationen mellan modellens olika komponenter. Lagrangebeskrivning Eulerbeskrivning 46

Penaltybaserad metod En penaltybaserad kopplingsalgoritm håller koll på relativa förskjutningen mellan fluid och struktur. Nodkrafter, proportionella mot relativa förskjutningen, tvingar fluid och struktur att följas åt. Senare Följ partikeln,, och applicera en kraft proportionell mot d. d fluidelement Kontakt detekteras Lagrangestruktur Markera en partikel i fluiden 47

Airbag inlet 48

Airbag 49

Airbag 50

TURBULENCE MODELLING IN RANS AND LES Urban Svennberg, Leif Persson & Christer Fureby Totalförsvarets Forskningsinstitut, FOI Vapen & Skydd Grindsjöns forskningscentrum 51

RANS, URANS,, LES, DNS and all that Reynolds Average Navier Stokes (RANS) 2D/3D stationary solution with turbulence modelling The turbulence model often dictates the resolution Does not necessarily converge to DNS Wide range of models Unsteady RANS (URANS) 2D/3D unsteady solution with turbulence modelling Large Eddy Simulations (LES) 3D unsteady solution with partial (SGS) modelling wall-resolved LES (y + <2, x + <100, z + <15) LES VLES CSC Hybrid RANS/LES wall-modelled LES MILES O(Re 3/2 ) celler SGS turbulence models physics on macro and meso scales correctly treated Direct Numerical Simulations (DNS) 3D time accurate solution O(Re 9/4 ) cells, high numerical accuracy No modelling, all scales resolved all physics correctly treated 52

RANS Average the NSE over time or across an ensemble of flows (ergodicity) ( v v ) = p + ( S R) + f, v = 0 where R= v v Need to close these equations by modelling R Different levels of modeling different cost and accuracy Two-equation models (R=ν t D, ν t =c µ k 2 /ε) 2 ( k v ) = 2 νt D + (( ν+ νt/ σk) k) ε ( ε v ) = P + (( ν+ ν / σ ) ε) R ε ε Non-linear two-equation models Differential stress models t T 2 ( R v ) = R D + D R+ ( νk R R) + c1 ( ε/ k) R 3 c 2 εi More complex models more physics better resolution 53

The Filtering Approach to LES Convolving the NSE with the filter kernel G(x, ) yields the LES equations v t ( v) + ( v v) = p + ( S B) + f+ m ; v= 0 where B ( v v v v) = ( v v v v) + ( v v+ v v ) + ( v v ) v m = [, G ]( v v+ pi S) in which [, G ] Φ= Φ Φ Need to close these equations by modelling B and m v, or B neglecting m v SGS models usually based on isotropy assumptions some physics not included (e.g. near wall effects) EVM SSM & MM DRSM B= 2ν k D B= v v v v 2ν k D T T t ( B) + ( B v) = ( LB + BL ) + M + Π + E Improvements (modifications) necessary for high Re complex flows. E.g. wall-resolved LES wall-modelled LES MILES y + <2 νbc = νbc ( τw, yp, vp ) particular numerics 54

Monotone Integrated LES (MILES) Alternative concept for LES introduced by Boris et al, (1992) and under rapid development: Fureby & Grinstein, (1998, 1999, 2000), Karniadakis et al (2000), Knight et al (1998, 2000). Idea MILES uses the features of particular numerical methods to construct implicit (built-in) SGS models by means of the leading order truncation error + no commutation error + improved generality no parameters +/ strong coupling with the numerics The FV, FD or FE discretization acts as an implicit low-pass filter same temporal scheme as in conventional LES same treatment of diffusive and source terms as in conventional LES Monotonicity preserving or TVD schemes for the convective terms (often using flux limiters Γ) T T 2 Modified equations B= CL + LC + χ Ld Ld, C= C( v, Γ), χ= χ( Γ) 55

Circular and rectangular jets Aim: SGS modelling, jet-flow physics Re D =10 4 to 10 6 Grids: 10 5 to 10 6 Free Shear Flows Spatially Developing Transitional Jet ln(e/(vrms 2 λi)) (b) Energy spectra in farfield (isotropic) region ln(kλi) 1.4 v/v0 1.2 1 0.8 Jet centerline velocity vs axial distance 0.6 0.4 0.2 Vorical regions (II>0) colored by ω 0 x/d 0 10 20 30 40 50 In collaboration with NRL, SBD & KTH Fureby C. & Grinstein F.F.; 1998, AIAA Paper No 98-0537, AIAA.J., 37, p 544. Fureby C. & Grinstein F.F.; 2000, 8 th European Turb. Conf., Barcelona, Spain. 56

Wall Bounded Flows Fully Developed Turbulent Channel Flow Re τ =180, 395, 590 (DNS), 2030 (EXP) and 10000 Grids: 60 3, 60 2 90 and 90 3 LES: SMG, DSMG, OEEVM, DSM MILES wall-resolved and wall modelled LES 30 25 20 15 10 DNS Re=395 EXP Re=2030 OEEVM WL Re=395 OEEVM1 Re=395 OEEVM2 Re=395 OEEVM WL Re=2030 OEEVM Re=2030 OEEVM WLRe=10000 v + =κ -1 ln(y + )+B v /u τ 5 log-region 0 10 1 10 0 10 1 10 2 10 3 10 4 5 4.5 4 3.5 3 v /u τ DNS Re=395 EXP Re=2030 OEEVM WL Re=395 OEEVM Re=395 OEEVM2 Re=395 OEEVM WL Re=2030 OEEVM Re=2030 OEEVM WLRe=10000 2.5 2 1.5 wall-modelled OEEVM, 60 3 1 0.5 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Fureby C., Gosman A.D., Sandham N., Tabor G., Weller H.G., & Wolfstein M.; 1997, TSF 11 Fureby C. & Grinstein F.F.; 2000, AIAA Paper No 00-2307, J. Comp. Phys 57

Supersonic Flows Base Flow at Ma=1.5 Expansion Waves Recompression Waves Ma=2.5 Free Shear Layer C L Recirculation region Trailing Wake Iso-surface of II= 1 10 3 colored by v x, and contours of ρ Statistics v x rms vortex-rings jet v x Fureby C., Nilsson Y. & Andersson K.; 1999, AIAA Paper No 99-0537. 58

Concluding Remarks LES is not currently fully developed, a few pacing items remain to be solved before LES is useful for engineering calculations How do unknown inflow conditions affect transition of unresolved BL? Laminar/transitional boundary layer Separating shear layers Effects of SGS on coherent structures (and vice-versa) are not well understood. Wake SGS eddy CS How is SGS turbulence affected by rapid strain and distortion? Leading edge Turbulent boundary layer Viscous sublayer not resolved on LES grid. How can τ w be modelled? τ w v v 59

Turbulence Modeling S. Wallin 60

RANS modelling activities at Flygteknik, FFA Stefan Wallin Aeronautics Division, FFA, FOI, Sweden Contents: Overview Some theory and examples of EARSM Curvature effects Passive scalar flux Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 61

Overview NASA Langley Wing tip vortices = Conf. paper = J. publication RST Scalar flux Curvature and rotation Afterbody Planforms Inlet ducts EARSM TurMMAC ETMA ESA turb AVTAC FMV (FoT) EUROLIFT HiAer FLOMANIA 93 94 95 96 97 98 99 2000 2001 2002 2003 2004 RST EARSM, RST Trans pred. Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 62

Statistical approach Time dependent Navier-Stokes equations Reynolds decomposition ũi = t NS ( ũ ) i j ũ i ( x, t ) = U i ( x ) + u i ( x, t ) Reynolds averaged Navier-Stokes (RANS) equations ũi = NS t i ( ũ j ) Reynolds stress tensor Ui = t NS ( U ) i j ( ui u x j ) j u i u j Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 63

Some definitions Reynolds stress anisotropy tensor u i u j a a ij --------- K 2 --δ 3 ij Mean flow strain and rotation rate tensors (normalized) 1 S S ij -- K 2 --- U i U j + ε x j x i 1 Ω Ω ij -- K 2 --- ε U i U j x j x i Turbulent kinetic energy K 1 2 --u i u i Dissipation rate of turbulent kinetic energy ε Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 64

Modelling approaches RST ARSM Tr( a) = f a ( S, Ω, a) 0 = f a ( S, Ω, a) EARSM a = f e ( S, Ω) Non-linear eddy-viscosity models Linear eddy-viscosity models a Boussinesq (1877) = a = f N-L ( S, Ω) 2C µ S U uv = ν t y Turbulence scales Tr( K ) = f K ( K, ε, S, a) Tr( ε) = f ε ( K, ε, S, a) 65 Aeronautics Division, FFA (this frame will not be printed) FOI konferensen, oktober 2001 Stefan Wallin

Aeronautics Division, FFA Rapidly sheared homogeneous flow 25 20 Eddy-viscosity model 15 10 W&J consistent EARSM RDT 5 EARSM, fixed P ε 0 0 2 4 6 8 10 T FOI konferensen, oktober 2001 Stefan Wallin K 66

Aeronautics Division, FFA 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0-1.0 Channel flow u 2 w 2 uv v 2 0. 20. 40. 60. 80. 100. 120. 140. y+ FOI konferensen, oktober 2001 Stefan Wallin u u i j 67

Shock induced separation RAE2822, Case10 2D transonic profile LANN 3D transonic wing, 47.5% span -1.50-1.00-0.50 Cp std_kw SST_kw WJ_skw WJ_kw LWJ_skw WJ_Kkw expr -1.50-0.50 skw WJ_skw expr 0.00 Cp 0.50 0.50 1.00 0.00 0.20 0.40 0.60 0.80 1.00 x/c 1.50-0.20 0.27 0.73 1.20 x/c Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 68

Aeronautics Division, FFA Inlet ducts (M2129 by SAAB) taken from Ericsson, J. 2000, Master thesis, SAAB, GDFP-00.0025 FOI konferensen, oktober 2001 Stefan Wallin 69

Curvature effects Weak-equilibrium assumption Da Dt Da ------- = 0 Dt -> algebraic relation The advection, and consequently also the algebraic model, depend on the coordinate system representing the components. a ij Da Dt = 0 Most generic cases can be transformed so that (rotating homogeneous shear, rotating channel, vortices, rotating pipe,...) Complex flows do not have a general transformation. Streamline-based advection Da ------ = T Dt tdtatt ---------------- T a---------t DTt T Dt Dt tdt -------a Dt A ( aω ( r ) Ω ( r ) a ) Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 70

Isolated wing-tip vortex Computed vortex circulation compared to field measurements (Campbell et al. 1996, 1997). Taken from Wallin & Girimaji (AIAA J. 2000). : Initial : RST (L-SSG) : EARSM (L-SSG) : EARSM (non-corrected) : EVM (e.g. std ) K ε Curvature corrected EARSM and RST very similar Basic EARSM as bad as EVM 1.20 0.80 Gamma 0.40 0.00 Initial RST EVM EARSM (curv) EARSM (std) 0.0 5.0 10.0 15.0 r Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 71

Rotating channel, Ro=0.77 1.80 0.25 1.20 U/Um -0.25 uv+ 0.60-0.75 0.00-1.25-1.00-0.33 0.33 1.00 y Fully developed channel flow, DNS Alvelius & Johansson (2000). -1.00-0.33 0.33 1.00 y : WJ : CC-WJ : non-corrected CC-WJ. Aeronautics Division, FFA FOI konferensen, oktober 2001 Stefan Wallin 72

Scalar turbulent flux Turbulent mixing of temperature, species concentration, pollutants, etc. Usually modelled by a eddy diffusivity model (EDM) u i θ = ν t Θ ------- Pr t xi EDM gives the flux aligned with the gradient Even in simple shear flows the flux is not aligned with the gradient (se homogeneus shear) Need for improvements The explicit algebraic model HWWJ, (Wikström, Wallin & Johansson, Phys. Fluids, 2000) K Θ u i θ = ( 1 c θ4 )B ij ( S, Ω)u j u k --- ------- ε x k 73 Aeronautics Division, FFA (this frame will not be printed) FOI konferensen, oktober 2001 Stefan Wallin

Homogeneous shear flow Mean scalar gradient in three different directions. Proposed model (HWWJ) compared with DNS (Rogers et al. 1986) and standard eddy diffusivity model (EDM) Proposed model (HWWJ) captures the flux direction (not aligned with the gradient) Q U u i θ EDM HWWJ DNS U DNS HWWJ EDM u i θ Q U Q DNS HWWJ EDM u i θ 74 Aeronautics Division, FFA (this frame will not be printed) FOI konferensen, oktober 2001 Stefan Wallin

Channel flow The HWWJ model solved together with the low Reynolds number EARSM and the K ω model. Comparision of the HWWJ model with and without diffusion model (DM) model and the eddy-diffusivity model model (EDM). 0 0.2 Θ 0.4 0.6 0.8 1 0 50 100 150 200 250 y + HWWJ+DM HWWJ EDM symbols: DNS data (Wikström 1998) y + 75 Aeronautics Division, FFA (this frame will not be printed) FOI konferensen, oktober 2001 Stefan Wallin

Transition prediction 76 Ardeshir Hanifi FOI/FFA Aeronautics Division, FFA 1

local 3D separation boundary layer slat wake slat wake main wing wake flap separation 77 shock / boundary layer interference transition transition separation bubble transitional separation bubble separation bubble Complex flow phenomena in high lift conditions Aeronautics Division, FFA 2

acoustic disturbances roughness elements 78 instability waves external disturbances Aeronautics Division, FFA 3

Instability Theory Laminar-Turbulence transition is assumed to be caused by breakdown of small disturbances inside the boundary layer. Q(x, y, z, t) = Q(x, y, z)+q(x, y, z, t) 79 Fourier expansion qm,n(x, y)e i(nβz mωt) n= m= q(x, y, z, t) = Aeronautics Division, FFA 4

Governing equations Mean flow with weak streamwise-variation, WKB or Multiple scales type: qm,n(x, y) =ˆqm,n(x, y)e i x x 0 αm,n(x )dx. scale separation: 80 x = O(R 1 ), V = O(R 1 ). Collecting terms up to O(R 1 ) gives a set of nearly parabolic differential equations + C 2ˆqm,n y 2 + D ˆq m,n x = F m,n, Aˆqm,n + B ˆq m,n y Solution is obtained by marching along x direction with ˆq(x = x0) =ˆq0. Aeronautics Division, FFA 5

Different level of approximation: Local theory: =0 Eigenvalue problem x Linear non-local theory: 81 Fm,n =0 Linear parabolic eqs. Non-linear non-local theory: All terms are kept Non-linear parabolic eqs. Aeronautics Division, FFA 6

NoLoT-code (Developed at FFA and DLR) Solves Parabolized Stability Equations (PSE) Local/non-local theory 82 Linear/non-linear equations Compressible/incompressible General orthogonal curvilinear coord. Aeronautics Division, FFA 7

displacement body 10 0 end plate DNS Q inf PSE 10 1 flat plate 10 2 c=500 mm 10 3 Amplitude 83 10 4 10 5 10 6 0 0.2 0.4 0.6 0.8 x/c Nonlinear PSE vs DNS (Högberg & Henningson). Stationary crossflow mode (0,1) and its higher harmonics (0,2)-(0,7). Aeronautics Division, FFA 8

x II Amplitude x I x Frequency 84 stable unstable x x I x II Schematic of neutral stability curve. Aeronautics Division, FFA 9

Transition prediction: e N -method N factor f 3,β 3 ) ln(a/ai ) ( ln A AI ( N = max f,β 85 f 2,β 2 ) αi dx xi = max f,β f 1,β 1 x The value of N at onset of transition is obtained by correlation of computational and experimental data. Aeronautics Division, FFA 10

86 Application of the e N method (flat plate, adiabatic wall). From Mack (1975), Arnal (1989). Aeronautics Division, FFA 11

Oblique-mode breakdown in supersonic boundary layer 0.5 10 0 1,1 0,0 0,2 10 2 0.4 10 4 urms 10 6 0.3 skin friction coefficient x10 3 87 A 0 =0.1% A 0 =0.01% 10 8 A 0 =0.001% 0.2 1500 2000 2500 3000 3500 R 10 10 1000 1500 2000 2500 3000 3500 R Mach number=1.6, F =6 10 6, β/r =0.25 10 4 Aeronautics Division, FFA 12

Flight test Non-linear, non-local transition analysis 88 Calculations performed by S. Hein using NOLOT/PSE (DLR/FFA) code. Aeronautics Division, FFA 13

Strömningsstyrning och aerodynamisk optimering Martin Berggren Flygteknik, FFA Flow Control Utilize flow instabilities/sensitivities to accomplish large effects by small efforts, e.g. Vortex control Werle, 1963 Separation control Head, 1982 89 1

Transition control Transonic wave drag control Alfredsson & Matsubara, 2000 Cp 1.20 0.80 0.40 0.00-0.40-0.80-1.20-1.60-2.00 + o o + o o + oo ++ + ++++++++++++++++++++++++ + + + o o o oo o oooooooooooooooooooooooo + oooo + o o o o + + + + ++++ oo o + o +++ o + o + +++ o o oo + ++++ o + oo + + o + o o + ++ o+ + + ++ o o + o + o + o + +++ o o o ++ ++ + oo + + + +++++++ oo o o o o o o+ oo o + o ooooo ++++++++++++++ o o oo o oo o + o o/ = design +/ = initial Lorenzen, 1999 Aeronautical Applications of Flow Control Active inlets Fluidic thrust vector control Nose vortex control Active Core Exhaust (ACE) Drag reduction, increased lift (Hamstra et al, ICAS 2000) 90 2

FOI project: Optimal Design and Control of Fluid Flows Project leader: Dan Henningson Computational Aerodynamics: Martin Berggren, Mattias Chevalier, Ardeshir Hanifi, Jan Pralits, Olivier Amoignon Experimental Aerodynamics: Jens Österlund etc. Systems Control: Martin Hagström, Sven-Lennart Wirkander Activities in the FOI project Computational/Theoretical Algorithm development for control and optimization Methods development for automated design Supercomputer simulation of complete flow control systems (incl. sensors, actuators), currently for CF-instability control Experimental Active control of flow in S-duct diffusor 91 3

PhD Projects in cooperation with KTH and UU Mattias Chevalier Jan Pralits Olivier Amoignon Markus Högberg Ori Levin Astrid Herbst Optimal control of boundary layers Optimal design wrt low drag Aerodynamic shape optimization Optimal control of channel flows Flow control in boundary layers Flow control in diffusor flows FOI SSF:IVS, FOI/EU PSCI, FOI/EU VR ramprogram STEM PSCI, SAAB Optimal control/design using Navier-Stokes eq. ϕ NS optimization ϕ J ANS 92 4

This scheme is applied to Optimal control in boundary layers (Chevalier, Högberg) Drag minimization in Edge (Amoignon, Berggren) Design of optimal suction on wings (Hanifi, Pralits) Natural laminar flow technology (Hanifi, Pralits) The control can sometimes be expressed in terms of a pre-computed feed-back law. No iterations needed Boundary layer on a swept wing y U W x U z W 93 5

Cross-flow vortices on a swept wing Direct numerical simulation using the Navier-Stokes equations Slice of a periodic array of vorticies in a Falkner-Skan-Cooke boundary-layer Control of CF-vortices Direct Numerical Simulation of FSC-flow with/without control Control off Control on 94 6

FOI S-duct experiment Test bed for actuators and sensors (pulsed micro jets, pressure shear stress) Test bed for control concepts (system identification, optimal control) Fan for low speed operation Rock chamber for high speeds CAD geometry, under construction L = 1548 mm, H = 464.4 mm, φ = 218 mm, φ = 258mm 1 2 95 7

HIGH SPEED TURBULENT COMBUSTION Christer Fureby, Per Walmerdahl & Marco Kupiainen Totalförsvarets Forskningsinstitut, FOI Vapen & Skydd Grindsjöns forskningscentrum 96

Introduction Multi-diciplinary field involving: (i) fluid dynamics, (ii) thermodynamics, (iii) chemical kinetics and (iv) thermal radiation Premixed Combustion Non-Premixed Combustion Heat release Pr δ L Radiation Re Heat release Fu Pr Radiation µ=µ(t) Baroclinic torque effects Baroclinic torque effects Ox Areas of research Premixed turbulent combustion (jet-engine afterburners, LPP combusters) Non-premixed turbulent flames (engine flames, gas turbines) Supersonic combustion (ram- and scramjets) Fire spread in confined spaces Pool fires Explosions and ignition effects 97

Governing Equations of Reacting Flow The governing equations for the reactive flow problem consists of t ( ρ) + ( ρv ) = 0 N N t ( ρv) + ( ρv v) = p + S+ ρf (P ij I i) (P ij I i) i=1 i=1 t ( ρh) + ( ρvh) = p + SD + h+ ρσ t( ρyi) + ( ρvyi) = ji+ wi n N θ T p= ρ RTΣi = 1[ Yi/ Mi], h= Σi= 1[ Yi( hi, f+ CP idt = µ T T D = κ 0, )], S 2 D, h N N ji= λ i Yi; Σi= 1[ Yi] = 0, Σi= 1[ ji ] = 0 n Σ i = 1 ( Pij Pij ) N P j TAj / T wi= [ Pij Pij ] wj; wj= ρ kjπ i= 1 [ Y ij α i ]; kj= AjT e complex physics (turbulence, chemical reactions, volume expansion, heat release) wide range of length & time scales hard to estimate all parameters very large system of equations to solve for practical fuels equations generally stiff Simplifications required! 98

Premixed Turbulent Combustion Global or simplified reaction mechanisms with Arrhenius chemistry using MILES N (P ij I i) (P ij I i) i=1 j < 4, i<10 i=1 N t ( ρ) + ( ρv ) = 0 t( ρv) + ( ρ v v) = p + ( 2 µ DD) + ρf t ( ρh) + ( ρvh) = p + SD + ( κ T) + ρσ t( ρ Y i) + ( ρvy i ) = ( λ i Y i ) + P ij w j, i=1,,5, j=1,2 If carried out with explicit filtering (LES) several additional terms needs to be modeled. Flamelet models using LES The flame is assumed to be a thin wrinkled interface t ( ρ) + ( ρv ) = 0 t( ρ ) ( ρ ) p ( µ D ) ρ v + v v = + 2 D + B + f t( ρh ) + ( ρv h ) = p + SD + ε+ ( κ T + bh) + ρσ t ( ρξ ) + ( ρ ξ v ) = b ξ ρ u S u Ξ ξ SGS models required for B, b h, b ξ and ε! Ξ and S u require modelling Ξ by a modelled transport equation S u by correlations 99

Non-Premixed Turbulent Combustion Global or simplified reaction mechanisms with Arrhenius chemistry using MILES N (P ij I i) (P ij I i) i=1 j < 4, i<10 i=1 N t ( ρ) + ( ρv ) = 0 t( ρv) + ( ρ v v) = p + ( 2 µ DD) + ρf t ( ρh) + ( ρvh) = p + SD + ( κ T) + ρσ t( ρ Y i) + ( ρvy i ) = ( λ i Y i ) + P ij w j, i=1,,5, j=1,2 If carried out with explicit filtering (LES) several additional terms needs to be modeled. Flamelet models using LES Introduce a mixture fraction, such that z=z(y i ). The eqns can then be expressed t ( ρ) + ( ρv ) = 0 t( ρv ) + ( ρ v v ) = p + ( 2 µ D D+ B) + ρf 1 t( ρh ) ( ρ h ) p Y ε ( κ T i= β (,) z χ Y i() z dzd χ 0 0 + v = + SD + + + bh) + ρσ t ( ρz ) + ( ρv z ) = ( λ z + b z ) SGS models required for B, b h, b z and ε! Thin flame located at z=z st. 100

Numerical Methods in Reacting Flow Stiffness avoided by using either global schemes or flamelet models! Finite-Volume (FV) discretization Continuity and momentum equations combined to form a Poisson equation for p Convective fluxes reconstructed with 2 nd order CD For MILES a 2 nd order FCT scheme is used Diffusive/viscous fluxes represented by 2 nd order CD Crank Nicholson time integration Scheme of O( t 2, x 2 ) PISO-type loop adopted for the p-equation Segregated solution approach (Co<0.2) 101

3 2.5 2 1.5 1 0.5 0 3 2.5 2 Combustion in a Jet-Engine Afterburner x 2 /h 1 0 1 2 3 x /h 2 <v 1 >/v 0 3 2.5 2 1.5 1 0.5 0 3 2.5 2 x 2 /h 1 0 1 2 3 x /h 2 <v 1 >/v 0 3 2.5 2 1.5 1 0.5 0 3 2.5 2 x 2 /h 1 0 1 2 3 x /h 2 <v 1 >/v 0 Re h =44,000 v in =17m/s, T in =288K, C 3 H 8, φ=0.61 0.2 0.18 0.16 0.14 0.12 1.5 1.5 1.5 0.1 0.08 1 1 1 0.06 0.04 0.5 0 3 2.5 2 1.5 1 0.5 0 0.5 1 x /h 2 v 1 rms /v0 0.5 0 3 2.5 2 1.5 1 0.5 0 0.5 1 x /h 2 v 1 rms /v0 0.5 0 3 2.5 2 1.5 1 0.5 0 0.5 1 x /h 2 v 1 rms /v0 Re h =32,000 v in =34m/s, T in =600K, C 3 H 8, φ=0.61 0.02 0 0 500 1000 1500 2000 0 <T> 0 0 1000 2000 x /h 2 3 <T> 0 1000 2000 x /h 2 3 0 <T> 0 1000 2000 x /h 2 3 0.05 0.045 2.5 2 1.5 2.5 2 1.5 2.5 2 1.5 0.04 0.035 0.03 0.025 0.02 0.015 0.01 1 0.5 0 0 0.5 1 <Y CO > 1 0.5 0 0 0.5 1 <Y CO > 1 0.5 0 0 0.5 1 <Y CO > 0 0 500 1000 1500 2000 Volvo Aero, Sjunnesson et al., 1991 0.005 Weller H.G., Tabor G., Gosman A.D. & Fureby C.; 1998, 27 th Int. Symp. on Comb, p 899. Fureby C., Grinstein F.F. & Kailasanath K.; 2000, AIAA Paper No 00-0863 Fureby C.; 2000, Comb. Sci & Tech, 161, p 213. Fureby C., Grinstein F.F., Menon S. & Weller H.G.; 2001, 2 nd Int. Conf. on Turb. Shear Flow Phen., Stockholm. 102

Combustion in a Jet-Engine Afterburner cont. Re h =44,000 v in =17m/s, T in =288K, C 3 H 8, φ=0.61 Re h =32,000 v in =34m/s, T in =600K, C 3 H 8, φ=0.61 103

Scramjet Combustion x 2 /d 9 Jet penetration comparison 7 5 Schlieren (Ben-Yakhar & Hansen, 1998) 3 1 4 9 14 19 x 1 /d 4000 20 LES with Arrhenius chemistry 3000 15 2000 10 1000 5 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 4000 20 3000 15 2000 10 1000 5 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Scalar statistics Fureby C., Ben-Yakar A. & Hanson R.; 2000, FOA-R--00-01288-310--SE. 104

Concluding Remarks Simulations of reacting flows very complicated more complex physics (reactions, turbulence, radiation, ) a wider range of scales (spatial and temporal) to consider Specific treatment of different combustion regimes (non-premixed / premixed) Families of models RANS out of the question due to the strong interactions between the flame and the reactions. Much research (experimentally, theoretically & computationally) to be done! Important military applications 105

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Ram Jet Robot Calculations M. Tormalm 123

124 AERONAUTICS DIVISION 1 (4) Att med hjälp av CFD beräkningar skapa ett aerodynamiskt simuleringsunderlag för en ramjetmotordriven robot. Målsättning: Ramjetrobotberäkningar vid FFA

Ramjet motorn Luftintag Brännkammare Dysa M > 0 Bränsle Flamhållare Fördelar: Nackdelar: Enkel konstruktion Kräver initial hastighet för att starta Bra bränsleekonomi vid höga Machtal Dålig bränsleekonomi vid låga Machtal Reglerbar AERONAUTICS DIVISION 2 (4) 125

Implementation av VAC:s motormodell i EDGE Två nya randvillkor Intagsytan utloppsytan (Massflöde, medeltryck och -temperatur) (Massflöde, tryck och -temperatur) VAC:s ramjetmotor modell 1D CET89 AERONAUTICS DIVISION 3 (4) 126

Status Ramjetrobotberäkningar 2001-10-30: VAC:s motormodul implementerad i EDGE Underlag framtaget för RB73_m2 och jämfört med vindtunneldata. God överrensstämmelse! Jämförelse med VAC:s simuleringsdata ej möjlig pga olika intagsareor. Separata luftintagsräkningar med bleed genomförda i Euler. Nya beräkningar med modifierat luftintag genomförda. Jämförelse med VAC:s simuleringsdata gav stora motståndsskillnader. Simulering ej möjlig med FFA:s underlag. Undersökning av skillnader pågår. AERONAUTICS DIVISION 4 (4) 127

AERONAUTICS DIVISION Tvärteknikprojektet A multi-disciplinary project involving the design of a stealthy supersonic strike missile Johannes Johansson 128

AERONAUTICS DIVISION Agenda What is "Tvärteknikprojektet"? Design requirements Aerodynamic calculations RCS calculations Current and future work Configuration T60, Mach 1.5 Configuration U0, Mach 0.5 129

What is "Tvärteknikprojektet"? "Tvärteknikprojektet" is a multi-disciplinary project involving: Computational aerodynamics Experimental aerodynamics Structures Radar signature IR signature Flight simulations Goal is to design a stealthy supersonic strike missile capable of given design requirements AERONAUTICS DIVISION 130

Launch area AERONAUTICS DIVISION Design requirements Mission profile cruise at Mach 1.5 (low altitude) 400 km r < 200 m Target 131

d = 0.35 m AERONAUTICS DIVISION Design requirements Payload m = 500 kg L = 2.2 m Warhead from KEPD 350 132

Design requirements Signature Radar: Missile should have "low RCS" in given sector 45 360 10 IR: Missile should have "low IR signature" AERONAUTICS DIVISION 133

AERONAUTICS DIVISION Initial design Wing planform design Developing planform using Wingbody panel method program Example shows some of the evaluated planforms. 134

AERONAUTICS DIVISION Aerodynamic calculations CFD Euler calculations using Edge Unstructured mesh (generated with Tritet) Example shown: Pressure coefficient at Mach 0.5, 30 angle of attack 135

AERONAUTICS DIVISION Aerodynamic calculations 9 different configurations 2 main Mach numbers plus sweep Angles of attack up to 50 Sideslip at low and high angles of attack About 200 different cases calculated 136

RCS calculations Calculations with FOPOL (using physical optics) Uses same surface mesh as CFD calculations Y [m] Y [m] Vinge med rak spetskorda 2 1.5 1 0.5 0 0.5 1 1.5 2 0 1 2 3 4 5 6 7 8 9 X [m] Enbart kropp 2 1.5 1 0.5 0 0.5 1 1.5 2 0 1 2 3 4 5 6 7 8 9 X [m] 180 180 1000 100 210 150 1000 100 210 150 1000 100 210 10 10 konfiguration F60 konfiguration KROPP 10 konfiguration F60 konfiguration KROPP 1 60 1 90 1 120 KROPP F60 Example shows RCS calculations with and without wing. 10 GHz Horisontal polarisation 10 below XY-plane In XY-plane 30 above XY-plane 180 150 konfiguration F60 konfiguration KROPP 0.1 0.01 0.001 0.0001 240 120 0.1 0.01 0.001 0.0001 240 120 0.1 0.01 0.001 0.0001 240 270 90 270 90 270 300 60 300 60 300 330 30 330 30 330 30 0 0 0 AERONAUTICS DIVISION 137

Current and future work Structures Structural design of body and wings Flutter and other aeroelastic effects AERONAUTICS DIVISION 138

Wind-tunnel testing Testing in S4 at FFA 14 different wing configurations 2 fin sizes Deflection of elevators, ailerons and fin Mach 1.52 (cruise), Mach 0.5 (final turn) and transition Mach numbers Small angles of attack and sideslip at Mach 1.52 Large angles of attack and sideslip at Mach 0.5 AERONAUTICS DIVISION 139

AERONAUTICS DIVISION Current and future work Development process Analyse of wind-tunnel test Evaluate stability and control characteristics Refine wing design Improve sizing of control surfaces Simulate to prove concept 140

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Ò Ë ÑÙÐ Ø ÓÒ Å Ø Ó Ö Ò Æ Ë Ä Ò Ð Ý Ê Ö ÒØ Ö ÅÓ ÐÐ Ò Ô ÖØÑ ÒØ Ó ÁÒ ÓÖÑ Ø ÓÒ Ì ÒÓÐÓ Ý Ë ÒØ ÓÑÔÙØ Ò ÍÔÔ Ð ÍÒ ¹ Ì À ÇÖ Ö Ò Ø «Ö Ò Å Ø Ó ÓÖ Ø ÙÐ Ö Æ Ú Ö¹ËØÓ Ò Å ÜÛ ÐÐ ÕÙ Ø ÓÒ ÆÓÖ ØÖĐÓÑ Ã ÖÐ ÓÖ Ö Å Ö Àº ÖÔ ÒØ Ö Â Ò Å ØØ ÓÒ Å ÒÙ ËÚĐ Ö ² Ê Ö Ù Ø ÓÒ Ã Ò ÂÓÙÖÒ Ð Ó ÓÑÔÙØ Ø ÓÒ Ð È Ý ÎÓÐ ½ ÆÓº ¾ ½ ÔÔº ½¹ ÂÓÙÖÒ Ð Ó ÓÑÔÙØ Ø ÓÒ Ð È Ý ÎÓÐ ½ ÆÓº ¾ ½ ÔÔº ¾½¹ ÂÓÙÖÒ Ð Ó ÓÑÔÙØ Ø ÓÒ Ð È Ý ÎÓÐ ½ ¾¼¼½ ÔÔº ½ ¹½ ÇÁ¹Ê¹¼½¾¼¹Ë Ù Ñ ØØ ¼ Ç ØÓ Ö ¾¼¼½ Ú Ö ØÝ Ô ÖØÑ ÒØ Ó ÁÒ ÓÖÑ Ø ÓÒ Ì ÒÓÐÓ Ý Ë ÒØ ÓÑÔÙØ Ò ÍÔÔ Ð ÍÒ ¹ Ì Ú Ö ØÝ Ô ÖØÑ ÒØ Ó ÁÒ ÓÖÑ Ø ÓÒ Ì ÒÓÐÓ Ý Ë ÒØ ÓÑÔÙØ Ò ÍÔÔ Ð ÍÒ ¹ Ì Ú Ö ØÝ 143

Ñ Ø ÓÒ Ú ÐÓÔ Ò Û Ñ Ø Ó º Ê Ð Ø Ø Ñ Ø Ñ Ø Ò ÒÙÑ Ö º ÈÖÓÓ ÓÖ ÐÐ ÒÙÑ Ö Ð Ø Ò ÕÙ ÑÔÐ Ñ ÒØ º ¼ Ç ØÓ Ö ¾¼¼½ 144

½ ¼ ÙÚ Ü Ü ÙÚµ Ü ½ ÙÚµ Ü ¼ Ù Ü Úµ Í Î µ È Í Ì È Î Í Æ Î Æ Í¼Î¼ Í Î µ È ½ Ø ÓÖÝ Ë È ÙÑÑ Ø ÓÒ Ý Ô ÖØ µ ÓÔ Ö ØÓÖ ÓÒØ ÒÙÓÙ Ö Ø Ù Ú Ü µ Í È ½ ÉÍ È È Ì É É Ì ½ ¼ ¼ ½ ÈÖÓÓ ¼ Ç ØÓ Ö ¾¼¼½ Í Î µ È Í Ì ÉÎ Í Ì É Ì µî È ½ ÉÍ µ Ì ÈÎ Í Ì Î 145

È Ü ½ Ø ÓÖÝ Ü ÑÔÐ Ì Ë È ÓÔ Ö ØÓÖ Ò Ø ÓÒ ÓÖ Ö º ½ ¾ Ü ¼ ¾ ¾ ½ ¼ ½ ½ ¼ ½ ¾ ¾ ½ ¼ ½ ¾ ½ ¼ Ç ØÓ Ö ¾¼¼½ ½ ½ ¾ ½ 146

ÀÄ ¼ ½ º º º ¼ ½ ÀÊ ½ Ø ÓÖÝ Ü ÑÔÐ Ì ÒÓÖÑ Ò Ø Ò Ö Ð º È ¾ Ñ Ø ÓÖ Ö Ñ ÀÄ Àʵ Ö ÝÑÑ ØÖ Ð Ñ Ñ ÐÓ ¼ Ç ØÓ Ö ¾¼¼½ 147

ÍØ È ½ É Í È ½ ͼ ص صµ ¼ È Ò ÐØÝ ÓÖÑÙÐ Ø ÓÒ ÓÖ ÓÙÒ ÖÝ ÓÒ Ø ÓÒ Ì ÓÒØ ÒÙÓÙ ÔÖÓ Ð Ñ Í Ø Í Ü ¼ Ø ¼ ¼ Ü ½ Í ¼ ص ص Ì Ò Ö Ý¹Ñ Ø Ó Ý Ð Ì Ñ ¹ Ö Ø ÔÔÖÓÜ Ñ Ø ÓÒ Í ¾ Ø Øµ¾ Í ½ ص ¾ Ì Ò Ö Ý¹Ñ Ø Ó ½µ Ý Ð Í ¾ Ø Øµ¾ Í Æ Øµ ¾ ͼ ص صµ ¾ ¼ Ç ØÓ Ö ¾¼¼½ 148

ÁÜ Å È ½ Ý É Ýµ ßÞ Ð Ü Ý ÉÜ É Ì Ü Ü ÉÝ É Ì Ý Ý µ ¾ ÓÖÑÙÐ Ø ÓÒ ÓÒØ ÒÙÓÙ Ë Ñ ¹ Ö Ø ÁÒØ Ö Ø ÓÒ Ý Ô ÖØ È ½ Ü É Ü Å Áݵ ÍØ ßÞ Ð ÙØ Ü Ý ¼ ¼ Í Ì ÈÜ Å ÈÝÍØ Í Ì ÉÜ Å Èݵ Í Ì ÈÜ Å Éݵ ¼ Í Ì ÈÜ Å ÈÝÍØ ÜÍ µ Ì ÈÜ Å ÈÝ Í Ì Ü Å Èݵ ¼ ¼ Ç ØÓ Ö ¾¼¼½ 149

ÙÒ ÐÐ Ö Ñ ÓÒ Â Ò ÆÓÖ ØÖĐÓÑ ² ÙÒ ÐÐ ÃÖ Æ ÃÌÀ ÖØ Ð Ô Ø ÓÒ Ò ÙÖ Ý ÓÛÒ ØÖ Ñ Ó ËÐ ØÐÝ Î ÓÙ Ë Ó ¼ Ç ØÓ Ö ¾¼¼½ ËÁ Å ÂÓÙÖÒ Ð Ó ÆÙÑ Ö Ð Ò ÐÝ ÎÓÐ ÆÓº ¾¼¼½ ÔÔº ½ ¹½ Á ÓÒ Ö Ò Ô Ô Ö ÆÓº ¾¼¼½¹¾ ¼ Ò Ñ ÂÙÒ ¾¼¼½ 150

½¼ ½ ½ ¹¹ ½ Ì Ñ ¼ Ç ØÓ Ö ¾¼¼½ ÖÖÓÖ ½¼ ¼ ½¼ ½ ½¼ ¼ ½¼ ½ ½¼ ¾ ½¼ ½¼ ½¼ ½ ÙÖ ½ ÖÖÓÖ Ò Ø ÒÙÑ Ö Ð ÓÐÙØ ÓÒ ÙÒØ ÓÒ Ó Ø Ñ º ÐÐ ÒØ Ö ØÖ ØÐÝ Ø Ð ÓÖÑÙÐ Ø ÓÒ Ú ÖÝ Ò º 151

¼ Ç ØÓ Ö ¾¼¼½ ÖÖÓÖ ½¼ ¾ ½¼ ½ ½¼ ¼ ½¼ ½ ½¼ ¼ ½¼ ½ ½¼ ¾ ½¼ ½¼ ½¼ ½ ½ ¹¹ ½ Ì Ñ ÙÖ ½ ÖÖÓÖ Ò Ø ÒÙÑ Ö Ð ÓÐÙØ ÓÒ ÙÒØ ÓÒ Ó Ø Ñ º ÐÐ ÒØ Ö ÒÓØ ØÖ ØÐÝ Ø Ð ÓÖÑÙÐ Ø ÓÒ Ú ÖÝ Ò º 152

1 0 1 1 1 0 0 1 ¼ Ç ØÓ Ö ¾¼¼½ ÇÖ Ö Ò Ø «Ö Ò ÔÔÖÓÜ Ñ Ø ÓÒ Ó Ð ØÖÓÑ Ò Ø À ÈÖÓÔ Ø ÓÒ ÐÓ ØÓ Å Ø Ö Ð ÓÒØ ÒÙ Ø Ï Ú Ê Ö Ù Ø ÓÒ ² Â Ò ÆÓÖ ØÖĐÓÑ 153

1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 ¼ Ç ØÓ Ö ¾¼¼½ ÙÖ ½ Ì Û Ú Ò Ø ÓÑ Ò ÓÖ Ôº µ Ø Û Ú ÔÖÓÔ Ø Ò ØÓ Ø Ð Ø µ Ø Û Ú ÔÖÓÔ Ø Ò ØÓ Ø Ö Ø µ Ø ØÓØ Ð Û Ú µ µ µ 154

Â Ò ÆÓÖ ØÖĐÓÑ Ã ÖÐ ÓÖ Ö Å ÖØ Ò ĐÓÖ ² ÖÐ Ñ ÓÒ Ì Ô ÖØÑ ÒØ Ó ÁÒ ÓÖÑ Ø ÓÒ Ì ÒÓÐÓ Ý Ë ÒØ ÓÑÔÙØ Ò ÍÔÔ Ð ÍÒ ¹ Ò Ø ÎÓÐÙÑ Å Ø Ó Ò ËØÖ Ø ËØ Ð ØÝ ÔÔÐ ÆÙÑ Ö Ð Å Ø Ñ Ø ÎÓÐ ¾¼¼½ ÔÔº ¾ ¹¾ ÇÁ¹Ê¹¼½¾½¹Ë Ù Ñ ØØ º ¼ Ç ØÓ Ö ¾¼¼½ Ú Ö ØÝ Ô ÖØÑ ÒØ Ó ÁÒ ÓÖÑ Ø ÓÒ Ì ÒÓÐÓ Ý Ë ÒØ ÓÑÔÙØ Ò ÍÔÔ Ð ÍÒ ¹ Ì Ú Ö ØÝ 155

Ñ Ø ÓÒ Ò ÐÝÞ Ø Ø Ð ØÝ Ò ÙÖ Ý Ó ÓÙÖ ÔÖÓ ÙØ ÓÒ Ó ËÙ Ø ÑÔÖÓÚ Ñ ÒØ º ¼ Ç ØÓ Ö ¾¼¼½ 156

ÍØ È ½ É Í È ½ ͼ ص صµ ¼ Ù ¼ Ù ½ Ù¾ Ù ÙÆ ¾ ÙÆ ½ ÙÆ Ù Æ Ü¼ ܽ ܾ Ü ÜÆ ÜÆ ¾ ÜÆ ½ ÜÆ ÐÐ ÒØ Ö ØÖÙØÙÖ ÔÔÖÓÜ Ñ Ø ÓÒ ÍÊ ÆÍ˵ ¼ Ç ØÓ Ö ¾¼¼½ ÅÓÚ Ò Ø ÙÑÑÝ ÔÓ ÒØ ØÓ Ø ÓÙÒ Ö Ý Ð Ø Ë È ÓÖÑÙÐ Ø ÓÒ Û Ð ØÓ ØÖ Ø Ø Ð Øݺ 157

º º º ½ ÖÆ ÖÆ È Ü ¼ Ö¼ ½ Ö¼ ½ Ö¼ ½ ¾ Ö¼ ½ ½ ½ ¾ ÖÆ ½ ÖÆ ¼ Ç ØÓ Ö ¾¼¼½ ½ 158

159

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# 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 ) "+* ( ' &% $ "! 173

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!! * #!! # 0 Convergence against πi, x refinment 10 1 10 2 max(abs(eig(d) pi*i)) 10 3 10 2 10 3 Number of Nodes " / & *. " - *,+! * ( ) %'& $! " 4 & 32 0"! ) 1 0*" * 178

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!! +! #!! 10 0 Convergence against 2πi, y refinment max(abs(eig(d) 2*pi*i)) 10 1 10 2 10 3 Number of nodes +./ " +-,! + ) * &(' $ % " ' 181

Aeroacoustics G. Efraimsson 182

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The interaction between a lightning flash and an aircraft in flight Anders Larsson FOI Swedish Defence Research Agency Grindsjön Research Centre Weapons and Protection Division Warheads and Propulsion 188

Methods and Technologies for Aircraft Safety and Protection against Electromagnetic Hazards (EM-Haz) EU-project within Key Action New Perspectives in Aeronautics P ar t ne r s Saab Avionics (S) AEA Technology (UK) Aerospatiale-Airbus (F) British Aerospace (UK) CEAT (F) DaimlerChrystler Aerospace Dornier (D) Eurocopter Deutschland (D) Eurocopter France (F) ONERA (F) Aerospatiale CCR (F) FOI, subcontractor to ONERA 189

190 By courtesy of Prof. Zen Kawasaki, Osaka, Japan

Illustration of swept stroke phenomena Direction of aerodynamic flow 191

Bi-leader model Zoning strategy E-field magnitude and direction Lightning current Lightning channel characteristics Inception points Sweeping model Zoning Aircraft geometry Aerodynamic flow 192

Typical lightning current Curre nt 15 pulses? 10 pulses 3 ms 850 A 330 A 1 A 20 ms Time 250 µs 200 ms Eo Voltage gradient of lightning channel E ri l d d I t 193

Example of swept stroke simulation Puncture Dielectric part 194

Future challenges Detailed modelling of the lightning channel - Transient currents - Turbulence and 3D dynamics Arc root phenomena - Influence of rivets, joints etc. Experimental validation 195

IR Calculations M. Andersson 196

IR CALCULATIONS Marlene Andersson and Ingmar Karlsson Radiative heat transfer Wavelengths: λ 0.7 14 µm x-ray ultra violet infra red gamma thermal radiation micro wave wavelength λ [µm] 10-5 10-4 10-3 10-2 10-1 1 10 10 2 10 3 10 4 30 OKT 01 197

Sources of IR Radiation 2000 1800 1600 1400 1200 1000 800 600 400 Intensity [arb. units] 200 0 17048 17050 17052 17054 Wavenumber [cm -1 ] A body with T > 0 K Hot gases (as plumes) Gives an IR signature For some military vehicle a low IR signature is important 198

Calculation of IR Signature Intensity given by the equation of heat transfer: s s κ η ds ' = + κ η ds ' 0 0 I e η I η (0) I b η 1 e Ray tracing: Body Plume View point 199

The Module Based Code SIGGE Under development Calculate the IR signature Uses the CFD solution and mesh as input data Uses ray tracing Needs a database of gas data (i.e. absorption coefficients) Extendable software design Visualisation of the result 200

FOI Workshop / 1 Local Preconditioning for Low-Speed Compressible and Incompressible Turbulent Flows Shia-Hui Peng FFA/FOI, SE-172 90 Stockholm (E-mail: peng@foi.se) Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 201

FOI Workshop / 2 Improve convergence rates for low-speed flow computations robustness of compressible codes for general configurations coupled with time-marching algorithms, where the local time step is inversely proportional to the largest eigenvalue of the equation system improve convergence for multigrid Improve convergence rates for high-speed flow computations Á Use the same code for compressible and incompressible flows Á Handle low-speed flows with local compressible effects Á Handle wall-bounded, incompressible viscous flows Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 Motivation 202

FOI Workshop / 3 Diminish the large disparity between the eigenvalues of the equation system Ù and ) at low Mach (Ù numbers the time derivative terms in the equation system are premultiplied by a preconditioning matrix to re-scale the eigenvalues (and brings down the condition number to the order of unity) the transient nature of the system is thus changed, but the converged steady solution should not be modified (for stationary flow computations) For time-accurate computations, the dual time stepping method is used, where a pseudo-time derivative is introduced into the system, and the solution at each physical time step is treated as being steady Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 Basic principle of local preconditioning 203

0 & & & & & & & & ) FOI Workshop / 4 & & & & " ". ".! " * + "/, Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 %'& & & & & ( Preconditioning methodology The governing equations 204 where! " $# %'& ( ) * +! ", %'& ( )!!-! * +!-"!, %'& ( ) The preconditioned system 13254 6 7 1 254 6 8 9 : or equivalently,

FOI Workshop / 5 Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 205 The preconditioning matrix,, must be positive definite not introduce time reversal into the diffusive terms maintain well-conditioned inviscid eigenvalues (based on, and ) The preconditioning-based variables are not necessary to be a conservative set. For primitive variables,, e.g. in a non-conservative system Retaining the conservative fluxes in the system, we employ a selected set of solution variables,,! #" %$ '& ( )

FOI Workshop / 6 Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 206 Transformation of preconditioning matrices based on different dependent variables Local preconditioning is essentially to precondition the spatial residuals Res using local information from the node, ( Comparing to the eigenvalues ) of the unpreconditioned system, the preconditioned "! $&%(' # ) - ' ) /. 0*1. 2 acoustic eigenvalues 3 may 4.6587.(9&: typically ; read ' 3! 2 < = 7..4 with * +,,

Local Scaling Characteristic Solution Time-accurate FOI Workshop / 7 Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 207 Main consequences due to local preconditioning time step based on the preconditioned eigenvalue (becomes larger) of artificial viscosity rescaled (may become smaller) based boundary conditions Riemann invariants are reformulated for the pseudo-acoustic waves updating based on the selected variable set,, and the conservative variables,, are indirectly updated computation from!

FOI Workshop / 8 Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 7 8:9 ; 208 Implemented preconditioning methods Turkel s preconditioner, system low-mach number external aerodynamic flows Choi-Merkle s preconditioner, system low-mach number external flows and low-re number internal flows Hakimi s preconditioner, system low-mach number compressible flows Hakimi s preconditioner,!"# system low-re number flows and non-newtonian fluid flows Weiss-Smith preconditioner, $ system low-speed compressible and incompressible flows, available for % % & ' The gauge quantities are defined by ( *)+, -( ).,. ) /0 %,!"( 1$23 & ),45) 6)+, %

FOI Workshop / 9 Example Viscous flow over a RAE 2822 airfoil ¼ ¼½, o ½, Ê ½¼ Ž «Standard turbulence model, C-type mesh ¾ with nodes. Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 209

FOI Workshop / 10 RAE 2822 airfoil: Residual convergence and preconditioning effect 10 0 10 2 10 4 Unpreconditioned Turkel Choi Merkle Hakimi Hg Hakimi Eg 1 0.8 0.6 0.4 10 6 Max. Residuals 10 8 10 10 0.2 0 Ô 0.2 0.4 0.6 0.8 Unpreconditioned Turkel Choi Merkle Hakimi Hg Hakimi Eg 10 12 0 500 1000 1500 2000 2500 3000 3500 4000 1 0 0.2 0.4 0.6 0.8 1 Work units Residual convergence Effect on pressure Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 Ü 210

FOI Workshop / 11 Example Incompressible flow over a backward-facing step Ž ¼ ½¾ (normalized: Ž ¼ ¼¼ ), Ê ½¼, Ê ¼¼¼ domain, low-re number model, with ¾ ½ ¾¾ nodes. Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 211

FOI Workshop / 12 Backward-facing step flow: Residual convergence Unpreconditioned Preconditioned 10 2 10 3 Max Residuals 10 4 0 2000 4000 6000 8000 10000 Work Units Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 212

FOI Workshop / 13 Backward-facing step flow: Profiles at Ü ¼, ¾,, ½ (from left to right) (Compared with an incompressible code) 4 3.5 3 Unprecond. Incomp code Precondition Experiment 4 3.5 3 Unprecond. Incomp code Precondition Experiment 2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 0 0 0.5 1 1.5 2 2.5 3 3.5 U/Umax+x 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 k/umax 2 +x Mean streamwise velocity Turbulent kinetic energy y/h y/h Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 213

FOI Workshop / 14 It is promising to use preconditioning for both inviscid and viscous lowspeed external flows, and is very encouraging for internal viscous flows; In spite of the same (or very similar) preconditioned eigenvalue, various preconditioners enjoy different degrees of success when dealing with different type of flows; The parameter chosen in the preconditioning system plays a significant part in the convergence acceleration; Comprehensive evaluation and comparison are being made on several typical preconditioners in applications to a wide range of flows; Extensive validations and effort are on progress to implement preconditioning for time-accurate computations of incompressible flows in un- steady RANS and LES. Computational Aerodynamics, FFA Shia-Hui Peng, Ursvik, 30 October 2001 Some remarks 214

Utsikter för kavitationsmodellering Niklas Wikström &GöranBark 215

Vattenturbin & Fartygspropeller För att förstå vad som låtter. Spetsvirvelkavitation avslöjar Ubåt. Buller redan vid låg propellerbelastning. 216

Något om kavitation Gasblå sor skapas i lågtrycksområde, ofta invid struktur. Konvekteras till region med högre tryck där kollaps på börjas och bubblan förintas. Snabb kollaps kan skapa mycket höga tryckpulser, som i sin tur accelererar kollaps hos grannbubblor; Bubbelmoln kollapsar ofta mycket våldsamt. Vid ej våldsam kollaps - fluktuation lägre men hörbara tryckpulser. Skrovinteraktion - Taxfree-klirr. 217

Skiktkavitation Bildas från bladets framkant, på sugsidan. Större skikt som stundom beter sig mycket våldsamt i olika kollapsförlopp... 218

...Skiktkav. Två viktiga förlopp Hela skiktet kollapsar som en bubbla. Returstråle: Del snörps av och kollapsar. (Bild.) Ofta flera återstudsar, molnkavitation 219

Erosionsskada från molnkavitation 220

Spetsvirvelkavitation... Kraftiga virvlar rullas upp från bladspets och nav. Löst gas faller ut, och förångning av virvelkärnan. Skiktkavitet sugs in. Cylindrisk pulserande kavitet. 221

Numerisk simulering för förståelse Utveckla modell för kavitation i Navier-Stokeslösare. Vi siktar inte på att lösa upp kollapsförloppens oerhört korta tidsskalor. Kännedom om storskaligt förlopp kan ge ledtrådar om fortsatt utveckling. 222

Krångligheter Två fasproblem (minst), med skarp fasgräns. Kraftig krökning - ytspänning elak. Komplex strömning. Fasövergång som funktion av trycket. 223

Fri vätskeyta. Lagrange vs. Euler "Interface capturing" Level Set & VOF 224

Level Set: Avst ndsfunktion Level Set & Volume of Fluid φ τ + (φ U ) = S VoF: Proportionell mot fluidparametrar 225

Exempel på modell av fasövergå ng ( ρ U t U ) + ( ρ UU = 1 m ( ρ l ) = τ p + F 1 ) ρ v φ 1 + ( φ U ) = m t ρ l + m = C φ min( 0, p pv ) + C φ 2 226

Level Set, med gasfasen exkluderad? Panelmetoder är långt utvecklade för kavitation. Nästan uteslutande skiktkaviteter. Enkel topologi. Goda resultat. Tittar på dem. Randvilkor för fri vätskeyta inne i domänen. Ångtryck på bubbelranden driver expansion/ kollaps. Slipper empiriska källtermer. Hittills blott endimensionell implementering. 227

UNDERWATER VEHICLE HYDRODYNAMICS Niklas Alin, Urban Svennberg & Christer Fureby Totalförsvarets Forskningsinstitut, FOI Vapen & Skydd Grindsjöns forskningscentrum 228

Introduction and Motivation When designing submarines and UV vehicles hydrodynamic studies are needed to estimate performance characteristics examine and predict signatures (flow, pressure, noise, EM, internal waves, ) help optimize tactical behaviour study manouvering characteristics study launch and recovery of torpedo, UUV, etc. hull-propulsor coupling Potential flow, RANS and LES methods Re=O(10 6 ) O(10 10 ) resolution problems Improved turbulence and SGS models Basic research in turbulence necessary for applied research } Homogenization MILES Interest in simulations of global and detailed flow features Need to study a wide range of problems (sphere fully appended submarine) some examples will be presented 229

Overview of CFD methods For naval applications we utilize the incompressible NSE t ( v) + ( v v) = p + ( 2 D) + f; v= 0 ν Potential Flow Models Stationary potenial flow Reynolds Average Navier Stokes (RANS) 2D/3D stationary solution with turbulence modelling The turbulence model often dicates the resolution Does not necessarily converge to DNS Wide range of models Large Eddy Simulations (LES) 3D unsteady solution with partial (SGS) modelling O(Re 3/2 ) celler SGS turbulence models physics on macro and meso scales correctly treated Direct Numerical Simulations (DNS) 3D time accurate solution O(Re 9/4 ) cells, high numerical accuracy No modelling, all scales resolved all physics correctly treated RANS & LES useful at different stages in the ship design chain RANS first order statistics & parameter studies LES second order statistics & flow dynamics 230

Summary of RANS and LES RANS Time or ensemble averaged NSE ( v v ) = p + ( ν v R) Model the Reynolds stresses R= v v Two-equation models (variants of the k-ε model) Differential stress models LES Low-pass spatially filtered NSE v+ ( v v) = + ( ν v B) t p Model the subgrid scale stresses Eddy-viscosity subgrid models Wall models B= ( v v v v) B 2νkD with νk= c k k Numerics FV-discretization, CD for momentum, no additional diffusion 3pt backward differencing in time PISO-type algorithm for the pressure-velocity coupling Segregated approach with Co<0.4 231

Flow Around a 6:1 Prolate Spheroid cont. Oil-flow Simpson et al., 1998, AIAA.J., 36, p 557 α=20 C p 0.1 0 0.1 0.2 0.3 0.4 Static pressure coef. x/l=0.772 wall-model Legend EXP + EXP MILES OEEVM SMG Oil-flow visualizations α=20 0.5 0 20 40 60 80 100 120 140 160 180 φ 232

Flow Around a 6:1 Prolate Spheroid v v L=1.36 m u 0 =40 m/s Re=4 10 6 α=0 30 L=1.36 m natural transition LDV data at x/l= 0.660 & 0.772 OEEVM α=20 x/l=0.772 α=20 x/l=0.772 α=20 x/l=0.772 Exp. by Chesnakas, C.J. & Simpson, R.L.; 1996, J. Fluids Eng., 118, p 268. EXP OEEVM+WM Hedin, P.-O., et al.; 2001, AIAA Paper 01-1035. Fureby C.; 2001, Keynote Lecture, In Direct and Large Eddy Simulation IV, Kluwer. 233

(m) The DARPA Suboff Studies NACA0020 ϕ D=0.51 L=4.36 x/l=0.975 Re=u 0 L/ν=12 10 6 u 0 =43 m/s Grid 1: 7.4 10 5 RANS Grid 2: 1.1 10 6 DARPA AFF 8 Configuration Grid 3: 1.4 10 6 LES Grid 4: 2.1 10 6 y + 20-50 Groves, N.C. et al., Report DTRC/SHD-1298-01, 1989 Huang, T.T., et al., Proc. 19th Symp. on Naval Hydrodynamics, Seoul, Korea, 1992 234

The DARPA Suboff Studies cont. Flow Physics Hydrogen bubbles and v x contours secondary horseshoe vortex primary horseshoe vortex Oil-flow visualizations colored by τ w Animation of v x in a plane moving aft and instantaneous streamlines Alin N., Berglund M. & Fureby C.; 2000, AIAA Paper No 00-0543. Hedin P.-O., Alin N. & Fureby C.; 2001, The 25 th Symp. on Naval Hydrodynamics, Bulgaria. 235

The DARPA Suboff Studies cont. Comparison between LES and RANS LES 1 0.8 (a) meridian plane 1 0.8 (b) sail 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 v x ω x 0.4 0.6 0.8 1 LES pot RANS RNG ke RANS REAL ke exp 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 RANS 1.6 1.4 1.2 1 RANS rng ke LES OEEVM LES OEEVM WM exp º º º º º º x/l=0.714 0.8 0.6 v x ω x 0.4 x/l=0.978 0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 236

Concluding Remarks RANS is a well-established method from which v and p can be predicted LES is a more recent method that predicts not only v and p but also the dynamics of the flow Both methods are needed in the field of naval hydrodynamics Vital to study the flow around naval ships to determine their hydrodynamic and accoustic signatures 237

Numerical Methods Finite Volume discretization of RANS and LES equations i [ ] β δ t C, ρ n+ i V P f F f = 0 m n+ i β i t Cv, Dv, Bv, n+ i n+ i i = 0 ( αi( v) P + δ V f[ Ff + Ff + Ff ] ) βi( ) P P = p t Crank-Nicholson time-integration Linear reconstruction of convective fluxes 2 nd order central scheme Dv, F f Central difference approx. for inner derivatives in and 2 nd order central scheme Bv, F f PISO pressure-velocity decoupling algorithm 2 3 Segregated approach with Co<0.3 The modified equations ( v ) = 0 SGS term leading order truncation error t ( v) + ( v v) = p + ( νeff v) + {( d d)[ 1 8 v+ ν v] + } 1 6 238

Surface Ship HYDRODYNAMICS Urban Svennberg & Eric Lillberg Totalförsvarets Forskningsinstitut, FOI Vapen & Skydd Grindsjöns forskningscentrum 239

On Turbulence Modelling for Bilge Vortices: A Test of Eight Models for Three Cases S. Urban Svennberg Department of Naval Architecture and Ocean Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden, 2001 240

Introduction 241

Characteristic Problems 1. High Reynolds number: 10 6 10 9 Large interval of length scales Thin boundary layers Resolution problems 2. Free water surface Robust algorithms for generic free-surface representation Mesh topology and refinement issues 3. Three dimensional curved surfaces Grid generation problems Pressure gradients Vortex separation and decay 4. Moving geometries (propellers, rudders) Grid generation problems, complex geometries, moving grids and huge number of cells 242

Surface Grid, KVLCC2 X Z Y X Z Y 243

RSM model, four grids Z 0.00 Z 0.00-0.01-0.01-0.02-0.02-0.03-0.03-0.04-0.04-0.05-0.05-0.06-0.06 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 Coarse Y -0.07 Fine -0.075-0.050-0.025 0.000 0.025 0.050 0.075 Z 0.00 Z 0.00-0.01-0.01-0.02-0.02-0.03-0.03-0.04-0.04-0.05-0.05-0.06-0.06 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 Medium Y -0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 Extra Fine Y Y 244

-0.075 0.8-0.075 0.000 0.025 0.050 0.075 Y -0.075 RNG -0.07-0.050-0.025 0.000 0.025 0.050 0.075 Y 0.2-0.075 0.0 0.2 SST -0.07-0.06-0.06 1.0-0.05-0.05 0.8-0.04-0.04 0.6-0.03-0.03 0.4-0.02 0.2-0.01-0.02 0.0-0.075 0.0 0.2 BSL -0.01-0.025 Z 0.00-0.050-0.07 Z 0.00 KE -0.07-0.06-0.06 1.0-0.05-0.05 0.6-0.04 0.4-0.03-0.04 0.2-0.075 0.0 KO -0.07-0.03 0.0 0.075 Y -0.02 0.050-0.01 0.025-0.02 0.000-0.01-0.025 Z 0.00-0.050 Z 0.00 Exp -0.07-0.06-0.06 1.0-0.05-0.05 0.8-0.04-0.04 0.6-0.03-0.03 0.4-0.02-0.02 0.2-0.01-0.01 0.0 Z 0.00 0.6 0.6 0.6-0.050 0.4-0.050 0.4-0.050 0.4 0.8 0.8 0.8-0.025 1.0-0.025 1.0-0.025 1.0 0.000 0.000 0.000 0.025 0.025 0.025 0.050 0.050 0.050 0.075 Y 0.075 Y 0.075 Y 0.0-0.075-0.075 0.0 0.2 0.2-0.075 0.0 0.2 0.6 0.6 0.6-0.050 0.4-0.050 0.4-0.050 0.4 RSM -0.07-0.06-0.05-0.04-0.03-0.02-0.01 Z 0.00 CLS -0.07-0.06-0.05-0.04-0.03-0.02-0.01 Z 0.00 GS -0.07-0.06-0.05-0.04-0.03-0.02-0.01 Z 0.00 0.8 0.8 0.8-0.025 1.0-0.025 1.0-0.025 1.0 Velocity Field, Propeller Plane Z 0.00 245 0.000 0.000 0.000 0.025 0.025 0.025 0.050 0.050 0.050 0.075 Y 0.075 Y 0.075 Y

Velocity Field, X=0.5226 0.00 0.00 Z 0.00 Z Z -0.01-0.01-0.01-0.02-0.02-0.02-0.03-0.03-0.03-0.04-0.04-0.04-0.05-0.05-0.05-0.06 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 GS -0.06-0.06 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 Y -0.075-0.050-0.025 0.000 0.025 0.050 0.075 Exp KO Y Y 0.00 Z 0.00 Z 0.00 Z -0.01-0.01-0.01-0.02-0.02-0.02-0.03-0.04-0.03-0.04-0.03 246-0.04-0.05-0.05-0.05-0.06 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 CLS -0.06 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 BSL Y Y Y -0.06 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 KE Z Z 0.00 0.00 0.00 Z -0.01-0.01-0.01-0.02-0.02-0.02-0.03-0.03-0.03-0.04-0.04-0.04-0.05-0.05-0.05-0.06 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 RSM -0.06 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 SST -0.06 0.0 0.2 0.4 0.6 0.8 1.0-0.07-0.075-0.050-0.025 0.000 0.025 0.050 0.075 RNG Y Y Y