Scrutinizing Velocity and Pressure Coupling Conditions for LES with Downstream RANS Calculations

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1 Scrutinizing Velocity and Pressure Coupling Conditions for LES with Downstream Calculations Dominic von Terzi, Wolfgang Rodi and Jochen Fröhlich* * Present address: Chair of Fluid Mechanics, Technical University of Dresden, Germany Second Symposium on Hybrid -LES Methods, 17/18 June 2007, Corfu, Greece 1 Dominic von Terzi Institut für Hydromechanik

2 Introduction Compute complex turbulent flows at realistic Reynolds numbers Predictions using not accurate enough or information about instantaneous flow structures required Only critical regions with LES to make computational costs affordable embedded LES Here: Extent of LES/ regions controlled independently by user via predefined /LES interfaces Types of interfaces based on mean velocity normal to interface: 1. LES-outflow 3 2. LES-inflow 2 LES 1 3. Tangential interface 3 (combination of 1 & 2) LES-outflow as possible basis for tangential coupling 2 Dominic von Terzi Institut für Hydromechanik

3 Numerical Method and Turbulence Models Flow solver LESOCC2 developed at IfH (University of Karlsruhe) Incompressible (filtered) Navier-Stokes equations LES: Smagorinsky model (C s =0.065 and 0.1) : Spalart-Allmaras model Curvilinear finite volumes, collocated grids, blockwise grid refinement Pressure correction method 3-stage Runge-Kutta in time (+ implicit for transport equations of model) 2 nd order central schemes for all terms, (+ HLPA scheme for convective fluxes of -model transport equation) Block-structured suitable for zonal LES- 3 Dominic von Terzi Institut für Hydromechanik

4 Velocity Coupling Conditions u = u LES 1. Enrichment: Quéméré & Sagaut (2002) - empirical determination: u = j C E u j 1 = C E LES LES ( u u ) j 1 0 << C E 1 ; CE 0.98 j-1 j u LES = u + u 2. Convective condition: von Terzi, Fröhlich & Mary (2006) - assuming: u t U n + U n > 0 u n = 0 U n = u n (*) U n >> u n - discrete implementation: (1 st order upwind, θ-scheme in time, i.e. 2 nd order implicit for θ = st order implicit for θ = 1) Note: Methods identical for C 1 =C 2 =0 and C 3 =C E in (*) u m 1 m m m+ 1 + j = C u j + C u j 1 + C u j 1 C C C C ~ U 3 n ~ = 1+ θ U = ~ ( 1 ( 1 θ ) U n ) ~ ( 1 θ ) U / C ( ) = ~ = θ U = U n n n / C 0 n Δt / Δn / C Dominic von Terzi Institut für Hydromechanik

5 Velocity Coupling Conditions Enrichment as a discrete convective condition? 1 st order upwind in space and 1 st order implicit in time discretization of (*): C 2 = 0 (since θ = 1) C 1 = 0 only if U n however, then C E = C 3 = 1 A constant C E implies the same convections speed everywhere across the interface With this model, problems are expected for enrichment if C E < 0: U n < 0 (violates convective assumption) C E > 1: U n > (unphysical!) C E << 1: lacks terms due to time-derivative in (*) reflections? If U n varies strongly across the interface or becomes small (near walls) 5 Dominic von Terzi Institut für Hydromechanik

6 Pressure Coupling Conditions Incompressible flows require a continuity constraint variable governed by an elliptic Poisson equation: here pressure Convective condition inappropriate, 2 alternative couplings considered: 1. Solve Poisson equation for union of LES and domain (issue of modified pressure) 2. Decouple pressure fields and apply an explicit mass flux correction to velocities on both sides of the interface (global or local mass flux correction?) Local mass flux correction applied here: - determine mean mass flux across interface as average - compute scaling factor for each side - scale velocities on each side m & iface = 1/ 2 LES + m& iface fm = m& u = i f m ( m& m& ) side u * i 6 Dominic von Terzi Institut für Hydromechanik

7 Turbulent Channel Flow Setup Re b =7000, Re τ =395 [Reference DNS: Moser et al. (1999)] 80 x 100 x 80 cells in main LES domain and inflow generator Δx + = 32, Δz + = 16, y + 1 = 1.45 with stretched grid in y Δt = 0.01, t ave = 350 δ/u b Smagorinsky SGS-model with C s =0.065, Spalart-Allmaras (SA) model 7 Dominic von Terzi Institut für Hydromechanik

8 Turbulent Channel Flow Results E2: E3: Instantaneous and mean streamwise velocities at: y=1 (center) y=0.1 (y + =40) y= (y + =1.45) C4: D-C4: Cases: E2: C E =0.1 E3: C E =0.98 C4: convective D-C4: C4 & pressure decoupled 8 Dominic von Terzi Institut für Hydromechanik

9 Turbulent Channel Flow Results Statistics at grid line next to interface [DNS: Moser et al. (1999)] Cases: E2: C E =0.1 E3: C E =0.98 C4: convect. D-C4: C4 & pressure decoupled 9 Dominic von Terzi Institut für Hydromechanik

10 Periodic Hills Flow Setup Configuration of Mellen et al., 2000: L x =9h, L y =3.035h, L z =4.5h Re h = U bulk h/ν = 10, x 64 x 92 cells from hill to hill Wall-functions [Reference LES: Fröhlich et al. (2005), Breuer & Jaffrézic (2005)] inflow data generator inflow BC (u,v,w) LES- interface locations outflow BC (Neumann condition) periodic LES LES 3D 2D spanwise grid coarsening (92:1) 10 Dominic von Terzi Institut für Hydromechanik

11 Periodic Hills Flow Results Case E3 (CE=0.98): Interface at crest of hill mean streamlines instantaneous u-velocity 11 Dominic von Terzi Institut für Hydromechanik

12 Periodic Hills Flow Results Case D-C4: Interface before hill mean streamlines instantaneous u-velocity 12 Dominic von Terzi Institut für Hydromechanik

13 Periodic Hills Flow Results Case E3: Interface before hill contours of instantaneous streamwise velocity Case D-E3: Case D-C4: 13 Dominic von Terzi Institut für Hydromechanik

14 Conclusions Investigated velocity (and pressure) coupling conditions for LES-to- interfaces for incompressible flow Pressure coupling can be critical, then decoupled pressure with explicit mass flux correction performs best Enrichment for velocity coupling with C E 1 valid for many flows Deficiencies of enrichment explained using convective coupling condition Convective velocity coupling with decoupled pressure field and explicit mass flux correction performed best and was the most reliable method (in particular for hill flow with interface upstream of hill) Outlook: Scrutinizing pressure coupling in more detail [TSFP-5: von Terzi & Fröhlich (2007)] Testing the presented techniques for tangential interfaces (e.g. free-stream boundaries and wall-modeling for LES) 14 Dominic von Terzi Institut für Hydromechanik

15 Periodic Hills Flow Results Mean streamwise velocity [Reference LES: Breuer & Jaffrézic (2005)] x=2 x=7 15 Dominic von Terzi Institut für Hydromechanik

16 Thanks Questions? 16 Dominic von Terzi Institut für Hydromechanik

17 Periodic Hills Flow Results Case D-C4: Interface before hill mean streamlines instantaneous u-velocity <v v > 17 Dominic von Terzi Institut für Hydromechanik

18 Introduction Motivation Compute complex turbulent flows at realistic Reynolds numbers Predictions using not accurate enough or information about instantaneous flow structures required Only critical regions with LES to make computational costs affordable embedded LES attached TBL separation vortex shedding recirculation zone LES 18 Dominic von Terzi Institut für Hydromechanik

19 Introduction Why zonal coupling? Extent of LES/ regions controlled independently by user using predefined /LES interfaces LES/ regions fixed independent of computational grid, solution parameters, IC, etc. allows for grid convergence studies without changing the turbulence modeling at the same time suitable LES and models can be selected independently according to the modeling requirements in their zone avoids problems of non-zonal methods, e.g. issue of consistency of models (in grey areas ) Consequences: a priori knowledge about the flow necessary how to handle interfaces? 19 Dominic von Terzi Institut für Hydromechanik

20 Introduction Types of interfaces Based on mean velocity normal to interface: 1. LES-outflow 3 2. LES-inflow 2 LES 1 3. Tangential interface 3 (combination of 1 & 2) LES-outflow as possible basis for tangential coupling LES Dominic von Terzi Institut für Hydromechanik

21 Introduction Potential application Swirl-stabilized model combustor: Identical configuration except for outlet r p r p Pierce and Moin, 1998 Downstream information is essential for accurate flow field predictions How far upstream can a zone be placed (quality of interface)? 21 Dominic von Terzi Institut für Hydromechanik

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