Implicit LES of Low and High Speed Flows Using High-Resolution and High-Order Methods

Transcription

1 Implicit LES of Low and High Speed Flows Using High-Resolution and High-Order Methods Dimitris Drikakis Cranfield University Aerospace Sciences Department Fluid Mechanics & Computational Science Group

2 Classical & Implicit LES Classical & Implicit LES + = + + i j j i j ij j i j i x u x u x p u u x t u ν δ ) ( j i j i j i ij u u u u u u = = SGS:τ ξ ξ ξ d )d, ( ), ( ), ( ), ( ) ( ), ( t t t t x G t x t x x t x = + = U U U U U Implicit LES (no explicit filtering and dissipation) Classical LES (filtering of the Navier-Stokes equations) j ij i j j i j ij j i j i x x u x u x p u u x t u + = + + τ ν δ ) (

3 Some issues about classical LES Commutation errors: Masking of the SGS terms by the truncation errors Aliasing errors in high-order methods used in classical LES, e.g., spectral schemes Design of SGS models in high-re (wall-bounded) number flows Quantification of errors associated with SGS terms (Geurts & Frölich, POF, 2002) Coupling with RANS: Mathematically and numerically inconsistent LES : U( x, t) = RANS : U( x) = 1 lim T T G( x ξ, t T 0 U( x, t)dt t ) U( ξ, t)dt dξ

4 Remarks SGS models provide the dissipation for unresolved scales and numerical stability but the models and numerics cannot be decoupled unless the flow is fully resolved Are LES (and DNS) fully resolved? This always requires explicit verification Does this occur in practice? Most often not What about under-resolution (intermittency!)? Less resolution means non-smooth solutions locally this motivates the use of high-resolution (nonlinear) methods Not all high-resolution methods are good for ILES

5 LES of Bifurcating and Transitional Suddenly Expanded Flows Numerical Methodology

6 Implicit Large-eddy Simulation The physical link: The Taylor series expansion of the subgrid stress tensor (Approximate Deconvolution) is exactly the same as the conversion from a cell averaged to a cell centred value Thus a 3 rd order accurate MUSCL scheme contains inherently a 2 nd order subgrid model This is a structural model dissipation is dependant on the resolved scales

7 Shock-Capturing Methods for Turbulence: Theoretical Basis 5 Kolmogorov (1941): K L = ( u) 3 t 4 Bethe (1942): S = G ρ 6c 3 3 s c T 2 ( u) 3 S= entropy V=specific volume K=kinetic energy L=length scale G= curvature of the isentrope

8 If your theory is found to be against the second law of thermodynamics, I give you no hope; there is nothing for it but to collapse in deepest humiliation. Sir Arthur Eddington

9 Shameless advertising Examples of Highresolution methods: F i+ 1 = ( F 2 + F 1 ) 2 A ( U U 1/ 2 L R R L ) low high Fi + / 2 Fi + 1/ 2 + φ( Fi + 1/ 2 F low 1 = i+ 1/ 2 Initial data ) Averaging (Godunov-type) Characteristics-based solution Flux Calculation

10 Implicit Model This presentation will focus on two reconstruction methods: 2 nd order Minmod reconstruction 3 rd order limiting method Dissipation can be determined by writing the fluxes as

11 Implicit Model U Momentum Eqn. The truncation error of the Minmod limiter is For the third order limiter

12 Implicit Model U Momentum Eqn. The kinetic energy dissipation for the third order limiter is The kinetic energy dissipation for the expansion of the exact subgrid tensor gives Very good agreement

13 Homogeneous decaying turbulence in a triply periodic cube Isosurfaces of Vorticity at The flow field is initialised from a kinetic energy spectrum Mach = 0.1, Four resolutions investigated 32 3,64 3,128 3 and If KE decay rate is not in the correct range then the simulation will rapidly decorrelate from reality Generally accepted that KE decays as: The decay exponent p varies from in recent experimental results, standard LES from were quoted Mesh Minmod 3 rd order Resolution

14 Velocity Derivative Skewness Calculated as: Most recent high Re experiments ~ -0.34, typical experimental values are -0.5, DNS ~ -0.4 to -0.5 Mesh Minmod 3 rd order Resolution

15 The Experiment Half-height experiment reported by Holder and Barton (IWPCTM, 2004)

16 Video of the experiment (Courtesy of Holder and Barton, IWPCTM, 2004)

17 Numerical Method Finite volume Godunov scheme using a characteristics based solver THCM gas mixture model (5 additional equations) 2 nd order MUSCL reconstruction in space, third order Runge Kutta in time Mesh resolution 600 x 160 x 320 Slip wall boundary conditions 1-D extended domain for the drain hole Ratio x/m = 1E(-04)

18 SF 6 density (b/w)

19 SF 6 density (colour)

20 Comparison with experiment

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23 Volume fraction

24 Shock / SF 6 Position Excellent agreement with SF 6 and shock position Slight discrepancy in shock angle due to diffusion in experiment

25 Shock / SF 6 Position Good overall matching of experiment and results No oscillations at shock front or SF 6 boundaries

26 Very high-order (5 th & 9 th order) ILES: Richtmyer-Meshkov Turbulent Mixing

27 Richtmyer-Meshkov

28 Time evolution comparison of experiment (Jacobs) with WENO5 ILES code

29 Time evolution comparison of experiment (Jacobs) with WENO5 ILES code

30 Time evolution comparison of experiment (Jacobs) with WENO5 ILES code

31 Time evolution comparison of experiment (Jacobs) with WENO5 ILES code

32 Time evolution comparison of experiment (Jacobs) with WENO5 ILES code

33 Time evolution comparison of experiment (Jacobs) with WENO5 ILES code

34 Incompressible Lid-Driven Cavity Standard benchmark case Detailed experimental data available for laminar, transitional and turbulent flows Re= 3,200 (laminar), 5,000 (transitional), 10,000 (fully turbulent) 64x64x64 Fully-developed turbulent flow

35 Validation (Laminar)

36 Validation (Turbulent)

37 Validation (Transitional)

38 Compressible, Open Cavity Flows Strouhal Number Comparison of DNS and ILES Coarse grid ILES: 15 times coarser grid than DNS

39 Turbulent Heat Transfer in Cooling Devices JET Fusion Facility

40 Transitional and turbulent vortical flow Re=250,000, low speed ILES using 3M grid points Experiment Manchester Univ.

41 Comparison with the experiment No forcing Forcing (prescribed spectrum)

42 U U j = j = Re = U j d ν 14.0 m/s (PIV) Re = Synthetic jet configuration Average velocity during expulsion phase of cycle in experiments 1150 Sine wave as inflow boundary condition at cavity base u = A sin( 2 pi f t) Experimental data provided by NASA Langley Research Centre. Max amplitude Frequency of oscillation

43 Synthetic Jets in Quiescent Air Streamwise velocity contours with streamlines at various phase angles

44 Synthetic Jets in Quiescent Air Isosurfaces of vorticity at various phase angles

45 Comparison with experiments Velocity profiles across the slot exit at 1mm above the slot exit at phase angle of u-velocity m/s CFD PIV data v-velocity m/s CFD PIV data position across slot mm Streamwise velocity position across slot mm Cross streamwise velocity

46 Comparison with experiments Velocity profiles across the slot exit at 1mm above the slot exit at phase angle of u-velocity m/s -3-4 CFD PIV data v-velocity m/s CFD PIV data position across slot mm Streamwise velocity position across slot mm Cross streamwise velocity

47 Work in Progress Various strategies of Hybrid ILES and RANS Multi-phase flows Contaminant dispersion (indoor and outdoor configurations) Coupling ILES with acoustic models: high-order BEM and Ffowcs-Williams-Hawkings

48 Hybrid ILES-RANS FLOWer code DLR & ILES Method (Cranfield) 2 nd -order RANS model High-Resolution Scheme (Cranfield)

49 2 nd -order RANS model High-Resolution Model DLR, Germany (Cranfield)

50 Ventilation and Contaminant Dispersion in Aircraft Problem: Ventilation flow analysis in Airbus A380 aircraft cabin

51 DLR experiment Experimental Data

52 RANS Computations Experiment 1.5 RANS computation Velocity Y X

53 High-speed flows: Schematic view of foreshock/aftershock interactions on regions of a re-entry vehicle

54 Instabilities in high-speed flows and their control Pulsation mode around a spiked cylinder (M=6.0). Oscillation mode (M=6.0).

55 Contaminant Propagation Wind ppm emission Concentartion (ppm) Distance (ft) Concentration (ppm) Distance (ft) Critical level Acceptable level

56 Coupling ILES with Acoustic Models High-order BEM, FW-H

57 Acknowledgements Fluid Mechanics & Computational Science Group, Cranfield: Ben Thornber Andrew Mosedale Marco Hahn Sanjay Patel Zeshan Malick Evgeniy Shapiro Chara Papachristou Anthony Milonas Bowen Zhong David Youngs (AWE) Fernando Grinstein, Bill Rider (LANL) Thorsten Schwartz, Klausdieter Phalke (DLR) Sponsors: MOD EPSRC AWE UKAEA Eaton Aerospace BAE Systems European Union DLR Eurocopter Turbomeca

58 Short Course Large Eddy Simulation of Transitional and Turbulent Flows: Numerical, Physical & Implementation Issues Cranfield University 6-8 November large_eddy_simulation.htm