TURBULENCE MODELLING Prof. Paul Tucker given by Tom Hynes 1
STRUCTURE The formidable turbulence modelling task Overview RANS modelling Overview LES Discuss mixing LES & RANS models 2
KEY ROLE OF TURBULENCE Drag generation Heat transfer Particle dispersion Scalar mixing Sound generation 3
TURBULENCE l y + Transition da Vinci - describes the clouds as scattered and torn Van Gogh 4
FORMIDABLE TASK I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic Sir Horace Lamb FRS (1849-1934) 2 nd Wrangler Trinity College Turbulence is the last great unsolved problem in classical physics Richard Feynman (Nobel Prize in Physics - quantum electrodynamics ) Do not even know the Karman constant (l = y 0.38 < < 0.45) or if it is a constant!!! Spalart (2006) 2% decrease in gives 1% decrease in predicted aircraft drag 5
MODEL BASIS Phenomenological but we do not fully understand the phenomena!!! Spalart & Allmaras (1994) La Recherche Aerospatiale, No 1, 5-21 Abstract A transport equation for turbulent viscosity is assembled based on empiricism and arguments of dimensional analysis 6
DICTIONARY DEFINITION Empiricism - Philosophy. the doctrine that all knowledge is derived from sense experience. - Undue reliance upon experience, as in medicine; quackery. 7
WHAT IS RANS MODELLING NS(u)=0 NS(U+u )=0 time average RANS(U)=0 u = U + u Identical to NS(U) but μ = μ t + μ 8
SA MODEL BASIS D t Dt C 1 S t Diffusion Term[C 2, ] Shearing for production ρ Dμ Dt t S 2 Γ μ t 9
CALIBRATION 2D mixing layer max = 0. 01( ΔU) 2 Wake max = 0. 06( ΔU) 2 Calibration suggests 0.6<σ<1; 0.1375< C 1 <0.1275 & 0.6< C 2 <0.7 Pick:2/3, 0.1355, 0.622. Acknowledge plane jet spreading rate 38% too high 10
HEAT TRANSFER 11
URANS Linear models Non-linear models OK - has spectral gap - unusual Liu and Tucker (2007) IJNME 12
URANS T [K] 13
The Resolved Solution in Different Approaches By Strelets group 14
WHAT IS LES? RANS = Resolve time average of flow LES = Resolve all large eddies l y x Modelled < 2 Resolved/solved for 15
DNS, LES & RANS IN A CHANNEL From K. Hanjalic 16
L. F. Richardson s (1922) Rhyme & Kolmogorov (1941) Big whorls have little whorls, which feed on their velocity, and little whorls have lesser whorls, and so on to viscosity (in the molecular sense). Big whorls Kolmogorov (1941), smaller whorls or eddies isotropic Energy α k -5/3 Scale separation 17
LES FILTERING 18
KEY LES PROBLEM Resolving streaks Trent 1000 fan at cruise 10 7 LES Cost α Re 2.5* Hinze (1975) Hybrid LES-RANS Cost α Re 0.5 y + =90 DES type problem By Forsythe, Wurtzler, Squires, Cobalt *Piomelli, AIAA-2008-396 19
CHAPMAN (1975) THE DREAM 10 14 flops N = 10 9 -> Road Runner (2008) 10 15 flops Chow and Moin (2012) confirmed Chapman s estimates GPUs provide cheap computing 20
Fan engine scale LES RESOLUTION REQUIREMENTS LES Hybrid N f(re) Adapted from Leschziner (2009), Piomelli and Balaras (2002) 21
GRID REQUIREMENTS 22
WING-FLAP [Re = 23 x 10 6, 3.3 million cells] ZONAL ILES-RANS vorticity contours Model C L % Error RANS +24 Zonal (I)LES-RANS -5 (I)LES -16 23
PROBLEM AEROSPACE FLOWS 24
CHEVRON ILES-RANS 25
Flow Visualization U u u u v 26
Vorticity Contours 50 x 10 6 12 x 10 6 6 x 10 6 27
SENSITIVITY TO REAL INFLOW/ GEOMETRY Geometry and Near Nozzle Blocking Structure Vorticity Contours 28
Pylon Geometry Instantaneous Streamwise Velocity Time Averaged Streamwise Velocity 29
JET PYLON-WING-FLAP INTERACTION AND MORE Mesh Blocking Topology u grad(ρ) Big noise impact Rig tests difficult!! 30
COMPRESSOR/TURBINE LES s DONE USING YOUR CODE 31
NEW PHYSICS AND PALLIATIVES. Vorticity magnitude isosurfaces s RANS SA RANS-SA-HJ LES C pt,pa 32
NEW PHYSICS - ENDWALLS 33
FAN BLADE 34
CUTBACK TRAILING EDGES 35
RIBBED PASSAGE 36
HIGH PRESSURE COMPRESSOR DRUM & LAB SEALS 37
TURBINE BLADE Re 0.6 million, N > 5 million 10% DS Interface 38
LPT LES/DNS Iso-surface contours of Vorticity Magnitude (From DNS) 39
EXPLORE NEW PHYSICS Blade vibration alters reattchment location by 8% Turbine blade surface topography damaged by Spallation 40
DES of F-15 Post-Stall By Forsythe, Wurtzler, Squires, Cobalt 41
Work of L. Hedges, NASA Funded URANS SRANS, Partly Converged Vorticity Magnitude DES 42
Generic Heavy Truck in Cross- Wind By Wurtzler, Forsythe, Cobalt 43
RUNWAY IN CROSSWIND 44
LES SIMULATIONS 45
Combustion Noise URANS + LES + High- Fidelity Models 46
Open rotor engines Today s aircraft fly from London to Berlin, a distance of 581 miles, on six tonnes of fuel. Planes with open-rotor engines could fly nearly 900 miles, or from London to Rome, on the same amount. 47
BFM: WAKE MODELLING 48
BIFURCATED INTAKE Surface Mesh: Full View 49
BIFURCATED INTAKE Surface Mesh: Lips detail 50
BIFURCATED INTAKE Surface Mesh: Vanes and Branches 51
BIFURCATED INTAKE Surface Mesh: Vanes detail 52
Y0 PLANE Total Pressure Contours 53
Y0 PLANE Vtheta Contours showing asymmetric flow in XZ and XY planes and due to wake entrainment 54
BIFURCATED INTAKE Surface Mesh: Full View 55
CONCLUSIONS Vast number of RANS models, choice can have substantial impact - CFD use a specialist activity CFD predict correct delta s To predict exact levels extreme insights into turbulence model and many other CFD aspects + calibration data Many practical flows are highly three dimensional in which inviscid pressure driven structures occur and then turbulence stresses become less important However, if the 3D structures are unsteady in nature, other challenges arise 56
CONCLUSIONS URANS can help Zonal RANS-LES & LES with take over but when? Depends on HPC/GPU developments Zonal RANS-LES & LES still need physical insight by analyst 57
SCALE SEPARATION 58