Energy backscatter and small/large scale interactions in turbulent reacting flows

Transcription

1 Energy backscatter and small/large scale interactions in turbulent reacting flows JAVIER URZAY * and MATTHIAS IHME AFOSR * Engineering Research Associate Center for Turbulence Research Stanford University

2 Outline I. General considera6ons II. SGS backsca9er in diffusive supersonic combus6on

3 I. GENERAL CONSIDERATIONS

4 Kine6c- energy backsca9er in turbulent flows - Richardson s direct cascade is sa6sfied in the average, but local regions of backsca9er do arise (up to 41% of the flow field, Piomelli et al. 91) - Phenomenon caused by interac6on of scales (Brasseur & Wei 94) Filter scale Large scales dissipa6on (net) (SGS model) MODELED Small scales reverse transfer (SGS Backsca9er) RESOLVED MODELED vel. cross correla6on LES DNS 6me He et al. 02

5 Combus6on- induced backsca9er Combus6on energy à Thermal expansion à Kine6c energy Broadening of small scales ν ~ T 1.7 Momentum decay ρ ~ 1/ T ν ~ T 1.7 Filter scale RESOLVED MODELED

6 II. SGS BACKSCATTER IN DIFFUSIVE SUPERSONIC COMBUSTION

7 SGS energy transfer in turbulent reac6ng flows t LARGE- SCALE KINETIC- ENERGY EQUATION k =!u i!u i / 2 ( ρk) + x i ( ρ u i k) = α + Π ε v ε SGS ε SGS = T ij! Sij SGS DISSIPATION Rate of energy- dissipa6on needed to sustain the resolved turbulent mo6on upon filering out the small scales < 0 BACKSCATTER > 0 FORWARDSCATTER Π = p u i Π = P!u i x i x i LARGE- SCALE PRESSURE- DILATATION WORK Converts thermal energy into kine6c energy (and vice versa) Only appears in dilata6onal flows

8 SGS energy transfer in turbulent reac6ng flows k =!u i!u i / 2 BACKSCATTER CAUSES DEPLETION OF SGS KINETIC ENERGY WHICH MAY BE REPLENISHED THROUGH DILATATION EFFECTS (Piomelli et al. 91, Ghosal et al. 95, Domaradzki & Saiki 97)

9 The H 2 /air supersonic turbulent mixing layer H 2 /O 2 kine6cs by Hong et al. 10

10 The H 2 /air supersonic turbulent mixing layer Ma C * Re θ * Re ω * Ma t η Convec6ve Mach Number 2.47 Reynolds number (momentum based) Reynolds number (vor6city based) Inert Reac=ng Turbulent Mach number Kolmogorov length (in grid- spacing units)

11 Results outline 1. Zones under backsca9er 2. Backsca9er vs dilata6on joint sta6s6cs 3. Aerothermochemical field 4. Backsca9er and dilata6on vs mixture frac6on joint sta6s6cs 5. Volume- based budget of energy- transfer modes 6. Eddy viscosity vs backsca9er joint sta6s6cs

12 Localiza6on of SGS Backsca9er BACKSCATTER OCCURS PREFERENTIALLY UNDER VOLUMETRIC EXPANSION INERT REACTING Streamwise cross- sec6ons Spanwise cross- sec6ons Non- dim. span distance Non- dim. cross- shear distance non- dimensional streamwise distance non- dimensional streamwise distance White = Backsca9er, Gray = Forwardsca9er Black contours =boundaries of posi6ve dilata6on. Red line= Stoichiometric mixture frac6on

13 SGS Backsca9er / pressure- dilata6on joint pdfs INERT REACTING SGS Dissipa6on SGS Dissipa6on Pressure- Dilata6on SGS Dissipa6on SGS Dissipa6on Pressure- Dilata6on Pressure- Dilata6on Work Pressure- Dilata6on Work BACKSCATTER OCCURS PREFERENTIALLY (~90%) UNDER VOLUMETRIC EXPANSION

14 Aerothermochemical field REACTING DENSITY GRADIENT Red line: OH isocontours Green line: Stoichiometric mixture frac6on (H- element) TEMPERATURE

15 SGS Backsca9er/ dilata6on / mixture frac6on joint pdfs INERT REACTING SGS Dissipa6on ɛ SGS SGS Dissipa6on ɛ SGS Pressure- Dilata6on Π Pressure- Dilata6on Π REACTING ZONES DO NOT LEAD TO ANY APPRECIABLE AUGMENTATION OF BACKSCATTER OR DILATATION AT THESE HIGH MACH NUMBERS Ec = Mixture Frac6on dilatation (high-speed compressibility) dilatation (chemical heat release) Mixture Frac6on = γ AMa 2 A c p,at A QY F,F Z st = O(10)!

16 Eddy viscosity and energy- transfer modes EDDY VISCOSITY: WITH SGS forwardsca9er Flow compression 42% SGS dissipa6on 24.1% Posi6ve eddy viscosity 69% Dyn. pressure- dilata6on work SGS backsca9er Nega6ve eddy viscosity Posi6ve eddy viscosity 21% 31% SGS backsca9er Flow expansion 30% REACTING

17 Eddy viscosity and energy- transfer modes REACTING SGS Dissipa6on SGS Dissipa6on Pressure- Dilata6on Maximum probability ridge Dynamic- pressure dilata6on work NEGATIVE EDDY VISCOSITIES BECOME INCREASINGLY LESS CORRELATED WITH BACKSCATTER AS THE SGS MACH NUMBER INCREASE

18 Summary 1. SGS backsca9er occurs preferen6ally in regions undergoing volumetric expansion: 34% volume in backsca9er, 90% of it is under expansion. 2. The nega6ve values of the eddy viscosity become increasingly uncorrelated with SGS backsca9er as SGS Mach number increase. 3. For such a high Mach number flow, chemical heat released from combus6on has only slight effects on SGS backsca9er and pressure- dilata6on work.

19 REACTING CASE