Developing LES Models for IC Engine Simulations. June 14-15, 2017 Madison, WI

Transcription

1 Developing LES Models for IC Engine Simulations June 14-15, 2017 Madison, WI 1

2 2 RANS vs LES Both approaches use the same equation: u i u i u j 1 P 1 u i t x x x x j i j T j The only difference is turbulent viscosity model In RANS ν T more complicated In typical LES (e.g. Smagorinsky) ν T is very simple The conceptual winner: RANS

3 3 RANS and LES RANS has better turbulence modeling LES must have better: Grid resolution Numerical accuracy Large eddies come from the non-linear transport terms Grid to resolve eddies Numerical accuracy for phase coherence The conceptual winner: LES More reliance on basic momentum equation Less reliance on models

4 Physical Fidelity Physical Fidelity and Mesh DNS / Experiments RANS Number of mesh cells Images: Som et al

5 Physical Fidelity Physical Fidelity and Mesh DNS / Experiments LES RANS Number of mesh cells Images: Som et al

6 6 RANS and LES: Overlap Unsteady RANS with high grid resolution Eddies may develop but only if flow is inherently non-stationary LES with better sub-grid models Best of both worlds Non-linear transport terms and physics based models Engines require extensive sub-grid modeling Asymptotically approach DNS (?)

7 Physical Fidelity Physical Fidelity and Mesh DNS / Experiments Improved submodels LES RANS Number of mesh cells 7

8 8 Modeling Technologies RANS Scaling laws Dimensional analysis Asymptotic analysis LES Scale similarity Dynamic procedure Approximate de-convolution New LES technologies Dynamic systems for submodels Stochastic coefficients

9 Fuel Injection Modeling Standard injection approach Specify cone angle for Lagrangian parcel injection velocities Uniform random perturbation on velocity angles Generates ensemble-average injection dispersion Spray angle Perturbation does not promote development of large scale liquid structures found in experiments [1] and DNS [2] [1] Fujimoto et al ILASS Europe [2] Deshpande et al Physics of Fluids 9

10 Large Eddies in Liquid Spray LES mesh can support these structures Structure origins Basic instabilities: require extreme meshing to capture Alternative: injection modeling Deshpande et al

11 Injection Modeling: Synthetic Eddy Method Chi-Wei Tsang PhD Thesis, June 2017 Initiate and track virtual, Lagrangian eddy structures Dynamic system Sum virtual eddy effects on boundary mesh point to obtain injection velocities Velocity scale: velocity perturbations Length scale: in summation V inj,z = V 0 + R zz v z, V inj,x = R xx v x, N v j t = 1 N k=1 ε kj V C l s 3 f x inj x k (t l s f y inj y k (t l s f z inj z k (t l s V inj,y = R yy v y, Jarrin et al

12 Stochastic KH-RT Model Standard KH-RT limitations Results are sensitive to model coefficients Coefficients must be tuned to match data Each mechanism uses only a single set of scales Stochastic modeling Chi-Wei Tsang PhD Thesis, June 2017 Use distribution of droplet sizes Example KH time scales Standard KH: τ KH = 3.726B 1 r d (Λ KH Ω KH ) Stochastic KH: τ KH = 3.726B 1 r d,stokh (Λ KH Ω KH ) Sample f r d,stokh, t r from log-normal distribution Similar concept for RT droplet sizes Use droplet size distributions in standard KH-RT length and times scale expressions Apte et al. IJMF,

13 13 Droplet Diameters Vaporizing spray A Mean and rms Case 1: std KH-RT + cone angle Case 2: sto KH-RT + cone angle Case 3: std KH-RT + syn eddy Case 4: sto KH-RT + syn eddy Stoch. KH-RT effects

14 y (mm) Mean Liquid Projected Mass Density Non-vaporizing spray A X-ray experiment Synthetic eddy effects z (mm) Case 1, std KHRT, cone angle Case 2, sto KHRT, cone angle Case 3, std KHRT, syn eddy Case 4, sto KHRT, syn eddy μg/mm 2 Stoch. KH-RT effects 14

15 1: std KH-RT + cone angle 2: sto KH-RT + cone angle 3: std KH-RT + syn eddy 4: sto KH-RT + syn eddy 15 Vapor Penetration Vap A Vap A high T and low den. Syn. eddy effects Vap A low inj. P Vap H

16 16 Mesh Resolution Vapor penetration; vaporizing spray A 0.5 mm, 0.25 mm, and mm meshes Case 4 shows less grid sensitivity Better models; lower mesh requirements Case 1: std KHRT + cone angle Case 4: sto KHRT + syn eddy Dashed lines indicate change in tip penetration speed

17 1: std KH-RT + cone angle 2: sto KH-RT + cone angle 3: std KH-RT + syn eddy 4: sto KH-RT + syn eddy 17 ERC Optical Engine Stoch. KH-RT effects

18 18 Uncertainty Quantification: UQ Big data tool for CFD Repeated simulations with small variations in parameters Model parameters Break-up coefficients, reaction mixing rate, etc. Systematic, non-biased method for studying coefficient sensitivities Physical parameters Spray angle, discharge coefficient, etc. Efficient method to develop shot-to-shot variation, cyclic-variability, etc.

19 UQ: Parameter Sensitivities Correlation coefficients between UQ variables and simulation results High correlations for liquid penetration Complex correlations for vapor Shows why model tuning is difficult Hongjiang Li, et al

20 UQ: Vapor Penetration Variation Non-reacting diesel spray Mean liquid and vapor penetration curves UQ variables Spray cone angle Discharge coefficient Initial fuel temperature Injected fuel mass Error bars indicate one standard deviation Hongjiang Li, et al

21 UQ: Vapor Probability Contours Schlieren UQ Vapor probability contours for non-reacting gasoline sprays UQ variables: Transition We number; Discharge coefficient; Bag rupture time constant Spray cone angle S.E. Parrish, 2014 Hongjiang Li, et al

22 22 Conclusions Models matter more than mesh Additional LES modeling technologies Using stochastic concepts in submodels Dynamic systems for models and/or boundary conditions Uncertainty Quantification Non-biased method for studying coefficient sensitivities Introduce natural variability into results