An improved sub-grid scale flow model f An improved sub-grid scale flow model f Federico Perini, Rolf D. Reitz Federico Perini, Rolf D. Reitz Motivation Sub-grid scale near-nozzle flo Motivation • Combustion efficiency and noise control in engines require multiple injection strategies • Transients become a relevant part of the injection, affecting spray jet Sub-grid scale near-nozzle flo • A sub-grid scale, transient flow prediction (u sgs ) is used for the spray calculation • Transients become a relevant part of the injection, affecting spray jet properties • Computational efficiency of the model is crucial to extend its operation to realistic engine geometries & multiple nozzles instead than under-resolved momentum cell values ( ) + Δ + ′ = u θ θ θ sgs t sgs p n d t , Efficient collision modeling with extended outcomes • Estimate Radius-of -Influence (ROI) based on a tetrahedralization of the to realistic engine geometries & multiple nozzles Δ d t ( ) ( ) - = - + Δ + + Δ + ′ = u r E u u u θ θ θ n n B uvw B sgs p sgs t sgs p n B m S m d t d t , , 1 • Estimate Radius-of -Influence (ROI) based on a tetrahedralization of the drops inside the computational parcel S ρ p r p V c r k d = ∑ ∈ Ω ∉ ′ - + Δ + ′ Ω ∈ Ω ∉ Δ + Δ = jet 3 3 4 jet jet 3 p , 1 3 4 p 0, p , 1 3 4 n n t p n B p p i p p p B p p uvw r d Δt d t r N d t d t r N S θ θ θ πρ πρ 3 4 V N k r ROI - = π • Implicit coupled solution with SIMPLE solv β L θ S θ rel θ 0 r ( ) ∑ ∈ Ω ∈ ′ - Δ + + Δ + ′ + = 4 jet 3 p 3 jet p d t 1 3 4 1 3 i p n n sgs t p n B p p n n p B p p u r d t r N d Δt θ u θ θ r πρ 3 9 4 2 6 p V p N k r ROI - = π • ROI-based collision estimation is O(n 2 ), n number of particles filter impossible collisions based on squared distance function between two • Implicit coupled solution with SIMPLE solv • Transient turbulent gas-jet model used to the effective gas jet assumption: L ρ impossible collisions based on squared distance function between two droplets within the timestep () () () ( ) c bt at t t t t d t f rel rel + + = - + - + = = 2 2 0 , 2 0 , 1 0 , 2 0 , 1 2 2 2 1 2 , 2 , x x θ x x θ x x v Strouhal u x f ≈ = ( ) ( ) exp 1 , - - + = ∫ t t t x u u • Pre-processing filter of eligible parcel couples by running a kd-tree ( ) ( ) ROI t d t t t if possible collision a b t ≤ Δ ≤ > → - = min min min min & & 0 2 ( ) ( ) ( ) () ( ) 2 0 , , , exp 1 , 0 = - - + = ∫ axis entr sgs t t inj axis t x x f t r x t t x u u u u • Pre-processing filter of eligible parcel couples by running a kd-tree based radius-of-influence search 2 S ROI 1 S ROI eligible eligible not ( ) 2 2 2 2 12 1 , , + = entr sgs K x r t r x u • Stokes number and turbulent entrainment L t θ Δ GA-based study of spray mode • Deterministic bouncing, stretching separation (‘grazing’), reflexive separation, coalescence prediction L ROI L • 5 objective functions: vapor penetration, liquid standard deviation, mixture fraction distribution • 6 optimized model variable: C RT , C ΛRT , B 1 , St, K e separation, coalescence prediction 6 7 Spray A, C 12 H 26 , 900K, O 2 =0.0, t inj =1.5ms Experiment simulation 1 m] Initial ramp 2 3 4 5 penetration [cm] 0.4 0.6 0.8 liquid penetration [cm 1 f 2 f 0 0.5 1 1.5 2 x 10 -3 0 1 time [s] 0 1 0 0.2 time [s] UNIVERSITY OF WISCONSIN - for transient fuel sprays for transient fuel sprays Funding Sponsor – Sandia National Laboratories Funding Sponsor – Sandia National Laboratories w modeling 0.16 w modeling vel. particle vel. field = = θ u 0.08 0.12 0.16 e fraction [-] experiment simulation z = 30 mm r 20 30 40 50mm axial vel. particle = θ x r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.04 distance [cm] mixture z axial Validation • Sandia Spray A and mixture preparation in a light duty optical diesel engine B u u = θ drag F distance [cm] sgs u u = B u u = θ 36 μs 16 μs 76 μs 56 μs 116 μs 136 μs 0 0.2 0 ver iteration maintained jet Ω 0.4 0.6 0.8 ver iteration maintained represent the sub-grid scale flow field using 1 [cm] 1.5 Squish plane p inj = 500 bar Squish plane p inj = 860 bar Squish plane p inj = 1220 bar p I Stokes τ τ = ≈ ( ) ( ) 0 , ∂ - - inj d t u u τ τ τ τ 0 0.5 1 1.5 experiment ( ) ( ) ( ) 0 , ∂ ∂ - - - inj inj inj d x x St t u u τ τ τ τ τ 1.5 0 0.5 1 CA = -15.0 CA = -10.0 CA = -5.0 phi [-] Rim plane CA = -15.0 CA = -10.0 CA = -5.0 Rim plane CA = -15.0 simulation CA = -10.0 CA = -5.0 Rim plane 0 0.5 1 1.5 experiment function f entr are model constants el constants 0 0.5 1 CA = -15.0 CA = -10.0 CA = -5.0 phi [-] Bowl plane CA = -15.0 CA = -10.0 CA = -5.0 Bowl plane simulation CA = -15.0 CA = -10.0 CA = -5.0 Bowl plane transient, steady state liquid penetration and n entr , γ max 0 0.5 1 1.5 1.5 experiment 1.2 1.4 m] Spray A, C 12 H 26 , 900K, O 2 =0.0, t inj =1.5ms ( ) l σ phase 4 f 0 0.5 1 CA = -15.0 CA = -10.0 CA = -5.0 phi [-] CA = -15.0 CA = -10.0 CA = -5.0 CA = -15.0 simulation CA = -10.0 CA = -5.0 0.4 0.6 0.8 1 liquid penetration [cm l 3 f References [1] Perini F and Reitz RD, “An effieient atomization, collision and sub-grid scale momentum coupling model for transient vaporizing engine sprays”, Int J Multiphase Flow, submitted, 2 x 10 -4 ] 0 0.5 1 1.5 2 x 10 -3 0 0.2 time [s] coupling model for transient vaporizing engine sprays”, Int J Multiphase Flow, submitted, 2015 ENGINE RESEARCH CENTER As of April 17, 2015