An Eulerian stochastic fields (ESF) method for large eddy simulation of turbulent combustion in compressible flow Cheng Gong

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1 A Euleria sochasic fields (ESF) mehod for large eddy simulaio of urbule combusio i compressible flow Cheg Gog Divisio of Fluid Mechaics Lud Uiversiy, Swede Divisio of Fluid Mechaics, Lud Uiversiy

2 Moivaio ad iroducio Euleria sochasic fields (ESF) is a Moe-Carlo mehod o solve he raspored pdf equaios i Euleria frame. I is easy o coupled wih covecioal CFD code; I has bee used i differe combusios, e.g., premixed/opremixed e flame, spray combusios. ESF mehod has oly bee coupled wih pressure based solver. Pressure-velociy coupled usig SIMPLE or PISO ype mehod; Eergy is solved i sochasic fields wih eglecig he exchage wih kieic eergy; Usage is Limied i low speed codiios (Ma<0.3) Divisio of Fluid Mechaics, Lud Uiversiy

3 Moivaio ad iroducio High speed e flame Supersoic combusio Su e al. Exp. Therm. Fluid Sci., 2012 Bo Zhou e al., combus. Flame, 2015 Divisio of Fluid Mechaics, Lud Uiversiy

4 Compressible LES solver Traspored equaios u x 0 u ( uiu p i ) ( i, i ) i x x E ( Eu pu ) k u q H x x x i, i Toal eergy 1 E e uiui k 2 Molecular hea flux (uiy Lewis umber) q Pr h x Uclosed erms: u u u u i i i H Eu Eu pu pu u u i i, i, Divisio of Fluid Mechaics, Lud Uiversiy

5 Compressible LES solver Sub-grid scale models k k u k u i cd ( k ) x x Pr x x 3/2 c k Closure for momeum equaio 1 2 i 2 Si Skki k i 3 3 Closure for eergy equaio h ui k H i ui Pr x x x Divisio of Fluid Mechaics, Lud Uiversiy

6 Euleria sochasic fields mehod Joi pdf equaio Impossible o solve direcly due o he Muli-dimesios (Ns + 5). Usually, i is solved usig Moe-Carlo approaches. ESF mehod N Ns 1 P ( ;x, ) 1 N N 1 1 d u d ( ) d ( ) d x x x i i 1 C ( ) d 2 dwi, 2 x i N 1 Divisio of Fluid Mechaics, Lud Uiversiy

7 Numerical implemeaio LES equaios The LES solver is a modified versio of rhoceralfoam i OpeFOAM. The covecive erms of he equaios are discreed usiog he Kurgaov ad Tadmor scheme. ESF equaios mix ( ) ( ) (, ) ( ) ad wie mix ( ) u ( ) x x x ad i i wie i ( ) 2 1 (, ) C ( ) 2 2 x i dw Sep 1: Advecio-diffusio-Wieer ( ) ( ) ( ( )) (1) (1) ad wie Sep 2: Micro-mixig 0.5 C ( ) (2) (1) (2) (1) Sep 3: Eergy correcio (3) (2) 1 N m(2) h h h h N m 1 Sep 4: Chemical reacio implici Euler explici (3) (3) 1 ( ) d, 0 : 0 Divisio of Fluid Mechaics, Lud Uiversiy

8 Validaio case Divisio of Fluid Mechaics, Lud Uiversiy

9 No-reacig flow field Divisio of Fluid Mechaics, Lud Uiversiy

10 Reacig flow field Time average durig 1.2 ms, wih NF=8, Cphi=2.0 Divisio of Fluid Mechaics, Lud Uiversiy

11 Flame sabilizaio Two pairs of recirculaio zoes: 1) Iduced by he fuel iecio; 2) Iduced by he sru. The flame is sabilized by he sru iduced recirculaio zoes. Local exicio/re-igiio behavior aroud he fuel iecio iduced recirculaio zoes. Local exicio re-igiio Divisio of Fluid Mechaics, Lud Uiversiy

12 Compariso wih WSR model Mos previous sudies failed o predic he emperaure profile close o he sru (x= 11 mm); The ESF mehod provide good agreeme a x= 11 mm, which reveals ha he ESF ca capure he local exicio /re-igiio behavior, successfully. Divisio of Fluid Mechaics, Lud Uiversiy

13 Coclusios The Euleria sochasic fields mehod was implemeed o a compressible LES solver i OpeFOAM; The LES-ESF solver was validaed o he sru-sabilized combusio i a supersoic combusor; The compressible LES solver provide good performace o he supersoic flow field; Comparig o he WSR model, he ESF mehod ca provide much beer predicio for he local exicio ad re-igiio behavior i he prese codiio. Divisio of Fluid Mechaics, Lud Uiversiy

14 Thaks for your aeio Divisio of Fluid Mechaics, Lud Uiversiy