Combustion Laboratory Pohang University of Science and Technology. Karam Han, Seonghan Im, Daero Jung and Kang Y. Huh

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1 Development of Turbulent Combustion Libraries based on Conditional Averaging in OpenFOAM for Engineering Problems 15 June th OpenFOAM workshop Penn State university Combustion Laboratory Pohang University of Science and Technology Karam Han, Seonghan Im, Daero Jung and Kang Y. Huh

2 Fundamentals Difficulty in turbulent combustion modeling Turbulent Combustion Large Fluctuations of all Scalar and Vector Quantities Problems both in Measurement and Computation

3 Fundamentals Typical flame structures in turbulent combustion Nonpremxed Premixed Partially Premixed Tight Coupling between Flamelets (Localized Reaction Zone) and Turbulent Eddies (causing Mixing)

4 Fundamentals We need to perform averaging Favre averaged conservation equations with nonlinear terms r + rv% k = 0 t x k ry% i + r ²v Y = - Jik + w& t x x k k i i k Nonlinear Reaction Term p rv% + r ²v kvi = - + t + g t x x x i ik i k i k N ² p m h 1 1 Yi rh% + r v kh = + [ + må( - ) hi ] t x t x s x Sc s x k k k i= 1 i k Nonlinear Convection Term p = r RT% h% = h( Y%, p, T% ) i

5 Fundamentals Closure assumptions for nonlinear terms Is it OK to make assumptions valid in nonreacting turbulence or laminar flows? ²v" F " = - DtÑF % w& = AYY % % n i jt % F exp( - Ea / RT % ) (Eddy Diffusivity) (Arrhenius in terms of Means) The answer is No! Then What Can We do? DNS/LES: No/Minimal averaging Stochastic PDF Transport: Monte Carlo Phenomenological Modeling (RANS): Limited applicability Conditional Averaging (RANS): CMC/LFM

6 Fundamentals What is conditional averaging? For a fluctuating variable Φ, there exists a fluctuating variable x which is closely related with fluctuation of Φ. n å i i i i= 1 i= 1 n å P = 1, P f X = f X Probability f X DX 1 P 1 f X 1 Flame Structure DX 2 P 2 f X 2 DX n Pn f X n Temp. Distribution PDF

7 Fundamentals What is conditional averaging? Zonal conditioning (TPF) Bimodal Variation e.g. turb/nonturb, burned/unburned, etc. Surface conditioning (TNF) Continuous Variation e.g. mixture fraction, reaction progress variable Ref. Chen and Kollman (Turb Reacting Flows Ch. 5, 2 nd ed. 1994)

8 Fundamentals Mathematical procedure Fine grained pdf : d = d ( x -h) pdf for fluctuating x : P( h) = d ( x -h) x h : Fluctuating variable : sampling variable for x h Conservation equation for an arbitrary scalar f ( rx ) + Ñ ( rvx ) = Ñ ( rdñx ) t ( rf ) + Ñ ( rvf ) = Ñ ( rdñf ) + rw& F t fd =< f h > P( h) h Q =< f h > 2 ( rdh ) + Ñ ( rvdh ) = - ( rnd ) 2 h t h 2 2 Q ( rdhf ) + Ñ ( rvdh F ) = rdh N - Q ( rnd ) 2 2 h t h h

9 Fundamentals Mathematical procedure conditional averaged Eqns and pdf After averaging, we get Q =< f h > N º DÑ x Ñx 2 ( rh P( h)) + Ñ ( rh v h P( h)) = - ( r N P( )) 2 h h h t h Assumed beta-function PDF in terms of ( rx% ) é m ù t + Ñ ( r u% % x ) = Ñ ê Ñ % x ú t êë Sc % x úû % % x and P% ( h; x) = + Ñ r % x é = Ñ m Ñ % x ù + 2m Ñ % x - rc% ë û 2 ( rx '' ) 2 t 2 t 2 ( u% '' ) ê '' ú ( ) t êsc % 2 Sc 2 x '' ú % x '' x " ²2 ò 1 0 h (1 -h) a -1 b -1 ( ) (1 ) + a b x -x dx

10 Fundamentals CMC vs LFM CMC : Based on rigorous mathematical procedure for conditional averaging Conditional submodels required for conditional velocity, scalar dissipation rate, etc LFM : Based on physical assumption of a flamelet structure Flame structure in terms of stoichiometric SDR Lagrangian handling of a transient effect (RIF) Applicable range? - Major uncertainties in many engineering combustion problems are in the PDF s due to turbulent mixing, rather than in conditional flamelet structures.

11 Fundamentals Conditional submodels reaction and convection - Reaction Term (1 st order closure) Yi " Yj " < wi ( Y, T, P) h >» wi ( Q, QT, P)(1 + + T1 + T2 ) Q Q i j - Convection Term Mean velocity Linear scaling Gradient diffusion Conservation of higher order conditional fluxes (Mortensen 2005)

12 Fundamentals Conditional submodels scalar dissipation rate AMC model Amplitude mapping closure to Gaussian reference field for homo turbulence (Pope 1991, Gao 1991) Girimaji s model Evolution of beta pdf according to pdf transport eq for homogeneous turbuelnce (Girimaji 1992) PDF integration (steady state) Direct double integration of spatially dependent local pdf (Bilger 1999)

13 TNF CMC 1D model Schematic diagram for interation between OpenFOAM and CMC routine CMC routine CMCreactingFoam (based on OpenFOAM 1.7.x) CMC thermo-chemistry library

14 TNF CMC 1D model Bluff body ML1 flame case description Description Fuel Specification CH3OH (methanol) Fuel jet / Bluff body radius (mm) 1.8 / 25 Fuel / Air mean Vel (m/sec) 80 / 40 Fuel Temp (K) 373 Adiabatic flame temp (K) 2260 Stoichiometric mixture fraction Slip wall Coflow (40m/s) Fuel jet (80m/s) Axis 0.705m Instantaneous and mean compositional structure of bluff body stabilized nonpremixed flames, B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, Combustion and Flame, 114: (1998) 0.07m

15 TNF CMC 1D model Bluff body ML1 flame results (mixture fraction space) Conditional mean temperature with respect to the mixture fraction O2 H2O CH3OH O2 H2O CH3OH O2 H2O CH3OH CO2 CO2 CO2 Major species mass fractions with respect to the mixture fraction

16 TNF CMC 1D model Bluff body ML1 flame results (mixture fraction space) H2 H2 H2 OH OH OH H2 and OH mass fractions with respect to the mixture fraction CO CO CO CO mass fraction with respect to the mixture fraction

17 TNF CMC 1D model Bluff body ML1 flame results (radial distribution) Radial distributions of the Favre mean mixture fraction and r.m.s fluctuation of the mixture fraction

18 TNF CMC 1D model Bluff body ML1 flame results (radial distribution) T T T OH OH OH Radial distributions of the Favre mean temperature and OH mass fraction CH3OH O2 O2 H2O O2 H2O CH3OH H2O CO2 CO2 CO2 Radial distributions of the major species mass fractions

19 CI engine - CMC-ISR model Governing equations of CMC model Conditional mean mass fraction and enthalpy equation Conditional mean reaction rate Spatially integrated conditional mean mass fractions and enthalpy equation Vaporization source terms Mean mixture fraction ξ : Mixture fraction µ t : Turbulent viscosity Mean mixture fraction variance Sc ξ : Schmidt number for mixture fraction ( = 0.9 ) Sc ξ2 : Schmidt number for mixture fraction variance (= 0.9 ) s ξ C : Vaporization source term for mixture fraction : Correlation coefficient

20 CI engine - CMC-ISR model Multiple flame structure consideration Concept of multiple flame structures Multiple flame structures to consider combustion of the sequentially evaporated fuel groups Favre averaged mass fraction F % j (j = 1, 2,, N) is the mass fraction of the j-th flame group. represents the conditional mean mass fraction of the i-th species in the j-th flame group. Weighting factor

21 CI engine - CMC-ISR model Schematic diagram for interation between OpenFOAM and CMC routine CMCdiesel EngineFoam (based on OpenFOAM 1.7.x) CMC routine CMC thermo-chemistry library

22 CI engine - CMC-ISR model ERC diesel engine case description Description Engine Specification Caterpillar 3401E Engine speed (rpm) 821 Bore (mm) x Stroke (mm) x Compression ratio 16.1 Displacement (Liters) 2.44 Combustion chamber geometry In-piston Mexican Hat with sharp edged crater Max injection pressure (MPa) 190 Number of nozzle 6 Nozzle hole diameter (mm) Spray angle (deg) 125 Operating conditions EGR level (%) 7*, 27, 40 SOI timings (ATDC) -20, -15, -10*, -5, 0, 5 Injection duration (deg) 6.5 * represents reference case Kong S. C. et al, SAE Cylinder head liner Piston 3-D sector mesh of 60 deg. with periodic boundary condition. Fuel spray ; Initial droplet size is determined by Rosin-Rammler distribution function w/ the SMD of 14 micron Injected fuel temp : 311K Skeletal mechanism for n-heptane 44 species and 114 elementary steps NOx chemistry included Initial swirl ratio ; 0.978

23 CI engine - CMC-ISR model ERC diesel engine results Spatial distributions of the mean temperature and fuel sprays Spatial distributions of the mean mixture fraction

24 CI engine - CMC-ISR model ERC diesel engine results Conditional mean temperature and scalar dissipation rate with respect to the mixture fraction Major species mass fractions with respect to the mixture fraction

25 CI engine - CMC-ISR model ERC diesel engine results Pressure trace w.r.t different injection time

26 CI engine - CMC-ISR model ERC diesel engine results Pressure trace w.r.t different injection time

27 GAS JET MODEL Grid dependency of standard spray models Schematic of two-phase spray flow Representative large CFD mesh and spray volumes are different the momentum transfer is dampened gas-phase momentum is under-predicted resulting in under-penetration The two-phase spray flow has two components; The motion of the group of droplets which forms the liquid phase and the movement of the air entrained The motion of the group of droplets which forms the gas phase Correct prediction of the gas-phase is crucial To reducing grid-dependency numerical errors, either of the phases could be corrected [1] Abani, N. et al. An improved spray model for reducing numerical parameter dependencies in diesel engine CFD simulations. SAE Technical Paper, (2008)

28 GAS JET MODEL Schematic diagram for interation between OpenFOAM and gasjet routine Gasjet routine (OP x 0 & OP 2L BK ) (OP>x 0 & OP 2L BK ) gasjetdieselfoam (based on OpenFOAM 1.7.x) (OP>2L BK ) equivalent diameter of the gas jet : entrainment constant : breakup length :

29 GAS JET MODEL Simulation Conditions Results Constant volume chamber(20mmx20mmx120mm) Standard k-ε turbulence model KH-RT breakup model Compared spray tip penetration on various cell size (1mm,2mm,4mm) at injection pressure 120MPa and 99Mpa Experimental conditions [2] Injection nozzle Type Hole nozzle DLL-S Number of holes 1 Hole diameter [mm] 0.2 Injection pressure Δp [MPa] Injection duration [ms] Fuel amount [mg] 12 Ambient gas N 2 Ambient pressure [MPa] 1.5 Ambient temperature Room temperature ( K) Ambient density [kg/m 3 ] 17.3 Fuel N-tridecane (C 13 H 28 ) [2] Dan, T., Takagishi, S., Senda, J. & Fujimoto, H. Effect of ambient gas properties for characteristics of non-reacting diesel fuel spray. SAE paper (1997)

30 Gas Turbine Combustor Steady Solver alternatereactingfoam by Markus è OpenFOAM 1.7.x(modification) Steady reactingfoam, PaSR, standard k-e model RK ode solver for 1step chemistry(methane/air) Xeon E5530, 12 GHz(Execution time : 6.2 h for 3000 step) 60 sector, fluid region, 6.3 million polyhedral cells(star-ccm+ Ver.2.10) è converting STAR-CD mesh(vrt, cel, bnd) è converting OpenFOAM mesh(startofoam) Grid for the gas turbine combustor Temperature distribution

31 NOx formation pathway High Pressure Jet-Stirred Reactor by Rutar[3] 6.5 atm, preheated inlet(573k) Residence time : 0.754, 4 ms Standard k-e, PaSR with GRI 3.0 2D axi-symmetric 420 structured cell 1. Premixed CH4/air è Turbulence source Specification of the experiment 6.5 atm, preheated(573k) overall residence time [ms] Equivalence ratio Inlet velocity [m/s] Heat loss è constant T Wall Outlet Air CH mm Computational grids of HP-JSR [3] Rutar, T, 2000, NOx and CO Formation for Lean-Premixed Methane-Air Combustion in a Jet- Stirred Reactor Operated at Elevated Pressure, PhD Thesis, University of Washington, Seattle, Washington.

32 NOx formation pathway NOx mechanism Chemical kinetic modeling by Rutar Irreversible Zeldovich (dno/dt) ZELD = 2k N2+O [O][N2] N2O (dno/dt) N2O = 2k N2O+O [O][N2O] + 2k N2O+H [H][N2O] Prompt (dno/dt) PROMPT = 2k N2+CH [CH][N2] NNH (dno/dt) NNH = 2k NNH+O [O][NNH] CFD Zeldovich N2O 1. N2 + O N + NO 2. N + O2 NO + O 3. N + OH NO + H 1. N2 + O + M N2O + M 2. N2O + O 2NO 3. N2O + H NO + NH 4. NH + O NO + H Prompt 1. N2 + CH HCN + N 2. HCN + O NCO + H 3. NCO + H NH + CO 4. NH + H N + H2 5. N + OH NO + H

33 NOx formation pathway NOx mechanism Ø 4 ms case : Twall = 1700K Ø ms case : tksource = 1.0e+09 kg/ms 3 è Contribution of Nitrous NO increases in high pressure condition NOx formation contribution by chemical kinetic modeling and numerical simulation 6.5 atm, preheated inlet(573k) Overall residence time[ms] Measured NO[ppmv, wet] Approach ckm sim ckm sim Tg [K] Zeldovich NO[ppmv, wet] Nitrous NO[ppmv, wet] Prompt NO[ppmv, wet] NNH NO[ppmv, wet] Total NO [ppmv, wet]

34 Conclusion 1. Conditional averaging is a powerful approach to handle the complicated problem of turbulence-chemistry coupling in many engineering combustion problems. 2. The CMC model is implemented in Openfoam ver. 1.7.x for turbulent nonpremixed combustion. Two different implementation strategies are employed, 1-D Eulerian for steady TNF flames and 0-D Lagrangian with multiple flame groups for diesel engines. 3 The <c> transport model is implemented with the turbulent burning velocity specified to simulate turbulent premixed combustion. It is applied to simulate spark ignition and turbulent flame propagation in an SI gasoline engine. 4. The KH-RT spray breakup model is extended with the gas jet model to reduce grid size dependence due to inappropriate resolution of the gas phase around spray droplets. 5. The PaSR model in Openfoam is applied with single step chemistry for a gas turbine combustor. The PaSR is combined with GRI 3.0 chemistry to simulate a simple combustor to analyze relative contribution of different NOx mechanisms. 6. Currently we are having problems with the steady solver combined with multistep skeletal chemistry. There is no rezoning logic for IC engines, which incurs about twice as much more computation time as compared with KIVA. No valve motion logic for intake/exhaust strokes in the current Openfoam version. No steady solver with coal particle tracking and combustion.

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