Pantano, Carlos

Pullin, Dale I.

English

CaltechCONF

Large Eddy Simulation of a Turbulent Reacting Compressible JetC. Pantano   and D.I. PullinGraduate Aeronautical Laboratories,California Institute of Technology 105-50,1200 E. California Blvd., Pasadena CA 91125September 10, 2003We report results of a Large Eddy Simulation (LES) effort of turbulent compressible nonpremixed reactive jets. Itis well known that there are several difficulties associated with compressible reactive flows in comparison with incom-pressible flows. In incompressible flows, the energy and mass conservation (for constant density flows) equations aredecoupled from the velocity field. Moreover, the subgrid terms that are required in these flows need only provide withthe deviatoric part of the subgrid contributions. The isotropic part can be absorbed in the pressure term. In reactingincompressible flows, one can also avoid the need to integrate the conservation equations for mass and energy by usinga conserved scalar approach. In this case, both temperature and density are determined from a state relationship thatis known beforehand. On the other hand, for compressible reacting flows one is not allowed to discard the energy andmass conservation equation since acoustics and in some cases shocks coexist with heat release. In the present investi-gation we use the totally conservative formulation in terms of total sensible energy. Other forms of the energy equationrequire closure for pressure velocity correlations, [1]. This is not requited in the total sensible energy form, althoughsome other correlations are needed, notably, those between enthalpy and mass fractions of species. Furthermore, weare interested in using local subgrid models. The advantages of this kind of approach are self evident, specially incomplex geometries. The results discussed in this abstract are obtained with the stretched vortex model for turbulenttransport [2], scalar transport [4] and subgrid scalar variance [3]. Here, we consider a model problem of a turbulentplanar nonpremixed reacting jet. The modeling assumptions are described next, followed by some preliminary results.1 Formulation and ResultsFor variable density flows, the LES governing equations are formulated using Favre filtered variables, defined as 	, where the “conceptual” filter operator is denoted by the overbar. Conservation of mass, momentum andenergy are expressed in the usual form, [5], in terms of filtered density, 	 , velocity,  , and pressure 	 and the totalsensible energy conservation equation is			ﬀﬂﬁﬃ !ﬁ"#$!!%ﬁ&')(+* (1)whereis the resolved thermal conductivity. The resolved Newtonian viscous stress tensor is given as usual with ,as the resolved shear viscosity. The dependence on temperature of , andis typically not small for combusting flow,primarily, due to the large temperature variations in the flow. They are approximated here by ,,-  -ﬀ/. and01-  -ﬀ2., where 354*76 . Finally, the total sensible energy,	is given by	8	:9;=<>@?A&		BC (2)whereBDFEG&Hﬀ> is the subgrid kinetic energy. The Favre filtered enthalpy is decomposed into a resolvedpart and a subgrid part through,;0JIKMLON; ﬀP;RQ@C ;QﬃJIKSLONE;P&; ﬀPﬁC (3)Te-mail:cpantano@galcit.caltech.edu1Figure 1: Mixture fraction and subgrid kinetic energy distribution.where U is the number of species,; is the enthalpy of component V , given by; ﬀ5;-XWZY[[]\_^$` _aﬀ2b _aC (4)and the system of equations is closed by the equation of state,	c	ed- fIKSLONPgQCQ8	hd-IKSLONE iP& Pg(5)^` is the specific heat of component V ,;- is the enthalpy of formation of the corresponding species,d- is the gasconstant and g  is the molecular weight of species V .Combustion is handled through the conserved scalar approach, where a a mixture fraction field, j , is used to obtainthe mass fraction of the different species. The quantities that need to be modeled are the subgrid momentum stresses,scalar transport and subgrid total energy transport, defined as'!8	E!"&!kﬁC'l!8	Ej!"&j!%ﬁC'(!8	E;!:&;!@ﬁ	>ZE!"&E!%ﬁ* (6)The triple correlations in'(!of Eq. (6) are neglected and the other terms are modeled using the stretched vortexmodel. The combustion related terms,;Qand Q, are closed through an assumed beta pdf model, where the subgridscalar variance needed in the assumed pdf model is obtained from the approximate reconstruction model of [3]. Thegoverning equations are integrated using a compact Pade´ scheme in space of sixth order and a third-order low-storageRunge-Kutta scheme in time. The chemistry is modeled as an infinitely fast one step methane-air reaction. Thisdetermines a state relation of the formPPjﬀ. The stoichiometric mixture fraction was set to 0.2. The coldReynolds number was set equal to 20000 and the jet Mach number was equal to 0.6. Figure 1 shows mixture fractionisosurfaces (a) and subgrid kinetic energy (b) at one instant in time. Further details will be provided in the presentation.References[1] A.W. Cook and J.J. Riley. Subgrid-scale modeling for turbulent reacting flows. Combustion and Flame,112(4):593–606, 1998.[2] A. Misra and D.I. Pullin. A vortex-based subgrid model for large-eddy simulation. Phys. Fluids, 9:2243, 1997.[3] C. Pantano and S. Sarkar. A subgrid model for nonlinear functions of a scalar. Phys. Fluids, 13(12):3803–3819,2001.[4] D.I. Pullin. Vortex-based model for subgrid flux of a passive scalar. Phys. Fluids, 12:2311, 2000.[5] F. A. Williams. Combustion Theory. Benjamin/Cummings, Menlo Park, CA, 1985.2

Large Eddy Simulation of a Turbulent Reacting Compressible Jet

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