The gas-droplet two-phase reacting flow in a model combustor with the V-gutter flame holder is studied by an Eulerian-Lagrangian large-eddy simulation (LES) approach. The k-equation subgrid-scale model is used to simu...The gas-droplet two-phase reacting flow in a model combustor with the V-gutter flame holder is studied by an Eulerian-Lagrangian large-eddy simulation (LES) approach. The k-equation subgrid-scale model is used to simulate the subgrid eddy viscosity, and the eddy-break-up (EBU) combustion subgrid-scale model is used to determine the chemical reaction rate. A two-step turbulent combustion subgrid-scale model is employed for calculating carbon monoxide CO concentration, and the NO subgrid-scale pollutant formation model for the evaluation of the rate of NO formation. The heat flux model is applied to the prediction of radiant heat transfer. The gas phase is solved with the SIMPLE algorithm and a hybrid scheme in the staggered grid system. The liquid phase equations are solved in a Lagrangian frame in reference of the particle-source-in-cell (PSIC) algorithm. From simulation results, the exchange of mass, moment and energy between gas and particle fields for the reacting flow in the afterburner with a V-gutter flame holder can be obtained. By the comparison of experimental and simulation results, profile temperature and pollutant of the outlet are quite in agreement with experimental data. Results show that the LES approach for predicting the two-phase instantaneous reacting flow and pollutant emissions in the afterburner is feasible.展开更多
In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, whi...In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, which include the well-known p-system. From this viewpoint, the author establishes the global existence and the nonlinear stability of travelling wave solutions by L-2 energy method.展开更多
The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the ...The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.展开更多
We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics...We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.展开更多
In this paper,we study the zero dissipation limit with a vacuum for the reacting mixture Navier-Stokes equations.For proper smooth initial data that the initial density tends to zero as the relevant physical coefficie...In this paper,we study the zero dissipation limit with a vacuum for the reacting mixture Navier-Stokes equations.For proper smooth initial data that the initial density tends to zero as the relevant physical coefficients tend to zero,we demonstrate that the solution tends to a rarefaction wave connected to a vacuum on the left side coupled with a zero mass fraction of reactant.What is more,the uniform convergence rate is obtained.展开更多
We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture.When the corresponding Riemann problem for the Euler system ad...We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture.When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave,it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable,provided the strength of contact discontinuity and the initial perturbation are suitably small.We apply the approach introduced in Huang,Li and Matsumura(2010)[1]and the elemen tary L2-energy met hods.展开更多
In this paper,we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dime...In this paper,we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension.If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only,it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves,while the initial perturbation and the strength of rarefaction waves are suitably small.展开更多
文摘The gas-droplet two-phase reacting flow in a model combustor with the V-gutter flame holder is studied by an Eulerian-Lagrangian large-eddy simulation (LES) approach. The k-equation subgrid-scale model is used to simulate the subgrid eddy viscosity, and the eddy-break-up (EBU) combustion subgrid-scale model is used to determine the chemical reaction rate. A two-step turbulent combustion subgrid-scale model is employed for calculating carbon monoxide CO concentration, and the NO subgrid-scale pollutant formation model for the evaluation of the rate of NO formation. The heat flux model is applied to the prediction of radiant heat transfer. The gas phase is solved with the SIMPLE algorithm and a hybrid scheme in the staggered grid system. The liquid phase equations are solved in a Lagrangian frame in reference of the particle-source-in-cell (PSIC) algorithm. From simulation results, the exchange of mass, moment and energy between gas and particle fields for the reacting flow in the afterburner with a V-gutter flame holder can be obtained. By the comparison of experimental and simulation results, profile temperature and pollutant of the outlet are quite in agreement with experimental data. Results show that the LES approach for predicting the two-phase instantaneous reacting flow and pollutant emissions in the afterburner is feasible.
文摘In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, which include the well-known p-system. From this viewpoint, the author establishes the global existence and the nonlinear stability of travelling wave solutions by L-2 energy method.
文摘The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.
基金Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(EP/E035027/1)the NSFC under a joint project Grant 10728101+4 种基金the Royal Society-Wolfson Research Merit Award(UK)Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101Yongqian ZHANG was supported in part by NSFC Project 11031001NSFC Project 11121101the 111 Project B08018(China)
文摘We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.
基金supported by the National Natural Science Foundation of China (11971193 and 12171001)。
文摘In this paper,we study the zero dissipation limit with a vacuum for the reacting mixture Navier-Stokes equations.For proper smooth initial data that the initial density tends to zero as the relevant physical coefficients tend to zero,we demonstrate that the solution tends to a rarefaction wave connected to a vacuum on the left side coupled with a zero mass fraction of reactant.What is more,the uniform convergence rate is obtained.
基金supported by the National Natural Science Foundation of China(11871341).
文摘We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture.When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave,it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable,provided the strength of contact discontinuity and the initial perturbation are suitably small.We apply the approach introduced in Huang,Li and Matsumura(2010)[1]and the elemen tary L2-energy met hods.
基金supported by the Beijing Natural Science Foundation(1182004,Z180007,1192001).
文摘In this paper,we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension.If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only,it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves,while the initial perturbation and the strength of rarefaction waves are suitably small.
