We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant....We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the existence and dynamic behavior, including stability, regularity, and large-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations with constant adiabatic exponent γ and specific heat Cv. Our approach for the existence and regularity is to combine the difference approximation techniques with the energy methods, total variation estimates, and weak convergence arguments to deal with large jump discontinuities; and for large-time behavior is an a posteriori argument directly from the weak form of the equations. The approach and ideas we develop here can be applied to solving a more complicated model where γand cv vary as the phase changes; and we then describe this model in detail and contrast the results on the asymptotic behavior of the solutions of these two different models. We also discuss other physical models describing dynamic combustion.展开更多
Cylinder pressure fluctuation during combustion process of internal combustion engine is closely related to combustion noise and knock.The current studies are based on cylinder pressure test to obtain information on c...Cylinder pressure fluctuation during combustion process of internal combustion engine is closely related to combustion noise and knock.The current studies are based on cylinder pressure test to obtain information on combustion noise and knock,but there is little for simulation of combustion pressure fluctuation.Based on effects of combustion process in the combustion chamber on cylinder pressure by using wave equation,the mechanism of pressure fluctuation during combustion is researched with three-dimensional acoustic wave equation and flow field model of KIVA program.The cylinder pressure fluctuation curve,temperature field and acoustic field are obtained from the coupled calculation of the wave equation and KIVA program.The frequency spectrum analysis is taken with the cylinder pressure oscillation of cylinder pressure measured and calculated.The calculation result is consistent with the experimental result.This indicates that the cylinder pressure fluctuation can be correctly calculated with the wave equation.Analysis of calculation results of temperature field and acoustic field shows that sound field changes faster than flame propagates,and distribution of sound field is more complicated.Combustion pressure oscillation in the diesel engine is under highly unstable condition.This indicates that the combination of cylinder pressure fluctuation model and combustion model is an effective method to study the pressure oscillations and a new method to study the combustion noise and knock.展开更多
Combustion oscillations in a supersonic combustor with hydrogen injection upstream of a cavity flameholder are investigated using nonlinear analysis based on experimental measurements.Time series of both flamefront an...Combustion oscillations in a supersonic combustor with hydrogen injection upstream of a cavity flameholder are investigated using nonlinear analysis based on experimental measurements.Time series of both flamefront and wall pressure are acquired,and the state space reconstruction approach is adopted to characterize the nonlinear behavior of the combustion oscillations.Three overall equivalence ratios,0.038,0.076 and 0.11,are considered.The existence of a chaotic source in the present combustion system is demonstrated.The correlation dimension and the largest Lyapunov exponent tend to become larger with the increasing equivalence ratio,indicating a more complicated and unstable combustion system.In particular,it is found that the correlation dimension for the highest equivalence ratio is much greater than those of the two lower equivalence ratios.Two possible reasons responsible for the observed nonlinear behaviors are identified.One is the shock-related instabilities and the other is the transition of combustion stabilization mode between the cavity and jet-wake stabilized mode.展开更多
基金Supported in part by the National Science Foundation under Grants DMS-9971793, INT-9987378,and INT-9726215.Supported in part by the National Science Foundation under Grant DMS-9703703.Supported in part by the National Science Foundation under Grants
文摘We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the existence and dynamic behavior, including stability, regularity, and large-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations with constant adiabatic exponent γ and specific heat Cv. Our approach for the existence and regularity is to combine the difference approximation techniques with the energy methods, total variation estimates, and weak convergence arguments to deal with large jump discontinuities; and for large-time behavior is an a posteriori argument directly from the weak form of the equations. The approach and ideas we develop here can be applied to solving a more complicated model where γand cv vary as the phase changes; and we then describe this model in detail and contrast the results on the asymptotic behavior of the solutions of these two different models. We also discuss other physical models describing dynamic combustion.
基金supported by National Natural Science Foundation of China (Grant No. 50706032 and No. 50476065)PhD Programs Foundation of Ministry of Education of China (Grant No. 20070056011)
文摘Cylinder pressure fluctuation during combustion process of internal combustion engine is closely related to combustion noise and knock.The current studies are based on cylinder pressure test to obtain information on combustion noise and knock,but there is little for simulation of combustion pressure fluctuation.Based on effects of combustion process in the combustion chamber on cylinder pressure by using wave equation,the mechanism of pressure fluctuation during combustion is researched with three-dimensional acoustic wave equation and flow field model of KIVA program.The cylinder pressure fluctuation curve,temperature field and acoustic field are obtained from the coupled calculation of the wave equation and KIVA program.The frequency spectrum analysis is taken with the cylinder pressure oscillation of cylinder pressure measured and calculated.The calculation result is consistent with the experimental result.This indicates that the cylinder pressure fluctuation can be correctly calculated with the wave equation.Analysis of calculation results of temperature field and acoustic field shows that sound field changes faster than flame propagates,and distribution of sound field is more complicated.Combustion pressure oscillation in the diesel engine is under highly unstable condition.This indicates that the combination of cylinder pressure fluctuation model and combustion model is an effective method to study the pressure oscillations and a new method to study the combustion noise and knock.
基金supported by the National Natural Science Foundation of China(Grant Nos.50906098,91016028)Fok Ying Tung Education Foundation(Grant No.131055)
文摘Combustion oscillations in a supersonic combustor with hydrogen injection upstream of a cavity flameholder are investigated using nonlinear analysis based on experimental measurements.Time series of both flamefront and wall pressure are acquired,and the state space reconstruction approach is adopted to characterize the nonlinear behavior of the combustion oscillations.Three overall equivalence ratios,0.038,0.076 and 0.11,are considered.The existence of a chaotic source in the present combustion system is demonstrated.The correlation dimension and the largest Lyapunov exponent tend to become larger with the increasing equivalence ratio,indicating a more complicated and unstable combustion system.In particular,it is found that the correlation dimension for the highest equivalence ratio is much greater than those of the two lower equivalence ratios.Two possible reasons responsible for the observed nonlinear behaviors are identified.One is the shock-related instabilities and the other is the transition of combustion stabilization mode between the cavity and jet-wake stabilized mode.
