Finite-volume method for the calculation of compressible chemically reacting flows

<title>Numerical analysis of vibrational nonequilibrium flows in supersonic nozzles of CO2 gas dynamic laser</title>

“…= pr,b ( + p) (9) where Le"1' and Pr are the Lewis number and the Prandtl number of vibrational mode 1, respectively. q1 is the heat flux vector which is represented as q1= (10) where C is the specific heat at constant pressure by molecular translational and rotational motions, ic is the molecular heat conductivity coefficient, Pr is the turbulent Prandtl number. The equation of state for perfect gas is available in the translational mode gas of = 1.4 using the method of Ruse " , which is almost minimum length, and (3) a S.(Straight) nozzle, which is conical behind the throat.…”

Simulation of Supersonic Reacting Hydrocarbon Flows with Detailed Chemistry

“…However, the application of multigrid methods to reactive flow calculations has been limited. Bussing and Murman (1988) The approach taken in this paper is to use a previously validated multigrid solver (Martinelli, 1987;Martinelli and Jameson, 1988;Tatsumi et al, 1994) and include chemical source terms on all levels (Sheffer, 1997;Sheffer et al, 1997b). The coarse grid corrections to the species densities are limited to ensure that no mass fraction becomes negative.…”

“…The chemical source vector w was treated in a point implicit manner (Bussing and Murman, 1988). An explicit treatment of the source terms leads, in general, to a time step restriction due to the stability limitation of the explicit scheme.…”

“…In this formulation due to Bussing and Murman (1988), the source term at the next time level is linearized about the current time level, leading to a fully explicit equation at the cost of a matrix inversion. This action has the effect of preconditioning Downloaded by [Nanyang Technological University] at 15:41 13 June 2016 the species continuity equations, rescaling the chemical characteristic time so that it is of the same order as the convective characteristic time.…”

Explicit Time-Scale Splitting Algorithm for Stiff Problems: Auto-ignition of Gaseous Mixtures behind a Steady Shock

“…Reacting flows in the hypersonic regime [5][6][7], reactive mixing layers [8], flames [9], detonations [10][11][12] and nonequilibrium nozzle flows [13] are modeled by systems of partial differential equations (PDEs) and are frequently solved by a local implicit treatment of the stiff source terms according to the method of lines and the time-step or operator splitting approach. Preconditioning techniques are also used to solve steady state problems efficiently [11,14,52].…”