Calculation of the chemically nonequilibrium flow of a multicomponent gas through a nozzle

Abstract

We shall describe a method for calculating the flow of a complex gas mixture not in chemical equilibrium, based on selection of the time scale for the problem solution and “sectioning” of the reaction velocities in the near-equilibrium mode of their flow. The method permits derivation of calculation programs possessing wide applicability for systems with a large number of reactions. The application of the method is illustrated through calculations on a system, the components of which contain H,O,C,N, and Cl elements. Calculation of the parameters of the flow of a multicomponent gas through a nozzle under given conditions requires consideration of the kinetics of the chemical reactions which occur in the system. Mathematically, such a problem leads to the simultaneous numerical solution of the gas-dynamics equations for the flow parameters and the chemical kinetic equations for the concentration of the individual components. Several difficulties exist, the most basic of which are calculation of the region of near equilibrium flow and the transonic flow region with transition across the sonic point, and calculation of a large number of chemical reaction velocities of greatly differing magnitudes, in the case of a complex gas mixture. In order to obtain a stable solution in the near-equilibrium flow region, several methods have recently been proposed, which permit consolidation of the integration step. We note the use of a local linearization of the chemical kinetic equation system, as employed in [1]. This method in practice is useful for relatively slow change in component concentrations. In [2] at each integration step the kinetic equations are transformed into a system of L algebraic equations (where L is the number of reactions), and with an increase in the number of reactions (L⪞20) the laboriousness of such a calculation increases sharply. The implicit differential schemes of integration presented in [3, 4] appear more acceptable, but in fact they too have been tested only for systems with a relatively small number of reactions. The difficulty of calculating the transonic flow region, as is well known, is connected with selection of the unique value of mass flow G, at which the transition to supersonic flow is realized. This may be avoided by defining over the length of the nozzle one of the gas-dynamic functions (for example, pressure distribution [4]), which are not highly sensitive to chemical nonequilibrium, the values being taken from supplementary calculations of nonequilibrium flow through the nozzle. Several investigators have limited their examination to the supersonic flow region (see, for example, [5]), but with this method the results may lack sufficient accuracy, since in some cases (for high gradients of the gas-dynamic magnitudes) the transonic region produces a comparable contribution to the general effect of nonequilibrium. We will describe below a method with which a practically universal system of calculating the nonequilibrium flow of a complex gas mixture through a nozzle can be realized. In practice, up to 60 of the most significant reactions may be considered, out of a practically unlimited number initially present. The method is based on “sectioning” of the reaction velocities in the near-equilibrium mode. This permits attainment of a stable solution in the near-equilibrium flow region with acceptable machine-time expenditures. The method describes the transition through the sonic point, since the systematic error introduced by its use (within the limits of calculation accuracy) improves the convergence of the iteration process used in finding G. In applying the method it is useful to select the more important of those reactions theoretically possible, and also to conduct calculations for equilibrium flow conditions of the individual chemical reactions; the latter permits evaluation of the maximum possible contribution of reactions for which the velocity constants are unknown.