Non Equilibrium Centered Expansion Of A Supersonic Reacting Gas Flow

A detailed analysis is presented of the nearly frozen, nonequilibrium supersonic expansion of a dissociated diatomic gas around a sharp, two dimensional corner, assuming an incoming stream in dissociation equilibrium. The analysis is based on a small perturbation technique in which small local departures from frozen flow near the corner are treated. The analysis is necessarily restricted in lateral extent but covers the entire angular range of the flow field and, therefore, brings out the nonlinear aspects of the nonequilibrium behavior. An exact analysis is presented (in similitude form for a diatomic gas) in which numerical procedures are required to effect the solution. However, in the exact solution, the expression for the atomic species mass fraction has been placed in closed form and, in conjunction with appropriate approximations, is used to determine the thermochemical field in an additional solution (applicable to hypersonic flow) which is approximate but entirely in closed form. Some numerical results for the first order nonequilibrium flow field are presented.

A second-order numerical method of characteristics was used to solve the equations of motion for three-dimensional, steady, supersonic, nonequilibrium, chemically reacting flow of a system of thermally perfect gases in an exhaust nozzle. A production type computer program which is capable of solving a wide variety of supersonic nozzle problems was developed for the CDC-6500 computer. A bicharacteristic method of characteristics due to D.S. Butler and a special implicit method for the species continuity equations were employed. The chemical kinetic model considers 19 species formed from the 6 elements--carbon, hydrogen, ocygen, nitrogen, flourine and chlorine--and 48 chemical reactions (13 dissociation-recombination reactions and 35 binary exchange reactions). In addition to the nonequilibrium chemistry model, the program also considers frozen and equilibrium flows, and flows with constant specific heat ratios. The absolute accuracy and order of accuracy of the method was shown by comparing the computed solution for spherical source flow with the exact solution for isentropic flow, and by comparing the computed solution for an axisymmetric, nonequilibrium flow with the results of an existing two-dimensional method. (Author).

Chemical and vibrational nonequilibrium phenomena in steady inviscid flow fields are studied by the analysis of flow past curved boundaries. Possible alternative choices of the state variables to be used are considered. General features of the nonequilibrium flow are studied by examination of the mathematical properties of the nonlinear flow equations. An axisymmetric nonequilibrium flow of air through a supersonic nozzle is analyzed by means of numerical computations. The coupling effects between nonuniformity (across a nozzle section) and nonequilibrium, not taken into account in the quasi-one-dimensional flow approximation, are revealed by the present analysis.

A method of characteristics for computing the supersonic, nonequilibrium flow of a reacting and relaxing gas was formulated. The theory was specialized to the ideal dissociating gas of Lighthill and the procedures coded on the IBM 7094. Complete listings of the FORTRAN programs are provided together with instructions as to their use. As examples of the computation techniques, the flows over a wedge and cone were computed and described in detail. For both the wedge and the cone, there developed downstream from the vertex an entropy layer near the wall, a relaxation layer near the shock where the quantities change rapidly, and a near equilibrium layer in between. It was found that it is important to keep the size of the mesh small enough to adequately represent the relaxation layer if satisfactory convergence to the equilibrium state is to be obtained. (Author).