Accurate Spatial Resolution Estimates for Reactive Supersonic Flow with Detailed Chemistry

Abstract

Ar obust method is developed and used to provide rational estimates of reaction zone thicknesses in onedimensional steady gas-phase detonations in mixtures of inviscid ideal reacting gases whose chemistry is described by detailed kinetics of the interactions of N molecular species constituted from L atomic elements. The conservation principles are cast as a set of algebraic relations giving pressure, temperature, density, velocity, and L species mass fractions as functions of the remaining N‐L species mass fractions. These are used to recast the N‐L species evolution equations as a self-contained system of nonlinear ordinary differential equations of the form dYi/dx = fi (Y1 ,..., YN‐L). These equations are numerically integrated from a shock to an equilibrium end state. The eigenvalues of the Jacobian of fi are calculated at every point in space, and their reciprocals give local estimates of all length scales. Application of the method to the standard problem of a stoichiometric Chapman‐Jouguet hydrogen‐air detonation in a mixture with ambient pressure of 1 atm and temperature of 298 K reveals that the finest length scale is on the order of 10 −5 cm; this is orders of magnitude smaller than both the induction zone length, 10 −2 cm, and the overall reaction zone length, 10 0 cm. To achieve numerical stability and convergence of the solution at a rate consistent with the order of accuracy of the numerical method as the spatial grid is refined, it is shown that one must employ a grid with a finer spatial discretization than the smallest physical length scale. It is shown that published results of detonation structures predicted by models with detailed kinetics are typically underresolved by one to five orders of magnitude.