A GENERALIZED ASYMPTOTIC METHOD FOR THE SOLUTION OF REACTING LAMINAR BOUNDARY LAYER FLOWS. PART I. THREE-DIMENSIONAL FLOW OF AIR AT CHEMICAL EQUILIBRIUM NEAR A STAGNATION POINT,
ARMY MISSILE COMMAND REDSTONE ARSENAL ALA ARPA DIV
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In this report the asymptotic method is properly generalized and applied to the solution of the laminar boundary layer flow of dissociated air in the vicinity of a stagnation point on a general surface, S. The flow is considered to be in chemical equilibrium and belongs to the similarity class. Geometric considerations are manifested by a parameter c whose range is 0 or c or 1, the two bounds corresponding respectively to the special cases of two-dimensional and rotationally symmetric flows. Basically, the solution of the example problems consists in solving several coupled nonlinear equations subject to specified boundary conditions constant wall and stream enthalpy, equilibrium concentration of species at the wall and in the stream and the choice of a preselected thermo-chemical model. The main reason for discussing general three-dimensional stagnation point flows, other than their technical importance, is to assess the accuracy of the asymptotic method in computing the flow field, local friction and heat transfer for a class of the simpler problems. The test for c 1 is provided by the often quoted numerical results of Fay and Riddell. Care has been taken to reproduce their transport properties and their reaction model. This is the only numerical work required. In the special case of no reactions and constant properties, the earlier results of the authors, found to be in excellent agreement with the corresponding numerical solutions of Howarth, are recovered. These provide an auxiliary check.
- Physical Chemistry
- Fluid Mechanics