Asymptotic Solutions of Problems of One-Dimensional Time-Dependent Combustible Gas Flows in the Presence of Thermal Action

Abstract

In a development of studies [1, 2], asymptotic solutions of the Navier-Stokes equations are found for one-dimensional combustible gas flows in the presence of various forms of thermal action on a moving surface (x=xw(t)). In the problems considered, the temperature or the heat flux qw(t) is specified on the surface or the surface is the interface between a combustible gas and a moving heated piston or another gas (for example, in a shock tube). Use is made of the fact that, as t → ∞, in many cases the values of vw=(dx/dt)w and qw are bounded. This leads to a steady-state flow in the flame zone in the coordinate system moving with its front and homogeneous uniform flow ahead of and behind it. Solutions of all these problems are given for the burnt-gas boundary layer region adjacent to the surface. The numerical calculations performed confirm the results obtained. A velocity law leading to time invariability of the flow pattern obtained with allowance for the interaction between the boundary layer and the burnt-gas homogeneous flow is found, including in the problem of the breakdown of an arbitrary discontinuity. The results are generalized to include the case of motion at an angle of incidence with an additional velocity component aligned with the surface.