Simulation of a nonstationary flow in a channel with a distributed blow from the channel walls and forced pressure oscillations

Abstract

UDC 532.529 A nonstationary flow in a channel with a blow was simulated on the basis of the Reynolds-averaged Navier- Stokes equations and the two-parameter k-e model of turbulence. The pressure near the left end of the chan- nel changes by the harmonic law. It was established that the k-e model of turbulence can be used for calculating the nonstationary flows formed in the indicated channel by a blow. Introduction. The oscillations of the parameters of a working substance in the combustion chamber of a solid-propellant engine (SPE) represent a dangerous effect that can disturb the normal working conditions of the en- gine and, in some cases, cause its failure. These oscillations are due to the vibrating combustion or the hydrodynamic instability of the flow of the fuel combustion products. A model of a fluid flow in a channel with permeable walls can be used for simulation of a flow of combus- tion products in the channel of an SPE charge because this model reflects the significant process of transfer of a solid fuel from the burning surface of the charge. However, in the indicated model, the decomposition and combustion of the fuel in the thin near-surface layer of the charge are not taken into account. The inner flow of a working substance in the channel of an SPE is turbulent, and complex physical processes proceed in the working space of the SPE against the background of its general gasdynamic state. The turbulence of the gas flow in the indicated channel influences its characteristics and intensifies the heat transfer at the surfaces of the prenozzle space and the nozzle unit of the SPE. The nonstationarity of this gas flow can be caused, e.g., by a change in the rate of gas blow along the generatrix of the channel or by the forced oscillations of the pressure near the left (closed) end of the channel. A laminar flow of an incompressible viscous fluid in a straight round tube with a nonstationary blow was in- vestigated in (1, 2). The stationary solution of this problem obtained in (3) (the rate of blow along the generatrix of the cylinder was assumed to be constant) shows that the disturbances arising near the left closed end of the tube lead to the formation of a plane acoustic field in it. The interaction of this field with the fluid blown into the tube leads to the generation of a vortex along its side surface. Between the side surface of the tube and the line found at a distance of half the radius of the tube from its symmetry axis, there arise large radial gradients of the axial flow velocity (4). The nonstationary calculations carried out in (5) show that the vorticity of a flow of an incompressible vis- cous fluid in a tube is inversely proportional to the Mach number, which is in agreement with the theoretical data (3, 6) and the numerical calculations (7). The axial derivative of the radial flow velocity is of the order of O(M 3 ), which is smaller than the radial derivative of the axial flow velocity. For simplicity, in (5), the case of disturbance of the rate of a fluid flow by the cosine law was considered. It has been established that the distribution of the vorticity front and its form are determined by the diffusion processes in the radial direction and the convective transfer in the axial direction. The diffusion of the vorticity in the direction of the tube axis results in the velocity of movement of the vorticity front of the compressible fluid being increased as compared to that of a nonviscous flow. The movement of the vorticity front in the nonstationary flow of an incompressible viscous fluid in a plane channel with a closed left end at small Mach numbers was investigated in (8), where the parabolic formulation of the problem was used. External nonstationary disturbances with different wave numbers were imposed on the rate of the blow. In the case of nonstationary blow, at the wall of the channel there arise comparatively large velocity and tem-