The effect of a sudden density change on a slightly non-uniform flow

Abstract

The effect of combustion or heating on a slightly non-uniform flow in a tube of constant radius is explored by examining a simplified model, in which a density decrease occurs across a plane actuator-disk normal to the axis of the tube. The flow is considered to be steady, axi-symmetric, incompressible and inviscid and to originate at an injector-plate which is situated upstream of the disk. This paper analyses and discusses the effects caused by the density decrease when the velocity of flow through the injector-plate has a fractional non-uniformity u_e, when there is a curvature θ_e, of the injector-plate, and when the density decrease has a fractional non-uniformity δ₂. It is shown that the non-uniformity of the flow far downstream of the disk caused by the disturbances u_e and θ_e is diminished by the density decrease; while that due to the disturbances δ₂ is increased, unless the density decrease occurs close to the injector-plate. The distance separating the injector-plate and actuator-disk is found to be an important parameter. When this distance is small, compared to the radius of the tube, and the density decrease is severe, a small disturbance u_e, θ_e or δ₂ may set up a pressure variation at the injector-plate of many times the inlet dynamic pressure of the flow. It is conjectured that this pressure variation could affect the uniformity of velocity and composition of the flow through the injector-plate, and thus cause the disturbances u_e and δ₂ to grow or diminish.