Unsteady vorticity generation and evolution in a model of a solid rocket motor

Abstract

The cylindrical, axisymmetric Navier-Stokes equations are solved numerically to study the generation and evolution of vorticity in an injection-induced transient shear flow. An initially steady internal flowfield driven by constant sidewall injection is disturbed by positive transient sidewall injection, which simulates the unsteady mass input from propellant burning variations. The disturbance amplitude is as large as that of the steady sidewall injection to ensure that nonlinear effects influence the vorticity field evolution. Initial value solutions show that relatively intense vorticity is generated at the sidewall and eventually fills the cylinder with a rotational flow. Although the pressure response is essentially that found in acoustic stability theory, the axial and radial velocity components contain large local radial velocity gradients that cannot be predicted from acoustic theory alone.

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

“…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 viscous 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…”

“…The nonstationary calculations carried out in [5] show that the vorticity of a flow of an incompressible viscous 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…”

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

“…The axially distributed transverse velocity on the sidewall is a prescribed function of time with different wave numbers and the temperature of the injected gas is specified. This work extends that of Hegab [5], Hegab and Kassoy [6], who study the velocity and the thermal fields in similar channel and Kirkkopru et al [7,8] who study the velocity and the vorticity fields in a cylinder with one open end and similar sidewall boundary conditions, but do not consider the vorticity generation and thermal effects at resonance frequencies and high wave number sidewall velocity.…”

“…Reflection-preserving numerical boundary conditions are used to ensure that the computed acoustic field is an accurate solution to the posed initial-boundary value problem. In particular, the present acoustic response includes eigenfunctions predicted by Staab et al [9] as well as the forced modes seen in Kirkkopru et al [7]. All earlier computational studies cited here are missing eigenfunction responses that are predicted by analogous acoustic analysis for the semi-confined systems considered.…”

“…In both cases the acoustic disturbances are generated by imposed pressure variations along an axial location rather than from a prescribed time-dependent mass addition on the sidewall. A more detailed result, with better radial spatial resolution was given by Kirkkopru et al [7] for the case of transient mass addition. More recently, Kirkkopru et al [8] has made a detailed comparison of asymptotic and computational solutions to the Navier-Stokes to demonstrate the accuracy of the former results for relatively large disturbances.…”