Streaming Effects in Liquid Injection Rocket Engines with Transverse Mode Oscillations

This research is an analytical investigation of wave interactions in a simulated liquid rocket engine with uniform injection imposed at the faceplate. Of significant interest are the secondary nonlinear flows, particularly acoustic streaming, induced by transverse wave impingement over the engine injector surface. The corresponding cylindrical chamber has a small length-to-diameter ratio with respect to solid and hybrid rockets. Given their low chamber aspect ratios, liquid thrust engines are known to experience severe tangential and radial oscillation modes more often than longitudinal ones. Experimental evidence demonstrates the production of large peak-to-trough amplitude flow oscillations along with the development of a strong central vortex structure in many unstable liquid engines. These phenomena are accompanied by elevated heat transfer to the injector faceplates, strong roll torques and chamber over pressurization. In order to model this behavior, tangential and radial waves are superimposed onto a basic mean-flow model that consists of a steady, uniform axial velocity throughout the chamber. Considerable effort is given to correctly satisfy the no-slip condition at the chamber’s injector face. The viscous boundary layer used to satisfy the no-slip condition is the location at which acoustic streaming develops. Sidewall boundary layers that develop at the lateral wall are not considered, being inconsequential to the flow in the vicinity of the headwall. Using perturbation tools, both potential and viscous flow equations are linearized in the pressure wave amplitude and solved to the second order. The effects of the headwall Mach number are leveraged as well. While the potential flow analysis does not predict any acoustic streaming effects, the viscous solution carried out to the second-order approximation gives rise to steady secondary flow patterns near the headwall. These axisymmetric, steady contributions to the tangential and radial traveling waves are induced by the convective flow motion through interactions with inertial and viscous forces. Suppressing either the convective terms or viscosity at the headwall can lead to spurious solutions that are free from streaming. In the present research, streaming is initiated at the headwall, within the boundary layer, and extends throughout the chamber. The study suggests that nonlinear streaming effects of tangential and radial waves inside a cylinder with headwall injection act to alter the outer solution. As a result of streaming, the radial wave velocities are intensified in one half of the domain and reduced in the opposite half at any instant of time. Similarly, the tangential wave velocities are either enhanced or weakened in two opposing sectors that are at a 90 degree angle to the radial velocity counterparts. The second-order viscous solution that is obtained clearly displays both an oscillating and a steady flow component. It is found that the steady contribution due to streaming can potentially promote the development of large amplitude steepened wave forms. The delineation of this mechanism is crucial for the advancement of analytical tools employed in the prediction of combustion instability. In the present study, streaming is examined in the context of traveling transverse waves. Extending the analysis to standing wave motion is carried out and reported in a straightforward fashion.