Acoustic streaming in simplified liquid rocket engines with transverse mode oscillations

Abstract

This study considers a simplified model of a liquid rocket engine in which uniform injection is imposed at the faceplate. 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. 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. Using perturbation tools, both potential and viscous flow equations are then 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 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. We find that suppressing either the convective terms or viscosity at the headwall leads to spurious solutions that are free from streaming. In our problem, streaming is initiated at the headwall, within the boundary layer, and then extends throughout the chamber. We find that nonlinear streaming effects of tangential and radial waves act to alter the outer solution inside a cylinder with headwall injection. 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 waves are either enhanced or weakened in two opposing sectors that are at 90°angle to the radial velocity counterparts. The second-order viscous solution that we obtain clearly displays both an oscillating and a steady flow component. The steady part can be an important contributor to wave steepening, a mechanism that is often observed during the onset of acoustic instability.

On the Sidewall Boundary Layer of Transverse Waves in Simulated Liquid Rocket Engines

“…These correspond to four zeroes of m J  listed in Eq. (17). Everywhere, the pressure contours represent snapshots taken in a polar plane at 0 s, , tz  where red and blue colors denote positive and negative acoustic pressures, respectively.…”

“…This is achieved at 0.1 t  , 0.4 r  , 1 3   , 0.03 b M  and a thrust chamber with a unit aspect ratio. 17 The corresponding plots capture the oscillatory motion for the first-tangential with first-radial modes using 11 k .…”

“…(10) consists of an assortment of four equations, these can be systematically reduced to a single PDE, which represents a modified form of the wave equation. By subtracting the derivative of the acoustic mass conservation from the divergence of the momentum equation, an extended form of the wave equation 17 may be readily revealed, specifically…”

“…17,22 In both geometric configurations, the velocity adherence constraint is imposed at the injecting surfaces, and these correspond to either the headwall or the sidewall of the simulated LRE and SRM, respectively. However, since the vortical waves driven by the injecting surfaces are determined in previous studies, [17][18][19] slippage along the non-injecting surface (sidewall) must not be allowed in the improved formulation. Consistent with other boundary layer studies, attenuation of the unsteady vorticity component is expected away from the sidewall.…”

Transient Temperature Measurements of Combustor Walls Enclosing a 2-D Model Coaxial Injector

“…They described the association between the injection system and combustion chamber for exciting and sustaining combustion instabilities with linear or non-linear behavior. Fischbach et al (2007) studied １０ acoustic effects with traveling transverse wave oscillation and showed the effects could accelerate the amplitude of the wave fronts.…”