https://hal.archives-ouvertes.fr/hal-01320509/document

Exploration of combustion instability triggering using Large Eddy Simulation of a multiple injector Liquid Rocket Engine

Nonlinear, transverse-mode, liquid-propellant-rocket-motor combustion instability is examined with a two-dimensional model. The three-dimensional equations are integrated over the axial direction, for a multi-orifice short nozzle. Nonlinear transverse-wave oscillations in the circular combustion chamber are examined with the primary flow in the axial direction. Turbulent mixing of methane and gaseous oxygen with coaxial injection is analyzed. The combustion has two characteristic times, one for mixing and the other for chemical kinetics, producing a time lag in the energy-release rate relative to pressure. Then, the coupled combustion process and wave dynamics are calculated for a 10-injector chamber with methane and gaseous-oxygen propellants. The linear first tangential mode is imposed initially. Nonlinear triggering occurs; above a critical initial amplitude, the amplitude grows; otherwise, it decays with time. The second tangential mode also develops, and the nonlinear resonance creates a subharmonic ...

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Two-Dimensional Model for Liquid-Rocket Transverse Combustion Instability

This work seeks to provide a closed-form analytical solution for the transverse vorticoacoustic wave in a circular cylinder with headwall injection. This particular configuration mimics the conditions leading to the onset of traveling radial and tangential waves in an idealized liquid rocket engine. Assuming a short cylindrical chamber with two injection showerhead models (a top hat, uniform flow, and a bell-shaped sinusoidal profile), regular perturbations are used to linearize the problem’s conservation equations. Flow decomposition is subsequently applied to the first-order disturbance equations, thus giving rise to a compressible, inviscid, acoustic set that is responsible for driving the unsteady motion, and to an incompressible, viscous, vortical set that is driven by virtue of coupling with the acoustic mode along solid boundaries. While the acoustic mode is readily recovered from the wave equation, the induced vortical mode is resolved using boundary-layer theory and a judicious expansion of the r...

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Transverse Waves in Simulated Liquid Rocket Engines

This work seeks to provide a closed-form analytical solution for the transverse vortical wave generated at the sidewall of a circular cylinder with headwall injection. This particular configuration mimics the conditions leading to the onset of traveling radial and tangential waves in an idealized liquid rocket engine chamber. Assuming a short cylindrical enclosure with axisymmetric injection, regular perturbations are used to linearize the problem’s conservation equations. Flow decomposition is subsequently applied to the first-order disturbance equations, thus giving rise to a compressible, inviscid, acoustic set responsible for driving the unsteady motion and to an incompressible, viscous, vortical set driven by virtue of coupling with the acoustic mode along both the sidewall and headwall. While the acoustic mode is readily recovered from the wave equation, the induced vortical mode is resolved using boundary-layer theory and an expansion of the rotational equations with respect to a small viscous para...

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Sidewall Boundary Layer of Transverse Waves in Simulated Liquid Rocket Engines

On the Formulation and Numeric Solution of Vortico-Acoustic Fields

*† In this study, the transverse vorticoacoustic wave in a circular cylinder is characterized for a variable velocity profile at the injector faceplate. This particular configuration mimics the conditions leading to the onset of traveling radial and tangential waves in a simple liquid rocket engine (LRE). To capture the unsteady behavior in this physical setting, we consider a short thrust chamber with an injecting headwall and combine the benefits of three techniques: regular perturbations, Helmholtz decomposition, and boundary layer theory. First, regular perturbations are leveraged to linearize the equations of motion and, in the process, help to identify the unsteady interaction equations. Second, a Helmholtz decomposition of the first-order disturbance equations gives rise to a compressible, inviscid, and acoustic set that is responsible for driving the unsteady motion. This is accomplished in conjunction with an essentially incompressible, viscous, and vortical set that materializes by virtue of coupling with the acoustic wave at the boundaries. After recovering the acoustic mode from the resulting wave equation, the last step is to solve for the vortical mode by applying boundary layer theory and a judicious expansion of the rotational set with respect to a small viscous parameter,  . After some effort, an explicit formulation for variable headwall injection is obtained and validated by means of a limiting process verification that is based on two previously investigated cases, the uniform and bell-shaped injection profiles. The solution is then illustrated using two new configurations corresponding to laminar and turbulent profiles. In the process of comparing the four representative cases, the characteristics of the vorticoacoustic wave, including its penetration depth, spatial wavelength, and overshoot factor, are systematically explored and discussed. Most characteristics are found to depend on the penetration and Strouhal numbers along with the distance from the centerline. Along the axis of the chamber, the waves attributed to different injection profiles behave similarly to the extent that behavioral deviations among them increase as the sidewall is approached. This work also accounts for the presence of a downstream boundary that stands to produce left-traveling reflections whose pairing with the right-traveling waves promotes the establishment of a standing wave environment. The combined waves are formulated analytically and shown to be appreciable in view of their amplitudes that twice exceed those associated with traveling waves.

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Charles T. Haddad

Papers

Transverse Waves in Simulated Liquid Rocket Engines

Sidewall Boundary Layer of Transverse Waves in Simulated Liquid Rocket Engines

Transverse Waves in Simulated Liquid Rocket Engines

Transverse Waves in Simulated Liquid Rocket Engines with Variable Headwall Injection

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