Taro Shimizu

Intense Tangential Pressure Oscillations Inside a Cylindrical Chamber

Intense tangential pressure oscillations due to oscillatory combustion are generated experimentally inside a cylindrical chamber and are analyzed to understand their characteristic features. To generate the tangential mode, a coaxial injector is installed offcenter on the closed side of the chamber. Hydrogen and nitrogen-diluted oxygen are used as working gases under atmospheric conditions. The features of the side-wall pressure in the first tangential mode (1T mode) at high amplitude, whose amplitude is over 30% of the chamber pressure, differ from those of the side-wall pressure in the 1Tmode at low amplitude in the followingmanner: 1) The positive half-wave of the pressure oscillation has twin sharp peaks. 2) The amplitude of the positive half-wave (zero to positive peak) of the pressure oscillations is larger than that of the negative half-wave (negative peak to zero). The acoustical features of the signals are reproduced and investigated by conducting an analysis and anumerical simulation under similar configurations. It is found that the characteristic feature of the intense signal is originated in the nonlinearity due to the large amplitude of the pressure oscillation.

On acoustic damping of a cylindrical chamber in resonant modes

Acoustic damping of a cylindrical chamber with open and closed ends in resonant modes is analytically and numerically investigated to understand the low damping characteristic of the chamber without chocked nozzle. First, on the basis of the analytic solution of resonant acoustic modes inside a cylinder, the damping by radiation from the open end is calculated analytically using simple acoustic source modeling for velocity fluctuation. The effect of viscosity is also considered as an attenuation mechanism. The values of acoustic damping calculated for the first longitudinal and tangential modes are in good agreement with the corresponding values obtained using numerical simulation. The damping is also investigated for a configuration of the chamber with an injector installed off-center. Finally, we numerically and semi-analytically investigate the acoustic damping for a configuration that includes a hot-gas injection. The obtained mode is found to be a spinning tangential mode and the radiated wave also has a spinning feature. The damping for the spinning tangential mode is found to be larger than that for the symmetric dipole-like radiation under a uniform standing condition, but much smaller than the chamber with a chocked nozzle. Therefore, the chamber with an open end has the low damping characteristic suitable for intentionally generating oscillatory combustion.

ERENA: A fast and robust Jacobian-free integration method for ordinary differential equations of chemical kinetics

Abstract We herein propose a fast and robust Jacobian-free time integration method named as the extended robustness-enhanced numerical algorithm (ERENA) to treat the stiff ordinary differential equations (ODEs) of chemical kinetics. The formulation of ERENA is based on an exact solution of a quasi-steady-state approximation that is optimized to preserve the mass conservation law through use of a Lagrange multiplier method. ERENA exhibits higher accuracy and faster performance in homogeneous ignition simulations compared to existing popular explicit and implicit methods for stiff ODEs such as VODE, MTS, and CHEMEQ2. We investigate the effects of user-specified threshold values in ERENA, to provide trade-off information between the accuracy and the computational cost.

Examination of Sound Suppression by Water Injection at Lift-off of Launch Vehicles

Analytical investigation of noise suppression effect of water injection to exhaust plume from rocket motors was carried out. The results showed acoustic absorption by water droplets, acoustic scatter by water droplets, absorption through air, and water curtain effect increase as frequency becomes high. It was also confirmed that acoustic absorption by water droplets has the most significant effects among the four effects. Furthermore, steady 2D-axisymmetric Reynolds-Averaged Navier-Stokes (RANS) simulations of a supersonic free jet were carried out in order to evaluate reduction of jet energy due to water injection. The reduction of the acoustic source strength along the jet axis was evaluated considering the difference of ρk value between with and without water injection. The far field sound power level (SPL) was analyzed using an empirical prediction method, NASA SP-8072 and compared to sub-scale motor test data. The strength of the acoustic source power along the jet axis was set based on the reduction rate of the ρk value due to water injection and the propagation to the far filed points was analyzed based on the NASA SP-8072. The results showed that the water injection effect can be reasonably evaluated by using both the analytical prediction methodology and the evaluation methodology of reduction of the jet energy based on the change of ρk .

Slit resonator design and damping estimation in linear and non-linear ranges

A practical design method of slit resonator for rocket engines is being developed. First a weak linear acoustic solution inside the resonator is obtained by finite element method. Using this result the viscous and thermal damping at the wall of resonator is calculated as a post process. Then, a multi-objective evolutionary computation is applied for finding the slit shapes with high linear damping characteristics. The obtained three slit shapes are investigated intensively. In the actual design, however the resonator is exposed to large amplitude of pressure oscillation. Therefore a non-linearity appears and the damping mechanism changes from that in the linear range. Recent numerical study has revealed the non-linear damping mechanism, that is, the generation of the vortex at the inlet of resonator. In order to estimate the resonators with complex structure, we are now developing a numerical tool to solve Navier-Stokes equations on unstructured grid. The non-linear damping characteristics of the three shapes are investigated and compared with the linear ones. Some problems of estimating the resonator damping in the non-linear range are also discussed.

Theoretical and Numerical Estimation of Acoustic Damping of a Model Combustion Chamber

Acoustic damping of a cylindrical chamber with open and closed ends is analytically and numerically investigated. In the analysis, based on the analytic solution of resonant acoustic modes inside cylinder, the damping from the open end is calculated by a simple acoustic source modeling for velocity fluctuation. The effect of viscosity is also considered as an attenuation mechanism. Acoustic damping calculated for first longitudinal and tangential modes are in good agreement with that obtained by numerical simulation. When a longitudinal mode exists, the directivity of radiation becomes like monopole and the damping is large. On the other hand, when a tangential mode exists, it is found that the dipole like directivity is obtained and the damping is small compared to that for the longitudinal mode. A configuration of the chamber and an injector installed off-centered is also investigated. Under non-resonant condition between injector and chamber acoustics, it is found that the acoustic radiation from the open end of the injector is negligible but the viscous effect becomes important. Finally we investigate the acoustic damping with hot gas injection numerically and semi-analytically. The obtained mode is found to be a spinning tangential mode due to the asymmetry of the mean flow field. The radiated wave has also a spinning feature and the damping is found to be much larger than that for symmetric dipole like radiation under uniform condition. The simple acoustic radiation modeling applied for the analysis also works well for this general non-uniform mean flow condition.

Large-Eddy Simulation of High-Frequency Combustion Instability in a Single-Element Atmospheric Combustor

Large-eddy simulation is performed to simulate high-frequency combustion instability in a single-element atmospheric combustor. Simulations are conducted for corresponding combustion-instability experiments, and the self-excited combustion instability is successfully captured. The first tangential mode of the combustion chamber is excited in the large-eddy simulation, and the amplitude and frequency of the pressure fluctuations are consistent with the experimental observations. The first tangential mode in the large-eddy simulation was observed at 1xa0kHz, and the peak-to-peak amplitude was approximately 4% of time-averaged pressure. The higher-order modes were also observed in the large-eddy simulation at frequencies ranging from 2 to 4xa0kHz, although those amplitudes were approximately one-fourth of the first tangential mode. The coupling mechanism between the flame and acoustic mode is explored based on the large-eddy-simulation results. The periodic ignition of the unburnt H2/O2 mixture exhibits lifted c...

Acoustic structure and damping estimation of a cylindrical rocket chamber during oscillation

2 Acoustic structure inside a cylindrical rocket chamber is numerically and theoretically investigated, which is the key for determining the damping performance of the whole chamber to measure the combustion instability. When a mean flow is present, the boundary conditions for acoustics are expressed by complex numbers which is called impedance or admittance. It depends on the Mach number of the mean flow, the frequency, the mode of the oscillation and the shape of the inlet (with injectors) and convergent part of a nozzle. In this study the first tangential mode is intensively investigated for some chamber configurations. First the acoustic structure is investigated with and without a mean flow. Then the damping characteristics is estimated numerically and explained from the theoretical point of view. Finally, the intense first tangential pressure oscillation with a mean flow is numerically reproduced and the characteristic features are compared with those without a mean flow.

Fundamental Study on Pressure Oscillation in a Liquid Rocket Engine Combustion Chamber

An oscillation of the combustion field is numerically studied inside a model combustor with two-dimensional configuration. It is found that the pressure oscillation consists of transverse and longitudinal modes and the amplitude of the pressure fluctuation is less than 0.5% of the chamber pressure. The periods of each oscillation mode is estimated and visualized by the numerical results. In addition, for deep understanding of the cause of the combustion instability, we estimate a fluctuation energy of the flow field based on the numerical results and discuss its ability to explain the numerical results.

Stability Index for Injection-Coupled Instability in Full-Scale Firing Tests

To construct a stability estimation tool for injection-coupled instability in rocket engines, a linear stability analysis was applied. The amplifying factor related to injector-element acoustics and the damping factor related to chamber acoustics were defined. A complex vector, which is a function of these factors, was introduced. The stability for gain and that for phase were defined by the vector, and the bulk stability was defined by these stabilities. Because of time-lag findings obtained from subscale firing tests, the instability index, which was defined as inverse of the bulk stability, was defined only by the stability of gain. To validate the tool, the stability of cryogenic oxygen/hydrogen firing tests with a full-scale chamber was rated. The average acceleration was applied as an instability index for the firing tests. By setting the instability index by the tool at 1×103 as the threshold that divides “unstable” and “stable,” the stability obtained by the tool and that of the firing test showed...