ACOUSTIC–MEAN FLOW INTERACTION AND VORTEX SHEDDING IN SOLID ROCKET MOTORS

The present work is devoted to the numerical simulation of two important phenomena in the field of solid propellant rocket motors: the first is acoustic boundary layers that develop above the burning propellant; the other is a periodic vortex-shedding phenomenon which is the result of a strong coupling between the instability of mean flow shear layers and acoustic motions in the chamber. To predict the acoustic boundary layer, computations were performed for the lower half of a rectangular chamber with bottom-side injection. The outflow pressure is sinusoidally perturbed at a given frequency. For the highest CFL numbers the implicit scheme is not able to compute the unsteadiness in the acoustic boundary layer. With very low CFL numbers or with the explicit scheme the main features of the acoustic field are captured. To simulate the vortex-shedding mechanismin a segmented solid rocket motor, the explicit version is used. This computation shows a mechanism for ‘self-excited’ vortex shedding close to the second axial mode frequency. The use of the flux-splitting technique reduces substantially the amplitude of the oscillations. A few iterations are done with flux splitting, then the computation is performed without this technique. In this case both the frequency and the intensity are well predicted. A geometry more representative of the solid rocket motor is also computed. In this case the vortex-shedding process is more complex and pairing is observed.     

Model for the Formation of Acoustic Self-Oscillations in a Chamber with a Jet Flowing Through its Nozzle

This paper describes free acoustic oscillations of gas in a chamber with a jet flowing through its nozzle in the case of nonstationary intensity component of vortex sheet flowing down from the edge of the nozzle. There is established feedback between acoustic oscillations and oscillations induced by a corresponding vortex sheet component. It is shown that, in the presence of given feedback, there could be instability of acoustic oscillations, which would result in acoustic self-oscillations in the chamber. The boundaries of the domain in which instability is formed are determined by developing a mathematical model of stable acoustic oscillations in the chamber with account for the influence of the vortex sheet.     

Analysis of self-sustained oscillation sources in segmented flows

The analysis of self-sustained oscillations in segmented flow generated through porous walls has been carried out over a wide range of velocity levels; in fact, we studied a cold gas flow induced by injection through different wall injecting blocks. We have attempted in this study to analyse the potential unstable development occurring in solid propellant rocket motors. We lay emphasis upon the phenomenon of wall vortex shedding insofar as it conduces to acoustic mode resonance in the whole chamber, within whose confines impingement of such structures generates a source of noise. It is on account of segmented flow that the thin shear layer develops and that the aforementioned vortex shedding comes to induce aero-acoustic coupling. Subsequent experimental results highlight a link in such flows between these two noise sources - they also allow one to observe a pronounced form of selectivity in the energy transfer, i.e. in longitudinal acoustic mode amplification, which has an attested effect upon all of the pressure oscillations in the chamber.     

Stability of the combustion process in elastic combustion chambers

High-frequency instability phenomena in rigid combustion chambers have been studied theoretically in [1–3]. This phenomenon is attributed to the interaction between the combustion processes and combustion-product fluctuations in the chamber. One of the possible mechanisms of formation of high-frequency instability is examined in [3], where the combustion rate is represented in the form of a retarded pressure functional. In this case, the problem is reduced to studying the stability of a certain distributed self-oscillating time-lag system.If the oscillation frequencies of the combustion products are comparable to the natural vibrations of the shell which forms the combustion chamber, then it is natural to expect that the elasticity of the chamber walls will affect the combustion process. Coupled effects of acoustoelastic instability can arise, in whose development the vibrations of the chamber wall play a substantial role. These effects are particularly undesirable from the point of view of the vibrational stability of combustion chambers.In this paper, a theory of high-frequency instability of stationary combustion is developed with allowance for elastic deformations of the combustion chamber walls. The theory is based on the mechanism of vibrational combustion [1–3], according to which the combustion front is assumed to the concentrated, while the velocity jump at the front is expressed through a retarded pressure functional. It is assumed that the combustion product flow is one-dimensional and isentropic and that the chamber is cylindrical. The deformations of the chamber are described via the moment theory of shells. The existence is revealed of additional instability regions produced by the interaction between the elastic vibrations of the chamber walls and the acoustic oscillations of the combustion products. The influence of the relation between the elastic and acoustic frequencies and of the structural damping factor in the combustion chamber walls on the stability of the stationary combustion process is examined. The problem discussed is treated as a mathematical model for more complex asymmetric problems in which the elastic and acoustic frequencies can be of the same order.     

喷嘴结构对液氧煤油火箭发动机高频燃烧不稳定性的影响

为了筛选高压补燃循环液氧煤油火箭发动机的喷嘴,在喷注单元低压高频燃烧不稳定性模拟实验系统上开展实验,研究了喷嘴结构对燃烧稳定性边界的影响。实验使用气态空气与氧气的混合物作为氧化剂,加热的煤油蒸汽作为燃料;喷嘴为全尺寸气液同轴直流离心式喷嘴,模拟燃烧室与真实燃烧室的固有声学频率相等。根据测量模拟燃烧室内的脉动压力区分大幅振荡、小幅振荡和稳定工作。研究结果表明,喷嘴长度、缩进室长度和入口节流嘴直径对高频燃烧不稳定性裕量有很大影响,并存在相对最佳值。     

Pressure-based method for combustion instability analysis

An improved pressure-based method has been applied to predict the two-dimensional instability analysis of liquid-fuelled rocket engines. This method is non-iterative for transient flow calculations and applicable to all-speed flows. Validation cases include the shock-tube problem, the blast flow field and unsteady spraycombusting flows. Computations for the combustion instability analysis were carried out for various combustion parameters such as spray initial conditions and combustor geometries. Unsteady behaviours of the stable and unstable spray flame fields and effects of acoustic oscillations on the fuel droplet vaporization and combustion process are studied in detail. The present numerical model successfully demonstrates the capability of predicting combustion instability as well as fast transient compressible flows at all speeds.     

A combined analytical and numerical analysis of the flow-acoustic coupling in a cavity-pipe system

The generation of sound by flow through a closed, cylindrical cavity (expansion chamber) accommodated with a long tailpipe is investigated analytically and numerically. The sound generation is due to self-sustained flow oscillations in the cavity. These oscillations may, in turn, generate standing (resonant) acoustic waves in the tailpipe. The main interest of the paper is in the interaction between these two sound sources. An analytical, approximate solution of the acoustic part of the problem is obtained via the method of matched asymptotic expansions. The sound-generating flow is represented by a discrete vortex method, based on axisymmetric vortex rings. It is demonstrated through numerical examples that inclusion of acoustic feedback from the tailpipe is essential for a good representation of the sound characteristics.     

Acoustic resonance phenomena in air bleed channels in aviation engines

The existence of axial–radial acoustic resonance oscillations of the basic air flow in bleed channels of aviation engines is demonstrated theoretically and experimentally. Numerical and analytical methods are used to determine the frequency of acoustic resonance oscillations for the lowest modes of open and closed bleed channels of the PS-90A engine. Experimental investigations reveal new acoustic resonance phenomena arising in the air flow in bleed channel cavities in the core duct of this engine owing to instability of the basic air flow. The results of numerical, analytical, and experimental studies of the resonance frequencies reached in the flow in bleed channel cavities in the core duct of the PS-90A engine are found to be in reasonable agreement. As a result, various types of resonance oscillations in bleed channels can be accurately described.     

Unsteady turbulent flow of a gas suspension in a channel under conditions of injection and forced pressure oscillations

A turbulent flow of a suspension of solid particles in a gas is considered. The suspension is located in a channel with permeable walls (the pressure at the left end face of the channel follows a sinusoidal law). The flow considered here reflects the principal features of the flow in the combustion chamber of a solid-propellant rocket motor. The unsteady flow of the gas suspension is described by using the Eulerian-Lagrangian approach. A stochastic variant of the discrete-trajectory approach is used for modeling the particle motion. The influence of the condensed phase on the turbulence characteristics and acoustic oscillations of the parameters of the working medium in the channel in the case of injection is discussed. The calculated results are compared with data obtained in a physical experiment.     

Acoustically Induced Flashback in a Staged Swirl-Stabilized Combustor

This paper describes a joint experimental and numerical investigation of the interaction between thermoacoustics and flashback mechanisms in a swirled turbulent burner. An academic air/propane combustor terminated by a choked nozzle is operated up to 2.5 bars. Experiments show that the flame can stabilize either within the combustion chamber or flashback inside the injection duct, intermittently or permanently. The present study focuses on the mechanisms leading to flashback: this phenomenon can occur naturally, depending on the swirl level which can be adjusted in the experiment by introducing axial flow through the upstream inlet. It can also be triggered by acoustic waves, either through acoustic forcing or self-excited thermoacoustic instability. Flashback is difficult to study experimentally, but it can be investigated numerically using LES: in a first configuration, the outlet of the chamber is treated as a non-reflecting surface through which harmonic waves can be introduced. In this case, a 20 kPa acoustic forcing is sufficient to trigger permanent flashback after a few cycles. When the LES computational domain includes the choked nozzle used experimentally, no forcing is needed for flashback to occur. Self-excited oscillations reach high levels rapidly, leading to flame flashback, as observed experimentally. These results also suggest a simple method to avoid flashback by using fuel staging, which is then tested successfully in both LES and experiments.     

Generation of tones due to flow past a deep cavity: Effect of streamwise length

Shear flow past a deep cavity can generate self-sustained oscillations, including locked-on flow tones, due to coupling between the inherent instability of the separated shear layer and an acoustic mode of the cavity resonator. This investigation focuses on the dimensionless pressure amplitude response within a deep cavity, as a function of the streamwise length of the cavity opening; for each length, the pressure response is characterized over a wide range of dimensionless inflow velocity. Criteria for locked-on flow tones are assessed. They include a measure of the strength of lock-on, SoL and the quality factor Q. All self-excited oscillations are assessed using both of these criteria, in order to interpret dimensionless forms of the fluctuation pressure amplitude. The dimensionless pressure amplitude response of the cavity involves several successive regimes, due to variations of streamwise length L of the cavity opening. These regimes are defined in relation to L/θ, where θ is the momentum thickness of the inflow boundary layer. Below a minimum value of L/θ, flow tones cannot be generated. Furthermore, these regimes are defined in terms of the possible hydrodynamic modes (stages) of the unsteady shear layer and the acoustic modes of the deep cavity.     

Absolute and convective instability of a liquid sheet with transverse temperature gradient

The spatial–temporal instability behavior of a viscous liquid sheet with temperature difference between the two surfaces was investigated theoretically. The practical situation motivating this investigation is liquid sheet heated by ambient gas, usually encountered in industrial heat transfer and liquid propellant rocket engines. The existing dispersion relation was used, to explore the spatial–temporal instability of viscous liquid sheets with a nonuniform temperature profile, by setting both the wave number and frequency complex. A parametric study was performed in both sinuous and varicose modes to test the influence of dimensionless numbers on the transition between absolute and convective instability of the flow. For a small value of liquid Weber number, or a great value of gas-to-liquid density ratio, the flow was found to be absolutely unstable. The absolute instability was enhanced by increasing the liquid viscosity. It was found that variation of the Marangoni number hardly influenced the absolute instability of the sinuous mode of oscillations; however it slightly affected the absolute instability in the varicose mode.     

Oscillations of a gas-vapor bubble in an acoustic field

It is shown that at large vapor contents, as a result of the combined action of phase transitions and capillary effects, the small radially symmetric oscillations of gas-vapor bubbles in an acoustic field are unstable in amplitude. The critical vapor concentration in the bubble separating regions of qualitatively different bubble behavior in the acoustic field is determined. Expressions are obtained for the decay rate of the radial oscillations of the gas-vapor bubble and the growth rate characterizing the rate of increase of oscillation amplitude in the region of instability. It is shown that adding only a slight amount of gas to the vapor bubble leads to a marked decrease in the growth rate. It is found that in the particular case of a vapor bubble the tine growth rate characterizing the development of the instability is of the same order as the second resonance frequency of the vapor bubble. This may serve to explain why in the case of vapor bubble oscillations the second resonance effect, which has been established in a number of theoretical studies and is widely discussed in the literature, has not yet been experimentally confirmed. The problem of spherically symmetrical processes around gasvapor bubbles was posed in [1], and their small oscillations are investigated in detail in [2–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 79–33, May–June, 1986.The authors are grateful to R. I. Nigmatulin for useful discussions.     

LES Investigation of the Flow Through an Effusion-Cooled Aeronautical Combustor Model

The present study is devoted to the analysis of the behaviour of the flow through an effusion-cooled aeronautical combustor model. High-fidelity calculations are performed on an experimental model of a combustion chamber multi-perforated wall and compared to experimental measurements. The effect of combustion instability on the effusion-cooling system is investigated by studying the interaction of an acoustic wave with the jets-in-crossflow issued from the cooling plate. It is shown that the mass-flow rate through the plate can be drastically reduced by the acoustic wave, which demonstrates the destructive effect that such instability may have on the cooling of an aeronautical combustion chamber.     

水下声波传播过程的时域间断Galerkin有限元方法

本文构建了声压波动方程的改进时域间断Galerkin有限元方法.传统时域连续有限元方法在计算高梯度、强间断特征水中声波传播问题时往往会出现虚假数值振荡现象,这些数值振荡会影响正常波动的计算精度.为了解决这一问题,本文通过引入人工阻尼的方式构建了改进的时域间断Galerkin有限元方法,并针对具有高梯度、强间断特征的多障...     

A theoretical and experimental study on flow characterisation in an acoustically excited chamber

Flame–acoustic wave interactions have been studied widely in the combustion community; however the whole physicochemical mechanism is still not clear. The present research aims to analyse the acoustic model inside an enclosed combustion chamber and to gain more detailed data to further study flame/acoustic interactions theoretically. The acoustic coupling can be calculated by using linear acoustic equations. The theoretical acoustic model has been developed to analyse the acoustic response for the present square tube and acoustical system. A good agreement between experimental measurements and theoretical predictions were proved by measuring the pressure and velocity fields of acoustic wave. The first four measured harmonic frequencies match well with theoretical prediction. The measured acoustic pressure node and anti-node region were also the same as theoretical prediction. However, due to the neglect of pressure drop loss in the upper end of the tube, the theoretical prediction data was from 23% to 43.3%, higher than that of the experimental measurements.     

Effect of the acoustic regularization of initial perturbations on the development of ordered structures

Mechanisms are considered by which acoustic oscillations influence the structure of subsonic shear flows. Analysis of the experimental data [1–7] confirms the assumption made in [6] that the regularization of initial perturbations, which causes a higher degree of ordering and an increase in the life of vortices formed because of the development of instability waves or interaction of acoustic oscillations with the edge of the nozzle, is one of the mechanisms by which acoustics influences various shear flows. Photographs are given which show the regularizing effect of acoustics on the development of vortices in the wake behind the edge.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–174, January–February, 1986.     

Two modes of operation of a model combustion chamber as a thermoacoustic autooscillating system

It is shown that soft and hard modes of operation of a model combustion chamber as an autooscillating system are possible. In the case of oscillations with transverse acoustic waves we: a) determined the ranges of these modes experimentally; b) detected oscillatory hysteresis (persistence) effects and observed the abrupt appearance and disappearance of oscillations during gradual variation of the parameters. We also noted excitation of autooscillations when finite perturbations acted on the gas column in the combustion chamber in the case of the hard mode.     

Thermo-mechanical instability in vibration absorbers

We analyze a problem of the thermo-mechanical instability caused by small changes of a viscous damping in vibration absorbers. The nonlinear coupling between the oscillations and temperature takes place due to a linear thermal dependence of the coefficient of energy dissipation. This provides typical phase–amplitude frequency patterns inherent in unstable regimes. While the damping coefficient decreases with the increase in the temperature, the effect of bifurcated oscillations can be exhibited brightly as some abnormal operating regimes. The vibration absorber appears as a complex dynamical system, behaving strongly upon the ambient temperature. Typical thermo-mechanical instability patterns are traced in detail within a parametric analysis along an approach closed to the Lie method. This study would explain some unwanted dynamical effects accompanying the utilizing of vibration absorbers.