Transverse Pressure Waves Research Articles

Analysis of self-excited transverse combustion instability in a rectangular model rocket combustor

A methane/oxygen mixture is considered to be an appropriate propellant for many future rocket engines due to its practicality and low cost. To better understand the combustion instability in methane/oxygen-fed rocket engines, the spontaneous transverse combustion instability in a rectangular multi-element combustor (RMC) was analyzed both experimentally and numerically. Severe combustion instabilities occurred in the RMC during repeatable hot-fire tests. The physical mechanisms were systematically investigated through numerical simulations based on the stress-blended eddy simulation and flamelet-generated manifolds method with detailed chemical mechanisms (GRI Mech 3.0). The numerical results for the frequency spectrum and spatial modes agree well with the theoretical analysis and experimental data. The driven regions of the combustion instability were identified on both sides of the combustion chamber through a Rayleigh index analysis. The longitudinal pressure oscillations in the oxidizer post were found to be coupled with the transverse pressure waves in the combustion chamber and led to periodic oscillations of the mass flow rate of propellant. Moreover, the mixing was highly enhanced when the pressure wave interacted with walls of the combustion chamber. Therefore, a sudden release of heat occurred. The pressure oscillations were enhanced by pulsated heat release. A closed-loop system with positive feedback associated with periodic oscillations mass flow rate of the propellant, and sudden heat release, was believed to account for the present combustion instability.

Comparison of blockage performance of pressure wave in structural baffle injector and fluidic baffle injector

The role of the structural baffle injectors and blades in the liquid rocket engine is to block the transverse pressure waves that are caused by combustion instability. Although the protection of the liquid rocket system from high-frequency combustion instability is essential, there are side effects such as increased weight of the rocket and thermal effect. In this study, a fluidic baffle injector was applied to the simulant spray system, expecting that it would operate with the same performance as a structural baffle injector. The development of the additive manufacturing technology allows for the designing of various geometrical injector arrays such as the combination of a gas-centered swirl injector and shear coaxial injector. This study aimed to compare the blockage performance of a structural baffle injector with that of a fluidic baffle injector using damping capacity and various injector arrays. The damping capacity was high in the structural baffle injector because the pressure wave was completely blocked. However, the amplitude was similar in the shear coaxial injector. This means that the blockage performance of the shear coaxial injector as a fluidic baffle injector is noteworthy.

Modelling of the transition of a turbulent shock-flame complex to detonation using the linear eddy model

In the current study, the influence of turbulent mixing and local reaction rates on the transition to detonation of a turbulent shock-flame complex was investigated using a state-of-the-art large eddy simulation (LES) strategy. Specifically, detonation attenuation by a porous medium, and the subsequent re-initiation for methane–oxygen, a moderately unstable mixture, was considered. The purpose of the investigation was to validate the numerical strategy with previous experimental observations, and to determine what specific roles turbulent mixing and shock compression have on flame acceleration during the final stages of deflagration to detonation transition (DDT). The modelling procedure adopted was a grid-within-a-grid approach: The compressible linear eddy model for large eddy simulation (CLEM-LES). It was found that average turbulent velocity fluctuations greater than the laminar flame speed by an order of magnitude were required in order to maintain wave velocities above the Chapman–Jouguet (CJ)-deflagration velocity threshold, a precursor requirement for detonation re-initiation to occur. It was also found that sufficient turbulent burning on the flame surface was required in order to drive pressure waves to sufficiently strengthen the leading shock wave, locally, in order to trigger auto-ignition hot spots in the wave front. These local explosion events, which were found to burn out through turbulent surface reactions, drive transverse pressure waves outward. Upon subsequent shock reflections or interactions of the transverse waves, new local explosion events occurred, which further strengthened the adjacent leading shock wave above the CJ-detonation speed. Eventually, through this process, the wave sustained the CJ-detonation speed, on average, through the cyclic mechanism of local explosion events followed by turbulent surface reactions. Finally, combustion of the flame acceleration process was found to lie within the thin-reaction zones regime.

Transient response of a liquid injector to a steep-fronted transverse pressure wave

Motivated by the dynamic injection environment posed by unsteady pressure gain combustion processes, an experimental apparatus was developed to visualize the dynamic response of a transparent liquid injector subjected to a single steep-fronted transverse pressure wave. Experiments were conducted at atmospheric pressure with a variety of acrylic injector passage designs using water as the working fluid. High-speed visual observations were made of the injector exit near field, and the extent of backflow and the time to refill the orifice passage were characterized over a range of injection pressures. A companion transient one-dimensional model was developed for interpretation of the results and to elucidate the trends with regard to the strength of the transverse pressure wave. Results from the model were compared with the experimental observations.

Lattice Boltzmann direct numerical simulation of interface turbulence over porous and rough walls

To discuss the turbulent flow physics over porous walls, direct numerical simulation (DNS) of a porous-walled channel flow at the bulk Reynolds number of 3000 is performed by the D3Q27 multiple-relaxation time lattice Boltzmann method. The presently considered porous layer, whose porosity is 0.71, consists of interconnected staggered cube arrays. For understanding the influence of the wall permeability on turbulence, DNS of an impermeable rough walled channel flow is also conducted. By two-point autocorrelation, one-dimensional energy spectrum and proper orthogonal decomposition (POD) analyses, the existence and characteristics of the transverse pressure waves induced by the Kelvin–Helmholtz (K–H) instability over the porous and rough walls are elucidated. The structure, wave lengths and power spectra of the transverse waves are discussed in detail. The influence of the K–H instability on turbulence is also clarified.

Triggering and Restabilization of Combustion Instability with Rocket Motor Acceleration

The probability of a liquid-propulsion rocket motor to develop screeching instability is studied computationally. The combustion chamber is accelerated as a rigid body using a prescribed acceleration time history; it is found that accelerations of proper magnitude, duration, and frequency induce a pressure wave inside the combustion chamber that grows to a screeching acoustic wave limit cycle. For a rectangular rocket motor, a reciprocating transverse acceleration leads to the development of a transverse pressure wave limit cycle; for a cylindrical rocket motor, the limit cycle may be either a standing wave, for a transverse reciprocating acceleration, or a spinning wave, for a transverse rotating acceleration. It is found that a limit cycle may be induced by either a large acceleration pulse of short duration or a smaller acceleration pulse of a longer duration. The polynomial chaos expansion method is used to study the probability of growth to a limit-cycle oscillation when the amplitude and frequency of the transverse acceleration pulse are random.

Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine

AbstractThe combustion stability of a liquid-propellant rocket engine experiencing a random, finite perturbation from steady-state conditions is examined. The probability is estimated for a nonlinear resonant limit-cycle oscillation to be triggered by a random disturbance. Transverse pressure waves are considered by using a previously published two-dimensional nonlinear pressure wave equation coupled with Euler equations governing the velocity components. The cylindrical combustion chamber is a complex system containing multiple co-axial methane–oxygen injectors; each co-axial jet is analysed for mixing and burning on its own local grid scheme, with the energy release rate coupled to the wave oscillation on the more global grid. Two types of stochastic forcing for the random disturbance are explored: a travelling Gaussian pressure pulse and an oscillating pressure dipole source. The random variables describing the pulse are magnitude, location, duration and orientation of the disturbances. The polynomial chaos expansion (PCE) method is used to determine the long-time behaviour and infer the asymptote of the solution to the governing partial differential equations. Depending on the random disturbance, the asymptote could be the steady-state solution or a limit-cycle oscillation, e.g. a first tangential travelling wave mode. The asymptotic outcome is cast as a stochastic variable which is determined as a function of input random variables. The accuracy of the PCE application is compared with a Monte Carlo calculation and is shown to be significantly less costly for similar accuracy.

High-speed flames and DDT in very rough-walled channels

An experimental investigation of flame acceleration in a narrow rectangular cross-section channel with various lower boundary conditions is presented. The boundary conditions investigated include a smooth surface and a rough surface with and without porosity. Tests were performed with a mixture of nitrogen diluted stoichiometric methane–oxygen, i.e., CH4+2(O2+2/3N2), at initial pressures in the range of 9–15kPa. The explosion front velocity was measured via ionization probes and pressure transducers and the explosion wave front structure was visualized by high-speed shadowgraph video. For tests performed with a porous rough surface the flame achieves a velocity that approaches the speed of sound of the combustion products. In the case of the rough surface without porosity, a globally quasi-steady high-speed flame is produced with a velocity between the combustion products speed of sound and the Chapman–Jouguet detonation velocity. It is proposed that flame acceleration beyond the speed of sound of the combustion products is possible due to enhanced burning that is driven by chemical–acoustic interactions. Such interactions occur as the turbulent flame brush is traversed by transverse pressure waves produced by the passage of the explosion front shock wave over the rough surface. It is also observed that under certain conditions a smooth transition from a diffusion driven flame to a shock ignition detonation is possible.

Chemical energy release in one-dimensional detonation waves in gaseous explosives

The Zel'dovich-von Neumann-Doring (ZND) model of a one-dimensional, steady state detonation wave in a gaseous explosive is extended to include the thermal relaxation processes which precede and follow the exothermic chemical reconstitution reactions. In this nonequilibrium model the detonation wave consists of four main zones: a very thin leading shock front in which the unreacted explosive mixture is compressed and accelerated in the direction of shock propagation; a much thicker relaxation zone in which the rotational and vibrational modes of the unreacted explosive gases approach thermal equilibrium; a relatively thin zone in which the chemical energy is released by rapid chain propagation and branching reactions into highly vibrationally excited reaction product gases; and another very thick relaxation zone in which the product gases expand and vibrationally relax toward thermodynamic equilibrium at the Chapman-Jouguet (CJ) state. Quantitative calculations for the H 2Cl 2, O 3, and H 2O 2 systems based on experimental chemiluminescent and crossed molecular beam product energy distribution data show that the amount of chemical energy initially released as product vibrational energy is greater than the sum of CJ equilibrium vibrational energy plus the amount of chemical energy required to sustain the constant velocity shock front. The physical mechanism by which this vibrational energy sustains the shock front is postulated to be the chemical amplification of transverse pressure waves, which propagate through the vibrationally excited products and eventually overtake the leading shock front.

Chemical energy release in self-sustaining detonation waves in condensed explosives

The nonequilibrium Zel'dovich-von Neumann-Doring (ZND) model of a one-dimensional detonation wave is applied to condensed phase (solid and liquid) explosives in this paper. In condensed explosives, the detonation wave is assumed to consist of four main zones: a narrow leading shock wave; a much thicker induction zone in which the intra- and intermolecular vibrational degrees of freedom rapidly equilibrate and the rate-determining endothermic bond-breaking reaction then proceeds at a rate governed by the equilibrium von Neumann spike conditions; a narrow chemical reconstitution zone in which the unreacted explosive rapidly decomposes and recombines into highly vibrationally excited reaction products; and another thick relaxation zone in which the reaction products expand and approach thermal equilibrium at the Chapman-Jouguet (CJ) state. Gruneisen-type equations of state are used to calculate the energy release in several condensed explosives at various initial densities. Along with kinetic and chemical energy release, the release of potential or cold compression energy in the exothermic chemical reconstitution and vibrational deexcitation zones sustains the leading shock front. The conditions for amplification of transverse pressure waves in the zone of highly vibrationally excited reaction products are shown to exist for condensed explosives. The effects of the resulting complex cellular structure of detonation waves on the energy release in homogeneous (liquid) and heterogeneous (solid) explosives are qualitatively discussed.

Experiments on the stability of converging cylindrical detonations

This paper describes some recent experiments on the stability of cylindrical converging detonations in a gaseous explosive. Perturbations are generated on the symmetrical detonation front by placing a cylindrical rod in its path. Observations of the phenomenon are obtained by spark schlieren photography. Iy was found that converging detonations are stable in the sense that there exists a curvature distribution mechanism whereby local perturbations are distributed by a set of transverse pressure waves propagating tangentially to the front. Provided these disturbances are created before significant cumulation behind the converging front has occurred, the amplitudes of the transverse waves are found to decay rapidly with travel and the front regains its former symmetry.