Simulation of unsteady combustion in a solid-propellant rocket motor

Various regimes of combustion in end-burning-grain solid-propellant rocket motors were examined within the framework of the phenomenological theory of unsteady combustion. A system of equations capable of describing the interaction between the process of burning and acoustic waves was derived. A specific feature of the problem is that its formulation involves two characteristic times: the acoustic time and oscillation amplitude variation time. These characteristic times differ by about three orders of magnitude, a circumstance that requires a high accuracy of calculations. Based on the quadratic approximation in oscillation amplitude, a simpler method for solving the problem was proposed, according to which only the effects associated with the oscillation amplitude variation time are taken into account. Numerical results were obtained for the simplest model of propellant burning, which contains the minimum number of parameters and disregards entropy waves in the combustion products. The steady and unsteady regimes of burning were identified. In the latter case, nonlinear effects may generate shock waves in the combustion chamber.     

Combustion of a propellant and its extinction upon rapid depressurization: A comparison of theory and experiment

The combustion of a nitroglycerin-based propellant and its extinction as a result of exponential pressure decay was studied on a bomb-receiver setup. At moderate depths and rates of pressure decay, the transient process ends with adoption of a new steady-state combustion mode. There are critical values of the depth and rate of pressure decay above which combustion ceases. Numerical simulations are used to determine a relationship between the critical values of these quantities (extinction curves). The calculations are performed within the framework of the phenomenological theory of unsteady combustion of energetic condensed systems using known steady-state laws of propellant combustion. A comparison of experimental and theoretical results demonstrates their satisfactory agreement.     

Response of a burning heterogeneous propellant to small pressure disturbances

A numerical code for the simulation of heterogeneous propellant burning is used to examine the response to the pressure field of an incident acoustic wave. It is shown that there are two natural response functions, one defined by the perturbation mass flux beyond the combustion field, the other by the perturbation energy flux beyond the combustion field. The first of these plays an essential role in L* instability (a coupled propellant–rocket-chamber phenomenon), and the second in whether the acoustic wave is amplified on reflection (a phenomenon exclusive to the propellant). We show, for several choices of parameter values and propellant morphology, that the two responses are qualitatively similar, albeit they differ in magnitude by modest amounts. We show that in some cases each response displays a single maximum or peak as a function of frequency, in other cases multiple peaks are obtained. A tentative hypothesis is proposed as a predictor of multiple peaks.     

Simulation and modelling of the waves transmission and generation in a stator blade row in a combustion-noise framework

The combustion noise in aero-engines is known to have two different origins. First, the direct combustion noise is directly generated by the flame itself. Second, the indirect combustion noise is caused by the acceleration in the turbine stages of entropy spots generated by the combustion. In both cases, the turbo-machinery is involved in the combustion-noise transmission and generation. Numerical simulations are performed in the present study to assess the global noise for a real aeronautical configuration. On the one hand, the acoustic and entropy transfer functions of an isolated blade row are obtained using two-dimensional unsteady simulations. The transfer functions of the blade row are compared with the model of Cumpsty and Marble that assumes an axially compact configuration. On the other hand, the acoustic and entropy sources coming from a combustion chamber are calculated from a three-dimensional Large Eddy Simulation (LES). This allows an evaluation of the error introduced by the model for the present combustion chamber using the previous numerical simulations. A significant error is found for the indirect combustion noise, whereas it stays reasonable for the direct one.     

Influence of the composition and ionizing radiation on the stability of combustion of composite propellants

The results of an experimental study of the acoustic admittance of the burning surface of composite propellants performed with the use of a two-end combustion chamber (T-chamber) are presented. The effects of the composition of the composite propellant (type of fuel-binder, content of aluminum powder, burning rate catalysts) and of ionizing γ-radiation on the acoustic admittance, which characterizes the tendency of the combustion chamber to high-frequency instability, are analyzed.     

Improved method of measuring pressure coupled response for composite solid propellants

Pressure coupled response is one of the main causes of combustion instability in the solid rocket motor. It is also a characteristic parameter for predicting the stability. The pressure coupled response function is usually measured by different methods to evaluate the performance of new propellant. Based on T-burner and “burning surface doubled and secondary attenuation”, an improved method for measuring the pressure coupled response of composite propellant is introduced in this article. A computational fluid dynamics (CFD) study has also been conducted to validate the method and to understand the pressure oscillation phenomenon in T-burner. Three rounds of tests were carried out on the same batch of aluminized AP/HTPB composite solid propellant. The experimental results show that the sample propellant had a high response function under the conditions of high pressure (~11.5 MPa) and low frequency (~140 Hz). The numerically predicted oscillation frequency and amplitude are consistent with the experimental results. One practical solid rocket motor using this sample propellant was found to experience pressure oscillation at the end of burning. This confirms that the sample propellant is prone to combustion instability. Finally, acoustic pressure distribution and phase difference in T-burner were analyzed. Both the experimental and numerical results are found to be associated with similar acoustic pressure distribution. And the phase difference analysis showed that the pressure oscillations at the head end of the T-burner are 180° out of phase from those in the aft end of the T-burner.     

Suppression of vortex core precession in a swirling reacting flow

The influence of combustion effect on unsteady vortex structure in the form of precessing vortex core was studied using the non-intrusive method of laser Doppler anemometry and special procedure of extracting the non-axisymmetric mode of flow fluctuations. The studies show that combustion has a significant effect on the parameters of such a core, reducing the amplitude (vortex deviation from the burner center) and increasing precession frequency. At the same time, the acoustic sensors detect almost an order reduction in the level of pressure pulsations generated by the precessing vortex core. Moreover, distributions of tangential velocity fluctuations and cross-correlation analysis show that vortex precession is quite pronounced even under the combustion conditions, bringing a significant coherent component to distributions of velocity fluctuations.     

Importance of lateral momentum equation to the modeling of sandwich propellant combustion

This paper reports the results of numerical studies carried out for a periodic sandwich propellant geometry with two-dimensional unsteady gas and condensed phase. A non-planar regressing surface along with a kinetic model of two reaction steps in the gas phase was used. This paper discusses the importance of lateral momentum equation to the combustion of sandwich propellants. It demonstrates that the instabilities in sandwich combustion reported in literature are due to neglect of lateral momentum equation and incorrect boundary conditions at the regressing surface. It demonstrates that neglect of momentum equations will lead to a different result from the one obtained considering the momentum equations for sandwich propellants.     

Nonlinear simulations of combustion instabilities with a quasi-1D Navier-Stokes code

As lean premixed combustion systems are more susceptible to combustion instabilities than non-premixed systems, there is an increasing demand for improved numerical design tools that can predict the occurrence of combustion instabilities with high accuracy. The inherent nonlinearities in combustion instabilities can be of crucial importance, and we here propose an approach in which the one-dimensional (1D) Navier-Stokes and scalar transport equations are solved for geometries of variable cross-section. The focus is on attached flames, and for this purpose a new phenomenological model for the unsteady heat release from a flame front is introduced. In the attached flame method (AFM) the heat release occurs over the full length of the flame. The nonlinear code with the use of the AFM approach is validated against analytical results and against an experimental study of thermoacoustic instabilities in oxy-fuel flames by Ditaranto and Hals [Combustion and Flame 146 (2006) 493-512]. The numerical simulations are in accordance with the experimental measurements and the analytical results and both the frequencies and the amplitudes of the resonant acoustic pressure modes are reproduced with good accuracy.     

Combustion response of an aluminum droplet burning in air

The combustion in air of a 100 μm-diameter aluminum droplet is studied by direct Navier–Stokes simulations. The model only considers the gas phase and includes a reduced Al/O₂ kinetic scheme with 8 species and 10 reactions. The model is validated against experimental burn time data and appears to be fairly correct despite its simplicity. The unsteady combustion is then investigated by superimposing an acoustic disturbance to the mean flow. The velocity-coupled response is computed for different frequencies and slip Reynolds numbers. A resonance peak is found to occur when the acoustic time scale matches the gas diffusion time scale. For lower frequencies however (typically below a few kHz), a quasi-steady regime seems to hold out which means that assuming quasi-steady combustion (e.g., given by a D² model) is valid in this case. In this regime, the computed response corresponds with a theoretical expression obtained by a linearization of the Ranz–Marshall correction term. This implies that unsteady aluminum combustion is strongly dependent on convection effects.     

Impact of symmetry breaking on the Flame Transfer Function of a laminar premixed flame

This work presents a numerical study of the acoustic response of a laminar flame with tunable asymmetry. A V-shaped premixed flame is stabilised in the wake of a cylindrical flame holder that can be rotated. The configuration is symmetric when the flame holder is fixed but increasing its rotation rate breaks the symmetry of the flow. This configuration is submitted to acoustic forcing to measure the effect of rotation of the flame holder on the Flame Transfer Functions. It appears that the asymmetry of the two flame branches changes their respective time delays, resulting in interference in the global unsteady heat release rate fluctuations. Consequently, the Flame Transfer Function exhibits dips and bumps, which are studied via laminar Direct Numerical Simulation. Potential applications for the control of combustion instabilities are discussed.     

Three-step approach for prediction of limit cycle pressure oscillations in combustion chambers of gas turbines

Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damages to combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. This work presents a three-step method to find stability margins within which gas turbines can be operated without going into self-excited pressure oscillations. As a first step, a set of unsteady Reynolds-averaged Navier–Stokes simulations with the Flame Speed Closure (FSC) model implemented in the OpenFOAM® environment are performed to obtain the flame describing function of the combustor set-up. The standard FSC model is extended in this work to take into account the combined effect of strain and heat losses on the flame. As a second step, a linear three-time-lag-distributed model for a perfectly premixed swirl-stabilized flame is extended to the nonlinear regime. The factors causing changes in the model parameters when applying high-amplitude velocity perturbations are analysed. As a third step, time-domain simulations employing a low-order network model implemented in Simulink® are performed. In this work, the proposed method is applied to a laboratory test rig. The proposed method permits not only the unsteady frequencies of acoustic oscillations to be computed, but the amplitudes of such oscillations as well. Knowing the amplitudes of unstable pressure oscillations, it is possible to determine how these oscillations are harmful to the combustor equipment. The proposed method has a low cost because it does not require any license for computational fluid dynamics software.     

Characteristics of composite propellant ignition by a CO2-laser

The delay time of ignition of a composite propellant based on ammonium perchlorate by a CO₂-laser is measured at various pressures and radiant flux densities. The characteristics of the propellant at the moment of ignition are calculated. The obtained rate constants of the reactions in the propellant are compared to the respective rate constants of the reactions in the c-phase occurring during the combustion of the composite propellant.     

Time-domain characterization of the acoustic damping of a perforated liner with bias flow

Combustion instabilities are caused by the interaction of unsteady heat releases and acoustic waves. To mitigate combustion instabilities, perforated liners, typically subjected to a low Mach number bias flow (a cooling flow through perforated holes), are fitted along the bounding walls of a combustor. They dissipate the acoustic waves by generating vorticity at the rims of perforated apertures. To investigate the absorption of plane waves by a perforated liner with bias flow, a time-domain numerical model of a cylindrical lined duct is developed. The liners' damping mechanism is characterized by using a time-domain "compliance." The development of such time-domain compliance is based on simplified or unsimplified Rayleigh conductivity. Numerical simulations of two different configurations of lined duct systems are performed by combining a 1D acoustic wave model with the compliance model. Comparison is then made between the results from the present models, and those from the experiment and the frequency-domain model of previous investigation [Eldredge and Dowling, J. Fluid Mech. 485, 307-335(2003)]. Good agreement is observed. This confirms that the present model can be used to simulate the propagation and dissipation of acoustic plane waves in a lined duct in real-time.     

Phase synchronization and collective interaction of multiple flamelets in a laboratory scale spray combustor

In this paper, we investigate the coupled behvior of the acoustic field in the confinement and the unsteady flame dynamics in a laboratory scale spray combustor. We study this interaction during the intermittency route to thermoacoustic instability when the location of the flame is varied inside the combustor. As the flame location is changed, the synchronization properties of the coupled acoustic pressure and heat release rate signals change from desynchronized aperiodicity (combustion noise) to phase synchronized periodicity (thermoacoustic instability) through intermittent phase synchronization (intermittency). We also characterize the collective interaction between the multiple flamelets anchored at the flame holder and the acoustic field in the system, during different dynamical states observed in the combustor operation. When the signals are desynchronized, we notice that the flamelets exhibit a steady combustion without the exhibition of a prominent feedback with the acoustic field. In a state of intermittent phase synchronization, we observe the existence of a short-term coupling between the heat release rate and the acoustic field. We notice that the onset of collective synchronization in the oscillations of multiple flamelets and the acoustic field leads to the simultaneous emergence of periodicity in the global dynamics of the system. This collective periodicity in both the subsystems causes enhancement of oscillations during epochs of amplitude growth in the intermittency signal. On the contrary, the weakening of the coupling induces suppression of periodic oscillations during epochs of amplitude decay in the intermittency signal. During phase synchronization, we notice a sustained synchronized movement of all flamelets with the periodicity of the acoustic cycle in the system.     

Unsteady regimes of propellant combustion in a semiclosed space

Numerical simulations were used to study the nonstationary modes of propellant combustion in a semiclosed volume outside the boundaries of stationary combustion. The analysis was performed within the framework of phenomenological theory of nonstationary combustion for the simplest propellant combustion model containing the minimum number of governing parameters. It was demonstrated that the variation of one of the parameters can bring about the changeover from the stationary regime to the chaotic one according to the Feigenbaum scenario. A still further increase in the bifurcation parameter initiates transition to experimentally observed combustion regimes (extinction and so-called sneezing).     

Automatic control of propellant combustion stability in a semiclosed space

The possibility of changing the boundary of stable combustion of propellants in a semiclosed space is examined within the framework of the linear automatic control theory. Analysis is performed using the Zel’dovich-Novozhilov theory in conjunction with the isothermal approximation for the combustion products. Characteristic equations for determining the stability boundary were derived for various control laws: proportional, proportional-differential, and proportional-integral ones. It was demonstrated that, depending on the values of the governing parameters (propellant properties, apparatus constant) and control law form, the stability boundary could expand or contract.     

Thermal stability of the burning of the base subsystem of components of a composite propellant

The problem of the thermal stability of the base subsystem of components of a composite solid propellant with respect to the introduction of heat-absorbing agents, inhibitors, and burning rate catalysts was considered. It was demonstrated that the response of the base subsystem to the introduction in it of additives is equivalent to a change in the initial temperature of the propellant, i.e., is determined by its burning rate temperature sensitivity. The competition of the fuel components for oxidative species and the role of this phenomenon in the formation of the structure of the combustion wave were examined. Extensive experimental data on the effect of heterogeneous fillers of various natures on the burning rate of the composite system were obtained.     

On the thermo-acoustic Fant equation

A ‘reduced complexity’ equation is derived to investigate combustion instabilities of a Rijke burner. The equation is nonlinear and furnishes limit cycle solutions for finite amplitude burner modes. It is a generalisation to combustion flows of the Fant equation used to investigate the production of voiced speech by unsteady throttling of flow by the vocal folds [G. Fant, Acoustic Theory of Speech Production. Mouton, The Hague, 1960]. In the thermo-acoustic problem the throttling occurs at the flame holder. The Fant equation governs the unsteady volume flow past the flame holder which, in turn, determines the acoustics of the entire system. The equation includes a fully determinate part that depends on the geometry of the flame holder and the thermo-acoustic system, and terms defined by integrals involving thermo-aerodynamic sources, such as a flame and vortex sound sources. These integrals provide a clear indication of what must be known about the flow to obtain a proper understanding of the dynamics of the thermo-acoustic system. Illustrative numerical results are presented for the linearised equation. This governs the growth rates of the natural acoustic modes, determined by system geometry, boundary conditions and mean temperature distribution, which are excited into instability by unsteady heat release from the flame and damped by large scale vorticity production and radiation losses into the environment. In addition, the equation supplies information about the ‘combustion modes’ excited by the local time-delay feedback dynamics of the flame.     

Quench collection of nano-aluminium agglomerates from combustion of sandwiches and propellants

An experimental investigation has been carried out to measure the size of nano-aluminium agglomerates emerging from the combustion of nano-aluminized sandwiches and composite solid propellants. Nano-aluminium of median size of 50 nm produced in-house by the electrical wire explosion method is used in these samples. Propellants with different sizes of coarse and fine ammonium perchlorate are considered. Surface features of sandwiches and a propellant whose burning was interrupted by rapid depressurization are examined in a scanning electron microscope. The combustion products of the sandwiches and propellants are quenched close to the burning surface and collected in a quench collection set-up. The surface features of rapid-depressurization quenched sandwiches exhibit relatively large nano-aluminium clusters—of the order a few micrometres—particularly in the binder lamina. Quench-collected nano-aluminium exhibits significant agglomeration, but only a small fraction of the agglomerates are in the 1–3 μm range, except for both the coarse and fine AP particles used in the formulation being large, but even there they do not exceed ∼5 μm in size. This is expected to be benign for reduced smoke propellant applications from exhaust signature point of view, and to decrease the specific impulse losses without sacrificing the energetics of the propellant.