Instability In Solid Rocket Motors Research Articles

Experimental Study on Submerged Nozzle Damping Characteristics of Solid Rocket Motor

Acoustic instabilities in solid rocket motors (SRMs) can lead to severe performance deterioration and structural damage. Nozzle damping accounts for the main acoustic dissipation source, and it is highly dependent on geometric parameters and operating conditions. This study experimentally investigated the acoustic damping characteristics of submerged nozzles in SRMs, focusing on the effects of submerged cavity dimensions, nozzle convergent angle, throat-to-port area ratio, and mean pressure variations on the longitudinal instability. The steady-state wave decay method was used to quantify the acoustic damping, and a designed rotary valve system was employed to introduce periodic pressure oscillations in the high-pressure combustion chamber. The results revealed that a larger submerged cavity would reduce the nozzle damping efficiency, with the elimination of the submerged cavity enhancing the nozzle decay coefficient magnitude by 41.9%. Furthermore, increasing the nozzle convergent angle was found to amplify acoustic wave reflection, thereby diminishing damping performance. A linear inverse relationship was observed between the throat-to-port area ratio and the decay coefficient, with a 125% increase in the ratio resulting in a 24.3% reduction in the decay coefficient. Interestingly, despite the formation of complex vortices in the submerged cavity, the mean pressure variation presented negligible effects on acoustic damping characteristics, and its damping performance is similar to a simple nozzle without a cavity. These findings provide valuable experimental data for predicting the stability of a solid rocket motor with a submerged nozzle and offer insights into the optimization of submerged nozzle designs for higher acoustic damping in SRMs.

Experimental and numerical investigation of aluminum particle combustion driven instability in solid rocket motors

Aluminum particles are extensively employed to enhance the energetic properties of propellants. However, the heat release rate (HRR) fluctuations resulting from aluminum combustion can potentially affect the stability of solid rocket motors (SRMs). Using a self-made high-pressure combustion diagnostics system and laser ignition system, this work investigates the combustion behavior of single aluminum particle under propellant atmosphere and acoustic excitation. An unsteady aluminum combustion model using Ranz-Marshall correlation and involving the heat and mass transfer equation was developed. The D2 law of aluminum particle combustion in a real propellant under 0.5 MPa was fitted as t = D2/0.31. The measured combustion rate of laser-ignited aluminum particles was found to increase from 0.381mm2/s to 0.465 mm2/s when an acoustic excitation of sine wave(200 Hz, 20Pa) was applied to the propellant, which agreed well with the prediction of the proposed unsteady combustion model whose error was 4.7%. Then, the verified correlation was included in the SRM to calculate the HRR fluctuation of the aluminum on acoustic boundary near the propellant burning surface. The effects of particle diameter, gas velocity, oscillation amplitude and frequency on the HRR fluctuation were obtained. It was found that the HRR fluctuation increases with the increasing particle diameter, gas velocity, and oscillation amplitude, and that due to the acoustic boundary effect, the HRR fluctuation is more sensitive under low-frequency oscillation. Based on the HRR fluctuation of aluminum combustion and particle damping, the growth rate of instability resulting from aluminum combustion in an SRM was investigated. The results showed that the growth rate of instability resulting from aluminum combustion were 9.38s-1 and 24.06s-1, while the particle damping (−25.8s-1) caused by combustion residuals, which suggests the aluminum particles play a critical role in SRMs combustion instability.

A NOVEL METHOD TO ANALYZE THE SELF-EXCITED AND PULSED T-BURNER EXPERIMENTAL DATA AT WIDE PRESSURE AND FREQUENCY RANGES

This paper describes the extended work for the methods of analysis of the T-burner experimental data which was published earlier this year. The combustion instability in solid rocket motors is mostly addressed using a T-burner by the measurement of response function for a given solid propellant. The experimental data could be reduced to the required response function by many methods. Six different methods of analyzing the experimental self-excited T-burner data at 1 MPa were presented in the previous work which consisted of Perry's method, Culick's method, and an exponential method with different combinations. It was observed that Culick's method is better when compared to the other methods. However, the recent investigations revealed that Culick's method has issues when analyzing the response data at higher pressures and for pulsed tests. This paper revisits those methods, compares them with new methods, and finally arrives at a method which is acceptable for any pressure and any test result (self-excited/pulsed). It was observed that the modified Perry method is better for all the different kinds of T-burner data to deduce the combustion response at different pressures and frequencies. The advantages of this method are brought out. This method is working better than Culick's method and is useful in all the T-burner test data analyses from which the stability prediction of solid rocket motors could be developed.

METHODS OF ANALYSIS OF T-BURNER EXPERIMENTAL DATA

The measurement of response function for a given solid propellant is mostly done using a T-burner to address the issue of combustion instability in solid rocket motors. Once the experiment has been conducted, it becomes important to carefully analyse and reduce the data to the required response function using the measured pressure. Six different methods of analysing the experimental T-burner data are presented in this paper. An experiment conducted at 1 MPa pressure at 390 Hz frequency is utilized for this purpose. Detailed procedure is given to calculate the growth rate, decay rate and the response function for a self-excited test. These methods include Perry's method, Culick's method and exponential method with different combinations which is reported for the first time. Analyzing with different methods revealed that Culick's method is better and more consistent than the other methods. The response function of the given solid propellant calculated using this method for the self-excited tests of T-burner is in good qualitative agreement with the response measured using Laser Doppler Velocimetry technique.

Aluminum combustion instabilities: Dimensionless numbers controlling the instability in solid rocket motors

This article is focused on the analysis of the aluminum combustion dynamics, induced by acoustic oscillations, in solid rocket motors. This dynamics is expected to drive self-sustained pressure oscillations which can lead to structural damages of the rocket. In order to control this thermoacoustic instability, theoretical developments are presented in this paper to highlight the main parameters of the thermoacoustic source. These new theoretical developments are based on a linear model of the thermoacoustic source which has been verified with a numerical simulation in a previously published work. With some assumptions and reductions, this article clearly demonstrates that (i) the thermoacoustic source depends on 4 dimensionless numbers (Sherwood number, Stokes number, combustion Strouhal number, flow Strouhal number), (ii) if the source can be split into two contributions (flame dynamics around an evaporating droplet and droplet combustion end-dynamics), both contributions have different tendencies, (iii) the acceleration of the mean flow along the motor leads to this thermoacoustic instability. Under some assumptions (aluminum combustion model, linear or weakly nonlinear dynamics), these results make it possible to control this instability in a solid rocket motor.

Sound Production due to Swirl–Nozzle Interaction: Model-Based Analysis of Experiments

Indirect noise due to the interaction of flow inhomogeneities with a choked nozzle is an important cause of combustion instability in solid rocket motors and is believed to be important in aircraft engines. A previously published experiment (Kings, N., and Bake, F., “Indirect Combustion Noise: Noise Generation by Accelerated Vorticity in a Nozzle Flow,” International Journal of Spray and Combustion Dynamics, Vol. 2, No. 3, 2010, pp. 253–266.) demonstrated that interaction of a nozzle with time-dependent axial swirl can also be a source of sound. This axial swirl was generated by intermittent tangential mass injection upstream from a choked nozzle in a so-called vortex wave generator. The present work discusses the impact of swirl–nozzle interaction in this experiment on the acoustic waves detected downstream of the nozzle. The main source of sound appears to be the reduction in mass flux through the choked nozzle, which depends quadratically on the swirl number. This effect is quantitatively predicted by a quasi-steady and quasi-cylindrical analytical model. The model, combined with empirical data for the decay of axial swirl in pipe flows, predicts the observed influence of the distance between the vortex wave generator and the nozzle. The findings presented here contradict the hypothesis found in the literature, which presumes that sound production in the aforementioned experiment is due to the acceleration of vorticity waves through the nozzle.

Nonlinear characteristics of the triggering combustion instabilities in solid rocket motors

The triggering combustion instability in the solid rocket motor is investigated from a nonlinear dynamical system perspective. A coupling model taking both the nonlinear acoustics in the chamber and the unsteady combustion of the solid propellant into consideration is adopted. Its typical responses to different excitations are compared systematically for varying parameters. The boundaries for the different responses in the parameter space are then investigated from the bifurcation analysis. It is shown that the triggering region of the solid rocket motor, corresponding to the bistable region of the coupling model, is confined by two curves consisting of bifurcation points, which intersects at a high order bifurcation point, the cusp point. The complex geometry of bistable region in multi-dimensional parameter space indicates the influences of parameters on the triggering combustion instability of the solid rocket motor can be quite different. The results suggest a comprehensive consideration on different parameters is needed in evaluating the combustion instability of an solid rocket motor.

A reduced-order model of thermoacoustic instability in solid rocket motors

A finite-dimensional dynamical system is derived from a coupled system of partial differential equations modeling the thermoacoustic oscillations inside a solid rocket motor. The governing equations for the coupling between the chamber acoustics and combustion of the solid propellant are derived from conservation laws and existing combustion models. Model reduction is carried out for the unsteady burning rate model based on a pseudo-spectral truncation, leading to a three-dimensional dynamical system. The resulting low-dimensional dynamical system is shown to be able to capture the main bifurcation behavior of the original infinite-dimensional system. The reduced-order model can be used to predict the nonlinear thermoacoustic behavior of a solid rocket motor at reduced computation costs.

Aluminum Combustion Can Drive Instabilities in Solid Rocket Motors: T-Burner Study

This paper reports experimental and numerical works devoted to the role of aluminum combustion on the stability of solid rocket motors. An experimental setup, known as the velocity-coupled T-burner, which provides measurements of the contribution of aluminum combustion to stability, has been developed and used. Experiments unambiguously show that aluminized propellants have a strong destabilizing contribution, whereas nonaluminized do not. This destabilizing behavior is found to depend much on aluminum agglomerate size distribution. In addition, two-phase numerical simulations are conducted on the setup and confirm experiments. It is found that the instability arises due to a thermoacoustic coupling between pressure waves and the heat release from aluminum combustion. Simulations also stress the role of aluminum agglomerate particle size as in experiments. This work experimentally and numerically proves that aluminum combustion represents a source of instability in solid rockets that should not be overlooked. This suggests that the widely accepted viewpoint that particle phase always damps pressure waves may not be always true for some aluminized propellants.

Modified computation of the nozzle damping coefficient in solid rocket motors

In solid rocket motors, the bulk advection of acoustic energy out of the nozzle constitutes a significant source of damping and can thus influence the thermoacoustic stability of the system. In this paper, we propose and test a modified version of a historically accepted method of calculating the nozzle damping coefficient. Building on previous work, we separate the nozzle from the combustor, but compute the acoustic admittance at the nozzle entry using the linearized Euler equations (LEEs) rather than with short nozzle theory. We compute the combustor's acoustic modes also with the LEEs, taking the nozzle admittance as the boundary condition at the combustor exit while accounting for the mean flow field in the combustor using an analytical solution to Taylor–Culick flow. We then compute the nozzle damping coefficient via a balance of the unsteady energy flux through the nozzle. Compared with established methods, the proposed method offers competitive accuracy at reduced computational costs, helping to improve predictions of thermoacoustic instability in solid rocket motors.

Jet noise-based diagnosis of combustion instability in solid rocket motors

Diagnosis of combustion instability in a solid rocket motor usually involves in-situ measurements of pressure in the combustor, a harsh environment that poses challenges in instrumentation and measurement. This paper explores the possibility of remote diagnosis of combustion instability based on far-field measurements of rocket jet noise. Because of the large pressure oscillations associated with combustion instability, the wave process in the combustor has many characteristic features of nonlinear acoustics such as shocks and limit cycles. Thus the remote detection and characterization of instability can be performed by listening for the tell-tale signs of the combustor nonlinear acoustics, buried in the jet noise. Of particular interest is the choice of nonlinear acoustic measure (e.g., among skewness, bispectra, and Howell-Morfey Q/S) that best brings out the acoustic signature of instability from the jet noise data. Efficacy of each measure is judged against the static test data of two tactical motors (one stable, the other unstable).

Numerical Research on The Nozzle Damping Effect by A Wave Attenuation Method

Abstract Nozzle damping is one of the most important factors in the suppression of combustion instability in solid rocket motors. For an engineering solid rocket motor that experiences combustion instability at the end of burning, a wave attenuation method is proposed to assess the nozzle damping characteristics numerically. In this method, a periodic pressure oscillation signal which frequency equals to the first acoustic mode is superimposed on a steady flow at the head end of the chamber. When the pressure oscillation is turned off, the decay rate of the pressure can be used to determine the nozzle attenuation constant. The damping characteristics of three other nozzle geometries are numerically studied with this method under the same operating condition. The results show that the convex nozzle provides more damping than the conical nozzle which in turn provides more damping than the concave nozzle. All the three nozzles have better damping effect than that of basic nozzle geometry. At last, the phase difference in the chamber is analyzed, and the numerical pressure distribution satisfies well with theoretical distribution.

Influence of thermal inhibitor position and temperature on vortex-shedding-driven pressure oscillations

Vortex-acoustic coupling is one of the most important potential sources of combustion instability in solid rocket motors (SRMs). Based on the Von Karman Institute for Fluid Dynamics (VKI) experimental motor, the influence of the thermal inhibitor position and temperature on vortex-shedding-driven pressure oscillations is numerically studied via the large eddy simulation (LES) method. The simulation results demonstrate that vortex shedding is a periodic process and its accurate frequency can be numerically obtained. Acoustic modes could be easily excited by vortex shedding. The vortex shedding frequency and second acoustic frequency dominate the pressure oscillation characteristics in the chamber. Thermal inhibitor position and gas temperature have little effect on vortex shedding frequency, but have great impact on pressure oscillation amplitude. Pressure amplitude is much higher when the thermal inhibitor locates at the acoustic velocity anti-nodes. The farther the thermal inhibitor is to the nozzle head, the more vortex energy would be dissipated by the turbulence. Therefore, the vortex shedding amplitude at the second acoustic velocity anti-node near 3/4L (L is chamber length) is larger than those of others. Besides, the natural acoustic frequencies increase with the gas temperature. As the vortex shedding frequency departs from the natural acoustic frequency, the vortex-acoustic feedback loop is decoupled. Consequently, both the vortex shedding and acoustic amplitudes decrease rapidly.

Thermoacoustic instability in a solid rocket motor: non-normality and nonlinear instabilities

An analytical framework is developed to understand and predict the thermoacoustic instability in solid rocket motors, taking into account the non-orthogonality of the eigenmodes of the unsteady coupled system. The coupled system comprises the dynamics of the acoustic field and the propellant burn rate. In general, thermoacoustic systems are non-normal leading to non-orthogonality of the eigenmodes. For such systems, the classical linear stability predicted from the eigenvalue analysis is valid in the asymptotic (large time) limit. However, the short-term dynamics can be completely different and a generalized stability theory is needed to predict the linear stability for all times. Non-normal systems show an initial transient growth for suitable initial perturbations even when the system is stable according to the classical linear stability theory. The terms contributing to the non-normality in the acoustic field and unsteady burn rate equations are identified. These terms, which were neglected in the earlier analyses, are incorporated in this analysis. Furthermore, the short-term dynamics are analysed using a system of differential equations that couples the acoustic field and the burn rate, rather than usingad hocresponse functions which were used in earlier analyses. In this paper, a solid rocket motor with homogeneous propellant grain has been analysed. Modelling the evolution of the unsteady burn rate using a differential equation increases the degrees of freedom of the thermoacoustic system. Hence, a new generalized disturbance energy is defined which measures the growth and decay of the oscillations. This disturbance energy includes both acoustic energy and unsteady energy in the propellant and is used to quantify the transient growth in the system. Nonlinearities in the system are incorporated by including second-order acoustics and a physics-based nonlinear unsteady burn rate model. Nonlinear instabilities are analysed with special attention given to ‘pulsed instability’. Pulsed instability is shown to occur with pressure coupling for burn rate response. Transient growth is shown to play an important role in pulsed instability.

Prediction of unsteady non-linear combustion instability in solid rocket motors

The influence of the surrounding motor structure on the appearance of unsteady non-linear axial combustion instability symptoms in a solid rocket motor internal combustion chamber is investigated. The numerical simulation model consists of three coupled physical components, including the combined propellant and motor casing structure, the motor core fluid flow, and the corresponding propellant combustion. A transient frequency-dependent burning-rate model and an updated erosive burning-rate component model are incorporated in the current overall numerical simulation model. The results of simulating a hot-flow unsteady motor firing indicate that structural vibrations directly affect the burning rate and the axial pressure wave development within the chamber that appears as a primary symptom of combustion instability. Comparison of the predicted results with the experimental test results indicates that a good correlation exists between the two, providing support for the present simulation model.

Acoustic Instability of the Slab Rocket Motor

This article provides rigorous mathematical details leading to an improved formulation of acoustic instability in solid rocket motors. The evaluation of stability growth rate factors is carried out both numerically and asymptotically. Analytical expressions for the stability factors are obtained over a broad spectrum of operating parameters. For all representative rocket motors under investigation, the analytical estimates exhibit an error of 5% or less. Both numerics and asymptotics converge in predicting markedly less stable systems than projected by classic stability theory. The dramatic differences can be ascribed to the dismissal of time-dependent rotational coupling in the previous formulation. The current study unravels the details of six additional growth rate corrections not accounted for previously. These include the rotational flow, mean vorticity, viscosity, pseudo acoustic, pseudo vorticity and unsteady nozzle growth rate factors. The fourth and fifth terms are due to acoustical and vortical interactions with the often neglected pseudopressure. The sixth is due to the energy associated with the unsteady rotational flow exiting the nozzle. This study enables us to isolate the impact of various flow attributes on stability. These involve the motor aspect ratio, surface Mach number, viscous parameter, oscillation mode shape number, and surface admittance. Based on the slab motor geometry, we find that the flow turning correction is cancelled identically by another rotational term not accounted for previously. We also find that the unsteady nozzle damping effect is offset by another source of instability due to the pseudopressure.

A COMPUTATIONAL STUDY OF THE L* INSTABILITY WITH A NONLINEAR FREQUENCY

A numerical model, including a nonlinear, transient gas-phase description of the propellant combustion is developed to study the L* instability in solid rocket motors. The model has been shown to predict the critical L* as well as other features of L* instability. It is found that stability boundary in log(L*cr) vs. log(p ) plane is not a straight line even with a constant pressure index, n, as given by QSHOD model. It is also found that parabolic stability boundary is possible with lower surface temperatures. The predicted frequency and combustion delay time compare well with the experimental data.

Determination of Triggering Condition of Vortex-Driven Acoustic Combustion Instability in Rocket Motors

A method to determine the sufe cient condition for the occurrence of acoustic combustion instability in solid rocket motors with slotted-tube grain is proposed. The condition is obtained by comparing the frequency of the shedding vortices at the entrance of the slots and the acoustic oscillation frequency in the upstream cylindrical port. To obtain the vortex shedding frequency, a transient e ow analysis is conducted with the consideration of grain-surfaceregression. The method is assessed by analyzing e ve practical solid rocket motors employing slottedtube grain in which acousticcombustion instability occurs in threecases, whereastheothertwo showno signie cant pressureoscillations.Theresultsprovetobesuccessfulforalle vemotors.Furthermore,goodagreementisobtained between the measurements and predictions, not only for the oscillatory frequencies but also for the occurrence time.

Methodology for Analysis of Postshock Oscillations During Pulse-Triggered Instability

Past experimental studies have suggested that the propagatingshock wave associated with pulse-triggered instability in solid rocket motors is followed by postshock oscillations.A new methodologywas developed to conŽ rm the existence and evaluate the nature of these oscillations. This methodology is composed of a new time-marching frequency and a time-frequency analysis. The new time-marching analysis follows the evolution of the time-averaged frequency content of the postshock oscillations throughout a Ž ring, whereas with the time-frequency analysis, it is possible to obtain a qualitative estimate of the temporal evolution of the amplitude of the frequency content of postshock oscillations for a single shock-wave cycle. The new methodology was developed and tested with model signals and then successfully applied to a sample experimental signal.

Structural resonance influences on flow-induced acoustic amplification

An experimental investigation of the influence of structural resonance on the acoustic response to vortex shedding is presented. Flow-induced amplification of acoustic energy is of interest in the field of combustion instability in solid rocket motors. Baffles located at the junction of motor segments can cause generation of flow vortices and amplification of acoustic energy. This investigation examines the hypothesis that an additional amplifier of acoustic energy is provided by the vibratory response of these baffles. Flow through a cylindrical cavity is interrupted by annular baffles that extend radially inward from the cylinder walls. Baffle configurations are controlled to induce various frequencies of vortex shedding. Acoustic pressure and baffle vibratory responses for various combinations of baffle resonance and vortex shedding frequency are recorded using a modal analysis technique. This provides the database used to quantify the influence of vortex shedding frequencies and structural resonance on acoustic pressure amplitudes. A theoretical model of the interactions of different baffle configurations with chamber acoustics is presented and shown to be in general agreement with the acoustic pressure amplitudes measured in the test section. [Work supported by Morton Thiokol, Inc.]