Pressure-coupled Response Research Articles

Theoretical and experimental study on combustion response of aluminized solid propellant under acceleration effects

The combustion performance of solid propellants is significantly affected by the external operating parameters of rocket motors. In this paper, the combustion response characteristics of aluminized solid propellant under acceleration conditions have been studied theoretically and experimentally. A theoretical model of unsteady burning for aluminized solid propellant, considering transient heat transfer and acceleration effects, is developed based on the Zel'dovich-Novozhilov solid-phase energy conservation. The pressure-coupled responses of the solid propellant are also measured experimentally under different normal accelerations using the T-burner and centrifuge. The model is well validated by comparison with literature and experimental results. The unsteady burning of propellants is analyzed in detail, and the effects of acceleration and propellant properties on combustion response are investigated. The results show that there is a significant difference between the transient and quasi-steady burning rate under dynamic environments. As normal acceleration increases from 0 g to 1000 g, the fluctuation amplitude of the net heat flux on the burning surface continues to decrease, the magnitude of the pressure-coupled response peak decreases significantly by 69 %, and the frequency of the response peak shifts from 140 Hz to 230 Hz. Moreover, the pressure exponent and thermal conductivity plays a positive role in the pressure-coupled response. The model presented in this paper can be helpful for predicting the differences between flight and ground test performance and evaluating the combustion stability of solid rocket motors.

Numerical study of triggered thermoacoustic instability driven by linear and nonlinear combustion response in a solid rocket motor

Thermoacoustic instability (TAI) has consistently presented challenges to the development of solid rocket motors (SRMs), making the prediction of TAI critically important. Most existing TAI predictions rely on linear instability theory, which is inadequate for predicting certain nonlinear TAI, such as triggered TAI. To address this challenge, this study has constructed the nonlinear response model for the burning rate, known as the nonlinear pressure-coupled response function (PCR). The nonlinear PCR is capable of considering the effects of both frequency and amplitude of pressure oscillations. By integrating the PCR into the computational fluid dynamics framework, this study successfully replicated the nonlinear triggered TAI. When exclusively employing the linear PCR, the model demonstrates typical multi-order resonant modes, and the stability map exhibits either persistent stability or persistent instability, contingent upon the distribution of the linear PCR function. However, by incorporating the nonlinear PCR, this study effectively reproduces nonlinear pulse-triggered instability. This instability arises only when the pulse intensity surpasses the threshold value due to SRM damping. The nonlinear response framework allows for the identification of the instability boundary, facilitating a more comprehensive assessment of SRM performance. This study fills a critical gap in predicting triggered TAI in SRMs, providing insights into nonlinear TAI mechanisms.

AP/HTPB combustion response simulation with a new equivalent linear system method

In the study of solid rocket motor (SRM) combustion instability, modeling and analyzing the combustion response of the solid propellant is a laborious task. We propose a new idea, an equivalent linear system method, for modeling solid propellant combustion response with three steps: first, simulating the transient combustion process under pulse pressure excitation for only one CFD case; then, treating the combustion process as a black-box and obtaining the transfer function of the combustion process from the CFD result; finally, predicting and analyzing the combustion response based on the transfer functions. For the AP/HTPB sandwich propellant withp¯=3MPa, the amplitude, duration, and direction of excitation pulses are studied. The new method is also verified, with a maximum relative error of 4.3% for burning rate response under p˜≤1MPa (as high as one-third of the pressure DC). Applicability of this new method is demonstrated for another two AP/HTPB sandwich propellants with different configuration under p¯=8MPa and p¯=10MPa, showing that the system-simulated combustion responses of burning surface temperature and burning rate are consisted well with the CFD results and the maximum relative error of burning rate response is 2.1%. Asymmetric combustion response for positive and negative pressure perturbations is a new finding based on the CFD and simulation results. Besides, a new approach using dual transfer functions is proposed to ensure high accuracy for the simulation of solid propellant combustion. The pressure-coupled response function is predicted by this method for the sandwich propellant under p¯=5MPa and p˜=20kPa within a wide continuous frequency range (0–3000 Hz). The comparison with CFD results indicates that the relative bias of Rp is less than 2%. With the proposed method, the combustion response to arbitrary pressure excitations can be simulated with high accuracy, high time-resolution, and high speed. The method shows great advantage and potential in simulating and predicting combustion instability.

Experimental and numerical study on measuring solid-propellant pressure-coupled response using an improved rotary valve

A small-scale experimental burner with an improved rotary valve has been designed to measure solid-propellant pressure-coupled response for mean pressures on the order of 2.2–2.9 MPa and oscillating frequencies of 23–161 Hz, within 9% amplitudes. This paper proposes an indirect method for measuring the instantaneous valve area and phase delay angle based on a circular grating system and a corresponding mathematical model, and the validity of which is confirmed by several cold-gas experiments and numerical simulations. The effects of frequency on oscillating pressure, exhaust mass flow rate and pressure-coupled response are studied by carrying out several hot-gas experiments and numerical simulations. The results show that the mean pressure is not affected by the oscillating frequency and maintains at 2.9 MPa. The exhaust mass flow rate of the rotary valve is determined by the instantaneous valve area and independent of frequency. The peak-to-peak pressure is inversely proportional to the oscillating frequency, reducing from 0.539 MPa at 23 Hz to 0.053 MPa at 161 Hz. The magnitude of pressure-coupled response appears to be constant (0.8) at 23–161 Hz, with pressure oscillations lagging instantaneous valve area by 0.504π-0.531π。The study is expected to benefit research on similar rotary valves and can serve as a basis for measuring the solid-propellant pressure combustion response.

Perturbation analysis of the Heterogeneous Quasi 1-D model – a theoretical framework for predicting frequency response of AP–HTPB composite solid propellants

In this paper, the Heterogeneous Quasi 1-D model for steady combustion of AP–HTPB propellants is extended to the unsteady regime. The extended model is used to calculate the pressure-coupled frequency response () of low-smoke (non-aluminised) multi-modal AP–HTPB propellants. The of a multi-modal propellant is expressed in terms of that of the individual binder-matrix coated AP particles constituting the statistical particle path. The weighting function, as expected from the serial burning approach, is the burn-time of particles. A closed-form expression is derived for the of the particles by perturbation analysis of the quasi 1-D burn rate model. In this equation, all except the two parameters that quantify the amplitude () and phase () of fluctuating heat flux on the solid side of the interface, are shown to be from the steady-state model. This result establishes a strong connection between the steady and unsteady framework as compared to earlier models, where (propellant pressure index) as was explicitly imposed. The model is used to predict for a few low-smoke compositions. Effects of AP particle size distribution, mean pressure and initial temperature are brought out. When expressed as vs (non-dimensional frequency based on conduction time scale), the peak response magnitude is of and occurs close to non-dimensional frequency () value of 1. While this conclusion is in line with the earlier results, it does not explain the ubiquitous nature of acoustic instability in tactical missile rockets, which requires the peak response to be at least an order of magnitude higher than n. Burn rate oscillations associated with the binder-melt effect caused by inhibitors is brought out as the most likely mechanism for the observed instabilities. Methods to extend the theory to include this effect is outlined.

Numerical analysis on combustion instabilities in end-burning-grain solid rocket motors utilizing pressure-coupled response functions

The combustion instability has been one of severe problems suffered by solid rocket motors (SRMs) for a long term. This paper proposes a burning rate model utilizing the pressure-coupled response function for description of the spatiotemporal burning of AP-HTPB composite propellant grains in SRMs. The model is successfully incorporated to the axisymmetric internal ballistic simulation by the source terms of gas-phase governing equations. The prediction of propellant combustion connected with acoustic pressures can be realized by means of an in-house high-order numerical solver, in which the numerical fluxes are reconstructed by the fifth-order WENO scheme and the viscous terms are discretized by a sixth-order compact scheme. The thermoacoustic combustion instabilities in the longitudinal modes are triggered by a burning rate pulse imposed to the steady flow. The analysis indicates that the pressure oscillations grow as a primary symptom of combustion instabilities. The influences of several factors on production of the instability symptom are discussed. It is shown that the pressure-coupled response function, the pressure index, and the reaction heat of the propellant, and the specific heat ratio of the burnt gas promote the pressure oscillation growth process evidently, but the magnitude and the imposed region of burning rate pulses have less effects.

Modeling and analysis of triggering pulse to thermoacoustic instability in an end-burning-grain model solid rocket motor

Occurrences of pulse-triggered instabilities in combustion chambers always trouble solid rocket motors (SRMs) in application. This paper performs numerical simulation of the pulse-triggered nonlinear instabilities in the end-burning-grain SRM, in use of the pressure-coupled response function to describe the spatiotemporal burning rate of AP-HTPB composite propellant grains. A high-order numerical solver realizes the cooperation of the burning rate model into the axisymmetric internal ballistic simulation of SRMs via the source terms in gas-phase governing equations. The analysis of high-amplitude pressure oscillations, which are the primary symptom of nonlinear thermoacoustic instabilities, provides the insight into the nature of the longitudinal instability growth process after the pulse triggering. The change rate of pressure fluctuation over the pressure fluctuation in the chamber is independent of the pulse intensity and triggering position. The growth characteristics of pressure oscillations for the present combustor system is neither affected by the pressure pulse intensity nor by the imposed regions in the flow field, while the higher pressure-coupled response function of the propellant promotes the growth process evidently. The present study is expected for the guidance of grain design in SRMs.

Vorticoacoustic Stability of Solid Rocket Motors: A Numerical Study

This work presents highly resolved Navier–Stokes simulations in a cylindrical solid rocket motor. The study focuses on the vorticoacoustic interactions and their role on motor stability. This paper proposes comparisons between simulations and available theories on unsteady axial velocity but also radial velocity, pressure, temperature, and entropy. Overall, the agreement is excellent except for pressure, which is found to be purely acoustic in simulations (i.e., no vortical pressure). The role of radial velocity is further investigated because it gives rise to the rotational correction term in stability integrals. This paper shows that this term strongly depends on the definition of the propellant admittance, and it can actually be viewed as a part of the classical propellant pressure-coupled response. This study has also estimated damping terms directly by studying the decay of pressure perturbations in simulations and has compared them to classical stability integrals from theory. In keeping with the aforementioned results, the agreement is much better when rotational correction and vortical pressure terms are dropped.

Pressure-Coupled Responses of LOX Droplet Vaporization and Combustion in High-Pressure Hydrogen Environments

The dynamic responses of liquid oxygen (LOX) droplet vaporization and combustion to externally imposed pressure oscillations in high-pressure hydrogen and water environments are studied systematically. Both subcritical and supercritical conditions are considered, under a broad range of pressures at 10–200 atm. A unified treatment of general fluid thermodynamics and a self-consistent numerical method are developed to treat the droplet behaviors over the entire fluid thermodynamic regime. Results are correlated with the instantaneous value of the liquid-phase thermal diffusion time normalized by the oscillation frequency, . The magnitudes of the vaporization and combustion response functions increase with increasing ambient pressure. The magnitude of the combustion response function is much smaller than its corresponding gasification response due to the damping effect associated with vapor accumulation near the droplet surface. Significant difference exists between hydrogen/oxygen and hydrocarbon/air systems in terms of the cut-off and resonant values in the characteristic frequency spectrum.

EFFECTS OF INITIAL BULK TEMPERATURES ON A PROPELLANT'S PRESSURE-COUPLED RESPONSE

The relationship between the burning rate, temperature sensitivity, and initial bulk temperature to a propellant's pressure-coupled response are explored in this paper. A parametric analysis is performed using the Zeldovich−Novozhilov method to illuminate the linkage between a propellant's initial temperature and its resulting pressure-coupled response. Previous testing of an ammonium perchlorate/hydroxyl-terminated polybutadiene propellant in a temperature conditioned T-burner by the author has shown a direct link between a propellant's initial temperature and its pressure-coupled response. The results from this parametric analysis are compared with these data takenby a temperature-conditioned T-burner. This investigation of this linkage between the initial temperature and pressure-coupled response will show that of all the input parameters, the temperature-sensitivity parameter has the largest effect on the pressure-coupled response.

Analytical Solution for Pressure-Coupled Combustion Response Functions of Composite Solid Propellants

This paper extends the classical analytical solution for small perturbation analysis of the pressure-coupled response of a homogeneous propellant to any two-component composite propellant. The solution obtained is general and can be used with any particular model for propellant combustion. As an example, the Cohen and Strand ammonium perchlorate propellant model for a single ammonium perchlorate particle size was used in this work. The results and their mechanistic significance are presented and discussed. It is shown that, for a two-component composite propellant, two forms of pressure exponents arise from the analysis. The significance of the second exponent is that it enables the composite propellant to be viewed as a homogeneous propellant with a frequency-dependent exponent via the coupling coefficients. It is found that the ammonium perchlorate is the main source of instability because of its condensed phase exothermicity and monopropellant flame kinetics. This will be a problem with energetic materials in general. The inert binder provides a stabilizing influence because of its endothermicity and the diffusion flame formed with the ammonium perchlorate. Effects of ammonium perchlorate particle size and pressure stem from the changing flame structure and its effect on burning rate.

Oscillatory vaporization and acoustic response of droplet at high pressure

Open-loop dynamic responses of vaporizing droplet to high-frequency pressure waves are theoretically-numerically investigated. Conservation equations for liquid and gas phases are solved separately for spherically symmetric vaporization and transports, and flow parameters are matched at liquid–vapor interfacial boundary. The pressure-coupled response of the droplet vaporization is commanded by the coupling between the acoustic and thermal processes occurring in an immediate vicinity of the interfacial boundary. The vaporization response strongly depends on the ambient pressure, and the acoustic instabilities are expected at higher pressures and lower frequencies.

Pulse-echo measurements of unsteady propellant deflagration

This article discusses a laboratory test method for the measurement of nonsteady deflagration rates and combustion-stability properties of solid propellants. The method combines ultrasonic pulse-echo measurement, fluidic pressure modulation, and digital signal processing techniques to compute the real and imaginary components of pressure-coupled response functions of solid propellants. A description of the apparatus identifies the major components and their functions. A section on the experimental procedure illustrates the steps necessary to conduct a test, and a section on the data reduction technique describes the sequence of steps employed to compute the nonsteady burn rate and the pressure-coupled response. A detailed implementation of the technique as it applies to two representative tests follows, in which graphs and tables illustrate the intermediate data reduction steps. Details of the evaluation of the uncertainties associated with the technique and the data reduction algorithms are also presented.

Ultrasonic Measurement of the Pressure-Coupled Response Function for Composite Solid Propellants

Transient phenomena associated with solid-propellant combustion are examined by means of an oscillatory burner designed to create pressure oscillations through the use of a rotary nozzle. The oscillatory burner is designed to operate at pressures up to 20.7 MPa (3000 psi), with the target operating pressure achieved through prepressurization with an inert gas (helium) and manipulation of constant and variable-area nozzle diameters. A spherically focused 1-MHz ultrasound transducer is pulsed at 2.5 kHz through the bottom of the propellant to obtain the thickness-time profile of the propellant, which is then converted to a burning rate by taking the time derivative. Two piezoelectric pressure transducers simultaneously record the pressure-time history of each experiment. The burning rate and pressure are then used to calculate the pressure-coupled response of each test. The experiments presented here were motivated by three primary goals. The first was to investigate the effect of propellant composition on the response function. The second was to evaluate effect of mean pressure on the response of propellants, and the third was to investigate the response of a propellant within a plateau region. These experiments targeted mean pressures of 2.0, 5.0, and 12.5 MPa at frequencies ranging from 20-200 Hz.

Inconsistent Definitions of Pressure-Coupled Responses and Admittances of Solid Propellants

Inconsistent Definitions of Pressure-Coupled Responses and Admittances of Solid Propellants

Evaluation of Ultrasound Technique for Solid-Propellant Burning-Rate Response Measurements

The development of an ultrasound technique for precisely measuring the instantaneous regression rate of a solid-rocket propellant under transient conditions is reviewed. The technique is used to measure the burning-rate response of several solid propellants to an oscillatory chamber pressure with a frequency of up to 300 Hz. This measurement is known as the propellant's pressure-coupled response function and is used as an input into rocket stability prediction models. The ultrasound waveforms are analyzed using cross-correlation and other digital signal processing techniques to determine burning rate. Digital methods are less prone to bias and offer greater flexibility than other techniques previously used. The resulting data are corrected for compression effects. The effects of a changing thermal profile on the measurement are discussed. Other phenomena that may corrupt the measurement, such as surface roughness, are also covered. Results of the experiments are compared to data from two other measurement techniques: a T-burner and a magnetic flowmeter.

Oscillatory Combustion of Fine-AP/HTPB Propellants: Disproportionate Pyrolysis Response

The combustion of hydroxyl-terminated polybutadiene (HTPB)propellants containing e neammonium perchlorate (AP) was investigated using laser-excited, combustion recoil at 1 ‐5 atm. At 1 atm, binder-rich (70‐75% AP), monomodal e ne-AP (2‐50 µm) propellants exhibit a prominent non-quasi-steady gas and surface reaction zone, homogeneous propellant, one-dimensional e ame response peak at 100 ‐300 Hz, with frequency varying inversely with AP size. Adding coarse AP (resulting in a wide, bimodal AP distribution ) causes this response to disappear at 1 atm. Raising the pressure to 2 atm causes the response to reappear and increase in frequency to 600 ‐800 Hz (2-µm AP). This oscillatory combustion behavior is attributed to time-varying selective or disproportionate pyrolysis of AP and HTPB (unsteady accumulation and depletion of AP at the propellant surface ) and the associated compositional (stoichiometric ) e uctuations that occur in the fuel-rich, premixed gas-phase reaction zone adjacent to the e ne-AP/HTPB solid region. A low Peclet number appears to be a requirement of achieving this condition. Combustion recoil and thermocouple measurements at 1 atm without laser excitation exhibited spontaneous oscillations in the monomodal e ne-AP propellants and corroboratethe disproportionate pyrolysis interpretation of the laser-excitedresonant response. This e nding of a strong disproportionationresponsein compositepropellants with e ne AP or binder-rich, e ne-AP matrix regions has important implications for pressure-coupled response and solid rocket motor stability in that the same response mechanism could operate under oscillatory pressure conditions and at elevated pressures.

Solid-Propellant Combustion Response Function from Direct Measurement Methods: ONERA Experience

Usually, the pressure-coupled response function of a solid propellant is determined using the traditional indirect methods such as T-burner or modulated exhaust jet technique. A few direct methods, based on wave propagation through the solid-propellant grain, exist: microwave and ultrasound techniques. There is also the magnetohydrodynamic technique derived from magnetic velocimetry through the gas phase. The theoretical approaches of each method are explained and are coupled with an acoustic analysis of the pressure oscillations. The response function is determined using these direct and nonintrusive methods for the Ariane V solid propellant (HTPB‐ AP‐ Al) and a nonmetalized propellant. Results obtained for composite propellants, such as that of the Ariane V, show the accuracy of each method and underline the advantages or disadvantages of each method as far as ONERA’ s experience can carry it out. Direct methods are nonintrusive but are limited because of their principle itself. There is a frequency limit above which the measurement cannot be performed. Finally, the objectives of future ONERA work are proposed.

Magnetic Flowmeter Measurement of Pressure-Coupled Response of a Plateau Solid Propellant

A magnetic  owmeter was used to measure the pressure-coupled response of a plateau solid propellant. The magnetic  owmetermeasures the one-dimensionalacousticgasvelocity as a function of the height abovethe surface of a burning-propellantstrand subjected to forced pressure oscillations.Theunsteadygasvelocitywasmeasured by externally imposing a strong magnetic Ž eld in a region containing the propellant surface. The combustion product gashas sufŽ cient ionizationto be electrically conductiveandgenerates an electrical potentialproportionalto the gas velocity in a direction perpendicular to both themagnetic Ž eld and the gas velocity andmeasured by two electrodes at the edges of thecombustiongas ow.Thepositionofthepropellantsurfacerelativeto themeasurement stationwas measured with an ultrasound transducer. The acoustic velocity, together with an acoustic pressure measurement as a function of distance above the burning propellant, was combined with a one-dimensional acoustic analysis of the  ow to obtain the acoustic admittance at the propellant surface and thus the propellant response. Responses were measured at pressures up to 2000 psi (13.8 MPa) for frequencies between 300 and 1800 Hz. Results for a nonaluminized composite plateau propellant formulation are shown.

Leading-Edge Flame Detachment: Effect on Pressure-Coupled Combustion Response

An experiment was conducted to establish the critical role of a detailed aspect of the e amelet structure in composite propellants in determining the overall combustion response to pressure oscillations during combustor instability. Nomenclature ab = velocity of sound of gases in T-burner gc = units conversion factor L = length of interior cavity of T-burner Rp = pressure-coupled response function r = burning rate Sb = cross-sectional area of cavity of T-burner Sc = burning surface area of propellant sample c = combustion amplie cation d = burner damping during burning 1 = exponential growth rate during burning, decay rate in pulse test 2 = decay rate after burnout 2(t1) = decay rate corrected to frequency during burning s = density of solid propellant