Liquid Propellant Rocket Motors Research Articles

A novel in-flight thrust modulation technique for SPRM: proof of concept

Thrust modulation (termination or reduction) is one of the most sophisticated topics in rocket motors. Thrust termination is employed when combustion must be terminated to ensure proper stage separation, to avoid motor explosion, to attain certain range, or for research purposes. While liquid and hybrid propellant rocket motors have the ability to extinguish thrust, thrust termination in solid propellant rocket motors (SPRMs) need the use of specialized technology. In-flight thrust termination of (SPRMs) can be achieved by sudden and sufficient increase in throat area. Increasing throat area causes high depressurization rate which consequently leads to extinguishing the rocket motor. In contrast, in-flight thrust reduction can be theoretically attained either by reducing chamber pressure to a new equilibrium level or by reducing the divergent section length. The objective of the present paper is to prove the concept of using Linear Shaped Charge (LSC) for thrust modulation; a technique novel to SPRM applications. Thrust termination concept is proved via a set of static firing tests on a standard test motor. In addition, a mathematical model is developed to predict the drop in thrust due to cutting the nozzle at any arbitrary location. The model is validated by comparing with published experiments for thrust termination and reduction. A parametric study is conducted based on model results. It is confirmed that by cutting the nozzle along its divergent section, thrust reduction less than 20% can be attained. Further reduction can be achieved by cutting the nozzle along its convergent section.

Thrust termination of solid rocket motor

Rocket motors are engines that create the necessary thrust for the rocket motion. There are different types of rocket motors based on the propellant state, such as solid propellant rocket motors, liquid propellant rocket motors, and hybrid propellant rocket motors. One of the biggest disadvantages of solid propellant rocket motors, in comparison to liquid and hybrid propellant rocket motors, is that they are extremely difficult to extinguish, necessitating the use of specific devices. This paper reviews various ways for thrust termination such as fluid injection, rapid increase in throat area, and sudden opening of an additional port at the forward section of the motor, which increases the depressurization rate (dp/dt) required for extinguishing. The rate of depressurization varies depending on propellant components, combustion pressure, and exhaust pressure, and may be investigated using experimental approaches. The change in the critical area for a motor can be predicted by using MATLAB code to ensure the complete extinguishing by decreasing the pressure under the deflagrationlimit with high depressurization rate.

Non-fragile H∞ controller for combustion process in rocket motors

The aim of this paper is to analyse the problem of robust non-fragile H∞ controller for the combustion process in liquid propellant rocket motors chamber. Based on the delay decomposition approach, the whole delay interval is divided into two equidistant subintervals and a new Lyapunov-Krasovskii functional (LKF) which contains some triple-integral terms and augment terms is introduced on each interval. By using L-K stability theorem, integral inequality method together with free weighting matrix approach, a new delay-dependent bounded real lemma (BRL) is formulated. Then, by applying the BRL, non-fragile H∞ controller is formulated in terms of linear matrix inequalities (LMI), where no any parameter needs to be turned and apt to realisation. Finally, simulation results are given to illustrate that the designed controller has good robust and non-fragile performance.

Non-fragile H∞ controller for combustion process in rocket motors

The aim of this paper is to analyse the problem of robust non-fragile H∞ controller for the combustion process in liquid propellant rocket motors chamber. Based on the delay decomposition approach, the whole delay interval is divided into two equidistant subintervals and a new Lyapunov-Krasovskii functional (LKF) which contains some triple-integral terms and augment terms is introduced on each interval. By using L-K stability theorem, integral inequality method together with free weighting matrix approach, a new delay-dependent bounded real lemma (BRL) is formulated. Then, by applying the BRL, non-fragile H∞ controller is formulated in terms of linear matrix inequalities (LMI), where no any parameter needs to be turned and apt to realisation. Finally, simulation results are given to illustrate that the designed controller has good robust and non-fragile performance.

Dissipativity-Based Reliable Sampled-Data Control With Nonlinear Actuator Faults

In this paper, the problem of reliable sampled-data control design with strict dissipativity for a class of linear continuous-time-delay systems against nonlinear actuator faults is studied. The main objective of this paper is to design a reliable sampled-data controller to ensure a strictly dissipative performance for the closed-loop system. Based on the linear matrix inequality (LMI) optimization approach and Wirtinger-based integral inequality, a new set of sufficient conditions is established for reliable dissipativity analysis of the considered system by assuming the mixed actuator fault matrix to be known. Then, the proposed result is extended to unknown fault matrix case. Also, the reliable sampled-data controller with strict dissipativity is designed by solving a convex optimization problem which can be easily solved by using standard numerical algorithms. Finally, a numerical example based on liquid propellant rocket motor with a pressure feeding system model is presented to illustrate the effectiveness of the developed control design technique.

Dissipative based adaptive reliable sampled-data control of time-varying delay systems

This paper is concerned with the problem of dissipative based adaptive reliable controller for a class of time delay systems subject to actuator failures and time-varying sampling with a known upper bound on the sampling intervals. By constructing a proper Lyapunov-Krasovskii functional which fully uses the available information about the actual sampling pattern and time delays, a new set of sufficient conditions is derived to obtain the required result. Then, a dissipative based adaptive sampled-data controller is designed such that the resulting closed-loop system is reliable in the sense that it is asymptotically stable and has the prescribed dissipative performance under given constraints. The existence condition of the desired dissipative based adaptive reliable sampled-data controller is obtained in terms of linear matrix inequalities. Further, the performance of the proposed controller is implemented on a liquid propellant rocket motor with a pressure feeding system model. The simulation results show the effectiveness and better performance of the proposed adaptive reliable sampled-data controller over conventional reliable controller.

Driving Mechanisms for Combustion Instability

The processes affecting the nonlinear acoustic stability of a combustor are examined in an overview fashion. Emphasis is placed on liquid-propellant rocket motors but other systems are briefly mentioned and some broadly applied principles and observations are discussed. A nonlinear wave equation is developed for a two-phase mixture and the roles of various terms in the equations are discussed. A review is made of various combustion processes, their associated characteristic times, and the impacts on stability in certain cases. Many relevant scales for length and time are identified. Special issues for supercritical and transcritical combustion are discussed. Bistable operational domains are shown to be present in some systems, making nonlinear triggering of an instability a possibility. Relations between the natural frequency of oscillation for the combustion chamber and the characteristic combustion times are identified with regard to impact on the combustor stability. The amplitude of the limit cycle and the transient time for limit-cycle development are related to the mean-flow Mach number. The role of shock-wave dissipation in amplitude determination is described.

Degradation of CVD-SiC coated PIP-C/SiC composites exposed to the hot firing test based on MMH/N2O4 bipropellants

Ablation property of CVD-SiC coated PIP-C/SiC composites was investigated by using a hot-firing test in a liquid propellant rocket motor. The effect of the combustion temperature was studied; then ablation mechanisms of coated composites were discussed. The degradation of PIP-C/SiC composites was determined by analyzing surface variations. Two different ablation modes of C/SiC composites were discussed. The coupling effects (thermal–mechanical denudation and thermal–chemical erosion) worsened the degradation of the coated PIP-C/SiC composites. CVD-SiC coating provided better protection for the composites under the MMH/N2O4 bipropellants tests.

Numerical Studies on Air-Core Vortex Formation During Draining of Liquids from Tanks

The gas-liquid interface dips during the draining of a liquid through a discharge port of a vessel or a tank. The dip develops into a gas-core vortex which subsequently enters the discharge port. This entry can be either gradual or sudden, depending on the intensification of the rotational flow currents during the draining process. The extension of the gas-core into the drain port reduces the flow area and consequently the flow rate. In liquid propellant rocket motors, this phenomenon can have adverse effect on the performance as well as lead to under utilisation of the propellant. In this paper, the authors have tried to find the reason why such an air-core vortex develops in the first place, and the factors that influence its intensification over time, as reported in literature. These investigations have been carried out through simulations done using the commercial ANSYS Fluent code to validate the findings from the CFD results. The simulations are carried out using the volume of fluid (VOF) method, which obtains the volume fraction of each of the fluid throughout the domain and thereby captures the gas-liquid interface motion. Thereafter, the air-core vortex height predictions are validated with results reported in the literature.

Spray Combustor Design/Performance: Chemical Engineering Contributions and the Emergence of an “Interacting Population-Balance” Perspective

Spray combustors are now widely used in many technologies, spanning commodity chemical synthesis (combustion of molten sulfur en route to sulfuric acid (H2SO4) and phosphorus en route to phosphoric acid (H3PO4), ...), and nanoparticle synthesis (eg., via “spray pyrolysis”), to energy conversion (oil-fired furnaces or boilers) and chemical propulsion (aircraft gas turbines and liquid-propellant rocket motors). While important space, weight, and pollutant constraints inevitably differ from application to application, spray-“fuel”-fed combustors share certain common performance characteristics, and there is a considerable economic incentive to develop rational yet tractable design methods for them. While this intrinsically interdisciplinary subject continues to evolve, here, we briefly review some of the principal contributions to these challenging goals published by chemical engineers since the inception of Industrial and Engineering Chemistry (I&EC). Not surprisingly, the earliest contributions focused on ...

Condensation-Induced Surface Boiling of Alcohol Fuel Droplets in Combustion Chambers

F OR ordinary hydrocarbon liquid fuels, droplet energy-balance considerations have previously been used to clearly delineate combustion-chamber conditions under which injected fuel droplets will be driven to either a stable (wet-bulb) temperature less than both its boiling point and its thermodynamic critical temperature or to a transcritical statewith vanishing latent heat (see, for example, Rosner andChang [1]).When one is far from criticality, the notion of a stable wet-bulb droplet temperature that is systematically less than the prevailing fuel boiling point is based on the physical notion of evaporative cooling [2,3]. Although energy is indeed necessary to evaporate the fuel component for combustion, when the fuel is (or contains) an alcohol [as in the case of ethanol (C2H5OH, hereafter abbreviated as EtOH) used for the historic German V-2 liquidpropellant rocket motor], it can also condense/absorb its own combustion product: H2O. In the course of our recent theoretical studies of the performance of idealized high-pressure spray combustors (see, for example, Rosner et al. [4] and Rosner and Arias-Zugasti [5]), we have encountered combinations of fuel composition and chamber conditions in which the heat of H2O condensation is actually capable of driving injected droplets to their prevailing bubble points. Indeed, when condensation heating contributes to the droplet energy balance along with Fourier heat diffusion, the following quantitative algebraic condition plays the role of a singular locus: Twb Tbp. Here, Twb (a function of droplet composition and chamber conditions) is the droplet temperature at which the net rate of droplet heating vanishes in the prevailing environment, and Tbp (a function of droplet composition and chamber pressure) is the prevailing thermodynamic bubble point of the multicomponent liquid-fuel feed at pressure p. This condition is shown here to delineate the boundary between two interesting domains of possible operation: one in which small injected droplets will tend to be driven to a stable temperature below the prevailing bubble point (during which diffusion-controlled evaporation can proceed in nearly quasi-steady fashion [1,4]) or one in which small droplets are driven to an unstable state of surface boiling beyond which the normal laws of nearly isobaric diffusion-controlled vaporization no longer apply. It is perhaps not fortuitous that the V-2 rocket and some of its higher-performance derivatives (e.g., the Russian RD-101) [6], operated rather close to, but apparently not on, this singular locus (see Sec. IV and Fig. 1). Although the simplified predictive methods outlined/illustrated subsequently are tailored to the comparatively well-studied binary EtOH=H2O system, we believe that this condensation-induced boiling (CIB) condition is an important and rather general one and that the possibility of such situations should be anticipated early in the design stage for any spray combustor.

Acoustic characteristics of a rocket combustion chamber: Radial baffle effects

This paper describes methods used for determining the characteristic acoustic modes and frequencies of a liquid–propellant rocket–motor combustion chamber and effects of radial baffles on the chamber’s acoustic field. A multi-point sensing experimental setup, including stationary and moving sensors, was used to measure characteristic frequencies and mode shapes of a combustion chamber. A new technique based on the comparison of signal phase angles from stationary sensors to that of a moving sensor was used to map complex characteristic mode shapes of a combustor. A three-dimensional Helmholtz acoustic solver was also developed using an efficient finite volume approach for complex geometries to simulate the acoustic field inside a combustor. Using this approach the effects of the convergent section of the nozzle and the number of radial baffles on the chamber’s dominant acoustic modes with no mean flow were investigated. We have shown that the classical reduction of characteristic frequency of tangential modes caused by radial baffles is due to longitudinalization of tangential modes and is a function of the blade length and weakly dependent on the number of blades. Also, conjugate spinning modes are decoupled and do not spin in any baffled combustor, independent of the number of blades. On the other hand the converging nozzle section of a combustion chamber modifies pure longitudinal modes in the radial direction and pure tangential modes in the longitudinal direction. Existence of some mixed tangential–longitudinal modes in a combustor is dependent on the ratio of the nozzle throat diameter to the combustor head plate diameter.

Continuous Spin Detonations

Results on controlled continuous spin detonation of various fuels in liquid-propellant rocket motors and ramjet combustors are reported. Schemes of chambers, combustion in transverse detonation waves, and typical photographic records of transverse detonation waves are given. The flow structure, existence conditions, and basic properties of continuous detonation are considered. An analysis of physical, chemical, and geometric parameters determining spin detonation is presented. Results of studying continuous spin detonation of C 2 H 2 + air and H 2 + air mixtures in an annular ducted chamber 30.6 cm in diameter are reported. The range of existence of continuous spin detonation in fuel-air mixtures is determined as a function of the governing parameters. In the case of high-quality mixing, the transverse detonation wave velocity and structure are extremely stable in a wide range of the ratios of propellant components and in the examined range of pressures in the chamber.

A method for the transverse modulation of reactive flows with application to combustion instability

A method allowing the transverse excitation of non-reactive or reactive flows is described. The method relies on a characteristic wave modulation applied on the lateral sides of the computational domain. It is shown that this procedure can be used to induce a transverse sloshing motion in the region of interest. Two two-dimensional geometries are studied: in the first, the flow features one or two wakes embedded in a high-speed stream; the second configuration involves a premixed reactive jet flame. The excited flow structure calculated in this last case is found to be similar to that observed in an experiment carried out previously. As the simulations are performed in two dimensions, they cannot describe many of the processes taking place in a turbulent flow. They are, however, valuable when the flow is dominated by a large-scale organized motion induced by a transverse acoustic modulation. The present calculations indicate that the method in combination with a large eddy simulation flow solver could be used to study combustion response to transverse acoustic perturbations. With additional developments this might be used to study liquid propellant rocket motor instabilities coupled by transverse acoustic modes in the high-frequency range.

Study of a New Kind of Multipulse Rocket Motor

A new method for multi-ignitable rocket motor design has been proposed in this paper, by analyzing e ow, heat-transfer, and combustion of a non-Newtonian pasty propellant, in which oxidizer and fuel binder are mixed homogeneously. The new motor has advantages found in both solid- and liquid-propellant rocket motors. The motor discussed in this paper is also thrust adjustable. Moreover, because the propellant is ignited by surplus heat from thecombustion chamberno additional ignition energyisneeded. Thekey technology ofthisnewmethod isthe proposedreignitableigniter.Atwo-dimensionale owandheat-transfermodelofthepropellantinsidethereignitable igniter has been developed. Control equations have also been solved numerically. Propellant temperatures inside the igniter holes have been obtained, in conjunction with a simple ignition criterion. The relationship between igniter temperatures, igniter length, igniter diameter, and drive pressure has also obtained. A combustion model applicable to the new pasty propellant is proposed on the basis of the current solid-propellant BDP (BecksteadDerr-Price)combustionmodel.Aprototypetestapparatushasalsobeen builtformultipulsee ring.Sevenoperation pulses were obtained. Each pulse lasts about 5 s, and the time interval between pulses is approximately 2 s. Nomenclature A = area k = consistency coefe cient L = length m = mass n = e ow exponent P = pressure Q = e ow mass rate R = radius r = burning rate T = temperature t = time u = velocity x; y = coordinate ´ = viscous coefe cient ¸ = heat conduct coefe cient π = dynamic viscous coefe cient Ω = density ? = shear stress

Variable structure control of time-delay systems with a simulation study on stabilizing combustion in liquid propellant rocket motors

The dynamical model of combustion in liquid propellant rocket motors is an unstable time-delay system. When it is stabilized by a linear state feedback controller, the robustness of the closed-loop system is not satisfactory. In this paper a variable structure control approach to stabilize the combustion is presented. First, the concept of switching functional is introduced, and hence a systematic design method is established for the variable structure control of general time-delay systems. Secondly, the proposed theory is applied to the stabilization of combustion in liquid monopropellant rocket motors. Simulation results show that the robustness of the closed-loop system against variations in time lag δ and pressure exponent y is considerably improved. Specifically, the controller designed according to the nominal value δ = 1.0 can still stabilize the system with δ = 0, i.e. the system without time delay. This conclusion provides a powerful basis for the reliable design of rocket motor control systems.

Effects of size distribution on the combustion efficiency of a liquid propellant rocket motor

Abstract This paper studies the effects of size distribution of sprays on the combustion efficiency of a one‐dimensional, steady state liquid propellant rocket motor in terms of (i) mean radius, (ii) degree of dispersity, (iii) range of droplet size, and (iv) the shape of the distribution. The combustion process of the droplet groups is analysed by a step‐by‐step numerical scheme. Results indicate that better combustion efficiency can be achieved by reducing the droplets size and improving the monodispersity of the sprays. The effects of the range of droplet size and the shape of the distribution on the combustion efficiency are relatively small, and may be ignored in most cases.

Theoretical investigation of nonlinear three-dimensional instabilities in liquid rockets with real nozzles

An approximate analytical technique has been developed for the solution of nonlinear three-dimensional, transverse and axial combustion instability problems that are frequently observed in liquid-propellant rocket motors. This theory is an extension and generalization of previous analyses, which could analyze either transverse or axial instabilities in liquid combustors with quasi-steady nozzles, to the practical situations of three-dimensional instabilities in combustors with conventional DeLaval nozzles. Unlike the quasi-steady nozzle, the presence of a conventional nozzle imposes restrictions upon the behavior of both the amplitudes and phases of the oscillations at the nozzle entrance plane. The applicability of the solution technique, which is based on the Galerkin method, is demonstrated by analyzing the nonlinear stability of a cylindrical liquid-rocket combustor with uniform injection of propellants at one end and a conventional nozzle at the other end. Crocco's pressure sensitive time-lag model is used to describe the unsteady combustion process. Calculated results for transverse and axial instabilities indicate that the developed model can predict the transient behavior and nonlinear wave shapes that have been observed during unstable motor operation as well as limit-cycle amplitudes and frequencies typical of unstable motor operation. These results establish the relationship that exists between the resulting instability (i.e., waveform, final amplitude, and final frequency), the combustion parameters (i.e., interaction index, n, and time-lag, \\ ̄ gt), and the chamber Mach number and length-to-diameter ratio. Results indicate that the limit-cycle amplitude increases with increasing sensitivity of the combustion process to pressure oscillations. For transverse instabilities, calculated pressure waveforms exhibit sharp peaks and shallow minima, and the frequency of oscillation is always within a few percent of the frequency of one of the chamber's acoustic modes. For axial instabilities, the theory predicts the presence of a steep-fronted wave moving back and forth along the combustor. In both cases calculations of pressure and velocity perturbations at the nozzle entrance plane show that the approximation to the nozzle boundary condition is very good. The studies presented in this paper represent significant progress toward the development of a unified nonlinear theory for the solution of general three-dimensional, transverse and axial combustion instability problems.

Barrier Film Cooling Study

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Application of the Galerkin Method in the Solution of Non-linear Axial Combustion Instability Problems in Liquid Rockets

Abstract A nonlinear analysis of the stability of longitudinal combustion-driven oscillations in liquid propellant rocket motors is presented. A modified version of the Galerkin method is used to obtain solutions valid for moderate amplitude instabilities in rocket combustors having a low Mach number mean flow. Linear stability of a variety of liquid-rocket motors is investigated. Computed nonlinear results show that the resultant instability will exhibit a shock-type behavior with the number of shocks present in the system determined by the characteristics of the unsteady combustion process. These predictions are in qualitative agreement with available experimental data. Contrary to other solution techniques, the approach presented in this paper can predict both the transient and final periodic behavior of the instability. The final limit cycles are independent of the nature of the initial conditions. The relationship between the final limit cycles and the characteristics of the unsteady combustion process are discussed. Finally, the application of the Galerkin Method requires relatively little computation time and it offers considerable physical insight into the behavior of the instability.