Experimental investigation of ram accelerator propulsion modes

Experimental investigations on the propulsive modes of the ram accelerator are reviewed in this paper. The ram accelerator is a ramjet-in-tube projectile accelerator whose principle of operation is similar to that of a supersonic air-breathing ramjet. The projectile resembles the centerbody of a ramjet and travels through a stationary tube filled with a premixed gaseous fuel and oxidizer mixture. The combustion process travels with the projectile, generating a pressure distribution which produces forward thrust on the projectile. Several modes of ram accelerator operation are possible which are distinguished by their operating velocity range and the manner in which the combustion process is initiated and stabilized. Propulsive cycles utilizing subsonic, thermally choked combustion theoretically allow projectiles to be accelerated to the Chapman-Jouguet(C-J) detonation speed of a gaseous propellant mixture. In the superdetonative velocity range, the projectile is accelerated while always traveling faster than the C-J speed, and in the transdetonative regime (85–115 % of C-J speed) the projectile makes a smooth transition from a subdetonative to a superdetonative propulsive mode. This paper examines operation in these three regimes of flow using methane and ethylene based propellant mixtures in a 16 m long, 38 mm bore ram accelerator using 45–90 g projectiles at velocities up to 2500 m/s.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Propagation of near-limit gaseous detonations in small diameter tubes

In this study, detonation limits in very small diameter tubes are investigated to further the understanding of the near-limit detonation phenomenon. Three small diameter circular tubes of 1.8, 6.3, and 9.5 mm inner diameters, of 3 m length, were used to permit the near-limit detonations to be observed over long distances of 300 to 1500 tube diameters. Mixtures with high argon dilution (stable) and without dilution (unstable) are used for the experiments. For stable mixtures highly diluted with argon for which instabilities are not important and where failure is due to losses only, the limit obtained experimentally appears well to be in good agreement in comparison to that computed by the quasi-steady ZND theory with flow divergence or curvature term modeling the boundary layer effects. For unstable detonations it is suggested that suppression of the instabilities of the cellular detonation due to boundary conditions is responsible for the failure of the detonation wave. Different near-limit propagation regimes are also observed, including the spinning and galloping mode. Based on the present experimental results, an attempt is made to study an operational criterion for the propagation limits of stable and unstable detonations.     

不稳定性对爆轰波楔面马赫反射的影响规律研究

采用一种两步化学反应模型对胞格爆轰波的楔面马赫反射过程进行了数值研究,从而澄清和解释胞格不稳定性对马赫反射发展模式和自相似性的影响。考虑到反应欧拉方程源项的刚性问题,本文采用附加RungeKutta方法耦合非刚性对流项和刚性反应源项,对流项的离散采用五阶精度的WENO格式。计算结果表明,对于稳定胞格爆轰波而言,其马赫反射过程本质上与ZND爆轰波的马赫反射是一致的,整体上不存在自相似性,胞格不稳定性只是造成了三波点轨迹线局部小振幅的波动。在楔面顶点附近,由于马赫杆是强过驱的,爆轰波的马赫反射过程是自相似的。在远场,爆轰波马赫反射的三波点轨迹线渐近的趋向于一条直线,说明重新获得了自相似性。对于不稳定的爆轰波,由于自身的不稳定性可以与马赫反射的强度相匹配,定义其三波点的轨迹是困难的,进行自相似性分析没有意义。     

Dynamics of oblique detonations in ram accelerators

Time-accurate numerical simulations are used to study the dynamic development of oblique detonations on accelerating projectiles in ram accelerators. These simulations show that the oblique detonation can be stabilized on the projectile. The high pressure generated behind the detonation can result in accelerations up to 10⁶G and propel the projectile to velocities higher than 4.0 km/s. The detonation structure on the projectile is sensitive to the projectile geometry. A small change in the projectile shape is sufficient to alter the overall detonation structure and significantly affect the pressure distribution on the projectile. In order to maximize the thrust, an appropriate projectile shape has to be chosen to generate the detonation structure just behind the widest part of the projectile body. The projectile acceleration also has strong effects on the flow field and the detonation structure. During the acceleration, the location of the oblique detonation moves upstream from one reflected shock to another. However, one the detonation is stabilized behind the upstream shock, it remains at the new location until the transition to the next upstream shock occurs. In the simulations, the Non-Inertial-Source (NIS) technique was used to accurately represent of the projectile acceleration. Also, the Virtual-Cell-Embedding (VCE) method was employed to efficiently treat the complex projectile geometry on cartesian grids.     

Visualization of burning flow around a ram accelerator projectile by coaxial simultaneous shadow/direct photography

Experimental investigations with flow visualization of a ram accelerator are reported. The ram accelerator at Hiroshima University uses a tube with a rectangular cross section and a two-dimensional projectile. Observation windows installed on the flat wall of the rectangular tube enable visualization of the flow field around the projectile. In addition to the instantaneous shadow photography method conventionally used for visualization, a direct photography method has been introduced. This direct photography can detect the precise position and brightness of combustion that cannot be observed by shadowgraph. The experiments were conducted at various projectile velocities in the thermally choked mode. The propellant mixture is stoichiometric methane-oxygen diluted by carbon dioxide. It is observed that a tiny flamelet, assumed to be the remains of the starting process, adheres to the projectile forebody, however, visible light emission could not be detected there by direct photography. The brightest emission from combustion is observed around the rear of the projectile, and strong emission is found in the boundary layer on the surface of the projectile afterbody and at the center of the tube behind the projectile. It is also found that the gas mixture is burned over a shorter distance when the projectile moves more slowly.     

Detonation wave initiation of ram accelerator propellants

The current ram accelerator operations have shown that data on the ability of the propellants to detonate are required. Previous studies examined the efficacy of initiation techniques based on piston impact. The purpose of the present work is to analyze the effects of detonation wave transmission from a detonating mixture into a low sensitivity mixture. One-dimensional modeling based on the analysis of pressure vs particle velocity for the mixtures is used to interpret experimental data. Furthermore, calculations based on chemical kinetics (CHEMKIN code) are provided. Experimental data together with the modeling of the detonation transmission provide some new insight into the limiting conditions necessary to establish a Chapman-Jouguet (CJ) wave in a detonable mixture. Received 11 January 2000 / Accepted 15 September 2000     

Numerical simulation of Mach reflection of cellular detonations

The Mach reflection of cellular detonation waves on a wedge is investigated numerically in an attempt to elucidate the effect of cellular instabilities on Mach reflection, the dependence of self-similarity on the thickness of a detonation wave, and the initial development of the Mach stem near the wedge apex. A two-step chain-branching reaction model is used to give a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. A sufficiently large distance of travel of the Mach stem is computed to observe the asymptotic behavior in the far field. Depending on the scale at which the Mach reflection process occurs, it is found that the Mach reflection of a cellular detonation behaves essentially in the same way as a planar ZND detonation wave. The cellular instabilities, however, cause the triple-point trajectory to fluctuate. The fluctuations are due to interactions of the triple point of the Mach stem with the transverse waves of cellular instabilities. In the vicinity of the wedge apex, the Mach reflection is found to be self-similar and corresponds to that of a shock wave of the same strength, since the Mach stem is highly overdriven initially. In the far field, the triple-point trajectory approaches a straight line, indicating that the Mach reflection becomes self-similar asymptotically. The distance of the approach to self-similarity is found to decrease rapidly with decreasing thickness of the detonation front.     

Computational study of reacting flow establishment in expansion tube facilities

We study the temporal evolution of the combustion flowfield established by the interaction of ram accelerator-type projectiles with an explosive gas mixture accelerated to hypersonic speeds in an expansion tube. The Navier-Stokes equations for a chemically reacting gas mixture are solved in a fully coupled manner using an implicit, time accurate algorithm. The solution procedure is based on a spatially second order, total variation diminishing scheme and a temporally second order, variable-step, backward differentiation formula method. The hydrogen-oxygen-argon chemistry is modeled with a 9-species, 19-step mechanism. The accuracy of the solution method is first demonstrated by several benchmark calculations. Numerical simulations of expansion tube flowfields are then presented for two different geometries: an axisymmetric projectile and a ram accelerator configuration. The development of the shock-induced combustion process is followed. The temporal variations of the calculated thrust and drag forces on the ram accelerator projectile are also presented. In the axisymmetric projectile case, which was designed to ensure combustion only in the boundary layer, the radial extent of the flame front during the initial transient phase was surprisingly large. In the ram accelerator configuration the flame propagated upstream along both the projectile and tube wall boundary layers, resulting in unstart. Received 25 September 1996 / Accepted 15 January 1997     

Experiments on spinning detonations with detailed analysis of the shock structure

Spinning detonations are characteristic of detonation limit phenomena in round tubes. In this work we study experimentally the structure of the transverse wave of single-headed spinning detonations. The flow field is experimentally analysed and an original approach enables us to calculate the overall shock structure. The calculations and experimental results indicate that the actual structure of the spinning detonation tries to match closely to the condition where the state parameters (pressure and temperature) reach their maximum values. This condition corresponds to a spinning head where the Mach stem is normal to the incoming flow and could be readily used as boundary condition by further investigators to determine the structure of spinning detonations. Received 1 August 1997/ Accepted 13 July 1998     

Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H ₂/O ₂ diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes. The English text was polished by Yumming Chen.     

The applications of unsteady, multi-dimensional studies of detonation waves to ram accelerators

Since much of the early work on the concepts on which ram accelerators are based dates back to the 1960s, although many of these are still being actively pursued, it is difficult to formulate a completely logical approach. This situation is compounded by the use of presently unacceptable treatments of unidimensional detonations in the early work and unfortunately extended to some of the more modern treatments. My approach has been to start by dealing with the early work and recent work impinging upon it, then to re-emphasise recent work on detonations, particularly that dealing with the influence of changes in confinement on quenching and re-initiation of detonations. However, some knowledge of this is inferred in suggestions made in Part 2 for possible improvements in the techniques. Latter sections cover the development of the ram accelerator, the use of various types of projectiles, developments in experimental techniques and finally on areas in space flight where the results from ram accelerators might be utilised. Received 14 January 1999 / Accepted 16 June 1999     

Diaphragm rupture. Impingement by a conically-nosed, ram-accelerator projectile

The effect of diaphragm rupture by a conically-nosed projectile on the gasdynamics related to ram accelerator operation was experimentally and numerically studied. The experiments were conducted using a 25-mm-bore ram accelerator. Either air or nitrogen was used as the test gas. Using a high-speed image converter camera, it was observed that during the process of the diaphragm rupture a region with strong radiation developed between the diaphragm and the approaching projectile/sabot. This radiating region corresponds to the shock-heated gas which is originated from a precursory shock wave driven by the accelerating projectile/sabot. The flow around the projectile upon entering the test section by rupturing the diaphragm was visualized by holographic interferometry. During the diaphragm rupture, the system of oblique shock waves around the conical nose of the projectile was seen undisturbed on the downstream side of the diaphragm. Under the same condition as the experiment, numerical simulation was conducted using GRP (Generalized Riemann Problem) scheme which was extended to the computation of compressible flow fields bounded by moving surfaces. Two diaphragm rupture models were examined: (1) the diaphragm deformed by wrapping tightly around the moving projectile; (2) the diaphragm was ruptured instantly at the moment the projectile touched the diaphragm. Comparing these models with the experimentally visualized flow, the former was found to express the diaphragm rupture process much better than the latter. Received 9 February 1998 / Accepted 9 September 1998     

Real gas effects on the prediction of ram accelerator performance

The analysis of ram accelerator performance is based on one-dimensional modelling of the flow process that propels the projectile. The conservation equations are applied to a control volume travelling with the projectile, and quasi-steady flow is assumed. To date the solution obtained, namely the generalized thrust equation, has been based on the ideal gas assumption. At the high level of pressure that is encountered during the ram accelerator process, this assumption cannot be regarded as adequate. Thus, a more appropriate equation of state (EOS) should be used instead. Depending upon the level of pressure, several equations of state are available for dense gaseous energetic materials. The virial type of EOS can be more or less sophisticated, depending upon the extent of complexity of the intermolecular modelling, and turns out to be totally appropriate for most gaseous explosive mixtures that have been investigated at moderate initial pressures, i.e., less than 10MPa. In the present case the Boltzmann EOS was applied. It is based on very simplified molecular interactions, which makes it relatively easy to use in calculations. Moreover, the energetic EOS needs to be taken into account. This concerns all the calorimetric coefficients, as well as the thermodynamic parameters, which can no longer be expressed as only a function of temperature. The higher the pressure level, the more sophisticated these corrections become, but the main relationships that account for real gas effects are basically the same. These include the use of a general form of analytical operators applied to correct the thermodynamic functions and coefficients. The equations governing the one-dimensional model were taken as a basis for the real gas corrections and were solved analytically. The parameters which play the most crucial roles in this correction can thus be highlighted. A complete set of equations involving the real gas effects are presented in this paper. The QUARTET code was used in this investigation, especially for determining chemical equilibrium compositions. This more accurate model can better predict the projectile acceleration of the thermally choked propulsive mode. Although the present analysis is applied to the fuel-rich methane-oxygen-nitrogen mixture currently used in the ram accelerator experiments, its general formulation makes it readily applicable to any other mixture. The projectile velocity and acceleration histories determined by the Hugoniot analysis for the thermally choked ram accelerator mode, assuming the Boltzmann EOS, turn out to be in much better agreement with experimental observations up to the CJ detonation velocity than that when based on the ideal gas assumption. Received 9 August 1996 / Accepted 23 May 1997     

Propagation mechanism of dust detonations

This paper summarizes the studies on dust detonations at the Stosswellenlabor of RWTH Aachen since 1987. The onset and propagation mechanism of heterogeneous dust detonations are similar to those of marginal gas phase detonations. A self-sustained dust detonation has transverse wave structures that provide the coupling between shock and reaction. Large transition distances and transverse wave spacings require large sized tubes for the propagation of self-sustained dust detonations. The Hugoniot analysis of the Chapman-Jouguet detonation predicts equilibrium detonation states being in reasonable agreement with the self-sustained dust detonations observed. Shock matching calculations at the triple point adequately determine the wave structures of those stable dust detonations.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

On the influence of low initial pressure and detonation stochastic nature on Mach reflection of gaseous detonation waves

The two-dimensional, time-dependent and reactive Navier–Stokes equations were solved to obtain an insight into Mach reflection of gaseous detonation in a stoichiometric hydrogen-oxygen mixture diluted by 25 % argon. This mixture generates a mode-7 detonation wave under an initial pressure of 8.00 kPa. Chemical kinetics was simulated by an eight-species, forty-eight-reaction mechanism. It was found that a Mach reflection mode always occurs for a planar detonation wave or planar air shock wave sweeping over wedges with apex angles ranging from \(5^\circ \) to \(50^\circ \) . However, for cellular detonation waves, regular reflection always occurs first, which then transforms into Mach reflection. This phenomenon is more evident for detonations ignited under low initial pressure. Low initial pressure may lead to a curved wave front, that determines the reflection mode. The stochastic nature of boundary shape and transition distance, during deflagration-to-detonation transition, leads to relative disorder of detonation cell location and cell shape. Consequently, when a detonation wave hits the wedge apex, there appears a stochastic variation of triple point origin and variation of the angle between the triple point trajectory and the wedge surface. As the wedge apex angle increases, the distance between the triple point trajectory origin and the wedge apex increases, and the angle between the triple point trajectory and the wedge surface decreases exponentially.     

Analysis of the shock structures in a regular detonation

Time-dependent two-dimensional numerical simulations have been used to investigate the detailed shock structures and patterns of energy release in the regions of the triple points and transverse waves in a planar detonation. As the system of shock triple points evolves between collisions, they trace a well shaped cellular pattern characteristic of detonations in argon-diluted, low-pressure mixtures of hydrogen and oxygen. In the region of the triple points, the shock structure evolves continuously from a single Mach structure to a double Mach structure and finally to a complex Mach structure characteristic of spinning detonations. Most of the energy released in the region of the triple points. The amount of energy release increases as the triple point comes closer to a collision with a wall or another triple point. Just before the collision, there is a large region of energy release that covers the length of the interacting transverse waves. The result is a rectangular high-energy region which boosts the propagation of the new detonation cell.     

一维与二维爆轰传播的时空关联特性数值研究

一维爆轰传播的理论完备、计算准确, 二维斜爆轰传播由于壁面与黏性效应, 大尺度、高精度预测还有一定难度. 利用Euler方程和H₂-Air基元反应模型, 对二维有限长楔面诱导的斜爆轰和活塞驱动一维非定常正爆轰进行计算比较研究, 从时空两个维度方面, 分析了两者在起爆过程、稀疏波传播、爆轰波面演化中的关联特性. 研究结果表明: 在过驱动度相同的条件下, 经过时空变换的活塞驱动一维爆轰传播与二维驻定斜爆轰在起爆区波系结构、波面演化特征和主要参数分布规律方面无论定性或者定量对比均符合较好, 所以, 一维非定常爆轰和二维驻定斜爆轰具有时空相关性. 两者的差异主要体现在过驱动斜爆轰受稀疏波影响过渡到近Chapman-Jouguet (C-J)爆轰状态所需的弛豫时间不同, 原因可能是起源于活塞和壁面稀疏波强度的差异. 本文提出的一维与二维爆轰传播的时空关联方法不仅有助于认知斜爆轰起爆、过驱爆轰产生、胞格爆轰演化的三阶段规律, 还可以对比揭示壁面、边界层和黏性效应的影响, 应用在斜爆轰发动机燃烧室设计中能够有效节约计算时间和成本, 并降低复杂度.      

Detonation properties of dense methane-oxygen-diluent gaseous mixtures: application to ram accelerators

Using a 90mm-bore, 3.15 m long detonation tube, experimental detonation characteristics (detonability limits, detonation velocities and peak pressures) of stoichiometric methane-oxygen-diluent mixtures at an initial pressure up to 3.5 MPa have been experimentally investigated. A parametric study has been carried out as a function of both amount and nature of diluent, namely carbon dioxide, nitrogen and helium. The experimental results allowed the adjustment and validation of computations of the Chapman-Jouguet characteristics by means of a thermochemical code. These experimental data associated with validated computations provide a valuable tool, among others, for the choice of the most appropriate mixture composition in the superdetonative combustion mode for ram accelerator (ramac) experiments. The investigations were organized to determine the upper detonable areas of dense ternary mixtures, and to provide detonation velocity data in order to adjust a series of intermolecular parameters involved in the thermochemical code. Received 8 May 1997 / Accepted 15 December 1997     

Helium dilution for ram accelerator operation

Experimental detonation characteristics (detonability limits and detonation velocities) of methane-oxygen-helium mixtures at initial pressures of up to 5 MPa were measured in a 90 mm caliber, 11.7 m long (130 calibers) smooth-bore detonation tube. Stoichiometric as well as fuel-rich mixtures were investigated in order to provide performance data for ram accelerator applications. The experimental results were used to adjust and validate calculations of the Chapman-Jouguet detonation characteristics by means of a thermochemical code based on various real gas equations of state. On the basis of the detonation velocity data, a series of intermolecular parameters involved in the thermochemical code was determined. Furthermore, the investigation enabled to determine of the upper detonable area of these dense ternary mixtures under the present experimental conditions. Received 25 February 2000 / Accepted 24 January 2001