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     

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.     

Computational analysis of dense gas shock tube flow

Nonclassical phenomena associated with the classical dynamics of real gases in a conventional shock tube are studied. A TVD predictor-corrector (TVD-MacCormack) scheme with reflective endwall boundary conditions is used for the one-dimensional Euler equations to simulate the evolution of the wave field of a van der Waals gas. Depending upon the initial conditions of the gas, wave fields are produced that contain nonclassical phenomena such as expansion shocks, composite waves, splitting shocks, etc. In addition, the interactions of waves reflected from the endwalls produce both classical and nonclassical phenomena. Wave field evolution is depicted using plots of the flow variables at specific times and withx-t diagrams.     

Three-dimensional effects on line-of-sight visualization measurements of supersonic and hypersonic flow over cylinders

Flow visualization experiments were performed for supersonic and hypersonic nitrogen test gas flows over a cylinder. The results were used to quantify the influence of three-dimensional effects on optical line-of-sight visualization measurements. Images of cylindrical models of varying aspect ratios (length to diameter) were taken. Shock stand-off distance measurements for the models were compared with a two-dimensional approximation and numerical simulations. For aspect ratios of two and above, the two-dimensional approximation was acceptable within experimental uncertainty. The measured shock stand-off decreased by less than 5% from an asymptotic value for an infinite length cylinder. For smaller aspect ratios, a correction factor for the shock stand-off needs to be applied if comparisons between the two-dimensional approximation and experimental measurements are to be drawn. An estimate of this correction factor has been derived from an empirical fit to the available data.      

Detailed flowfields of a RAMAC device in H2−O2 full chemistry

Numerical simulations of a RAMAC device were performed for a range of speeds and grid densities. For certain initial conditions the detonation was unstable and propagated ahead of the projectile in a normal detonation wave, similar to the experimental phenomenon of unstart. The unstart was observed to develop within the narrow space between projectile and tube wall (the throat), so we focus on that area. Detailed flowfield views of the throat reveal a separated flow rotating in one large vortex. The detonation is overdriven but steady for fast enough upstream velocities. The vortex has an important role in triggering off the unstart by creating a condition at the throat whereby the detonation can propagate against the flow. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995.     

The numerical and experimental simulation of hypervelocity flow around the HYFLEX vehicle forebody

Numerical and experimental techniques are used to model the flow and pressure distribution around the forebody of the HYFLEX hypersonic flight vehicle. We compare numerical simulation results with modified Newtonian theory and flight data to determine the accuracy of the computational fluid dynamics (CFD) technique used. The numerical simulations closely match the trends in flight data, and show that real gas effects have a small but significant influence on the nose pressure distribution. We also present pressure results from a scale-model tested in a shock tunnel, and compare them with simulation results. For the shock tunnel experiment, the model was placed such that part of the upper surface was in a region of the test flow where nonuniformities were significant, and it was shown that the numerical simulation could adequately capture these experimental flow features. The binary scaling parameter (describing the similarity in species dissociation between flight and model) was used to design the scale-model tests in the shock tunnel, and its effectiveness is discussed. We find that matching the flight Mach number in the shock tunnel experiment is not critical for reproducing flight pressure data, so long as flight velocity is matched, and binary scaling is maintained. Received 11 June 1998 / Accepted 1 September 1998     

Aerodynamic calibration of TCM2 facility and study of a bow shock layer by emission and laser spectroscopy

Flow properties in the TCM2 free piston shock tube/tunnel are determined by time-resolved pressure and heat flux measurements in numerous points of the shock tube and the nozzle, and in the free flow for two stagnation enthalpy conditions (3.5 and 11 MJ/kg). These measurements demonstrate the homogeneity of the flow during more than 1 ms. The cleanness of the useful test time is shown with time-resolved emission measurements at critical wavelengths. NO fluorescence profiles are established with local and planar laser-induced fluorescence in the shock layer around a cylindrical model. It allows to determine the shock stand-off distance for both enthalpy conditions. The problems of quenching and amplified spontaneous emission are considered. The importance of atomic oxygen and atomic nitrogen densities as well as temperature effects is also shown. Evaluation of the temperatures behind the shock front through spectroscopic data agrees with calculations. The proof of the presence of vibrationally excited NO ahead of the shock layer is given. Received 14 March 2000 / Accepted 18 June 2001     

On the role of turbulence in detonation induced by Mach stem reflection

A series of experiments conducted by Chan has shown that while some shock waves may not be strong enough to induce detonation when they collide with an obstacle the resulting Mach stem will induce detonation if it collides with a subsequent obstruction. A series of numerical simulations, however, failed to demonstrate the expected results if either the Euler or laminar Navier-Stokes equations are solved. On the other hand, calculations using the Favre averaged Navier-Stokes equations with a k--F turbulence model are able to reproduce the experimental results, indicating that turbulent effects may play an important role in the ignition process. A detailed examination of the results shows that turbulence causes the formation of activated kernels in a similar process to that observed in deflagration-detonation transition. The simulations in this paper have been undertaken using a modern high resolution hydrocode and a reduced kinetics mechanism for hydrogen combustion. The paper describes the reduced mechanism, the solution methods employed in the hydrocode and discusses the results of the simulations and their implications. Received 28 October 1997 / Accepted 30 April 1998     

Heating enhancement caused by a transverse control jet in hypersonic flow

Experiments are reported in which the heat flux distribution near a single circular, sonic transverse jet on a flat plate exposed to a hypersonic (Mach 6.7) freestream flow was quantitatively measured using thermochromic liquid crystals. The freestream conditions were such that the boundary layer growth on the plate ahead of the jet was laminar. The results indicate that the interaction of the jet with the freestream flow created a complex flowfield with regions of separation and reattachment which caused localised enhancements to the heat flux upstream and to the side of the jet, the magnitudes of which were sensitive to both jet plenum pressure and jet gas composition. Received 28 August 1996 / Accepted 6 June 1997     

Gradients at a curved shock in reacting flow

The inviscid equations of motion for the flow at the downstream side of a curved shock are solved for the shock–normal derivatives. Combining them with the shock–parallel derivatives yields gradients and substantial derivatives. In general these consist of two terms, one proportional to the rate of removal of specific enthalpy by the reaction, and one proportional to the shock curvature. Results about the streamline curvature show that, for sufficiently fast exothermic reaction, no Crocco point exists. This leads to a stability argument for sinusoidally perturbed normal shocks that relates to the formation of the structure of a detonation wave. Application to the deflection–pressure map of a streamline emerging from a triple shock point leads to the conclusion that, for non–reacting flow, the curvature of the Mach stem and reflected shock must be zero at the triple point, if the incident shock is straight. The direction and magnitude of the gradient at the shock of any flow quantity may be written down using the results. The sonic line slope in reacting flow serves as an example. Extension of the results – derived in the first place for plane flow – to three dimensions is straightforward. Received 12 February 1997 / Accepted 10 June 1997     

Near-resonant holographic interferometry of hypersonic flow

Near-Resonant Holographic Interferometry is a powerful technique which extends the established advantages of conventional holographic interferometry by allowing a species-specific number density to be determined. It has been tested in the harsh flow conditions generated in a high enthalpy facility yielding information about the shock shape on a cylindrical body and on the distribution of a trace species seeded into the flow. Received 7 April 2000 / Accepted 1 November 2000     

Aerodynamic thermal environment around transonic tube train in choked/unchoked flow

The aerodynamic thermal environment in an evacuated tube transport (ETT) system is an important factor in ensuring the operational safety of tube trains, where choking can further worsen air flow and aerodynamic heating. A compressible flow solver based on total variation diminishing (TVD) schemes was used to calculate the transonic aerodynamic behaviour of a capsule train in a confined space under low pressure conditions, and the flow fields and aerodynamic heating effect on the train were obtained. The results showed that the flow state around the train could be classified into choked and unchoked flow according to the blockage ratio (BR) and train speed based on the Kantrowitz limit. The wall viscosity caused a difference in the boundary-layer flow and potential flow in the annular space between the train and the tube with an increase in the BR. The choked flow was driven forward by the train, passing through its throat at the speed of sound. Owing to the complicated compressible flow in the tube, the thermal environment around the train gave rise to extreme temperature changes on its surface. In transonic choked flow, the temperature rise of the train head reached a maximum of 525 K, whereas local cooling could occur in the afterbody, causing the surface temperature to fall below the ambient temperature under certain conditions. The findings can be used to guide the design of ETT systems.     

Simulation of unsteady hypersonic combustion around projectiles in an expansion tube

The temporal evolution of combustion flowfields established by the interaction between wedge-shaped bodies and explosive hydrogen-oxygen-nitrogen mixtures accelerated to hypersonic speeds in an expansion tube is investigated. The analysis is carried out using a fully implicit, time-accurate, computational fluid dynamics code that we recently developed to solve the Navier-Stokes equations for a chemically reacting gas mixture. The numerical results are compared with experimental data from the Stanford University expansion tube for two different gas mixtures at Mach numbers of 4.2 and 5.2. The experimental work showed that flow unstart occurred for both the Mach 4.2 cases. These results are reproduced by our numerical simulations and, more significantly, the causes for unstart are explained. For the Mach 5.2 mixtures, the experiments and numerical simulations both produced stable combustion. However, the computations indicate that in one case the experimental data were obtained during the transient phase of the flow; that is, before steady state had been attained. Received 7 February 2000/ Accepted 20 February 2001     

Numerical investigation of transient nozzle flow

Abstract. The starting process of two-dimensional and axisymmetric nozzle flows has been investigated numerically. Special attention has been paid to the early phase of the starting process and to the appearance of a strong secondary shock wave. For both cases, shock intensities and velocities are obtained and discussed. The flow evolution in the axisymmetric case is proved to be more complex and the transient starting process is slower than in the plane case. Finally, the effects of changing the nozzle angle and the incident shock wave Mach number on the transient flow are addressed. It is shown that a faster start-up can be induced either by decreasing the nozzle angle or increasing the Mach number of the incident shock wave. Received 16 November 2001 / Accepted 24 September 2002 / Published online 4 December 2002 Correspondence to:A.-S. Mouronval (e-mail: mouronv@coria.fr)     

Generalized reference enthalpy formulations and simulation of viscous effects in hypersonic flow

A generalized reference enthalpy formulation for the skin friction, heat transfer and radiation-equilibrium temperature distributions over aerodynamic surfaces in attached hypersonic / hyperenthalpic flow is proposed. The formulation, which has been extensively employed in various forms by numerous investigators in the perfect gas regime, has also been recently demonstrated to provide adequate estimates of the heat transfer distribution in thermochemically active high enthalpy flow conditions when coupled to thermochemically active Euler solutions. It is now used to reveal the relevant similitude parameters for viscous effects in hypersonic flow, and the importance of the temperature distribution across the boundary layer and of the temperature-viscosity relation. It is shown that, although reproduction of the flight total flow enthalpy as well as surface temperature is the obvious solution for full viscous simulation in (perfect gas) hypersonic flow, the hot surface testing requirement and, in a number of practical applications, also the hot flow requirement may be relaxed with reasonably small error that can be of the same order as the measurement accuracy in present-day hypersonic testing. This similitude error, however, may increase significantly in cases exhibiting strong viscous/inviscid interaction or when the laminar-turbulent transition process becomes important. In this respect, alternative full simulation solutions, which are less demanding in terms of reproduction of the high levels of flight freestream and surface temperature or even Reynolds number, are discussed. Received 6 May 1997 / Accepted 8 October 1997     

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments. Received 15 November 1996 / Accepted 3 February 1997     

Validation of hypersonic chemical equilibrium flow calculations using ballistic-range data

The hypersonic flow field over a sphere flying in a ballistic-range is numerically simulated for the purpose of validating a hypersonic chemical equilibrium flow solver. The numerical results obtained are compared with available experimental data on the stand-off distance and the shape of the detached bow shock wave. In the calculation, an adaptive mesh is employed for a crisp capturing of the shock wave. Comparison with the experimental data reveals that the equilibrium flow solver can yield a fairly accurate prediction of the flow field. Received 18 November 1997 / Accepted 10 November 1998     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

A study on non-steady flow of upper-convected maxwell fluid in tube

The transient response of an upper-convected Maxwell fluid flow in a circular tube is analysed by variational approach of Kantorovich and the method of finite difference. The solution of the variational method is in agreement with the numerical results by the difference schemes. The results show that the method of Kantorovich is suitable for the study of non-steady flow of non-Newtonian fluids and the effect of elasticity of the fluid has an influence on the non-steady flow. project supported by National Natural Science Foundation of China