Shock waves at microscales

We present a model for the effects of scale, via molecular diffusion phenomena, on the generation and propagation of shock waves. A simple parametrization of the shear stresses and heat flux at the wall leads to the determination of new jump conditions, which show that, for a given wave Mach number at small scales, the resulting particle velocities are lower but the pressures are higher. Also, the model predicts that the flow at small scale is isothermal and that the minimum wave velocity can be subsonic. Experiments with a miniature shock tube using low pressures to simulate the effects of small scale have shown qualitative agreement with the proposed model. In fact, the effects of scale appear even more important than what has been incorporated in the model.PACS: 47.40.-xReceived: 14 November 2002, Accepted: 2 April 2003, Published online: 18 June 2003     

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.      

Shock waves in aviation security and safety

Accident investigations such as of Pan Am 103 and TWA 800 reveal the key role of shock-wave propagation in destroying the aircraft when an on-board explosion occurs. This paper surveys shock wave propagation inside an aircraft fuselage, caused either by a terrorist device or by accident, and provides some new experimental results. While aircraft-hardening research has been under way for more than a decade, no such experiments to date have used the crucial tool of high-speed optical imaging to visualize shock motion. Here, Penn State's Full-Scale Schlieren flow visualization facility yields the first shock-motion images in aviation security scenarios: 1) Explosions beneath full-size aircraft seats occupied by mannequins, 2) Explosions inside partially-filled luggage containers, and 3) Luggage-container explosions resulting in hull-holing. Both single-frame images and drum-camera movies are obtained. The implications of these results are discussed, though the overall topic must still be considered in its infancy. Received 22 July 2001 / Accepted 19 July 2002 Published online 4 November 2002 Correspondence to: G.S. Settles (e-mail: gss2@psu.edu) An abridged version of this paper was presented at the 23rd International Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001.     

A mesoscopic modelling approach for direct numerical simulations of transition to turbulence in hypersonic flow with transpiration cooling

A rescaling methodology is developed for high-fidelity, cost-efficient direct numerical simulations (DNS) of flow through porous media, modelled at mesoscopic scale, in a hypersonic freestream. The simulations consider a Mach 5 hypersonic flow over a flat plate with coolant injection from a porous layer with 42 % porosity. The porous layer is designed using a configuration studied in the literature, consisting of a staggered arrangement of cylinder/sphere elements. A characteristic Reynolds number ${\mathit{Re}}_c$ of the flow in a pore cell unit is first used to impose aerodynamic similarity between different porous layers with the same porosity, $∊$, but different pore size. A relation between the pressure drop and the Reynolds number is derived to allow a controlled rescaling of the pore size from the realistic micrometre scales to higher and more affordable scales. Results of simulations carried out for higher cylinder diameters, namely 24 μm, 48 μm and 96 μm, demonstrate that an equivalent Darcy-Forchheimer behaviour to the reference experimental microstructure is obtained at the different pore sizes. The approach of a porous layer with staggered spheres is applied to a 3D domain case of porous injection in the Darcy limit over a flat plate, to study the transition mechanism and the associated cooling performance, in comparison with a reference case of slot injection. Results of the direct numerical simulations show that porous injection in an unstable boundary layer leads to a more rapid transition process, compared to slot injection. On the other hand, the mixing of coolant within the boundary layer is enhanced in the porous injection case, both in the immediate outer region of the porous layer and in the turbulent region. This has the beneficial effect of increasing the cooling performance by reducing the temperature near the wall, which provides a higher cooling effectiveness, compared to the slot injection case, even with an earlier transition to turbulence.     

Numerical study of the oscillations induced by shock/shock interaction in hypersonic double-wedge flows

In this paper, the shock pattern oscillations induced by shock/shock interactions over double-wedge geometries in hypersonic flows were studied numerically by solving 2D inviscid Euler equations for a multi-species system. Laminar viscous effects were considered in some cases. Temperature-dependent thermodynamic properties were employed in the state and energy equations for consideration of the distinct change of the thermodynamic state. It was shown that the oscillation results in high-frequency fluctuations of heating and pressure loads over wedge surfaces. In a case with a relatively lower free-stream Mach number, the shock/shock interaction structure maintains a seven-shock configuration during the entire oscillation process. On the other hand, the oscillation is accompanied by a transition between a six-shock configuration (regular interaction) and a seven-shock configuration (Mach interaction) in a case with a higher free-stream Mach number. Numerical results also indicate that the critical wedge angle for the transition from a steady to an oscillation solution is higher compared to the corresponding value in earlier numerical research in which the perfect diatomic gas model was used.      

Nonequilibrium excitation of internal molecular degrees of freedom in the shock layer during hypersonic flight

A kinetic scheme of processes including the formation and quenching of electronically and vibrationally excited particles is proposed for the shock layer adjacent to the surface of a body flying at hypersonic speed. We present results of a numerical calculations for the stagnation point obtained under the thin viscous shock layer approximation for space shuttle flight conditions.We show that the release of atom recombination energy into the internal molecular degrees of freedom and the finite rate of relaxation reduce the calculated heat flux by 20 %.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.     

Behavior of shock trains in a hypersonic inlet/isolator model with complex background waves

The background flow field of a scramjet isolator that accommodates a shock train contains complex compression and expansion waves, referred as ??background waves,?? causing large streamwise and transverse parameter gradients upstream of the shock train. Therefore, the available results of shock train research obtained by direct-connect methods might be not applicable for real scramjet isolators. Special tests are therefore performed for an inlet/isolator model. Close coupling is found between the shock train and the background shocks. The pointing direction of the leading shock switches upwards and downwards repeatedly during the upstream propagation of the shock train. Three unstable stages with substantial oscillations are also observed, interlaced with four stable stages. In addition, the interference of the background shock waves increases the sustainable back-pressure ratio and decreases the length of the shock train. However, this does not mean that the background waves in the isolator should be intensified intentionally.     

Shock waves in an elliptical cavity with varying height

Transient shock waves in a confined elliptical chamber are experimentally investigated. Quantitative results of the pressure distribution are obtained for an air-filled cavity. Lower bounding surfaces of different geometrical shapes can be inserted making it possible to get chambers with varying height. An electrical discharge across a pair of electrodes inside the cavity gives rise to the shock waves. Double pulsed holographic interferometry is used to study the propagation and focusing process of the waves. The results are quantitatively evaluated by using the method of two-reference-beam holography. The angular pressure distribution behind the converging wave front is presented for different geometries of an air-filled cavity. The pressure distribution is non-homogeneous but symmetric along the wave front. The pressure level is higher for the geometry where the height of the chamber decreases with the radial distance from the outgoing focus and lower for increasing height of the chamber. In addition, shock waves in a water-filled cavity are studied. In this case qualitative results are obtained. Received 3 November 1996 / Accepted 5 January 1997     

Shock wave propagation in a branched duct

The propagation of a planar shock wave in a 90° branched duct is studied experimentally and numerically. It is shown that the interaction of the transmitted shock wave with the branching segment results in a complex, two-dimensional unsteady flow. Multiple shock wave reflections from the duct's walls cause weakening of transmitted waves and, at late times, an approach to an equilibrium, one-dimensional flow. While at most places along the branched duct walls calculated pressures are lower than that existing behind the original incident shock wave, at the branching segment's right corner, where a head on-collision between the transmitted wave and the corner is experienced, pressures that are significantly higher than those existing behind the original incident shock wave are encountered. The numerically evaluated pressures can be accepted with confidence, due to the very good agreement found between experimental and numerical results with respect to the geometry of the complex wave pattern observed inside the branched duct. Received 15 July 1996 / Accepted 20 February 1997     

Shock wave propagation into a surface depression

An aircraft travelling at supersonic speeds close to the ground generates a bow wave which is reflected off the ground surface. If a valley is traversed a complex reflection pattern will be generated. Similar patterns will evolve with a plane wave traversing a depression on a surface or structure. To simulate the process a planar shock wave, generated in a shock tube, is moved over several notched wedge configurations. Schlieren photographs were produced to assist in identifying the resulting complex three-dimensional wave structures and then verified and extended by three- dimensional computations. The valley geometries investigated are rectangular, triangular, parabolic and conical with a number of valley floor inclinations. The main features are extracted in surface models to demonstrate the complexity of the flow, and in particular in the case where the reflection is regular on the ground plane and Mach reflection in the valley.      

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     

Shock propagation along a two-layer interface in confined geometry

The paper presents direct numerical simulations of the propagation of a strong planar shock wave along a two-layer interface confined between two walls. Transient stage and steady state of the propagation are described. In the steady state regime, a stationary irregular refraction of the shock and a vorticity sheet are characterized. Physics of the stationary irregular refraction state is explained. Shock velocity is studied. Quantities are shown to verify a set of generalized Rankine–Hugoniot relations. The unknown coupling mechanism between shear layer and pressure step is predicted by a neural network which leads to a predictive, gray-box type model.     

An extension of CVDV model to Zeldovich exchange reactions for hypersonic non-equilibrium air flows

A new preferential vibration-dissociation-exchange reactions coupling model – labelled CVDEV – resulting from an extension of the well-known Treanor and Marrone CVDV model, has been derived to take into account the coupling between the vibrational excitation of the and molecules and the two Zeldovich exchange reactions. Analytical expressions for the exchange reactions coupling factor and for the average vibrational energy lost – or gained – by a molecule through an exchange reaction have been developed. The influence of such a coupling has been shown by means of numerical simulations of hypersonic air flows through normal and bow shock waves. Code-to-code comparisons between our model and other recent approaches have been conducted. The infrared radiation of nitric oxide behind a normal shock wave resulting from computations with the CVDEV model has been compared with other coupling model results and to recent shock tube experimental data. These comparisons have shown a good agreement of our model results with the experimental data. In this context, the results show the prominent influence of vibration coupling on the first Zeldovich reaction, and the absence of vibration coupling effects on the second Zeldovich reaction. Received 30 June 1997 / Accepted 3 December 1997     

Two-equation turbulence models for prediction of heat transfer on a transonic turbine blade

Two versions of the two-equation k–ω model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier–Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k–ω models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multi-block grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.     

Simulation of supersonic and hypersonic flows

A simple convection algorithm for simulation of time-dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well-known perfect gas flows.     

Vortex collapse and turbulence

Recent calculations related to the self-induced collapse of large-scale vortex structures into fine scale, possibly singular, structures in the Euler and Navier–Stokes equations are described. The practical importance of these intense events is their possible role in turbulence through the effects of strong intermittency and how that will direct turbulence modelling. Despite a concerted international effort to simulate these events over a decade ago, their dynamical origin remains largely unknown. A new international collaboration designed to push our understanding of the Euler singularity problem is described. These events are closely related to one of the outstanding mathematical questions of our time: whether solutions of the three-dimensional incompressible Navier–Stokes equations, lying in a bounded domain with finite energy and no external forcing, remain regular for arbitrarily long times (www.claymath.org/Millennium_Prize_Problems).     

Shock induced temperature in MgO,Ag, and Ta

From a system-independient formulation of the thermodynamics of high pressures, it is posible to predict the shock induced temperatures at a given shock compressed state. The formalism is applied, and results are presented in detailed form for magnesium oxide, silver and tantalum. Calculated values for pressure and temperature compare well with values estimated from radiation intensities recently reported by Svendsen and Ahrens for Ag and Ta. For MgO, however, strong discrepancies are found between values reported by these authors, and values calculated using our formalism. There is not apparent reason for this inconsistency.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.     

A theoretical computational model of a plate in hypersonic flow

A theoretical model of an elastic panel in hypersonic flow is derived to be used for design and analysis. The nonlinear von Kármán plate equations are coupled with 1st order Piston Theory and linearized at the nonlinear steady-state deformation due to static pressure differential and thermal loads. Eigenvalue analysis is applied to determine the system’s stability, natural frequencies and mode shapes. Numerically time marching the equations provides transient response prediction which can be used to estimate limit cycle oscillation amplitude, frequency and time to onset. The model’s predictive capability is assessed by comparison to an experiment conducted at a free stream flow of Mach 6. Good agreement is shown between the theoretical and experimental natural frequencies and mode shapes of the fluid–structure system. Stability analysis is performed using linear and nonlinear methods to plot stability, flutter and buckling zones on a free stream static pressure vs temperature differential plane.     

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