Evolution of blast wave profiles in simulated air blasts: experiment and computational modeling

Shock tubes have been extensively used in the study of blast traumatic brain injury due to increased incidence of blast-induced neurotrauma in Iraq and Afghanistan conflicts. One of the important aspects in these studies is how to best replicate the field conditions in the laboratory which relies on reproducing blast wave profiles. Evolution of the blast wave profiles along the length of the compression-driven air shock tube is studied using experiments and numerical simulations with emphasis on the shape and magnitude of pressure time profiles. In order to measure dynamic pressures of the blast, a series of sensors are mounted on a cylindrical specimen normal to the flow direction. Our results indicate that the blast wave loading is significantly different for locations inside and outside of the shock tube. Pressure profiles inside the shock tube follow the Friedlander waveform fairly well. Upon approaching exit of the shock tube, an expansion wave released from the shock tube edges significantly degrades the pressure profiles. For tests outside the shock tube, peak pressure and total impulse reduce drastically as we move away from the exit and majority of loading is in the form of subsonic jet wind. In addition, the planarity of the blast wave degrades as blast wave evolves three dimensionally. Numerical results visually and quantitatively confirm the presence of vortices, jet wind and three-dimensional expansion of the planar blast wave near the exit. Pressure profiles at 90° orientation show flow separation. When cylinder is placed inside, this flow separation is not sustained, but when placed outside the shock tube this flow separation is sustained which causes tensile loading on the sides of the cylinder. Friedlander waves formed due to field explosives in the intermediate-to far-field ranges are replicated in a narrow test region located deep inside the shock tube.     

High‐resolution p‐adaptive DG simulations of flows with moving shocks

High‐order accurate DG discretization is employed for Reynolds‐averaged Navier–Stokes equations modeling of complex shock‐dominated, unsteady flow generated by gas issuing from a shock tube nozzle. The DG finite element discretization framework is used for both the flow field and turbulence transport. Turbulent flow in the near wall regions and the flow field is modeled by the Spalart–Allmaras one‐equation model. The effect of rotation on turbulence modeling for shock‐dominated supersonic flows is considered for accurate resolution of the large coherent and vortical structures that are of interest in high‐speed combustion and supersonic flows. Implicit time marching methodologies are used to enable large time steps by avoiding the severe time step limitations imposed by the higher order DG discretizations and the source terms. Sufficiently high mesh density is used to enable crisp capturing of discontinuities. A p ? type refinement procedure is employed to accurately represent the vortical structures generated during the development of the flow. The computed solutions showed qualitative agreement with experiments. Copyright © 2014 John Wiley & Sons, Ltd.     

SPH simulation of oblique shocks in compressible flows

The Lagrangian smoothed particle hydrodynamics (SPH) method is used to simulate shock waves in inviscid, supersonic (compressible) flow. It is shown for the first time that the fully Lagrangian SPH particle method, without auxiliary grid, can be used to simulate shock waves in compressible flow. The wall boundary condition is treated with ghost particles combined with a suitable repulsive potential function, whilst corners are treated by a novel ‘angle sweep’ technique. The method gives accurate predictions of the flow field and of the shock angle as compared with the analytical solution. The study shows that SPH is a good potential candidate to solve complex aerodynamic problems, including those involving rarefied flows, such as atmospheric re‐entry. Copyright © 2016 John Wiley & Sons, Ltd.     

Simplified modeling of blast waves from metalized heterogeneous explosives

The detonation of a metalized explosive generates a complex multiphase flow field. Modeling the subsequent propagation of the blast front requires a detailed knowledge of the metal particle dynamics and reaction rate. Given the uncertainties in modeling these phenomena, a much simpler, 1D compressible flow model is used to illustrate the general effects of secondary energy release due to particle reaction on the blast front properties. If the total energy release is held constant, the blast pressure and impulse are primarily dependent on the following parameters: the proportion of secondary energy released due to afterburning, the rate of energy release, the location the secondary energy release begins, and the range over which it occurs. Releasing the total energy over a longer time period in general reduces the peak blast overpressure at a given distance. However, secondary energy release reduces the rate of decay of the shock pressure, increases the local gas temperature and hence increases the velocity of the secondary shock front. As a result, for certain values of the above parameters, the peak blast impulse may be increased by a factor of about two in a region near the charge. The largest augmentation to the near-field peak impulse results when the secondary energy is released immediately behind the shock front rather than uniformly within the combustion products.     

Numerical investigation of inviscid shock wave dynamics in an expansion tube

Highly complicated shock wave dynamics has been numerically calculated by solving the Euler equations for a circular shock tube suddenly expanded three times of the original tube diameter atx=0. Shock waves of different shock Mach number,M _s =1.5 and 2.0, have produced remarkably distinct blast jet structures. A planar shock wave took its final form after the blast by repeated Mach reflections of the blast wave: the first one at the wall and the second one at the central axis. The central Mach disc overtook and merged with the annular Mach stem before the planar shock wave was formed. In contrast to the blast wave which would propagate spherically in an open space, the present blast wave undergoes complex morphological transformation in the restricted flow passage, resulting in an unstable and oscillatory blast jet structure of highly rotational nature. The slipstream tube emanating from the shock tube exit corner decomposed into a chain of small vortex rings that interacted with the barrel shock of the jet, which caused periodic collapse of the jet structure. The finite volume-FCT formulation equipped with the time-dependenth-refinement adaptive unstructured triangular mesh technique in the present paper has contributed to resolution of the intricate physical discontinuities developing in the blast flow fields.     

纳米示踪平面激光散射技术在激波复杂流场测量中的应用

在激波以及激波边界层相互作用这类含激波的复杂流场中,流场结构具有明显的三维特征.研究这类流场,采用纹影、阴影和干涉等传统流动显示技术空间分辨率较低,难以分辨流场的三维特性.基于纳米示踪的平面激光散射技术(nano-tracer planar laser scattering,NPLS),是作者近年来开发的一种新的研究超声速流场的测试与显示技术,可对超声速复杂三维流场进行高时空分辨率流动显示与测量.NPLS技术的特点使其成为测量激波复杂流场的有力手段.近年来,作者以NPLS技术为主要手段,对航空航天领域典型的激波复杂流场进行了试验研究,包括超声速弹头绕流、超声速混合层、超声速边界层,以及激波边界层相互作用流场,显示出NPLS技术在激波复杂流场精细测试与流动显示中优势.本文简要介绍NPLS技术在激波复杂流场测量中应用的研究进展.      

Time-resolved stereo PIV measurements of shock–boundary layer interaction on a supercritical airfoil

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave–boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 × 10⁶ are analyzed regarding the origin and nature of the unsteady shock–boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa.     

Numerical study of spherical blast-wave propagation and reflection

The objective of this study is to understand the flow structures of weak and strong spherical blast waves either propagating in a free field or interacting with a flat plate. A 5th-order weighted essentially non-oscillatory scheme with a 4th-order Runge-Kutta method is employed to solve the compressible Euler/Navier-Stokes equations in a finite volume approach. The real-gas effects are taken into account when high temperature occurs. A shock-tube problem with the real-gas effect is first tested in order to verify the solver accuracy. Moreover, unsteady shock waves moving over a stationary wedge with various wedge angles, resulting in different types of shock wave reflections, are also tested. It is found that the computed results agreed well with the existing data. Second, the propagation of a weak spherical blast wave, created by rupture of a high-pressure isothermal sphere, in a free field is studied. It is found that there are three minor shock waves moving behind the main shock. Third, the problem of a strong blast wave interacting with a flat plate is investigated. The flow structures associated with single and double Mach reflections are reported in detail. It is found that there are at least three local high-pressure regions near the flat plate. Received 27 July 2000 / Accepted 25 January 2002 – Published online 17 June 2002     

The flow gradients in the vicinity of a shock wave for a thermodynamically imperfect gas

Supersonic rotational planar and axisymmetric flows of a non-viscous, non-heat-conductive gas with arbitrary thermodynamic properties in the vicinity of a steady shock wave are studied. The differential equations describing the gas flow upstream and downstream of the discontinuity surface and the dynamic compatibility conditions at this discontinuity are used. The gas flow non-uniformity in the shock vicinity is described by the spatial derivatives of the gasdynamic parameters at a point on the shock surface. The parameters are the gas pressure, density, and velocity vector. The derivatives with respect to the directions of the streamline and normal to it, and of the shock surface and normal to it, are considered. Spatial derivatives of all gasdynamic parameters are expressed through the flow non-isobaric factor along the streamline, the streamline curvature, and the flow vorticity and non-isoenthalpy factors. An algorithm for determining these factors of the gas flow downstream of a shock wave is developed. Example calculations of these factors for imperfect oxygen and thermodynamically perfect gas are presented. The influence coefficients of the upstream flow factors on the downstream flow factors are calculated. The gas flow in the vicinity of the shock is described by the isolines of gasdynamic parameters. Uniform planar and axisymmetric flows at different distances from the axis of symmetry are examined; the isobars, isopycnics, isotachs and isoclines are used to characterize the downstream flow behind a curved shock in an imperfect gas.     

Free-convection flow through an annular porous medium

This study addresses the Brinkman-extended Darcy model (Brinkman flow) of a laminar free-convective flow in an annular porous region. Closed form expressions for Velocity field, Temperature field, Skin-friction and Mass flow rate are given, under a thermal boundary condition of mixed kind at the outer surface of the inner cylinder while the inner surface of the outer cylinder is isothermal. The governing independent parameters are identified to be Darcy number (Da) and ratio of outer to inner radii (R). It is hoped that the study of such flows gives limiting conditions for developing flows and provides an analytical check on numerical solutions for more complex problems dealing with non-Darcian free-convection flow in an annular region.     

A study of blast wave loading on cantilevers

A study has been made of the response of elastic-plastic and brittle circular-cross-section cantilevers when subjected to blast wave loading. It is demonstrated how the deformation or failure of such cantilevers enables them to be used as blast wave gauges. In addition, the deformation of cantilever-type structures can be used to assess the characteristics of accidental explosions. Two numerical models have been developed to describe the deformation of a dynamically loaded cantilever. Both models assume that the plastic deformation is localized in a region near the fixed end, and that the loading force is a function of the dynamic-pressure time-history and a variable drag coefficient, which depends on the Reynolds number, Mach number and angle of attack of each discretized element of the cantilever. The first model assumes a rigid-plastic response of the cantilever. It was found that this model accurately described the response of cantilevers made of 50/50 lead/tin alloy. It overestimated the deformation of cantilevers made of more elastic materials when exposed to blast waves from high explosives and in a shock tube. The second model assumes an elastic-plastic response. The algorithm is based on the premise that the elastic curvature of the cantilever is limited by the plastic yield stress of the material and that as the curvature approaches this limit the cantilever rotates by the amount needed to keep the curvature constant and equal to this maximum. It has been shown that this algorithm minimizes the curvature of the cantilever at the base. This model provided good predictions of the deformation of cantilevers made of aluminum and steel. The numerical models were evaluated by studying the response of cantilevers exposed to shock waves in a shock tube, and to the blast waves from two explosions of ammonium-nitrate/fuel-oil charges of approximately 2.5 kt. The response to the shock tube flows was recorded by high speed photography which showed good agreement between the observed modes of deflection and those predicted by the elastic-plastic model. The models also provided good predictions of the deformation of a wide range of cantilevers, made of a variety of materials and of different diameters and lengths, when exposed to the free field blast waves. It is demonstrated how the numerical models can be used to determine the type of cantilever that might be used as a gauge for monitoring the blast wave from an explosion, or for evaluating the deformation of a cantilever exposed to the blast wave from an accidental explosion so as to characterize the explosion. Received 23 September 1996 / Accepted 11 November 1996     

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.     

Numerical simulation of 1-D unsteady two-phase flows with shocks

In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the fiow parameters for the gas antiparticle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.     

Characteristics of unsteady type IV shock/shock interaction

Characteristics of the unsteady type IV shock/shock interaction of hypersonic blunt body flows are investigated by solving the Navier–Stokes equations with high-order numerical methods. The intrinsic relations of flow structures to shear, compression, and heating processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous surface-heating peak is caused by the fluid in the “hot spot” generated by an oscillating and deforming jet bow shock (JBS) just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer interaction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the interaction of the JBS and the shear layers formed by a supersonic impinging jet, and then the interaction of the freestream bow shocks and the compression waves results in entropy and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of the flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.     

流场非均匀性对非平面激波诱导的Richtmyer-Meshkov不稳定性影响的数值研究

基于Navier-Stokes方程组,采用可压缩多介质黏性流动和湍流大涡模拟程序MVFT (multi-viscousflow and turbulence),模拟了均匀流场与初始密度呈现高斯函数分布的非均匀流场中马赫数为1.25的非平面激波加载初始扰动air/SF6界面的Richtmyer-Meshkov (RM)不稳定性现象。数值模拟结果表明,初始流场非均匀性将会影响非平面激波诱导的RM不稳定性演化过程。反射激波加载前,非平面激波导致的界面扰动振幅随着流场非均匀性增强而增大;反射激波加载后,非均匀流场与均匀流场条件下的界面扰动振幅差异有所减小。进一步,定量分析流场中环量分布及脉动速度统计量揭示了前述规律的原因。此外,还与平面激波诱导的RM不稳定性进行了简单对比,发现由于非平面激波波阵面区域的涡量与激波冲击界面时产生的涡量的共同作用,使得非平面激波与平面激波诱导的界面失稳过程存在差异。     

Research of influence of reduced-order boundary on accuracy and solution of interior points

The flow field with a high order scheme is usually calculated so as to solve complex flow problems and describe the flow structure accurately.However,there are two problems,i.e.,the reduced-order boundary is inevitable and the order of the scheme at the discontinuous shock wave contained in the flow field as the supersonic flow field is low.It is questionable whether the reduced-order boundary and the low-order scheme at the shock wave have an effect on the numerical solution and accuracy of the flow field inside.In this paper,according to the actual situation of the direct numerical simulation of the flow field,two model equations with the exact solutions are solved,which are steady and unsteady,respectively,to study the question with a high order scheme at the interior of the domain and the reduced-order method at the boundary and center of the domain.Comparing with the exact solutions,it is found that the effect of reduced-order exists and cannot be ignored.In addition,the other two model equations with the exact solutions,which are often used in fluid mechanics,are also studied with the same process for the reduced-order problem.     

Numerical simulation of flow fields induced by a supersonic projectile moving in tubes

Numerical study of the shocked flows generated by a supersonic projectile released from a launch tube into a big chamber has been performed in this paper. Based on fixed Cartesian grids, the two-dimensional axisymmetric Euler equations are solved by the fifth-order WENO scheme implemented with moving boundary conditions. Both the level set technique and ghost fluid method are used for capturing the moving interface of the projectile implicitly. The numerical results show that complex shock phenomena exist in the transient shock flow, resulting from shock-wave reflection, shock-wave focusing, shock-wave/projectile interaction and shock-wave/contact surface interactions. The relationships between the acceleration of the projectile and the transient shock flow are also discussed in detail.     

Three-dimensional effects on regular reflection in steady supersonic flows

The reflection of shock waves between two symmetrical wedges is investigated for the case of three-dimensional flows. Oblique shadowgraphs at various optical angles of yaw and pitch were used to examine the nature of fully three-dimensional flows, with wedge aspect ratios as low as 0.25 being considered. These images were used to construct surface models of the overall flow field for various reflection patterns and aspect ratios, which provides a visual indication of the flow field shape. For a Mach number of 3.1, and suitable wedge angles, the flow field with regular reflection on the tunnel centreline and Mach reflection further out is examined. The point of transition from regular reflection to the peripheral Mach surfaces is identified for various wedge angles and aspect ratios. It is shown that the transition points move outwards from the central plane as the aspect ratio decreases. This shows that three-dimensional flows favor regular reflection, because of the increasing curvature of the incident shock as the wedge becomes narrower, causing a decrease in the local angle of incidence. The height of the Mach stem is shown to be highly dependent on the geometry of the test wedge models. The Mach stem height decreases with aspect ratio due to the three-dimensional relieving effect, where the increase in lateral flow relieves the pressure over the surfaces of the wedges. Experimental evidence of the existence of the strong oblique shock solution in steady flows is presented.Received: 7 July 2003, Revised: 20 October 2003, Accepted: 6 November 2003, Published online: 10 February 2004PACS: 47.40.Nm Correspondence to: B.W. Skews     

Pressure-based method for combustion instability analysis

An improved pressure-based method has been applied to predict the two-dimensional instability analysis of liquid-fuelled rocket engines. This method is non-iterative for transient flow calculations and applicable to all-speed flows. Validation cases include the shock-tube problem, the blast flow field and unsteady spraycombusting flows. Computations for the combustion instability analysis were carried out for various combustion parameters such as spray initial conditions and combustor geometries. Unsteady behaviours of the stable and unstable spray flame fields and effects of acoustic oscillations on the fuel droplet vaporization and combustion process are studied in detail. The present numerical model successfully demonstrates the capability of predicting combustion instability as well as fast transient compressible flows at all speeds.