ALBERT

Description: 〈h3〉Abstract〈/h3〉 〈p〉In this study, a less-dissipative hybrid AUSMD scheme considering the linearized approximated solution around the material interfaces of compressible multi-component flows is proposed. A high-resolution reconstruction scheme, so-called MUSCL + THINC, has been devised by combining the MUSCL method with the Tangent of Hyperbola for Interface Capturing technique (THINC) under the boundary variation diminishing concept, which is used to determine the cell-interface values to evaluate the AUSMD flux. Several perfect gas and multi-component flow problems are selected as the benchmark test cases. The flow models we use here are the perfect gas Euler equations and the multi-phase five-equation flow model. We compared the proposed MUSCL + THINC-type AUSMD scheme with the original MUSCL-type AUSMD scheme to verify its capability of capturing shock waves, expansion fans, and material interfaces, which are identified as a well-defined sharp jump in volume fraction. Numerical results of all benchmark tests show that the MUSCL + THINC-type AUSMD solver is superior to the original MUSCL-type AUSMD in resolving shock waves, expansion fans, and interfaces. In particular, the solution quality for expansion fans and interfaces on coarse grids is greatly improved by the MUSCL + THINC-type AUSMD scheme. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉SLAU2 and AUSMPW〈span〉 〈span〉\(+\)〈/span〉 〈/span〉, both categorized as AUSM-type Riemann solvers, have been extensively developed in gasdynamics. They are based on a splitting of the numerical flux into advected and pressure parts. In this paper, these two Riemann solvers have been extended to magnetohydrodynamics (MHD). The SLAU2 Riemann solver has the favorable attribute that its dissipation for low-speed flows scales as 〈span〉 〈span〉\(O(M^{2})\)〈/span〉 〈/span〉, where 〈em〉M〈/em〉 is the Mach number. This is the physical scaling required for low-speed flows, and the dissipation in SLAU2 for MHD is engineered to have this low Mach number scaling. The AUSMPW〈span〉 〈span〉\(+\)〈/span〉 〈/span〉, when its pressure flux is replaced with that of SLAU2, has the same low Mach number scaling. At higher Mach numbers, however, the pressure-split Riemann solvers were found not to function well for some MHD Riemann problems, despite the fact that they were engineered to have a dissipation that scales as 〈span〉 〈span〉\(O(\vert M\vert )\)〈/span〉 〈/span〉 for high Mach number flows. The HLLI Riemann solver (Dumbser and Balsara in J Comput Phys 304:275–319, 〈span〉2016〈/span〉) has a dissipation that scales as 〈span〉 〈span〉\(O(\vert M\vert )\)〈/span〉 〈/span〉, which makes it unsuitable for low Mach number flows. However, it has very favorable performance for higher Mach number MHD flows. Since the two families of Riemann solvers perform very well over a range of intermediate Mach numbers, the best way to benefit from the mutually complementary strengths of both these Riemann solvers is to hybridize between them. The result is an all-speed Riemann solver for MHD. We, therefore, document hybridized SLAU2–HLLI and AUSMPW〈span〉 〈span〉\(+\)〈/span〉 〈/span〉–HLLI Riemann solvers. The hybrid Riemann solvers suppress the oscillations that appeared in single-solver solutions, and they also preserve contact discontinuities, as well as Alfvén waves, very well. Furthermore, their better resolution at low speeds has been demonstrated. We also present several stringent one-dimensional test problems.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The HLLC (Harten–Lax–van Leer contact) approximate Riemann solver for computing solutions to hyperbolic systems by means of finite volume and discontinuous Galerkin methods is reviewed. HLLC was designed, as early as 1992, as an improvement to the classical HLL (Harten–Lax–van Leer) Riemann solver of Harten, Lax, and van Leer to solve systems with three or more characteristic fields, in order to avoid the excessive numerical dissipation of HLL for intermediate characteristic fields. Such numerical dissipation is particularly evident for slowly moving intermediate linear waves and for long evolution times. High-order accurate numerical methods can, to some extent, compensate for this shortcoming of HLL, but it is a costly remedy and for stationary or nearly stationary intermediate waves such compensation is very difficult to achieve in practice. It is therefore best to resolve the problem radically, at the first-order level, by choosing an appropriate numerical flux. The present paper is a review of the HLLC scheme, starting from some historical notes, going on to a description of the algorithm as applied to some typical hyperbolic systems, and ending with an overview of some of the most significant developments and applications in the last 25 years.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Presented are results from a parametric investigation of wind-tunnel test-section configurations with a goal of stabilization of normal-shock-wave structure. The test section includes a two-flow-passage arrangement, where each passage is separated by a shock-wave-holding plate. The top wall for the top passage is contoured relative to the streamwise-flow direction, and a choking flap is located at the downstream portion of the bottom flow passage. Altered are the streamwise and spanwise positions of the shock-wave-holding plate, angle of the choking flap, and amount of venting. Of interest are shadowgraph flow visualization images, grayscale spectral energy variations, and integrated grayscale spectral energy levels. Higher static-pressure ratio downstream of the shock wave (caused by higher choking-flap angle, lower shock-wave-holding-plate position, and less venting) is associated with greater shock-wave-standoff distance (relative to the shock-wave-holding plate) and decreased flow unsteadiness. The most optimal arrangement includes a stabilized normal shock wave and lambda foot, which are largely two dimensional over the shadowgraph visualization volume.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Experiments have been conducted in a supersonic rectangular duct (Mach 1.4), with a normal shock wave/boundary layer interaction. The duct is designed in a modular fashion so that its aspect ratio can be varied without a change in the flow geometry. The shock location, duct height, and Mach number are kept constant, while varying the aspect ratio. Conventional and inclined schlieren techniques have been used to visualize the normal shock. The height and width of the “normal part” of the normal shock have been measured. A parameter termed 〈em〉area fraction of the normal shock〈/em〉 is used to quantify the extent of shock bifurcation, and the effect of the duct aspect ratio on this parameter is studied. It has been found that a nearly square duct is the preferred geometry for maximizing the 〈em〉area fraction of the normal shock.〈/em〉〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉It is well known that hypersonic boundary-layer transition is sensitive to a surface roughness since the roughness may either trigger an early transition or delay the transition. Hypersonic transition is still poorly understood as there are a very limited number of studies in the literature. In the present work, we conduct a computational study on the transition process of a hypersonic Mach 6 flow over a flat plate with a gap. An implicit large eddy simulation approach based on the flux reconstruction/correction procedure via a reconstruction method is used to investigate the interaction between the hypersonic boundary layer and a gap. Flow structures with and without the gap are compared to analyze the local skin friction coefficient overshoots before and after the gap. Two inlet angles of attack are investigated. The evolution of the skin friction coefficient shows that the gap has a very limited influence on the oblique transition at a zero angle of attack. In contrast, the gap can trigger an early transition at a negative angle of attack. In this case, the transverse feedback mechanism is believed to be the main cause, which amplifies the broadband instability waves.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Regimes of continuous spin detonation and continuous multifront detonation in a hydrogen–oxygen mixture are obtained in a plane-radial combustor with an inner diameter of 100 mm and exhaustion toward the periphery. The fuel-lean limits of detonation in terms of the specific flow rate of the mixture are determined. For continuous spin detonation, transverse detonation waves and the flow in their vicinity in the combustor plane are reconstructed. The detonation wave is found to be significantly curved because of the increase in the tangential component of the velocity along the combustor radius. It is demonstrated that the scale effect is manifested only in the number of rotating waves. However, their velocity increases with increasing the combustor size. The velocity deficit of continuous detonation is 20–40% as compared to the velocity of the ideal Chapman–Jouguet detonation. (The smaller value corresponds to the fuel-lean mixture.) 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The Hydrogen Unconfined Combustion Test Apparatus (HUCTA) was designed and built to study the blast waves produced from unconfined hydrogen/oxygen deflagrations. The HUCTA uses evacuated balloons of up to 2 m in diameter which are filled with a combustible combination of gaseous hydrogen–oxygen mixtures. The well-mixed gases are ignited with an electric spark at the center of the sphere, resulting in a gaseous deflagration propagating through the mixture and a shock wave produced in the air. The combinations of balloon size and fuel/oxidizer ratios allow for a wide range of blast waves to be produced. Overpressures are measured with standard blast gauges at a variety of locations, demonstrating a high degree of radial symmetry and repeatability in the shock wave pressures, as well as the ability to produce non-ideal shock wave pressure profiles under some conditions. The range of peak pressures and explosive impulses obtainable is described as a function of mixture ratio. High-speed retroreflective shadowgraphy is used to visualize shock wave propagation and coalescence in individual frames and digital streak images. Since HUCTA is elevated approximately 2 m off the ground, there is a significant area around the apparatus where non-noisy, un-reflected, symmetric blast waves propagate; this area is ideal for testing items whose response to blast waves is desired for safety considerations.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Projectile accelerations above 〈span〉 〈span〉\(500~\hbox {ms}^{-2}\)〈/span〉 〈/span〉 are commonly encountered in aerodynamic applications, but suitable validation data are rare in this regime. Experimental transonic velocity range data for a sphere decelerating under its own drag have been used to validate a numerical model for decelerating objects. The validated model is then used to explore the flow field ahead of objects decelerating from supersonic to subsonic Mach numbers. To model the non-inertial frame of the projectile, source terms were included in the momentum and energy equations in a computational fluid dynamics model. In decelerating cases, the bow shock formed in supersonic flight persists in the subsonic regime. The differences in the flow field between the steady and unsteady cases are explained using the concept of flow history. In the experiment, a tubular insert was present near the observation window in the ballistic range. The insert was numerically modelled, and it is shown that the resulting bow shock behaviour can be explained in terms of the Kantrowitz criterion, in conjunction with flow history. The RAE2822 aerofoil was used to explore the effects of shock overtaking and propagation during deceleration from supersonic to low subsonic Mach numbers. In this case, the bow shock wave persists from the initial supersonic speed to projectile Mach numbers lower than 0.4. The expansion wave and tail shock are shown to overtake the decelerating projectile and propagate forward, behind the bow shock.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Although several mechanisms have been suggested as explanations for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions, questions remain on causes and effects. In this effort, we examine the observed asymmetry in large-scale shock motions to highlight which of the suggested mechanisms is most consistent with shock-speed observations and accompanying separation dynamics. The analysis is based on a flowfield obtained from a validated large eddy simulation of a fully separated interaction. A statistical analysis is used to determine the speed of bubble collapse relative to dilation. The low-pass filtering required to separate upstream from downstream motions in the presence of higher-frequency jitter is accomplished with a relatively new technique, empirical mode decomposition, that is very appropriate for this purpose. The dynamics of bubble dilation versus collapse are then elaborated with conditional dynamic mode decomposition (DMD) analyses on the respective pressure fields. Bubble breathing is shown to have a different structure during dilation than during collapse—larger structures are observed during collapse when fluid is expelled from the bubble. The nature of the DMD mode associated with Kelvin–Helmholtz (K–H) shedding in the mixing layer also differs between dilation and collapse: When the bubble is dilating, the structures at the dominant K–H frequency are larger than when the bubble is collapsing. Additionally, a link is established between the convecting K–H structures and corrugation observed along the reflected shock. Some aspects of the nature of the asymmetry are linked to the ease of eddy formation (K–H structures), which plays an important role in the collapse of the bubble.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Detonation velocity as a function of charge diameter is reported for Alliant Bullseye powder. Results are compared to those of mixtures of ammonium nitrate mixed with aluminum and ammonium nitrate mixed with fuel oil. Additionally, measurements of free surface velocity of flyers in contact with detonating Bullseye are presented and results are compared to those of hydrocode calculations using a Jones–Wilkins–Lee equation of state generated in a thermochemical code. Comparison to the experimental results shows that both the free surface and terminal velocities were under-predicted. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Experimental investigations and numerical simulations of normal shock waves of different strengths propagating inside ducts with roughness are presented. The roughness is added in the form of grooves. Straight and branching ducts are considered in order to better explore the mechanisms causing attenuation of the shock and the physics behind the evolution of the complex wave patterns resulting from diffraction and reflection of the primary moving shock. A well-established finite-volume numerical method is used and further validated for several test cases relevant to this study. The computed results are compared with experimental measurements in ducts with grooves. Good agreement between high-resolution simulations and the experiment is obtained for the shock speeds and complex wave patterns created by the grooves. High-frequency response time histories of pressure at various locations were recorded in the experiments. The recorded pressure histories and shock strengths were found in fair agreement with the two-dimensional simulation results as long as the shock stays in the duct. Overall, the physics of the interactions of the moving shock and the diffracted and reflected waves with the grooves are adequately captured in the high-resolution simulations. Therefore, shocks propagating in ducts with different groove geometries have been simulated in order to identify the groove shape that diminishes shock strength.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The constrained reaction volume (CRV) method for shock-tube experiments makes it possible to conduct chemical kinetics studies at nearly constant pressure while inhibiting remote ignition. The application of end-wall imaging revealed, however, that CRV experiments are susceptible to vertical stratification at the interface of the test and buffer gases. This work identifies gravity currents as the mechanism leading to the test gas stratification, providing both a theoretical development and experimental investigation of their behavior in a shock tube. Parametric studies are conducted with both the gate valve and stage-filled CRV methods using a novel beam-split laser absorption diagnostic. The speed of gravity-current-induced mixing in both gate valve and stage-filled CRV experiments is shown to depend on the molecular weight matching of the gases and the fill pressure. Mixing velocity in gate valve experiments is shown not to depend on the gate valve speed. In stage-filled experiments, mixing time is seen to be a strong function of the test gas length. Recommended practices for avoiding gravity-current-induced mixing and stratification are described, including gas density matching, utilizing double diaphragms, increasing test gas length in stage-filled experiments, and implementing a gas interface diagnostic.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉To further refine the existing high-temperature combustion chemistry mechanisms of Sarin surrogates or to develop new ones, the ignition delay times of mixtures containing various Sarin surrogates have been studied in the authors’ laboratory, namely dimethyl-methylphosphonate, diethyl-methylphosphonate (DEMP), and triethylphosphate, and the results are compared for the first time herein. They were each measured in a heated shock tube, with the DEMP-related ignition delay times being the new data reported in this paper. The Sarin surrogates were studied in neat mixtures with oxygen or seeded to baseline mixtures of hydrogen or methane at around 1.5 atm. Noticeable differences were observed between the ignition delay times of the three simulants, whether sole or mixed with a fuel. Comparisons of OH* time histories obtained from each surrogate highlight the similarities and differences in chemical structure among the different compounds. In mixtures with oxygen and Ar, the three surrogates present similar ignition delay times below 1380 K, whereas the ignition delay time results rapidly diverge above this temperature. When the surrogates were added into 〈span〉 〈span〉\(\hbox {H}_{2}/\hbox {O}_{2}\)〈/span〉 〈/span〉 or 〈span〉 〈span〉\(\hbox {CH}_{4}/\hbox {O}_{2}\)〈/span〉 〈/span〉 mixtures, large changes in the reactivity of the mixtures were observed. These changes in reactivity are however dependent on the surrogate, for each fuel investigated.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉This paper investigates the structure of a normal shock wave using the continuum model for steady one-dimensional flow of a viscous non-ideal gas under heat conduction. The coefficients of viscosity and heat conductivity are assumed to be directly proportional to a power of the temperature. The simplified van der Waals equation of state for the non-ideal gas has been assumed in this work. The smooth and rough sphere models of the gas molecules in the kinetic theory of gases are used for the viscosity of a non-ideal gas. Assuming the Prandtl number to be 3 / 4, the complete integral of the energy equation, exact velocity, density, pressure, Mach number, change in entropy, viscous stress, and heat flux across the shock transition zone have been obtained in a perfect and a non-ideal gas under both constant and variable properties of the medium. The validity of the continuum hypothesis with respect to Mach number is examined for the study of shock wave structure in both the smooth and rough sphere models of ideal and non-ideal gas molecules. It has been shown that the continuum theory gives reasonably valid results for flows with higher Mach numbers in the case of a non-ideal gas in comparison with an ideal gas. The inverse thickness of the shock wave is calculated and compared for constant and variable properties of the gases. The shock wave thickness is also discussed as a function of mean free path of the gas molecules computed at different points between the boundary states. It is found that the inverse shock thickness decreases with the increase in non-idealness of the gas. In the rough sphere model of gas molecules, the increase in the non-idealness of the gas and the temperature exponent in the coefficients of viscosity and heat conductivity significantly increases the validity limit of the continuum model.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The use of conjugate circular arcs in rocket nozzle contour design has been investigated by numerically comparing three existing sub-scale nozzles to a range of equivalent arc-based contour designs. Three performance measures were considered when comparing nozzle designs: thrust coefficient, nozzle exit wall pressure, and a transition between flow separation regimes during the engine start-up phase. In each case, an equivalent arc-based contour produced an increase in the thrust coefficient and exit wall pressure of up to 0.4 and 40% respectively, in addition to suppressing the transition between a free and restricted shock separation regime. A general approach to arc-based nozzle contour design has also been presented to outline a rapid and repeatable process for generating sub-scale arc-based contours with an exit Mach number of 3.8–5.4 and a length between 60 and 100% of a 15〈span〉 〈span〉\(^{\circ }\)〈/span〉 〈/span〉 conical nozzle. The findings suggest that conjugate circular arcs may represent a viable approach for producing sub-scale rocket nozzle contours, and that a further investigation is warranted between arc-based and existing full-scale rocket nozzles.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉A time delay is created between elastic and plastic wave fronts because of the difference between the elastic longitudinal sound speed and the plastic shock wave velocity. Over a short propagation distance, the time delay between the elastic and plastic wave fronts at the Hugoniot elastic limit (HEL) is nonlinear, while at larger distances, the time delay is linear. In this work, a new time delay model is introduced that is based on the distance traveled by the waves and using the Rayleigh–Hugoniot jump relations for elastic–perfectly plastic materials. The results of the model have shown in FCC metals the subsonic shock velocity is due to the reduction of shear stress in an unsteady wave being greater than the one in the steady wave. The reduction of the plastic shock wave speed and formation of the elastic shock at the moment of impact are found to result in the nonlinear relationship of the lag between elastic and plastic wave fronts. For calculating the nonlinear time delay in a relaxing material, the lower HEL must be used; the elastic shock is important when the difference between the longitudinal elastic sound speed and the plastic shock wave speed is very small or when the ratio of the HEL to the applied stress is high. In BCC metals, V, Cr, and W, a different behavior has been observed which is in contrast to FCC metals, Ag, Al, and Cu. Therefore, the different behavior is due to a different mechanism that occurs in BCC metals.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉 The present study focuses on the long-term behavior of low-enthalpy 〈em〉M〈/em〉 = 7 flows over double wedges that have a fixed fore angle of 30° and aft angles ranging from 45° to 60°. Although there are numerical and experimental studies available in the literature, they mostly consider the short-term behavior of such flows. In one of those studies, Durna et al. (Phys. Fluids 28:096101, 〈span〉2016〈/span〉) foresee the presence of an aft angle threshold for transition from steady flow to complex shock–boundary layer interactions. The present study investigates the presence of periodicity by performing computations up to 50 times the duration of the previous study. Our analyses show that beyond a threshold value of 47°, the flows become time-periodic. We are able to describe complex interaction mechanisms of the periodic flow by utilizing the density gradients, shock locations, separation angle, and distributions of the pressure and heat flux over the wedge surfaces. The computational results show that as the aft angle is increased, the period of the flow shortens, and the duration, when the transmitted shock impinges on the wedge surface, decreases.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉This paper is aimed at finding the primary cause and mechanisms of flow structure rearrangement (stable/unstable) behind the front of strong shock waves (SW) in gases. Results of experimental and calculated investigations of strong shock waves in atomic gases obtained by the authors of this work and other researchers for the last several decades are analyzed. A unique analytical approach, referred to by the authors as the source of electrons method, is used, which makes it possible to determine the relationship between the kinetic processes of ionization of particles and the energy exchange in a non-equilibrium flow (avalanche ionization region) behind a shock wave in argon in a wide range of flow conditions: 〈em〉M〈/em〉 = 10–30, pressure ahead of the shock wave front 〈em〉p〈/em〉〈sub〉1〈/sub〉 = 1–25 torr. In addition to the basic processes, the following additional mechanisms are considered: (a) associative ionization in interatomic collisions with participation of highly excited atoms, (b) integral radiation losses, (c) convective energy transfer, and (d) electrons heating in the polarization electric field. It is found that the primary cause of flow structure instability in shock waves is the presence of flow boundaries responsible for (i) weak gas-dynamic perturbations and (ii) local (near-wall) inhomogeneity of the medium ahead of the shock wave front and behind it. The mechanism of structural instability of the shock wave in atomic gases at low Mach numbers is caused by a cardinal change in the relationship of the basic and additional kinetic and energy exchange processes between the ionized flow components behind the front, even in the case of a weak perturbation of the atomic–ionic component temperature. In the range of high Mach numbers, the instability mechanism is due to the thermal effect induced by wall and near-wall gas layers heating ahead of the SW front by precursor radiation and also due to possible energy release initiated by polarization of the electric field near the wall behind the shock wave front.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉This work describes a theoretical study on shock wave modification by the electrical discharge generated with a DC voltage. Weakly ionized and high-density assumptions for nonthermal plasma were examined to demonstrate heat and momentum transfer contributions in supersonic flow control. The momentum equation for the plasma electrons and ions was considered to evaluate the changes in the incident flow velocity by the plasma. The change in the incident flow temperature was studied by applying source terms arising from a weakly ionized and high-density plasma to the energy equation. It was concluded that the momentum transfer from a nonthermal plasma into the incoming supersonic flow was responsible for the increasing shock wave angle. On the other hand, a nonthermal plasma with a remarkably high ionization degree increases the incident flow temperature drastically, while a weakly ionized plasma has a negligible effect on flow temperature. Our numerical results show that the electric field distribution has a significant role in the plasma flow control mechanisms, suggesting a new tailoring parameter via cathode geometry. The results of this work are in good agreement with respective experimental validation data and can be used in plasma-based shock wave control apparatus.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉We present a numerical analysis of the shock–bubble interaction with uncertainty in bubble density. We considered a bubble with density uncertainty with a Gaussian distribution, of which effects on the flow structures are analyzed using a stochastic collocation method. The uncertainty is modeled by polynomial chaos, and the effects of the uncertainty are evaluated from the simulation results that are associated with the quadrature points of the bubble density with random fluctuations. Specifically, we focus on the impact of the density uncertainty in a bubble on the flow structures over the entire computational domain. The statistics of the density field, such as mean and standard variance, are investigated. The analysis reveals that the uncertainty of bubble density affects different flow structures with different significance, which provides a global sensitivity map for the whole solution domain. Efforts have been also made to quantify the uncertainties in the motions of different waves and fronts. It is observed that the velocities of different waves/fronts exhibit large differences in the response to the bubble-density uncertainty, which is in accordance with the existing experimental and numerical studies.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉A series of six, large-scale tests were performed at the Eglin Air Force Base blastpad facility to serve as a validation benchmark for the explosive dispersal of particles. The series contained two baseline tests, one tungsten liner test, and three steel liner tests. Careful emphasis was placed on design of the experiments to allow ease of simulation, uncertainty quantification of experimental inputs, and extraction of prediction metrics. Design decisions, such as using a casing that is negligible to the flow, serve to greatly reduce the computational effort to perform validation. Attention is also paid to quantifying uncertainty in experimental inputs such as explosive density, particle size distribution, particle density, volume fraction, and ambient conditions. For each test, data were collected from four high-speed cameras, 54 inground pressure transducers, and eight unconfined momentum traps. From these diagnostics, prediction metrics are extracted measuring the shock time of arrival, peak pressure, impulse per unit area, and the contact/particle front position. The high-speed video shows significant differences between the steel and tungsten liners. The tungsten particles were incandescent as they dispersed and concentrated in a bright, dense band followed by alternating bright and dark striations. There was little to no incandescence in the dispersed steel particles. The steel liner tests exhibited instabilities with fine fingers racing ahead of the front. The instabilities, however, were so numerous that they are not easily distinguishable from each other, preventing their characterization.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉A class of high-order nonlinear filter schemes by Yee et al. (J Comput Phys 150:199–238, 1999), Sjögreen and Yee (J Comput Phys 225:910–934, 2007), and Kotov et al. (Commun Comput Phys 19:273–300, 2016; J Comput Phys 307:189–202, 2016) is examined for long-time integrations of computational aeroacoustics (CAA) turbulence applications. This class of schemes was designed for an improved nonlinear stability and accuracy for long-time integration of compressible direct numerical simulation and large eddy simulation computations for both shock-free turbulence and turbulence with shocks. They are based on the skew-symmetric splitting version of the high-order central base scheme in conjunction with adaptive low-dissipation control via a nonlinear filter step to help with stability and accuracy capturing at shock-free regions as well as in the vicinity of discontinuities. The central dispersion-relation-preserving schemes as well as classical central schemes of arbitrary orders fit into the framework of skew-symmetric splitting of the inviscid flux derivatives. Numerical experiments on CAA turbulence test cases are validated. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉To gather test data of the nonequilibrium flow in CO〈sub〉2〈/sub〉 and investigate the influence of the two-temperature nonequilibrium model on numerical simulations, measurements of shock standoff distances over hypersonic spheres in CO〈sub〉2〈/sub〉 have been taken in the hypervelocity ballistic ranges of the Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center. Corresponding numerical simulations using the two-temperature model were also performed. The measurements were made for spheres with diameters of 10 mm and 20 mm, flight velocities between 2.122 and 4.220 km/s, and ambient pressures between 2.42 and 14.74 kPa. Test flow fields were visualized by the shadowgraphy for the measurement of shock standoff distances. The shock standoff distances generally decrease as 〈em〉ρR〈/em〉 (freestream density × radius of the model, namely the binary scaling parameter) increases. The flow is mainly nonequilibrium when 〈em〉ρR〈/em〉 is of the order of 10〈sup〉−4〈/sup〉 kg/m〈sup〉2〈/sup〉, and the two-temperature nonequilibrium model is applicable for the calculation of the flow field under such conditions. When 〈em〉ρR〈/em〉 increases to the order of 10〈sup〉−3〈/sup〉 kg/m〈sup〉2〈/sup〉, the flow approaches the equilibrium state.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉In this study, free-flight tests of a sphere for Reynolds numbers between 3.9 × 10〈sup〉3〈/sup〉 and 3.8 × 10〈sup〉5〈/sup〉 and free-flight Mach numbers between 0.9 and 1.6 were conducted using a ballistic range, and compressible low-Reynolds-number flows over an isolated sphere were investigated with the schlieren technique. The flow visualization was carried out under low-pressure conditions with a small sphere (minimum diameter of 1.5 mm) to produce compressible low-Reynolds-number flow. Also, time-averaged images of the flow near the sphere were obtained and compared to previous numerical results for Reynolds numbers between 50 and 1000. The experimental results clarified the structure of shock waves, recirculation region, and wake structures at the Reynolds number of 10〈sup〉3〈/sup〉–10〈sup〉5〈/sup〉 under transonic and supersonic flows. As a result, the following characteristics were clarified: (1) the amplitude of the wake oscillation was attenuated as the free-flight Mach number increased; (2) use of singular value decomposition permitted extraction of the mode of the wake structure even when schlieren images were unclear due to severe condition, and different modes in the wake structure were identified; (3) the Reynolds number had little effect on the separation point, but the length of the recirculation region increased as the Reynolds number decreased; and (4) the wake diameter at the end of the recirculation region decreased as the Mach number increased.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Shock waves are used to treat musculoskeletal injuries and trigger the body’s mechanisms to initiate healing; however, the cellular and molecular working mechanisms are not fully known. Raman spectroscopy may be a useful tool to provide information on structural changes. Solid collagen type I from rat tail (〉 90% pure) was suspended in water and was exposed in vitro to different numbers of shock waves and energy flux densities. Raman spectra were recorded at 2 h, 1 week, and 3 weeks after shock-wave treatment. The spectral analysis indicated that varying the number of shock waves and the energy flux density induced molecular changes in the collagen structure. Varying the energy flux density induced more significant changes than modifying the number of shock waves; however, in most cases, the collagen recovered its original conformation 3 weeks after treatment. A significant decrease in the relative intensities of the conformational bands, which include amide I, amide III, and stretching C–C, was observed at different energy flux densities. In many clinical cases, the natural repair of tissue is improved after shock-wave treatment. Raman spectroscopy revealed that varying the energy flux density of the shock waves applied to rat collagen type I induced strong conformational molecular changes. Approximately 2–3 weeks after shock-wave treatment, a phase of “molecular ordering” tending to a “recovering molecular sequence repair” was observed.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The propagation of a planar shock wave through a split channel is both experimentally and numerically studied. Experiments were conducted in a square cross-sectional shock tube having a main channel which splits into two symmetric secondary channels, for three different shock wave Mach numbers ranging from about 1.1 to 1.7. High-speed schlieren visualizations were used along with pressure measurements to analyze the main physical mechanisms that govern shock wave diffraction. It is shown that the flow behind the transmitted shock wave through the bifurcation resulted in a highly two-dimensional unsteady and non-uniform flow accompanied with significant pressure loss. In parallel, numerical simulations based on the solution of the Euler equations with a second-order Godunov scheme confirmed the experimental results with good agreement. Finally, a parametric study was carried out using numerical analysis where the angular displacement of the two channels that define the bifurcation was changed from 〈span〉 〈span〉\(90^{\circ }\)〈/span〉 〈/span〉, 〈span〉 〈span〉\(45^{\circ }\)〈/span〉 〈/span〉, 〈span〉 〈span〉\(20^{\circ }\)〈/span〉 〈/span〉, and 〈span〉 〈span〉\(0^{\circ }\)〈/span〉 〈/span〉. We found that the angular displacement does not significantly affect the overpressure experience in either of the two channels and that the area of the expansion region is the important variable affecting overpressure, the effect being, in the present case, a decrease of almost one half.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉This paper presents experimental data on incident overpressures and the corresponding impulses obtained in the test section of an explosively driven 〈span〉 〈span〉\(10^\circ \)〈/span〉 〈/span〉 (full angle) conical shock tube. Due to the shock tube’s steel walls approximating the boundary conditions seen by a spherical sector cut out of a detonating sphere of energetic material, a 5.3-g pentolite shock tube driver charge produces peak overpressures corresponding to a free-field detonation from an 816-g sphere of pentolite. The four test section geometries investigated in this paper (open air, cylindrical, 〈span〉 〈span〉\(10^\circ \)〈/span〉 〈/span〉 inscribed square frustum, and 〈span〉 〈span〉\(10^\circ \)〈/span〉 〈/span〉 circumscribed square frustum) provide a variety of different time histories for the incident overpressures and impulses, with a circumscribed square frustum yielding the best approximation of the estimated blast environment that would have been produced by a free-field detonation.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉In this study, an intensive simulation platform is developed and implemented to simulate the three stages in the operational cycle of the liquid-fueled pulse detonation engine. The three stages encompass the liquid fuel injection and evaporation process, deflagration-to-detonation transition process, and detonation propagation process. The Lagrangian–Eulerian approaches are employed to model the discrete liquid fuel droplets and the continuous vapor phase, respectively. The breakup and evaporation of liquid droplets are modeled using sub-models, while the interactions between the liquid droplets and the vapor phase are expressed through the two-way interaction models. The Jet-A liquid fuel is injected into the detonation chamber as the fuel for the engine, while the air flow is used as the oxidizer. A reduced chemical kinetic model of fuel/air is used to model the combustion process. The simulation platform is systematically validated against the experimental data for every stage of the operating cycle. To study the influence of the inlet and operating conditions, the numerical simulations are performed for three different operating conditions, which are the change in inlet air temperature, the change in inlet air flow velocity, and the change in liquid fuel mass flow rate. The obtained results indicate that the mass fraction of pre-vaporization of fuel plays an important role in the successful DDT process and/or detonation onset. The deflagration can successfully transit to detonation for both the cases of complete and incomplete vaporization of the liquid droplets inside the detonation chamber. The deflagration cannot successfully transit to detonation for the case of too lean or too rich fuel vapor in the mixture. The calculated burning temperature and Chapman–Jouguet (C–J) detonation velocity are slightly lower in the cases of the incomplete vaporization when compared to the complete vaporization cases. In addition, our numerical results show that the burning process occurs in two stages in the incomplete vaporization case: The first burning stage plays a main role in the successful DDT process, while the second burning stage only plays the role of augmentation.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Accurate measurement of ignition delay in a shock tube is extremely important for developing chemical mechanisms of different fuels. In ideal shock-tube experiments, the test gas behind the reflected shock is expected to ignite uniformly. However, in practical shock-tube experiments, non-uniform ignition occurs due to different factors such as boundary layer growth and boundary layer–reflected shock interaction. Such non-uniform ignition greatly complicates the interpretation of measurements and affects the accuracy of ignition delay measurement. Even without boundary layer and multi-dimensional effects, non-uniform ignition can still happen since the reflected shock itself can induce the spatial gradient of ignition delay. This was first studied numerically by Melguizo-Gavilanes and Bauwens (Shock Waves 23(3):221–231, 〈span〉2013〈/span〉) using a simplified three-step chemical mechanism. They found that non-uniform ignition can greatly affect the determination of ignition delay in a shock tube. As an extension of Melguizo-Gavilanes and Bauwens’ work, in the present study we conduct simulations considering detailed chemistry for two fuels, hydrogen and n-heptane, without and with low-temperature chemistry. Moreover, the detonation development for different mixtures is interpreted through comparing the local sound speed and reaction front propagation speed. The ignition delay recorded at different positions away from the end wall is compared to that in a homogeneous system. A large deviation in ignition delay is observed. The deviation is shown to change linearly with the distance away from the end wall, and a correlation is proposed to accurately describe such deviations. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The effects of jet temperature on acoustic waves generated by a supersonic jet are investigated using large eddy simulation (LES) based on a high-fidelity computational code. The sixth-order compact scheme and the fourth-order Runge–Kutta scheme are employed for spatial derivatives and time integration, respectively. First, a verification and validation study is conducted using simulations of a cold supersonic jet with a jet Mach number of 2.0 and Reynolds number of 〈span〉 〈span〉\(9.0 \times 10^5\)〈/span〉 〈/span〉, and the effects of grid resolution and disturbance strength are evaluated. The verification and validation study shows that 〈span〉 〈span〉\(6.5 \times 10^8\)〈/span〉 〈/span〉 grid points are sufficient for qualitative discussion of acoustic wave generation phenomena and that the addition of disturbances is important for suppressing the acoustic waves caused by the turbulent transition at the nozzle exit, as seen in previous studies for a subsonic jet. Then, LESs of supersonic jets with a jet Mach number of 2.0 and Reynolds number of 〈span〉 〈span〉\(9.0 \times 10^5\)〈/span〉 〈/span〉 are performed for three temperature cases where the ratios of chamber to atmospheric temperature are 1.0, 2.7, and 4.0. The present results illustrate that different jet temperatures do not change the shear layer thickness, but the shear layer develops more inside the jet as the jet temperature increases, resulting in a shorter potential core for the hot jet. With regard to the acoustic fields, as the jet temperature increases, stronger Mach waves are emitted from a wider source region at wider radiation angles. We observe multiple Mach waves with different angles in the hot jet cases.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉An Eulerian approach for simulations of wave propagation in multiphase, viscoelastic media is developed in the context of the Advection Upstream Splitting Method (AUSM). We extend the AUSM scheme to the five-equation model for simulations of interfaces between gases, liquids, and solids with constitutive relations appropriately transported. In this framework, the solid’s deformations are assumed to be infinitesimally small such that they can be modeled using linear viscoelastic models, e.g., generalized Zener. The Eulerian framework addresses the challenge of calculating strains, more naturally expressed in a Lagrangian framework, by using a hypoelastic model that takes an objective Lie derivative of the constitutive relation to transform strains into velocity gradients. Our approach introduces elastic stresses in the convective fluxes that are treated by generalizing AUSM flux-vector splitting (FVS) to account for the Cauchy stress tensor. We determine an appropriate discretization of non-conservative equations that appear in the five-equation multiphase model with AUSM schemes to prevent spurious oscillations at material interfaces. The framework’s spatial scheme is solution adaptive with a discontinuity sensor discriminating between smooth and discontinuous regions. The smooth regions are computed using explicit high-order central differences. At discontinuous regions (i.e., shocks, material interfaces, and contact surfaces), the convective fluxes are treated using a high-order Weighted Essentially Non-Oscillatory (WENO) scheme with 〈span〉 〈span〉\(\hbox {AUSM}^+\)〈/span〉 〈/span〉-up for upwinding. The framework is used to simulate one-dimensional (1D) and two-dimensional (2D) problems that demonstrate the ability to maintain equilibrium interfacial conditions and solve challenging multi-dimensional and multi-material problems.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉An enhanced 〈span〉 〈span〉\(\hbox {AUSM}^+\)〈/span〉 〈/span〉-up scheme is presented for high-speed compressible two-phase flows using a six-equation two-fluid single-pressure model. Based on the observation that the 〈span〉 〈span〉\(\hbox {AUSM}^+\)〈/span〉 〈/span〉-up flux function does not take into account relative velocity between the two phases and thus is not stable and robust for computation of two-phase flows involving interaction of strong shock waves and material interfaces, the enhancement is in the form of a volume fraction coupling term and a modification of the velocity diffusion term, both proportional to the relative velocity between the two phases. These modifications in the flux function obviate the need to employ the exact Riemann solver, leading to a significantly less expensive yet robust flux scheme. Furthermore, the Tangent of Hyperbola for INterface Capturing (THINC) scheme is used in order to provide a sharp resolution for material interfaces. A number of benchmark test cases are presented to assess the performance and robustness of the enhanced 〈span〉 〈span〉\(\hbox {AUSM}^+\)〈/span〉 〈/span〉-up scheme for compressible two-phase flows on hybrid unstructured grids. The numerical experiments demonstrate that the enhanced 〈span〉 〈span〉\(\hbox {AUSM}^+\)〈/span〉 〈/span〉-up scheme along with THINC scheme can efficiently compute high-speed two-fluid flows such as shock–bubble interactions, while accurately capturing material interfaces.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉This paper is written in honor and memory of my esteemed friend and colleague, Meng-Sing Liou, with whom I worked closely in the 1990s on the development of AUSM-family schemes and their extensions to reactive, “all-speed,” and multi-phase flows. The purpose of this paper is to revisit the thought processes and concepts that led to the rapid evolution of the AUSM family as a highly efficient, highly accurate method for discretization of the Euler equations and their various extensions. No new results are presented; rather, the focus is on (re-)discovering the common threads that link the various members of the AUSM family. Special attention is given to the strategies that lead to accurate results at all flow speeds, and some reviews of more current work in this area are presented. The paper concludes with a few reflections, personal and otherwise, relating to my interactions with Meng over the years and to my view of the essential elements of AUSM-family schemes. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below 〈span〉 〈span〉\(M=10^{-5}\)〈/span〉 〈/span〉, which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the 〈span〉 〈span〉\({\mathrm{AUSM}}^{+}\)〈/span〉 〈/span〉-up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉In this paper, the AUSM〈sup〉+〈/sup〉-up scheme is compared to other numerical flux schemes in the framework of a RANS/URANS code for turbomachinery applications. The considered advection schemes include central discretizations with artificial dissipation and the Roe upwind scheme. The comparison is carried out by studying a low-aspect-ratio turbine cascade over a wide range of expansion ratios that encompasses almost incompressible up to supersonic flow conditions. It is found that the dissipation scaling associated with the AUSM〈sup〉+〈/sup〉-up scheme was effective over the whole range of analysed flow conditions. A detailed assessment with the aid of the available measurements will be exploited to show how the AUSM〈sup〉+〈/sup〉-up is capable of a detailed and faithful reproduction of secondary flow features, with accuracy comparable to that of the Roe scheme and superior to that of central schemes.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉A series of three-dimensional, unsteady simulations have been conducted to illuminate the behavior of annular gaseous injectors that are frequently used in rotating detonation engine combustors. The strength (detonation overpressure history) and number of detonation waves in the combustor are investigated as operational parameters along with the injector design (area ratio and length) to assess the impact on the unsteady response of the injection system to the imposed detonation model. Attenuation of the imposed overpressure and reflection off the assumed mass flow inlet boundary are features that are highlighted. The unsteady flow at the exit of the injector as a result of these interactions is found to fluctuate by 〈span〉 〈span〉\(+\)〈/span〉 〈/span〉 80 to − 200%. Strong wave attenuation in the near-exit region of the injector is observed, but acoustic perturbations are seen to propagate throughout the injector, which along with the corresponding reflections persist during the transient injection.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉A sharp interface method has been developed for treating interfacial discontinuities in compressible multi-phase fluids on three-dimensional Cartesian cut-cell grids. The evolution of the interfacial discontinuities in the Cartesian grid is captured by the level-set method. The intersections between interfacial fronts and Cartesian grids are interpolated using level-set function values at the vertices of Cartesian grids. Triangular surfaces are then constructed on the interfacial fronts. A novel cell merge method is used for complex topological changes. Jump conditions across discontinuous interfaces are enforced by reconstruction of interfacial flow variables using a constrained least-squares method. The inviscid flux across internal faces of the same fluid is calculated by the local Lax–Friedrichs flux. Manufactured solutions for interfaces are suggested for validation of the reconstruction method. Laplace’s law test results show that the present method drastically reduces the parasite currents compared to conventional interface treatment methods. Bubble rise problems also show the validity and accuracy of the proposed sharp interface method for immiscible two-phase fluids. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉A semi-analytical model is presented for predicting the trajectory of the transverse detonation during the re-initiation process of a diffracted cellular detonation wave from a channel. Numerical simulations based on the two-dimensional reactive Euler equations with a detailed hydrogen/oxygen chemistry model were first performed to observe key characteristics of cellular detonation wave diffraction and to obtain required input parameters for the model construction. The present numerical observations indicate that the transverse detonation stems from a location on the expansion wave front, and the horizontal distance from this initial location to the channel exit can be scaled by a constant multiplied by the detonation cell width for large deviation angles of the channel. The velocity of the transverse detonation basically equals the Chapman–Jouguet detonation wave velocity consisting of two orthogonal components: the expansion velocity of the diffracted wave front and the relative velocity to the diffracted wave front. The shape of the decoupled wave front is not affected by local explosion and thus can be predicted by the Chester–Chisnell–Whitham theory. Based on these numerical observations and the Chester–Chisnell–Whitham theory, a semi-analytical model is constructed to predict the wave trajectories as well as the distances of the wall reflection point for various deviation angles and initial pressures. The model prediction agrees with the corresponding numerical results. The model result shows that the distance of the wall reflection point varies from 15 to 20 multiples of the cell width with a minimal dependence on deviation angle, independent of the initial pressure. The trajectory calculated by the model is self-similar and determined by the horizontal distance of the initial location. The dimensionless trajectories divided by the horizontal distance are coincident for different initial pressures. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Evolution of a single-mode interface triggered by a cylindrically converging shock in a V-shaped geometry is investigated numerically using an adaptive multi-phase solver. Several physical mechanisms, including the Bell–Plesset (BP) effect, the Rayleigh–Taylor (RT) effect, the nonlinearity, and the compressibility are found to be pronounced in the converging environment. Generally, the BP and nonlinear effects play an important role at early stages, while the RT effect and the compressibility dominate the late-stage evolution. Four sinusoidal interfaces with different initial amplitudes (〈span〉 〈span〉\(a_\mathrm {0}\)〈/span〉 〈/span〉) and wavelengths (〈span〉 〈span〉\(\lambda \)〈/span〉 〈/span〉) are found to evolve differently in the converging geometry. For the very small 〈span〉 〈span〉\(a_\mathrm {0}\)〈/span〉 〈/span〉/〈span〉 〈span〉\(\lambda \)〈/span〉 〈/span〉 interfaces, nonlinearity is negligible at the early stages and the sole presence of the BP effect results in an increasing growth rate, confining the linear growth of the instability to a relatively small amount of time. For the moderately small 〈span〉 〈span〉\(a_\mathrm {0}\)〈/span〉 〈/span〉/〈span〉 〈span〉\(\lambda \)〈/span〉 〈/span〉 cases, the BP and nonlinear effects, which, respectively, promote and inhibit the perturbation development, coexist in the early stage. The counterbalancing effects between them produce a very long period of growth that is linear in time, even to a moment when the amplitude over wavelength ratio approaches 0.6. The RT stabilization effect at late stages due to the interface deceleration significantly inhibits the perturbation growth, which can be reasonably predicted by a modified Bell model.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The transient shock dynamics and drag characteristics of a projectile flying through a pipe 3.55 times larger than its diameter at transonic speed are analyzed by means of time-of-flight and pipe wall pressure measurements as well as computational fluid dynamics (CFD). In addition, free-flight drag of the 4.5-mm-pellet-type projectile was also measured in a Mach number range between 0.5 and 1.5, providing a means for comparison against in-pipe data and CFD. The flow is categorized into five typical regimes the in-pipe projectile experiences. When projectile speed and hence compressibility effects are low, the presence of the pipe has little influence on the drag. Between Mach 0.5 and 0.8, there is a strong drag increase due to the presence of the pipe, however, up to a value of about two times the free-flight drag. This is exactly where the nose-to-base pressure ratio of the projectile becomes critical for locally sonic speed, allowing the drag to be estimated by equations describing choked flow through a converging–diverging nozzle. For even higher projectile Mach numbers, the drag coefficient decreases again, to a value slightly below the free-flight drag at Mach 1.5. This behavior is explained by a velocity-independent base pressure coefficient in the pipe, as opposed to base pressure decreasing with velocity in free flight. The drag calculated by CFD simulations agreed largely with the measurements within their experimental uncertainty, with some discrepancies remaining for free-flying projectiles at supersonic speed. Wall pressure measurements as well as measured speeds of both leading and trailing shocks caused by the projectile in the pipe also agreed well with CFD.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Computational fluid dynamics analysis is required to accurately reconstruct the test flows produced by expansion tube wind tunnel facilities. These simulations must resolve complex transient wave processes, viscous, and high-temperature gas effects, and need to time-accurately track these processes for the entire duration of the experiment. The result is that simulations become computationally expensive and challenging, and even when best practise is applied, it is usually not possible to fully reconcile simulation results with the limited available experimental diagnostic data. Furthermore, shot-to-shot variation between experiments means that the actual test flow will, to varying degrees, differ between experiments, yet it is not practical to recompute CFD simulations on a shot-by-shot basis. This paper proposes a methodology to correct CFD-calculated test flow properties to address both of these issues, using readily measured experimental diagnostics which are blind to the facility internal flow processes. The methodology is assessed using simulated experiments with a one-dimensional impulse facility simulation code, taking into account unsteady longitudinal wave processes and high-temperature gas effects. It is shown to correctly adjust a range of baseline test flows to account for the effects of simulated shot-to-shot variation.〈/p〉

Description: 〈p〉In the original article publication, Equation no. 2 is incorrectly published. The correct equation is:〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Particle-resolved 3-D inviscid simulations of a planar shock interacting with a bed of randomly distributed spherical particles are carried out. The aim of this study is to investigate the importance of flowfield fluctuations caused by a random distribution of particles during shock–particle interaction. We present the volume-averaged governing equations. The volume-averaging process results in the appearance of the Reynolds stress term in the momentum equation, and similar terms also arise in the energy equation. These terms are generally neglected in the Euler–Lagrange or the Euler–Euler simulations of shock–particle interaction, and hence, the motivation for this study is to determine the importance of these stresses. The spatiotemporal evolution of the flow inside the particle bed is studied by presenting the mean and the fluctuating flow properties. We compute the RMS velocity, the magnitude of pseudo-turbulent Reynolds stress, and the magnitude of fluctuations in the pressure and total energy. We compare our results with previous studies involving shock interaction with a curtain of cylindrical particles. It is found that the strength of the fluctuating field is much weaker for the spherical particle case compared with the cylindrical particle case. Our results are also in good agreement with the recent study on a planar shock interacting with a random bed of spherical particles under viscous conditions. 〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Most numerical schemes for solving high-speed compressible flow problems exhibit an instability that usually occurs inside the numerical shock structure in low-dissipative shock-capturing finite volume methods. In examining several test cases, the flux-difference splitting and the AUSM family of schemes cannot satisfy the robustness requirement, which manifests as the carbuncle phenomenon on two-dimensional triangular grids. This paper presents an accurate and robust AUSM-family scheme (〈span〉 〈span〉\(\hbox {AUSMDV}^+\)〈/span〉 〈/span〉 scheme) that is verified against shock-induced anomalies on two-dimensional triangular grids. The linearized discrete analysis of an odd–even decoupling problem is applied to investigate the perturbation damping mechanism of these schemes. The corresponding recursive equations show that the 〈span〉 〈span〉\(\hbox {AUSMDV}^+\)〈/span〉 〈/span〉 scheme is less sensitive to these anomalies than are other schemes in the AUSM family. Finally, the presented scheme is extended to achieve second-order solution accuracy. Its robustness and efficiency are then evaluated on both structured and unstructured triangular grids. The 〈span〉 〈span〉\(\hbox {AUSMDV}^+\)〈/span〉 〈/span〉 scheme yields a physically meaningful solution for all test cases without introducing an additional shock fix technique.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Despite their simple formulations, advection upstream splitting method (AUSM)-type flux schemes treat linear and nonlinear waves of complex flow fields in a robust and accurate manner. This paper presents the progress of AUSM-type fluxes augmented with pressure-based weight functions introduced by the authors and their colleagues. Starting from a flux designed for single-phase gas dynamics (AUSMPW+), its extensions to capture multi-phase flow physics with phase transition (AUSMPW+_N) have been carried out. The accuracy of the computed results by the AUSMPW+_N scheme for multi-phase flows is then further improved by introducing a simple phase interface-sharpening procedure, which scales the volume fraction in a mass-conserving manner. Various all-speed compressible tests ranging from interactions between a shock and phase interfaces, two- and three-dimensional interface-only problems, to a cryogenic three-component flow with phase change are computed to demonstrate the effectiveness of the proposed method.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Shock-induced plasticity in FCC crystals has been demonstrated in many experimental and numerical simulation studies. Even though some theories have been proposed with regard to dislocation nucleation, the phenomenon occurring in the elastically shock-compressed region and the elastic–plastic transition region, which might be the origin region for dislocation nucleation, is largely unexplored. In this work, we present a molecular dynamics simulation of the shock compression of a Cu single crystal along the 〈110〉 direction specifically focusing on the mechanisms observed in the elastically compressed and the elastic–plastic transition regions. A distribution of planes of high and low atomic volume is observed in the elastically compressed region near the shock front, but the distribution becomes random as the elastic–plastic transition regime is approached. Density variations are also observed. It is observed that the formation of the defects initiates through local atomic shuffling/rearrangement. Shear stress distribution shows values greater than those required for homogeneous nucleation, and Shockley partials are observed at a certain region behind the shock front. Potential energy variations are also observed in these regions, explaining the mechanisms leading to dislocation nucleation. The present findings shed new insight into the mechanism of dislocation nucleation in shock-induced single-crystal FCC metals.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉For stoichiometric C〈sub〉2〈/sub〉H〈sub〉4〈/sub〉–O〈sub〉2〈/sub〉 and C〈sub〉2〈/sub〉H〈sub〉2〈/sub〉–O〈sub〉2〈/sub〉 mixtures with or without argon dilution, the processes of detonation diffraction have been investigated in a two-dimensional setup through high-speed schlieren imaging, with the characteristic length and the stability of detonation varied by regulating the initial pressure and argon mole fraction of the mixture. In particular, a length relevant to the process of supercritical diffraction (i.e., distance from the channel end corner to reflection point of the transverse detonation on the channel end face, reflection point distance in short) was deduced from obtained sequential schlieren images and analyzed. The reflection point distance can be idealized for the infinitely wide donor channel, and thus, it can be a parameter in which properties intrinsic to each detonable mixture are manifested. Experimental results showed that the reflection point distance was roughly inversely proportional to the initial pressure for identical mixtures and independent of the width of the donor channel at high initial pressures. For a certain combination of the fuel and oxidizer, correlations between the reflection point distance and the initial partial pressure of fuel were very similar regardless of the argon mole fraction. Critical conditions of the diffraction problem could be given for the ratio of the reflection point distance to the channel width, and it was suggested that the critical value lies in a range of 3–5 and does not significantly depend on the stability of the mixture.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉A series of compaction experiments was conducted to evaluate the mechanical, reactive, and deflagration-to-detonation transition behavior in Alliant Bullseye powder. Using a novel application of photonic Doppler velocimetry and light fibers, the experiments measured both compaction and combustion waves in porous beds of Bullseye subjected to impact by gun-driven pistons. Relationships between initial piston velocity and transition distance are shown. Comparison is made between the Bullseye response and that found in classic Type I DDT.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉Recently, we experimentally studied, in a shock tube environment, shock waves propagating over horizontal free water layers having depths of 10, 20, and 30 mm for shock wave Mach numbers 〈span〉 〈span〉\(M_\mathrm {is}\)〈/span〉 〈/span〉 equal to 1.1 and 1.4. The qualitative interaction process was observed by means of high-speed visualizations, and the pressures arising in the air and in the water layer were measured and interpreted in terms of the various incident and refracted shock waves in air and water; in particular, it was concluded that the compression wave in the water is driven by the planar shock wave in the air. Additional experiments have been conducted and the novel contributions of the present technical note are quantitative results regarding the liquid-surface entrainment. At low Mach number (〈span〉 〈span〉\(M_\mathrm {is}=1.1\)〈/span〉 〈/span〉), we show that the velocity of the droplets ejected into the air is independent of the water depth, unlike the wavelength of initial ripples and the angle of ejection. When the shock wave strength increases (〈span〉 〈span〉\(M_\mathrm {is}=1.4\)〈/span〉 〈/span〉), the dispersion of a very thin droplet mist and a single large wave take place. We show that the thickening of the water mist and the velocity of the subsequent large wave decreases with the water-layer depth.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The interaction of a weak shock wave with a heavy elliptic gas cylinder is investigated by solving the Eulerian equations in two-dimensional Cartesian coordinates. An interface-capturing algorithm based on the 〈span〉 〈span〉\(\gamma \)〈/span〉 〈/span〉-model and the finite volume weighed essential non-oscillatory scheme is employed to trace the motion of the discontinuous interface. Three gas pairs with different Atwood numbers ranging from 0.21 to 0.91 are considered, including carbon dioxide cylinder in air (air–〈span〉 〈span〉\(\hbox {CO}_2\)〈/span〉 〈/span〉), sulfur hexafluoride cylinder in air (air–〈span〉 〈span〉\(\hbox {SF}_6\)〈/span〉 〈/span〉), and krypton cylinder in helium (He–Kr). For each gas pair, the elliptic cylinder aspect ratio ranging from 1/4 to 4 is defined as the ratio of streamwise axis length to spanwise axis length. Special attention is given to the aspect ratio effects on wave patterns and circulation. With decreasing aspect ratio, the wave patterns in the interaction are summarized as transmitted shock reflection, regular interaction, and transmitted shock splitting. Based on the scaling law model of Samtaney and Zabusky (J Fluid Mech 269:45–78, 〈span〉1994〈/span〉), a theoretical approach is developed for predicting the circulation at the time when the fastest shock wave reaches the leeward pole of the gas cylinder (i.e., the primary deposited circulation). For both prolate (i.e., the minor axis of the ellipse is along the streamwise direction) and oblate (i.e., the minor axis of the ellipse is along the spanwise direction) cases, the proposed approach is found to estimate the primary deposited circulation favorably.〈/p〉

Description: 〈h3〉Abstract〈/h3〉 〈p〉The use of complex multi-parameter equations of state in computational fluid dynamics is limited due to their expensive evaluation. Tabulation methods help to overcome this limitation. We propose in this work a tabulation approach for real equations of state that is also suitable for multi-component flows and multi-phase flows with phase transition based on the homogeneous equilibrium method. The tabulation method is based on piecewise polynomials and allows adaptive refinement in state space, a local variation of the degree of the polynomials and even cut-cells to represent saturation lines. A detailed analysis of the benefits of the chosen tabulation approach is provided showing results of benchmark problems for nitrogen under sub- and trans-critical conditions. The tables are used in numerical simulations based on the finite volume approach. To provide reference solutions, an exact Riemann solver is constructed for the tabulated real EOS. Several numerical flux calculations based on approximate Riemann solutions and flux vector splitting approaches are modified for the tabulated equation of state. Besides the comparison for benchmark problems, two applications are depicted, a shock–bubble interaction and an injection of a trans-critical jet, which demonstrate the applicability of this approach to more complex flow simulations.〈/p〉