Showing papers on "Shock wave published in 2023"

Direct numerical simulation of supersonic internal flow in a model scramjet combustor under a non-reactive condition

Abstract: A Mach 1.5 non-reactive flow in a cavity-stabilized combustor of a model scramjet is studied via a direct-numerical simulation approach, and the analysis is focused on the interaction among boundary layer, free shear-layer above the cavity and shock wave. It is found that the impingement of the free shear-layer on the aft wall of the cavity leads to strong turbulence kinetic energy, high local pressure, and a fan of compression waves. The compression waves evolve into an oblique shock, which reflects between the upper and lower walls and interacts with the boundary layers attached to the two walls. The analysis of the turbulence production reveals that the amplification of turbulence in the core of the shear-layer and around the reattachment point is mainly due to the shear production, but the deceleration production mechanism presents a significant impact in the regions above the aft wall of the cavity and around the shock interaction points. The very low frequency commonly observed in shock wave/boundary layer interactions is not observed in the present research, which might be due to the low Reynolds number of the studied case.

Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration

Abstract: The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave equation using the new extended direct algebraic method. As a result, the soliton patterns of the Riemann wave equation have been successfully illustrated, with exact solutions offered by the plane solution, trigonometry solution, mixed hyperbolic solution, mixed periodic and periodic solutions, shock solution, mixed singular solution, mixed trigonometric solution, mixed shock single solution, complex soliton shock solution, singular solution, and shock wave solutions. Graphical visualization is provided of the results with suitable values of the involved parameters by Mathematica. It was visualized that the velocity of the soliton and the wave number controls the behavior of the soliton. We are confident that our research will assist physicists in predicting new notions in mathematical physics.

Modeling acoustic emissions and shock formation of cavitation bubbles

Abstract: Despite significant progress in understanding and foretelling pressure-driven bubble dynamics, models that faithfully predict the emitted acoustic waves and the associated shock formation of oscillating or collapsing bubbles have received comparably little attention. We propose a numerical framework using a Lagrangian wave tracking approach to model the acoustic emissions of pressure-driven bubbles based on the Kirkwood–Bethe hypothesis and under the assumption of spherical symmetry. This modeling approach is agnostic to the equation of the state of the liquid and enables the accurate prediction of pressure and velocity in the vicinity of pressure-driven bubbles, including the formation and attenuation of shock fronts. We validate and test this new numerical framework by comparison with solutions of the full Navier–Stokes equations and by considering a laser-induced cavitation bubble as well as pressure-driven microbubbles in excitation regimes relevant to sonoluminescence and medical ultrasound, including different equations of state for the liquid. A detailed analysis of the bubble-induced flow field as a function of the radial coordinate r demonstrates that the flow velocity u is dominated by acoustic contributions during a strong bubble collapse and, hence, decays predominantly with [Formula: see text], contrary to the frequently postulated decay with [Formula: see text] in an incompressible fluid.

The Riemann problem for a traffic flow model

Abstract: A traffic flow model describing the formation and dynamics of traffic jams was introduced by Berthelin et al. [5], which consists of a pressureless gas dynamics system under a maximal constraint on the density and can be derived from the Aw-Rascle model under the constraint condition $\rho\leq\rho^*$ by letting the traffic pressure vanish. In this paper, we give up this constraint condition and consider the following form $$ \left\{\begin{array}{ll}\rho_t+(\rho u)_x=0,\(\rho u+\varepsilon p(\rho))_t+(\rho u^2+\varepsilon up(\rho))_x=0,\end{array}\right .\eqno{} $$ in which $p(\rho)=-\frac{1}{\rho} . $ The Riemann problem for the above traffic flow model are solved constructively. The delta shock wave arises in the Riemann solutions, although the system is strictly hyperbolic, its first eigenvalue is genuinely nonlinear and the second eigenvalue is linearly degenerate. Furthermore, we clarify the generalized Rankine-Hugoniot relations and $\delta$-entropy condition. The position, strength and propagation speed of the delta shock wave are obtained from the generalized Rankine-Hugoniot conditions. The delta shock may be useful for the description of the serious traffic jam. More importantly, it is proved that the limits of the Riemann solutions of the above traffic flow model are exactly those of the pressureless gas dynamics system with the same Riemann initial data as the traffic pressure vanishes.

Numerical study of the mechanisms of the longitudinal pulsed detonation in two-dimensional rotating detonation combustors

Abstract: A numerical study of the longitudinal pulsed detonation (LPD) is conducted in the present paper. The occurrence mechanism of the LPD, called shock wave amplification by coherent energy release (SWACER) is verified preliminarily in this study. To be specific, upstream propagating shock waves, which originate from the outlet, induce a specific gradient of reactant distribution and then detonation waves are ignited and evolve along the gradient in close succession. It is worth noting that the occurrence of LPD does not mean that the LPD will necessarily be sustained. The low injection pressure ratio PR (i.e. the ratio of inlet pressure to outlet pressure) = 1.3 is found to be conducive to the sustenance of the LPD instability in the baseline model. A lower PR (PR {less than or equal to} 1.2) or a slightly higher PR (1.4 {less than or equal to} PR {less than or equal to} 1.8) shall lead to an unstable detonation or a quenching of detonations, while a much higher PR (PR > 1.8) contributes to the formation of stable canonical rotating detonation waves. In addition, the combustion regimes of five combustors of different heights at different PR are explored. As the combustion chamber height increases, the PR of the sustainable LPD is nearly linearly increasing and its operating frequency decreases gradually. The calculation formula between the sustainable LPD propagating frequency and natural acoustic resonance frequency of the combustor is employed and discussed, but in consideration of its imperfection further investigation is required.

Numerical simulation of carbon separation with shock waves and phase change in supersonic separators

Abstract: The current study evaluated a potential carbon separation method. Based on engineering thermodynamics, heat transfer and phase transition dynamics, a mathematical model is proposed to predict the phase change in high pressure supersonic flow, and a flue gas model after dehydration, desulfurization and denitration is established. The flow features with shock waves and spontaneous condensation in the supersonic separator are clarified, the influence of flow model on shock waves and flow features is quantified, and the energy recovery process with phase change is studied. The results show that flue gas enters the supercooled state near the throat, reaches Wilson point at x = 0.077 m, and the nucleation rate surges from 0 to 4.46 × 1020 m−3 s−1. When vapor molecules reach the surface of droplets, droplets grow, and latent heat is transferred from droplets to the vapor phase, resulting in condensation wave. A shock wave is generated at the diffuser inlet, and the flow and liquid phase parameters change abruptly after the shock wave. The single-phase model incorrectly predicted the separator refrigeration capacity, flue gas expansion capacity, location and intensity of the shock wave, and the maximum deviation is up to 65.5%. Excessive improvement of pressure recovery efficiency results in reducing the liquefaction capacity of the separator.

Dynamics and head-on collisions of multidimensionaldust-acoustic shock waves in a self-gravitating magnetized electron depleteddusty plasma

Abstract: The dynamics and collisions of dust-acoustic (DA) shock excitationstraveling in opposite directions are theoretically investigated in athree-dimensional self-gravitating magnetized electron-depleted dusty plasma(EDDP) whose ingredients are extremely massive warm positive and negativecharged dust grains as well as ions that follow the $q-$nonextensivedistribution. The linear analysis and the extended Poincare-Lighthill-Kuo(PLK) method are used to derive the dispersion relation, the two-sidedKorteweg-de Vries Burgers (KdVB) equations as well as the phaseshift that occurs due to the wave interaction. It is found that gravitationintroduces jeans-like instability, reduces the wave damping rate, decays theaperiodic oscillatory structure of DA excitations, and strongly affects theamplitude, steepness, and occurrence of monotonic compressive andrarefactive shocks. Numerical simulations also highlighted the stabilizingrole of the magnetic field and the singularities of the collision process ofmonotonic shock fronts as well as the undeniable influence of viscosity, ionnonextensivity, and obliqueness between counter-traveling waves on the phaseshift and collision profiles. The present results may be useful to betterunderstand interactions of dust acoustic shock waves (DASHWs) in thelaboratory and astrophysical scenarios such as dust clouds in the galacticdisk, photo-association regions separating H II regions from dense molecularclouds, Saturn's planetary ring, and Halley Comet.

Numerical Simulation on the Shock Wave Focusing Detonation Process in the Semicircle Reflector

Abstract: Shock wave focusing is considered a new type of initiation method that does not require external ignition devices. For this method, understanding the shock wave/flame interaction accurately is one of the critical issues for revealing the ignition and triggering mechanisms during shock wave focusing processes. In this study, numerical simulations was carried out to investigate the detailed flow field evolution of the focusing process with kerosene as fuel. Two detonation initiation modes were found during the shock wave focusing processes, which were the direct initiation mode and the reflected shock wave collision initiation mode, respectively. At the detonation wave propagation stage, the primary detonation wave decouples and fails to propagate out of the cavity. The multiple initiation phenomenon occurs in the cavity and it dominated detonation waves to propagate outside of the cavity to accomplish one thermal cycle. There is no positive correlation between jet temperature and detonation wave propagation velocity. When the jet temperature is low, the detonation wave velocity dominated by multiple initiation mode is the fastest. The analysis of the shock wave focusing process under different jet velocities showed that when the jet velocity was lower than 2Ma, the decoupling of the primary detonation wave failed to induce multiple detonation waves. Driven by the vortex in the semicircular cavity, the flame is almost stationary, which means the failure of the detonation wave propagation process.

On low-frequency unsteadiness in swept shock wave–boundary layer interactions

Abstract: Abstract We derive a scaling law for the characteristic frequencies of wall pressure fluctuations in swept shock wave/turbulent boundary layer interactions in the presence of cylindrical symmetry, based on analysis of a direct numerical simulations database. Direct numerical simulations in large domains show evidence of spanwise rippling of the separation line, with typical wavelength proportional to separation bubble size. Pressure disturbances around the separation line are shown to be convected at a phase speed proportional to the cross-flow velocity. This information is leveraged to derive a simple model for low-frequency unsteadiness, which extends previous two-dimensional models (Piponniau et al., J. Fluid Mech., vol. 629, 2009, pp. 87–108), and which correctly predicts growth of the typical frequency with the sweep angle. Inferences regarding the typical frequencies in more general swept shock wave/turbulent boundary layer interactions are also discussed.

Phenomenological Introduction of Standoff Distance of Sonic Ring Impelling Entropy Waves and Aerodynamic Heating of Hypersonic Vehicles

Abstract: The fundamental understanding of the Sanal flow choking and/or sonic fluid throat effect (V.R.S.Kumar et al., Physics of Fluids, 34(4 & 10), 2022) in real-world fluid flow system sheds lights on the theoretical discovery of the standoff distance of the Sonic Ring/Jacket impelling entropy waves and aerodynamics heating on supersonic and hypersonic vehicles. Since all fluids in nature are viscous, all flying objects exhibit zero velocity over its surface. It implies that there will be several continuous sonic points away from the surface, which are around the supersonic/hypersonic vehicles. The line joining all these continuous sonic points defined herein as unique “Sonic Ring (2D case) and/or Sonic Jacket (3D case).” The distance of the sonic point from the surface of the supersonic/hypersonic vehicle is coined herein as the “Standoff Distance.” The Sonic Ring is a creation of series of sonic fluid throat effect because of streamline compression and flow choking, which occurs at a critical total-to-static pressure ratio. During the turning of the freestream flow over the vehicle due to the geometry effect or otherwise, streamline compression occurs due to gas stickiness because of the enhanced viscosity. The viscosity of the gas increases due to an increase in gas temperature. The freestream gas temperature increases due to the entropy waves originated from shock waves (oblique/normal shock). Oblique shock will occur when the hypersonic/supersonic flows encounter a corner that effectively turns the flow into itself and compresses. Nature established that during the transition to subsonic flow, due to singularity, the supersonic/hypersonic flows will create normal shock waves leading to the generation of entropy wave throughout the Sonic Jacket. The strength of the shock wave and/or the magnitude of entropy enhancement depends on the incoming flow Mach number and the heat capacity ratio of the gas. Across a shock wave, the static pressure, temperature, and gas density increases almost instantaneously. The changes in the flow properties are irreversible and the entropy of the entire system increases. Admittedly, to remove the singularity and achieve a smooth transition from hypersonic/supersonic flow to subsonic flow is a challenging task. Nevertheless, as envisaged by E.W.Beans (JPP 1994) for an internal flow system, the smooth transition from hypersonic to subsonic regime requires a unique relationship between area change, heat transfer, and frictional effects. This physical situation is similar to the benchmark condition set in a circular duct and/or a Streamtube for achieving the Sanal flow choking for diabatic flows. In this pilot paper, 2D and 3D in silico simulations have been carried out using various validated flow solvers to compare qualitatively the Standoff Distance of Sonic Ring of hypersonic and supersonic flying objects having classical shapes to demonstrate the concept. In silico results reveal that the Sonic Ring observed for sphere, bullet and a double wedge airfoil at hypersonic speeds are much closer to the surface as compared to the supersonic flow. This observation is a very significant contribution to any highspeed vehicle (M>1) design as it establishes the theoretical concept of Sonic Ring/Sonic Jacket and it further aids for the envelope design optimization of supersonic and hypersonic vehicles with confidence. We concluded that in addition to the geometry optimization, the Standoff Distance of Sonic Ring/Jacket can be increased by injecting fluid with a high heat-capacity-ratio than the operating fluid to the Streamtube flow choking region; and thereby we can reduce the intensity of aerodynamic heating by creating a thick shock layer region near to the hypersonic vehicles. The theoretical discovery of the standoff distance of Sonic Ring/Jacket presented herein is a paradigm shift in the design optimization of supersonic, hypersonic, and re-entry vehicles with credibility.

Effect of hydrogen concentration distribution on flame acceleration and deflagration-to-detonation transition in staggered obstacle-laden channel

Abstract: A staggered arrangement of solid obstacles promotes flame acceleration (FA) and the deflagration-to-detonation transition (DDT) in a homogeneous concentration field. Many combustible premixed gases, however, are inhomogeneous. The present numerical study explores the effects of different hydrogen-air distributions on the FA and DDT processes in a staggered obstacle-laden channel. The results show that, in the early stage of flame evolution, the flame accelerates faster when there are no obstructions on the side of the channel with the high hydrogen concentration. Under the suction effect of the aperture formed between an obstacle and the wall, the flame experiences multiple periods of velocity augmentation during its evolution. In terms of detonation initiation, the process can be classified as either detonation induced by the interaction between the flame surface and the reflected shock wave from the wall/obstacle, or detonation induced by the collision between the leading shock wave and the reflected shock wave from the obstacle. As the detonation wave propagates, regions with a hydrogen content of less than 12.7 vol% cause a decoupling of the detonation wave. The morphology of the detonation wave (length, angle, and height) is related to the specific distribution of the hydrogen concentration. From the overall FA and DDT processes, a more homogeneous hydrogen concentration distribution leads to faster flame state variations and a faster triggering of the detonation.

Structural dynamics of water in a supersonic shockwave

Abstract: We explore the pressure evolution and structural dynamics of transient phase transitions in a microfluidic water jet after a laser-induced dielectric breakdown. To this end, we use a combined approach of nearfield holography with single femtosecond X-ray free-electron laser pulses and X-ray diffraction. We observe chaotic perturbations with thin filamentation during the gas expansion after dielectric breakdown, and shockwave emission along the jet. The formation of the shockwave is accompanied by pronounced changes in the structure factor, indicating a transition to a high density liquid phase induced by the transient pressure rise.

On the accuracy of one-way approximate models for nonlinear waves in soft solids.

Abstract: Simple strain-rate viscoelasticity models of isotropic soft solid are introduced. The constitutive equations account for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. A nonlinear viscous wave equation for the shear strain is obtained exactly and corresponding one-way Burgers-type equations are derived by making standard approximations. Analysis of the travelling wave solutions shows that these partial differential equations produce distinct solutions, and deviations are exacerbated when wave amplitudes are not arbitrarily small. In the elastic limit, the one-way approximate wave equation can be linked to simple wave theory and shock wave theory, thus, allowing direct error measurements.

Low-frequency unsteadiness of recompression shock structures in the diffuser of supersonic ejectors

Abstract: Supersonic ejectors are passive gasdynamic devices that compress a low-pressure fluid by utilizing the kinetic energy of a high-pressure fluid in a variable area duct. The ejector consists of a primary supersonic nozzle in a mixing duct where the secondary flow is entrained and mixed. The mixed flow can undergo a series of recompression shocks resulting in a subsonic flow in the diverging portion to aid pressure recovery. Recompression shocks usually lead to unsteady shock boundary layer interactions. The performance of the ejector is influenced by shear layers, shock and expansion waves, and their mutual interactions. While existing literature has extensively dealt with mixing of the primary and secondary flows, the unsteadiness in flow resulting from recompression shocks has been seldom investigated. Fluctuations in pressure due to the unsteadiness of the shock often lead structural fatigue issues. This paper reports a detailed investigation on low-frequency unsteadiness of recompression shock using high-speed schlieren images and dynamic pressure measurements. Modal analyses using proper orthogonal decomposition and dynamic mode decomposition techniques are used to determine the dominant spatial modes and associated frequencies. Multimodal frequencies ranging between 80 and 300 Hz are observed. These findings are further corroborated by Fourier and wavelet transformations of the experimentally measured wall static pressure signals. Subsequently, scaling parameter is established for the dominant frequencies based on flow velocities upstream of the shock and the distance between two consecutive shocks. This results in a unique scaling frequency of 4.58% ± 18%, for the recompression shock independent of operating conditions.

Implosion of a bubble pair near a solid surface

Abstract: A compressible two-phase flow solver is developed for the simulation of a collapsing bubble pair. With the adaptive mesh and high-resolution scheme, the discontinuities and shock waves due to bubble collapse are well captured. Numerical results show that the collapse of two bubbles horizontally arranged ($\ensuremath{\phi}={0}^{\ensuremath{\circ}}$) produces the highest wall pressure peak among the oblique angles (${0}^{\ensuremath{\circ}}\ensuremath{\le}\ensuremath{\phi}\ensuremath{\le}{90}^{\ensuremath{\circ}}$) while the perpendicular arrangement ( $\ensuremath{\phi}={90}^{\ensuremath{\circ}}$) leads to the lowest wall pressure peak, even weaker than that of the single bubble collapse.

Spectral Analysis of a Shock Wave Turbulent Boundary Layer Interaction In a Circular Test Section

Abstract: Instantaneous streamwise mass flux data gathered using hot-wire anemometry during a series of Mach 2.5 shock wave boundary layer interaction experiments in a circular test section have been reduced to study the spectral content of the interaction. The shock wave was generated by inserting a cone-cylinder into the supersonic flowfield. Concentric and non-concentric placement of the cone-cylinder produced symmetric (2D) and asymmetric (3D) interactions, respectively. The region of interest was where the shock impinged on the naturally occurring boundary layer on the test section wall. Both unseparated and separated boundary layer cases were considered. The probability density functions of the mass flux signal near the wall in the interaction region were found to be bimodal for the separated cases. Evidence of reflected shock unsteadiness was also seen as bimodal distributions in the probability density functions. The power spectral densities of the mass flux signal showed increased low frequency contributions in the separated regions, with a peak frequency one order of magnitude lower than the intermittency frequency of the incoming boundary layer. Downstream of the interaction, the reflected shock wave continued to influence the boundary layer. The peak frequencies were measured near the edge of the boundary layer, and it corresponded to the zero-crossing frequency of the reflected shock wave in the interaction region. For the asymmetric interactions, normal hot-wire measurements were only taken at locations where the cone was closest to and furthest away from the wall. From streamwise measurements, no discernible difference was observed between the symmetric and asymmetric interactions.

Theoretical investigations on a variable-coefficient generalized forced-perturbed Korteweg-de Vries-Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Abstract: Recent theoretical-physics efforts have been focused on the probes for nonlinear pulse waves in the variable-radius arteries. With respect to the nonlinear waves in an artery full of blood with certain aneurysm, pulses in a blood vessel or features in a circulatory system, this paper symbolically computes out an auto-Backlund transformation via a noncharacteristic movable singular manifold, certain families of the solitonic solutions as well as a family of the similarity reductions for a variable-coefficient generalized forced-perturbed Korteweg-de Vries-Burgers equation. Aiming, e.g., at the dynamical radial displacement superimposed on the original static deformation from an arterial wall, our results rely on the axial stretch of the injured artery, blood as an incompressible Newtonian fluid, radius variation along the axial direction or aneurysmal geometry, viscosity of the fluid, thickness of the artery, mass density of the membrane material, mass density of the fluid, strain energy density of the artery, shear modulus, stretch ratio, etc. We also call the attention that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.

Shock-induced melting of [100] lithium fluoride: Sound speed and Hugoniot measurements to 230 GPa

Abstract: Although [100] lithium flouride (LiF) is the most widely used optical window material in dynamic compression experiments, its high stress ($>100\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$) shock compression response, including melting, is not well understood. To address this need, we measured wave profiles in plate impact experiments to determine the Hugoniot states and longitudinal sound speeds in [100] LiF crystals shock compressed to 231 GPa. The measured peak states are fitted well by a linear shock velocity--particle velocity relation, providing an accurate determination of the LiF Hugoniot curve to significantly higher stresses than previous experiments. The longitudinal sound speeds show a near linear increase with density compression to 182 GPa. Between 182 GPa and 195 GPa, the sound speed and the longitudinal modulus decrease abruptly, due to shock-induced melting. The increasing sound speeds and moduli at higher stresses suggest that shock compressed LiF is fully liquid at 195 GPa and above, allowing determination of the Gr\"uneisen parameter for liquid LiF. The melt stress determined here differs from that predicted by current multiphase equations of state for LiF. Our results provide important insight into the high stress solid and liquid states of shock compressed LiF and point to the need for an improved multiphase equation of state at high pressures and high temperatures.

Separation length scaling for dual-incident shock wave–turbulent boundary layer interactions with different shock wave distances

Abstract: Abstract In this study, the length scaling for the boundary layer separation induced by two incident shock waves is experimentally and analytically investigated. The experiments are performed in a Mach 2.73 flow. A double-wedge shock generator with two deflection angles ($\alpha _1$ and $\alpha _2$) is employed to generate two incident shock waves. Two deflection angle combinations with an identical total deflection angle are adopted: ($\alpha _1 = 7^\circ$, $\alpha _2 = 5^\circ$) and ($\alpha _1 = 5^\circ$, $\alpha _2 = 7^\circ$). For each deflection angle combination, the flow features of the dual-incident shock wave–turbulent boundary layer interactions (dual-ISWTBLIs) under five shock wave distance conditions are examined via schlieren photography, wall-pressure measurements and surface oil-flow visualisation. The experimental results show that the separation point moves downstream with increasing shock wave distance ($d$). For the dual-ISWTBLIs exhibiting a coupling separation state, the upstream interaction length ($L_{int}$) of the separation region approximately linearly decreases with increasing $d$, and the decrease rate of $L_{int}$ with $d$ increases with the second deflection angle under the condition of an identical total deflection angle. Based on control volume analysis of mass and momentum conservations, the relation between $L_{int}$ and $d$ is analytically determined to be approximately linear for the dual-ISWTBLIs with a coupling separation region, and the slope of the linear relation obtained analytically agrees well with that obtained experimentally. Furthermore, a prediction method for $L_{int}$ of the dual-ISWTBLIs with a coupling separation region is proposed, and the relative error of the predicted $L_{int}$ in comparison with the experimental result is $\sim$10 %.

A phenomenological analysis of droplet shock-induced cavitation using a multiphase modeling approach

Abstract: Investigations of shock-induced cavitation within a droplet are highly challenged by the multiphase nature of the mechanisms involved. Within the context of heterogeneous nucleation, we introduce a thermodynamically well-posed multiphase numerical model accounting for phase compression and expansion, which relies on a finite pressure-relaxation rate formulation. We simulate (i) the spherical collapse of a bubble in a free field, (ii) the interaction of a cylindrical water droplet with a planar shock wave, and (iii) the high-speed impact of a gelatin droplet onto a solid surface. The determination of the finite pressure-relaxation rate is done by comparing the numerical results with the Keller–Miksis model, and the corresponding experiments of Sembian et al. and Field et al., respectively. For the latter two, the pressure-relaxation rate is found to be [Formula: see text] and [Formula: see text], respectively. Upon the validation of the determined pressure-relaxation rate, we run parametric simulations to elucidate the critical Mach number from which cavitation is likely to occur. Complementing simulations with a geometrical acoustic model, we provide a phenomenological description of the shock-induced cavitation within a droplet, as well as a discussion on the bubble-cloud growth effect on the droplet flow field. The usual prediction of the bubble cloud center, given in the literature, is eventually modified to account for the expansion wave magnitude.

Generalized Scaling Analysis of the Separation Zone Induced by Shock Wave–Turbulent Boundary Layer Interactions

Abstract: Shock wave–turbulent boundary layer interaction (SWTBLI) exists widely in the internal and external flow fields of supersonic and hypersonic vehicles, and has a significant influence on the aerodynamic performance. Separation scaling analysis for SWTBLIs has been pursued by researchers for decades. This paper took into consideration the downstream expansion fan to present a generalized scaling analysis of the separation zones induced by three types of interactions—incident SWTBLIs, compression corner SWTBLIs, and normal SWTBLIs. To establish this scaling correlation, SWTBLI flow-field data under the condition of free-stream Ma0 of 3.5 and Rδ of 2.34×105 were simulated numerically. The influence of the expansion fan on the wall pressure distributions and the scaling of the separation zone was analyzed in detail. The size of the separation zone was found to be related closely to the pressure increase at the reattachment point. The scaling of the separation zone and the reattachment pressure increase are rendered dimensionless by the displacement thickness of the incoming boundary layer and the dynamic pressure of the incoming free stream, respectively. The generalized scaling of the separation zone was found to follow a simple power function against the reattachment pressure coefficient. This generalized scaling correlation fits a wide range of published experimental data and numerical simulation results.

Analytical model for curved-shock Mach reflection

Abstract: Mach reflection (MR) is an essential component in the development of shock theory, as the incident shock curvature is found to have a significant effect on the MR patterns. Curved-shock Mach reflection (CMR) is not yet adequately understood due to the rotational complexity behind curved shocks. Here, CMR in steady, planar/axisymmetric flows is analyzed to supplement the well-studied phenomena caused by oblique-shock Mach reflection (OMR). The solution from von Neumann's three-shock theory does not fully describe the CMR case. A CMR structure is presented, characterized by an incident shock, reflected shock, Mach stem, and expansion/compression waves over the slipline, or occasionally an absence of waves due to pressure equilibrium. On the basis of this CMR structure, an analytical model for predicting the Mach stem in the CMR case is established. The model reduces to the OMR case if the shock curvature is not applicable. Predictions of the Mach stem geometry and shock structure based on the model exhibit better agreement with the numerical results than predictions using previous models. It is found that the circumferential shock curvature plays a key role in the axisymmetric doubly curved CMR case, which results in a different outcome from the planar case.