Oblique Shock Wave Reflection Research Articles

Underwater oblique shock wave reflection from submerged hydraulic structures

This paper investigates the effect of obliquity on impulse imparted to the hydraulic structures by an underwater shock wave. In this regard, the oblique shock reflection phenomenon due to a planar shock wave impingement on an inclined rigid surface is numerically modeled. Results from simulations are presented in this manuscript for different shock strengths and angles of structure obliquity. The study reveals that impulse transmitted to the structure due to oblique shock reflection is lower than that of normal incidence. In specific regimes of structure obliquity to incident shock direction, the formation of Mach-stem is observed, i.e., triple point configuration at a certain distance from the structure. Inside these regimes, the stem height decreases with the increase in structure obliquity and vice versa. Locus of the triple point has a direct implication on the magnitude of transmitted impulse, which reduces with the increase in stem height, i.e., more the locus of the triple point is away from the structure, less is the transmitted impulse. Results presented in this manuscript may help in understanding the physics of shock reflections from submerged hydraulic structures and subsequently framing mitigation strategies.

Suppression of reflected oblique shock wave by multi-filamentary plasma

This paper describes the results of experimental study of stripwise near-surface plasma effect on oblique shock wave (SW) reflection from a solid wall in a M = 2 duct-driven shock-dominated airflow. Methods applied include schlieren visualization, plasma characterization with electric probes and optical emission spectroscopy, wall pressure measurements along the test section. The transient filamentary plasma is generated by means of a Quasi-DC electric discharge between flush mounted surface electrodes in a spanwise array. Test arrangement includes a shock wave (SW) generator installed on the bottom wall of the test section and the plasma generator installed on the upper wall. The SW generated from the bottom wall impinges the significantly disturbed boundary layer (BL) generated by the plasma array. The effect of reflected SW mitigation is demonstrated due to the interaction with the plasma-modified BL. The model of interaction is discussed and supported by the results of numerical simulation.

A parametric study of laminar and transitional oblique shock wave reflections

High-resolution particle image velocimetry measurements were performed on laminar and transitional oblique shock wave reflections for a range of Mach numbers ($M=1.6{-}2.3$), Reynolds numbers ($Re_{x_{sh}}=1.4\times 10^{6}{-}3.5\times 10^{6}$) and flow deflection angles ($\unicode[STIX]{x1D703}=1^{\circ }{-}5^{\circ }$ or $p_{3}/p_{1}=1.11{-}1.64$). The laminar interactions revealed a long, flat and triangular shaped separation bubble. For relatively strong interactions ($p_{3}/p_{1}>1.2$), the bubble grows linearly in the upstream direction with increasing shock strength. Under these conditions, the boundary layer keeps an on average laminar velocity profile up to the shock impingement location, followed by a quick transition and subsequent reattachment of the boundary layer. For weaker interactions ($p_{3}/p_{1}<1.2$), the boundary layer is able to remain laminar further downstream of the bubble, which consequently results in a later reattachment of the boundary layer. The pressure distribution at the interaction onset for all laminar cases shows excellent agreement with the free-interaction theory, therefore supporting its validity even for incipiently separated laminar oblique shock wave reflections.

Effects of Different Equations of State on the Oblique Shock Wave Reflection in Solids

The equations of state of solids under high pressure are more complicated than that of gases in a variety of forms. While the existing studies on the oblique shock wave reflection usually take just one of the equations of state, lacking of the comparisons among them. This paper aims at the investigation of oblique shock wave reflection in solids through shock polar methodology. Four different forms of equations of state are considered, principal shock taking with vN particle velocity relationship and second shock taking with Grüneisen equation of state(1Du2Grüneisen), principal and second shock both taking with vN particle velocity relationship (1Du2Du), principal shock taking with vN particle velocity relationship and second shock taking with stiffened gas equation of state (1Du2Gamma), and principal and second shock both taking with stiffened gas equation of state (1Gamma2Gamma). The effects of different equations of state on the pressure behind the reflected shock show: different combination of EOS may lead to diverse results. In our opinion, the 1Du2Grüneisen and 1Du2Du shows almost the same trends in most conditions and is suitable for the theoretical analysis of oblique reflection, and 1Du2Gamma and 1Gamma2Gamma should be carefully employed in studies to avoid the incorrect result.

Numerical and experimental investigation of oblique shock wave reflection off a water wedge

Shock wave interaction with solid wedges has been an area of much research in past decades, but so far very few results have been obtained for shock wave reflection off liquid wedges. In this study, numerical simulations are performed using the inviscid Euler equations and the stiffened gas equation of state to study the transition angles, reflection patterns and triple point trajectory angles of shock reflection off solid and water wedges. Experiments using an inclined shock tube are also performed and schlieren photography results are compared to simulations. Results show that the transition angles for the water wedge cases are within 5.3 % and 9.2 %, for simulations and experiments respectively, compared to results obtained with the theoretical detachment criterion for solid surfaces. Triple point trajectory angles are measured and compared with analytic solutions, agreement within $1.3^{\circ }$ is shown for the water wedge cases. The transmitted wave in the water observed in the simulation is quantitatively studied, and two different scenarios are found. For low incident shock Mach numbers, $M_{s}=1.2$ and 2, no shock wave is formed in the water but a precursor wave is induced ahead of the incident shock wave and passes the information from the water back into the air. For high incident shock Mach numbers, $M_{s}=3$ and 4, precursor waves no longer appear but instead a shock wave is formed in the water and attached to the Mach stem at every instant. The temperature field in the water is measured in the simulation. For strong incident shock waves, e.g. $M_{s}=4$, the temperature increment in the water is up to 7.3 K.

Influence of the nozzle angle on refrigeration performance of a gas wave refrigerator

A gas wave refrigerator (GWR) is a novel refrigerating device that refrigerates a medium by shock waves and expansion waves generated by gas pressure energy. In a typical GWR, the injection energy losses between the nozzle and the expansion tube are essential factors which influence the refrigeration efficiency. In this study, numerical simulations are used to analyze the underlying mechanism of the injection energy losses. The results of simulations show that the vortex loss, mixing energy loss, and oblique shock wave reflection loss are the main factors contributing to the injection energy losses in the expansion tube. Furthermore, the jet angle of the gas is found to dominate the injection energy losses. Therefore, the optimum jet angle is theoretically calculated based on the velocity triangle method. The value of the optimum jet angle is found to be \(4^{\circ }\), \(8^{\circ }\), and \(12^{\circ }\) when the refrigeration efficiency is the first-order, second-order, and third-order maximum value over all working ranges of jet frequency, respectively. Finally, a series of experiments are conducted with the jet angle ranging from \(-4^{\circ }\) to \(12^{\circ }\) at a constant expansion ratio. The results indicate the optimal jet angle obtained by the experiments is in good agreement with the calculated value. The isentropic refrigeration efficiency increased by about 4 % after the jet angle was optimized.

Effect of particle momentum transfer on an oblique-shock-wave/laminar-boundary-layer interaction

Numerical simulations of solid particles seeded into a supersonic flow containing an oblique shock wave reflection were performed. The momentum transfer mechanism between solid and gas phases in the shock-wave/boundary-layer interaction was studied by varying the particle size and mass loading. It was discovered that solid particles were capable of significant modulation of the flow field, including suppression of flow separation. The particle size controlled the rate of momentum transfer while the particle mass loading controlled the magnitude of momentum transfer. The seeding of micro- and nano-sized particles upstream of a supersonic/hypersonic air-breathing propulsion system is proposed as a flow control concept.

Experimental Study into the Effects of Forced Transition on a Shock-Wave/Boundary-Layer Interaction

This study investigates the effects of boundary-layer tripping on an oblique shock-wave reflection (, ) by means of particle image velocimetry. Laminar boundary layers are sensitive to adverse pressure gradients, and the interaction with an oblique shock wave () results in the formation of a large separation bubble (). The bubble can be removed by tripping the boundary layer a short distance upstream of the incident shock wave. Three types of tripping devices were investigated in this study: a stepwise trip, a patch of distributed roughness, and a zigzag strip. The step was found to be least effective at tripping the boundary layer, yielding a turbulent boundary layer downstream of the trip; whereas the other two trips required a distance of only . Consequently, at the same trip–to-shock-wave distance, the step was found to be less effective at removing separation than the other two trips. Although tripping the boundary layer allows for the removal of the separation bubble, it does come at the price of having a substantially thicker boundary layer () downstream of the interaction.

On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions

The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two- and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria. We found that at a critical deflection angle across the incident shock wave, the perturbations related to the turbulent boundary layer cause bi-directional transition processes between regular and irregular shock patterns for a free-stream Mach number of$\mathit{Ma}_{0}=2$. Computational results show that the mean deflection angle across the separation shock is decoupled from the incident shock wave and can be accurately modelled by the generalised free interaction theory. On the basis of these observations, and the von Neumann and detachment criteria for the asymmetric intersection of shock waves, we derive the critical incident shock deflection angles at which the shock pattern may/must become irregular. Numerical data for a free-stream Mach number of$\mathit{Ma}_{0}=3$confirm the existence of the dual-solution domain predicted by theory.

Parallel implicit anisotropic block-based adaptive mesh refinement finite-volume scheme for the study of fully resolved oblique shock wave reflections

A new parallel, fully implicit, anisotropic block-based adaptive mesh refinement (AMR) finite-volume scheme is proposed, described and demonstrated for the prediction of laminar, compressible, viscous flows associated with unsteady oblique shock reflection processes. The proposed finite-volume method provides numerical solutions to the Navier–Stokes equations governing the flow of polytropic gases in an accurate and efficient manner on two-dimensional, body-fitted, multi-block meshes consisting of quadrilateral computational cells. The combination of the anisotropic AMR and parallel implicit time-marching techniques adopted is shown to readily facilitate the simulation of challenging and complex shock interaction problems, as represented by the time-accurate predictions of unsteady oblique shock reflection configurations with fully resolved internal shock structures.

High-resolution PIV measurements of a transitional shock wave–boundary layer interaction

This study investigates the effects of boundary layer transition on an oblique shock wave reflection. The Mach number was 1.7, the unit Reynolds number was 35 × 106 m?1, and the pressure ratio over the interaction was 1.35. Particle image velocimetry is used as the main flow diagnostics tool, supported by oil-flow and Schlieren visualizations. At these conditions, the thickness of the laminar boundary layer is only 0.2 mm, and seeding proved to be problematic as practically no seeding was recorded in the lower 40 % of the boundary layer. The top 60 % could, however, still be resolved with good accuracy and is found to be in good agreement with the compressible Blasius solution. Due to the effects of turbulent mixing, the near-wall seeding deficiency disappears when the boundary layer transitions to a turbulent state. This allowed the seeding distribution to be used as an indicator for the state of the boundary layer, permitting to obtain an approximate intermittency distribution for the boundary layer transition region. This knowledge was then used for positioning the oblique shock wave in the laminar, transitional (50 % intermittency) or turbulent region of the boundary layer. Separation is only recorded for the laminar and transitional interactions. For the laminar interaction, a large separation bubble is found, with a streamwise length of 96 ??i,0 . The incoming boundary layer is lifted over the separation bubble and remains in a laminar state up to the impingement point of the shock wave. After the shock, transition starts and a turbulent profile is reached approximately 80–90 ??i,0 downstream of the shock. Under the same shock conditions, the transitional interaction displays a smaller separation bubble (43 ??i,0 ), and transition is found to be accelerated over the separation bubble.

Oblique shock wave reflection from the wall

Regular and Mach (irregular) reflection of an oblique shock wave from the wall is considered. Criteria for the transition from regular to irregular reflection are described: von Neumann criterion and the criterion for fixed Mach configuration. Specific incident shock wave intensities corresponding to the two criteria for the transition from regular to irregular reflection were plotted. The area of ambiguity solutions was demonstrated in which both regular and Mach reflection is not prohibited by the conditions of dynamic compatibility. Areas in which the transition from one type of reflection to another is possible only by a shock wave were described, as well as areas of a possible smooth transition. Dependence of the magnitude of this abrupt change in reflected discontinuity intensity from the intensity of the incident shock wave was plotted. Intensity dependences of the reflected discontinuity from the intensity of the shock wave incident on the wall for all types of reflections were shown.

Flow control of an oblique shock wave reflection with micro-ramp vortex generators: Effects of location and size

This study investigates the influences of micro-ramp size and location on its effectiveness as a flow control device for oblique shock wave reflections. The effectiveness is measured in terms of the size of the shock-induced separation bubble and the reflected shock unsteadiness. Particle image velocimetry measurements were carried out on the interaction region and the mixing region between micro-ramp and interaction. The separation bubble is shown to be most sensitive to the momentum flux contained in the lower 43% of the incoming boundary layer. The momentum flux added to this region scales linearly with micro-ramp height and larger micro-ramps are shown to be more effective in stabilizing the interaction. Full boundary layer mixing is attained 5.7δ downstream of the micro-ramp and this forms a lower limit on the required distance between micro-ramp and the start of the interaction region. Typical reductions in the average separated area and the shock unsteadiness of 87% and 51%, respectively, were recorded. Results, however, depend strongly upon the spanwise location, with the micro-ramp being most effective along its centerline.

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.

Shock reflection and oblique shock waves

The linear stability of steady attached oblique shock wave and pseudosteady regular shock reflection is studied for the nonviscous full Euler system of equations in aerodynamics. A sufficient and necessary condition is obtained for their linear stability under three-dimensional perturbation. The result confirms the sonic point condition in the study of transition point from regular reflection to Mach reflection, in contrast to the von Neumann condition and detachment condition predicted from mathematical constraint.

An experiment on imploding conical shock waves

Over the past decade and a half there have been a number of numerical studies of the reflection of oblique axisymmetric shock waves from the axis of symmetry. Many of these have shown a complex Mach reflection pattern together with a strong toroidal vortex which significantly distorts the Mach disk. This geometry has never been captured experimentally. This note describes a special rig for the generation of strong imploding conical shocks, and presents photographs of the predicted reflection pattern.

Two-dimensional shock tube flow for dense gases

Non-stationary oblique shock wave reflections for fluids in the dense gas regime are examined for selected cases. A time-accurate predictor-corrector TVD scheme with reflective boundary conditions for solving the Euler equations simulates the evolution of a wave field for an inviscid van der Waals gas near the thermodynamic critical point. The simulated cases involve shock tube flows with compressive wedges and circular arcs. Non-classical phenomena, such as disintegrating shocks, expansion shocks, composite waves, etc., demonstrate significant differences from perfect gas flow fields over similar geometries. Detailed displays of wave field structures and thermodynamic states for the dense gas flow fields are presented and analysed.

A NON-OSCILLATORY NO-FREE-PARAMETER FINITE ELEMENT AND ITS APPLICATIONS IN CDF

SUMMARY A non-oscillatory no-free-parameter finite element method (NNFEM) is presented based on the consideration of wave propagation characteristic in different characteristic directions across a strong discontinuity through flux vector splitting in order to satisfy the increasing entropy condition. The algorithm is analysed in detail for the one-dimensional (1D) Euler equation and then extended to the 2D, axisymmetric and 3D Euler and Navier‐ Stokes equations. Its applications in various cases—inviscid oblique shock wave reflection, flow over a forward step, axisymmetric free jet flow, supersonic flows over 2D and 3D rectangular cavities—are given. These computational results show that the present NNFEM is efficient in practice and stable in operations and is especially capable of giving good resolution in simulating complicated separated and vortical flows interacting with shock waves.

Reconsideration of oblique shock wave reflections in steady flows. Part 1. Experimental investigation

The reflection of shock waves over straight reflecting surfaces in steady flows was investigated experimentally using the supersonic wind tunnel of Laboratoire d'Aerothermique du CNRS, Meudon, France. The results for a flow Mach number M0 = 4.96 contradict the state of the art regarding the regular [harr ] Mach reflection transition in steady flows. Not only was a hysteresis found to exist in this transition, but, unlike previous reports, regular reflection configurations were found to be stable in the dual-solution domain in which theoretically both regular and Mach reflection are possible.

Reconsideration of oblique shock wave reflections in steady flows. Part 2. Numerical investigation

The reflection of shock waves over straight reflecting surfaces in steady flows was investigated numerically with the aid of the LCPFCT algorithm. The findings completely supported the experimental results which were reported in Part 1 of this paper (Chpoun et al. 1995). In addition, the dependence of the resulting shock wave configuration on the distance between the trailing edge of the reflecting wedge and the bottom surface, inside the dual-solution domain, was studied. As a result of this study, as well as the one reported in Part 1, the state of the art of shock wave reflections in steady flows was reconsidered.