Shock Wave Diffraction Research Articles

Verification and characteristics of continuous rotating detonation waves in a novel rounded-rectangle hollow combustor

A noncircular cross-sectioned combustor holds the potential to facilitate the flexible design of continuous rotating detonation (CRD) engines, meeting the demands of airframe/engine integration. In this study, we propose and validate a novel rounded-rectangle hollow combustor comprising arc and straight segments. We conduct experimental and numerical investigations into the detailed propagation and combustion characteristics of the CRD wave in this combustor. The results demonstrate that a single hydrogen–air CRD wave can be achieved and sustained over a wide equivalence ratio (ER) range. As the ER increases from 0.71 to 1.25, the CRD wave's propagation velocity escalates from 1837.1 to 2190.8 m/s, with a substantial decrease in the relative standard deviation from 9.76% to 0.85%. The curvature variation along the combustor circumference influences the local propagation velocity, combustion intensity, shock wave strength, and shock wave system. Specifically, the constraints imposed by the arc segment significantly enhance combustion intensity and amplify shock wave strength. This is evident through a higher heat release rate fraction (fHRR), increased pressure peaks, and elevated propagation velocity. At the straight segment, the shock wave system comprises the CRD wave, leading, and trailing diffracted shock waves. However, the constraint from the arc segment leads to the formation of an additional reflected shock wave, altering the shock wave system to include the CRD wave, the reflected shock wave, and the leading diffracted shock wave. Thus, this study advances our understanding of CRD characteristics in noncircular cross-sectioned combustors, providing insight to the design theory for CRD engine combustors.

Computational study of shock diffraction over convex edges

Numerical analysis of normal shock diffraction over various step corners is presented using an implicit second-order upwind least squares cell-based method. Slipstream angle calculation for various corner angles and Mach numbers, variation of pressure load and specific heat flux with incident shock Mach numbers and different step corners along the step wall, separation point movement, and reattachment of the streamlines are some of the key features of the present study. Detailed studies have been conducted about the perturbed region enclosed within the diffracted shock wave and the last running expansion wave with the increase in the incident shock Mach numbers. The finite Volume Method is used to solve the governing equations numerically for the simulation of the moving shock. Various flow characteristics such as secondary shock, contact surface, expansion wave, slipstream, vortex, etc are well captured. Apart from isopycnics; Mach contours, isobars, and isotherms are plotted as well. The reattachment region formed after the flow separation near the step edge is mentioned and corresponding lengths over various steps are presented. Separation point movement along the step wall is highlighted and a relevant increase in reattachment length is reported. The slipstream angles get increased with incident shock Mach numbers and with corner angles. However, the rate of increment of slipstream angle decreases gradually. The core of the vortices generated and the reattachment of the separated streamlines are indicated by the two downfalls in the heat flux values.

BYCFoam: An Improved Solver for Rotating Detonation Engines Based on OpenFOAM

A rotating detonation engine (RDE) is a highly promising detonation-based propulsion system and has been widely researched in recent decades. In this study, BYCFoam, the latest gaseous version of the BYRFoam family, is developed specifically for RDE simulations. It is based on the standard compressible flow solver rhoCentralFoam in OpenFOAM and incorporates several enhancements: improved reconstruction variables and flux schemes; detailed chemistry and transport properties; the utilization of an adaptive mesh refinement (AMR) and dynamic load balancing (DLB). A series of comprehensive numerical tests are conducted, including the shock-tube problem, shock-wave diffraction, homogeneous ignition delay, premixed flame, planar detonation, detonation cellular structure and rotating detonation combustor (RDC). The results demonstrate that BYCFoam can accurately and efficiently simulate the deflagration and detonation processes. This solver enhances the capability of the BYRFoam family for the in-depth exploration of RDE in future research.

Numerical study of turbulent kinetic energy amplification during shock-wave diffraction

Numerical study of turbulent kinetic energy amplification during shock-wave diffraction

A novel coupled Euler–Lagrange method for high resolution shock and discontinuities capturing

AbstractThe accurate capturing of shock waves by numerical methods has long been a focus of attention in engineering owing to singularity problems in discontinuities. In this article, a novel coupled Euler–Lagrange method (CELM) is proposed to capture shock waves and discontinuities with high resolution and high order of mapping accuracy. CELM arranges the Lagrange particles on an Euler grid to track the discontinuous points automatically, and the data pertaining to the grids and particles interact via a weighted mutual mapping method that not only achieves fourth‐order accuracy in a smooth area of the solution but also maintains a steep discontinuous transition in the discontinuous area. In the virtual particle method, virtual particles are derived from the existing real particles; thus, the inflow and outflow of the particles and interpolation accuracy of the boundary are more easily realized. An accuracy test and energy convergence test demonstrated the fourth‐order convergence accuracy and low energy dissipation of the CELM; the method exhibited lower error and better conservation ability than high‐precision schemes such as WENO3 and WENO5. The Sod shock tube problem and Woodward–Colella problem showed higher discontinuity resolution of the CELM and ability to accurately track discontinuity points. Examples of Riemann problems were employed to prove that the CELM exhibits lower dissipation and higher shock resolution than WENO3 and WENO5. The CELM also showed an accurate structure based on particle distribution. Shockwave diffraction tests were conducted to prove that the CELM results showed good agreement with the experimental data and exhibited an accurate expansion wave. The CELM can also accurately simulate the collision of an expansion wave and vortex.

Numerical studies of shock–vortex interaction over a wedge during shock-wave diffraction—A new approach

In this study, shock wave diffraction has been investigated through a numerical simulation of a moving normal shock incident on a sharp-edged wedge. Schardin's problem is revisited using some existing and new mathematical tools. Two-dimensional compressible Navier–Stokes equation is solved using a higher-order version of the rhoCentralFoam solver in the OpenFOAM platform. Overall flow structures are captured with high efficacy. The divergence of the Lamb vector is used to probe the interaction between vorticity bearing and fluid straining motion, which increases dramatically inside the primary vortex after collision with the reflected Mach stem and increases the turbulent kinetic energy (TKE). In the separated shear layer that emerges from the wedge tip, there is a reduction of TKE after the collision between the lambda shock and accelerated shock. The vorticity pumping into the mean flow by the baroclinic torque is dominant in the separated shear layer before the above collision, whereas after collision it is only dominant inside the primary vortex. A new vector M is introduced here, which is the cross product of the vorticity vector and the pressure gradient vector. The divergence of M shows the interaction between the pressure gradient and the vorticity gradient. This interaction affects the separation bubble formed over the base wall of the wedge due to the shock-wave/boundary layer interaction induced by the lambda shock. Dynamic mode decomposition shows a dominant mode at a frequency of 125.7 Hz, which is due to low-frequency shock oscillation.

Vortex Ring Formation Following Shock Wave Diffraction in Low-Pressure Environments

Compressible vortex rings have been widely investigated for decades under ambient atmospheric conditions, and understanding this transient phenomenon is important for improving the thrust vector and avoiding surface impingement and contamination. However, how the vortex ring behaves in a reduced pressure environment remains unknown. This work provides schlieren imaging and pressure measurement results of the vortex ring when the environmental pressure is lower than 1 atm. The basic structure of the compressible vortex ring in low-pressure environments has been captured. The reduced environmental pressure will degenerate the internal flow structure, including the shock wave, the CRVRs, and the vortices due to the Kelvin–Helmholtz instability, which is consistent with the conclusion of previous numerical work. The vortex ring is confirmed to exist when the environmental pressure is approximately 1.0 kPa.

High-Speed Flow Visualization by a Nanosecond Volume Discharge during Shock Wave Diffraction on an Obstacle

We study the spatial structure of nonstationary inhomogeneous supersonic airflows as shock wave diffraction on an obstacle occurs in a shock tube of a rectangular cross section. The Mach numbers of shock waves were 2.7–4.4 at initial air pressures of 10–30 Torr. The supersonic flow in the discharge chamber was visualized by high-speed shadowgraphy and by the registration of radiation of combined volume discharge by photo camera and by ICCD camera. In experiments, a combined volume discharge with a current duration of ~ 500 ns was initiated 40–150 μs after the initial shock wave have passed an obstacle. It has been established that the radiation of the volume phase of discharge lasts 400–700 ns, and the displacement of the flow during this time does not exceed 0.6 mm. A correlation is established between the spatial distribution of discharge radiation and the low-density local areas determined as a result of two-dimensional Navier-Stokes based numerical simulation of the flow. As visualized by the glow of the discharge, the shape of the shock wave front is in good agreement with the results of shadowgraphy at different stages of diffraction and with the numerical simulation results.

Effects of an Explosion-Proof Wall on Shock Wave Parameters and Safe Area Prediction

To study the influences of an explosion-proof wall on shock wave parameters, an air explosion protection experiment was performed, the time history of shock wave pressure at different positions before and after the explosion-proof wall was established, and the characteristics of shock wave impulse and dynamic pressure were analyzed. The explosion-proof working conditions of five different diffraction angles were simulated and analyzed using Autodyn software(2019R3). Results indicated the following findings. The explosion-proof wall exerted an evident attenuation effect on the explosion shock wave, but considerable pressure still existed at the top of the explosion-proof wall. Overpressure behind the wall initially increased and then decreased. The larger the diffraction angle, the faster the attenuation speed of the diffraction overpressure of the shock wave in the air behind the wall. The history curve of shock wave pressure exhibited an evident bimodal structure. The shock wave diffraction of the wall made the shock wave bimodal structure behind the wall more prominent. The characteristics of the bimodal structure behind the wall (the interval time of overpressure peak Δt was less than the normal phase time of the diffracted shock wave T+) caused the shock wave impulse to stack rapidly, significantly improving its damage capability. The peak value of dynamic pressure on the oncoming surface was approximately two times the peak value of overpressure, and the inertia of air molecules resulted in a longer positive duration of dynamic pressure than overpressure. The maximum overpressure on the ground behind the explosion-proof wall appeared at approximately two times the height of the explosion-proof wall, while the maximum overpressure in the air behind the explosion-proof wall appeared at approximately one times the height of the explosion-proof wall. The relatively safe areas on the ground and in the air behind the wall were approximately 4–4.5 times and 3.5–4 times the height of the explosion-proof wall, respectively.

Shock wave diffraction in micro-shock tubes with sudden expansion

Shock wave diffraction in micro-shock tubes with sudden expansion

Influence of Variable Blocking Ratio on DDT Process

The influence of a variable blocking ratio on the DDT process is investigated through numerical simulation and experiment. Two dimensionless parameters, the average blocking ratio (BR¯) and the blocking ratio change rate (α), are specified to characterize the blocking ratio of obstacles. Four arrangements are utilized to describe the variation trend of the blocking ratio in a combustor. The main results are as follows: The obstacles can stretch the flame surface and facilitate reflection and diffraction of shock waves, which causes the acceleration of the flame front. The “hot spot” plays a vital role in the formation process of detonation waves. The overdriven detonation waves generated from “hot spots” promote the energy in the primary reaction zone, stimulating the formation of self-sustaining detonation. Compared with the fixed blocking ratio arrangement, the variable blocking ratio of obstacles can shorten the DDT distance. When BR¯=0.43, |α| = 0.03, and the variation trend (0.52–0.34–0.49) is adopted, the minimum DDT distance is obtained in numerical and experimental results. This paper can help with the design of detonation combustors in the future.

Blast shock wave attenuation in square cross-sectional truss based meso-scale lattice architectures

With the rapid growth in defense and civilian industry interests, high-performance materials like lattice materials capable of resisting high strain-rate loads are urgently required. Researchers mainly focus on the irreversible plastic deformation of lattice core sandwich structures under out-of-plane loads, whereas the potential application of cellular core without sandwiched face sheets has not been explored. In fact, when shock waves directly act on a cellular core without sandwiched face sheet, the energy would be consumed in the voids during the wave propagation. This article gives an insight into the shock wave attenuation characteristics and the attenuation mechanisms of square cross-sectional truss based meso-scale lattice architectures. Two types of lattice configurations with the same porosity but different truss sectional arrangements are employed. It is reported that both types of the lattice architectures can considerably dissipate the shock wave. The variation trends of overpressure-time history for the meso-scale lattice architectures are significantly different from those obtained in the free air field. As the truss-sectional size decreases the detected first peak overpressure decreases and becomes gradually lower than the second peak overpressure due to the increasing truss layers. When the edge length of truss section, d, decreases from 0.4 mm to 0.1 mm at a constant scaled distance of 0.896, the attenuation efficiency of the peak overpressure is increased by 30 % to 70 %, and the efficiency of the impulse is increased by 60 %, together with a highly-improved increasing rate for the delaying efficiency of the arrival time. Considering distinct scaled distances, the type II architecture and type I architecture behave superiorly with respect to the attenuation efficiencies of peak overpressure and impulse, respectively. Compared to the free field scenario, a shorter wave propagation distance could be observed for the meso-scale lattice architectures to achieve the same peak overpressure and impulse. The considerable shock wave attenuation of the meso-scale lattice architecture is attributed to the complex interactions of the shock wave reflection, diffraction, and superposition around the truss sections and in the voids. This investigation provides a novel method for the shock wave attenuation and energy consumption to protect vital targets and precise equipment.

Diffraction of shock waves through a non-quiescent medium

An investigation of shock diffraction through a non-quiescent background medium is presented using both experimental and numerical techniques. Unlike diffracting shocks in quiescent media, a spatial distortion of the shock front occurs, producing a region of constant shock angle. An example of this process arises in the exhaust from a pulse-detonation combustor. As the background velocity is increased, such as through the inclusion of a converging nozzle at the exhaust, the spatial distortion becomes more apparent. Numerical simulations using a compressible Euler solver demonstrate that the distortion is not due to the geometrical influence of the nozzle, but rather is a function of the magnitude of the background flow velocity. The distortion is studied using a modified geometrical shock dynamics formulation which includes the background flow and is validated against experiments. A simple model is presented to predict the shock distortion angle in the weak-shock limit. Finally, the axial decay behaviour of the shock is investigated and it is shown that the advection of the shock by the background flow delays the arrival of the head and tail of the expansion characteristic at the centreline. This leads to an increase in the rate of decay of the shock Mach number as the background flow velocity is increased.

Formation of Bow Shock Waves Around a Blunt Body in Magnetohydrodynamics Flows

The diffraction of a shock wave over a stationary body is a problem of interest associated with the starting of shock tubes and expansion tubes, which are well suited to studies of hypersonic magnetohydrodynamic flows. However, these facilities are characterized by very short test times. The transient parameters during the establishment of the detached bow shock in such impulsive facilities are important for both data processing and experimental design. In the present study, based on the low magnetic Reynolds number assumption and dipole magnetic field distribution, the influence of magnetic field on the diffraction of an incident shock wave over a sphere was studied numerically. The incident shock Mach number ranges from 11 to 15 under different magnetic field intensities. Time histories of the shock-detached distance and stagnation pressure were first obtained. Moreover, the time needed to establish the steady flows over the sphere was also displaced against the magnetic interaction parameter. The larger the magnetic interaction parameter, the longer the time needed to establish a steady bow shock for experiments, which further challenges the facilities to have sufficient test times for conducting hypersonic magnetohydrodynamic flow experiments.

平面衝撃波が様々な姿勢の円柱に及ぼす非定常流体力の研究

Studying the reflection and diffraction of shock waves generated around complex shapes is essential to clarify the blast phenomena caused by objects. In this study, a two-dimensional circular cylinder and a flow field impinging on a three-dimensional circular cylinder were analyzed by CFD using the three-dimensional Euler equations and the immersed boundary method. As a result, we confirmed pressure distributions that qualitatively simulated the previous study and the experimental results. However, more detailed discussions on the reflection and diffraction of shock waves are needed.

О влиянии выбора численного потока на решение задач с ударными волнами разрывным методом Галеркина

The paper compares various numerical flows in the calculation of flows with the presence of shock waves by first-order schemes and second-order DG method on schemes from the Quirk’s list, namely: the Quirk problem and its modifications, shock wave diffraction at a 90 degree angle, the problem of double Mach reflection. It is shown that the use of HLLC and Godunov’s numerical flows in calculations can lead to instability, the Rusanov-Lax-Friedrichs flow leads to high dissipation of the calculation. The most versatile in carrying out production calculations are hybrid numerical flows, which allow suppressing the development of instabilities and maintaining the accuracy of the method.

Negative Mach Reflection with Multiple Three-Shock Configurations for Shock Wave Diffraction on a Wedge

Within the framework of the Euler equations, a numerical study of the structure of a self-similar flow for various types of negative Mach reflection during diffraction of a shock wave by a wedge is performed. Along with the known modes of double and triple Mach reflection, a qualitatively new mode of negative Mach reflection with multiple three-shock configurations is observed. Peculiarities of the transition from multiple Mach reflection to regular reflection when changing the wedge angle are noted. Keywords: shock wave, three-shock configuration, double Mach reflection, negative Mach reflection

Numerical Experiments and Analysis of Shock Wave Diffraction around Structures

Flows with adverse pressure gradients are more challenging to simulate numerically due to the boundary layer separation. However, the computational fluid dynamics have been used successfully to improve the understanding of the complex fluid dynamics of the transient shock-induced shear layers. The present research tries to investigate the eligibility of the inviscid, viscous (laminar), and turbulent solvers to find which ones reveal realistic results and agree best with the experiments. The solvers are based on the Euler, the Navier-Stokes equations, and the Reynolds averaged Navier-Stokes equations coupled with the SST turbulence model, respectively. A mesh-adaptive high-order AUSM+ numerical scheme is applied. A systematic validation is performed with three cases focusing on the mechanism of the shock wave diffraction and the behavior of the shear layer. They are shock wave diffraction over a backward-facing step, convex 8o sharp splitter, and curved splitter. The investigation reveals that it is crucial to apply a turbulent solver for flows with separation due to the adverse pressure gradient. The lack of viscosity is responsible for the deviation of the inviscid and laminar resolutions from experiments. Moreover, the CFD simulation reveals tiny details about the shock wave diffraction around curved structure not appear in the experimental schlieren and shadowgraph.

A numerical method for self-similar solutions of ideal magnetohydrodynamics

We present a numerical method to obtain self-similar solutions of the ideal magnetohydrodynamics (MHD) equations. Under a self-similar transformation, the initial value problem (IVP) is converted into a boundary value problem (BVP) by eliminating time and transforming the system to self-similar coordinates (ξ≡x/t,η≡y/t). The ideal MHD system of equations is augmented by a generalized Lagrange multiplier (GLM) to maintain the solenoidal condition on the magnetic field. The self-similar solution to the BVP is solved using an iterative method, and implemented using the p4est adaptive mesh refinement (AMR) framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in the present method. Numerical tests illustrate that the present self-similar solution to the BVP exhibits sharper discontinuities than the corresponding one solved by the IVP. We compare and contrast the IVP and BVP solutions in several one dimensional shock-tube test problems and two dimensional test cases include shock wave refraction at a contact discontinuity, reflection at a solid wall, and shock wave diffraction over a right angle corner.

Reaction of the preloaded rotation shell with the rigid nose part of the apparatus to a shock wave in the liquid

The article investigates the problem of hydro-elastic interaction of a weak shock wave with a rigid nosed rotation shell preloaded with axial forces. The shell is enclosed in a rigid parabolic screen, i.e. the impact of the end face and the shock wave diffraction are not considered. Liquid is regarded to be perfectly compressible. Its applied summing hydrodynamic pressure during complex interaction with the shell surface can be classified into the incident, reflected and radiated waves. The problem of hydro-elastic interaction of these shock fronts with a preloaded parabolic rigid nosed shell in a related setting is reduced to the solution of the wave equations of nonlinear system of equations for shell motion under particular initial and boundary conditions, in which the dimensionless displacement of this nose section under the impact of hydrodynamic forces is determined by integrating its motion equation. The equations, describing the dependences of nose section displacements on shock wave interaction time, take into account generalized hydrodynamic forces, including the second category directly related to the mass of the attached fluid. Determination of stress-strain state in case of interaction with the shock wave in the liquid of elastic rotation paraboloid in the form of the shell containing a rigid insertion in the nose section is reduced to the solution of a nonlinear equations system of shell motion considering the boundary conditions along fastenings at the end face of the shell and interface conditions of the shell and insertion. Dimensionless displacements of the nose section caused by hydrodynamic forces are defined by integrating the equations of motion under the initial conditions along insertion offsets in the axial directions.