Shock Wave Diffraction Research Articles

Numerical investigations on the Schardin's problem

When shock waves passes through a triangle wedge (Schardin's problem), some complicated physical phenomena, including shock wave Mach refection and diffraction, wedge wake, vortexlet, etc. may occur. In this paper, the Schardin's problem is investigated numerically with the combination of the third-order WENO scheme, structured adaptive mesh refinement (AMR) method and immersed boundary method. Our numerical results show clearly the interaction between the incident shock wave and the triangle wedge, the Mach reflection on the wedge surface, its diffraction at the wedge tips, and the induction of the main vortex, which accord excellently with Schardin's experimental and previous numerical results. In addition, our numerical results display in detail the induction process of the vortexlet along the slip layer of the main vortex and the interaction of the shock wave with the vortexlet, and the generation of the serial acoustic waves, which have not been reported in the literature.

Experimental and Numerical Study on a Straight Exhaust Pipe

ABSTRACTIn this study, radiated noise is investigated by experimental and numerical methods for a straight exhaust pipe of diameter 23mm that replaces the original exhaust pipe of a motorcycle of EZ 125cc provided by Kwang Yang Motor Co. In experiment, temperature, pressure and flow speed of the exhausted gas have been measured for different engine speeds ranging from 3000-5000rpm without loading. Sound pressure levels (SPL) at a distance of 0.5m from the exhaust pipe exit for different inclination angles (0° ∼ 90°) were recorded and compared with the result of simulation. In numerical simulation, a high-resolution 5th-order Euler solver was used and conducted on a parallel computation system with a cluster of 4 personal computers with dual processors. It is found that the back-and-forth reflection of expansion waves inside the pipe due to the shock wave diffraction around the pipe exit is the mechanism of radiating sound waves from the exhaust pipe. The numerical result shows the exhausted-gas flow with complicated vortex rings and its associated acoustic field. The acoustic field indicates that there are three sound lobes with different directivities for the engine speed of 4000rpm.

Shear layer behavior resulting from shock wave diffraction

All previous studies on shock wave diffraction in shock tubes have spatial and temporal limitations due to the size of the test sections. These limitations result from either the reflection of the expansion wave, generated at the corner, from the top wall and/or of the reflection of the incident diffracted shock from the bottom wall of the test section passing back through the region of interest. This has limited the study of the evolution of the shear layer and its associated vortex, which forms a relatively small region of the flow behind the shock with an extent of only a few centimeters, and yet is a region of significant interest. A special shock tube is used in the current tests which allow evolution of the flow to be examined at a scale about an order of magnitude larger than in previously published results, with shear layer lengths of up to 250 mm being achieved without interference from adjacent walls. Tests are presented for incident shock wave Mach numbers of nominally 1.3–1.5. Studies have been undertaken with wall angles of 10, 20, 30 and 90°. Significant changes are noted as the spatial and temporal scale of the experiment increases. For a given wall angle, the flow behind the incident shock is not self-similar as is usually assumed. Both shear layer instability and the development of turbulent patches become evident, neither of which have been noted in previous tests.

Simulation of shock wave diffraction by a square cylinder in gases of arbitrary statistics using a semiclassical Boltzmann–Bhatnagar–Gross–Krook equation solver

The unsteady shock wave diffraction by a square cylinder in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space. The numerical method is based on the discrete ordinate method for discretizing the velocity space of the distribution function and high-resolution method is used for evolving the solution in physical space and time. The specular reflection surface boundary condition is employed. The complete diffraction patterns including regular reflection, triple Mach reflection, slip lines, vortices and their complex nonlinear manifestations are recorded using various flow property contours. Different ranges of relaxation times corresponding to different flow regimes are considered, and the equilibrium Euler limit solution is also computed for comparison. The effects of gas particles that obey the Maxwell–Boltzmann, Bose–Einstein and Fermi—Dirac statistics are examined and depicted.

Simulation of Shock Wave Diffraction over 90° Sharp Corner in Gases of Arbitrary Statistics

The unsteady shock wave diffraction over a 90° sharp corner in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space. The numerical method is based on the usage of discrete ordinate method for discretizing the velocity space of the distribution function; whereas a second order accurate TVD scheme (Harten in J. Comput. Phys. 49(3):357–393, 1983) with Van Leer’s limiter (J. Comput. Phys. 32(1):101–136, 1979) is used for evolving the solution in physical space and time. The specular reflection surface boundary condition is assumed. The complete diffraction patterns are recorded using various flow property contours. Different range of relaxation times approximately corresponding to continuum, slip and transitional regimes are considered and the equilibrium Euler limit solution is also computed for comparison. The effects of gas particles that obey the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are examined and depicted.

An improved CE/SE scheme and its application to dilute gas–particle flows

An improved space–time Conservation Element and Solution Element (CE/SE) scheme is constructed by proposing a new structure of solution elements and conservation elements based on the rectangular mesh. Furthermore, the improved CE/SE scheme was applied to dilute gas–particle two-phase flows. A two-fluid model and two corresponding chemical reaction models, i.e., two-step reaction model and detailed chemical reaction model, were used to describe the physical and chemical characteristics in the two-phase flows. Shock wave reflection in gas, shock wave diffraction in air–sand mixture, explosive synthesis of TiO2 nanoparticle and air–fuel two-phase detonation were simulated by the improved CE/SE scheme and appropriate physical and chemical models. All the numerical results were compared and discussed carefully. The results show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for the above-mentioned problems. Thus, the improved CE/SE scheme can be applied to gas–particle flows widely.

Effect of primary jet geometry on ejector performance: A cold-flow investigation

The following cold-flow study examines the interaction of the diffracted shock wave pattern and the resulting vortex loop emitted from a shock tube of various geometries, with an ejector having a round bell-shaped inlet. The focus of the study is to examine the performance of the ejector when using different jet geometries (primary flow) to entrain secondary flow through the ejector. These include two circular nozzles with internal diameters of 15 mm and 30 mm, two elliptical nozzles with minor to major axis ratios of a/ b = 0.4 and 0.6 with b = 30 mm, a square nozzle with side lengths of 30 mm, and two exotic nozzles resembling a pair of lips with axis ratios of a/ b = 0.2 and 0.5 with b = 30 mm. Shock tube driver pressures of P 4 = 4, 8, and 12 bar were studied, with the pressure of the shock tube driven section P 1 being atmospheric. High-speed schlieren photography using the Shimadzu Hypervision camera along with detailed pressure measurements along the ejector and the impulse created by the ejector were conducted.

Analysis and prediction of shock-induced near-field acoustics from an exhaust pipe

In this study an acoustic problem of a single shock wave moving through a circular pipe instead of a real pulsating flow with blast waves is considered. Due to the failure of a linear acoustic theory for the problem of interest, the method of computational fluid dynamics is employed to analyze the present problem. For this purpose, the axisymmetric Euler equations are solved by a high-resolution method which consists of a fifth-order weighted essential non-oscillation scheme for spatial discretization and a fourth-order Runge–Kutta method for time integration. In order to reduce the large computational time on a single computer, parallel computation with seven personal computers has been conducted. The detailed flow and sound pressure fields inside and downstream of the pipe are studied. The near-field sound pressure level downstream of the pipe was computed. The sound lobe and its orientation are investigated. In particular, an interesting phenomenon of spatial variation of velocity components associated with the sound lobe is reported. It is found that the spatial variations of the streamwise velocity component and pressure are in phase. However, the spatial variations of the radial velocity component and pressure are out of phase. Moreover, the generation mechanism of acoustics is attributed to the fact of the back-and-forth reflections of upstream-moving expansion waves generated at the pipe wall corner when the shock wave diffracts around the corner. The back-and-forth wave reflections result in the formation of interlacing high- and low-pressure regions that change with time.

Shock wave diffraction about a wedge in a gas-microdroplet mixture

Shock wave interacts with the droplets as a high-speed flight vehicle penetrates cloud or rain storm in the earth’s atmosphere. Interaction of the shock with the gas-droplet two-phase medium significantly affects the aerodynamic performance of the flight vehicle. In the present paper, we investigate the aerodynamic field and wall variables as the moving shock wave diffracts over a wedge in the droplet-gas mixture. We used the compressible two-fluid model equations that have been solved by the HLL-based weighted average flux (WAF) method. The viscous drag force and the heat transfer terms have been included in the model to let the gas and the droplet phases interact. We investigate the effects of the three parameters associated with the microdroplets: the void fraction, the size and the material. We elaborate how the relaxation zone created by the shock wave diffraction is structured and changed in the droplet-gas mixture.

Shock wave-induced vortex loops emanating from nozzles with singular corners

The focus of the current study is to examine experimentally the diffracted shock wave pattern and the consequent vortex loop formation, propagation, and decay from nozzles having singular corners. Non-intrusive qualitative and quantitative techniques: schlieren, shadowgraphy, and particle image velocimetry (PIV) are employed to analyze the induced flow-fields. Eye-shaped nozzles were used with the corner joints representing singularities. The length of the minor axes are a = 6 and 15 mm, with the major axis b = 30 mm for both cases. The experiments are performed for flow Reynolds numbers in the range 0.8 × 105 and 4.6 × 105. Air is used in both driver and driven sections of the shock tube.

Computation on pipe dynamic response induced by deflagration of H2 and air mixture

Computation is devoted to evaluating structural safety of a heat exchanger inside a reactor whose geometry can be simplified as outer and inner pipes as well as a chamber. This paper has numerically studied deflagration of hydrogen air mixture and pipe dynamic responses. The Navier-Stokes equations coupled with multi-species mass equation are solved by TVD scheme to get flow-field solution based on MPI and multi-block methods. Combustion is described by a 11-species and 23-step reaction model. The source term is treated implicitly to involve species production and depletion. Ignition is approximated by input energy C p T per unit mass in a specified period and zone. Finally, contours of pressure and OH mass fraction at different time periods and pressure histories at fixed points are obtained. When loading is specified as wall pressure, virtual work theorem in Lagrangian frame which describes pipe response is solved by FEM to obtain stress and strain distributions. Results show that shock waves can be generated and reflected on the walls of the chamber and pipes. The shock waves and flame can not be dissipated in a narrow gap spanning 2 mm. Meanwhile, stress waves are generated. They propagate outwards on the inner and outer pipe walls. At the gap exit, shock wave diffracts and impacts on the inner pipe walls. Coupled with hot jet from the gap, re-ignition occurs on the inner pipe wall surfaces. Then, flame catches up the leading shock and shock front deforms into a planar one although the shock front passes through a short divergent section downstream. Also, stress concentrates along the intersected lines among the top, bottom and side walls. This means that the chamber is an easily damaged component. The methods provided in this paper can be used to evaluate structural safety.

Experimental study of toroidal shock wave focusing in a compact vertical annular diaphragmless shock tube

The paper reports results of experiments regarding toroidal shock wave focusing in a vertical shock tube as a part of a series of converging shock wave studies. This compact vertical shock tube was designed to achieve a high degree of reproducibility with minimum shock formation distance by adopting a diaphragmless operating system. The shock tube was manufactured in the Institute of Fluid Science, Tohoku University. An aspheric lens shaped cylindrical test section was connected at the open end of the shock tube to visualize the diffraction and focusing of the toroidal shock wave released from the ring shaped shock tube opening. Pressure transducers were flush mounted on the shock tube’s test section to measure pressure histories at the converging test section. Double exposure holographic interferometry was employed to quantitatively visualize the shock waves. The whole sequence of toroidal shock wave diffraction, focusing, and its reflection from the symmetrical axis were successfully studied. The transition of reflected shock waves was observed.

Normal shock interaction with a yawed wedge moving at supersonic speed

In this article, the interaction of a normal shock with a yawed wedge moving at supersonic speed has been considered. The vorticity distribution of a particle over the diffracted shock wave for various combinations of yawed angles, Mach number of the shock wave and Mach number of the moving wedge have been obtained. Further triple point angle χ in Mach reflection has been calculated for the various parameters.

Initiation and propagation of detonation waves in combustible high speed flows

The initiation and propagation of detonation waves in combustible high speed flows were studied experimentally. A planar detonation wave traveling in an initiation tube was transmitted into a test section where a combustible high speed flow was induced by an incident shock wave generated in a shock tube. In this study, the flow Mach numbers were obtained as 0.9 and 1.2. The experimental results show that depending on the flow velocity, the apparent propagation velocity of a detonation wave is higher in the upstream and lower in the downstream direction than the CJ velocity. Smoked plate records reveal cellular patterns deformed in the flow direction, and the calculated aspect ratios of the cell were found to agree well with the experimental ones on the basis of the assumption that the velocity of the transverse wave is not affected by the flowing mixture. By analyzing the shock-wave diffraction at the position where there is an abrupt change in the area, on the basis of Whitham’s theory, it was deduced that in the present experimental set-up, the detonation was initiated by the reflection of the diffracted shock waves on the sidewalls of the test section. The agreement between the experimental and calculated results regarding the position of the cellular patterns on the smoked plate record indicated that the position of detonation initiation in high speed flows is shifted downstream due to the flow velocity.

Shock and detonation wave diffraction at a sudden expansion in gas–particle mixtures

Numerical modeling of the propagation of shock and detonation waves is carried out in a duct with an abrupt expansion for a heterogeneous mixture of fine particles of aluminum and oxygen. A considerable difference from corresponding flows in pure gas is found. The influence of the size and mass loading of particles on the flow and shock wave structure behind the backward-facing step is determined. As in gaseous detonations, three types of scenarios of detonation development are obtained. Specific features of the flow structure are revealed such as deformation of the combustion front due to interaction between the relaxation zone and the vortex structure. The influence of particle size and channel width on detonation propagation is analyzed.

Shock tube flows past partially opened diaphragms

Unsteady compressible flows resulting from the incomplete burst of the shock tube diaphragm are investigated both experimentally and numerically for different initial pressure ratios and opening diameters. The intensity of the shock wave is found to be lower than that corresponding to a complete opening. A heuristic relation is proposed to compute the shock strength as a function of the relative area of the open portion of the diaphragm. Strong pressure oscillations past the shock front are also observed. These multi-dimensional disturbances are generated when the initially normal shock wave diffracts from the diaphragm edges and reflects on the shock tube walls, resulting in a complex unsteady flow field behind the leading shock wave. The limiting local frequency of the pressure oscillations is found to be very close to the ratio of acoustic wave speed in the perturbed region to the shock tube diameter. The power associated with these pressure oscillations decreases with increasing distance from the diaphragm since the diffracted and reflected shocks partially coalesce into a single normal shock front. A simple analytical model is devised to explain the reduction of the local frequency of the disturbances as the distance from the leading shock increases.

Numerical experiments with several variant WENO schemes for the Euler equations

AbstractNumerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126:202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.

Numerical study of shock-wave diffraction in variable-section channels in gas suspensions

The problem of shock-wave transition past a backward-facing step in a gas suspension is solved. The calculation method is tested on a similar problem for a pure gas, and good agreement with available experimental and numerical results is reached. The effect of shock-wave intensity, mass load factor of particles in the mixture, and particle size on the flow structure in the gas suspension is determined. It is shown that the greatest difference between the flow pattern in a two-phase mixture and the corresponding flow in a pure gas is observed in the range of times when the characteristic sizes of the structures being formed are commensurable with the scale of the relaxation zones.

Diffraction of a two-shock configuration by a concave cylindrical surface

Diffraction of a two-shock configuration by a concave cylindrical surface with a continuously varying angle of diffraction in a perfect (inviscid and non-heat-conducting) gas is numerically investigated. Peculiarities of flow formation in the perturbed region due to a large initial angle of diffraction are revealed. The reasons for the appearance of the reverse flow over the cylindrical surface, which causes a vortex, are found. The influence of the vortex on the behavior of the loose end of the TU layer (slipstream) is studied. It is shown that the structure of the loose end of the TU layer is determined by vortex-related mixing in the gas. The nonstationary interaction of the diffracting shock wave and a sublayer shock with a concave cylindrical wall and the symmetry plane, which is accompanied by a change in the type of reflection, is examined.

Simple treatment of non‐aligned boundaries in a Cartesian grid shallow flow model

AbstractA simple method is proposed for treating curved or irregular boundaries in Cartesian grid shallow flow models. It directly evaluates fictional values in ‘ghost’ cells adjacent to boundary cells and requires no interpolation or generation of cut cells. The boundary treatment is implemented in a dynamically adaptive quadtree grid‐based solver of the hyperbolic shallow water equations and validated against several test cases with analytical or alternative numerical solutions. The method is easy to code, accurate, and demonstrably effective in dealing with irregular computational domains in shallow flow simulations. Results are presented for still water in a basin of complicated geometry, steady hydraulic jump in an open channel with a converging sidewall, wind‐induced circulation in a circular shallow lake, and shock wave diffraction in a channel containing a contraction and expansion. Copyright © 2007 John Wiley & Sons, Ltd.