Shock Diffraction Research Articles

Pressure-Sensitive Paint Measurements of Transient Shock Phenomena

Measurements of the global pressure field created by shock wave diffraction have been captured optically using a porous pressure-sensitive paint. The pressure field created by a diffracting shock wave shows large increases and decreases in pressure and can be reasonably accurately captured using CFD. The substrate, a thin-layer chromatography (TLC) plate, has been dipped in a luminophore solution. TLC plates are readily available and easy to prepare. Illumination comes from two high-intensity broadband Xenon arc light sources with short-pass filters. The sample is imaged at 100 kHz using a Vision Research Phantom V710 in conjunction with a pair of long and short pass filters, creating a band. The PSP results are compared with numerical simulations of the flow using the commercial CFD package Fluent as part of ANSYS 13 for two Mach numbers.

On the vorticity distribution over a normal diffracted shock for small and large bends

Vorticity distributions over the diffracted shock both from Lighthill’s theory (Proc R Soc A 198:454–470, 1949) applicable for small bends and Sakurai and Takayama’s theory (Shock Waves 4:225–230, 2005) applicable for larger bends have been investigated for Mach numbers 1.80 and 1.95. Furthermore, Mach reflection effects for both theories for the same Mach numbers 1.80 and 1.95 have been investigated.

Self-similar solutions for the diffraction of weak shocks

We numerically solve a problem for the unsteady transonic small disturbance equations that describes the diffraction of a weak shock into an expansion wave. In the context of a shock moving into a semi-infinite wall, this problem describes the interaction between the reflected part of the shock and the part that is transmitted beyond the wall. We formulate the equations in self-similar variables, and obtain numerical solutions using high resolution finite difference schemes. Our solutions appear to show that the shock dies out at the sonic line, rather than forms at an interior point of the supersonic region.

Unsteady three-dimensional compressible vortex flows generated during shock wave diffraction

The results of an experimental and numerical investigation into the behaviour of the spiral vortex generated by shock wave diffraction over edges yawed to the incident shock wave are presented. Three-dimensional numerical simulations reveal significant distortion and bending of the free vortex in regions near the boundary of the flow domain, so as to meet it at a right angle. The results of numerical simulations were found to mimic the experimentally obtained photographs very well. The numerical results are used to explain the various features of the resultant flow fields, with particular emphasis placed on the behaviour and properties of the spiral vortex, as it evolves with time. The effects of bending on the structure of the vortex are examined. The rate of circulation production for the three-dimensional shock diffraction cases was calculated, and the trends observed correlated with those for the much published two-dimensional diffraction case.

On the Self-similar Diffraction of a Weak Shock into an Expansion Wavefront

We study an asymptotic problem that describes the diffraction of a weak, self-similar shock near a point where its shock strength approaches zero and the shock turns continuously into an expansion wavefront. An example arises in the reflection of a weak shock off a semi-infinite screen. The asymptotic problem consists of the unsteady transonic small disturbance equation with suitable matching conditions. We obtain numerical solutions of this problem, which show that the shock diffracts nonlinearly into the expansion region. We also solve numerically a related half-space problem with a “soft” boundary, which shows a complex reflection pattern similar to one that occurs in the Guderley Mach reflection of weak shocks.

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.

Lift and drag on a sphere above ground by a sliding shock

We consider the diffraction of a planar shock propagating parallel to a plate with a static sphere located above the flat plate. The shock wave reflection produces, in addition to a drag force, a lift component due to the asymmetric interaction with the flat plate. Spheres ranging from 10 µm to 10 mm diameter are considered, with a gap ratio h/ D in the range 0.0001–0.1. The shock Mach numbers are from 1.1 to 2. Both inviscid and laminar viscous flow computations are presented.

Numerical simulation and PIV study of compressible vortex ring evolution

Formation and evolution of a compressible vortex ring generated at the open end of a short driver section shock tube has been simulated numerically for pressure ratios (PR) of 3 and 7 in the present study. Numerical study of compressible vortex rings is essential to understand the complicated flow structure and acoustic characteristics of many high Mach number impulsive jets where simultaneously velocity, density and pressure fields are needed. The flow development, incident shock formation, shock diffraction, vortex ring formation and its evolution are simulated using the AUSM+ scheme. The main focus of the present study is to evaluate the time resolved vorticity field of the vortex ring and the shock/expansion waves in the starting jet for short driver section shock tubes—a scenario where little data are available in existing literature. An embedded shock and a vortex induced shock are observed for PR = 7. However the vortex ring remains shock free, compact and unaffected by the trailing jet for PR = 3. Numerical shadowgraph shows the evolution of embedded shock and shock/expansion waves along with their interactions. The velocity and vorticity fields obtained from simulation are validated with the particle image velocimetry results and these data match closely. The translational velocity of the vortex ring, velocity across the vortex and the centre line velocity of the jet obtained from simulation also agree well with the experimental results.

Numerical Simulation of Shock Diffraction on Cartesian Grid

Shock diffraction over geometric obstacles is performed on two-dimensional cartesian grid using the TVD WAF method in conjunction with the HLLC approximate Riemann solver and dimensional splitting. Present cartesian grid results for popular and challenging two-dimensional shock diffraction problems are presented and compared to experimental photographs. Benchmark and example test cases were chosen to cover a wide variety of Mach numbers for weak and strong shock waves, and for square and circular geometries. The results show that the comparisons between experimental and simulated images are consistent.

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.

Visualization of compressible vortex rings using the background-oriented schlieren method

In this article, we attempt to validate flow visualization using the high-speed background-oriented schlieren (HiBOS) method, which is the BOS technique combined with a high-speed video camera as the recording device in the experiment. The method has been applied to shock-induced flow near the open end of a shock tube. Three incident shock Mach numbers were examined so that the BOS measurements could be compared with results given in the literature of particle-image velocimetry (PIV) measurements. Using the HiBOS technique, we were able to clearly view developing, compressible vortex rings and diffracted shock waves discharged from the open end of the shock tube. From the BOS images, we extracted the history of the propagation velocity, the diameter of the vortex ring, and the diameter of the vortex core, all of which agree with the corresponding PIV values reported in the literature.

Diffraction of normal shock for monoatomic gases

In the present investigation, vorticity distribution of a particle over the normal diffracted shock has been obtained for monoatomic gases, CO2 and SF6. Further some results using Lighthill’s theory (Lighthill in Proc R Soc A 198:454–470, 1949) and Whitham’s theory (Whitham in J Fluid Mech 2:145–171, 1957) have been obtained.

Study of Detonation Interactions Inside a Two-Dimensional Ejector Using Detonation Transmission Tubing

The present experimental study employs a non-electrical (NONEL) tube placed inside a twodimensional convergent nozzle with an ejector system. The detonation initiates inside the NONEL tube, due to the reactants deposited on its internal surface, producing a shock wave and consequent products of combustion with repeatable results. High-speed shadowgraphy using the Shimadzu camera was employed to visualise the induced flow field. Pressure measurements were taken at different locations along the test section to study the flow quantitatively. The results revealed that the emergence of the products of combustion from the NONEL tube plays an important role in the flow dynamics within the ejector. The interaction between the combustion products and vortices formed due to shock diffraction lead to the early decay of the vortices. The presence of these vortices are vital in the entrainment of secondary flows through the ejector which is the main reason for the incorporation of ejectors in propulsion applications. Research Student, School of MACE, The University of Manchester, UK. AIAA Student Member Research Student, School of MACE, The University of Manchester, UK. Professor (Reader), School of MACE, The University of Manchester, UK. AIAA Senior Member Professor, Aerospace Engineering Department, IISc, India. AIAA Senior Member.

Sharp interface simulations with Local Mesh Refinement for multi-material dynamics in strongly shocked flows

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with levelset interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) is developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. In addition, the Riemann solver based GFM approach is augmented with a quadtree (octree in three-dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions. The paper reports on a conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundaries. The numerical examples presented in this paper clearly demonstrate that the methodology produces accurate benchmark solutions and effectively captures fine structures in the flow field.

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.

Interference and diffraction of pressure shocks in flow around bodies of revolution located near a surface

This paper presents the results of experimental and computational investigations of a supersonic (M∞ = 4.03, Re1 = 55⋅10 6 m −1 ) flow around two bodies of revolution with conical noses with an opening θ = 40 o and cylindrical cases with an extension λ = 5 located near a flat surface at zero angles of attack at a relative distance from each other Z = 1.4. We have made a comparison between the structure of the shock waves formed in the zone of hydrodynamic interference of the bodies of revolution in free flight and in flight over the surface at a distance Y = 0.96. We have demonstrated the possibility of satisfactory prediction of the hy- drodynamic structure of the realized flows and aerodynamic characteristics of the bodies under investigation on the basis of the numerical solution of Euler equations. Introduction. The investigation of the supersonic flows realized in the flight of a group of vehicles near a surface is an urgent problem of modern aerogas dynamics. A detailed analysis of their gas-dynamic structure is neces- sary for explaining the effects of aerodynamic interference and predicting the appearance therewith of forces and mo- ments. Since experimental studies of such complex flows are very difficult and require considerable expenses, an important role in solving problems of the considered class is played by the methods of computational aerodynamics. As is known, more complete modeling of the real properties of flows connected with viscous effects is only possible with the use of the methods of solving Navier-Stokes equations with different turbulence models (RANS) or direct nu- merical simulation (LES). These methods require huge computational resources and a considerable time expenditure. Therefore, in many cases, for practical purposes simpler and cheaper methods of obtaining necessary information on the basis of solving Euler equations are used. This was demonstrated, for example, in (1-9) in which a comparison between the results of numerical calculations of a nonviscous flow and the experimental data was made. The above- mentioned works showed a satisfactory agreement between the calculated and experimental aerodynamic characteristics of the investigated bodies, although in a number of cases considerable discrepancies in local pressure distributions were observed. Such differences are most often explained by the boundary-layer separations that take place in the real flow and are formed under the action of pressure shocks (8, 9). The present work is a sequel of the investigations presented in (1-4, 6-8, 10-12). The aim of the work is to consider in detail the wave structures formed in the process of interference-diffraction phenomena in the space between the bodies and the plate, as well as to check further the possibilities of using numerical calculations within the frame- work of Euler equations for investigating such complex flows. Experimental. Experiments were carried out in a T-313 supersonic wind tunnel of the S. A. Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences at a Mach number M ∞ = 4.03 and a Reynolds number Re 1 55⋅10 6 m −1 . The model consisting of a flat plate FP and two iden- tical bodies of revolution (B 1 and B 2 ) with an opening of their noses θ = 40 o located over it parallel to the flow is

Aerodynamic interference between high-speed slender bodies

Under supersonic flow conditions, slender bodies in close proximity induce aerodynamic interference effects. This paper aims to quantify the magnitude of the resulting interference loads and to understand the underlying flow-physics mechanisms that cause them. A pair of identical slender bodies are investigated through a series of wind-tunnel experiments and supporting computational fluid dynamics (CFD) predictions. The bodies induce a complex interference flowfield, which tends to be bespoke to each configuration. The flow features include impinging shock and expansion waves, conical shock reflections, strong skewing of the boundary-layer flows and shock diffraction. The effects of axial stagger, lateral separation and the strength of the primary disturbance flow field are evaluated. The interference loads are found to be most sensitive to the initial location of the primary disturbance but are also affected by its strength. In addition, maximum interference loads which equate to an effective incidence of up to 6° are observed. Finally, very good agreement is found between the measurements and the CFD predicted normal force and pitching moment.

Numerical simulation of detonation using an adaptive Cartesian cut-cell method combined with a cell-merging technique

A second-order accurate scheme for the Cartesian cut-cell method developed previously by the authors [Ji H, Lien F-S, Yee E. Comput. Methods Appl. Mech. Eng. 198 (2008), 432] is generalized for application to both two- and three-dimensional inviscid compressible flow problems. A cell-merging approach is used to address the so-called “small cell” problem that has plagued Cartesian cut-cell methods. In the present cell-merging approach, the conservative variables are stored at the cut-cell centroid (including the non-merged and merged cut-cells) rather than at the Cartesian cell center. Although this approach results in a more complicated search algorithm for the determination of the neighbor cells (required for the computation of the spatial gradients of the conservative variables), this approach enables the straightforward formulation of a higher than first-order accurate discretization scheme in the vicinity of the (complex and irregular) internal boundaries of the flow domain. Six test cases (including detonation problems) are used to demonstrate the accuracy and capability of the adaptive cut-cell method, for which both mesh refinement and derefinement techniques are employed in the case of an unsteady shock diffraction problem.

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.

Numerical methods for weak shock propagation and diffraction around a microphone.

There are two interrelated goals for this presentation. The first goal is to give an overview of available numerical approaches for weak shock propagation. There are multiple approaches available, including formulations based on the Burgers equation, KZK or NPE equations, the second-order equations of nonlinear acoustics, the Navier-Stokes equations, or the Boltzmann equation. There are also multiple numerical techniques for discretizing each of underlying equations, and while some approaches give special treatment to weak shocks others handle the shocks automatically. The second goal of this presentation is to show recent simulation results for an explosion shock interacting in two dimensions with a microphone. The diffraction of the weak shock around the microphone housing does turn out to be amplitude dependent. It is only a modest effect, increasing for higher amplitudes. This knowledge is important for precise, close-range blast source characterization. In the future, the nonlinear diffraction of weak shocks around transducers also should be investigated for finite amplitude biomedical ultrasound, since the mechanisms for nonlinear diffraction are almost identical for ultrasound and explosion waves. [Work supported by U.S. Army ERDC-CERL.]