Shock Wave Reflection Phenomena (Shock Wave and High Pressure Phenomena)

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Shocks are very thin, leading to very large gradients of velocity and temperature. Hence, shock waves are dissipative, irreversible processes that generate entropy and compress the flow. Static pressure, density, and temperature are increased after the shock. Shock waves are generated in a number of ways, creating violent changes in pressure.

Shock wave reflection phenomena

Take thunder, for example: The sudden heating caused by lightning makes the air around it expand faster than the speed of sound, which changes the air pressure and thus creates shock waves. These waves reach our ears a few seconds later as rumbling thunder. The rumbling sound occurs because a lightning bolt is a series of short bursts chained together and the resulting shock waves, which are generated at different altitudes, reach your ears at different times. You might also associate these powerful shock wave blasts with explosions or supersonic flight.

Lightning rapidly heats the air, leading to powerful shock waves that we hear as thunder. Image by Hansueli Krapf — Own work. Shock waves have unique properties that set them apart from sound waves. They travel faster than the speed of sound and also decrease in intensity faster than a sound wave.

These properties must be accounted for when designing applications such as transonic diffusers , which use shocks to slow down airflow. However, studying shock waves can be challenging due to the abrupt way they are generated. Shock tubes are instruments used in the testing of supersonic bodies as well as the study of compressible flow phenomena, high-temperature gases, and gas-phase combustion reactions.

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They consist of a tube closed at both ends and a diaphragm blocking any flow within the tube. The experiments can be conducted in the following steps:. A shock tube test apparatus at the University of Ottawa, Canada. Image by Christian Viau — Own work. Shock waves are not the only propagating disturbances observed in shock tube experiments.

Expansion fans travel in the opposite direction of shock waves and tend to expand the flow smoothly and continuously.

The values of static pressure, density, and temperature are decreased across the expansion fan, and entropy is conserved; this process is hence reversible. The analysis of the increment in the overpressure value due the multiple shock wave reflections has been executed, by positioning virtual gauges to measure them.

In the third group an urban environment has been modeled using 3D models. In that scenario, the overpressures of the shock wave from an explosion were studied. The models developed in these groups have some differences to enable the evaluation of different parameters, for example, the presence of obstacles between the explosion and the structures, positioning of the explosion and different internal layouts.


The results for shock wave overpressure were collected by gauges and has been analyzed. Quadrilateral elements have been used to modeling the simulations of the first 1D and second 2D groups, and volume elements has been used to modeling the simulations of the third group 3D. The models simulated share some similarities, for example, has been used Lagrangian mesh to model solids and Eulerian mesh to model fluids. The Lagrangian meshes are meshes based in Lagrangian methods.

In that case the modeled numerical mesh is enabled to move and distorts following the material motion.

The Eulerian mesh is a fixed mesh wherein the material flows through it. That mesh has a high computational cost to be processed due the large number of elements required to achieve accurate results [10]. The fluid-structure interaction can be achieved enabling the Euler-Lagrange coupling.

The remapping technique can be used to obtain computational time savings, as a good way to increase computational efficiency. This technique is based on a remap of the 1D analysis results in a 3D mesh. The boundary conditions used in the borders of air model allows the representation of unlimited air medium. The buildings simulated in third group were modeled as rigid and were assumed as resting on a rigid ground.

That assumptions enable an overall analysis of shock wave and a several gains of computational efficiency avoiding excessive deformations or fragmentation of the Lagrangian elements. The most simplified models to study blast waves consist in a detonation of spherical charge of TNT in free air in standard conditions. This first group of simulations were developed to involve this simplified conditions enabling a suitable comparative analysis with semi empirical models. Several meshes sizes were used in these simulations. The simulated models consist of a wedge formed by a combination of quadrangular elements filled with air Figure 2.

The charge of TNT was positioned in the center of model. The meshes sizes used were 5 mm, 10 mm, 20 mm, 50 mm. A 1kg TNT charge was detonated and the pressures was being measured at standoff distances 2,0 m, 2,5 m, 2,9 m, 3,3 m, 3,7 m, 4,0 m, 4,7 m, 5,0 m, 5,3 m, 5,9 m, 6,2 m, 6,7 m and 7,0 m.

The channeling effect occurs due complex environments geometries that can confine and canalize the energy of the explosion. This effect may increase the shock wave overpressures. In this group of simulations, four models were simulated Figure 3 to allow a comprehensive analysis of the channeling effect influence in the shock wave overpressures value. The 2D models simulated consist of a combination of quadrangular elements filled with air. Two rigid obstacles were positioned in this models in order to confine the explosion. A 50kg TNT charge was detonated Figure 4 and the pressures were being measured by gauges 1, 2 and 3 at standoff distances 2 m, 4 m and 8 m, respectively.

In this models were used Eulerian mesh to model explosion environment and Lagrangian mesh to define the obstacles. Large numerical models involving explosions may be modeled using mesh size of mm in order to achieve a certain degree of accuracy and a good computational efficiency [ 11 ]. However, in this case, a mesh size of 50 mm was used.

The real scaled experiments involving explosions in an urban environment may be very complex or uneconomical. In this case, the numerical approach may be a good way to avoid operational problems and develop a reliable study. The fundamental objective of this work is the analysis of the shock wave propagation and its interaction with rigid buildings. This enable the evaluation of overpressure history inside or outside the buildings.

Rigid concrete elements were used to model the edifications. This concept was utilized to develop six models, but a seventh model considering a free air blast was developed to allow a comprehensive comparative study.

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The models a and b have the same geometry and layout, but the positioning of the TNT charge is different. The models a , c and d have many similarities, but in the model c was used a 10kg TNT charge. Another difference is the obstacle between the explosion and the buildings modeled in d model. The models e and f are identical with a except the level of the openings of the buildings and the internal layout, respectively.

Figure 6 shows the positioning of the gauges at the mm over the ground. The mesh size of the buildings and the rigid soil surface are shown, too. Lagrangian elements were used to mesh the solids and the Eulerian mesh to model the fluids.

Pressure-Sensitive Paint Measurements of Transient Shock Phenomena

The standard ambient conditions were used in the models. The boundary conditions used in the models enables the structures and the soil to have rigid behavior. These assumptions allow an overall analysis of shock wave overpressures distribution and a gain of computational efficiency avoiding excessive deformations or fragmentation of the Lagrangian elements.

A mesh size of mm may be used to simulate urban environments with good accuracy [ 11 ]. But in this work a mesh size of 50mm was used.

Mach 6 shock wave generation and reflection

The results obtained from the 1D models were compared with the results from empirical formulas presented earlier and were plotted in Figure 7. The mesh sizes of 5 mm and 10 mm presented similar results with the Henrych and Brode predictions. The results for blast overpressures start an asymptotic convergence to large scaled distances. The successive peaks of shock wave overpressure are more frequently when the confinement is more accentuated. Shock tubes are an excellent method of delivering predictable step changes in pressure, allowing us to look at the response times of the PSP.

The aim of this work is to build upon the foundation laid by Asai et al. Shock wave diffraction around a large corner gives large positive and negative pressure changes and has been studied using a variety of other flow diagnostic techniques [ 11 — 13 ], meaning that this flow is relatively well understood.

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This work aims to investigate shock wave diffraction at two Mach numbers and compare the results with numerical data. Shock tubes are an ideal method to test the response time of an experimental technique. A region of high pressure region 4 is separated from a region of low pressure region 1 by a diaphragm. The diaphragm in the University of Manchester square shock tube is made up of acetate, which is burst by mechanical means.

After the rupture of the diaphragm, compression waves begin to travel from region 4 into region 1. These compression waves eventually coalesce into a discontinuous shock wave. The pressure at each location in the wave structure shown in Figure 1 can be analysed using the one-dimensional theory presented by Anderson [ 14 ]. The problem of shock wave diffraction around sharp corners has been investigated by several researchers since initial considerations by Howard and Matthews [ 15 ]. Many experimental all previous experimental work used density-based diagnostics and numerical simulations have been performed, showing different levels of flow features.

The basic structure of a strong shock wave diffracting around a corner was given by Skews [ 16 ]. The diffracting shock wave loses strength along its length as it rounds the corner.

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  5. This shear layer rolls up into a spiral vortex see Figure 2. Basic flow structure behind a shock wave diffracting around a sharp corner. The pressure rise generated by the incident shock and the pressure decrease found at the centre of the shed spiral vortex make this flow an excellent test case for high-speed PSP measurements.

    The expected flow schematic for these two Mach numbers is given in Figure 2. In Figure 2 , I is the incident shock, Ds is the diffracted shock, Rs is the reflected expansion wave, Cs is the contact surface, Ss is the shear layer, Mv is the main vortex and ET is a train of expansion waves and shocks. The bracket numbers represent regions of flow with different properties as they have been affected by different waves. The basic theory of intensity-based pressure-sensitive paint has already been covered in depth by many authors; as such, a full recollection is not warranted here.

    For information on the theoretical background of pressure-sensitive paint, the reader is directed to the excellent book by Liu and Sullivan [ 18 ].