Top PDF On Shock Wave Diffraction From Non-orthogonal Apertures

On Shock Wave Diffraction From Non-orthogonal Apertures

On Shock Wave Diffraction From Non-orthogonal Apertures

Figure 5.8: Possible Kelvin-Helmholtz instability of the primary shear layer for 60 ° cone at MApex of 1.11 The extended test campaign considered all except the highest apex Mach Numbers possible on the apparatus (due to safety restrictions) and only tests in which the flow was well centred on the axis of the apparatus were considered (see § 5.1.4.2 for more on this distinction). The description of the basic flow field will be based on the images for the M Apex of 1.11 flow in the left of Figure 5.9. In frame a) the shear layer can be seen extending between the triple points (one marked as TP in the figure) of the Mach reflection and the vortex ring toward the centre of the frame. While there are other vortex rings shed from the outer diffraction lip at later times for most of the Mach numbers, the vortex ring of interest here is the first one caused by the axial jet formed when the shock wave first reflects at the cone apex. It should be noted that the shape seen here of the line connecting the tangent edges of the shear layer defines a concave cone where the outer edges of the cone are at the same level as the protruding portion closer to the centre line. The angle between the incident, reflected, and Mach stem waves is already quite shallow at this time. While some striations are visible in the shear layer near the centreline, the tangent edge of the shear layer still appears smooth. In frame b), there is noticeable striation of the tangent edge of the shear layer suggesting a KHI. The shear layer is still a concave cone but the entire cone now appears to extend away from the plane of the base defined by the outer edge and the curvature is noticeably lower than at earlier times.
Show more

148 Read more

The diffraction, reflection and propagation of cylindrical shock wave segments

The diffraction, reflection and propagation of cylindrical shock wave segments

2.1 Geometric Shock Dynamics In Whitham’s theory, knowledge of the shock’s geometry and Mach number along its profile are sufficient to predict how it will evolve. In his 1956 paper, Whitham [ 13 ] applied this method to two dimensional shock waves diffracting on convex surfaces and reflecting on concave surfaces. A distinction is made between diffraction and reflection wherein, diffraction is characterised by expansion waves and reflection by compression waves. In addition shock diffraction and reflection, Whitham also used GSD to investigate the stability of shock waves with non–uniform initial profiles (portions of the shock being planar while some portions are concave). In its formulation, an arbitrary shock shape was considered making the theory applicable not only to Whitham’s preliminary investigations, but to a multitude of other cases.
Show more

176 Read more

Three-dimensional shock wave distortion in shock-square vortex loop interaction

Three-dimensional shock wave distortion in shock-square vortex loop interaction

Understanding of shock wave interaction with three-dimensional vortex loop is also a key issue for noise generation. Shimizu et al. [22] experimentally and theoretically investigated the mechanism of noise generation in shock-vortex ring interaction in a three-dimensional flow field. They focused on investigating noise generation at the early stage of the interaction. Noise generation comes from the scattered waves involving the shock diffraction, the acoustic wave, and the backward scattering by density inhomogeneity. Inoue et al. [32] numerically investigated sound generation in a long interaction process and showed large sound pressures occur due to shock wave focusing. Shock wave focusing in shock-vortex ring interaction had also been observed computationally by Takayama et al. [29]. Therefore, shock wave deformations such as diffraction, reflection, and focusing may lead to enhanced noise generation. Since non-circler vortex loops have self-induced vortex deformation, it leads to a more complicated mechanism for sound generation. This study focuses on investigating three-dimensional shock wave distortion and propagation phenomena. An experimental investigation of shock-square vortex loop interaction was conducted at an incident shock Mach number of 1.39 in a square cross-sectional open-end shock wave generating tube. The high-speed shadowgraph photography technique was used to evaluate flow characteristics.
Show more

16 Read more

Shock Wave Behavior of Particulate Composites

Shock Wave Behavior of Particulate Composites

The study of heterogeneous and anisotropic materials and non normal impact geometries neces- sitated the development out of plane velocity measurements. These measurements were subject to the same bandwidth limitations as those faced by normal velocity interferometers. Just as VISAR provided a solution for normal motion, one of several designs implemented to desensitize transverse displacement interferometers for use with slow recording equipment is the Variable Sensitivity Dis- placement Interferometer (VSDI) developed at Brown University [35]. VSDI is a diffraction assisted displacement interferometer capable of resolving both normal and transverse motion of a grating affixed to the rear surface of a target plate in gas gun experiments. Its primary use is to determine the structure and magnitude of a shear wave pulse traveling through a solid material undergoing combined pressure and shear loading. This experimental arrangement, known as Pressure Shear Plate Impact (PSPI) generates combined loading in a thin foil of a material of interest sandwiched between two high shock impedance anvils. The surface normal of the composite stack is then inclined relative to the direction of impact. A keyed gas gun is then used to propel a similarly inclined flyer plate, which generates normal and transverse motion in the target plate due to the impact direction being inclined relative to the impact surfaces.
Show more

180 Read more

The velocity of the arterial pulse wave: a viscous-fluid shock wave in an elastic tube

The velocity of the arterial pulse wave: a viscous-fluid shock wave in an elastic tube

The speed of the arterial pulse wave is commonly termed the pulse-wave velocity (PWV). It has been shown to increase during the course of certain diseases, and this increase has generally been attributed to "arterial stiff- ness" [4-7]. This interpretation is consistent with Equa- tion (1), the Korteweg-Moens Equation, which is based in part on the assumption that the fluid is not viscous. Lambossy [8] introduced a model for arterial blood flow in which viscosity results in shear force on the inner wall of an artery and the pressure gradient is a simple har- monic function of time, e iωt . In this model, is a con- stant, and ω is the frequency of oscillation. Other constants in the model are he viscosity of blood, denoted μ , and the density, denoted ρ . The arterial wall is a straight, rigid cylindrical tube of radius R.
Show more

6 Read more

Surface Effects on the Diffraction of P Wave by an Arbitrary Shaped Cavity

Surface Effects on the Diffraction of P Wave by an Arbitrary Shaped Cavity

In fact, the surface elasticity theory can be applied not only to the statics analysis, but also to the dynamics analysis. In the framework of surface elasticity theory, the scattering of plane compressional and shear waves by a single na- no-sized coated fiber and the multiple scattering by two cylinder inclusions, which embedded in an elastic matrix is studied by Ou and Lee using the method of eigenfunction expansion [7] [8]. Zhang et al . [9] used the wave function ex- pansion method to study the effect of nano-sized arrays on the longitudinal wave diffraction in elastic media, and gave the corresponding elastic diffraction fields. Ru et al . [10] considered the SV wave multiple scattering caused by a cluster of nano-cylindrical holes. Using the displacement potential method and the wave function expansion method, they derived the scattering field around the hole. Ou et al . [11] studied the effects of semi-cylindrical inclusions on the scattering of plane P wave in an elastic half-plane. The results show that surface energy has a significant effect on the scattering of plane P wave as the radius of the semi-cylindrical inclusions shrink to nanometers. Wang et al . [12] [13] used Gurtin’s surface elasticity model to analyze the diffraction of elastic wave by a nanosized inhomogeneity, and they also demonstrated that the surface energy has a significant effect on the diffraction of the elastic wave when the cavity ra- dius is reduced to the nanoscale.
Show more

12 Read more

Scattering from Perfectly Magnetic Conducting Surfaces: the Extended Theory of Boundary Diffraction Wave Approach

Scattering from Perfectly Magnetic Conducting Surfaces: the Extended Theory of Boundary Diffraction Wave Approach

The evaluation of the surface integrals needs high computation times for diffraction problems with complex geometries. TBDW method reduces the surface integral to a line integral, resulting in a significant improvement in the computation time. Moreover, the line integral reduction of the surface integrals enables one to evaluate the edge diffracted fields directly, by integrating the reduced integrand along the edge contour.

11 Read more

The Fractional Derivative Approach for the Diffraction Problems: Plane Wave Diffraction by Two Strips with the Fractional Boundary Conditions

The Fractional Derivative Approach for the Diffraction Problems: Plane Wave Diffraction by Two Strips with the Fractional Boundary Conditions

This study more deeply investigates the properties of such a new material which satisfies the fractional boundary condition. The theoretical description of electromagnetic plane wave scattering by the two strips with different dimensions is given in the theoretical section. After that, the total electric field distribution and Total Radar Cross Section (TRCS) are investigated and obtain numerical results. In the general case, the solution of the problem is reduced to a solution of a system of linear algebraic equations (SLAE) which can be obtained with a given accuracy. However, for the values of the fractional order (FO) α = 0 . 5, the solution is obtained in an analytical form which is the advantage
Show more

14 Read more

Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder

Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder

+ with the integer n depending on the radius of cylinder. Generally, the integer n increases for a cylinder of larger diameter. The usual approximation by Laguerre functions is extended by introducing a scale parameter. The convergence of Laguerre series is then dependent on the value of the scale parameter s. The ana- lytical and numerical computations of series coefficients are performed to study the number of se- ries terms to keep the same accuracy. Indeed, the choice of integer n depends on the scale para- meter. Furthermore, diffraction waves generated by a semi-sphere inside the cylinder are eva- luated on the cylinder surface. It is shown that the approximation by Laguerre series for diffrac- tion waves on the cylinder is effective. This work provides important information for the choice of the radius of control surface in the domain decomposition method for solving hydrodynamic problems of body-wave interaction.
Show more

6 Read more

Periodic Wave Shock solutions of Burgers equations

Periodic Wave Shock solutions of Burgers equations

In this paper we present a new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of non standard analysis.

11 Read more

Shock Wave Treatment for Achilles Tendinopathy

Shock Wave Treatment for Achilles Tendinopathy

In 90 of the 101 Achilles tendons (89%) with chronic painful mid-portion Achilles tendinosis, treatment was satisfactory and the patients were back on their pre-injury activity level after the 12-week training regimen. In these patients, the amount of pain during activity, registered on the VAS-scale decreased significantly from 6.7 to 1.0.

43 Read more

Air Plasma Mitigation of Shock Wave

Air Plasma Mitigation of Shock Wave

Shock wave is a detriment in the development of supersonic aircrafts; it increases flow drag as well as surface heating from additional friction; it also initiates sonic boom on the ground which precludes supersonic jetliner to fly overland. A shock wave mitigation technique is demonstrated by experiments conducted in a Mach 2.5 wind tunnel. Non-thermal air plasma generated symmetrically in front of a wind tunnel model and upstream of the shock, by on-board 60 Hz periodic electric arc discharge, works as a plasma deflector, it deflects incoming flow to transform the shock from a well-defined attached shock into a highly curved shock structure. In a sequence with increasing discharge intensity, the transformed curve shock increases shock angle and moves upstream to become detached with increasing standoff dis- tance from the model. It becomes diffusive and disappears near the peak of the dis- charge. The flow deflection increases the equivalent cone angle of the model, which in essence, reduces the equivalent Mach number of the incoming flow, manifesting the reduction of the shock wave drag on the cone. When this equivalent cone angle exceeds a critical angle, the shock becomes detached and fades away. This shock wave mitigation technique helps drag reduction as well as eliminates sonic boom.
Show more

11 Read more

Shock Wave and Boundary Layer Interaction

Shock Wave and Boundary Layer Interaction

Diffusers slow down the air entering the engines of supersonic aircraft to subsonic speeds to avoid damaging the engine. They typically do this by inducing shock waves prior to the engine inlet. In this report several diffuser geometries were modeled to cr eate oblique shock waves to reduce air speed with less stagnation pressure losses and drag than normal shock waves would create. These geometries include single ramp, double ramp, curved ramp, and a double ramp cone with external ramp and channel. This was done in Ansys Fluent using a refined mesh with an inflation layer along the diffuser surface. The CFD was run using a density based solver coupled with a turbulent model and the resulting stagnation pressure losses, drag, and boundary layer separation were compared.
Show more

45 Read more

Characterization of the Shock Wave Structure in Water

Characterization of the Shock Wave Structure in Water

CHARACTERIZATION OF THE SHOCK WAVE STRUCTURE IN WATER Emilie Maria Teitz, B.S. Marquette University, 2017 The scientific community is interested in furthering the understanding of shock wave structures in water, given its implications in a wide range of applications; from researching how shock waves penetrate unwanted body tissues to studying how humans respond to blast waves. Shock wave research on water has existed for over five decades. Previous studies have investigated the shock response of water at pressures ranging from 1 to 70 GPa using flyer plate experiments. This report differs from previously published experiments in that the water was loaded to shock pressures ranging from 0.36 to 0.70 GPa. The experiment also utilized tap water rather than distilled water as the test sample.
Show more

122 Read more

Non-negative orthogonal greedy algorithms

Non-negative orthogonal greedy algorithms

computational burden indicators of SNNOLS and NNOLS are shown in Fig. 2. It is noticeable that the number of iterations L required to reach a support of cardinality K is larger than K because of support compression. Specifically, the histograms of Fig. 2(b) show that on average, L is larger than K for NNOLS and even larger for SNNOLS (the average values are given in the last columns of Tab. I). This is consistent with the fact that the NNOLS selection rule is more involved but more reliable. Moreover, the standard deviation of L corresponding to the histograms of Fig. 2(b) is 17 and 12 for SNNOLS and NNOLS, respectively, which indicates that the size of the support found after k iterations may significantly vary between trials. In order to get meaningful evaluations, we choose to compute the average values of each indicator over the last t iterations, with t ∈ {0, . . . , K − 1}. When t = 0, only the last iteration is taken into account, so the current support is of size K. For larger values of t, the supports found during the last t iterations have varying sizes but the averaging operation remains meaningful, especially for the last iterations, which are the most costly. The curves displaying the average of each indicator over 200 trials and over the last t iterations are shown in Fig. 2(a). One can observe from the curve (1 − ρ ↓ ) that the rate of non-descending atoms gradually
Show more

17 Read more

Weak shock wave reflections due to transverse waves in a conventional shock tube

Weak shock wave reflections due to transverse waves in a conventional shock tube

Recently, Defina, Susin & Viero (2008) presented high-resolution numerical solutions of the depth averaged inviscid shallow water equations which provided new information on the weak shock reflection domain within the von Neumann paradox conditions. The authors computed shock reflections close to the Guderley and the Vasilev reflections which confirmed the validity of the four-wave theory, however they did not discover a complex sequence of supersonic patches predicted by Tesdall et al. (2002). The absence of the additional triple points and supersonic patches agrees with the suggestion by Vasil’ev et al. (2008) that the complex sequence of triple points only occurs during unsteady flow conditions, which is not the present case in the work of Defina, Susin & Viero (2008). It was noted that the four-wave model correctly predicts the wave pattern around the triple point but is not the solution of the GR, as the flow downstream of the Mach stem in the vicinity of the triple point is still supersonic and it is further turned towards the Mach stem. Defina, Susin & Viero (2008) therefore discuss a possible solution to better describe the developed wave characteristics of the GR. Note all results are based on the Froude number F 0 = 1.7
Show more

178 Read more

Free Lagrange simulations of shock bubble interaction in extracorporeal shock wave lithotripsy

Free Lagrange simulations of shock bubble interaction in extracorporeal shock wave lithotripsy

to Illodel the interaction of a lithotripter shoek wave with two stable spherical bubble, and to observe: • the re'flection, transmission and refraction of the shock waves • the collapse[r]

226 Read more

Exhaust Nozzle Plume and Shock Wave Interaction

Exhaust Nozzle Plume and Shock Wave Interaction

were generated for use on parallel processor systems. To reduce computational time on a large 3-D grid, inviscid wall boundaries were used for all nozzle surfaces. External flow conditions were run at Mach 2.2, an angle of attack of zero, and an Euler solution was generated. The wedge (Figure 3) was unswept with 2.5° half angle leading and trailing edges. This wedge permitted study of shock and expansion regions passing through a nozzle plume. The wedge was located at 57.1 in. above the nozzle centerline, and the leading edge of the wedge was located in a plane 13.14 in. upstream of the nozzle exit. In this case, the axial station for the leading edge of the wedge was close to the nozzle throat, not the nozzle exit. The upper boundary of the mesh contained the profile of the lower wedge surface where the boundary conditions were inviscid wall boundaries. All other boundary conditions were again set to the WIND-US ‘freestream’ boundary condition.
Show more

28 Read more

Shock wave propagation in periodically layered composites

Shock wave propagation in periodically layered composites

IX 3 Experimental Systems for Shock Compression of Solids C-l 3.1 High Velocity Planar Impact Loading System C-l 3.2 Experimental Techniques: Diagnostic Systems C-3 3.2.l Arrival Time De[r]

211 Read more

Shock Wave Mitigation by Air Plasma Deflector

Shock Wave Mitigation by Air Plasma Deflector

Theory shows that the shock wave angle and the shock structure depend on the cone angle of the wind tunnel model, and on the Mach number and the def- lection angle of the incoming flow [1]. In the present study, the cone angle of the wind tunnel model and the Mach number of the incoming flow are fixed, an on-board plasma deflector is introduced to study shock structure modification by the flow deflection [20]. The polarity of the applied voltage enables electron plasma to be accelerated in the upstream direction by the applied electric field, it forms a plasma deflector in the upstream region to deflect incoming flow through elastic collisions. Ion plasma also affects the incoming flow, but via a different process. Ions moving through their own gas are subject to charge transfer to the neutral gas, which is a predominant inelastic collision process in the low ion energy regime [21]. An ion becomes a neutral particle after the charge transfer, but retains its velocity, which is usually low. Thus, these par- ticles do not contribute to the shock wave formation. The ions converted from neutrals through charge-transfer are collected by the cathode and do not con- tribute to the shock wave generation either. The shock of the deflected flow is expected to have a larger shock angle (than that of the baseline one) and a mod- ified structure, representing a weaker shock.
Show more

18 Read more

Show all 10000 documents...