Interaction of a singular surface with a strong shock in the interstellar gas clouds

2021 ◽  
Vol 63 ◽  
pp. 342-358
Author(s):  
Jasobanta Jena ◽  
Sheena Mittal
Keyword(s):  
Strong Shock ◽  
Singular Surface ◽  
Acceleration Wave ◽  
Interstellar Gas ◽  
Surface Theory ◽  
Expansion Waves ◽  
Lie Group Of Transformations ◽  
Compression And Expansion ◽  
Particular Solution ◽  
Flow Variables

We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.   doi:10.1017/S1446181121000328

INTERACTION OF A SINGULAR SURFACE WITH A STRONG SHOCK IN THE INTERSTELLAR GAS CLOUDS

2021 ◽  
pp. 1-17
Author(s):  
J. JENA ◽  
S. MITTAL
Keyword(s):  
Strong Shock ◽  
Singular Surface ◽  
Acceleration Wave ◽  
Interstellar Gas ◽  
Surface Theory ◽  
Expansion Waves ◽  
Lie Group Of Transformations ◽  
Compression And Expansion ◽  
Particular Solution ◽  
Flow Variables

Abstract We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.

The Aerodynamic Characteristics of the Pantograph When the Train Passes Through the Tunnel

2017 ◽  
Author(s):  
Dilong Guo ◽  
Wen Liu ◽  
Junhao Song ◽  
Ye Zhang ◽  
Guowei Yang
Keyword(s):  
High Speed ◽  
Aerodynamic Force ◽  
Maximum Amplitude ◽  
Aerodynamic Characteristics ◽  
High Speed Train ◽  
Expansion Waves ◽  
Compression And Expansion ◽  
High Speed Trains ◽  
Current Characteristics ◽  
Pass Through

The aerodynamic force acting on the pantograph by the airflow is obviously unsteady and has a certain vibration frequency and amplitude, while the high-speed train passes through the tunnel. In addition to the unsteady behavior in the open-air operation, the compressive and expansion waves in the tunnel will be generated due to the influence of the blocking ratio. The propagation of the compression and expansion waves in the tunnel will affect the pantograph pressure distribution and cause the pantograph stress state to change significantly, which affects the current characteristics of the pantograph. In this paper, the aerodynamic force of the pantograph is studied with the method of the IDDES combined with overset grid technique when high speed train passes through the tunnel. The results show that the aerodynamic force of the pantograph is subjected to violent oscillations when the pantograph passes through the tunnel, especially at the entrance of the tunnel, the exit of the tunnel and the expansion wave passing through the pantograph. The changes of the pantograph aerodynamic force can reach a maximum amplitude of 106%. When high-speed trains pass through tunnels at different speeds, the aerodynamic coefficients of the pantographs are roughly the same.

scholarly journals The speed, reflection and intensity of waves propagating in flexible tubes with aneurysm and stenosis: Experimental investigation

2019 ◽  
Vol 233 (10) ◽  
pp. 979-988 ◽  
Author(s):  
Wisam S Hacham ◽  
Ashraf W Khir
Keyword(s):  
Reflection Coefficient ◽  
Wave Speed ◽  
Expansion Waves ◽  
Reflected Wave ◽  
Compression And Expansion ◽  
Contracting Heart ◽  
Propagation Of Waves ◽  
Flexible Tubes ◽  
Mother Tube

A localized stenosis or aneurysm is a discontinuity that presents the pulse wave produced by the contracting heart with a reflection site. However, neither wave speed ( c) in these discontinuities nor the size of reflection in relation to the size of the discontinuity has been adequately studied before. Therefore, the aim of this work is to study the propagation of waves traversing flexible tubes in the presence of aneurysm and stenosis in vitro. We manufactured different sized four stenosis and four aneurysm silicone sections, connected one at a time to a flexible ‘mother’ tube, at the inlet of which a single semi-sinusoidal wave was generated. Pressure and velocity were measured simultaneously 25 cm downstream the inlet of the respective mother tube. The wave speed was measured using the PU-loop method in the mother tube and within each discontinuity using the foot-to-foot technique. The stenosis and aneurysm dimensions and c were used to determine the reflection coefficient ( R) at each discontinuity. Wave intensity analysis was used to determine the size of the reflected wave. The reflection coefficient increased with the increase and decrease in the size of the aneurysm and stenosis, respectively. c increased and decreased within stenosis and aneurysms, respectively, compared to that of the mother tube. Stenosis and aneurysm induced backward compression and expansion waves, respectively; the size of which was related to the size of the reflection coefficient at each discontinuity, increases with smaller stenosis and larger aneurysms. Wave speed is inversely proportional to the size of the discontinuity, exponentially increases with smaller stenosis and aneurysms and always higher in the stenosis. The size of the compression and expansion reflected wave depends on the size of R, increases with larger aneurysms and smaller stenosis.

On the instantaneous cutting of a columnar vortex with non-zero axial flow

1997 ◽  
Vol 351 ◽  
pp. 41-74 ◽  
Author(s):  
J. S. MARSHALL ◽  
S. KRISHNAMOORTHY
Keyword(s):  
Vortex Core ◽  
Flow Model ◽  
Plug Flow ◽  
Axial Flow ◽  
Vortex Rings ◽  
Core Radius ◽  
Expansion Waves ◽  
Columnar Vortex ◽  
Cutting Surface ◽  
Compression And Expansion

A study of the response of a columnar vortex with non-zero axial flow to impulsive cutting has been performed. The flow evolution is computed based on the vorticity–velocity formulation of the axisymmetric Euler equation using a Lagrangian vorticity collocation method. The vortex response is compared to analytical predictions obtained using the plug-flow model of Lundgren & Ashurst (1989). The plug-flow model indicates that axial motion on a vortex core with variable core area behaves in a manner analogous to one-dimensional gas dynamics in a tube, with the vortex core area playing a role analogous to the gas density. The solution for impulsive cutting of a vortex obtained from the plug-flow model thus resembles the classic problem of impulsive motion of a piston in a tube, with formation of an upstream-propagating vortex ‘shock’ (over which the core radius changes discontinuously) and a downstream-propagating vortex ‘expansion wave’ on opposite sides of the cutting surface. Direct computations of the vortex response from the Euler equation reveal similar upstream- and downstream-propagating waves following impulsive cutting for cases where the initial vortex flow is subcritical. These waves in core radius are produced by a series of vortex rings, embedded within the columnar vortex core, having azimuthal vorticity of alternating sign. The effect of the compression and expansion waves is to bring the axial and radial velocity components to nearly zero behind the propagating vortex rings, in a region on both sides of the cutting surface with ever-increasing length. The change in vortex core radius and the variation in pressure along the cutting surface agree very well with the predictions of the plug-flow model for subcritical flow after the compression and expansion waves have propagated sufficiently far away. For the case where the ambient vortex flow is supercritical, no upstream-propagating wave is possible on the compression side of the vortex, and the vortex axial flow is observed to impact on the cutting surface in a manner similar to that commonly observed for a non-rotating jet impacting on a wall. The flow appears to approach a steady state near the point of impact after a sufficiently long time. The vortex response on the expansion side of the cutting surface exhibits a downstream-propagating vortex expansion wave for both the subcritical and supercritical conditions. The results of the vortex response study are used to formulate and verify predictions for the net normal force exerted by the vortex on the cutting surface. An experimental study of the cutting of a vortex by a thin blade has also been performed in order to verify and assess the limitations of the instantaneous vortex cutting model for application to actual vortex–body interaction problems.

On the integrability and exact solutions of the nonlinear diffusion equation with a nonlinear source

1998 ◽  
Vol 39 (4) ◽  
pp. 513-527 ◽  
Author(s):  
K. Vijayakumar
Keyword(s):  
Diffusion Equation ◽  
Exact Solutions ◽  
Vector Fields ◽  
Travelling Wave ◽  
Nonlinear Source ◽  
Lie Group Of Transformations ◽  
Generalized Symmetries ◽  
Nagumo Equations ◽  
Particular Solution ◽  
Complex Valued

AbstractThe generalized diffusion equation with a nonlinear source term which encompasses the Fisher, Newell-Whitehead and Fitzhugh-Nagumo equations as particular forms and appears in a wide variety of physical and engineering applications has been analysed for its generalized symmetries (isovectors) via the isovector approach. This yields a new and exact solution to the generalized diffusion equation. Further applications of group theoretic techniques on the travelling wave reductions of the Fisher, Newell-Whitehead and Fitzhugh-Nagumo equations result in integrability conditions and Lie vector fields for these equations. The Lie group of transformations obtained from the exponential vector fields reduces these equations in generalized form to a standard second-order differential equation of nonlinear type, which for particular cases become the Weierstrass and Jacobi elliptic equations. A particular solution to the generalized case yields the exact solutions that have been obtained through different techniques. The group-theoretic integrability relations of the Fisher and Newell-Whitehead equations have been cross-checked through Painlevé analysis, which yields a new solution to the Fisher equation in a complex-valued function form.

scholarly journals Approximate Analytic Solution of a Self-Similar Piston Moving in an Inhomogeneous Medium

2020 ◽  
pp. 1-9
Author(s):  
B.N. Prasad
Keyword(s):  
Spherical Symmetry ◽  
Analytic Solution ◽  
Density Ratio ◽  
Strong Shock ◽  
Power Laws ◽  
Ideal Gas ◽  
Approximate Analytic Solution ◽  
Piston Problem ◽  
Self Similar ◽  
Flow Variables

Self-similar motion for the flow between a piston and strong shock propagating in a non uniform ideal gas at rest has been studied. The solution to the problem is similar to that of hypersonic flows past the power law bodies. The gas ahead of the shock is assumed to be uniform and at rest. This is considered as a particular case of radiative piston problem. The shock is assumed to be very strong and propagating in a medium at rest in which density obeys power laws. This problem with spherical symmetry has got importance in astrophysics. To solve the gas dynamics problem, Chernyii’s expansion techniques have been used in which flow variables are expanded in a series of powers of ε, the density ratio across the strong shock. The approximate analytic solution has been obtained in closed form to the zeroth approximation. The problem discussed belongs to the self-similar motion of the first kind. The resulting analytic solution gives the flow variables distribution for plane, cylindrical, and spherical symmetry for different cases which satisfy the similarity conditions with accurate trend and values.

scholarly journals The focusing of weak shock waves

1976 ◽  
Vol 73 (4) ◽  
pp. 651-671 ◽  
Author(s):  
B. Sturtevant ◽  
V. A. Kulkarny
Keyword(s):  
Shock Waves ◽  
Wave Field ◽  
Amplification Factor ◽  
Strong Shock ◽  
Weak Shock ◽  
Expansion Waves ◽  
Initial Wave ◽  
Geometrical Acoustics ◽  
Complex Wave ◽  
Maximum Amplification

This paper reports an experimental investigation, using shadowgraphs and pressure measurements, of the detailed behaviour of converging weak shock waves near three different kinds of focus. Shocks are brought to a focus by reflecting initially plane fronts from concave end walls in a large shock tube. The reflectors are shaped to generate perfect foci, arêtes and caustics. It is found that, near the focus of a shock discontinuity, a complex wave field develops, which always has the same basic character, and which is always essentially nonlinear. A diffracted wave field forms behind the non-uniform converging shock; its compressive portions steepen to form diffraction shocks, while diffracted expansion waves overtake and weaken the diffraction shocks. The diffraction shocks participate in a Mach reflexion process near the focus, whose development is determined by competition between the convergence of the sides of the focusing front and acceleration of its central portion. In fact, depending on the aperture of the convergence and the strength of the initial wave, the three-shock intersections of the Mach reflexions either cross on a surface of symmetry or remain uncrossed. In the former case, which is observed if the shock wave is relatively weak, the wavefronts emerge from focus crossed and folded, in accordance with the predictions of geometrical acoustics theory. In the latter, the strong-shock case, the fronts beyond focus are uncrossed, as predicted by the theory of shock dynamics. It is emphasized that in both cases the behaviour at the focus is nonlinear. The overtaking of the diffraction shocks by the diffracted expansions limits the amplitude of the converging wave near focus, and is the mechanism by which the maximum amplification factor observed at focus is determined. In all cases, maximum pressures are limited to rather low values.

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