Probing of Flow Fields with Shock Waves—The Swing Probe

1971 ◽  
Vol 49 (10) ◽  
pp. 1340-1349 ◽  
Author(s):  
J. D. Strachan ◽  
B. Ahlborn
Keyword(s):  
Shock Waves ◽  
Source Term ◽  
Flow Fields ◽  
Inhomogeneous Media ◽  
Shock Propagation ◽  
Local Velocity ◽  
One Dimensional ◽  
Density Distributions ◽  
The One ◽  
Velocity Pressure

The one dimensional equations governing shock propagation into inhomogeneous media have been developed to allow a shock to be used as a probe. Shock waves which collide with unknown gas or plasma flow fields suffer a change in velocity. Pressure, density, particle velocity, and local energy input at the edge of an unknown flow can be determined from the measurement of unknown flow. The steady variation of the velocity of strong probing shocks reveals details of the local velocity and density distributions inside the unknown flow field. One further result is the extension of the general theory of shock propagation into inhomogeneous media to cover the case when an energy source term appears at the front.

Analysis of Normal Combustion Waves in CH4-Air System

2014 ◽  
Vol 656 ◽  
pp. 101-109 ◽  
Author(s):  
Daniel Eugeniu Crunteanu ◽  
Dan Racoti ◽  
Corneliu Berbente
Keyword(s):  
Shock Waves ◽  
Algebraic Equation ◽  
Combustion Wave ◽  
Normal Shock ◽  
Combustion Waves ◽  
Conservation Equations ◽  
One Dimensional ◽  
Air System ◽  
The One

In this study one analyses the detonation and deflagration waves starting with Euler one-dimensional conservative equations. We present two methods of computing the normal combustion waves and normal shock waves parameters. The second one, called Cpm method, uses the one dimensional conservation equations system of mass, impulse and energy reduced to an quadratic algebraic equation. Combustion wave ,in CH4-air system is presented as an application.

scholarly journals Well-posedness of the linear heat equation with a second order memory term

2020 ◽  
Vol 34 ◽  
pp. 03011
Author(s):  
Constantin Niţă ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Unique Solution ◽  
Source Term ◽  
Memory Term ◽  
Well Posedness ◽  
Dimensional Torus ◽  
One Dimensional ◽  
Linear Heat ◽  
The One

In this article we prove that the heat equation with a memory term on the one-dimensional torus has a unique solution and we study the smoothness properties of this solution. These properties are related with some smoothness assumptions imposed to the initial data of the problem and to the source term.

scholarly journals EXACT SOLUTIONS TO THE SPIN-2 GROSS–PITAEVSKII EQUATIONS

2012 ◽  
Vol 27 (02) ◽  
pp. 1350013 ◽  
Author(s):  
ZHI-HAI ZHANG ◽  
YONG-KAI LIU ◽  
SHI-JIE YANG
Keyword(s):  
Exact Solutions ◽  
Rotational Symmetry ◽  
Time Factors ◽  
Time Dependent ◽  
Spin Space ◽  
One Dimensional ◽  
Density Distributions ◽  
Hyperfine State ◽  
The One ◽  
Bose Einstein

We present several exact solutions to the coupled nonlinear Gross–Pitaevskii equations which describe the motion of the one-dimensional spin-2 Bose–Einstein condensates. The nonlinear density–density interactions are decoupled by making use of the properties of Jacobian elliptical functions. The distinct time factors in each hyperfine state implies a "Lamor" procession in these solutions. Furthermore, exact time-evolving solutions to the time-dependent Gross–Pitaevskii equations are constructed through the spin-rotational symmetry of the Hamiltonian. The spin-polarizations and density distributions in the spin-space are analyzed.

One-Dimensional Density Distributions of Powder Media in Dies Subjected to Multishock Compactions

1988 ◽  
Vol 110 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Y. Sano
Keyword(s):  
Shock Wave ◽  
Density Distribution ◽  
Friction Force ◽  
The Other ◽  
Wall Friction ◽  
Uniform Density ◽  
Simple Type ◽  
One Dimensional ◽  
Density Distributions ◽  
The One

A theoretical attempt to clarify the reason why the compacts of powder media have uniform density distributions as the density of the compacts becomes high, is made for the compaction of the copper powder medium of a simple type by punch impaction. Based on the one-dimensional equation of motion including the effect of die wall friction force, there are two main factors which influence the density distribution of the medium during the compaction process; one is the propagation of the shock wave passing through the medium, while the other is the friction force between the circumferential surface of the medium and the die wall. The equation reveals that the effect of the force increases little as the density becomes high as a result of the repetitive traveling of the shock wave between the punch and plug. The propagation or more definitely the repetitive traveling, on the other hand, increasingly unformalizes the density distribution during the process as the number of the traveling increases. Owing to the aforementioned effects of the two factors on the density distribution during the process, the high density compacts become uniform.

One-dimensional spherical shock waves in an interstellar dusty gas clouds

2021 ◽  
Vol 76 (5) ◽  
pp. 417-425
Author(s):  
Astha Chauhan ◽  
Kajal Sharma
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Differential Equations ◽  
Shock Propagation ◽  
Dusty Gas ◽  
Shock Strength ◽  
Efficient System ◽  
One Dimensional ◽  
Arbitrary Strength ◽  
Spherical Shock

Abstract A system of partial differential equations describing the one-dimensional motion of an inviscid self-gravitating and spherical symmetric dusty gas cloud, is considered. Using the method of the kinematics of one-dimensional motion of shock waves, the evolution equation for the spherical shock wave of arbitrary strength in interstellar dusty gas clouds is derived. By applying first order truncation approximation procedure, an efficient system of ordinary differential equations describing shock propagation, which can be regarded as a good approximation of infinite hierarchy of the system. The truncated equations, which describe the shock strength and the induced discontinuity, are used to analyze the behavior of the shock wave of arbitrary strength in a medium of dusty gas. The results are obtained for the exponents from the successive approximation and compared with the results obtained by Guderley’s exact similarity solution and characteristic rule (CCW approximation). The effects of the parameters of the dusty gas and cooling-heating function on the shock strength are depicted graphically.

scholarly journals Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Maxim Olshanii ◽  
Dumesle Deshommes ◽  
Jordi Torrents ◽  
Marina Gonchenko ◽  
Vanja Dunjko ◽  
...  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Initial Conditions ◽  
Broad Class ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
One Dimensional ◽  
Nonlinear Transport Equation ◽  
Bosonic Case ◽  
The One

The recently proposed map [5] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [1] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial (t=0) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times t<0t<0. A similar singularity appears at t = T/4t=T/4, where T is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at t > T/4t>T/4. Here, we first map—using the scale invariance of the problem—the trapped motion to an untrapped one. Then we show that in the new representation, the solution [5] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [7]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers’ equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the t=0 singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [9]. At t=T/8t=T/8, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [5] and the Damski-Chandrasekhar shock wave becomes invalid.

Shock waves and non-stationary flow in a duct of varying cross-section

1971 ◽  
Vol 46 (1) ◽  
pp. 111-128 ◽  
Author(s):  
Naruyoshi Asano
Keyword(s):  
Shock Waves ◽  
Cross Section ◽  
Small Amplitude ◽  
Stationary Flow ◽  
Shock Propagation ◽  
Sound Waves ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Propagation Law ◽  
Good Agreement

Sound waves of finite but small amplitude propagating into a quasi-steady, supersonic flow in a non-uniform duct are analyzed by means of a perturbation method. General properties of the flow and of the wave propagation are studied using a one-dimensional approximation. A shock propagation law in the unsteady flow is obtained. As an example, the formation and development of shock waves are discussed for a duct with a conical convergence. Comparisons of the theory with an experiment are also made; fairly good agreement is found.

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