Intrinsic coordinates algorithm for efficient simulation of weak-shock propagation in relaxing media

2021 ◽  
Vol 149 (4) ◽  
pp. A138-A138
Author(s):  
William A. Willis III ◽  
Mark F. Hamilton ◽  
John M. Cormack
Keyword(s):  
Weak Shock ◽  
Shock Propagation ◽  
Efficient Simulation

The determination of arc temperatures from shock velocities

1957 ◽  
Vol 240 (1220) ◽  
pp. 54-66 ◽  
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Wave Theory ◽  
New Method ◽  
Shock Propagation ◽  
Plane Shock ◽  
Gas Temperature ◽  
Specific Heats ◽  
Arc Discharges

The measurement of the high gas temperatures associated with arc discharges requires special techniques. One such method, developed by Suits (1935), depends on the measure­ment of the velocity of a sound wave passing through an arc column, although in fact Suits measured the velocity of a very weak shock wave. The new method described in the present paper is one in which temperatures are determined from the measurement of the velocity of a relatively strong shock wave propagated through an arc. The new method has the merit of consistently producing accurately measurable records and of increasing the accuracy of the temperature determination. The shock velocities are measured by means of a rotating mirror camera. Within the arc, the shock propagation is observable by virtue of the increased arc brightness produced by the shock. In the non-luminous regions surrounding the arc, the shock propagation is displayed by means of a Schlieren system. The interpretation of the measurements depends upon a one-dimensional analysis given in this paper which is similar to that of Chisnell (1955) and which describes the interaction of a plane shock with a con­tinuously varying temperature distribution. In our analysis account is taken also of the continuous variation in specific heats and molecular weight which are of importance under high gas temperature conditions. In practice plane wave theory cannot adequately describe the shock propagation, since attenuation occurs both in the free gas and in the arc column. The effects of this attenuation on the temperature determinations may be accounted for by the use of an experimentally determined attenuation relationship given in the paper. The finally developed method yields temperature values to an accuracy of ± 2%. Experiments are described for carbon and tungsten arcs in air and nitrogen for currents up to 55 amperes and pressures up to 3 atmospheres. The values obtained range from 6200 to 7700° K and are in good agreement with values determined by other techniques.

Shock Propagation in a Strain-Hardening Material

1969 ◽  
Vol 36 (2) ◽  
pp. 181-188 ◽  
Author(s):  
P. J. Rausch
Keyword(s):  
Shock Front ◽  
Stress Component ◽  
Weak Shock ◽  
Simple Wave ◽  
Entropy Change ◽  
Momentum Conservation ◽  
Shock Propagation ◽  
Wave Form ◽  
Hardening Material ◽  
Material State

Weak shock theory is used to analyze the propagation of the stress waves which are induced by nonuniform, instantaneous, internal heating of a nonlinearly elastic, semi-infinite solid. The material nonlinearity considered is caused by the increase in bulk modulus which occurs as the hydrodynamic stress component increases. Heating is assumed to occur instantaneously. Since the shock is assumed to be weak, the entropy change across it is negligible, and therefore the wave form both behind and in front of the shock is found by using a coordinate perturbation method to solve the nonlinear equations for constant entropy. This solution predicts a multivalued material state in the vicinity of the shock front without locating the front itself. The location of the shock front is found separately by using the principle of momentum conservation. If the front is then inserted at this location, a wave form is obtained for which the material state is everywhere single-valued. The results and conclusions which are presented are based on a comparison of the perturbation solution found in this paper, and a simple wave solution and on an assessment of shock strength.

scholarly journals A Measurement System for the Study of Nonlinear Propagation Through Arrays of Scatterers

2020 ◽  
Author(s):  
Carl R. Hart ◽  
Gregory W. Lyons
Keyword(s):  
Measurement System ◽  
Pulse Propagation ◽  
Acoustic Pulse ◽  
Weak Shock ◽  
Optical Methods ◽  
Nonlinear Propagation ◽  
Shock Propagation ◽  
Light Refraction ◽  
High Frequency Response ◽  
Laser Induced Breakdown

Various experimental challenges exist in measuring the spatial and temporal field of a nonlinear acoustic pulse propagating through an array of scatterers. Probe interference and undesirable high-frequency response plague typical approaches with acoustic microphones, which are also limited to resolving the pressure field at a single position. Measurements made with optical methods do not have such drawbacks, and schlieren measurements are particularly well suited to measuring both the spatial and temporal evolution of nonlinear pulse propagation in an array of scatterers. Herein, a measurement system is described based on a z-type schlieren setup, which is suitable for measuring axisymmetric phenomena and visualizing weak shock propagation. In order to reduce directivity and initiate nearly spherically-symmetric propagation, laser induced breakdown serves as the source for the nonlinear pulse. A key component of the schlieren system is a standard schliere, which allows quantitative schlieren measurements to be performed. Sizing of the standard schliere is aided by generating estimates of the expected light refraction from the nonlinear pulse, by way of the forward Abel transform. Finally, considerations for experimental sequencing, image capture, and a reconfigurable rod array designed to minimize spurious wave interactions are specified. 15.

scholarly journals Weak Shock Propagation with Accretion. III. A Numerical Study on Shock Propagation and Stability

2019 ◽  
Vol 878 (2) ◽  
pp. 150
Author(s):  
Stephen Ro ◽  
Eric R. Coughlin ◽  
Eliot Quataert
Keyword(s):  
Numerical Study ◽  
Weak Shock ◽  
Shock Propagation
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