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.

scholarly journals An Analytical Method for the Response of Coated Plates Subjected to One-Dimensional Underwater Weak Shock Wave

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Zeyu Jin ◽  
Caiyu Yin ◽  
Yong Chen ◽  
Xiuchang Huang ◽  
Hongxing Hua
Keyword(s):  
Shock Wave ◽  
Analytical Method ◽  
Weak Shock ◽  
Wave Theory ◽  
Time Sequence ◽  
Weak Shock Wave ◽  
One Dimensional ◽  
Coated Plate ◽  
Pressure Increment ◽  
Good Agreement

An analytical method based on the wave theory is proposed to calculate the pressure at the interfaces of coated plate subjected to underwater weak shock wave. The method is carried out to give analytical results by summing up the pressure increment, which can be calculated analytically, in time sequence. The results are in very good agreement with the finite element (FE) predictions for the coating case and Taylor’s results for the noncoating case, which validate the method that is suitable for underwater weak shock problem. On the other hand, Taylor’s results for the coating case are invalid, which indicates a potential application field for the method. The extension of the analytical method to q-layer systems and dissipation case is also outlined.

scholarly journals Прохождение плоской ударной волны через область тлеющего газового разряд

2019 ◽  
Vol 89 (1) ◽  
pp. 42
Author(s):  
Т.А. Лапушкина ◽  
А.В. Ерофеев ◽  
О.А. Азарова ◽  
О.В. Кравченко
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Wave Structure ◽  
Gas Discharge ◽  
Navier Stokes ◽  
Plane Shock ◽  
Two Dimensional ◽  
Gas Temperature ◽  
Discharge Region ◽  
Navier Stokes Equations

AbstractThe interaction of a plane shock wave ( M = 5) with an ionized plasma region formed before the arrival of a shock wave by a low-current glow gas discharge is considered experimentally and numerically. In the experiment, schlieren images of a moving shock-wave structure resulting from the interaction and consisting of two discontinuities, convex in the direction of motion of the initial wave, are obtained. The propagation of a shock wave over the region of energetic impact is simulated on the basis of the two-dimensional Riemann problem of decay of an arbitrary discontinuity with allowance for the influence of horizontal walls. The systems of Euler and Navier–Stokes equations are solved numerically. The non-equilibrium of the processes in the gas-discharge region was simulated by an effective adiabatic index γ. Based on the calculations performed for equilibrium air (γ = 1.4) and for an ionized nonequilibrium gas medium (γ = 1.2), it is shown that the experimentally observed discontinuities can be interpreted as elements of the solution of the two-dimensional problem of decay of a discontinuity: a shock wave followed by a contact discontinuity. It is shown that a variation in γ affects the shape of the fronts and velocities of the discontinuities obtained. Good agreement is obtained between the experimental and calculated images of density and velocities of the discontinuities at a residual gas temperature in the gas discharge region of 373 K.

A model for the atmospheric shock wave produced by a strong volcanic explosion

2020 ◽  
Vol 222 (2) ◽  
pp. 735-742
Author(s):  
Michele Dragoni ◽  
Dalila Santoro
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Sound Pressure ◽  
Strong Shock ◽  
Weak Shock ◽  
Volcanic Eruptions ◽  
Density Inhomogeneity ◽  
Acoustic Effect ◽  
Explosive Volcanic Eruptions ◽  
Spherical Shock

SUMMARY Atmospheric shock waves are a common phenomenon in explosive volcanic eruptions. We consider the motion of a spherical shock wave generated by a point source in the strong shock approximation. The shock front corresponds to discontinuities in the gas velocity, density, pressure and temperature, which are calculated as functions of the energy of the explosion. The problem is solved analytically for the distributions of velocity, density, pressure and temperature in the atmosphere as functions of the distance from the source. The motion of the shock wave being supersonic, the solution is valid for a few seconds after the explosion, corresponding to a distance of few kilometres. The acoustic effect of the shock wave, expressed by the peak sound pressure level, is calculated and may reach hundreds of decibels. The pressure waveform that could be recorded in the vicinity of the volcano is calculated and compared with typical waveforms in weak shock conditions. The change in the refractive index of air due to density inhomogeneity is calculated and the conditions under which a condensation cloud is formed behind the shock front are investigated.

Uniformly valid analytical solution to the problem of a decaying shock wave

1987 ◽  
Vol 185 ◽  
pp. 153-170 ◽  
Author(s):  
V. D. Sharma ◽  
Rishi Ram ◽  
P. L. Sachdev
Keyword(s):  
Shock Wave ◽  
Analytical Solution ◽  
Weak Shock ◽  
Simple Wave ◽  
Complete Agreement ◽  
Plane Shock ◽  
Propagation Law ◽  
Arbitrary Strength ◽  
Entire Flow ◽  
Basic Equations

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

Inviscid radiating flow over a blunt body

1967 ◽  
Vol 27 (4) ◽  
pp. 625-646 ◽  
Author(s):  
Ping Cheng ◽  
Walter G. Vincenti
Keyword(s):  
Shock Wave ◽  
Optical Thickness ◽  
Blunt Body ◽  
Axisymmetric Flow ◽  
Strong Shock ◽  
Molecular Transport ◽  
Transport Processes ◽  
The Body ◽  
Gas Temperature ◽  
Differential Approximation

The effect of thermal radiation is investigated for the axisymmetric flow over the blunt body associated with a given paraboloidal shock wave. Radiative transfer is treated by means of the differential approximation, which applies to multidimensional flow and is valid throughout the entire range of temperature and optical thickness. The gas is assumed to be perfect and optically grey, and molecular-transport processes are neglected. A semi-analytical solution for the flow and radiation fields is obtained by the method of series truncation.Results are presented, in the strong-shock approximation, for various values of the appropriate dimensionless variables. In general, radiation is found to have a significant influence on temperature and density, moderate effect on velocity, and little effect on pressure. The stand-off distance between the shock wave and the body is found to decrease significantly with increasing radiation; the body shape is less affected. The anomalous behaviour of the gas temperature on the body streamline as obtained by earlier investigators in the optically thin case does not appear in the present work. The results thus show correct physical behaviour throughout the flow field for all values of optical thickness. The detailed flow quantities exhibit a number of features of multidimensional radiating flow. They also provide a check on the special assumptions made in other, more approximate treatments. Similarities between radiating flow and non-equilibrium reactive flow over blunt bodies are apparent.

Stability of a supersonic flow over a wedge containing a weak shock wave satisfying the Lopatinski condition

2014 ◽  
Vol 11 (02) ◽  
pp. 215-248 ◽  
Author(s):  
A. M. Blokhin ◽  
D. L. Tkachev
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Wave Solution ◽  
Strong Shock ◽  
Weak Shock ◽  
Weak Sense ◽  
Strong Shock Wave ◽  
Weak Shock Wave ◽  
Heat Conducting ◽  
Shock Wave Solution

We study the stability problem for a stationary supersonic flow of inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. As it is known, this problem has two solutions: a solution with a strong shock wave (when the velocity behind the front of the shock wave is subsonic) and a solution with a weak shock wave (when the velocity behind the front of the shock wave is supersonic). We consider the case of a weak shock wave and we prove that if the Lopatinski condition for the shock wave holds (in a weak sense), then the corresponding linearized initial boundary-value problem is well-posed. We thus find a classical solution to this problem. Unlike the case when the uniform Lopatinski condition holds, additional plane waves appear. For compactly supported initial data we show that the solution of the linearized problem converges to the zero solution as time tends to infinity. Therefore, for the case of a weak shock wave and when the Lopatinski condition holds in a weak sense, these results complete the proof of the well-known Courant–Friedrichs' conjecture that the strong shock wave solution is unstable whereas the weak shock wave solution is stable.

scholarly journals Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone

2010 ◽  
Vol 199 ◽  
pp. 151-181 ◽  
Author(s):  
Gang Xu ◽  
Huicheng Yin
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Vertex Angle ◽  
Transonic Shock ◽  
Euler Flow ◽  
Flow Past ◽  
Curve Method ◽  
Sharp Cone ◽  
Supersonic Shock

AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the book Supersonic Flow and Shock Waves by Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

scholarly journals Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone

2010 ◽  
Vol 199 ◽  
pp. 151-181 ◽  
Author(s):  
Gang Xu ◽  
Huicheng Yin
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Vertex Angle ◽  
Transonic Shock ◽  
Euler Flow ◽  
Flow Past ◽  
Curve Method ◽  
Sharp Cone ◽  
Supersonic Shock

AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the bookSupersonic Flow and Shock Wavesby Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

The behaviour of a gas cavity impacted by a weak or strong shock wave

1996 ◽  
Vol 309 ◽  
pp. 183-209 ◽  
Author(s):  
Zhong Ding ◽  
S. M. Gracewski
Keyword(s):  
Strong Shock ◽  
Weak Shock ◽  
Adaptive Mesh ◽  
Bubble Collapse ◽  
Shock Propagation ◽  
Liquid Jet ◽  
Bubble Wall ◽  
Expansion Time ◽  
Present Context ◽  
Gas Cavity

Two-dimensional simulations of gas cavity responses to both weak shocks (p ≤ 30 MPa) and strong shocks (p ranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. A weak shock is defined in the present context as one that does not cause liquid jet formation upon impact with the bubble. For this case, a large pressure is created within the gas upon collapse due to rapid compression of the gas, ultimately causing the re-expansion of the bubble. The bubble collapse and re-expansion time predicted by this model agree well with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liquid jet is formed that propagates through the bubble to the opposite bubble wall. Jet speeds as high as 2000 m s−1 are predicted by this model.

Reconsideration of the So-Called von Neumann Paradox in the Reflection of a Shock Wave over a Wedge

2007 ◽  
Vol 566 ◽  
pp. 1-8
Author(s):  
Eugene I. Vasilev ◽  
Tov Elperin ◽  
Gabi Ben-Dor
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Triple Point ◽  
Mach Reflection ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Plane Shock ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Guderley Reflection

Numerous experimental investigations on the reflection of plane shock waves over straight wedges indicated that there is a domain, frequently referred to as the weak shock wave domain, inside which the resulted wave configurations resemble the wave configuration of a Mach reflection although the classical three-shock theory does not provide an analytical solution. This paradox is known in the literature as the von Neumann paradox. While numerically investigating this paradox Colella & Henderson [1] suggested that the observed reflections were not Mach reflections but another reflection, in which the reflected wave at the triple point was not a shock wave but a compression wave. They termed them it von Neumann reflection. Consequently, based on their study there was no paradox since the three-shock theory never aimed at predicting this wave configuration. Vasilev & Kraiko [2] who numerically investigated the same phenomenon a decade later concluded that the wave configuration, inside the questionable domain, includes in addition to the three shock waves a very tiny Prandtl-Meyer expansion fan centered at the triple point. This wave configuration, which was first predicted by Guderley [3], was recently observed experimentally by Skews & Ashworth [4] who named it Guderley reflection. The entire phenomenon was re-investigated by us analytically. It has been found that there are in fact three different reflection configurations inside the weak reflection domain: • A von Neumann reflection – vNR, • A yet not named reflection – ?R, • A Guderley reflection – GR. The transition boundaries between MR, vNR, ?R and GR and their domains have been determined analytically. The reported study presents for the first time a full solution of the weak shock wave domain, which has been puzzling the scientific community for a few decades. Although the present study has been conducted in a perfect gas, it is believed that the reported various wave configurations, namely, vNR, ?R and GR, exist also in the reflection of shock waves in condensed matter.

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