A Simplified Presentation of Shock Wave Parameters in Dissociating Air Flow

1960 ◽  
Vol 64 (595) ◽  
pp. 438-439
Author(s):  
T. R. F. Nonweiler
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Chemical Equilibrium ◽  
Incident Flow ◽  
Perfect Gas ◽  
Thermodynamic State ◽  
Independent Variables ◽  
Wave Parameters ◽  
Temperature And Pressure

As is well known, the analysis of shock waves is complicated when the gas becomes dissociated on passage through the wave. As well as showing a dependence on the Mach number of the incident flow and non-dimensional quantities characteristic of the nature of the gas, as does the analysis when applied to a perfect gas, it then also shows a dependence on the thermodynamic state of the upstream air, as described for instance by its temperature and pressure. A growing number of calculations is becoming available, especially for air in complete thermal and chemical equilibrium, but the interpolation to give results appropriate to the three independent variables (of upstream state and incident velocity) needed in any particular application can often be rather troublesome, and one has still less faith in extrapolation.

Conditions needed for generation of type II radio emission in the interplanetary space

2021 ◽  
Author(s):  
Immanuel Christopher Jebaraj ◽  
Athanasios Kouloumvakos ◽  
Jasmina Magdalenic ◽  
Alexis Rouillard ◽  
Vratislav Krupar ◽  
...  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Radio Emission ◽  
Interplanetary Space ◽  
Region Of Interest ◽  
Type Ii ◽  
Radio Observations ◽  
Wave Parameters ◽  
First Results ◽  
Radio Signature

<p>Eruptive events such as Coronal mass ejections (CMEs) and flares cangenerate shock waves. Tracking shock waves and predicting their arrival at Earth is a subject of numerous space weather studies. Ground-based radio observations allow us to locate shock waves in the low corona while space-based radio observations provide us opportunity to track shock waves in the inner heliosphere. We present a case study of CME/flare event, associated shock wave and its radio signature, i.e. type II radio burst.</p><p>In order to analyze the shock wave parameters, we employed a robust paradigm. We reconstructed the shock wave in 3D using multi-viewpoint observations and modelled the evolution of its parameters using a 3D MHD background coronal model produced by the MAS (Magnetohydrodynamics Around a Sphere).</p><p>To map regions on the shock wave surface, possibly associated with the electron acceleration, we combined 3D shock modelling results with the 3D source positions of the type II burst obtained using the radio triangulation technique. We localize the region of interest on the shock surface and examine the shock wave parameters to understand the relationship between the shock wave and the radio event. We analyzed the evolution of the upstream plasma characteristics and shock wave parameters during the full duration of the type II radio emission. First results indicate that shock wave geometry and its relationship with shock strength play an important role in the acceleration of electrons responsible for the generation of type II radio bursts.</p>

Shock Wave - Film Cooling Interactions in Transonic Flows

2001 ◽  
Author(s):  
P. M. Ligrani ◽  
C. Saumweber ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Film Cooling ◽  
Cross Flow ◽  
Injection Velocity ◽  
Film Cooling Effectiveness ◽  
Mach Numbers ◽  
Density Ratios ◽  
Film Cooling Holes

Interactions between shock waves and film cooling are described as they affect magnitudes of local and spanwise-averaged adiabatic film cooling effectiveness distributions. A row of three cylindrical holes is employed. Spanwise spacing of holes is 4 diameters, and inclination angle is 30 degrees. Freestream Mach numbers of 0.8 and 1.10–1.12 are used, with coolant to freestream density ratios of 1.5–1.6. Shadowgraph images show different shock structures as the blowing ratio is changed, and as the condition employed for injection of film into the cooling holes is altered. Investigated are film plenum conditions, as well as perpendicular film injection cross-flow Mach numbers of 0.15, 0.3, and 0.6. Dramatic changes to local and spanwise-averaged adiabatic film effectiveness distributions are then observed as different shock wave structures develop in the immediate vicinity of the film-cooling holes. Variations are especially evident as the data obtained with a supersonic Mach number are compared to the data obtained with a freestream Mach number of 0.8. Local and spanwise-averaged effectiveness magnitudes are generally higher when shock waves are present when a film plenum condition (with zero cross-flow Mach number) is utilized. Effectiveness values measured with a supersonic approaching freestream and shock waves then decrease as the injection cross-flow Mach number increases. Such changes are due to altered flow separation regions in film holes, different injection velocity distributions at hole exits, and alterations of static pressures at film hole exits produced by different types of shock wave events.

On the stability of plane shock waves

1957 ◽  
Vol 2 (4) ◽  
pp. 397-411 ◽  
Author(s):  
N. C. Freeman
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Plane Shock ◽  
Two Dimensional ◽  
Small Perturbations ◽  
Diverging Channel ◽  
Maximum Stability ◽  
The Stability ◽  
Fourier Type

The decay of small perturbations on a plane shock wave propagating along a two-dimensional channel into a fluid at rest is investigated mathematically. The perturbations arise from small departures of the walls from uniform parallel shape or, physically, by placing small obstacles on the otherwise plane parallel walls. An expression for the pressure on a shock wave entering a uniformly, but slowly, diverging channel already exists (given by Chester 1953) as a deduction from the Lighthill (1949) linearized small disturbance theory of flow behind nearly plane shock waves. Using this result, an expression for the pressure distribution produced by the obstacles upon the shock wave is built up as an integral of Fourier type. From this, the shock shape, ξ, is deduced and the decay of the perturbations obtained from an expansion (valid after the disturbances have been reflected many times between the walls) for ξ in descending power of the distance, ζ, travelled by the shock wave. It is shown that the stability properties of the shock wave are qualitatively similar to those discussed in a previous paper (Freeman 1955); the perturbations dying out in an oscillatory manner like ζ−3/2. As before, a Mach number of maximum stability (1·15) exists, the disturbances to the shock wave decaying most rapidly at this Mach number. A modified, but more complicated, expansion for the perturbations, for use when the shock wave Mach number is large, is given in §4.In particular, the results are derived for the case of symmetrical ‘roof top’ obstacles. These predictions are compared with data obtained from experiments with similar obstacles on the walls of a shock tube.

Rankine–Hugoniot-Berechnungen für Nichtgleichgewichts-Plasmen

1966 ◽  
Vol 21 (11) ◽  
pp. 1960-1963
Author(s):  
J. Artmann
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Pressure Ratio ◽  
Density Ratio ◽  
Charged Particles ◽  
Strong Shock ◽  
Ion Temperature ◽  
Saha Equation ◽  
Wave Parameters ◽  
Strong Shock Waves

In optically thin plasmas produced by strong shock waves the SAHA equation is no longer valid to describe the conditions directly behind the shock wave. Photoionisation may be neglected in the balance of production and recombination of charged particles. For the case of nonequilibrium a calculation assuming various ratios of electron to ion temperature (ϑ= TeT) shows that the shock wave parameters are described sufficiently well by the Korona-equation. Temperature, density ratio and electron density are increased with increasing ϑ whereas the pressure ratio is independent of the kind of equilibrium and ϑ.

The perturbed region behind a diffracting shock wave

1967 ◽  
Vol 29 (4) ◽  
pp. 705-719 ◽  
Author(s):  
B. W. Skews
Keyword(s):  
Shock Wave ◽  
Experimental Study ◽  
Mach Number ◽  
Shock Waves ◽  
Contact Surface ◽  
Fair Agreement ◽  
Number Range ◽  
Corner Angle ◽  
Theoretical Predictions

The results of an experimental study of the diffraction of shock waves on plane-walled convex corners are given for a Mach number range from 1·0 to 5·0. The behaviour of the disturbances produced in the region perturbed by the corner are discussed. It is shown that the position of the slipstream and tail of the Prandtl-Meyer fan, and the velocities of the contact surface and second shock become independent of corner angle for angles greater than 75°. Comparisons with theoretical predictions of Jones, Martin & Thornhill (1951) and Parks (1952) are included. In most cases fair agreement is obtained.

scholarly journals Triple configurations of pursuit shock waves in conditions of ambiguity of the solution

2017 ◽  
pp. 46-52
Author(s):  
M. V. Chernyshov ◽  
A. S. Kapralova
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Supersonic Flows ◽  
Tangential Discontinuity ◽  
Oncoming Flow ◽  
Perfect Gas

The article studies triple configurations of shock waves in supersonic flows of a perfect gas in view of the fact that it is not always possible to determine unambiguously the parameters of the remaining shocks in the configuration by specifying the properties of the oncoming flow and the branching shock wave. The values of the parameters of triple configurations with maximum relations of the parameters of the flow on the sides of the outgoing tangential discontinuity (extremal configurations) in conditions of the ambiguity of the physically realizable solution are found analytically and numerically.

scholarly journals Modern infinitesimals and the entropy jump across an inviscid shock wave

2018 ◽  
Vol 17 (4-5) ◽  
pp. 502-520
Author(s):  
Roy S Baty ◽  
Len G Margolin
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Euler Equations ◽  
Nonstandard Analysis ◽  
Generalized Solutions ◽  
Perfect Gas ◽  
One Dimensional ◽  
Number Systems ◽  
Shock Thickness ◽  
Modern Mathematics

This article applies nonstandard analysis to study the generalized solutions of entropy and energy across one-dimensional shock waves in a compressible, inviscid, perfect gas. Nonstandard analysis is an area of modern mathematics that studies number systems that contain both infinitely large and infinitely small numbers. For an inviscid shock wave, it is assumed that the shock thickness occurs on an infinitesimal interval and that the jump functions for the field variables are smoothly defined on this interval. A weak converse to the existence of the entropy peak is derived and discussed. Generalized solutions of the Euler equations for entropy and energy are then derived for both theoretical and realistic normalized velocity profiles.

scholarly journals Chemical equilibrium in a mixture of paraffins

1927 ◽  
Vol 116 (775) ◽  
pp. 501-515 ◽  
Keyword(s):  
Chemical Equilibrium ◽  
Equilibrium Composition ◽  
Phase Rule ◽  
Independent Variables ◽  
Liquid Phases ◽  
Temperature And Pressure ◽  
Two Independent Variables

In this paper the theory of chemical equilibrium is applied to a mixture of paraffins C n H 2 n +2 , and it is shown that the equilibrium composition of the vapour and liquid phases can be approximately calculated at any given tempera­ture and pressure. Such a mixture has two independent constituents so that according to the phase rule the composition of the phases, whenever there are two, will be determined by two independent variables such as the temperature and pressure. Consider the reaction C n -1 H 2( n -1)+2 + C n +1H 2( n -1)+2 = 2C n H 2 n +2 .

Further Properties of the Wave Charts

1962 ◽  
Vol 66 (624) ◽  
pp. 789-792 ◽  
Author(s):  
W. A. Woods
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Wave Speed ◽  
Pressure Waves ◽  
Perfect Gas ◽  
Expansion Waves ◽  
Isentropic Expansion ◽  
Constant State ◽  
Mach Numbers ◽  
Straight Lines

In a previous paper charts were given which related the flow Mach numbers on either side of a wave to a dimensionless wave speed. Charts were given for shock waves, isentropic expansion waves and isentropic non-steep pressure waves in a perfect gas. In this note it is shown that the lines of constant state ratio plotted on the charts constitute families of straight lines; this fact is particularly important in the case of the shock wave chart. The wave domains are also established and compared diagrammatically.

Solution of the Boltzmann equation at the upstream and downstream singular points in a shock wave

1974 ◽  
Vol 65 (3) ◽  
pp. 603-624 ◽  
Author(s):  
J. P. Elliott ◽  
D. Baganoff
Keyword(s):  
Shock Wave ◽  
Boltzmann Equation ◽  
Mach Number ◽  
Singular Point ◽  
Shock Waves ◽  
Strong Shock ◽  
Singular Points ◽  
The Boltzmann Equation ◽  
Closure Relations ◽  
Strong Shock Waves

A solution of the Boltzmann equation is obtained at the upstream and downstream singular points in a shock wave, for the case of Maxwell molecules. The fluid velocityu, rather than the spatial co-ordinatex, is used as the independent variable, and an equation for ∂f/∂uat a singular point is obtained from the Boltzmann equation by taking the appropriate limit. This equation is solved by using the methods of Grad and of Wang Chang & Uhlenbeck; and it is observed that the two methods are the same, since they involve not only an equivalent system of moment equations but also the same closure relations. Because many quantities are zero at a singular point, the problem becomes sufficiently simple to allow the solution to be carried out to any desired order. At the supersonic singular point, the solution converges very slowly for strong shock waves; but a simple modification to Grad's method provides a rapidly convergent solution. The solution shows that the Navier-Stokes relations, or the first-order Chapman-Enskog results, do not apply unless the shock-wave Mach number is unity, and that they are grossly in error for strong shock waves. The solution confirms the existence of temperature overshoot in a strong shock wave; shows that the critical Mach number in Grad's solution increases monotonically with the order of the solution; provides a simple explanation as to why Grad's closure relations fail and shows how they can be improved; and provides exact boundary values that can be used to guide future numerical solutions of the Boltzmann equation for shock-wave structure.

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