Analysis of vibrational relaxation regions by means of the Rayleigh-line method

1961 ◽  
Vol 10 (1) ◽  
pp. 25-32 ◽  
Author(s):  
N. H. Johannesen
Keyword(s):  
Heat Transfer ◽  
Shock Wave ◽  
Shock Waves ◽  
Vibrational Relaxation ◽  
Ideal Gas ◽  
Relaxation Frequency ◽  
Rayleigh Line ◽  
Exact Methods ◽  
Real Gas ◽  
Density Distributions

The physics of shock-waves with vibrational relaxation regions is recapitulated, and it is shown that exact methods of analysis can be developed from the classical Rayleigh-line equations by treating the real gas as an ideal gas with heat transfer. By using these methods to analyse experimental records of density distributions in relaxation regions, a large number of local values of the relaxation frequency, rather than a single over-all value, may be obtained from each shock-wave record.

Comparison of exact and approximate methods for analysing vibrational relaxation regions

1961 ◽  
Vol 10 (1) ◽  
pp. 33-47 ◽  
Author(s):  
P. A. Blythe
Keyword(s):  
Exact Solution ◽  
Shock Waves ◽  
Numerical Integration ◽  
Vibrational Relaxation ◽  
Relaxation Frequency ◽  
Rayleigh Line ◽  
Relaxation Equation ◽  
Approximate Methods ◽  
Exact And Approximate Methods

The validity of various solutions for the vibrational relaxation region in shock-waves, and of the assumptions on which they are based, has been assesed by comparison with an exact solution obtained by numerical integration of the relaxation equation, and also by use of the Rayleigh-line equations. Estimates of errors in the values of the relaxation frequency, determined by means of these solutions, are given.

scholarly journals Numerical investigation of the thermal-caloric imperfections on entropy enhancement across normal shock waves

2020 ◽  
Vol 48 (4) ◽  
pp. 285-308
Author(s):  
MEROUANE SALHI
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Molecular Size ◽  
Ideal Gas ◽  
Normal Shock ◽  
Wave Flow ◽  
Appreciable Effect ◽  
Real Gas ◽  
Normal Shock Wave ◽  
The Impact

Changes in flow properties across a normal shock wave are calculated for a real gas, thus giving us a better affinity to the real behavior of the waves. The purpose of this work is to develop shock-wave theory under the gaseous imperfections. Expressions are developed for analyzing the supersonic flow of such a thermally and calorically imperfect gas. The effects of molecular size and intermolecular attraction forces are used to correct a state equation, focusing on determination of the impact of upstream stagnation parameters on a normal shock wave. Flow through a shock wave in air is investigated to find a general form for normal shock waves. At Mach numbers greater than 2.0, the temperature rise is considerably below, and hence the density rise is well above, that predicted assuming ideal gas behavior. It is shown that caloric imperfections in air have an appreciable effect on the parameters developed in the processes considered. Computation of errors between the present model based on real gas theory and a perfect gas model shows that the influence of the thermal and caloric imperfections associated with a real gas is important.

Departures from the linear equation for vibrational relaxation in shock waves in oxygen and carbon dioxide

1963 ◽  
Vol 17 (4) ◽  
pp. 499-505 ◽  
Author(s):  
H. K. Zienkiewicz ◽  
N. H. Johannesen
Keyword(s):  
Carbon Dioxide ◽  
Shock Waves ◽  
Linear Equation ◽  
Vibrational Relaxation ◽  
Relaxation Frequency ◽  
Experimental Results ◽  
Detailed Structure ◽  
Relaxation Equation

The detailed structure of the relaxation region in shock waves in oxygen was investigated using Blackman's experimental results. Oxygen was found to display a behaviour similar in many ways to that found previously for carbon dioxide with the relaxation frequency, as defined by the simple relaxation equation, depending on the departure from equilibrium as well as on temperature. The previous results for carbon dioxide were further analysed by means of a separate relaxation equation for each mode.

Theoretical and experimental investigations of the reflexion of normal shock waves with vibrational relaxation

1967 ◽  
Vol 30 (1) ◽  
pp. 51-64 ◽  
Author(s):  
N. H. Johannesen ◽  
G. A. Bird ◽  
H. K. Zienkiewicz
Keyword(s):  
Shock Wave ◽  
Vibrational Relaxation ◽  
Experimental Investigations ◽  
Rayleigh Line ◽  
Dimensional Problem ◽  
Density Measurements ◽  
Wave Characteristic ◽  
One Dimensional ◽  
The One ◽  
Theoretical Results

The one-dimensional problem of shock-wave reflexion with relaxation is treated numerically by combining the shock-wave, characteristic, and Rayleigh-line equations. The theoretical results are compared with pressure and density measurements in CO2, and the agreement is found to be excellent.

Measurement of the relaxation frequency of the asymmetric stretching mode of carbon dioxide

1969 ◽  
Vol 35 (1) ◽  
pp. 171-183 ◽  
Author(s):  
J. P. Hodgson ◽  
R. J. Hine
Keyword(s):  
Carbon Dioxide ◽  
Shock Waves ◽  
Shock Tube ◽  
Vibrational Relaxation ◽  
Thermal Emission ◽  
Relaxation Frequency ◽  
Rate Of Change ◽  
Density Measurements ◽  
Bending Mode ◽  
Made In

The vibrational relaxation frequency of carbon dioxide has been determined by measuring the rate of change of thermal emission in shock waves near 4±3μ. This method of measuring the relaxation frequency depends mainly on the degree of excitation of the asymmetric stretching mode of the molecule, and the results are compared with those of earlier density measurements made in the same shock tube. The gas samples used are not optically thin, and it is shown that self-absorption can be taken into account. The results imply that the relaxation frequency of the asymmetric stretching mode is about 70% of that of the bending mode.

The interaction of a shock wave with a laminar boundary layer at a compression corner in high-enthalpy flows including real gas effects

1997 ◽  
Vol 342 ◽  
pp. 1-35 ◽  
Author(s):  
S. G. MALLINSON ◽  
S. L. GAI ◽  
N. R. MUDFORD
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shock Wave ◽  
Gas Flows ◽  
Perfect Gas ◽  
Experimental Conditions ◽  
Real Gas ◽  
High Enthalpy ◽  
Compression Corner ◽  
Real Gas Effects

The high-enthalpy, hypersonic flow over a compression corner has been examined experimentally and theoretically. Surface static pressure and heat transfer distributions, along with some flow visualization data, were obtained in a free-piston shock tunnel operating at enthalpies ranging from 3 MJ kg−1 to 19 MJ kg−1, with the Mach number varying from 7.5 to 9.0 and the Reynolds number based on upstream fetch from 2.7×104 to 2.7×105. The flow was laminar throughout. The experimental data compared well with theories valid for perfect gas flow and with other relevant low-to-moderate enthalpy data, suggesting that for the current experimental conditions, the real gas effects on shock wave/boundary layer interaction are negligible. The flat-plate similarity theory has been extended to include equilibrium real gas effects. While this theory is not applicable to the current experimental conditions, it has been employed here to determine the potential maximum effect of real gas behaviour. For the flat plate, only small differences between perfect gas and equilibrium gas flows are predicted, consistent with experimental observations. For the compression corner, a more rapid rise to the maximum pressure and heat transfer on the ramp face is predicted in the real gas flows, with the pressure lying slightly below, and the heat transfer slightly above, the perfect gas prediction. The increase in peak heat transfer is attributed to the reduction in boundary layer displacement thickness due to real gas effects.

Shock-wave strengthening by area convergence

1967 ◽  
Vol 27 (2) ◽  
pp. 305-314 ◽  
Author(s):  
David A. Russell
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Shock Tube ◽  
Higher Order ◽  
Real Gas ◽  
Half Angle

A 17 in. diameter shock tube was coupled to a 1 in. tube by a 10° half-angle conical convergence. Timing measurements showed that the shock waves emerged from the convergence at 2–3 times their entrance speeds, and then decelerated downstream. After the application of a viscous correction, the shock speeds at the convergence exit agreed to within 5% with equilibrium real-gas calculations of the model of Chester (1954), Chisnell (1957) and Whitham (1958). The downstream deceleration, due to viscosity and to higher-order interactions not included in the theory, was also briefly studied.

The Parameter Variation in Pressure Vessel during Loading Operation by Considering Heat Transfer Impact Based on Real Gas Model

2012 ◽  
Vol 516-517 ◽  
pp. 467-470
Author(s):  
Wei Qing Wang ◽  
Li Yang ◽  
Shi Gui Lv
Keyword(s):  
Heat Transfer ◽  
High Pressure ◽  
Pressure Vessel ◽  
Simulation Method ◽  
Ideal Gas ◽  
Molecular Volume ◽  
Real Gas ◽  
The Real ◽  
Ideal Gas Model ◽  
The Ideal

Since the molecular force and the molecular volume were ignored in the ideal gas model, and it was less accurate when the ideal gas model was used to depict characteristics of real gas under high pressure, so the real gas model was adopted and the heat transfer was considered, the dynamic variation model was set up for internal gas in the pressure vessel during loading operation. The model was solved by using the numerical simulation method of Runge-Kutta. Comparison was made between the ideal gas model and the real gas model under adiabatic and non-adiabatic conditions, it showed that under low pressure the results obtained by the two models were in good agreement, but under high pressure the deviation was enlarged, the real gas model with considering the heat transfer influenced would be more coincident with the reality.

Computer study of Br2 shock wave dissociation

1970 ◽  
Vol 48 (18) ◽  
pp. 2860-2865 ◽  
Author(s):  
J. K. K. Ip ◽  
George Burns
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Vibrational Relaxation ◽  
Vibrational Temperature ◽  
Distribution Functions ◽  
Computational Studies ◽  
Computer Study ◽  
Absorption Coefficients ◽  
Vibrational Levels ◽  
Wave Profiles

Computational studies of Br2 shock wave dissociation in argon were conducted, and the possibility of vibrational relaxation–dissociation coupling, stronger than previously suspected (2), was investigated. In order for such a coupling to occur, the vibrational temperature in the lower vibrational levels of Br2 must be lower than that in the higher vibrational levels. The approximate shapes of vibrational distribution functions were obtained, and corresponding shock wave profiles were computed. The calculations predict an appreciable difference between the translational and vibrational temperatures of the dissociating Br2. In order to check this conclusion, the Br2 absorption coefficients at 440 mμ, measured at equilibrium by heating Br2 in a furnace from 300 to 1250°K, were compared to the absorption coefficients measured in shock waves.

Investigation of shock-wave deformation history from recovered structure

1986 ◽  
Vol 44 ◽  
pp. 434-435
Author(s):  
M.A. Mogilevsky ◽  
L.S. Bushnev
Keyword(s):  
Shock Wave ◽  
Plastic Deformation ◽  
Dislocation Density ◽  
Shock Waves ◽  
Shock Front ◽  
Single Crystals ◽  
Residual Deformation ◽  
Deformation Structure ◽  
Deformation History ◽  
Deformation Velocity

Single crystals of Al were loaded by 15 to 40 GPa shock waves at 77 K with a pulse duration of 1.0 to 0.5 μs and a residual deformation of ∼1%. The analysis of deformation structure peculiarities allows the deformation history to be re-established.After a 20 to 40 GPa loading the dislocation density in the recovered samples was about 1010 cm-2. By measuring the thickness of the 40 GPa shock front in Al, a plastic deformation velocity of 1.07 x 108 s-1 is obtained, from where the moving dislocation density at the front is 7 x 1010 cm-2. A very small part of dislocations moves during the whole time of compression, i.e. a total dislocation density at the front must be in excess of this value by one or two orders. Consequently, due to extremely high stresses, at the front there exists a very unstable structure which is rearranged later with a noticeable decrease in dislocation density.

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