State specific vibrational relaxation and dissociation models for nitrogen in shock wave regions

2012 ◽  
Author(s):  
Zheng Li ◽  
Ilyoup Sohn ◽  
Deborah A. Levin
Keyword(s):  
Shock Wave ◽  
Vibrational Relaxation

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.

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.

Effects of Vibrational Relaxation on Weak Shock Wave Structure in Air

2011 ◽  
Author(s):  
Takeharu Sakai ◽  
Yoshikazu Makino ◽  
Yusuke Naka ◽  
Akira Murakami
Keyword(s):  
Shock Wave ◽  
Vibrational Relaxation ◽  
Fluid Dynamic ◽  
Species Conservation ◽  
Weak Shock ◽  
Wave Structure ◽  
Weak Shock Wave ◽  
Conservation Equations ◽  
Wide Range ◽  
Energy Equations

A computational fluid dynamic method is developed to calculate the long range propagation of weak shock wave with the vibrational relaxation in air. Vibrational relaxation kinetics among N2, O2, and H2O is accounted for by solving each species conservation equations with total mass, momentum and energy equations. The conservation equations are solved using a moving grid technique to capture the distortion of the wave during propagation. The propagation of the wave with an overpressure value typically observed in sonic boom on the ground is analyzed using the developed method. The computed results are mainly presented to show the ability to capture a dispersed nature in waves under different humidity conditions due to vibrational relaxation. The present result shows that the variation of a converged wave thickness dependent on a wide range of humidity can be recognized clearly by using the present method.

The Master Equation for the Dissociation of a Dilute Diatomic Gas IX. Rotation–Vibration Relaxation Times

1973 ◽  
Vol 51 (12) ◽  
pp. 1923-1932 ◽  
Author(s):  
E. Kamaratos ◽  
H. O. Pritchard
Keyword(s):  
Shock Wave ◽  
Relaxation Time ◽  
Vibrational Relaxation ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Relaxation Times ◽  
Rotational Relaxation ◽  
Relaxation Matrix ◽  
Coupling Case ◽  
Increasing Temperature

The relationships between individual rotational or vibrational transition probabilities and the eigenvalues of the 172nd order relaxation matrix describing the rotation–vibration–dissociation coupling of ortho-hydrogen are explored numerically. The simple proportionality between certain transition probabilities and certain eigenvalues, which was found previously in the vibration–dissociation coupling case, breaks down. However, it is shown that at 2000°K the second smallest eigenvalue of the relaxation matrix (dn−2), hitherto regarded as determining the "vibrational" relaxation time, is related more to the transition probability assigned to the largest rotational gap which lies in the first (ν = 0 ↔ ν = 1) vibrational gap, i.e. to the transition ν = 0, J = 5 ↔ ν = 0, J = 7, than to anything else; this clearly supports an earlier suggestion that the transient which immediately precedes dissociation in a shock wave has to be regarded as a rotation–vibration relaxation time rather than a vibrational relaxation time. It is suggested that the Lambert–Salter relationships can be rationalized on this assumption.An analysis is then made of the energy uptake associated with each eigenvalue at three temperatures. At 500°K, the greatest energy increment is associated with two eigenvalues (dn−13 and dn−24) and can be characterized as essentially a rotational relaxation: the calculations confirm that the observed rotational relaxation time should first decrease and then increase with increasing temperature, as was recently found to be the case experimentally. At 2000°K, large energy increments are associated with several eigenvalues between dn−2 and dn−14, and at 5000°K, with most of the eigenvalues dn−2 to dn−23; thus, the higher the temperature, the more complex is the (T–VR) rotation–vibration relaxation. Further, relaxation times for the same temperature measured by ultrasonic and shock-wave techniques need not agree.

On the interpretation of measured rotational and vibrational relaxation times. II. Sudden change experiments

1976 ◽  
Vol 54 (15) ◽  
pp. 2372-2379 ◽  
Author(s):  
Huw Owen Pritchard
Keyword(s):  
Shock Wave ◽  
Relaxation Time ◽  
Vibrational Relaxation ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Sudden Change ◽  
Heat Bath ◽  
Mode Analysis ◽  
Wave Excitation ◽  
Measured Relaxation

This paper examines, in terms of the normal-mode analysis developed earlier (Part I), the nature of relaxations in which a diatomic gas, highly diluted in a heat bath of inert gas atoms, is subjected to a sudden change as in shock-wave excitation or laser schlieren experiments.It is shown in detail how the observed relaxation time in a shock-wave excitation to a fixed final temperature depends on the initial temperature. At the same time, it is confirmed that the characterisation as 'mainly rotational' of the measured relaxation time in H2 when it is heated from room temperature to 1500 K in a shock wave is perfectly plausible.On the other hand, the calculations show that in laser schlieren experiments in which the v = 1, J = 1 level of H2 is overpopulated, the vibrational relaxation time of H2 at the temperature in question is recovered, although interesting effects should appear if other J levels were populated initially, or if the experiments were carried out at much higher ambient temperatures.The calculations also demonstrate that it is not generally possible to derive relaxation times by following the variation in population of any particular level of the molecule: multiple overshoots sometimes occur, and apparent relaxation times both longer or shorter than the true relaxation times could often result from attempts to follow level populations as a function of time.

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