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Vetter and Sturtevant experiment.

(the following is an extract of in the CVS repository)

Information about the experiments of Vetter and Sturtevant from "Experiments on the shock-excited interfacial instability at an air/SF6 interface". Proceedings of the 20th International Symposium on Shock Waves p.593-598.

Vetter and Sturtevant present the results of 7 different experiments of a shock traveling from air into sf6 bouncing off the end wall and reshocking the contact then exiting the domain. The initial shock strength is varied by changing the pressure of the SF6, and the length of the tube was adjusted in some experiments to insure the interaction of the reflected shock wave with the interface would be in the experimental field of view (a window of diameter 15cm at 42cm down stream).

Experimental setup:

The length of the tube (L) varies from 62cm to 123cm and the pressure (P_1) of the SF6 ranges from 55kPa to 8kPa. The cross-section of the domain is 27cm x 27cm


This is Table 1. from the paper.

Ms 1.18 1.24 1.43 1.45 1.50 1.50 1.98
P_1 55kPa 40kPa 31kPa 29kPa 23kPa 23kPa 8kPa
L 123cm 110cm 62cm 62cm 62cm 62cm 49cm
Mt 1.27 1.37 1.67 1.70 1.78 1.78 2.56
u0 56m/s 72m/s 126m/s 126m/s 150m/s 150m/s 287m/s
rate1 .94m/s 2.1m/s 3.0m/s 3.1m/s 4.0m/s 4.2m/s 7.5m/s
rate2 19.2m/s 17.0m/s 31.5m/s 35.5m/s 32.6m/s 37.2m/s 74.4m/s
reshock x 9.5ms 4.0ms x 3.5ms x 1.6ms
final   16.5ms 6.0ms   6.25ms   2.5ms

The data for cases I, IV, VI were done with single spark-schlieren cases II, III,V,VI were high-speed motion pictures.

Ms - Mach number of the incident shock in air

P_1 - Pressure of the SF6

L - Length of the test section

Mt - Mach number of the (transmitted) shock in SF6

u0 - the velocity (of the contact) behind the initially transmitted shock

rate1 - the growth rate of the mixing layer before reshock

rate2 - the growth rate of the mixing layer after reshock

The rows reshock and final come from Figure 1 and are only approximate reshock - the time at which the reshock occurred final - the final time of the experiment

Numerical simulations:

The numerical simulation imagines a tube with air and sf6 at equilibrium (same temperature and pressure) with a contact located at x=0.

A shock traveling to the right is initiated in the air to the left of the contact as the solution to a Riemann problem. This allows the shock to develop into a numerical shock before interacting with the contact.

This initial pressure of the unshocked gas is taken to be P_1, and the density given (for the air) results in a temperature of 286K (a room temp of about 56 F).

The conditions in the repository should simulate the initial shock of Mach 1.5 (cases V,VI).

The init.dat file:

 0.27885                #rho_air - unshocked   
 23000.00               #p_air   - unshocked  
 0.0                    #u_air   - unshocked   
 0.00                   #cloc    - location of contact  
 1.d2                   #amp     - inverse width of contact  
 -0.05                  #sloc    - location of shock  
 1.5d0                  #shockmach - machnumber of shock  

These conditions result in a computed transmitted shock with a Mach number of 1.78056 and and a contact velocity of ~155m/s. The time between shock and reshock is found to be approximately 0.0035s.

-- CarlosPantano - 09 Oct 2005

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