Shock Tube Representation

Up to this time, the pressure thruout the region from the piston to the advancing front remains constant. Even after the piston is stopped the front continues to advance at its previous supersonic velocity and the pressure remains at this constant value for a considerable distance behind the front. However, the movement away of the material immediately ahead of the piston creates a rarefaction, for there is nothing to take the place of removed air. The pressure within this rarefaction zone will fall below the original pressure and will even approach.a vacuum in some cases. While the shock front continues to advance, the rarefaction wave follows some distance behind. It has been shown that in an inert medium, such. a rarefaction wave will always advance faster than the original shock front and is bound to overtake 

Morrison (Ref 1, pp 38-42) described a shock tube (See Fig 1) containing inside a piston which separates two gases of two different states. One section of the tube is closed from the outside forming a reservoir. Assuming that the gas to the left of piston is at a higher pressure than the gas to the right of it, let the piston (starting 

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Figure B2.5.5. Schematic representation of a shock-tube apparatus. The diapliragm d separates the high-...

Fig. 6.9. Representation of events in a shock tube. The locations of the shock front, the contact surface and the rarefaction fan in the driven and driver sections of the tube after an interval t following the bursting of the diaphragm are marked.

Figure 9 shows a schematic representation of a typical shock tube. 

In this work a restricted use of the switching function method is proposed for practical apphcation to the shock tube experiment calculations. The eBWR equation of state proposed by Schreiber and Pitzer represents the pressure in the critical region rather accurately. The equation s major deficiency is in predicting the power law behavior of the isochoric heat capacity and the isothermal compressibifity near the critical point. This, in turn, leads to incorrect numerical results for soundspeed and F. A switching function similar to that of Chapela and Rowlinson is used to combine analytical and scaled representations of Cy . 

The extrapolation behaviour of empirical multi-parameter equations of state has been summarized by Span and Wagner. " Aside from the representation of shock tube data for the Hugoniot curve at very high temperatures and pressures, an assessment of the extrapolation behaviour of an equation of state can also be based on the so called ideal curves that were first discussed by Brown. While reference equations of state generally result in reasonable estimates for the Boyle, ideal, and Joule-Thomson inversion curves, the prediction of reasonable Joule inversion curves is still a challenge. Equations may result in unreasonable estimates of Boyle, ideal and Joule-Thomson plots especially when the equations are based on limited experimental data. 

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