67 discussed in a separate section (6.5) The reflected shock

In document A study of radiating argon flows at high opacities (Page 87-90)

contact surface needs to be discussed first.

6.3 INTERACTION OF THE REFLECTED SHOCK WITH THE CONTACT SURFACE

When the reflected shock comes to a discontinuity in

temperature, density and species of gas, as is present in the contact surface, the two boundary conditions to be satisfied are that the pressure and flow velocity normal to the surface should be identical on both sides of the interface, after shock reflection. In general the original shock produces both a transmitted wave into the driver, which is always a shock, and a reflected wave into the test gas, which may be a shock or a rarefaction.

This section is divided into two parts; the first discusses the effect of the interaction on the test gas and the second briefly considers the transmitted shock.

6.3.1 Reflected Disturbance through the Test Gas

This section briefly describes the disturbances so that they may be included in the theoretical analysis. Although more detailed descriptions are available in text books (e.g. Greene and Toennies [1964]), a brief review of the effects of the reflected shock

contact surface interaction is necessary as a prelude to understanding the theoretical model proposed.

The situation is best described with the help of a wave diagram. The three possibilities discussed previously are shown in figures 6.2 - 6.4. (In these diagrams, subscripts [1-5]are the same as before. The new subscript 7 refers to the conditions in the test slug after the disturbances from the reflected shock-contact surface pass through the test gas. Subscript 8 refers to conditions in the driver gas after the transmitted shock passes through).

If the pressure behind the transmitted shock is greater in the driver than in the test gas (this is termed overtailored and seen in Figure 6.2), the reflected wave will be a shock that will propagate into the test gas and reflect from the end wall, giving rise to

successively weakening multiple shock reflection between the wall and contact surface. The pressure and temperature in the test slug will then increase in a stepwise fashion. The contact surface will be brought to rest by these successive shocks.

If the pressure is greater in the test gas (this is termed undertailored and seen in Figure 6.3), the reflected wave is a rare­

faction wave. It will alternate between a rarefaction and a shock. The pressure and temperature in the slug will initially fall but subsequently rise and fall to a much lesser extent with subsequent reflected disturbances. In this case the contact surface reverses its direction.

In the special case where the pressures are identical (this is called tailored interface operation and is seen in figure 6.4), no disturbance is reflected from the contact surface and the conditions in the test slug remain unchanged. The contact surface is brought abruptly to rest in the interaction. Because the test slug is not disturbed this is the ideal case for operating.

The final pressure in region 7, termed stagnation pressure p-,, is almost independent of the initial pressure in the shock tube. For the stagnation pressure, p_,, is the pressure required to bring the contact surface to rest. Hence for the operating conditions considered here, the final pressures are approximately the same, regardless of whether the conditions are overtailored, tailored or undertailored. In fact the stagnation pressure, p^, will give a measure of the pressure, pg, required for tailoring.

69 2.5 ± 0.1 x 108 dynes/cm2 (Stalker 1967). For this investigation, the stagnation pressure was monitored each shot by the pressure trans­ ducer at the end of the shock tube (Chapter 3) .

As can be seen from Table 6.1, the case with an initial pressure of 50.8 torr would be very close to tailored but for the radiation loss. The radiation loss behind the incident shock causes the pressure

immediately behind the reflected shock to be much greater as the shock meets the contact surface after reflection at the end wall of the shock

tube. Thus in the 50.8 torr case the situation is an undertailored one. (At the lower initial shock tube pressures [ 12.7 and 25.4 torr ] the operation is overtailored). The streak photograph (figure 6.5) does not show any indication of the alternating rarefactions and shocks described previously. However this is probably due to the fact that only the outer layers of the gas are seen due to the optical depth of the test gas slug. From the photograph, a slight expansion of the test slug is apparent.

6.3.2 Transmitted Shock

Although the transmitted shock in itself has little relevance to the present thesis, it does give some information on the behaviour of the interaction of the reflected shock and the contact surface.

The equations holding for the transmitted shock in the driver will be the same as those for the simple reflected shock (Section 6.1), though there may be a residual velocity behind the transmitted shock. For most driver gases the relatively low temperatures and high pressures (20

atmospheres) mean that the ideal gas equations can be used (T “1000 K, T ß ~5000°K).

Thus in terms of the transmitted shock Mach No, M^, one has across the transmitted shock

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