The Free Piston Shock Tunnel

The development of the free piston shock tunnel has been outlined by Stalker [32]. He stated that some new generation aircraft and spacecraft were being developed that travelled at `hypervelocities', which generally means speeds in excess of 3 $km\,s^{-1}$ . Aircraft and spacecraft development requires the testing of models. This testing has traditionally been carried out in wind tunnels. Vehicles travelling at these speeds would generally be at very high altitudes, since aerodynamic heating would render flight at low altitudes impossible. Thus, to develop these new aircraft and spacecraft, it is necessary to use a facility that can simulate the fluid dynamic effects of air at high altitudes and at hypervelocities.

To simulate the flow pattern around an aircraft travelling at supersonic speeds it is necessary to reproduce the freestream Mach number. Where the behaviour of boundary layer flow is important, it is also necessary to reproduce the Reynolds number. Large power sources are required to satisfy these conditions at the test section of a conventional, recirculating wind tunnel. Hypersonic wind tunnels were developed in which air was released from a high pressure reservoir rather than being recirculated, and a heater stage was added making it possible to reproduce the required Mach numbers [32]. What was missing was the ability to reproduce real gas effects - the dissociation and ionisation of molecules - which would occur at these flight speeds and altitudes. To represent the real gas effects it was also necessary to match the energy of the test flow to that in flight. However, air at such energies can destroy wind tunnel components within a few seconds. One method of avoiding this destruction was to use an `impulse' facility which reduces the test time to fractions of a second.

A shock tunnel is one such impulse facility and consists of a shock tube driving a hypersonic wind tunnel nozzle. Operation is initiated by rupture of a high pressure diaphragm that separates the driver gas from the test gas. The driver gas expands violently sending a shock wave through the test gas. When this primary shock reflects at the end wall, the test gas is brought to rest creating a slug at high pressure and high temperature, which then expands through the nozzle creating the required conditions in the test section. As it moves upstream, the reflected shock interacts with the driver gas behind the interface, and, in general, causes a disturbance to travel downstream into the test gas. When this effect occurs, it limits the time for which gas conditions remain constant in the test gas to a period that is too short to allow useful experiments in the test section. Fortunately, for a given primary shock speed, it is possible to choose driver gas conditions such that the reflected shock that brings the test gas to rest is of just the right strength to also bring the gas behind the interface to rest. This is known as `tailored interface' operation. To achieve this condition for high shock speeds it is necessary to have a high speed of sound in the driver gas. The required speed of sound of the driver gas increases with the speed of the primary shock.

The free piston shock tunnel

High temperatures can be achieved for a short time in the driver gas by heating the driver gas with a rapid isentropic compression. This is all that is required to achieve even higher speeds in a shock tunnel. Such compression has been achieved by using a simple free piston apparatus [32].

**Figure 3.1:** Operation of a free piston shock tunnel (reproduced from Stalker [32])
$\resizebox*{0.9\textwidth}{!}{\includegraphics{shocktunnel.eps}}$

Operation of the shock tunnel after diaphragm rupture is illustrated in Figure 3.1(b) and Figure 3.1(c). It can be seen that the nozzle starting process commences after shock reflection at the downstream end of the shock tube. Since the shock tube is operated in the tailored interface mode, a period of steady nozzle flow follows the nozzle starting process. The testing period is terminated by the arrival of an expansion wave, generated by falling pressure in the driver section. The time of arrival of this wave is dictated by the need to bring the moving piston to rest before it strikes the end of the compression tube. It has been found that this can be achieved, while still delaying any large variations in driver gas pressure until approximately half of the volume of driver gas available at diaphragm rupture has passed into the shock tube.

Table 3.1 shows the dimensions and some other specifications of the T4 free piston shock tunnel at the University of Queensland.

**Table 3.1:** Specifications of T4 (reproduced from Skinner [31])
Cavity	Length	Diameter	Volume	Filled on	Error	Initial
	(m)	(mm)	(litres)			Pressure
Air	11.3	173	266	bourdon	$\pm 5\%$	-
Reservoir				gauge
Manifold	1	168	22.1	-	-	-
Compression	25.53	229	1052	diaphragm	$\pm 5\%$	$<$ 1 torr
Tube				strain gauge
Shock Tube	10	76	45	bourdon	$\pm 7\%$	$<$ 1 torr
				gauge
Nozzle	0.87	25 $\rightarrow$ 262	15	-	-	$<$ 1 torr
Test Section	1.2	450 mm $^{2}$	243	-	-	$<$ 1 torr
Dump Tank	2.5	650	1104	-	-	$<$ 1 torr
(x 2)
Piston: 90 kg mass, 0.47 m long, nylatron bearings
Primary Diaphragm: 1 $\rightarrow$ 6 mm mild steel, burst pressure $\sim$ 14.2 MPa per mm
Secondary Diaphragm: mylar located at nozzle throat

Test time limitation

Researchers using a free piston shock tunnel facility need to know what proportion of all their measurements occur under the conditions they are trying to simulate. The time interval over which these conditions occur is called the `test time'. Measurements of steady pressure in the test section have traditionally been used to estimate the effective test time, however Crane and Stalker [7] showed that the arrival of contaminating driver gas occurs earlier than the loss of steady pressure.

The loss of test gas to the boundary layer in a shock tube facility was investigated by Mirels [28]. He showed that the wall boundary layer between the shock and the contact surface acts as an aerodynamic sink and absorbs mass from the post-shock region. This causes the contact surface to accelerate, the shock to decelerate and the separation distance, $l$ (Figure 3.2), to drop below an ideal value. The separation distance approaches a limiting maximum value, $l_{m}$ .

In Figure 3.2, $\tau$ is the effective test time and $\tau_m$ is the maximum test time, as determined by Mirels.

**Figure 3.2:** Boundary layer effect on shock tube flow (reproduced from Mirels [28])
$\includegraphics{boundary.eps}$

The interaction of the reflected shock with the boundary layer was investigated by Davies and Wilson [9]. They discussed a mechanism first presented by Mark [19], where under high enough free-stream Mach numbers the reflected shock can bifurcate (Figure 3.3) as it interacts with the boundary layer. Davies and Wilson proposed that this would cause the driver gas to `jet' through the bifurcated shock system as it interacts with the contact surface. They concluded that the early arrival of driver gas is at least partially due to this mechanism.

**Figure 3.3:** Schematic diagram of bifurcated shock system (reproduced from Davies and Wilson [9])
$\resizebox*{0.9\textwidth}{!}{\includegraphics{bifurcate.eps}}$

Skinner [31] examined the possible causes of mixing of the test gas and the driver gas during the operation cycle of the shock tunnel. He investigated a number of possible mechanisms for driver gas contamination, namely:

A particular driver gas contamination problem

A design goal of the computer program developed in the current work was to produce a code that could be used to investigate driver gas contamination. Since Skinner's [31] experimental data was available, one of his shock tunnel runs was used to provide conditions for a simulation. Table 3.2 details the conditions for the run chosen.

**Table 3.2:** Run# 37
Driver gas composition	15% Ar, 85% He
Shock tube fill pressure	15kPa
Test gas	Air
Mach number of primary shock $M_{s}$	10.4
Length of shock tube	10m
Diameter of shock tube	76mm

A standard temperature of 300K in the shock tube was assumed. Shock tube relations from Liepmann and Roshko [17] were used to calculate the appropriate inlet conditions required to generate such a shock. These conditions were then normalised to set the post shock flow variables to unity (Appendix C).

Expected boundary layer thickness

Since the computer program developed does not model turbulence, a flat plate laminar boundary layer profile is expected behind the shock and also leading downstream from the inlet. A plot of this expected result is shown in Figure 3.4 and was produced using Equation 3.1 [15] for the computation conditions shown in Table 3.2.

Here, $\delta$ is the boundary layer thickness and $Re_{x}$ is the Reynolds number based on length $x$ .

**Figure 3.4:** Expected boundary layer profile assuming laminar flat plate flow
$\includegraphics{bplot.eps}$

In his determination of test time limitation, Mirels [28] developed a way to determine the expected boundary layer thickness at the contact surface, based on turbulent boundary layers. Figure 3.2(b) is a qualitative view, according to Mirels, of the expected boundary layer development in a shock tube. This diagram shows the boundary layer forming behind the primary shock in the test gas and the other boundary layer forming in the driver gas according to normal pipe flow processes. Figure 3.5 can be used to predict the boundary layer thickness at the contact surface, $\delta_m$ , for a given primary shock Mach number. For a primary shock Mach number of 10 in ideal air (Case II), $\delta _{m}=\frac{d}{4}$ , where $d$ is the tube diameter. Though the contact surface location is not drawn, Figure 3.4 shows that there is a discrepancy between Mirels' value and the expected boundary layer profile. This is due to the fact that Mirels' calculations were for a turbulent boundary layer - which would be the case in a real shock tube at these Reynolds numbers.

**Figure 3.5:** Boundary layer thickness at (reproduced from Mirels [28])
$\resizebox*{0.9\textwidth}{!}{\includegraphics{mirelscurve.eps}}$

The Free Piston Shock Tunnel

Shock tunnel development

The free piston shock tunnel

Test time limitation

A particular driver gas contamination problem

Expected boundary layer thickness