where I (x) is the modified Bessel function of the first kind, o
90 equilibrium or nonequilibrium, however the difference between the two
flows is essentially in the partitioning of the energy between enthalpy and velocity. Hence in test section flows it makes little difference if the flow was originally equilibrium or nonequilibrium. As long as the flow is hypersonic, the actual Mach number is not of great importance.
However, once the gas has passed through a shock in the test section a new concept of equilibrium or nonequilibrium is involved, in fact the situation is similar to the shock structure of the incident shock. The gas behind a shock will gradually go to equilibrium, due to possible atom-atom collisions, and then electron-atom collisions. (N.B. the two uses of equilibrium and nonequilibrium flow could be confusing, both nonequilibrium flows are "symptoms" of the same phenomenon, viz. lack of collisions. In fact, the only difference could be that because it has more electrons initially, the "nonequilibrium" nozzle flow goes to
"equilibrium" more quickly behind a shock than an "equilibrium" nozzle flow.)
Figure 7.3 shows some thermodynamic conditions behind a normal shock. The nozzle exit conditions from Table 7.2 were used ( viz
p = 6.72E-6 gm/cm2 , a = 0.039). In this case the thickness of the shock structure is 3mm. For weaker shocks the thickness would be larger, for a 35°wedge equilibrium is established 2.9cm after the gas flows through the shock front.
In the light of these results one must be careful in interpreting luminosity photographs. Experiments with wedges indicated reasonable agreement between the shock angles measured by schlieren and those
measured from the luminosity photograph. With the shock standing off a flat faced model the situation is more complex, however an indication of the variation of the shock front can be obtained.
7.4 THEORETICAL TEST SECTION FLOWS
behaviour of both the reservoir region and the hypersonic nozzle flow. The nozzle flow is very important for the discussion in Chapter 8. For
this reason two types of flow were studied; the wedge and a circular disc (placed normal to the flow). As each of these gave similar results for the characteristics of the nozzle flow and the flow over a wedge is well understood (Chapter 5 and Hayes and Probstein (1967)) only the flow over the flat faced body is discussed here. However the results from the other flows are brought into the discussion to confirm conclusions.
7.4.1 Formal Shock Analysis
With a flat faced body a shock stands off the front of the model, and equilibrium is reached a short distance behind the shock front. To a good approximation, this shock can be regarded as a normal shock and hence the normal shock relations of section 4.2 can be used to calculate the equilibrium thermodynamic conditions behind the shock. These results are shown in Figure 7.4, using values from the simple equilibrium nozzle
calculations without radiative energy loss. The thermodynamic conditions using the values from the nonequilibrium nozzle calculations with radiative energy loss and the corresponding equilibrium calculations are given in Table 7.6 . It is seen from this table that the thermodynamic conditions behind the normal shock are almost independent of whether the nozzle flow
is equilibrium or nonequilibrium.
Using the operating conditions of the driver gas in T2 (Section 7.2.3) the thermodynamic conditions behind a normal shock for a pure helium nozzle flow are given in Table 7.5 .
7.4.2 Flow Over Flat Faced Models
To obtain a slug of luminous gas suitable as a source for a time resolved spectra, various flat faced models were used. The most common one used was the simple square, which was very convenient for the gas quickly went to equilibrium and the resulting luminous slug was an ideal light source. Other measurements of this slug were also taken. A
92 monochromator (Chapter 3) recorded the radiation and streak photographs
recorded the shock stand off. At first, the shock standing off the model was treated as a normal shock (Section 4.2) in order to obtain the
conditions expected behind the shock. The actual solution is very complex and well outside the scope of this thesis (Belotserkovskii et.al. (1965)). However Allen (1971) working on an allied problem using Belotserkovskii’s method of integral relations provided the author with a solution for a
circular disc normal to the flow using the method of South (1964). This solution gives both the conditions behind the shock at various points» and the stand off distance. The stand off distances, 6 , were calculated for
a variety of gammas and Mach numbers and the results can be seen in Figure 7.5 . It has been graphed as against £» where zr--^1-^ca^ is the distance from the centreline of the model to the sonic point, which in this case will be at the edge of the model.
These results are used in Figure 7.11 to compare experimental and theoretical stand off distances, however there is no detailed
discussion. (N.B. For this thesis it was suggested by Hornung that for real gas flows for which a solution is not available, an ideal gas
approximation could be used. The appropriate y would be such as to give the correct density ratio across the normal shock, thus y = •)
As can be inferred from Figures 7.2 and 7.4 many of the
parameters that can be measured, i.e. the electron density, the electron temperature, the shock angle, the pitot pressure and the stand off
distance, are to a large degree independent of the exit flow velocity (and consequently the exit Mach number). If the test gas in the
reservoir region loses energy by radiation, slower exit flow velocities will result. Nevertheless the measured parameters, apart from the actual
loss by any measurement apart from the velocity is difficult. Yet, on the other hand, it does mean that the effect of radiation loss in the reservoir on the flow patterns over models in the test section, will not be very significant. However the analysis has shown that the flow patterns can be used to detect a major change in operating conditions.
7.5 EXPERIMENTAL ANALYSIS AND DISCUSSION
The results of various types of measurements are used in this section in order to assess the behaviour of the nozzle flow. These include photomultiplier traces and streak photographs at the nozzle exit, the pitot pressure, time resolved spectra and streak photographs of the shock heated gas in front of a flat faced body, and framing camera photographs of the flow over wedges.
The division of this section is according to the differing gas flows rather than experimental techniques. The first period 7.5.1
corresponds to the starting process. The second period 7.5.2 is that of the pure gas flow after the starting process. The third 7.5.3 is the flow that is contaminated, a discussion of a possible mechanism for contamination is given in section 7.6 .
7.5.1 Starting Process (Region I)
Due to the slow response time of the pitot pressure transducer (discussed in Chapter 3), no pressure measurements could be taken in the very short period of flow corresponding to the starting process.
Two photomultiplier traces are seen in Figure 7.6 . These are for the usual "initial" shock conditions (Mach 16.5 into 50.8 torr) with
the two available nozzles (d —zr ).These both show a short initial luminous t o
flash followed by a region of low luminosity and then a later rise. It was not possible to analyse the luminosity spectroscopically at the nozzle
94 heated gas in front of the flat faced model indicated that the early
radiation from the gas corresponded to argon. Hence it would appear that
the luminosity peak corresponds to the shock heated test gas between the
interface and the secondary shock of the starting process (Figure 7.1).
The less intense region behind the luminous peak probably is due
to the expansion fan behind the ''backward moving" shock. Calculations
indicate that the head of the expansion fan (i.e. the u-a wave) should be
about 5ysec behind the interface (0^ = 7.5°). Although no quantitative-
analysis was done on the test gas in the expansion fan it was thought that
the expansion fan would tend to keep the gas in equilibrium for a larger distance down the nozzle and hence a lovzer ionization fraction at the exit.
As the total luminosity is a measure of the decrease in luminosity
behind the initial flash followed by a subsequent rise in luminosity is
consistent with this explanation.
Two streak photographs corresponding to the photomultiplier
traces of Figure 7.6, are shown in Figure 7.7 . These show the same
general trend as the photomultiplier traces. However quantitative
analysis of the luminosity is not possible from these photographs. Using
the luminous features on these photographs, the velocity of these features
can be measured. Assuming that the first bright feature corresponds to
the shock heated test gas between the interface and the secondary shock
(Figure 7.1), the interface velocity at the exit can be measured. Values
are given in Table 7.7 and these are seen to be in qualitative agreement
with those of Table 7.1 .
7.5.2 Test Gas Flow (Region II)
Following the starting process a well behaved nozzle flow is
established. From the theory put forward in Chapter 6 it is expected
that the nozzle flow will be changing in this period due to the radiation