Single Shot Schlieren

Chapter IV: UV Radiation of Hypervelocity Flow Over Circular Cylinders

4.1 Single Shot Schlieren

A camera exposure of 700 ns is used for single shot schlieren imagery. Shutter exposure occurs 120 µs after the arrival of the contact surface measured by a pitot probe mounted underneath the model. This ensures that the bow shock has fully established. Figure 4.2 shows schlieren images of the M7-H8-A and M5-

Figure 4.1: Schematic of hypervelocity flow over a cylinder.

H6-A conditions with an air and nitrogen test gas. Images are mirrored about the stagnation streamline for comparison between test gases. The field of view is large enough to observe the majority of the bow shock curvature. Along the surface of the cylinder model, image distortion due to the boundary layer is visible in the images.

The presence of the boundary layer was confirmed by orienting the schlieren cutoff horizontally and visualizing the boundary layer for the upper half of the cylinder.

The largest standoff distance occurs with nitrogen as the test gas for both freestream conditions. In addition, the radius of curvature of the bow shock is largest with nitrogen. For the highest enthalpy freestream, chemiluminescence is observed in Fig. 4.2a downstream the bow shock. As the pco camera collects broadband light, the chemiluminescence can only be used to indicate regions of high chemical activity. The peak in luminescence is found to occur further downstream for the nitrogen freestream as opposed to the air case. This indicates that the induction time for the post-shock nitrogen to radiate is longer than in the air case. The presence of chemiluminescence is not captured in the images of M5-H6-A due to the lower freestream enthalpy. The image of the shock contains a larger gradient in pixel intensities for M5-H6-A, indicating higher post-shock densities. These schlieren observations will later be confirmed with the spectroscopy measurements, as the standoff distance is indicated by the appearance of radiation.

Using the method outlined in Leibowitz and Austin [55], standoff distance can be measured along the stagnation streamline by extracting pixel intensities. A region 17 pixels wide is binned at the centerline of the cylinder and a profile of pixel intensity versus streamwise distance is generated. The minimum intensity is selected as the location of the shock. As the boundary layer distorts the cylinder

(a) M7-H8-A Freestream (b) M5-H6-A Freestream

Figure 4.2: Single-shot schlieren of a 31.75 mm diameter cylinder in different freestream enthalpy and gas compositions. Boundary layer effects are present in the near surface of the cylinder.

surface, a flat mounting surface located 22.86 mm behind the cylinder tip serves as a reference for measurements. To estimate the uncertainty in the shock standoff distance measurement, an error propagation analysis is performed. The uncertainty in standoff distance is given as

σ_∆² =2c²

x_shock− x_body x₁−x₂

2

σ_x²₂+c²(σ_x²_shock +σ_x²_body), (4.1) where ∆ is the standoff distance, c is the millimeter-to-pixel conversion in units of mm/pixel, and xi are the location of features along the stagnation streamline in units of pixels. An uncertainty of σx = ±1 pixel is used. The cylinder mount geometry is used as a reference to obtainx₁andx₂for converting pixels to distance, which is typically c = 0.03 mm/pixel for cylinder images. If the shock location is measured relative to the cylinder surface, the value x_shock − x_body would be small and the first term can be neglected. Since the measurement of the shock standoff distance is performed relative to the mounting surface far downstream, this adds a non-negligible contribution to the error. The uncertainty in measured∆is calculated to be±0.05 mm from the error propagation analysis.

Mixture ∆_M7-H8-A, mm ∆_M5-H6-A, mm

N₂ 4.79 5.18

XO₂ =0.063 4.59 5.00

X_O2 =0.105 4.24 4.76

X_O2 =0.137 4.21 4.70

Air 4.14 4.56

X_O2 =0.273 4.02 4.48

Table 4.1: Measured standoff distance for each freestream condition and mixture.

An uncertainty of±0.05 mm is used for all reported values.

Schlieren experiments are carried out for various mixtures of O₂ and N₂. To vary the composition of the test gas, a 37 L mixing tank is used. The uncertainty in the individual partial pressures of N₂and O₂is±0.05 kPa. Each mixture is referenced by the oxygen mole fraction used in the driven section. The measured standoff distances can be found in Table 4.1, where air is taken as XO₂ = 0.210. For decreasing oxygen content, the standoff distance is observed to increase. This is expected, as the standoff distance scales as the ratio of the freestream density to the post-shock density. Hornung [38] proposed a scaling of the form

∆

a =2.14ρ∞

ρ¯

1+ 1 2

ρ∞

ρ¯

, (4.2)

whereais the radius of the cylinder, and ¯ρis the mean post-shock density. Chemi- cally frozen and equilibrium post-shock calculations are performed using the Shock and Detonation Toolbox for each of the mixture cases, assuming a perfect gas freestream, and are presented in Table 4.2. The chemically frozen calculation as- sumes translational-rotational-vibrational equilibrium in the post-shock state and results in a lower post-shock temperature than the thermally and chemically frozen case. Using the post-shock conditions in Table 4.2, the chemically frozen and equi- librium post-shock density is observed to decrease with decreasing oxygen content, thereby increasing the density ratio. To obtain an estimate of the mean density along the shock layer, the two-temperature reactive Landau-Teller model is used to compute the density profile along the stagnation streamline. Figure 4.3 plots the non-dimensional standoff distances from all schlieren experiments as a function of the computed ^ρ_ρ^∞_¯ using the two-temperature calculation. It is observed that the non- dimensional standoff distance varies linearly as a function of density ratio, agreeing with the linear dependence of the scaling for standoff distance. Equation 4.2 is plotted alongside the data points. Agreement is observed at low density ratios, cor-

0.210 0.790 6524 50.6 26.9 4127 52.9 37.8

0.273 0.727 6539 51.1 27.4 3883 53.7 40.4

M5-H6-A

0.063 0.937 5145 99.1 65.5 4332 101.5 75.3 0.105 0.895 5154 99.8 66.2 4017 103.2 81.2 0.137 0.863 5161 100.3 66.7 3860 104.2 84.8 0.210 0.790 5179 101.4 67.9 3674 106.0 90.5 0.273 0.727 5192 102.4 69.0 3592 107.3 93.9 Table 4.2: Calculated post-shock conditions for varying oxygen content and freestream condition.

Figure 4.3: Non-dimensional standoff distance of experiment compared with scal- ing proposed by Hornung [38]. Mean density along the stagnation streamline is computed using a two-temperature reactive Landau-Teller model.