Military jets fly at incredible speeds that exceed the speed of sound, called supersonic speeds. When describing supersonic speeds, we use Mach number to gauge that speed relative to the speed of sound. At a Mach number greater than 0.8, but less than 1.2, the speed is transonic. Above Mach 1.2, the speed is supersonic.

Let’s take a closer look at what is happening at these high speeds by analyzing air flow around a cone-shaped body. Above a Mach number of 0.3, the compressibility effects of air must be considered, because at these high speeds air has significant density changes. When the incoming flow speed is above Mach 1.0, an oblique shock wave forms from the nose of the cone or wedge, and expansion fans form around the moving body.

A shock wave is an extremely thin propagating disturbance, where abrupt changes in flow properties, like pressure, temperature, and density, occur. An expansion fan consists of an infinite number of waves and is caused when supersonic flow turns around a convex corner. The pressure, density, and temperature decrease continuously across the expansion fan, while the velocity increases. Since the density of air changes significantly within the shock wave and expansion fans, they can be visualized using a density-based flow visualization technique, called Schlieren Imaging.

The Schlieren method relies on refractive index, which is the ratio of light’s velocity in a vacuum, to its velocity within a specific medium. The change in refractive index is proportional to the change in density. Thus, as the density of air changes in the shock wave and expansion fan, so does the refractive index.

In Schlieren Imaging, a collimated light source shines on the body, and the variation in refractive index distorts the light beam. In order to visualize the deflection, a knife-edge is placed at the focal plane of the transmitted light, thus, blocking some of the deflected light, and enhancing the contrast of the projected image on screen. This results in an image of high and low light intensity, which maps the areas of high and low air density, thus enabling us to visualize the shock waves and expansion fans.

In this experiment, we will demonstrate the use of a Schlieren Imaging system to visualize the shock waves and expansion fans formed by Mach 2 air flow over a cone.

This experiment utilizes a Schlieren system to image shock waves generated by a supersonic wind tunnel around a 15° half-angle cone model. The Schlieren system used in this experiment is set up as shown.

First, activate the dryer towers to dehydrate the air. This will prevent ice formation due to local temperature drops in the test section. Then, open the text section, and secure the 15° half-angle cone model to the support structure inside. Check the test section to make sure it is clear of debris and any other objects. Then close the test section.

Make sure the main valve for the air flow control is closed, then turn on the compressor to pressurize the air storage tank, and let the tank reach 210 psi. If the compressor does not automatically shut off when pressure is reached, turn off the compressor manually. Now, turn on the controller for the high-speed valve.

To set up the Schlieren Imaging system, first turn on the light and cooling fan. Then place a piece of paper on the opposite side of the test section from the light source. Align the first concave mirror to allow light to pass through the test section, and check that the light hits the paper. Then, position a projecting screen where the image is formed.

Now, adjust the second concave mirror so that light passing through the test section is reflected onto the projecting screen. Adjust the knife-edge so that it is at the focal point of the second mirror. Then, adjust the knife-edge aperture to achieve the desired image quality.

To record the projected image, set a camera on a tripod that faces the screen. To record directly on the camera sensor, position the camera in front of the knife edge aperture. Now that the apparatus is set up, let’s run the experiment.

First, put on the appropriate hearing protection, then make sure that no one is near the air exhaust outside of the building. Start by opening the air supply to the fast valve controller. Then, open the main valve, which lets air into the system. Now, turn off the lights in the room so that the projected image is easier to see. Then, activate the wind tunnel by pushing the green button located next to the controller, which opens the fast valve.

Observe the Schlieren Image of the Mach 2.0 flow over the cone model. When finished, turn off the wind tunnel by closing the valves in reverse order, and then turning off the controller. Wait until the apparatus is done releasing air before removing your hearing protection.

Now, let’s take a look at the image acquired using the Schlieren setup. The model used in this experiment was a cone with a half angle of 15°, and it was subjected to supersonic flow at Mach 2.0. We can observe the presence of a shockwave, as shown here.

Theoretically, an oblique shock should form at the cone surface, at an angle of 33.9°. The oblique shock angle value is obtained from the Taylor-Maccoll Equation, which must be solved numerically. The experimental angle measured was 33.6°, a percent error of less than 1%, as compared to the theoretical data.

In addition, the Schlieren technique enables the visualization of expansion fans over the cone. The expansion fan is an expected expansion process that occurs when supersonic flow turns around a convex angle.

In summary, we learned how the Schlieren Method uses changes in refractive index to visualize shock waves and expansion fans in supersonic flow. We then utilized the imaging technique to visualize the shock and expansion wave patterns in the Mach 2.0 flow field over a cone.