Source: Jose Roberto Moreto, Jaime Dorado, and Xiaofeng Liu, Department of Aerospace Engineering, San Diego State University, San Diego, CA
Military jet fighters and projectiles can fly at incredible speeds that exceed the speed of sound, which means they are traveling at a supersonic speed. The speed of sound is the speed at which a sound wave propagates through a medium, which is 343 m/s. Mach numbers are used to gauge the flight speed of an object relative to the speed of sound.
An object traveling at the speed of sound would have a Mach number of 1.0, whereas an object traveling faster than the speed of sound has a Mach number greater than 1.0. The compressibility effects of air must be accounted for when traveling at such speeds. A flow is considered compressible when the Mach number is greater than 0.3. In this demonstration, Mach 2.0 supersonic flow over a cone will be analyzed by visualizing the formation of shock waves and compression waves in compressible flow using a Schlieren system.
Compressible flow, or high-speed flow, occurs when fluids experience significant changes in their density. When supersonic flow passes by a body, shock waves and expansion waves are formed around the body. A shock wave is an extremely thin region, on the order of 10-5 m, where flow properties significantly change. An expansion wave occurs when the pressure decreases continuously across a wave and the flow velocity increases.
The schlieren imaging method is a density-based flow visualization technique that detects changes in the refractive index of a fluid, which is proportional to the changes in fluid density across shock or expansion waves. This enables the visualization of shock and expansion wave patterns in supersonic flow fields.
As shown in Figure 1, a schlieren imaging system converts differences in angular light, which is caused by the density gradient in the flow, into differences in light intensity on the screen. The flow phenomena is visible by the inherent density changes. As shown in Figure 1, parallel light originates from a light source through the focal point of a convex lens, L1, and illuminates a compressible flow field in the test section of a supersonic wind tunnel. After traveling through the test section, the incident light ray converges through lens L2 at its focal point and further travels until it is projected onto a screen. The knife-edge, K, located at the focal plane of lens L2 is critical in ensuring the quality of the image on the screen. Blocking some of the deflected light significantly enhances the contrast of the projected image on the screen. Without appropriate blockage by the knife-edge, the visibility of the deflected incident light through the density varying fluid will be compromised.
Figure 1: A schematic of a schlieren imaging system showing the deflected light blocked by the knife-edge, K, located at the focal plane of lens L2.
The schlieren imaging system used in this experiment is shown in Figure 2, and it is an alternative setup to that shown in Figure 1. The major difference between the two configurations is that the pair of convex lenses in Figure 1, whereas a pair of concave lenses are used in Figure 2. All other components are the same.
Figure 2: Schematic of the schlieren imaging system used in the demonstration.
1. Visualizing shock waves using a schlieren imaging system
- Activate the dryer towers to dehydrate the air. This will ensure that the air flow does not contain moisture, and will prevent ice formation when the local temperature in the test section drops due to the supersonic flow.
- Open the test section and secure the 15° half-angle cone model to the support structure.
- Check if the test section is clear of debris or other objects, then close test section.
- Make sure the main valve for air flow control is closed, then turn on the compressor to pressurize the air storage tank. Allow the compressor to reach 210 psi before shutting it off.
- Turn on the controller for the high-speed valve and set the following parameters that are listed in Table 1.
Table 1: Control parameters for Mach 2 run.
- Turn on the light and cooling fan of the schlieren imaging system.
- Place a piece of paper on the opposite side of the text section from the light source.
- Align the first concave mirror to allow light to pass through the test section. Check that the light hits the paper.
- Adjust the second concave mirror so that the light that passes through the test section is reflected onto a projecting screen.
- Adjust the knife-edge so that it is at the focal point of the second mirror. And adjust the aperture of the knife-edge to achieve the desired image quality.
- Position a camera on a tripod directly in front of the knife-edge aperture to record the projected image.
- Put on the appropriate hearing protection, and check that no one is near the air exhaust located outside the building.
- Open the air supply to the fast-valve controller, then open the main valve that lets air into the system.
- Turn off the light in the room so the projected image is easier to see.
- Activate the wind tunnel.
- Observe the schlieren image of the Mach 2 flow over the cone model.
- Turn off the wind tunnel by closing the valves in reverse order. Then turn off the controller.
- Wait until all air has been released from the apparatus before removing your hearing protection.
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.
In this demonstration, a cone with a half angle of 15 degrees was subjected to a supersonic flow at Mach 2.0. In Figure 3, a shock wake and an expansion fan over the cone is observed. Theoretically, an oblique shock should form at the cone surface at an angle of 33.9°. The experimental angle was measured to be 33.6°, as shown by the red line in Figure 3B. Compared to the theoretical data, the percent error was found to be less than 1%. In addition, this flow visualization method was able to show the expansion fan over the trailing edge of the model.
Figure 3: Schlieren image of Mach 2 flow over a 15° half-angle cone. A) Original image. B) Highlighted features displaying a shock wave at the leading edge and expansion fan at the trailing edge.
Applications and Summary
The schlieren imaging technique is a classical optical flow visualization technique based on density changes in the fluid. It is a simple system built with concave mirrors, a knife-edge, and a light source. With this system, supersonic flow features, such as shock waves and expansion waves, can be visualized. This technique, however, has sensitivity limits to low-speed flows.
The schlieren imaging method may be used for a variety of applications, especially in the study of fluid mechanics and visualizing turbulence. Schlieren imaging provides valuable information on the spatial distribution of complicated flow structures in compressible, turbulent flow and in test flights.
This technique has also been used in air-to-air photography of supersonic aircraft, which involves using the sun and/or moon as a light source and the desert floor as the projecting surface to visualize the shock waves. Typically, supercomputers and wind tunnel testing are used to predict the formation, propagation, and merging of shock waves on an aircraft. To enhance the quality of these predictions, a database of sonic boom measurements are collected at various speeds and altitudes. This technique permits supersonic flow visualization of a full-scale aircraft, rather than a scaled-down model.
This technique may also be adapted to scramjets. Scramjets are airbreathing engines that rely on the pure speed of an aircraft to compress air into the engine before combustion. Focusing-schlieren visualization is able to show fuel jets, turbulent structures of mixing, and shock waves inside the scramjet engine.
|Supersonic wind tunnel||SDSU||Operational Mach numbers (1; 2; 3; 4.5)|
|Test section 6"x6"x10"|
|Cone model||SDSU||15-degree half angle.|
|Dresser reciprocating air compressor.|
|Air dryer.||Oriad||Each tower takes 4 hours to dry.|
|Large air receiver tank.|
|6-inches control valve.||The valve is pneumatically powered and electrically controlled.|
|EC-321 process loop controller.||Toshiba|