Transonic Airfoil Testing AAE 520 03 May 2007 John Tapee Alex Zaubi
Abstract In this experiment, Purdue s Transonic Educational Facility, a Mach 4 Ludwieg tube converted to a transonic test section, was used to observe the effects of transonic flow over a supercritical airfoil. This was accomplished using a Schlieren imaging system to view the density gradients in the flow surrounding an SC(2)-0714 airfoil at various driver pressures and Mach numbers. The different driver pressures simulated the effects of different Reynolds numbers on the flow. Using the images obtained from the Schlieren system, a qualitative analysis could be made of the flow in the transonic regime; these images also demonstrated the necessity of adaptive walls (or similar flow relief) in accurately testing airfoils at near supersonic speeds. The experiment produced very good results, with only small problems produced by problems with the imaging setup. In most of the test runs, the images provided were of good quality, and clearly depicted the effects of flow around a supercritical airfoil at speeds of approximately Mach.6 and Mach.8. In the Mach.8 test case, choking caused by the airfoil raised the Mach number to 1, and successfully demonstrated the need for adaptive walls in the test section. 1
INTRODUCTION When the speed of an airplane approaches Mach 1, the drag it experience sharply increases as a result of a phenomenon called drag divergence. Drag increases sharply as the speed nears Mach 1 and decreases again as the speed increases past Mach 1. This effect is becoming more and more important to the aerospace industry as aircraft begin to spend a significant amount of time in this transonic regime. As a result, research has been done into the development of certain design aspects to eliminate this increased drag, particularly that produced by the wings, as aircraft speed approaches Mach 1. One of the design improvements included the development of special supercritical airfoils. These airfoils were specially designed to optimize drag characteristics while operating in the transonic flight region. This did, however, result in a decrease, sometimes quite significantly, in performance outside the transonic region when compared with conventional airfoils. Since the number of aircraft operating in the transonic region is steadily increasing, it is important to gain an understanding of the characteristics of airflow in that region, as well as the effects of airfoils such as those in the supercritical family. In this experiment, Purdue s Mach 4 Ludwieg tube was converted to a transonic testing facility using a transonic diffuser and test section. The flow was tested at multiple Reynolds numbers by varying the pressures in the Ludwieg tube, and two different Mach numbers by altering a section of the tube. Through the use of a Schlieren imaging system, the results of the flow over a supercritical airfoil were observed visually. The part design, instrument setup, and the final results from these images should lay the groundwork for designing successful inserts for the adaptive wall test section. 2
BACKGROUND During the 1960 s and 1970 s, the general operating speed of airplanes began to approach the speed of sound. Within this flight regime, the airflow and drag characteristics over a wing began to differ greatly from those at lower speeds. Accordingly, an emphasis was placed on the development of an airfoil that could operate efficiently in this region while maintaining good low speed characteristics (2). Through research and testing at NASA, a family of airfoils, termed supercritical airfoils was developed to fill this need. Today, a majority of civilian airliners and many military aircraft spend a significant amount of time in the transonic region, so further testing of flow characteristics in the transonic region, especially those characteristics of supercritical airfoils, is important to improving future aircraft wing design. Supercritical Airfoils Supercritical airfoils feature high radius leading edge, and a significantly cambered trailing end (5). They also typically feature a small degree of trailing edge thickness. Figure 1 shows profiles of both a conventional airfoil and a supercritical airfoil. Figure 1 Drag Profile of Airfoils (1) Supercritical airfoils improve transonic flight performance by extending the region of supersonic flow so that the shock over the upper surface is much smaller. This results in a smaller pressure loss, which creates less drag (1). Many conventional airfoils often have a sharp trailing edge to eliminate as much drag as possible at this location. Supercritical airfoils were designed in such a way that the slopes of the upper and lower trailing edge were the same, which would result in structurally thin trailing edge regions would the trailing edges meet (2). It was also found that some degree of trailing edge thickness was beneficial at transonic speeds. This thickness, however, came at the expense of increased drag at speeds outside the transonic region (2). 3
Adaptive Wall Technology In any wind tunnel test, the effect of the tunnel walls on the data is always a cause for concern. This wall effect is minimized by using a model that is much smaller than the tunnel volume, with the intention of distancing the model from the walls as much as possible. To obtain meaningful results, however, the Reynolds number and Mach number must be matched to the free flight conditions; the smaller the model is, the less similar its Reynolds number is to these conditions. Higher Mach numbers also tend to decrease the test section size, as running large, high-speed wind tunnels becomes cost-prohibitive. These several conflicting issues mean that mimicking free flight in the transonic regime can be difficult to do in a wind tunnel. In fact, since the freestream air speed is near sonic, the wall effects and possible choking effect of the model in the test section can cause shocks where there should be no shocks when analyzing a supercritical airfoil designed to reduce shock losses, the presence or displacement of any shocks results in a fundamentally unusable data set. Several methods have been used to combat this wall effect problem. Adaptive wall test sections (AWTS) consist of changeable geometry walls, using some flexible liner and actuators to change the wall shape to accompany the flow around the test model. Figure 2 shows a diagram of an adaptive wall test section. Figure 2 Adaptive Wall Test Section (6) Depending on the size and pressure capability of a given tunnel, this solution can prove fairly expensive, having to provide the complex mechanism to adjust this wall shape when necessary. It does afford the tester with a reasonably smooth wall shape, though, so as not to create more turbulence while relieving flow blockage. A more common type of transonic wind tunnel approach is the ventilated test section, shown in Figure 3. Figure 3 Ventilated Test Sections, Slotted and Perforated (6) These ventilated sections are surrounded by a plenum so that the system is still closed, but the holes enable flow relief that does not exist with solid, straight-walled sections. With no moving 4
parts and a simple geometry, these ventilated sections are much cheaper than their adaptive wall counterparts, but the numerous material gaps can increase turbulence and induce pressure and energy losses along the test section. A third type of test section, the adaptive slotted test section, seeks to combine the benefit of the passive ventilated section with the controllability of the adaptive wall test section. This is a fairly new type of tunnel construction method and, as such, is beyond the scope of this project (6). When the transonic section for this Ludwieg tube was constructed, the decision was made to use a slight adaptation of the AWTS described earlier. Since the Ludwieg tube facility already existed and was not designed for a ventilated test section, the simplest and cheapest solution was to design an AWTS that could simply be swapped out with the Mach 4 nozzle and test section. To avoid a costly flexible wall and the adjustment hardware, however, this transonic facility is designed with removable wall sections, enabling experimenters to machine wall sections for any given model. If these wall inserts are made out of a cheap and easily-machinable material like plastic, the operation of this adaptive wall test section will remain low-cost yet still effective. Schlieren System The Schlieren imaging system operates by measuring variations in density, which allows compressibility effects to be clearly seen. Light from a source is reflected off one mirror and through the wind tunnel test section to another mirror. This mirror then reflects the light past a knife edge and onto another mirror. The final mirror projects the image toward a camera for viewing. The purpose of the knife edge is to control the amount of light reaching the camera. A diagram of the setup used in the Schlieren imaging system is given in Figure 4. (8) Figure 4 Schlieren Imaging System (10) 5
APPARATUS In this experiment, an SC(2)-0714 airfoil is tested using a transonic test section installed in a Mach 4 capable Ludwieg tube. The airfoil was chosen for study based on theoretical analysis performed by Matsumura (4). The tests were conducted at various pressures, and the flow over the airfoil was analyzed using a Schlieren imaging system. The coordinates for the airfoil were obtained from the NASA technical report detailing the development of supercritical airfoils, and including a list of all those airfoils falling into the supercritical family (2). This coordinate system is given in Table 1 in the Appendix. The airfoil was sized to fit the transparent window on the transonic test section used in the experiment. This window was slightly larger than three inches in diameter, so a three inch chord length was chosen for the test airfoil to maximize the amount of viewable area for the Schlieren images while maintaining a reasonably strong structural integrity. The span was chosen to fit the width of the test section, approximately four inches. Figure 5 Partial Machine Drawing of Test Airfoil The airfoil was machined from a block of aluminum using a CNC lathe. Thin pieces of rubber (neoprene, 1/32 thick) were attached with rubber cement to each span wise end of the airfoil where it connected to the glass viewing area. This was done in order to prevent any metal-glass surface contact. Any contact may have led to damage to the glass wall as a result of small vibrations of the airfoil caused by the airflow. The airfoil was secured to the test section by two bolts (steel, 6-32 thread) on each end placed along the chord line. This allowed the airfoil to be tested at an angle of zero degrees. Research conducted by NASA Langley on the SC(2)-0714 airfoil showed that it produced lift while operating at zero angle of attack, a characteristic desirable for producing visible results in the experiment (3). The placement of these bolt holes is given in the multi-view drawing of the test airfoil in Figure 27 in the Appendix. The placement is designed to maximize the amount of the airfoil visible in the test section window. In addition, it allows for the addition of another hole which would allow for testing at nonzero angle of attack in the future. Plastic tubes were placed lining the holes through the window in order to prevent the bolts from contacting the inner surface of the window, and Teflon washers were used on the outer surface of the window to prevent the bolt head from contacting the glass. 6
Schlieren Setup Window/Airfoil Location Figure 6 Schlieren Setup Successfully setting up the Schlieren proved to be much more of a trial and error procedure than a simple ordered process. With much assistance from and adjustments by Rodrigo Segura with experience with this Schlieren system, the Schlieren was finally able to take reasonably clean photographs of the flow. The basic procedure for setting up the Schlieren is outlined below. 1) Set up the light source, lenses, and pinhole to focus on the first mirror. 2) Adjust this first mirror so that the reflected light travels straight through the test section and hits the other mirror. 3) Set up the knife edge (vertical) at the focal point of the second mirror. 4) Set up another lens and the camera behind the knife edge to capture the image. Perfecting the image took much readjusting and realigning. Initially, light entering the room through gaps around the Ludwieg tube and the air vent near the ceiling was fouling the image captured by the camera. Cardboard was cut to size and taped to these areas to block the light. A recurring problem was the inability to position the knife edge in the exact spot it needed to be. While the light may have looked focused on the knife edge itself, the camera viewfinder showed a clear shadow when the knife edge was moved, indicating imperfect alignment. The light source used in setting up the Schlieren system was a pulsed light source set at 100 Hz. A high frequency was desired so that the image captured by the Schlieren would represent as 7
close to a single instant in time as possible 100 Hz was chosen as it was the highest frequency that the power source could provide. The shutter speed on the camera was adjusted to match. The light source was focused onto the mirror using a system of lenses as shown in Figure 7. The light was then reflected by the source-side mirror through the viewing area of the transonic test section, and reflected again by the camera-side mirror. The image then passed the knife edge, and was focused onto the camera by another lens, as shown in Figure 8. Figure 7 Source Side of Schlieren Optics Figure 8 Camera Side of Schlieren Optics Before the experiment was conducted, the Schlieren system was adjusted to provide optimum image quality. The adjustments were made by placing a heat gun in front of the viewing window to provide density changes that could be observed without actually running the tunnel. The knife edge was then adjusted to allow enough light that the image was as uniform as possible during no-flow conditions. However, too much light would make the density changes difficult to observe. 8
Testing Figure 9 Airfoil Mounted in Test Section To test the airfoil, one set of window blanks in the transonic section were removed. By attaching the airfoil to one window first and carefully sliding the window/airfoil combination through the window opening, mounting the airfoil in the tunnel proved quite easy. Diaphragm preparation was easily accomplished in the time it took for the vacuum pumps to evacuate the tank to about 4 torr, so no time was lost in this step. The operating procedures for the tunnel and associated systems are as follows. Operating Procedures The tunnel operating procedure listed on the next page is adapted primarily from Scott Munro s Masters Thesis (7), with additional information provided from the experience gained during this airfoil testing and from papers written by Ladoon (8) and Borg (9). The diaphragm preparation and vacuum pump operating procedures were written based on the experience gained while running the tunnel and the direction of Rodrigo Segura. While these sections were created independently of any documentation, similar procedures can be found in the Ladoon (8) and Borg (9) papers. 9
Tunnel Operating Procedure 1) When beginning to operate the tunnel, be sure to hang the placards warning of overpressurization on the Mach 2 tunnel and the supersonic jet. Close the valve to eliminate these pieces of equipment from the air circuit. 2) Turn on the current source for the diaphragm wires (this takes a while to warm up) do not turn on the pulse heater yet. 3) Check that the driver tube gauge and the vacuum tank gauge read atmospheric pressure (or close to it). If not, follow the procedure for equalizing and pressurizing the Ludwieg tube after a test run (step 9). Note the cases below. a. If these pressures are not equal, there is still an intact diaphragm (steel or Mylar) in the tube. If it is desirable to avoid bursting a Mylar diaphragm, take care to pressurize slowly as a pressure wave from rapid pressurization can burst a diaphragm, even without any current through the wires. b. If these pressures are equal but low, then the tunnel has simply not been pressurized after a test run. 4) Loosen the clamp near the diaphragm and use the hydraulic jack to open the tunnel. Insert a prepared diaphragm (see Preparing a Diaphragm below) and connect the wires. Close and clamp the tunnel, ensuring the wires do not become disconnected while moving. 5) Close the equalizing valve (valve #2, Fig. 10) to isolate the driver and driven sides of the tube. Turn on the vacuum pumps (see vacuum pump operating procedure below). a. If the desired driver pressure is less than atmospheric, open valve #2. Monitor the driver pressure gauge. When the desired pressure is reached, close the valve. 6) Shut off vacuum pumps when vacuum pressure reads 4 torr or less. 7) If the driver pressure is less than desired, open the supply pressure valve (valve #1) and slowly increase the pressure in the driver tube. Monitor the driver pressure gauge. When desired pressure is reached, close the supply valve. a. Note: if any leaks exist in the nozzle and/or test sections, the driver pressure will steadily drop once valve #1 is closed. It may be beneficial to pressurize the driver tube slightly more than is wanted (~ 0.5 psi or so), and as long as the leak is slow enough, the pressure gauge can be monitored and the run can be triggered when the driver pressure is correct. (The same yet opposite is true for vacuum pressures the driver pressure can rise, and it is suggested to evacuate the driver more than needed). 8) Record initial conditions (driver pressure and temperature, primarily). Ensure any data acquisition systems are operating and prepared for a test. Turn on pulse heater and fire when ready. Turn off pulse heater to ensure next diaphragm is not broken prematurely. 9) After a test run, the tube pressure will be well below one atmosphere. To pressurize the tunnel, open both the equalizing and air supply valves (valves #2 and #1, respectively). When atmospheric pressure is reached, close both valves. 10) The tunnel can now be opened to setup a new test (step 4). 10
11) When finished testing, shut all equipment off and reinsert the steel diaphragm. Open the vacuum-side shut-off valve for the Mach 2 tunnel and supersonic jet and remove the placards. Figure 10 Tunnel Plumbing Diagram (7) Preparing a Diaphragm 1) Based on the desired driver pressure, choose an appropriate thickness Mylar diaphragm (cut using the diaphragm template). 2) Remove the twelve screws securing the two halves of the diaphragm holder together. Separate these pieces and remove any leftover diaphragm material. 3) Insert new diaphragm into guide pins. Fasten the two halves together again, torquing the screws to about 9 in-lbs. 4) Clamp and tape down one heating wire to the diaphragm, being sure to leave enough extra wire so that it will stay attached to the diaphragm as it deforms due to the pressure difference. 5) Clamp and tape down the second wire, arching the center part so that the wires will not touch and short the circuit. 11
Vacuum Pump Operating Procedure Cooling Water Valve Vacuum Valves (behind table) Southernmost Pump Northernmost Pump Pump Oil Figure 11 Vacuum Pumps 1) Check the oil levels of both pumps. The oil windows are on the back sides (eastern sides) of both vacuum pumps there is a mirror nearby with which to check the levels. The oil should occupy at least half to three quarters of the oil window for smooth operation. a. The northernmost pump tends to lose oil and usually needs to be refilled before starting. If this is the case, unscrew the oil temperature gauge (on the top of the pump) and fill the oil reservoir. The pump oil and a funnel for pouring should be near the wall on the south side of the pumps. b. The southernmost pump seems to maintain a constant oil level. If the oil level is low, check with the ASL staff to refill it. 2) Open the cooling water valve just enough so that there is a steady trickle of water through the pump (less than 1/8 of a turn). This should be sufficient to keep the pumps from overheating. a. The water drains just outside room 28 near the 333 lab water experiments. If there is any question as to how quickly the water is flowing, check here. 3) Turn on the pumps, and then open the adjacent pump valves to begin pumping down the vacuum tank. A single pump will eventually evacuate the tank, but using both 12
pumps is recommended in order to cut pumping time down to about 15 minutes (to pump from atmospheric pressure to ~ 4 torr). 4) When finished pumping, close the pump valves before turning off the pumps. If the pumps are turned off before its corresponding valve is closed, the air will fairly quickly seep back through the pump into the lines, raising the line and tank pressure. 5) The cooling water should be left running between pump usages as an additional safeguard against pump overheating. Remember to shut off this cooling water at the end of the day. 13
ANALYSIS & DISCUSSION The experiment was conducted with two different struts to allow for testing at multiple Mach numbers. This was done in conjunction with a separate project. When using the original strut, which was located behind the airfoil in the Ludwieg tube, the cross sectional area of the strut was larger than that of the airfoil. Therefore, the flow was subsonic at the airfoil due to the choking affect of the strut. The Mach number was approximately 0.6 for the flow with the original strut. With the new strut, the cross sectional area of the airfoil was larger than that of the strut, causing the flow to choke at the airfoil. The flow at the thickest part of the airfoil was Mach 1, while the flow in front of the airfoil was roughly Mach 0.8. In addition to the Mach number, the driver pressure was also varied during the experiment. The pressures used were 12, 6, 0, and -6 psig. Additionally, the experiment was conducted with a driver pressure of -3 psig with the original strut. The Reynolds numbers for these pressures are given in the table below. Table 1 Driver Pressure and Reynolds Numbers Original Strut Driver Pressure (psig) Reynolds Number 12 1.67E+06 6 1.29E+06 0 9.20E+05-3 7.32E+05-6 5.44E+05 New Strut Driver Pressure (psig) Reynolds Number 12 2.00E+06 6 1.55E+06 0 1.10E+06-6 6.52E+05 Results using Original Strut (M 0.6) When obtaining the results, a sequence of pictures was taken to observe not only the initial state of the flow around the airfoil, but also the subsequent states as the flow decreased. The results of the experiment when conducted with the old strut did not differ significantly as the driver pressure was changed. In each case, a boundary layer of varying thickness was present on the upper surface of the airfoil, while a separated region formed on the lower surface of the airfoil. Images of each state are provided in Figures 12 through 16. 14
Figure 12 Schlieren Image at 12 psig Figure 13 Schlieren Image at 6 psig 15
Figure 14 Schlieren Image at 0 psig Figure 15 Schlieren Image at -3 psig 16
Figure 16 Schlieren Image at -6 psig On the lower surface of the airfoils in Figures 12 through 16, it can be observed that the area of separation begins at the point of maximum thickness, and is initially laminar. After approximately ½ inch, this laminar region becomes turbulent as vortices begin to form. It is also apparent that a boundary layer of increasing thickness forms on the upper surface, starting at the point of maximum thickness. In the images from the high pressure tests, the boundary layer is not always clearly visible because of the coloration, but it is present nonetheless. It appears that the size of both the vortices produced in the lower surface separation region and the upper surface boundary layer increase as the driver pressure decreases. The exception to this is Figure 15, in which the boundary layer and separation vortices are much smaller. It is likely, however, that the imaging system was disturbed prior to this test, leading to too much light being allowed to pass the knife edge. This decreased the sensitivity of the Schlieren to the density gradients. 17
Results using New Strut (Choked Airfoil) While the flow characteristics and Schlieren image remained relatively unchanged during the course of a test run with the original strut, the images captured using the new strut varied considerably as the run progressed. Ideally, each image would be matched to the driver (stagnation) pressure at the instant when the image was captured. Due to the limitations of the experimental setup, however, there was no way of knowing exactly when the camera took a picture (at a rate of about three pictures per second), so recording the pressure history was unimportant. Thus, each pressure listed (in reference to a Schlieren image) corresponds to the initial driver pressure for that run. For each driver pressure, at least three images were captured successfully during the run. To distinguish between these images and indicate their relative timing, the images are labeled 1, 2, 3, and so on, beginning with the initial image and increasing with time. Note that even the first image ( Image 1 ) will reflect some delay between the start of the run and the camera shutter, but this image will reflect an actual driver pressure closest to the initial, indicated driver pressure. The general characteristics of the flow field are similar for all driver pressures, with the higher pressures resulting in the strongest shock patterns. As such, the 12 psig case will be examined in detail, followed by a discussion of how the other cases differ. Figure 17 Flow at 12 psig, Image 1 18
Figure 18 Flow near Upper Surface, 12 psig, Image 1 The whole window image (Fig. 17) clearly shows that the flow chokes at the airfoil as expected, resulting in multiple shocks and poor flow quality on the upper and lower surfaces. On the upper surface (Fig. 18), the flow remains clean until about three-quarters of the chord where it encounters a relatively strong shock, followed by a series of additional shocks and their reflections. Of particular interest is that this leading upper surface shock seems to originate at the upper wall, not at the surface of the airfoil. This suggests that the Mach number is not uniform across the test section; it is higher near the airfoil. A fairly thick boundary layer is also visible on the upper surface, although it may not appear so at first. Following the contour of the black airfoil shadow, the upper surface appears almost completely horizontal from the point of maximum thickness to the trailing edge of the airfoil. This shape, of course, does not reflect the actual shape of the airfoil; it shows the separated boundary layer. The multiple shocks on the upper surface have little effect on this boundary layer, which seems to grow in thickness at a fairly steady rate. Very near the trailing edge, the flow shows no clear shocks or reflections but a region of high turbulence high enough to have a noticeable effect on the boundary layer. Figure 19 Flow near Lower Surface, 12 psig, Image 1 The flow around the lower surface of this airfoil (Fig. 19) shows a series of shocks and reflections that propagates over a greater chord length than that on the upper surface. These shocks occur before the air has separated from the airfoil surface; thus, the shock-airfoil 19
interactions are much more visible and less ambiguous. In fact, there are many distinct points along the lower surface where an incident shock is reflected. In this region, the surface is nearly flat, shaped so that the flow area below the airfoil increases at an almost constant rate. Since the flow is choked at the point of maximum thickness of the airfoil, the Mach number incident on the first shock along the lower surface is just over 1. The resulting shock is relatively weak, with a subsonic Mach number behind the shock near 1. A small increase in flow area will result in the flow becoming just supersonic before producing another shock. Since each of these shocks is so weak, the pressure ratio is similar across each shock. The relatively constant flow area increase combined with the weak shock strength results in the evenly-spaced series of shocks and reflections seen in the Schlieren photograph. Figure 20 Close-up of Trailing Edge of Lower Surface, 12 psig, Image 1 Figure 20 shows a close-up view of the lower surface behind the shock/reflection series. Vortex shedding is evident in this region as it was for the tests with the original strut (at lower Mach numbers). Yet, unlike the tests with the original strut, the vortices at a higher Mach number break down into a non-structured turbulence region fairly quickly. Also, a curious feature of this image is the dark region just after the shock/reflection series. The flow in the surrounding region suggests that separation and the vortex formation occurs here, and it is clearly not a shock. The process by which a Schlieren system produces an image can explain only that this area reflects a density change, but the flow physics that produce this density change are still unresolved. While analyzing the qualitative flow characteristics is the main focus of this experiment, it would be useful to determine a numerical value for the strength of the leading upper surface shock (the strongest shock in all test runs) so that the various driver pressures and associated images could be numerically compared. The absence of any measured pressures in this experimental setup precludes quantifying shock strength using a pressure ratio, so the Mach number incident to the shock must be determined if a numerical value for shock strength is desired. A simple method for doing so involves measuring the shock angle from the Schlieren image. At the shock location (or anywhere else along the airfoil, for that matter), the flow does not encounter a compression corner that would cause an oblique shock; however, by assuming the shock acts as a Mach wave with a deflection angle of θ = 0, the incident Mach number can be found from the measured shock angle (β) and the shock angle chart (Fig. 28). Figure 21 shows a sample angle analysis. 20
Shock Line β Chord (Reference) Line Figure 21 Shock Angle and Mach Number Analysis Example (12 psig, Image 1) The example shown above has a shock angle of 80. The shock angle chart (Fig. 28) shows that the Mach number is well below 1.05 for β 80 and θ = 0 the coarse resolution of the chart prevents a more precise measurement of the Mach number. In fact, this shock has the lowest shock angle (and, therefore, the highest incident Mach number) of all of the leading upper surface shocks in all of the measured images. While precise values of the incident Mach numbers and shock strengths are indeterminate, the relationship between shock angle and shock strength is still useful in comparing flow images. Figure 22 shows all three images captured for the 12 psig initial driver pressure case. Image 1 Image 2 Image 3 Figure 22 Time History of Flow, 12 psig Initial Driver Pressure It is immediately apparent that the flow changes considerably as the driver pressure decreases throughout the run. On the lower surface, the shock/reflection pattern all but disappears by the third image taken, and the curious dark area recedes as well. The shocks nearly vanish on the upper surface as well, but of most interest is the movement of the leading shock towards the leading edge, where it almost reaches the point of maximum thickness by the third image. Table 1 shows the leading shock angle for each of the 12 psig images. 21
Table 2 Leading Shock Angles, 12 psig Image # Shock Angle, β (Degrees) 12 psig, Img 1 80.0 12 psig, Img 2 85.0 12 psig, Img 3 87.5 From the relationship between shock angle and shock strength as discussed above, it is evident that the leading shock weakens as the run progresses. This image analysis is supported by the fact that the driver pressure drops as the run progresses. The driven pressure increases as well, but not by much, due to the much larger driven side volume. Both pressure changes cause a decrease in the pressure ratio across the shock, which is equivalent to a decrease in incident Mach number with regard to shock strength. After the flow chokes at the maximum thickness point on the airfoil, the shape of the airfoil and the tunnel walls provide a diverging section in which the air expands to M > 1. A decrease in pressure ratio across the test section means that the air cannot expand to as great an area and as high a Mach number before a shock occurs. As noted previously, the leading shocks are actually quite weak, so the overall change in shock strength is fairly minimal. However, the shape of the airfoil produces a very small da/dx (change in area with respect to distance along the chord line), so that the small effect the change in pressure ratio has on the expansion area causes the shock to move a substantial distance dx towards the leading edge of the airfoil. As mentioned previously, the general flow characteristics are similar for all initial driver pressures. Figures 23 through 25 show the initial images for the remainder of the test cases. Lambda Shock? Figure 23 Flow at 6 psig, Image 1 22
Figure 24 Flow at 0 psig, Image 1 Figure 25 Flow at -6 psig, Image 1 In addition to their overall similarities, these images show the same trends with respect to decreasing pressure as do all three images for the driver pressure of 12 psig as shown earlier: the lower the pressure, the weaker the shocks, and the closer the leading shock is to the leading edge. 23
In fact, the -6 psig image shows barely visible shocks on the upper surface and no evidence of supersonic flow on the lower surface. In these pictures, the boundary layer is actually much easier to see; also, the point at which the lower surface boundary layer separates seems to move forward towards the location of maximum thickness as the pressure decreases, a trend not easily visible in the 12 psig time history images. An interesting flow characteristic is seen in the 6 psig image: the leading upper surface shock is possibly a lambda shock (see Fig. 23). Lambda shocks occur because of a viscous boundary layer that creates a virtual compression corner and separates a shock into two separate shocks near a surface. Since the airfoil has no compression corners, its geometry should not create a lambda shock. Granted, the image does show the leading section of the possible lambda shock to be very weak, almost imperceptible weak enough that a small flow disturbance could have triggered a weak shock in front of the stronger leading shock, creating the appearance of a lambda shock. Since four pictures were captured for the 6 psig case (the other cases only had three each), the corresponding image series covers a greater percentage of the total run time than any of the other image series. Figure 26 shows this image series for the 6 psig. Image 1 Image 2 Image 3 Image 4 Figure 26 Time History of Flow, 6 psig Initial Driver Pressure The third image in this series shows very weak shocks on the upper surface of the airfoil, similar to the third image of 12 psig or the initial image of -6 psig. However, the fourth image shows no evidence of supersonic flow whatsoever, just a boundary layer and separation. At the time image 4 was captured, the pressure ratio had already reduced enough so that the flow is no longer even choked and is subsonic throughout the tunnel. As this image was captured no more than 1.5 seconds into the run, it illustrates one of the major limitations to this tunnel with the transonic 24
section: its runtime. Although the runtime with the Mach 4 test section is only a matter of a few seconds, the transonic section, with its much larger throat and choking areas, allows a much higher mass flow, resulting in a very short runtime. Also, images 2 through 4 show a recurring problem with the Schlieren system. The light band that is shown in these images appeared in about a quarter of the pictures, always in a different vertical position. The source of this light band could not be determined, and since the density gradients could still be seen in the lighter region, the light band was simply ignored. 25
CONCLUSION Given the shock patterns around the airfoil with the new strut in place, the need for an adaptive wall test section is clear. Studying the flow around this supercritical airfoil in a straight-walled test section was a good exercise in Schlieren optics and Ludwieg Tube operation (to name a few), but simulating free-flight transonic flow in the same section is not possible. Contoured (adaptive) walls are needed to provide flow relief so that the combination of model and tunnel walls does not cause the flow to choke. While wall effects are present in any wind tunnel experiment, the shocks that are formed where flow should be subsonic (in the free-flight case) make these wall effects much more problematic than they are in other experiments due to the discontinuous nature of a shock. Nevertheless, the Schlieren system has now been set up and adjusted to produce quality images within the transonic section. Getting this system to work properly was a very valuable experience, as learning by doing is often more effective than other learning by reading, for example. The initial frustrations and difficulties with the Schlieren proved to teach much more about how the system worked than had it worked perfectly from the time it was set up. In addition to the Schlieren, a supercritical airfoil is now available for future use in this tunnel, complete with quite a bit of backup mounting hardware as well. An interesting extension of this experiment would be to test the airfoil at different flow conditions. The airfoil was designed so that additional mounting holes could be placed near the leading edge of the airfoil, enabling the airfoil to be tested at different angles of attack. Unfortunately, this would cause a good portion of the airfoil near the trailing edge to be obscured from view, and as the results showed, the trailing edge region is where most of the flow problems occurred. Testing at different angles of attack would clearly require more preliminary analysis. The effect of Mach number on the airfoil could be investigated by attaching flow restriction wedges on the newly designed strut. However, one cannot investigate the Mach number effect until a proper adaptive wall contour is designed and tested otherwise, the flow will continue to choke at the airfoil, and trying to adjust the test section Mach number will be an exercise in futility. The instrumentation and techniques used in this experiment could definitely be improved upon. All Schlieren images shown in this report used a vertical knife edge, sensitive to density gradients in the streamwise direction (left to right). A more thorough imaging technique would involve capturing images using both vertical and horizontal knife edges so that the density gradient in the vertical direction could be captured as well. The horizontal knife edge would improve the understanding of the flow field, especially in regions such as the boundary layer, where there was a lack of definition from the vertical knife edge images. A major deficiency of this experimental setup is the inability to determine what the pressure conditions are for a given Schlieren image. A system in which the timing of a photograph and the driver pressure are recorded on an oscilloscope would solve this problem while the driver pressure is easy to record, the image timing proves more difficult. One possible idea is to use a single (instead of continuously) pulsed light source and a photodiode to record the pulses. However, the shutter would then need to be precisely synchronized with the light pulse, and the issue of overall camera speed (CCD and writing times) limits the number of pictures regardless of photograph timing. 26
While the Schlieren system is invaluable for flow visualization, it would be beneficial to be able to measure the pressure distribution on the airfoil. A pressure distribution would not only allow a simple lift calculation, but it would also serve as another metric with which the effectiveness of a contoured/adaptive wall section could be evaluated. Theoretically, pressure taps on the surface of the airfoil could provide that functionality, but machining pressure taps in the small airfoil and plumbing those taps properly so the pressures could be measured by an external bank of pressure transducers would be nearly impossible. A more graceful solution would involve the use of pressure-sensitive paint (or temperature-sensitive paint to measure the surface temperature). Granted, the viewing windows are fairly small, and obtaining a useful image of the airfoil with pressure-sensitive paint might prove prohibitively difficult. If it could be done, though, using pressure-sensitive paint could prove quite beneficial. 27
SOURCES 1. Anderson, John D. Fundamentals of Aerodynamics. McGraw Hill Publications. 2001. 2. Harris, Charles D. NASA Supercritical Airfoils. Technical Paper 2969, NASA. 1990. 3. Jenkins, Renaldo V., Acquilla S. Hill, and Edward J. Ray. Aerodynamic Performance and Pressure Distributions for a NASA SC(2)-0714 Airfoil Tested in the Langley 0.3- Meter Transonic Cryogenic Tunnel. NASA Technical Memorandum 4044, 1988. 4. Matsumura, Shin, Design of a Test Section for a Transonic Ludwieg Tube. AAE 415. Purdue University, 1998. 5. The Supercritical Airfoil. NASA Dryden Flight Research Center. TF-2004-13 DFRC, 2004. 6. Meyer, O. and W. Nitsche. Update on progress in adaptive wind tunnel wall technology. Technical University of Berlin, Institute of Aero- and Astronautics. 2004. 7. Munro, Scott. M.S. thesis. Purdue University, Dec. 1996. 8. Ladoon, Dale W. Wave Packets Generated by a Surface Glow Discharge on a Cone at Mach 4. Purdue University, Dec. 1998. 9. Borg, Matt. Instructions on Use of Purdue Mach 4/Transonic Ludwieg Tube. Purdue University, Mar. 2005. 10. Supersonic Wind Tunnel. AAE 520. Purdue University, 2007. 28
APPENDIX Table 3 SC(2)-0714 Airfoil Coordinates (2) 29
Figure 27 Machine Drawing of the Test Airfoil 30
Figure 28 Oblique Shock Angle Chart, γ = 1.4 31
Additional Schlieren Photographs, New Strut Figure 29 Flow at 0 psig, Image 2 Figure 30 Flow at 0 psig, Image 3 32
Figure 31 Flow at -6 psig, Image 2 Figure 32 Flow at -6 psig, Image 3 33