Cover Page for Lab Report Group Portion Compressible Flow in a Converging-Diverging Nozzle Prepared by Professor J. M. Cimbala, Penn State University Latest revision: Prof. Steve Lynch, 14 February 2017 Name 1: Name 2: Name 3: [Name 4: ] Date: Section number: ME 325. Group # Score (For instructor or TA use only): Lab experiment and results, plots, tables, etc. - Procedure portion Discussion Neatness & grammar TOTAL / 45 / 15 / 10 / 70 Comments (For instructor or TA use only):
Procedure and Presentations of Results Safety Precautions: Wear safety goggles at all times the air in the wind tunnel is pressurized. Leave the protective Plexiglas cover on the test section except when performing flow visualizations. Wear hearing protection if the sound level is bothersome. A hearing protector is available for each lab member. A. Getting familiar with the schlieren optical technique Before visualizing shock waves in the test section of the supersonic wind tunnel, familiarize yourself with the schlieren system by looking at some other simpler flow fields: 1. Turn on the LED light. Be careful not to bump any of the optics stands. 2. A schematic diagram of the schlieren setup is sketched In Figure 10. Verify that the schlieren imaging system is operating correctly. An image of the test section should be visible through the viewfinder of the camera. If the light passing through the test section is out of focus, adjust the manual focus ring on the camera lens. If the system falls out of alignment, get help from your instructor or TA. Figure 10. Schematic diagram of schlieren setup, view from the top. The key dimensions for this system are that the slit and knife-edge are located at the focal point of lens 1 and lens 2, respectively. These lenses are 70mm diameter with a 500mm focal length. The LED, condenser lens, and slit are all mounted together here. The knife edge is replaced by a color filter to convert from black-and-white schlieren imaging to color schlieren imaging. 3. With one group member holding the soldering iron inline with the test section, just inside the field of view of the schlieren system (do not touch the soldering iron tip to anything), the other group members can observe the image through the camera viewfinder. Turn on the soldering iron and see if you can observe a thermal plume. Take turns so that every group member gets to see the schlieren image. 4. Visualize other compressible flow phenomena, such as compressed air streaming out of a spray can, shop air exiting a nozzle (you should be able to see shock diamonds in the jet), the thermal plume from your hand, etc. B. Visualization of shock waves using the schlieren optical technique Before starting this section, make sure the schlieren system is working properly, and that your group can see the output from the camera on the TV monitor. The behavior in the nozzle changes as the system pressure decreases, so be ready to observe. The following procedure should be used to start the flow facility. Use Figures 8 and 9 of the Introduction as a guide. 1. Remove the Plexiglas protective cover from the test section. Everyone in the lab group should wear safety goggles. 2. Open backpressure Valve 3 (the large one) as fully open as you can, and open back pressure Valve 4 (the small one) as fully open as you can, to make the backpressure as low as possible. Ask the TA if you re not sure if they are open. 3. Open Valve 2 slowly until fully open. You should hear the rush of air through the system. The facility is now operating, and can be controlled somewhat by the two back pressure valves, Valves 3 and 4. Use Valve 3 for gross adjustment and Valve 4 for fine adjustment. Never close both back pressure valves completely; otherwise high pressure builds up in the test section, and the optical glass can shatter. Note: If at any time the pressure relief valve blows, or the test section glass shatters, shut off Valve 2 immediately, and call your instructor or TA. 4. With Valves 3 and 4 fully open, observe the flow patterns in the camera viewfinder as the air flows through the nozzle. Are you able to observe a shock wave? An example is shown in Figure 11. 1
(a) (b) Figure 11. Color schlieren images in the compressible flow rig: (a) back pressure such that a shock wave is observed just downstream of the throat, and (b) lower back pressure such that the shock wave is much further downstream and Mach lines are observed in the isentropic flow region upstream of the shock structures. Note that no compressible-flow phenomena are observed upstream of the nozzle throat. (4) 5. Briefly describe below what happens to the shock wave as the air tank drains down. Do your observations agree with the theoretical description of Figure 1 of the Introduction? 6. Close Valve 2 after the pressure gauge directly upstream of Valve 2 (near the wall) drops below 10 psig. The air compressor will immediately start recharging the air tank. Wait until the gauge reads above 120 psig (the air compressor should shut off at about 170 psig) before starting the next step. (3) 7. Reopen Valve 2 to start airflow, but after a few minutes when the shock has stopped moving around, slowly close Valve 3, and then slowly adjust Valve 4 to create higher backpressure. On a separate page, sketch the observed flow pattern for two flow conditions, including one with no shock present and one with a shock present in the nozzle. You may also record the images with the camera. To operate the camera, begin by turning it on (it should be powered either by an internal battery or plugged into the wall). The camera should be set to manual operation (M), with the f-stop set to 1.8 and the shutter to 2000. Adjust the f-stop by rotating the dial near the shutter button on the lens-side of the camera. The shutter is adjusted by the dial on the view-screen-side of the camera. The shutter may need to be adjusted to record a properly illuminated image depending on the knife-edge position. Keep the f-stop full-open at 1.8. Remove the camera memory card and use one of the computers to save the images. For more detailed camera instructions, see the instruction manual or ask your TA for assistance. See Figures. 2
C. Drain time of the air compressor tank Due to a miscalculation in the air compressor flowrate, the current system (as of Spring 2017) is undersized. This means that the air compressor cannot deliver enough flow continuously, and the air tank will be drained. In this section you will estimate the drain time of the tank and compare to a measurement. Equations (5) and (6) from the precalculations for this lab are useful here. (2) 1. Using any measuring equipment you can find (tape measure, yardstick, string?), measure the dimensions of the air compressor tank located across the hallway, outside of the lab. Your TA or instructor can point out the location of the compressor. What is your estimate of the volume of the air tank? 2. Look on the air compressor on the top of the tank for the rated flow delivery of the compressor (usually given in standard cubic feet per minute), and the outlet pressure at that delivery flow, and record below. Note here std refers to standard conditions (T std =23 C, P std =14.7 psia), and act refers to the delivery conditions. std = cfm (cubic feet/minute) P act = psig (psi, in gauge) (2) 3. Convert the standard volumetric flowrate to actual volumetric flowrate using the equation below. Assume that T act =1, and be careful to convert pressures to absolute. T std act= std T act P std (1) T std P act act = cfm (cubic feet/minute) Also find the mass flowrate from the compressor, using the definition of massflow and the ideal gas law: m compr = ρ act= P act RT act act (2) m compr = kg/s (3) 4. Using Equations (5)-(6) in the Precalculations for this lab and your answer for Question 6, update your calculation of the time required to drain the tank to a level of 25 psia, for the tank volume you just measured, and the initial pressure of the air tank as observed on the gauge next to Valve 2. The throat area A * is equal to 4.03 10-5 m 2 Show your work below: 3
Answer: Tank will reach 25 psia in minutes. (3) 5. Open Valves 3 and 4 fully. Get the stopwatch, and have one team member ready to start timing as soon as Valve 2 is opened, until the pressure gauge upstream of Valve 2 reads 25 psia (recall the gauge reports psig). Record the time below. How does this compare to your calculation? What might be some reasons for the difference? D. Measurement of mass flow rate The test rig contains two flow rate measuring devices: a) a diaphragm meter and b) a Venturi meter. Only the diaphragm meter will be used in this lab experiment. This device directly measures the volume of gas passing through the meter. It works by rotating a vane inside, which is attached by gears to a counter and a revolving pointer. You may have seen similar meters for measuring the volume flow of water or natural gas in your home. The accuracy of this type of flow meter is around 2%, except when the volume flow rate falls below 5% of rated capacity. For our meter, one revolution of the pointer corresponds to 5 cubic feet of air, which is equivalent to a volume of 0.142 m 3. To compute mass flow rate, use its definition, along with the ideal gas law, i.e. P V m Q (1) RT t where Q is the volume flow rate, measured as V t, where V is the volume of air passing through the meter in a measured time period t. Gas density is computed from the ideal gas law in Equation (7). Pressure P and temperature T must be measured just upstream of the flow meter. On the control panel, these correspond to the pressure toggle switch labeled Flow Meter Inlet, and thermocouple T 1 (number 1 on the dial). The control panel permits measurement of any of the pressure taps (see Figures 8 and 9 of the Introduction), with the pressure being read from the large Heise absolute pressure gauge. When measuring pressure, only one of the pressure toggle switches should be open at any time. The toggle switches merely connect the line from the chosen pressure tap directly into the input line for the Heise pressure gauge. Temperature is measured by thermocouples and a digital display unit. The temperature dial should be turned to the desired position to read the chosen temperature in degrees Centigrade. 1. Turn both Valve 3 and Valve 4 to their fully open (counterclockwise as far as possible) condition so that the imum flow rate is achieved through the system. Wait for the air tank to drain down, until the pressure just upstream of the flow meter is no longer changing with time. This may take several minutes. Once the pressure is steady, measure the pressure and temperature just upstream of the flow meter, as discussed above. Record (in the spaces provided below) these readings: P flow meter inlet = psia T flow meter inlet = T 1 = C (4) 2. With a stopwatch, measure the volume flow rate through the diaphragm meter, and calculate m using Equation (1). Show all your calculations in the space provided below. Show all units in your calculations, and be careful that the units combine correctly into kg/s. Note that 1 psia = 6894.8 N/m 2 = 6894.8 Pascals. 4
m = kg/s (2) 3. For this same set of flow conditions (imum flow rate), measure both P 0 and P b. On the control panel, these are labeled P 2 and P 10 respectively. Again, note that only one pressure toggle switch should be open at a time; otherwise the pressure reading will be in error. Calculate the back pressure ratio for these conditions. Record your measurements in the spaces provided below: P 0 = P 2 = psia P b = p 10 = psia P b /P 0 = (2) 4. The theoretical imum flow rate for air is given by * 0.6847PA m o (2) 1/ 2 RT o In our experimental test rig, the stagnation temperature T 0 is equal to T 3 on the control panel, and throat area A * is equal to 4.03 10-5 m 2. Calculate m for this same set of flow conditions. Show all your work (include units) in the space provided below: m = kg/s. 5. For this same set of flow conditions, measure and record pressures P 2 through P 10. Tabulate your results neatly in a table. This data will be used in Part F. (4) 6. Repeat Steps 1 through 5 above for two other back pressures by closing Valve 3, and turning Valve 4 slowly clockwise. Using the schlieren image as a guide, include a case where the shockwave is just in the nozzle throat, as well as a case where the flow is fully subsonic everywhere (no shock, Valve 3 fully closed and Valve 4 nearly closed). For each case, measure P 0, P b, P flow meter inlet, T o, T flow meter inlet, and the volume flow rate using the flow meter and stopwatch as in Step 2 above. Also sketch the flow conditions in the converging-diverging nozzle for each case, pointing out the shock wave (if one exists). Calculate P b /P 0, m, m, and m/ m for each case as well. Put all your results into a neatly labeled table. See Table. (4) 7. Plot m/ m as a function of back pressure ratio P b /P 0. Compare your results with Figure 1c. Have you observed choking? Explain. 5
See Figure. E. Measurement of pressure distribution in the converging-diverging nozzle (4) 1. Using the data collected in Part C for pressures P 2 through P 10, tabulate your results neatly in a table which should also include nondimensional pressure ratios P/P 0 for pressure tap locations 2 through 9, where again, P 0 is taken as pressure P 2. See Table. (4) 2. Using the table created in Part C Step 5, plot P/P 0 as a function of streamwise coordinate x for all your cases in Step 1 above on the same plot. Include on your plot both the subsonic and supersonic theoretical calculations of P/P 0 from Table 1. If a shock wave is present, indicate its location on your plot. Note: The values of streamwise coordinate x can be obtained from Table 1. See Figure. 3. Shut off the flow in reverse order from the procedure to turn on the flow. Make sure the schlieren light bulb is turned off. Turn off the digital thermometer display unit. Make sure the Plexiglas safety cover has been reinstalled on the test section for protection. 6
Discussion (5) 1. Briefly summarize what you have learned about choking, and what it means. (5) 2. How well do your measurements of pressure agree with those of Figure 1 of the Introduction for the various back pressure ratios? Discuss possible reasons for any disagreement. (5) 3. When a shock wave is present in the diverging part of the nozzle, does the pressure jump up suddenly as indicated in Figure 1b of the Introduction? Why or why not? 7