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: 13 January 2012
Name 1:
___________________________________________________
Name 2:
___________________________________________________
Name 3:
___________________________________________________
[Name 4:
___________________________________________________ ]
Date:
_______________________________
Section number:
ME 325._____
Group letter: (A, B, ...) _____
Score (For instructor or TA use only):
Lab experiment and results, plots, tables, etc. - Procedure portion
Discussion
Neatness & grammar
TOTAL
Comments (For instructor or TA use only):
_____ / 45
_____ / 15
_____ / 10
______ / 70
Procedure and Presentations of Results
Safety Precautions:



A.
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.
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.
B.
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.
Visualization of shock waves using the schlieren optical technique
The following procedure should be used to start the flow facility. Use Figures 8 and 9 of the Introduction as a guide.
1.
Ask your instructor or TA to check that the compressor is running.
2.
Open back pressure Valve 3 (the large one) at least two turns, and open back pressure Valve 4 (the small one) at
least two turns.
3.
Open Valve 2 slowly until fully open. You should hear the rush of air through the system. Let the system run for
several seconds  the sound should reach a steady state level.
The facility is now operating, and the flow rate is controllable 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.
Remove the Plexiglas protective cover from the test section. Everyone in the lab group should wear safety
goggles.
5.
Slowly adjust back pressure valves 3 and 4 and observe the flow patterns in the camera viewfinder. Are you able
to observe a shock wave? At this point, ask your instructor or TA to point out a few details about the shock wave,
an example of which is shown in Figure 11.
(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.
(5)
6.
Briefly describe below what happens to the shock wave as you increase and decrease the back pressure. Do your
observations agree with the theoretical description of Figure 1 of the Introduction?
(5)
7.
On a separate page, sketch the observed flow pattern for two or three 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
C.
.
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. A similar meter with a cut-away casing
has been placed under the flow rig for your viewing pleasure. The accuracy of this type of flow meter is around a couple
percent, 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 m3. 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 T1 (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
maximum flow rate is achieved through the system.
Measure the pressure and temperature just upstream of the flow meter, as discussed above. Record (in the spaces
provided below) these readings:
(5)
2.
Pflow meter inlet
=
_______________________________ psia
Tflow meter inlet
= T1 =
_______________________________ C
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/m2 = 6894.8 Pascals.
m =______________________________________ kg/s
(2)
3.
For this same set of flow conditions (maximum flow rate), measure both P0 and Pb. On the control panel, these are
labeled P2 and P10 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:
P0 = P2 =
______________________________________
psia
Pb = p10 =
______________________________________
psia
Pb /P0
______________________________________
=
(2)
4.
The theoretical maximum flow rate for air is given by
0.6847 Po A*
mmax 
1/ 2
 RTo 
(2)
In our experimental test rig, the stagnation temperature T0 is equal to T3 on the control panel, and throat area A* is
equal to 4.03  10-5 m2. Calculate mmax for this same set of flow conditions. Show all your work (include units) in
the space provided below:
mmax = ______________________________________ kg/s.
(5)
5.
Repeat Steps 1 through 4 above for several back pressures by turning Valves 3 and 4 slowly clockwise. Using the
schlieren image as a guide, be sure to include cases ranging from fully supersonic throughout the entire diverging
part of the nozzle (valves fully open) to fully subsonic everywhere (Valve 3 fully closed and Valve 4 nearly
closed). Be sure to include several cases where a shock wave is present somewhere in the diverging part of the
nozzle, and at least one case of fully subsonic flow (no shock). Also make sure that you include at least one case
where the shock wave is just barely visible near the throat. For each case, measure P0, Pb, Pflow meter inlet, To, Tflow
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
Pb /P0, m , mmax , and m / mmax for each case as well. Put all your results into a neatly labeled table.
See Table
(5)
6.
.
Plot m / mmax as a function of back pressure ratio Pb /P0. Compare your results with Figure 1c. Have you observed
choking? Explain.
See Figure _________ .
D.
Examination of choking and acoustic noise
Two microphones are mounted in the test rig, one upstream and one downstream of the converging-diverging nozzle,
as sketched in Figure 8 of the Introduction. Most of the flow-induced noise is generated downstream of the nozzle, where the
flow is highly turbulent. When the flow is subsonic, sound can propagate upstream as well as downstream, and both
microphones will pick up lots of noise. As discussed previously, however, when the flow becomes choked, noise can no
longer propagate upstream past the throat. The upstream microphone should therefore suddenly be exposed to a much quieter
flow whenever the nozzle chokes. (Ask your instructor or TA for help).
(3)
1.
Turn on the power supply (gray box) for the amplifier (black box), and turn up the volume on the amplifier. A
toggle switch on the amplifier allows you to select either the upstream or downstream microphone. Vary the back
pressure so that the flow goes from unchoked (subsonic everywhere) to choked. With the toggle switch pointed
upstream (i.e. with the upstream microphone connected), describe your observations below. You may keep the
schlieren system on to aid in your observations if you so desire. Does choking affect the sound recorded by the
upstream microphone? Explain.
(3)
2.
Repeat the above with the downstream microphone. Does choking affect the sound recorded by the downstream
microphone? At this point, ask the instructor or TA for assistance in the interpretation of your observations.
E.
Measurement of pressure distribution in the converging-diverging nozzle
(5)
1.
For several back pressure conditions (going the full range again from fully subsonic to fully supersonic), record
pressures P2 through P10. Tabulate your results neatly in a table which should also include nondimensional
pressure ratios P/P0 for pressure tap locations 2 through 9, where again, P0 is taken as pressure P2.
See Table
(5)
2.
Plot P/P0 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/P0 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.
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?