This lab covers the use of taps, probes and transducers for measurement of static and stagnation pressures in nominally steady, compressible (subsonic and supersonic) flows. In addition, it includes the use of the schlieren technique to visualize shock and expansion waves in supersonic flows. The various measurements are acquired in a supersonic, blowdown wind tunnel and a supersonic (converging/diverging) nozzle. The experiments also allows the student to experimentally investigate many interesting and important aspects of the behavior of supersonic flows.
Steady pressures are most conveniently and accurately measured using static taps or probes, and stagnation pressure probes. This is the approach used in this laboratory. Static taps and probes, as well as total or stagnation pressure probes (see Figure 1), have been introduced in earlier labs. Typically taps and probes are located quite a distance from the actual pressure transducer, thus they have a relatively slow response. Rapidly fluctuating pressures must be determined using other devices, such as microphones or piezoelectric transducers as covered in previous labs.
Figure 1. Schematic of a) static and b) Pitot pressure probes.
Transducers that can be used to measure pressure include gravitational transducers, such as mercury or oil manometers. Manometers can be of various shapes, including standard U-shaped tubes and straight long vertical tubes attached to a liquid filled reservoir. Manometers measure relative pressures, specifically the pressure difference between the two ends of the tube. For measurement of stagnation pressures in compressible flows, which can easily exceed 1 atm, long tubes are required (even for a dense liquid such as mercury, measurement of Δp=1 atm requires at least a 30 inch long tube).
Figure 2. Schematic of vertical type manometers: a) p < pat , b) p > pat, and c) a manometer bank (with pat=ambient pressure).
For vertical tubes connected to a reservoir, pressures below atmospheric are measured by connecting the tubing from the probe to the upper, open end of the manometer tube while the reservoir is open to the atmosphere (Figure 2a). Thus, the lower the value of the static pressure, the higher the mercury column in the manometer. On the other hand, if the pressure to be measured exceeds atmospheric (e.g., the total pressure in a blowdown type supersonic tunnel), the tubing from the probe is attached to the reservoir and the upper end of the manometer is left open (Figure 2b). If one is dealing with a manometer bank containing a number of tubes, the level in the reservoir drops as the mercury rises in the tubes. This must be compensated for by measuring the drop in level in a reference tube which is open to atmosphere (Figure 2c).
Another family of pressure measurement devices can be categorized as elastic transducers. In these devices, a deflection or deformation accompanying a balance of pressure and elastic forces is used to measure pressure. A classic example of an elastic pressure transducer is the Bourdon tubes (Figure 3) commonly found in pointer type pressure gages. In these devices an oval section tube is initially coiled into a circular arc. As a pressure is applied to the tube, the oval section tends to become more circular in cross-section. Since the inner and outer lengths of the tubes remain approximately the same as their initial values, the primary result of the applied pressure is an uncoiling of the arc. The uncoiling is coupled to the motion of a pointer, which is used to determine the pressure.
Figure 3. Basic Bourdon-type pressure transducer.
Another type of elastic transducer is the diaphragm type, where the pressure force causes a diaphragm to deflect. Examples of this type include Barocell/Barotron type transducers, in which the pressure deflects a thin diaphragm that forms one plate of a capacitor. Different pressures yield different capacitances that are converted to electrical voltages (and read using a voltmeter in this lab). Barocells and Barotrons typically provide very sensitive measurements of pressure, e.g., Torr/volt, with the calibration (sensitivity) usually supplied by the manufacturer. Other methods can be used to measure the change in the diaphragm, for example resistance strain gages can be applied to the diaphragm surface, and the measured strain can be related to the applied pressure through calibration. Relatively inexpensive transducers can be made by using semiconductor materials. In this case, the semiconductor resistors are “written” as a bridge circuit directly onto a substrate (e.g., silicon) that acts as the diaphragm. The strain on the semiconductor results in a change in semiconductor resistance; this is known as the piezoresistive effect. The change in semiconductor resistance is analogous to the change in metal resistors (recall the strain gauges used in the force balance experiments), except in the latter, the change in resistance is primarily due to the change in the metal resistor’s cross-sectional area as it is strained. For semiconductor materials, the resistance change is related to other changes in the internal structure of the semiconductor. This type of silicon diaphragm transducer will be used to make differential pressure measurements in the converging-diverging nozzle experiment.
Sudden changes in the density of a gas and the resulting gradient in refractive index can be visualized using the schlieren technique. Such steep refractive index gradients exist, for example, in flames or in shock waves. In this laboratory, shock waves, whose properties will be discussed in the next section, are visualized using schlieren imaging. In this technique (see Figure 4), the light from a source is allowed to expand and is then collimated using a large diameter, long focal length (typically biconvex) lens.
Figure 4. Schematic of a typical schlieren setup.
The resulting parallel beam is then passed through the test section of the wind tunnel before being refocused using a second biconvex lens of similar optical properties to those of the first. A stop placed at the focal point of the second lens blocks all of the undeflected light. However, any light rays that have been refracted in the test section by a refractive index gradient caused by, for example, a shock wave are no longer parallel to the optical axis of the system. These rays will, therefore, be focused at a different location in the focal plane of the second lens and will, thus, bypass the schlieren stop. A focusing lens is then used to create an image of the test region on a screen or photographic plate using only the refracted light. This image displays only those regions of the flow in which a steep refractive index gradient exists, i.e., the shock wave.
A brief description of compressible flows (summarizing important details covered in AE 2010) is given below. It is important to note that inviscid flow will be assumed throughout this discussion. When a gas, such as room temperature air, flows at velocities greater than approximately 100 m/s (or for Mach number M > 0.3), the density changes of the gas due to changing Mach number become significant, i.e., the flow becomes compressible. This results in some remarkable phenomena, especially at supersonic speeds. For example for subsonic flow in a nozzle, M increases as the cross-sectional area of the nozzle decreases; for supersonic flow this trend reverses. Furthermore, it turns out that an adiabatic flow can only increase from subsonic to supersonic speeds if the transition from M<1 to M>1, (i.e., M=1) occurs at the throat (minimum area) of a nozzle.
(1)
Let us now consider the flow in a converging-diverging nozzle (see Figure 5) connected to a high pressure supply at one end and open to the atmosphere at the other. As the pressure in the supply (reservoir pressure) is increased, air begins to flow through the nozzle. As long as the flow in the nozzle is everywhere subsonic, the Mach number increases in the converging part (region A) and decreases in the diverging part (region B) of the nozzle. The static pressure level in the nozzle behaves inversely as the magnitude of the Mach number. Thus for subsonic flow in the nozzle, the static pressure drops in the converging section and rises in the diverging section. At the exit of the nozzle, the flow should reach equilibrium with the back pressure (given by the local atmospheric pressure in this example). As the reservoir pressure is increased further, the mass flow rate through the nozzle increases, causing a change in Mach number and, thus, in static pressure. The Mach number in the converging part of the nozzle can keep increasing in this manner until the Mach number at the nozzle throat reaches unity. The nozzle is then called “choked”. The Mach number in region A can no longer be affected by increasing the reservoir pressure (or decreasing the back pressure), and the mass flow rate, for fixed upstream stagnation conditions, is a maximum once the flow is choked.
(2)
(3)
where we have assumed a stationary shock for the stagnation pressure ratio.
Figure 6. Schematic of shock on: a) probe and b) wedge in supersonic flow (θ = shock half angle, δ = wedge half angle).
If a supersonic flow encounters a solid body, part of the flow must be decelerated to stagnation conditions. Since this necessarily involves a transition from supersonic to subsonic flow, a shock stands ahead of the body. This shock provides the mechanism for the transition. In the case of a thin probe in supersonic flow a small, normal shock stands ahead of the probe tip (Figure 6a). A conically shaped bow shock trails from the normal shock. The bow shock weakens as one moves away from its leading edge and, eventually, turns into a Mach wave across which the flow properties no longer change significantly. Therefore, the stagnation pressure measured using a Pitot probe in supersonic flow is that behind a normal shock. In a static probe, on the other hand, the orifice is located far downstream of the probe tip. The effect of the normal shock is then no longer felt and the static pressure measured is essentially equal to that ahead of the shock. If the probe is replaced by a wedge (Figure 6b) a pair of oblique shocks is formed that attach to the tip of the wedge. The relationship between the flow Mach number and the half angles of the shock and of the wedge are plotted in Figure 7.*
*Similar plots can be found in most texts on compressible flow.
Figure 7. Variation of shock-wave angle with flow-deflection angle for various upstream Mach numbers for a thermal and calorically perfect gas with γ = 1.4.
This set of experiments is to be carried out in a converging-diverging (CD) nozzle made of Plexiglas (see Figure 5). The upstream side of the nozzle is attached to a high pressure supply (regulated so as not to exceed ~50 psig); the downstream side is connected to a settling chamber and an acoustic muffler before exiting into the room. Between the nozzle and the high pressure supply is a manual valve. The stagnation pressure entering the nozzle is controlled by the setting of this valve (and the pressure downstream of the valve can be monitored using a simple Bourdon tube type gauge). The nozzle is instrumented with two Pitot probes along the axis and eight static pressure taps along the wall. The first Pitot probe is located at the nozzle throat. The second probe is located near the last static pressure port in the nozzle (station 7).
As shown in Figure 5, one static pressure tap is located ahead of the nozzle throat, the second at the throat and five tops are located at one half inch intervals along the expanding part of the nozzle. Tap number eight measures the back pressure. The ten pressures will be measured by ten piezoresistive, silicon diaphragm transducers and recorded by a computer data acquisition system. Since some of the pressure gauges can be damaged by operation outside their pressure range, please carefully listed to any guidelines given by the TA’s with respect to the maximum pressure you should allow the CD inlet to reach.
In this facility, air from a large tank at approximately 120 psi is passed through a pressure regulator and a large, manual (butterfly) valve and into a supersonic tunnel of rectangular cross-section. The tunnel (Figure 8) consists, essentially, of a nozzle (2" × 1.778" at its throat) and a test section (2" × 3").
Figure 8. Schematic of supersonic blowdown tunnel.
The test section walls are fitted with two parallel windows in order to provide optical access. The tunnel is instrumented with a Pitot probe upstream of the nozzle and a removable Pitot-static probe that mounts in the test section. The orifice of the static pressure probe is aligned with the tip of the Pitot probe in the test section. The Pitot probe upstream of the nozzle is connected to a pressure gauge (which records gage pressure). The downstream Pitot probe can be connected to the Baratron for comparison to the ambient pressure. Similarly, the static pressure probe can be connected to the Baratron while the other side is open to atmosphere. Atmospheric pressure is measured using an electronic barometer. The probes in the test section may be removed and replaced by a wedge or by a solid body of some other configuration.
Figure 9. Schematic of schlieren setup attached to “2-d” blowdown windtunnel. The graduated color filter has a dark red pattern in the center that acts as the schlieren stop.
A schlieren system (Figure 9) is configured around the test section of the tunnel. A single lens is used to perform both the focusing of the collimated light and to image the test section on the screen. Also, a bicolor filter with an opaque band in the middle is used to produce the schlieren stop. Rays that pass above and below the focal point of the second lens pass through different colored filters. Thus rays that were deflected upwards will show up in one color in the image, while rays that were deflected downward will be a different color. Although the tunnel is fed from a large tank, running times are limited. It is, therefore, important to coordinate the measurements to be made before starting the tunnel. It is a good idea to watch the upstream stagnation pressure to make sure that it is not dropping with time (which would happen if you were overdraining the supply tanks). Since the Mach number in the tunnel depends only upon the area ratio of nozzle to test section (as long as the upstream pressure is sufficient to choke the nozzle), the test section Mach number is not affected by any pressure drop, but your pressure measurements will change.
The compressed air supply for this experiment is not infinite and the flow rate through the tunnels is substantial. As such, keep your runs to a minimum else you run the risk of running the tank down faster than the compressor can keep up with. If this occurs, you will need to wait for the compressor to charge the tank before being able to complete your experiments. To gauge the capacity of the tank open the valve to the blowdown tunnel and check the first pressure gauge in the line; it will read ~120 psi when full, and the compressor will kick in at ~85 psi. Pressures much below this may result in inability to complete the experiment.
The pneumatic fittings used in this experiment are all "push-to-connect" style. To make a connection firmly insert the tube until you feel the inner sleeve give and make the connection. To disconnect, do not pull on the tube without first pushing down the black plastic ring around the tube.
Take a tour of the equipment with the TAs. In particular you will look discuss:
The large grey tank outside the door, which feeds our experiments. This tank is charged by a compressor (that you won't see), automatically kicking in when the pressure drops to ~80 PSI.
The pneumatic system feeding both of our experiments from the wall (and ultimately the tank).
The CD Nozzle experiment, making sure to look at the nozzle directly and comparing it to the diagram.
The Blowdown experiment and its removable inserts.
PPE and other safety items.
The LabView VI.
Preparing the compressed air system
Close the small black-handled calibration valve labeled "AIR CAL" and the large red-handled valve labeled "AIR EXP CD".
Open the three shut-off valves on the wall, labeled "AIR SOV 1", "AIR SOV 2", and "AIR SOV 3". This opens the main compressed air feed from the large grey tank outside the door next to our experiment, and energizes both the CD nozzle experiment and blowdown tunnel for later.
Verify, using the pressure gauge labeled "PRESS CD", that the CD nozzle experiment is energized (around 80psi).
Check, using the pressure gauge on the blowdown tunnel labeled "PRESSURE BDN IN", what the main compressed air storage tank pressure is.
If the tank is fully charged it should read around 120psi
As the experiments are run this reading will gradually drop
The tank compressor will not kick in until this reads around 80psi, at which point it will take 15-20 minutes to charge the tank back up to 120psi
Keep an eye on the compressed air supply pressure (PRESS BDN IN) throughout the course of this lab... if you start losing velocity in the tunnels it's likely because the tank pressure is getting too low and you will need to wait for it to charge. Keep your runs as short as possible... wasted time is wasted air and then waiting time!
Preparing the instrumentation
Turn on the big screen and set the it so that: Scale = 200%, Display Resolution = 3840 x 2160, Multiple Displays = Extend These Displays.
Navigate to D:\AE3610 Fall 2021\Supersonic Flow and open the Supersonic VI in LabView. Drag it over to the big screen.
Power on the transducer box and check that the VI registers a voltage change
Calibrating the transducers
Connect all the tubes coming from the transducers to the calibration box. Check the calibration box labels for what goes where. Do not remove the black compression fittings from the calibration box tubes, or remove the tubes from the transducers.
!!! Put on your eye protection !!! (ear protection not required yet)
Follow the instructions in the VI for performing the calibration
Take a screenshot/picture of the final NULL and SCALE values for all 10 transducers, or manually record them, for later
Gather some "calibration check" data to verify your VI calibration values against the manometer as follows: By clicking "TAKE DATA" on the VI, record data using the VI at 3 different manometer pressures that you should also make a manual note of. As you go through this process, sanity check that the VI and manometer match. By slowly varying the black-handled calibration valve, the pressures you should evaluate are:
Whatever pressure you calibrated at (it should still be there)
Something roughly half of the previous pressure (it's not critical what this pressure is so don't waste time dialing it in)
0 psi (AIR CAL valve fully closed)
Open the save file to ensure your data has saved correctly. Do this in Notepad++ (to ensure there is no write conflict with the VI)
Make a manual note of the atmospheric pressure using the weather station on the desk.
Performing the experiment
Make sure AIR CAL is fully closed.
Connect the transducers to the correct pressure taps in the experiment (P1 to P7 followed by Pb go in order from left to right when viewed from the side of the test section nearest the gas turbine). Take care to not overly stress the tubes coming out of the CD nozzle.
!!! Put on your ear and eye protection !!! You are about to run the experiment, during which substantial air will flow, so be sure to read the following instructions carefully and discuss your plan of action before proceeding from here. You are welcome to, and indeed should, stop the tunnel at any time by closing the AIR EXP CD, if you wish to discuss something you've observed with your group, or want to plan on re-taking data. Remember: wasted time with the air running is wasted air!
Get a feel, without logging any data, for how sensitive the valve is and how pressures in the nozzle will change throughout the whole range of operation.
Do this by slowly opening AIR EXP CD and observing the VI pressures in real-time.
During this step discuss what the flow speed regime is, where the shock wave is, where the flow is choked, etc.
Identify what positions you are required to take data in the VI data
See if you can see the shock wave by eye (not always possible)
Now we will take data at the required points. Slowly open the AIR EXP CD valve to allow subsonic flow through the CD nozzle. Use the VI to record pressures in the nozzle at a high enough speed to see the subsonic pressure profile clearly, but without going supersonic
Open the valve further until the flow is just choked, i.e., throat has just reached Mach 1. You may also hear a distinct change in the noise from the nozzle. Use the VI to record the pressures.
Continue opening the valve until a shock is observed between stations 4 and 5. You will be able to detect the shock location by a change in sign in the pressure gradient in region B of the nozzle (refer to the figure in the VI for the regions). Once again, record all pressures with the VI.
Continue opening the valve until the shock passes station 6. The flow in most of the expanding part of the nozzle should now be supersonic. Once again, record all pressures using the VI. Note that, just before and during this phase, you will see P1 and P2 peak at ~20 psi and no longer rise. These transducers have a maximum safe pressure rating of 50 psi, but can only read valid pressures up to 20 psi, so they will seemingly stop reading at this point... a phenomenon called "saturation". Whilst saturated we will not know what the real pressure is so be sure to not exceed the valve position that creates a shock just past station 6.
Repeat steps 5.5 - 5.8. This will provide data to assess repeatability.
Close AIR EXP CD.
Check your data
Click Done on the VI to save all data.
Open the file you selected as your save file in MS Excel. If you didn't give it a file extension when you selected the save file you will need to add it now by right-clicking on the file, clicking Rename, and then adding ".xls" to the end of the filename.
Delete any rows you accidentally captured data at, or decided to over-write.
With the help of the TAs, visually observe that all data was saved properly and is of the rough order of magnitude of what it is supposed to be.
If you are missing any data or it is not correct, go back and collect it now.
Repeat Step 6.1-6.5 until you are satisfied the data is acceptable.
Shutting down the experiment
Purge the compressed air (we don't want high pressure sat in a flexible hose in case it comes loose and disconnects, potentially causing harm to someone)
Close AIR SOV 1
Open AIR EXP CD slowly, until there is steady flow to purge the line
Once the air stops flowing and CD PRESSURE reads 0, close AIR SOV 2 and AIR EXP CD
Power down the transducer box
Make a plot of the 3 pressure readings from the manometer ("true") versus the VI readings obtained using the calibration NULL and SCALE readings ("measured"). Discuss the accuracy the calibration and how it could be improved.
Convert all of the transducer readings to absolute pressure. These will be required for later calculations and plots.
Calculate the Mach numbers at stations 1 and 2 from the static and stagnation pressures determined at these locations for the following three conditions:
subsonic flow throughout the nozzle
the “just choked” condition
the condition where the shock stands between stations 4 and 5.
Calculate the Mach number at station 6 for supersonic flow in two ways:
using the static pressure at station 6 and a suitable stagnation pressure; and
using the stagnation pressures as measured by the Pitot probes located at the throat (station 2) and at station 7.
Note - be sure to use the correct value of the stagnation pressure in these calculations. It will be helpful to sketch for yourself a diagram of the nozzle indicating the position of the pressure taps and probes and the location of the shock wave.
Make a table of the sensitivity (scale) and zero offset values for each pressure transducer.
Make a table listing:
atmospheric pressure
the stagnation pressure measured using the two Pitot probes for the cases of:
subsonic flow
a shock between stations 4 and 5
supersonic flow through at least station 6.
Make a table listing the Mach numbers at stations 1 and 2 for the three conditions specified under Data Reduction step 3
Make a table listing the Mach number at station 6 as calculated by the two methods given under Data Reduction 4
Make a graph with axial distance as the abscissa and the ratio of local static pressure to supply stagnation pressure as the ordinate. On this single graph, plot the results for the static pressure measurements for the conditions of:
subsonic flow
a shock between stations 4 and 5
supersonic flow through at least station 6
Using different symbols, plot the repeated data on this graph as well. This will show the quality of the repeatability.
Make a plot like that described in step 5 above, except plot Mach number as the ordinate.
The compressed air supply for this experiment is not infinite and the flow rate through the tunnels is substantial. As such, keep your runs to a minimum else you run the risk of running the tank down faster than the compressor can keep up with. If this occurs, you will need to wait for the compressor to charge the tank before being able to complete your experiments. To gauge the capacity of the tank open the valve to the blowdown tunnel and check the first pressure gauge in the line; it will read ~120 psi when full, and the compressor will kick in at ~85 psi. Pressures much below this may result in inability to complete the experiment.
The pneumatic fittings used in this experiment are all "push-to-connect" style. To make a connection firmly insert the tube until you feel the inner sleeve give and make the connection. To disconnect, do not pull on the tube without first pushing down the black plastic ring around the tube.
Preparing the compressed air system
Ensure the main blowdown tunnel control valve, AIR EXP BDN, is fully closed
Ensure AIR SOV 3 is still open from when you opened it earlier
Repeat CD Nozzle Procedure Step 2.4 to verify air tank status
Ensure AIR REG 1 and AIR REG 2 are OPEN. And that AIR REG 3 is CLOSED.
Pitot tube experiments
Install the pitot tube plate into the test section
Connect the high pressure port of the manometer to the pitot tube stagnation port (the manometer low pressure port should be open to the atmosphere). Turn on manometer, zero, and change units to psi.
!!! Read the following instructions fully before commencing - wasted time is wasted air !!!
Ensure you are wearing your eye and ear PPE. Gradually open the main blowdown tunnel control valve until the upstream pressure, PRESS BDN US, reads around 14 psi. Make a note of the exact pressure obtained.
Record the pitot stagnation pressure on the manometer.
Working quickly, but not rushing, switch the manometer tube to the static pressure port and record the pressure once it's settled
Fully close AIR EXP BDN
Make a note of the atmospheric pressure using the weather station on the desk
Wedge experiments
Remove the pitot tube plate and replace it with the wedge plate
Connect the P1 port of the manometer to the TOP static port (the manometer P2 port should be open to the atmosphere).
Enable cooling air to the light source by opening the small black-handled valve
Have a TA turn on the Schlieren light system and wait for the lamp to warm up (avoid switching the light source on and off unnecessarily since this will shorten its life and may extend your time in the lab if it doesn't re-illuminate quickly)
Using your camera phone take a picture of the wedge's shadow on the screen. Be sure to get orthogonal to the screen and fill the frame as much as possible. Take multiple shots then select the best.
!!! Read the following instructions fully before commencing - wasted time is wasted air !!!
Position yourself around the screen to observe the wedge's shadow
Ensure you are wearing your eye and ear PPE
Have a TA slowly open the main control valve whilst you watch the screen; at some point you will see a new shadow appear around the wedge; the flow is now supersonic and this new shadow is the Mach cone. Tell the TA to stop opening the valve.
Record the following things:
Upstream pressure from the PRESS BDN US gauge near the TA
Static pressure on the manometer
A new picture of the Schlieren screen with the Mach cone visible. Be sure to get orthogonal to the screen and fill the frame as much as possible. Take multiple shots then select the best.
Close AIR EXP BDN.
Shutting down the experiment
Have the TA turn off the Schlieren lamp and wait for it to fully stop shining, at which point turn off the cooling air.
Close AIR SOV 3 valve.
Open AIR EXP BDN on the blowdown tunnel and wait for the air to fully purge through the wind tunnel (we don't want to leave any portion of the experiment charged with high pressure air!)
Close AIR EXP BDN and the Schlieren lamp cooling valve
Disconnect the manometer and pack it up in its case
Checking data before you leave
Have the TA sanity check your blowdown values before you leave
If you have time, draw your blowdown tubing schematic now as a group so the TAs can sign off on it. If you don't have time, take pictures and ask the TAs questions as required
Calculate the test section Mach number from the ratio of static to stagnation pressure in the test section. Be very careful to use the correct, measured stagnation pressure. A rough sketch of the position of the probes and the location of the shock may help you.
Calculate the test section Mach number using the measured stagnation pressures and the shock equations (listed in the Background section) or appropriate shock tables (preferred method).
Determine the Mach number in the test section using the values of the half angles of the wedge and the shock that you measured. Use Figure 7 or similar graphs from your compressible flow texts.
Make a schematic of the various configurations of tubing used in the pressure measurements.
Make a table listing the test section Mach number as calculated by using:
the ratio of static to stagnation pressure in the test section
the measured stagnation pressures in the test sections
the shock angle on the wedge
Bernoulli's equation, which was derived assuming constant density is no longer valid for compressible flow. Instead, the relationship between the static and stagnation pressures, e.g., , as a function of Mach number may be obtained for a calorically perfect gas (constant specific heats) from the following (more general) expression.
where is the specific heat ratio. As long as the flow remains isentropic, the stagnation pressure is constant everywhere. The static pressure, on the other hand, decreases as the Mach number increases since more potential energy, which gives rise to the static pressure, is now converted to kinetic energy. This is true for subsonic as well as supersonic flow.
Figure 5. Schematic of the converging-diverging nozzle showing location of pressure probes and taps (throat at ).
Increasing the reservoir to back pressure ratio above the value that corresponds to choking does, however, affect the flow conditions in region B. Beyond the choking condition, the flow downstream of the throat begins to go supersonic and increases in Mach number as the nozzle flow expands. However, is not yet high enough to result in completely supersonic (isentropic) flow throughout the entire region B. The flow adjusts to these conditions by suddenly reverting back to subsonic flow in a normal shock somewhere in the expanding part of the nozzle. Across this shock wave the static pressure rises. Behind the shock the flow is subsonic, and, therefore, decreases in Mach number as the nozzle continues to increase in area. The static pressure rises correspondingly until the back pressure is reached at the exit of the nozzle. As is raised still further, the position of the shock wave moves towards the nozzle exit, until eventually there is no shock in the nozzle.
The presence of the shock wave changes all flow conditions across it except the stagnation temperature (or, more precisely, the stagnation enthalpy) since across the shock the flow is adiabatic. The extent of the influence of the shock upon the flow conditions depends upon the Mach number of the flow going into the shock. For thermally and calorically perfect gases, the ratio of the static pressures across the shockas a function of Mach number ahead of the shockare given by
and the stagnation pressure ratio is
Figure 5. Schematic of the converging-diverging nozzle showing location of pressure probes and taps (throat at).
Run the VI by pressing the button, creating a folder for your group and setting that as your save folder, before verifying successful hardware connection (no flags thrown on run)
