02/04/2009

Advisor: Prof Knight| Group K1 Luigi Balarinni Tim Matlack

George Currier Simon Tang

Mikki Friedman

MAE ‘09 SUPERSONIC WIND TUNNEL

FINAL REPORT

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Supersonic Wind Tunnel Design Concept

Team Leader: Luigi BalarinniTeam Members:George Currier

Simon TangTim Matlack

Mikki Friedman

Project Advisor:Prof. Doyle Knight

Date: 01/29/09Team K1: 5 Members

The goal of this project is to create a portable version of a supersonic wind tunnel that can be utilized for classroom demonstrations. The wind tunnel will operate at Mach 3 using an air compressor to propel the flow through a converging-diverging nozzle. Harry Graham was awarded US Patent number 2805571 in 1957 for his design of a supersonic wind tunnel. Although many similar wind tunnels have since been created to test models, few have the benefit of being portable enough for classroom use. The project was initially broken up into five fields: Theory\ (Luigi), Compressor & Imag-ing (Simon), Nozzle Design (George), Electronics & Instrumentation (Mikki), and Prototyping & Fabrication (Tim). The diverging nozzle section will be created using the FORTRAN based Sivells code. This program will accurately determine the nozzle contour necessary to produce a Mach 3 flow. Boundary layer thickness along the walls of the wind tunnel will be calculated using the EddyBL code. The compressor selection was governed by compressible flow theory. This theory uti-lized the continuity equation , which related the mass flow out of the compressor to the mass flow through the throat. The wind tunnel will use a 20 gallon compressor at 150 psi. The air will enter a stagnation chamber which contains filters to reduce turbulence in the flow. An electronically controlled solenoid valve will control the flow into the stagnation chamber. Pressure in the stag-nation chamber will be verified by a pressure gauge. The air will flow through a throat of 1 cm by 1 cm before entering the test section of 1 cm by 4.2 cm. The test section will have clear Plexiglas side walls to allow for observation. There will be an airfoil fixed within the test section. Light will be projected through a lens and then the test section onto a white background in order to use the Shadowgraph method of flow visualization. A computer system with a webcam will be capable of capturing and displaying videos of the Shadowgraph flow visualization. All of the wind tunnel components will sit on a wheeled cart. The anticipated test time will be approximately 3 seconds. As the spring semester begins, the group will order necessary parts from the specified vendors. The budget will contain at least a 10% buffer to allow for damaged or broken parts and to allow for late repairs. The project is to be built for testing in March. The design has been final-ized, but it can be easily adjusted to achieve higher test time or higher test section area.

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1. Introduction

This senior design project is to create and design a tabletop version of a supersonic wind tunnel. Wind tunnels are often utilized to study the effects of air flowing around an object such as an airplane or a car. In supersonic wind tunnels, the air flows at speeds of Mach 1.2 to Mach 5. In order to achieve such speeds, the air must flow through a converging nozzle to reach sonic (Mach 1) speed. A diverging nozzle following the converging nozzle allows the air to reach supersonic speeds. While such supersonic wind tunnels are generally the size of entire classrooms, this model is intended to be presented within a classroom. Additionally, these wind tunnels are so large that they require huge amounts of compressed air, power, and money to operate. This model will be capable of demonstrating similar effects at a fraction of these resources. The wind tunnel will have a system to visualize the air flow around an airfoil and display it to a class.

2. Problem Statement

The tabletop wind tunnel will be designed to run for at least 1½ to 3 seconds for demon-stration. It will be fabricated out of lightweight materials, where possible, to allow for maximum portability. The wind tunnel will sit on a wheeled cart to aide in transportation. The wind tunnel will have a double throat design to lower the required initial stagnation pressure. The first throat will accelerate the flow to sonic speed while the second will prevent the shockwaves from interfer-ing with the test section flow. The first nozzle will be made of ABS plastic due to the capability of the FDM machine to make the difficult and accurate nozzle design for the critical section of the wind tunnel. The second ‘nozzle’ is not a critical design, but needs to be adjustable to be able to eliminate oblique shocks. This will be done by placing a movable flap at the end of the test section that will allow for angle changes to the second nozzle for an effective design. The flap angle will be controlled by a screw from the bottom of the tunnel to the back of the flap. There will also be a clear viewing section so that a user can employ some flow visualization system. The flow entering the first throat must be laminar so an impact plate and a honeycomb filter will be situated in the stagnation chamber. This system will use a pressurized air tank to generate the necessary air flow. The tank will be filled in a reasonable amount of time (5-10 min-utes) by an attached air compressor. The flow will be controlled by a solenoid valve between the stagnation chamber and the air tank. A pressure gauge will be used to verify the pressure in the stagnation chamber. A shadowgraph visualization system will use a light and a lens to project a representation of the flow onto a white background. The image will be capture by a webcam and displayed to the class on a laptop. All electrical components will run on US standard 110-120V outlets. The project was initially to be completely controlled through Labview, but was scaled down to a manual system for budgetary reasons.

3. Project Management

The project was initially divided into Theory, Compressor & Imaging, Nozzle Design, Elec-tronics & Instrumentation, and Prototyping & Fabrication. The end of the Fall semester marked the completion of the Design Generation phase of the project. Preliminary assembly should be

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completed in March. This would allow for adequate testing and revisions to the design. Most of the initial workload is dependent on either the theory or the nozzle design. These two areas are independent of each other, but determine the constraints for other aspects of the de-sign. The theory will determine the mass flow of air necessary for reasonable test times. This will govern which compressors are appropriate for this project. The nozzle design will be based on the Sivells and EddyBL code. This will influence the overall prototype dimensions and contour. Once both sections have been completed, the focus will shift to the prototyping and fabrication aspect of the project. Electronics and instrumentation selections operate independently of the other project areas. It will, how-ever, interface directly with the imaging design process.

4. Design Concept

Search Externally

General Wind Tunnel Design Some general concepts for the design of the wind tunnel were gathered from Harry Gra-ham’s 1957 patent for a supersonic wind tunnel1. Zola Coleman holds an earlier patent for a general wind tunnel2 and Frenzl Otto recieved a later patent for a high speed wind tunnel3. A paper on a miniature wind tunnel was submitted to the 1979 AIAA annual meeting and documented many of the same decisions faced in this project4.

Theory Luigi Balarinni was responsible for the flow theory of the wind tunnel. He received as-sistance from Professor Tobias Rossman and Professor Doyle Knight in order to correctly generate theoretical requirements of this model. Additionally, Modern Compressible Flow5 was an invalu-able tool for referencing governing equations and better understanding the theory.

Air Compressor Simon Tang was charged with the task of gathering information on various compressors. Simon gathered market information, compiled compressor specifications6, and negotiated reduced prices for some compressors. His work allowed the group to determine that the compressor will be one of the critical purchases for this project. The necessary compressors cost in the range of $200 to $400 which consumes a large portion of the budget. It was also helpful to understand the theory behind air compressors. The website www.about-air-compressors.com was an extremely useful resource. The website contained a ques-tion and answer section and an interactive forum. The information allowed Simon to understand everything he needed in order to select the compressor. In addition, Simon contacted Richard Woodward of Woodward Compressor Sales. Mr. Woodward provided invaluable advice about compressor selection for the project.

Visualization Simon was also responsible for the visualization system on the wind tunnel. This included researching the shadowgraph and Schlieren systems to determine which was more suitable for this project. Professor Rossman was once again very helpful in understanding the visualization meth-

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ods and even allowed Simon to view the Schlieren system on the Rutgers supersonic wind tunnel. Ye Cheng, a graduate student at Rutgers University also assisted the team by providing a Schlieren lab procedurexx. A PowerPoint presentation on both visualization systems was obtained from Iowa State Universityxx. Once the shadowgraph method was selected, Tim Matlack’s father was able to use his experience in the camera field to assist the team in lens selection. He was also able to notify the team of any inexpensive or complementary lenses. As a backup, a number of websites with lens information were located9. A patent for a laser shadowgraph was awarded to Mike Gardner and David Kuntz and was helpful in designing our own system10. For comparison, the two versions of the Schlieren were also researched through their patents11.

Electronics & Instrumentation Mikki Friedman researched the electronics and instrumentation components for the wind tunnel. John Petrowski of Rutgers University was contacted to advise the team on which electronic components would be necessary for the project. Through Mr. Petrowski, two team members met with Richard Patterson of National Instruments. Mr. Patterson was able to provide information on which models of data acquisition boards would be needed to interface with LabView. Mr. Petrows-ki also advised the team on which electronic components would be required to take temperature and pressure readings as well as actuate the solenoid. The National Instruments online forums were an excellent resource in ascertaining exactly what could and could not be done with the basic license of Labview. Although the design has since eliminated the use of Labview, the information provided by Mr. Petrowski helped Mikki create updated wiring diagrams and select the proper elements. All components were researched through a number of online vendors12.

Fabrication & Prototyping Timothy Matlack researched the fabrication techniques that will be used in this project. Mr. Petrowski made himself available to train Tim in using the Fused Deposition Modeling sys-tem. He also researched different materials for use in the wind tunnel to verify the best combina-tion of strength, weight, and cost. The overall concept of how the different components of the wind tunnel would join each other was also Tim’s responsibility.

Nozzle Design George Currier read the Linux for Dummies guide to familiarize himself with the linux system. He also contacted Rutgers graduate students Kellie Norton and Hadassah Nyman for as-sistance in customizing and running the FORTRAN based code on a linux system. George also read the associated documentation on the Sivells and EddyBL code.

Concept Generation

As stated earlier, many of the design areas operated independently of each other. This makes a concept generation of individual sections more appropriate. The theory is directly related to the selection of the pressure tank and compressor. It deter-mines the size of a tank and at what pressure the air must be stored in order to obtain the required

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test time. The tank and compressor can either be separate entities or a combined unit. For smaller application, such as this project, a combined tank and compressor is more suitable. This method is known as the blow down method. In compressible fluid flow theory, the desired flow rate can be related to a ratio of stagnation pressure to exit pressure. In our case, the desired flow rate is a Mach 3 flow and our exit pressure is intended to be atmospheric. Once the air is released from the tank, the pressure will begin to drop until it can no longer sustain the Mach 3 flow. Figure XX illustrates the comparison of the different compressors on the basis of test time versus the throat area.

[Edited Graph Here]

This graph was obtained by utilizing the conservation of mass equation for a control vol-ume13. The mass of air out of the tank must be equal to the mass of air flowing through the throat. From these equations it was clear that the test time was a function of the speed of sound, Mach number, test section area, and tank volume. The last two factors relate to our design choices. This set of equations also predicts a temperature drop in the air through the tunnel since the system is not isothermal. For wind tunnels operating at a higher Mach number, this often results in frozen particles forming in the flow. There is an option of heating the air before it enters the wind tunnel, but this proved to costly and impractical. The direct connection method assumes that a compressor can be selected to run continu-ously. Such a compressor would have to be capable of compressing air at the same volumetric rate that it is flowing out through the tunnel. This would require greatly oversizing the compressor, but would allow for adjustments to be made while the wind tunnel was running. Unfortunately, these compressors would greatly exceed our budget.

There were a few options regarding the design of the wind tunnel. One of the first was to choose whether the tunnel would have one throat or two. The one throated design almost halves the length of the tunnel and reduces the amount materials needed. However, the pressure required to prevent a normal shock from interfering with the test section flow is much greater than with a double throated design. A double throated design allows the group to direct oblique shockwaves out of the tunnel. This prevents atmospheric pressure from interfering with the test section flow.

Another design choice was the placement of the control valve. The valve could either be placed before the stagnation chamber or just before the nozzle. The valve placement in the nozzle presented a number of problems such as disruption of the flow and the overall size of the valve. By

Figure XX. Single and double throat designs.

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placing the valve before the stagnation chamber, any disruptions in the flow would be reduced by the later filter system. The size of the valve was also irrelevant at this location. The last main design concern for the tunnel was related to the shape of the stagnation chamber. The cham-ber could either be cylindrical or rectangular. The throat and test section were specified as rectangular according to the Sivells code. A cylindrical chamber would reduce turbulence due to corners and provide greater strength un-der pressure. A super ellipse would have to be created to bring the overall shape from a circle to a rectangle. This would be a very difficult feature to fabricate. A rectangu-lar chamber might have increased turbulence and stress at the corners, but would be easier to fabricate.

It was determined that the project could either be fully automated or manually operated. A fully automated design would use a computer and LabView to control the solenoid valve, data read-ings, and image capturing. If manually operated, a person would control the opening and closing of the valve and the image capturing. There are three component choices for the computer and display portion of the design: A desktop computer, a laptop computer, or a touch screen terminal. The desktop computer would be the least expensive option, but would also take up the most space. Since this wind tunnel is in-tended to be portable, size is an important issue. The laptop would have a moderately higher cost, but its smaller size would be a great benefit. The touch screen would be smaller than the laptop, but at an increased price. For the automated design, a data acquisition board would be necessary to allow the sensors and solenoid to interface with the computer. The DAQ board could either be installed into the com-puter or it could be an external USB model. The external USB board is slightly more expensive, but provides flexibility for a change in computer system. The pressure readings in the stagnation chamber can be taken either through the computer or from an analog gauge. A 0-200 psi pressure transducer would connect to the DAQ board and the readings could be displayed through LabView. For the manual design, the user would simply read the pressure from the integrated gauge. In either design, an enclosure will be used to house the electronics. An automated design would incorporate a solid state relay which would allow the low computer voltage to trigger the solenoid valve. In the manual design, a simple toggle switch would control the valve. A diaphragm solenoid was chosen to control the airflow from the compressor tank to the stagnation chamber. A hand controlled valve would not open quickly enough to allow the flow to proceed through the valve uniformly. Webcam style cameras allow for the option of video or still images and easily connect with any computer. A digital camera can be used for higher resolution images, but is more expensive and would need a tripod. NI Vision software allows LabView to control certain webcam models. The two major options for the electronic components can be summarized using two wiring diagrams. Figure XX represents a fully automated system which would utilize LabView to control the components. Figure XX shows a manual system where a person would control the valve and the video capture.

Figure XX. Rectangular stagnation chamber converging to nozzle.

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There were many options regarding the materials to be used for the tunnel. An all steel tunnel would be very strong, but difficult to machine. The FDM process could be used to produce the more complicated components, but the strength of the ABS plastic is much less than that of a metal. The test section would need transparent sides so Plexiglas would be an excellent choice. An impact plate and honeycomb filter are needed in the stagnation chamber in order to reduce the turbulence of the flow.

The test object must be fixed within the test section and be strong enough to withstand the stress of the Mach flow. An ABS plastic model can be easily produced using the FDM machine. As an alternative, an aluminum test object could be machined. These would be fixed in place by placing a thin bolt through the object and fastening it on the opposite side of the test section with a wing nut. The entire wind tunnel will sit atop a wheeled cart. This cart will have certain features to prevent it from rolling once the wind tunnel is in operation.

Concept Evaluation The theory was used to determine how large a tank would need to be in order to produce a Mach 3 flow for sufficient test time. An initial prediction was made that a fire extinguisher sized tank, pressurized to 120 psi, would produce adequate flow for 30 seconds. The theoretical data showed that these predictions were far from accurate. After refining the data, we found that a 20 gallon tank, pressurized to 120-150 psi, would produce a test time of about 3 seconds. This theory assumes that we are using a throat size of 1 cm by 1 cm. This also rules out using a continuously running compressor. The Sivells code was used to generate a profile of the diverging nozzle. This FORTRAN program provides a scalable contour for a nozzle based on the desired Mach number. The flow specification are input into the Sivells program through a program called SivInput.f. The data out-put by Sivells.f were imported into TecPlot in order to visualize the nozzle contour. The contour of the nozzle is a two dimensional function. The depth of the nozzle is a constant value determined by the EddyBL program.

Figure XX. Automated system wiring diagram

Figure XX. Manual system wiring diagram

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Figure XX. Tecplot output of diverging nozzle contour.

The EddyBL program determines the minimum depth needed in order to prevent viscous boundary layers from choking the flow. This is another FORTRAN program and it runs in con-junction with Setebl. Setebl uses output data from the Sivells code to model the boundary layer growth. Since the height of the test section is several times the depth, the most critical boundary layers are the ones formed on each vertical wall of the nozzle and test section. The boundary layers were calculated to be 1.2 mm on each wall at the end of the test sec-tion. Therefore, the minimum depth would be slightly larger than 2.4 mm. A depth of 1 cm was chose to en-sure that there would be suitable depth of flow across the test object. The converging end of the nozzle is not as re-strictive as the diverging section. The nozzle can also converge from either a rectangular or circular cross section. The rectangular option allows for a much simpler design. The only concern is whether the rect-angular stagnation chamber can handle the stress con-centration at the corners. The cylindrical design would have evenly distributed stress due to the fact that it has no corners. After designing both chambers and ana-lyzing the models in CosmosExpress, the rectangular chamber was determined to be strong enough to withstand the pressure. Thus, the rectangular cross section would be the most suitable design for this project. The following are the design decisions that were made after scoring the various choices. All decision charts are located in Appendix E. The two options for overall tunnel design were either a single or double throat variety. The lower compressor pressure added to a comparable cost and higher safety of the double throat de-sign. The advantage of locating the valve between the tank and the stagnation chamber is that any disruption in the flow due to the valve will be reduced by the filters. This location also makes future replacement of the valve easier due to increased accessibility. The laptop provided the best blend of size and cost for this project. Additionally, Professor

Figure XX. Dimensions of test sec-tion concepts.

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Knight donated a laptop to be used in this project which lowered our project costs. In the auto-matic version of the project, the external DAQ board was of comparable price to a similar internal component. However, the external board may be swapped from a desktop to a laptop or any other computer with a USB port. This flexibility makes it an obvious choice for this design. The analog pressure gauge is a more practical choice for our purposes as the pressure is only used to determine when the tank can no longer sustain Mach flow. In our case, the less expensive component is the better choice. Overall, the manually controller wind tunnel is a better option for this project. This design does not require a DAQ board, solid state relay, pressure transducer, or an additional AC/DC power supply. These items account for over half of the total budget for this project. After taking the costs of materials and other components into account, this was deemed unnecessary. The computer would still be used to capture and display images of the flow around the airfoil. The ABS plastic was chosen as the best material for both the airfoil and the nozzle sections. This material provides adequate strength and the ease of being able to produce the parts using the FDM machine. The stagnation chamber will be made of steel to allow for easier welding of flanges. A wheeled cart made of wood was designed to house the compressor and support the wind tunnel. The top of the cart will have a sheet metal section to allow fastening of the wind tunnel.

Design Refinement

The constraints of the FDM machine prevent either of the nozzle sections from being lon-ger than 12”. By modifying the Sivells code, a contour was generated to fit within this limit. The cart will contain wheel locks, but an alternate stopping device has been designed in the event that these do not prevent the cart from rolling. The selection of steel for metal sections was a refinement from the original choice of aluminum. This was to allow for easier welding of the flanges that will connect the various sections of the tunnel.

5. Detailed Design

Theory

Using the equation for test time and the specified 20 gallon compressor, the supersonic flow test time achieved is 3.04 seconds. The air is flowing through a 1 cm by 1 cm throat and then into the 1 cm by 4.2 cm test section. At this point the air will be flowing at Mach 3. While a complete derivation of the test time is provided later in this report, a short overview of the theory will be presented here. A conservation of mass equation ensures that the mass flow out of the pressure tank will be equal to the mass flow through the throat. The mass flow rate at a point in the flow is a function of the density of the flow, the cross sectional area, and the flow velocity. We know that the speed at the throat is sonic and that the flow through the stagnation chamber can be taken as isentropic. Therefore, the mass flow rate in the tunnel can be represented by the following equa-tions:

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Using a related equation, the stagnation pressure required for Mach 3 flow was also de-termined. To prevent normal shock in the test section, the exit pressure must be approximately atmospheric. By using this exit pressure for the exit nozzle, it is possible to backsolve for the mini-mum required stagnation pressure. This was found to be approximately 50 psi. When the pressure gauge falls below this reading, the wind tunnel can no longer sustain Mach 3 flow and should be shut down. The calculations of this value are shown below.

Compressor & Visualization

Once the theoretical specifications of the compressor were determined, a list of suitable compressors was compiled. These compressors would need to be capable of compressing air to 120 to 150 psi and containing a tank volume of approximately 20 gallons. Since the compressor was a high cost item, price was a critical deciding factor. A 20 gallon compressor capable of stor-ing air at 155 psi was found at the Milltown Home Depot. This compressor was about $30 less expensive than comparable compressors so it was selected for the project. This design will utilize the blow down method of connecting a compressor to a wind tun-nel. This less expensive method will store the air in the compressor tank for later use. The com-pressor will feed air to the wind tunnel through a XX ft air hose. The air hose will have a quick release port on one end and a 3/8” NPT thread on the other. The threaded end will fit into the solenoid valve. The visualization will be accomplished by using the shad-owgraph system. This consists of a focusing lens, a light source, and a housing to fix the items in place. The lens should be convex and typically costs around $30. The light will be focused through the lens and will show the shockwaves around an object in the test section. To calibrate the shadowgraph, a candle can be used in the test section. The candle would be placed in the test section and the light source would be focused until it projects an image of plumes appears on the white background. A Schlieren system is capable of visualizing more than a shadowgraph, but it is more expensive and complicated to produce. Since this system will only need to display shockwaves, a shadowgraph is sufficient. The shadowgraph system designed for this wind tunnel contains several important parts.

Figure XX. Shadow-graph of candles.

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1. Lens This is to focus the light in order to create the shadowgraph image. The lens is convex and has a diameter of 1”.

2. Light Source This is a flashlight that creates the light in order to produce a shad-owgraph image.

3. Light Housing This is an alumi-num rod with an outside di-ameter of 0.75”, an inside diameter of 0.5”, and a width of 1.25”. This holds the flashlight by using two threaded holes on top that tighten flashlight into place with thumb screws. There is a square hole in the bottom with a length of 0.31” and width of 0.2” in order to connect to the rod.

4. Lens Housing This is an aluminum rod with an outside diameter of 1.25”, an inside diameter of 1”, and a width of 0.3125”. This holds the lens by using three threaded holes 120° apart that tighten the lens in place with thumb screws. There is a square hole in the bottom with a length of 0.31” and width of 0.2” in order to connect to the rod.

5. Rod This is an aluminum rod that is 3” long with a diameter of 0.5”. On top is a square piece that is milled out in order to connect either the Light or Lens Housing, the square has dimensions of 0.31”x0.2”x0.2”. It also has holes in the sides in order to adjust the height by using a thumb pin.

6. Rod Housing This is an aluminum rod that has an outside diameter of 1”, an inside diameter of 0.5”, and a width of 0.25”. This is used to hold the rod in place in order for it to adjust its height. It has holes on top and through its sides. The top holes are used to hold the housing in place into the table so that it does not rotate. The holes on the side are for the pins that adjust the height of the rod.

7. Adjusting Thumb Screws These screws have a length of 1” and a thread size of 4-40. It is partially threaded with a threaded length of 3/4”. The head is 0.183” in diameter and a height of 0.112“. These are used to adjust the height of the rod.

8. Thumb Screws Tthese screws have a length of 0.5” and a thread size of 4-40. The head is 0.183” in diam-eter and a height of 0.112“.

Figure XX. Exploded view of shadowgraph design.

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Electronics & Instrumentation

The computer system used for this design will be a laptop computer donated by Professor Knight. The computer will be running Windows XP. The webcam will be a Logitech Quickcam 9000 Pro. This camera is capable of capturing video at a sufficient resolution and frame rate. The FreeWebcamRecorder program will be used to capture and store the video data. This program is available as a free license. The electronic system will be contained in a XX enclosure. A grounded electrical plug will power the components. The enclosure will contain a toggle switch to open and close the circuit. A .5 amp 3AG fuse will be held by a fuse holder. This fuse holder will be placed in the electrical circuit for safety. This system will control a solenoid with 3/8” NPT pipe thread on either side. The solenoid operates on 120 VAC so a standard wall outlet can be used. A pressure gauge capable of 0 to 200 psi will be used to obtain pressure readings from the stagnation chamber. The gauge has a XX thread and will screw into the top of the chamber.

Nozzle Profile Design

The 2-D converging-diverging nozzle was created using Sivells code. The shape of the nozzle was created modifying input variables in sivinput.f. These values were chosen for our wind tunnel’s specifications, and optimized in order to insure that the nozzle could be built in the FDM machine, which has a length constraint of 12 inches. The output file generated by sivinput.f (noz-zledesign0001.out) was then used by sivells.f to create the nozzle profile found in the Sivells section of the appendix. The variables used in creating the nozzle profile are detailed in Appendix F. CMC, and thus the height of the nozzle, was a given for our design. However, by manipulating ETAD, RC, and BMACH, we were able to render different nozzle lengths.

Minimum Nozzle Thickness

A maximum test time can be achieved by using a minimum throat area. However, there are limits to how small this area can be. Boundary layers that grow on the surface of the nozzle and test section dictate these minimum dimensions. Our 2-D nozzle design has vertical walls that are spaced more closely together than its top and bottom curved faces. Thus, the most critical bound-ary layers would be the ones formed on the sides of the nozzle and test section. A computer pro-gram called Eddybl was used to calculate these boundary layer heights. Presur.dat was modified as shown in Appendix XX. Setebl.f was run and modified to take into account our test section Mach number. The boundary layer height was found to be 0.0039ft or approximately 1.2 mm at the end of the test section (an estimated 1 ft downstream). Since a boundary layer grows on both walls, we must double this number to find the mini-mum depth. This minimum depth is 2.4 mm. However, there needs to be a suitable amount of flow across the test object in order to visualize a flow. We also must account for uncertainty in this number since it is ideal and does not take into account imperfections which may disturb the flow and increase the boundary layer height. One such imperfection considered was the joining of the

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ABS plastic nozzle with the test section. Based on these criteria, we will decided to use a depth of 1 cm.

Nozzle Safety Considerations

Analysis was done on the ABS plastic material used to build the nozzle. Although results show that this material is suitable to withstand the 150 psi at the converging section, concerns were raised about the safety of running such a high pressure through a porous plastic. Since the nozzle profile must be exact, budget limitations constrain us to using the FDM machine. In order to circumvent this problem, we will insert the ABS plastic nozzle into a 4” diameter steel pipe, 1 ft in length, and fill the remaining volume with expandable insulating foam. This design will ensure safety and prevent catastrophic failure of the nozzle at its most critical point.

Wind Tunnel Design

The tunnel section can be divided into the stagnation chamber, nozzle section, and test sec-tion. The tunnel will be made of mostly aluminum, steel, and ABS plastic. These materials were chosen because of their high strength, ease of manufacturing, and low cost.

Figure XX. Exploded view of stagnation chamber.

Stagnation Chamber: The stagnation chamber is composed of a system of plates and screens which create a lami-nar flow into the nozzle section. These subcomponents are:

1. Inlet Pipe : The inlet pipe is a 2” aluminum pipe with a 3/8” NPT thread. The pipe will be threaded and screwed into the air hose that connects to the compressor.

2. Stagnation Chamber: The square steel stagnation chamber is a foot long and has an outside dimension of 2.5”. The chamber has a wall thickness of 1/4”. There will be a 3/8” NPT tapped hole in the center of the back wall to fit the inlet pipe. There will also be a XX” hole tapped in the top of the chamber to accommodate the pressure gauge. The left (inlet) face of the chamber is a steel 2.5” square. This square will be welded to the steel outer shell of the chamber.

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At the right (outlet) opening there will be steel right angle brackets lining each side of the chamber. These brackets will be welded to the chamber. These brackets will serve as a flange to connect to the converging-diverging nozzle. The flange will use ¼” diameter screws. The chamber was tested using the Solidworks Cosmos program. When subjected to a 200 psi pressure on the inside of the chamber, alone without the inserts that will help reinforce the tunnel, the chamber has a safety factor of 2 and a maximum displacement of .00082”.

3. E, G, I, K. Filter dividers: These are pieces of 6061-aluminum square tubing of 2” sides and wall thickness of 1/4”. These dividers give the stagnation chamber its 1.5” x 1.5” internal cross-section. These pieces will be fitted into the stagnation chamber so that the filters will be secured at the correct distances apart without disrupting the flow. Dividers C and D are 3” long to allow for a gap before the impact plate and then another gap before the honeycomb filter. The 3” size was chosen because the honeycomb filter must be approximately 3” to 4” away from the impact plate. The first filter plate was then 2” from the honeycomb and then another inch separated the two filters. The spacing of the impact plate and two filters is not critical and these dimensions were chosen for ease and to somewhat evenly space the filters.

4. Impact Plate: The impact plate is also made from 6061-aluminum and is a ¼” thick. The impact plate has circular patterns of holes increasing in size, radiating from the center of the plate. The holes are of diameters 1/16”, 1/8”, and ¼”. The size of the hole or distance between the circular patterns was not a critical value. The radii of the patterns to the center of the holes are ¼” and ½” inches. The impact plate is used to create a uniform flow of air throughout the cross section of the chamber.

5. F. Honey-comb filter: The honey-comb filter is made of 1” long aluminum expanded aluminum. This part is the most critical filter in the chamber. The size of each side of the hexagon is 1/8”, and the thickness of the filter should be 8 times the length of the hexagon size; In this case 1”. As the flow travels through the honeycomb it becomes even and should be a laminar flow.

6. J. Filter Screen: This component will be a regular window screen mounted in an aluminum holding bracket. The bracket will be 1.5” square.

Converging Nozzle Section: The converging nozzle will be attached to the stagnation cham-ber with a flange that is built into the nozzle. The nozzle converges from the 1.5” square cross-section to a 1 cm square cross-section, but the contour of this nozzle is not critical.

Second Nozzle: This model may not be used to simplify the design process. This design is also made of ABS plastic and has a flange built in for easy attachment. The nozzle has a wall thickness of a quarter inch and

Figure XX. Converging nozzle.

16

the end half of the design is open, exiting to the atmosphere. The second nozzle is used to avoid a back shock. A flap made from ABS plastic will be used to deflect the supersonic flow at Mach 3, causing oblique shockwaves. The gear, also made from ABS plastic, will be used to manually adjust the angle in order to produce oblique shockwaves. By manually fine-tuning the angle of the flap, the compression and expansion waves will cancel continue to cancel each other out, ef-fectively fulfilling the requirement for the weakest shockwave at the tunnel exit.

Figure XX. Flap and gear system for directing shockwaves.

Test Section: The test section is where the all of the information will be gathered from the wind tunnel. The pressure gauge will be located in this fixture, as well as the shadowgraph setup. A small hole will be drilled through the acrylic sides to allow for a small aluminum rod to pass through the test section. The rod will pass through the center of a thin airfoil to create the test specimen. This rod will be fixed with butterfly nuts and sealed with rubber gaskets.

1. Acrylic Sides: The acrylic sides of the test section will be 3/8” thick and will be 3” long. There will be 1/4” thick acrylic blocks at the ends to be used as flanges. The acrylic blocks will be fused using acrylic cement. The flanges are designed to fit the same ¼” screws. The siding will be attached to the top and bottom of the test section with a series of bolts. A matching series of holes will be drilled in the acrylic and aluminum and then bolts will be used to secure the sides. These bolts will be sealed with rubber gaskets. The most critical aspect of the test section is the transpar-ency of the section. To gain a clear image from the shadowgraph the most transparent siding was required. Because of the 92% light transmission of acrylic, it seemed the logical option. It was tested in Cosmos and is strong enough to withstand the vacuum in the test section. Dimensions

2. Aluminum Lids The 6061-aluminum lids are a half inch aluminum squares with aluminum brackets mount-ed on the top to be used to secure the lids to the nozzles. The aluminum sections are necessary so that the acrylic sides can be removed to allow access to the air foil. Dimensions

Figure XX. Test section assem-bly.

17

3. Airfoils The two airfoils used for demonstration will be produced using the FDM machine. The first airfoil will be a diamond design, and the second will be semi-elliptic (opening facing down). Both airfoils are 7.5 cm in length, 1 cm in width, and tapped to 5 mm.

Figure XX. Airfoils for use in the test section.

6. Budget

The budget for this project is $1000, consisting of $500 from the Engineering Department and $500 from Prof. Knight. The budget has drastically changed not only our part choices, but the entire set of goals for our project. Initially, the wind tunnel was supposed to be fully automated us-ing Labview. After compiling a list of the electronic components, it was clear that this could not be done within the budget. At that point, the nonessential functions of the wind tunnel were removed. This effectively forced the project to be a manually operated wind tunnel and eliminated many of the more expensive parts.

Category CostElectronics XXCompressor/Tank XXTunnel XXShadowgraph XXBudget $1,000.00Materials Cost XXBalance XX

7. Parts ListName & De-scription

Part# M a n u f a c -turer

Supplier URL Purpose Price/item Qty Total Cost

Husky 20 Gal-lon Vertical Portable Com-pressor

M o d e l H1820F

Husky Home Depot ht tp://www.homede-pot.com/webapp/wcs/stores/servlet /ProductDisplay?storeId=10051&langId=-1&cat a l o g I d =10 0 53 & p roduc t Id=10 0653165

Create Pres-surized Air

$199 1 $199

18

Square Alumi-num Tube 2”x2”x12”x .25”

t63s2x.25 Speedy Met-als

Speedy Met-als

ht t ps: //w w w.speed-ymetals.com/p-4684-2 - s q -w a l l - s q - t u b e -6063-t52-aluminum.aspx

S t a g n a t io n C h a m b e r Spacing

$14.28 1 $14.28

S q u a r e Steel Tube 2.5”x2.5”x12”x .25”

4787 Speedy Met-als

Speedy Met-als

http://www.metalsde-pot.com/Car t3/view-Cart1.phtml?LimAcc=$LimAcc&aident=http://www.speedymetals.com/ps-4787-205-2-12-sq-x-14-wall-square-steel-tubing.aspx

S t a g n a t io n Chamber

$14.68 1 $14.68

Square Alu-minum Block .5”x.5”x 3”

61s1 Speedy Met-als

Speedy Met-als

ht t ps: //w w w.speed-ymetals.com/p-2498-1-sq-6061-t6511-alumi-num-extruded.aspx

Top of test section

$1.71 2 $3.42

Square Alu-minum Block 1.5”x1.5”x .25”

61s1.5 Speedy Met-als

Speedy Met-als

http://www.speedymet-als.com/pc-2500-8378-1-12-sq-6061-t6511-aluminum-ext ruded.aspx

Impact plate $1.12 1 $1.12

Square Alu-minum Block 1 . 5 ” x 1 . 5 ” x 0.125”

61s1.5 Speedy Met-als

Speedy Met-als

http://www.speedymet-als.com/pc-2500-8378-1-12-sq-6061-t6511-aluminum-ext ruded.aspx

Filter screens $1.12 1 $1.12

A l u m i n u m Right Angle structure 1”x1”x.25”x24”

A3114 Metals Depot Metals Depot h t t p : / / w w w . m e t -a l s d e p o t . c o m /C a r t 3 / v i e w C a r t 1 .

Use as flange to connect sections

$6.88 1 $6.88

3/8 X 12 X 12 Acrylic Sheet

AC381212 Pierce-Ohio Companies

Pierce-Ohio Companies

http://freckleface.com/shopsite_sc/store/html/product67.html

Clear siding for the test section

$9.35 1 $9.35

Logitech Quick-cam 9000 Pro

960-000048 Logitech Amazon ht tp://www.amazon.com / L og i t e ch -960 -0 0 0 0 4 8 - Q u i c k -C a m - P r o - 9 0 0 0 /d p /B000RZQZM0/ref=sr_1_1?ie=UTF8&s=electronics&qid=1228334061&sr=1-1

Capture the image of the airflow in the test section

$72.26 1 $72.26

Solenoid 4738k146 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com/

Regulate the air flow

$74.92 1 $74.92

Pressure Gauge (0-200 psi)

3847k71 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com/

Gives a read-out of pres-sure in the s t a g n a t i o n chamber

$9.17 1 $9.17

Toggle Switch 7343k184 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com/

M a n u a l l y open and close sole-noid

$4.74 1 $4.74

Fuse Holder 7343k184 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com/

Holds the fuse

$3.46 1 $3.46

Fuse (.5 A, 3AG, 1/4”x1-1/4”)

7085K81 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com/

S a f e t y against a blow out

$6.71 1 $6.71

19

Enclosure 75065K21 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com/

Contain elec-tronic com-ponents

$14.10 1 $14.10

Air Hose 9150K14 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com/

C o n n e c t compressor to tunnel

$31.66 1 $31.66

Aluminum Inlet Pipe

NA A Thyssen-Krupp Ma-terials, NA Company

Online Met-als

http://www.onlinemet-als.com/basket.cfm?pidadd=1210&CFID=14839793&CFTOKEN=23123044

Fixed inlet pipe into s t a g n a t i o n chamber

$1.10 1 $1.10

Nozzle Enclo-sure Steel Tube (4” diameter x 12’ length)

4457 Speedy Met-als

Speedy Met-als

http://www.speedymet-als.com/ps-4457-203-4-steel-pipe.aspx

Prevent cata-strophic fail-ure of abs nozzle

$27.55 1 $27.55

25.4mm Bi-Convex Lens

KBX052 Newport Newport ht tp://www.newpor t.com

S h a d o w -graph Focus Lens

$24.99 1 $24.99

Mini Maglite IK3A011 Maglite Maglite ht t p://www.magl ite.com

S h a d o w -graph Light Source

$6.99 1 $6.99

3” x 1/2” Alu-minum Rod

11r.5 Speedy Met-als

Speedy Met-als

ht t ps: //w w w.speed-ymetals.com

S h a d o w -graph Rods

$0.75 2 $1.50

1/4” x 1” Alu-minum Rod

11r1 Speedy Met-als

Speedy Met-als

ht t ps: //w w w.speed-ymetals.com

S h a d o w -graph Rod Housing

$0.76 2 $1.52

1 1/4” x 3/4” Aluminum Rod

11r.75 Speedy Met-als

Speedy Met-als

ht t ps: //w w w.speed-ymetals.com

S h a d o w -graph Light Housing

$0.74 1 $0.74

5/16” x 1 1/4” Aluminum Rod

11r1.25 Speedy Met-als

Speedy Met-als

ht t ps: //w w w.speed-ymetals.com

S h a d o w -graph Lens Housing

$0.86 1 $0.86

10 Pack 4-40 x 1” Socket Cap Screw

1TKL3 Grainger Grainger ht tp://www.grainger.com

S h a d o w -graph Ad-j u s t i n g T h u m b -screws

$6.40 1 $6.40

100 Pack 4-40 x 1/2” Socket Cap Screw

6XA45 Grainger Grainger ht tp://www.grainger.com

S h a d -o w g r a p h T h u m b -screws

$5.98 1 $5.98

Style 2 Met-ric Wing-Head Thumb Screw

92595A314 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com

Fasten Air-foil

$2.67 1 $2.67

10x Metric 18-8 Stainless Steel Wing Nut

94545A225 Mc M a s t e r-Carr

Mc M a s t e r-Carr

http://www.mcmaster.com

Fasten Air-foil

$5.04 1 $5.04

Total = XX

8. Conclusion

Many of the initial goals for this project have been satisfied by the current design. The de-sign allows for a Mach 3 flow to be observed by a class with some sort of projector installed. The very low test time requires the video capture to start before the air flow begins. The design also allows for changes in compressor size to provide more test time. By using the FDM machine, the nozzle section can also be easily scaled to provide either a larger test section or more test time. The

20

maximum object size of the FDM machine is actually the limiting factor in the size of the nozzle. The budget proved to be the most critical factor in the design. Much of the scope of the electronics section had to be downscaled for budgetary reasons. The group intends to complete the wind tunnel some time in March. This will allow for adequate testing and adjustments to the design. Another design concern is that certain components are designed in SI units and some are in Imperial units. This mix of units has already created problems for much more capable engineers in the NASA Mars Lander project. Looking forward, it would be a good idea to consolidate the design into a uniform set of units.

21

Footnotes

1. See Appendix A.2. See Appendix A.3. See Appendix A.4. See Reference 1.5. See Reference 2.6. See Appendix B.7. 8. 9. See Appendix C.10. See Appendix A.11. See Appendix A.12. See Appendix C.13. See Appendix D.

22

Appendix A - Patents

2805571 - Supersonic Wind Tunnel - Harry Graham - 1957 This patent provides a design for a supersonic wind tunnel. This wind tunnel utilizes a compressed air system similar to the one in this project. The wind tunnel in the patent also uses a heated air system to prevent condensation.

2515069 - Wind Tunnel - Colman Zola - 1950 This patent is for another supersonic wind tunnel. The design intends to use combustion to drive a high velocity flow.

2914941 - High-speed Wind Tunnels - Otto Frenzl - 1959 In 1959 Otto Frenzl proposed driving a high-speed air flow by using a hot water ejection system.

4341469 - Laser Shadowgraph - Mark Gardiner & David Kuntz - 1982 This early laser shadowgraph system was used for detecting defects in video discs. This system used a number of mirrors to direct the laser through the test object and then display the image on a screen.

6891980 - Method and Apparatus for Analysis of Schlieren - Michael Gerhard et al. - 2005 This patent describes the setup of a Schlieren system to visualize test objects.

3617130 - Simplified Schlieren System - Joseph Kelley & Robert Hargreaves - 1971 This Schlieren system provided the most practical design for our application. This sim-plified system included a light, lens, and a parabolic mirror.

23

Appendix B - Compressor Data

Brand HP Gallons Maximum PSI

Price ($)

Length (in)

Width (in)

Height (in)

Weight (lbs)

Husky 2 30 135 384 29 27 57 178Grip-Rite 2 3 125 168 21 8.9 20 38Campbell Hausfeld

1.7 13 125 280 24 15.5 39 69

Clarke 2 20 115 375 N/A N/A N/A 117Porter Cable

1.8 15 135 450 N/A N/A N/A 87

Senco 1 2.5 125 199 20.5 N/A 18.5 39Iron Force

N/A 20 150 275 N/A N/A N/A 83

Campbell Hausfeld

1.8 8 125 190 N/A N/A N/A 85

Campbell Hausfeld

1.3 15 125 219 N/A N/A N/A 110

Campbell Hausfeld

1.3 15 125 240 N/A N/A N/A 115

Campbell Hausfeld

1.7 20 125 250 38 21 31 80

Campbell Hausfeld

1.7 13 125 300 32 20 30 69

Puma 1 2 125 180 16 14.5 14 36Briggs & Stratton

1.5 4 125 275 20.6 15.2 17.1 62

Puma 2 4 125 290 19.2 19.6 18.8 68Ingersoll Rand

N/A 4.5 125 325 21 15 17 58

Maxus 1.3 4 135 350 21.9 18.5 18.9 55Maxus 1.3 4 125 320 22 18 22 58Maxus 1.8 4 125 390 22 18 22 61DeWalt 1.8 15 200 369 N/A N/A N/A N/ADeWalt 1.8 4.5 200 369 N/A N/A N/A N/AHitachi 2 4 N/A 240 N/A N/A N/A N/AHitachi 1.6 4 135 250 N/A N/A N/A N/A

24

Appendix C - Reference Websites

Compressor Datawww.aircompressorsdirect.comwww.everyaircompressor.comwww.lowes.comwww.homedepot.comwww.mcmaster.comwww.mscdirect.com

Lens Datawww.scientificsonline.comwww.sterlingprecision.comwww.crylight.comwww.philaoptics.com

Electronics Datawww.newegg.comwww.amazon.comwww.buy.comwww.ni.comwww.mcmaster.comwww.mscdirect.com

25

Appendix D - Theoretical Equations

Appendix D - Theoretical Equations

The condition for a normal shock at the exit is p2 = pa. If pa < p2, thenoblique shocks form outside. If pa < p2, a normal shock forms in the testsection. Thus, test duration is defined by p2 = pa.

Now,

p1 = p0

[1 +

γ − 1

2M2

1

] −γγ−1

p2 = p12γM2

1 − (γ − 1)

(γ + 1)

Thus, the condition is

p0

[1 +

γ − 1

2M2

1

] −γγ−1

∗ 2γM21 − (γ − 1)

γ + 1= pa

Thus

p0

pa=

[1 + γ−1

2M2

1

] γγ−1 [γ + 1]

[2γM21 − (γ − 1)]

M1p0pa

2.0 1.743.0 3.55

Assuming choked flow at throat

m=ρ0a0Ath(

2γ+1

) γ+12(γ−1)

Also,dm

dt= −dρ0V

dt

Thus,dρ0

dt= −ρ0a0Ath

Vα

1

Since flow in stagnation chamber is isentropic,

T0

T01

=

(ρ0

ρ01

)γ−1

Thus,

dρ0

dt= −ρ0

√γRT01

V∗(ρ0

ρ01

) γ−12

Athα

1 +γ − 1

2=γ + 1

2

Let η = ρ0ρ01

,

dη

dt= −η

(γ+1)2 a01

AthVα∫ η

1

dη

ηγ+12

= −∫ t

0a01

AthVαdt

1[1− γ+1

2

]η1− γ+12

∫ η

1= −a01

AthVαdt

2

1− γ[η

1−γ2 − 1

]= −a01

AthVαt

Thus,p0(t)

p01

=1[

1 + a01AthV

γ−12

2γ+1

γ+12

(γ−1)t] 2γγ−1

Define

β =γ − 1

2

2

γ + 1

γ+12

(γ−1)

= 0.1157 for air

Thenp0(t) =

p01[1 + a01

AthVβt] 2γγ−1

t =1

a01

(AthV

)β

(p01

pa

)[2γM2

1 − (γ − 1)]

(γ + 1)[1 + (γ−1)2M2

1 ]γ

(γ−1)

(γ−1)

2γ

− 1

2

(k) (ms

) (m2) (m3) (s)M1

p01pa

To a0 Ath V t

3 10 288 340 5× 10−5 3.927× 10−3 0.318− − − − 5× 10−4 1.571× 10−2 1.27

Throat Height Throat Depth Ath Test Section HeightM1 (cm) (cm) (m2) (cm)3.0 1.0 1.0 10−4 4.235

3

28

Appendix E - Concept Evaluation

Nozzle DesignCriteria Round Nozzle Rectangular NozzleStrength + StandardCost = StandardEase of Production - StandardEase of Design - Standard

Number of ThroatsCriteria Single Throat Double ThroatCost = StandardSize + StandardSafety - StandardSimplicity - Standard

Valve PlacementCriteria Before Stagnation Chamber Before ThroatCost = StandardAccessibility + StandardLaminar flow + Standard

Computer and DisplayCriteria Desktop Laptop Touch ScreenCost + Standard -Weight - Standard +Expandability = Standard -Size - Standard =

DAQ BoardCriteria Internal External (USB)Cost Standard =Size Standard =Future Flexibility Standard +

SensorsCriteria Pressure Gauge Pressure TransducerCost + StandardFuture Use of Data - StandardEase of Integration = Standard

29

Appendix F - FORTRAN Code Settings

SivellsInput Variable Value Purpose FILE NAME nozzledesign0001 A 16 character file name is

chosen to save the output gen-erated by sivinput.f.

JD -1 This creates a 2-D profile, as opposed to an axisymmetric profile.

ETAD XX This is expansion angle for the nozzle.

RC XX This variable determines the radius of curvature of the nozzle.

BMACH 2.9 This is the centerline Mach number that emanates from the inflection point on the profile. The inflection point is where the curvature changes to concave down from con-cave up.

CMC 3 The design Mach number. This is the Mach number that we wish to achieve in the test section.

SMOOTHING 1 No Smoothing

Below is the data generated by the Sivells code for the 2D diverging contour. This data represents the top face of the nozzle. This top face is simply mirrored about the X-Axis in order to create the full profile.

X-COORDINATE (CM) Y-COORDINATE (CM) 0.000000000000000 0.500000000000000 0.007080350000000 0.500004950000000 0.014177750000000 0.500020150000000 0.021299000000000 0.500045150000000 0.028431900000000 0.500080800000000 0.035596850000000 0.500127000000000 0.042812950000000 0.500182950000000 0.050016700000000 0.500250200000000 0.057277300000000 0.500328400000000 0.064562100000000 0.500416450000000 0.071862600000000 0.500516650000000

30

0.079234350000000 0.500628050000000 0.086604150000000 0.500751150000000 0.094071200000000 0.500884900000000 0.101539450000000 0.501032050000000 0.109118050000000 0.501191600000000 0.116715900000000 0.501364350000000 0.124427800000000 0.501549150000000 0.132189300000000 0.501749500000000 0.140066150000000 0.501964350000000 0.148029150000000 0.502194900000000 0.156107800000000 0.502440050000000 0.164314400000000 0.502704050000000 0.172641250000000 0.502986050000000 0.181137650000000 0.503287650000000 0.189762400000000 0.503608200000000 0.198598500000000 0.503952350000000 0.207578950000000 0.504319900000000 0.216807800000000 0.504712700000000 0.226202500000000 0.505130900000000 0.235879450000000 0.505579550000000 0.245752700000000 0.506059150000000 0.255934750000000 0.506572150000000 0.266349150000000 0.507119350000000 0.277094200000000 0.507706500000000 0.288116250000000 0.508334700000000 0.299482600000000 0.509007400000000 0.311175550000000 0.509725900000000 0.323221700000000 0.510497050000000 0.335652000000000 0.511322600000000 0.348442000000000 0.512205500000000 0.369453600000000 0.513727850000000 0.399554200000000 0.516064300000000 0.433952450000000 0.518962500000000 0.471356250000000 0.522383300000000 0.511074700000000 0.526323200000000 0.552748900000000 0.530794000000000 0.596155650000000 0.535807600000000 0.641149750000000 0.541377050000000 0.687629000000000 0.547508600000000 0.735515100000000 0.554200250000000 0.784751050000000 0.561439300000000 0.835287050000000 0.569208550000000 0.887093550000000 0.577492800000000 0.940149950000000 0.586278100000000 0.994446750000000 0.595552100000000

31

1.049979800000000 0.605302950000000 1.106750300000000 0.615520150000000 1.164762900000000 0.626193350000000 1.224024850000000 0.637313000000000 1.284545100000000 0.648869600000000 1.346333950000000 0.660854050000000 1.409399750000000 0.673257050000000 1.473753500000000 0.686069900000000 1.539405600000000 0.699283150000000 1.606360950000000 0.712887550000000 1.674626650000000 0.726873350000000 1.744205500000000 0.741230500000000 1.815097450000000 0.755948900000000 1.887297350000000 0.771017450000000 1.960801000000000 0.786424450000000 2.035588450000000 0.802158250000000 2.111644850000000 0.818205600000000 2.188945350000000 0.834552650000000 2.267457000000000 0.851185200000000 2.347137600000000 0.868087450000000 2.427933200000000 0.885242150000000 2.509788850000000 0.902632250000000 2.592632950000000 0.920237750000000 2.676384550000000 0.938038950000000 2.926347400000000 0.991169500000000 2.956374100000000 0.997546150000000 2.986373700000000 1.003923500000000 3.016359050000000 1.010298200000000 3.046345100000000 1.016668900000000 3.076345100000000 1.023048100000000 3.106372600000000 1.029425400000000 3.136441150000000 1.035814250000000 3.166563400000000 1.042213350000000 3.196753550000000 1.048621650000000 3.227023900000000 1.055051250000000 3.257387200000000 1.061488000000000 3.287855850000000 1.067951200000000 3.318441400000000 1.074430150000000 3.349156950000000 1.080934100000000 3.380013400000000 1.087462750000000 3.411022350000000 1.094014550000000 3.442194100000000 1.100599450000000 3.473540600000000 1.107205250000000 3.505071600000000 1.113850350000000 3.536797200000000 1.120516750000000

32

3.568727200000000 1.127223650000000 3.600870300000000 1.133958350000000 3.633236850000000 1.140730900000000 3.665834700000000 1.147537050000000 3.698672450000000 1.154378250000000 3.731757100000000 1.161258550000000 3.765097700000000 1.168170350000000 3.798700550000000 1.175126100000000 3.832572600000000 1.182109600000000 3.866720200000000 1.189140950000000 3.901148550000000 1.196197100000000 3.935864700000000 1.203300250000000 3.970873050000000 1.210431600000000 4.006178550000000 1.217605250000000 4.041784600000000 1.224810600000000 4.077696900000000 1.232052700000000 4.113918000000000 1.239329250000000 4.150451350000000 1.246636900000000 4.187298800000000 1.253981900000000 4.224464300000000 1.261351250000000 4.261949000000000 1.268760450000000 4.299754550000000 1.276187050000000 4.337882100000000 1.283654050000000 4.376331700000000 1.291134800000000 4.415105350000000 1.298651300000000 4.454202150000000 1.306183050000000 4.493622100000000 1.313742950000000 4.533363350000000 1.321319800000000 4.573426750000000 1.328916450000000 4.613809800000000 1.336531450000000 4.654511100000000 1.344157800000000 4.695527400000000 1.351804050000000 4.736858200000000 1.359452650000000 4.778499800000000 1.367122350000000 4.820449250000000 1.374785450000000 4.862703150000000 1.382468300000000 4.905257000000000 1.390140750000000 4.948108750000000 1.397826350000000 4.991253150000000 1.405502000000000 5.034686100000000 1.413182200000000 5.078401700000000 1.420853350000000 5.122397150000000 1.428519950000000 5.166666200000000 1.436177900000000 5.211203900000000 1.443822800000000 5.256003500000000 1.451459850000000

33

5.301061450000000 1.459075000000000 5.346370850000000 1.466682650000000 5.391926000000000 1.474260300000000 5.437719650000000 1.481831100000000 5.483747750000000 1.489363800000000 5.530003000000000 1.496889550000000 5.576479200000000 1.504370100000000 5.623170000000000 1.511840650000000 5.670067950000000 1.519265700000000 5.717168800000000 1.526674450000000 5.764465050000000 1.534036750000000 5.811950650000000 1.541377700000000 5.859617950000000 1.548671450000000 5.907463150000000 1.555939000000000 5.955478900000000 1.563157900000000 6.003659450000000 1.570347050000000 6.051997700000000 1.577486300000000 6.100490450000000 1.584592750000000 6.149130800000000 1.591647100000000 6.197913900000000 1.598667000000000 6.246833400000000 1.605632800000000 6.295887000000000 1.612563150000000 6.345068950000000 1.619436250000000 6.394375450000000 1.626274500000000 6.443801300000000 1.633052600000000 6.493345700000000 1.639797000000000 6.543004250000000 1.646477100000000 6.592774700000000 1.653126500000000 6.642653650000000 1.659707500000000 6.692641900000000 1.666260100000000 6.742737200000000 1.672741600000000 6.823222100000000 1.683045600000000 6.903979250000000 1.693225600000000 6.985009050000000 1.703264900000000 7.066308200000000 1.713184850000000 7.147878000000000 1.722985600000000 7.229715050000000 1.732657500000000 7.311819850000000 1.742194300000000 7.394192800000000 1.751612950000000 7.476830150000000 1.760915050000000 7.559732450000000 1.770073500000000 7.642900350000000 1.779111250000000 7.726330100000000 1.788033700000000 7.810022100000000 1.796822400000000 7.893977200000000 1.805480700000000

34

7.978191650000000 1.814025000000000 8.062665750000001 1.822441450000000 8.147400550000000 1.830721900000000 8.232392300000001 1.838889950000000 8.317641249999999 1.846931550000000 8.403148600000000 1.854836050000000 8.488910400000000 1.862629850000000 8.574927150000001 1.870294050000000 8.661200050000000 1.877824800000000 8.747725050000000 1.885246600000000 8.834502750000000 1.892530900000000 8.921534400000001 1.899690300000000 9.008815850000000 1.906742650000000 9.096347950000000 1.913644500000000 9.184131900000001 1.920435250000000 9.272163300000001 1.927107550000000 9.360443450000000 1.933637800000000 9.448973250000000 1.940062850000000 9.537748400000000 1.946348750000000 9.626770400000000 1.952514350000000 9.716038100000001 1.958568500000000 9.805552850000000 1.964473850000000 9.895310500000001 1.970278200000000 9.985311899999999 1.975942050000000 10.075558650000000 1.981487300000000 10.166046000000000 1.986917300000000 10.256775550000000 1.992205000000000 10.347748350000000 1.997394100000000 10.438959949999999 2.002429750000000 10.530412000000000 2.007367800000000 10.622104200000001 2.012171750000000 10.714034800000000 2.016852400000000 10.806203900000000 2.021409600000000 10.898609600000000 2.025841000000000 10.991251350000001 2.030148350000000 11.084128500000000 2.034333250000000 11.177238700000000 2.038396400000000 11.270581650000000 2.042337850000000 11.364154700000000 2.046158450000000 11.457957300000000 2.049858450000000 11.551986599999999 2.053438850000000 11.646241849999999 2.056899950000000 11.740719850000000 2.060243000000000 11.835419650000000 2.063468450000000 11.930337750000000 2.066577750000000

35

12.025473050000000 2.069571500000000 12.120821800000000 2.072451200000000 12.216382500000000 2.075217800000000 12.312151249999999 2.077872900000000 12.408126299999999 2.080417550000000 12.504303400000000 2.082853650000000 12.600680600000000 2.085182350000000 12.697253399999999 2.087405750000000 12.794019499999999 2.089525100000000 12.890974800000000 2.091539950000000 12.988114899999999 2.093454300000000 13.085437150000001 2.095270350000000 13.182936400000001 2.096990550000000 13.280609650000001 2.098616750000000 13.378451600000000 2.100151550000000 13.476458850000000 2.101596900000000 13.574626450000000 2.102952550000000 13.672949100000000 2.104222800000000 13.771423049999999 2.105411200000000 13.870042500000000 2.106520700000000 13.968803400000001 2.107553250000000 14.067700150000000 2.108508250000000 14.166726949999999 2.109392750000000 14.265879549999999 2.110209350000000 14.365152100000000 2.110959050000000 14.464538599999999 2.111644850000000 14.564034449999999 2.112271650000000 14.663633700000000 2.112841100000000 14.763330300000000 2.113355700000000 14.863119400000000 2.113820500000000 14.962995050000000 2.114236250000000 15.062951300000000 2.114607600000000 15.162983349999999 2.114937500000000 15.263085300000000 2.115227650000000 15.363251450000000 2.115483250000000 15.463477200000000 2.115704500000000 15.563756950000000 2.115896800000000 15.664085800000001 2.116061000000000 15.764458599999999 2.116201350000000 15.864871250000000 2.116319050000000 15.965318999999999 2.116417700000000 16.065797700000001 2.116498650000000 16.166303350000000 2.116565050000000 16.266832200000000 2.116618050000000 16.367381099999999 2.116660200000000

36

16.467946699999999 2.116692900000000 16.568526250000001 2.116717850000000 16.669117100000001 2.116736550000000 16.769717150000002 2.116750050000000 16.970937100000000 2.116766100000000 17.071553850000001 2.116770300000000 17.172173500000000 2.116772900000000 17.272795150000000 2.116774400000000 17.373418099999999 2.116775200000000 17.474041750000001 2.116775550000000 17.574665849999999 2.116775650000000 17.675290050000001 2.116775700000000 17.775914350000001 2.116775700000000 17.876538650000001 2.116775700000000

Pressur.dat is the pressure found at different locations in the wind tunnel. This model as-sumes that the critical boundary layers are those formed on the side walls of the nozzle and test section. This allows us to neglect the curve of the profile, and thus greatly simplifies the data. The 1 ft arc length is the point at the end of the test section.

Pressur.dat Arc length (FT) Pressure (LB/FT^2) 0.000000E 00 1.080000E 04 1.000000E 00 5.716900E 02 0.000000E 00 0.000000E 00

37

References

1. Perry, Raleigh Bradford Jr., “Miniature Supersonic Wind Tunnel Design and Testing on a Practical Basis,” AIAA 15th Annual Meeting and Technical Display, Washington, D.C., Feb-ruary 1979

2. Anderson, John D., Modern Compressible Flow With Historical Perspective, New York, McGraw-Hill Education, 2004

3. Poli, Corrado, Design for Manufacturing: A Structured Approach, Butterworth-Heine mann, 2001

4. Wilcox, D. C., “EddyBL,” DCW Industries, Inc., 19985. Sivells, James C., “Sivells Code,” AEDC6. Ulrich, K. T. and Eppinger, S. D., Product Design and Development, McGraw-Hill, 2000