asri flight packages

8/4/2019 ASRI Flight Packages

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Student Names:

William Le (41412295)

Jordan Palmer (41416145)

Daniel Wilcox (41450000)

Course Code: MECH 4552

Supervisor: Dr. Peter Jacobs

Submission Date: 29 October 2010

A thesis submitted in partial fulfillment of the requirements of the Bachelor of Engineering Degree in

Mechanical and Aerospace Engineering (Dual Major)

UQ Engineering

Faculty of Engineering, Architecture and Information Technology

MECH4552 Major Design Project:

The Development of an Air Data System


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Abstract

The aim of this project is to design and manufacture an air data system for the Zuni Rocket,

capable of recording flight characteristics such as Mach number, altitude and angle of attack

(pitch and yaw). The air data system is designed to be a 5-hole pressure probe which

operates in supersonic flow conditions. It incorporates a central transducer recording the

stagnation pressure on the nose of the cone and four transducers, located around the base,measuring the static pressures.

The project was approached from three different aspects; the design and data acquisition,

the CFD and the calibration process.

In terms of the design, a conical nose piece made from mild steel was manufactured. As

required, it had four base holes which were connected to MPX5700AP model transducers.

Additionally it had a central hole which interfaced with a P51-300-G-B-I36-4.5V-R transducer.

Furthermore, the supporting components to the air data system were also designed and

manufactured. The final assembly consisted of the nose cone, an electrical strip board unit

with supports, a new payload case and payload window cover. The assembly was designed

to meet the requirements of the mentioned air data system while still being mechanically

sound during the aggressive flight conditions.

Extensive computational fluid dynamic analysis was conducted to model the flow conditions

over the conical nose cone. The results were used to compare and calibrate our

experimental data. This data was obtained during a live flight experiment conducted at

Woomera launch range.

An in depth calibration process was established to model the five collected pressure values

and convert them into the desirable flight characteristics. As expected the rocket reached amaximum altitude of approximately 5200m. Furthermore, the process yielded a maximum

Mach number of about Mach 3. Finally, the rocket was found to be pitching and yawing

between 3. This data could be used to estimate the coning rate of the rocket which was

calculated to be 2Hz.


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Table of Contents

1 Contents2 Scope of Project ...............................................................................................................................1

2.1 Instrumentation and Nose Cone Design ...................................................................................1

2.2 Computational Fluid Dynamics ...............................................................................................1

2.3 Pressure Probe Calibration .......................................................................................................2

3 Literature Review.............................................................................................................................3

3.1 Pressure Probes ........................................................................................................................3

3.1.1 4 hole (Cobra Probe): .......................................................................................................3

3.1.2 5 hole pressure probes: ....................................................................................................4

3.2 Response Time: ........................................................................................................................5

3.3 Computational Fluid Dynamics ...............................................................................................6

3.3.1 Experimental Validation of Computational Fluid Dynamic Results .................................6

3.4 Calibration................................................................................................................................9

4 Background Theory....................................................................................................................... 12

4.1 Supersonic Flow and Shock Relations .................................................................................. 12

4.1.1 Types of Shocks ............................................................................................................ 12

4.1.2 Calculating Maximum Angle ........................................................................................ 14

4.1.3 Shock Relation Equations ............................................................................................. 14

4.1.4 Calculating Pressures for Yaw and Pitch Angles .......................................................... 18

4.1.5 Stagnation Temperature and Pressure ........................................................................... 19

4.2 Multi-hole Pressure Probe and Pitot-Static Tubes ................................................................ 19

4.3 Turbulence Effects over Cone............................................................................................... 20

4.4 Reflection of Pressure Waves ............................................................................................... 21

4.5 Computational Fluid Dynamics Usage in the Calibration of Pressure Probes...................... 22

4.5.1 Reducing the Computation Time .................................................................................. 23

4.5.2 Separating Velocity Components .................................................................................. 23

4.5.3 Similarities in Pitch and Yaw Pressures........................................................................ 23

4.5.4 Roll ................................................................................................................................ 24

4.6 Bolt Calculations ................................................................................................................... 25

4.7 Calibration............................................................................................................................. 27

4.7.1 Determination of Mach Number ................................................................................... 27

4.7.2 Determination of Flow Angles ...................................................................................... 29

4.7.3 Correction Factor........................................................................................................... 30


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4.7.4 Probe Calibration Matrix............................................................................................... 30

4.7.5 Determination of Altitude ............................................................................................. 31

5 Assumptions.................................................................................................................................. 33

6 Limitations .................................................................................................................................... 33

6.1 Zuni ....................................................................................................................................... 33

6.2 Manufacturing ....................................................................................................................... 33

6.3 Assembly............................................................................................................................... 34

6.4 CFD Simulations ................................................................................................................... 34

7 Previously Designed Components................................................................................................. 35

7.1 Data Acquisition.................................................................................................................... 35

7.1.1 Overview ....................................................................................................................... 35

7.1.2 Modifications ................................................................................................................ 36

7.1.3 Mode Switch ................................................................................................................. 37

7.2 Separation Module ................................................................................................................ 38

8 Detailed Design ............................................................................................................................. 39

8.1 Design Requirements ............................................................................................................ 39

8.2 Preliminary Design................................................................................................................ 39

8.2.1 Nose Cone ..................................................................................................................... 39

8.2.2 Pressure Transducers .................................................................................................... 40

8.3 Final Design .......................................................................................................................... 40

8.3.1 Nose Cone ..................................................................................................................... 40

8.3.2 Pressure Transducer Selection....................................................................................... 43

8.3.3 Strip Board and Interface .............................................................................................. 45

8.3.4 Payload Case and Window............................................................................................ 48

8.3.5 Manufacturing Processes............................................................................................... 50

8.3.6 Bolt Design .................................................................................................................... 51

8.3.7 Nosecone to Payload case bolts..................................................................................... 51

8.4 Calibration Code Design ....................................................................................................... 53

8.4.1 Introduction ................................................................................................................... 53

8.4.2 Importing Data .............................................................................................................. 55

8.4.3 Obtaining Initial Values ................................................................................................ 55

8.4.4 Mach Number................................................................................................................ 56

8.4.5 Total and Dynamic Pressure ......................................................................................... 58

8.4.6 Determination of Flow Angles ...................................................................................... 60

9 Procedure....................................................................................................................................... 64


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9.1 Trans Calibration of Transducers .......................................................................................... 64

9.2 Assembly............................................................................................................................... 64

9.3 Woomera Launch .................................................................................................................. 67

9.4 Computational Fluid Dynamics Procedure ........................................................................... 70

9.4.1 Geometry....................................................................................................................... 70

9.4.2 Meshing......................................................................................................................... 72

9.4.3 Pre-CFX ........................................................................................................................ 74

9.4.4 Solver ............................................................................................................................ 78

9.4.5 CFX-Post ....................................................................................................................... 78

9.5 Code Procedure ..................................................................................................................... 79

10 Results ....................................................................................................................................... 83

10.1 Pressure Transducer Calibration ........................................................................................... 83

10.2 Theoretical Results................................................................................................................ 84

10.3 Raw Data from Launch ......................................................................................................... 86

10.4 CFD Results .......................................................................................................................... 91

10.4.1 Meshing......................................................................................................................... 91

10.4.2 Testing........................................................................................................................... 91

10.4.3 Data ............................................................................................................................... 92

10.5 Final Results from Code........................................................................................................ 98

10.5.1 Flight Angles ................................................................................................................. 98

10.5.2 Flight Mach Number ................................................................................................... 100

11 Discussion ............................................................................................................................... 100

11.1 CFD Compared to Theoretical ............................................................................................ 100

11.2 Flight Angles ....................................................................................................................... 102

11.2.1 Angle of Yaw .............................................................................................................. 103

11.2.2 Angle of Pitch.............................................................................................................. 104

11.2.3 Mach Number.............................................................................................................. 105

11.3 Altitude ................................................................................................................................ 106

11.4 Error Analysis ..................................................................................................................... 107

11.4.1 CFD ............................................................................................................................. 107

11.4.2 Calibration................................................................................................................... 109

12 Conclusion............................................................................................................................... 112

13 Bibliography............................................................................................................................ 114

14 Appendix ................................................................................................................................. 117

14.1 Appendix A Engineering Drawings .................................................................................... 117


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14.1.1 Assembly ..................................................................................................................... 117

14.1.2 Nose Cone ................................................................................................................... 118

14.1.3 Payload Case................................................................................... ............................. 119

14.1.4 Payload Case Window ................................................................................................. 120

14.1.5 Strip Board Support Plate ............................................................................................ 121

14.1.6 Strip Board Support Ring ............................................................................................. 122

14.2 Appendix B Code ............................................................................................................... 123

14.3 Appendix C ASRI Payload Guide ....................................................................................... 138

14.4 Appendix D NACA1135 Charts........................................................................................... 194

14.5 Appendix D Correction Factors ......................................................................................... 197

14.6 Appendix E Probe Calibration Matrices ............................................................................ 202

14.7 Appendix F Pressure Calibration graphical results ............................................................ 207

14.8 Appendix G Transducer Data Sheets ................................................................................. 209

14.8.1 Freescale MPX5700AP ................................................................................................. 209

14.8.2 SSI Technology P51-300-G-A-I36-4.5OV-R .................................................................. 215

14.9 Appendix H Payload Description. ...................................................................................... 230

Appendix D payload information document template ....................................................................... 231

Description ofAir Data System: ...................................................................................................... 232

Description ofConical Nose Piece: .................................................................................................. 232

Description ofthe Data Acquisition Module: .................................................................................. 234

Payload weight ................................................................................................................................ 235

Protrusions ...................................................................................................................................... 235

Living material ................................................................................................................................. 236

Explosive material ........................................................................................................................... 236

Flammable material ........................................................................................................................ 236

Chemical material ........................................................................................................................... 236

Other hazardous material ............................................................................................................... 237

Calculated Coefficient of Drag......................................................................................................... 237

Assembly ......................................................................................................................................... 237

Preparation...................................................................................................................................... 238

Pre-launch ....................................................................................................................................... 239

Recovery .......................................................................................................................................... 240

Personnel......................................................................................................................................... 240

Procedures to be conducted during the launch sequence ............................................................. 242

14.10 APPENDIX I CFD RESULTS ............................................................................................. 247


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14.11 APPENDIX J RAW DATA ................................................................................................ 252

14.12 APPENDIX K APPENDED LIST OF CFD RESULTS ............................................................. 252

14.13 APPENDIX L CALIBRATED DATA .................................................................................... 252


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List of Figures

Figure 1: 5-hole Pressure Probe on Ares-X Rocket (Space Fellowship 2009)..........................................3

Figure 2: Cobra Probe (Chen, J et al 2000) ...............................................................................................4

Figure 3: 5-hole pressure probe (Porro 2010)..........................................................................................4

Figure 4: Devices for measuring angles of attack (allstar 2008) ..............................................................5

Figure 5: Variation of the settling time as a function of the length of the connecting tube, for different

internal diameters (Bajsi, et al 2007) .....................................................................................................5

Figure 6: The AIAA method for the validation of a particular CFD solver ................................................8

Figure 7: Neural Network Calibration Method ..................................................................................... 10

Figure 8: Figure showing the difference between Oblique shocks on the Left and Bow shocks on the

Right. (White, 2008) .............................................................................................................................. 13

Figure 9: The Definition of Prandtl-Meyer Expansion Waves (White, 2008)........................................ 14

Figure 10: How the velocity profile changes as it passes through an oblique shock, (White, 2008).... 15

Figure 11: Plot used to calculate the value for oblique shocks, (White, 2008) ................................. 17Figure 12: Conditions for calculating surface pressure (NACA1135) .................................................... 18

Figure 13: A Pitot-Static Tube (eFunda, 2010) ...................................................................................... 20

Figure 14: Cavitation Effect (Stanford University, 2000) ...................................................................... 21Figure 15: Roll Data vs. Pressure Coefficient for different Pitch Angles (NACA TN3967) ..................... 25

Figure 16: Angles of Pitch and Yaw ....................................................................................................... 27

Figure 17: Effect of Pitch on Total Pressure .......................................................................................... 28

Figure 18: Variation of Mach Number With Respect to Ratio of Average Static Pressure to Total

Pressure ................................................................................................................................................. 29

Figure 19: Example of Probe Calibration Matrix ................................................................................... 31

Figure 20: US Standard Atmosphere Model ......................................................................................... 32

Figure 21: F-Box data acquisition module (Lara 2007).......................................................................... 36

Figure 22: Channel Configuration ......................................................................................................... 36

Figure 23: Separation Module ............................................................................................................... 39

Figure 24: Preliminary design of nose cone .......................................................................................... 40

Figure 25: Comparing the section cut of the initial design to the final design ..................................... 41

Figure 26: Manufactured nose cone sitting on top of payload case ..................................................... 41

Figure 27: Inside of nose cone showing the protruding copper tubing ................................................ 42

Figure 28: Image showing the internal section of the forward facing cavity ........................................ 42

Figure 29: SSI Technology. P51-300-G-B-I36-4.5V-R ............................................................................. 44

Figure 30: Freescale MPX5700AP .......................................................................................................... 45

Figure 31: Picture from bottom of nose cone showing redundant bolt holes ..................................... 45

Figure 32: Redundant back plate designed to support the original strip board ................................... 46

Figure 33: Hole cut in the middle of the board to allow cables to reach the DAQ module .................. 46

Figure 34: The strip board assembly showing the support ring holding down the vero board to thesupport plate ......................................................................................................................................... 47

Figure 35: Electrical insulation on the support ring ad support plate .................................................. 47

Figure 36: Flexible hosing in boiling water ............................................................................................ 48

Figure 37: Original payload case (left) and the new payload case(right) .............................................. 49

Figure 38: Payload case cover ............................................................................................................... 49

Figure 39: Breakwire adaptor ................................................................................................................ 50

Figure 40: Forces acting on the nose cone. Shows the bolt position and configuration of a section cut

............................................................................................................................................................... 52


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Figure 41: Overview of Calibration Process .......................................................................................... 54

Figure 42: Determination of Coefficients of Pitch and Yaw .................................................................. 56

Figure 43: Ratio of Average Static Pressure to Total Pressure vs. Mach Number (M>1)...................... 57

Figure 44: Ratio of Average Static Pressure to Total Pressure vs. Mach Number (M


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Figure 87: Comparison of Theoretical and CFD Results for the Pressures on the Surface of the Cone

............................................................................................................................................................. 102

Figure 88: Rocket Initial Position ......................................................................................................... 103

Figure 89: Averaged Angle of Yaw vs. Time ........................................................................................ 104

Figure 90: Average Angle Of Pitch vs. Time ........................................................................................ 105

Figure 91: Averaged Mach Number vs. Time ...................................................................................... 106

Figure 92: Altitude Using Atmospheric Pressure ................................................................................ 107

Figure 93: Altitude using Static Pressure ............................................................................................ 107

Figure 15-1 Payload protrusions diagram.......................................................................................... 236

Table 18-1. Qualitative Measures of Likelihood................................................................................ 243

Table 18-2. Qualitative Measures of Consequences ......................................................................... 244

Table 18-3. Legend.............................................................................................................................. 244

Table 18-4. Risk Analysis Matrix ........................................................................................................ 244

Table 18-5 Risk analysis matrix ........................................................................................................... 246


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List of Tables

Table 1: Bolt Calculations (RoyMech 2008) .......................................................................................... 26

Table 2: Properties of Carbon Steel Bolts (Euler 2003) ......................................................................... 26

Table 3: Determined channels for each transducer .............................................................................. 37

Table 4: Mode switch set up for varying tasks ...................................................................................... 38

Table 5: Highest expected pressures for transducer locations ............................................................. 43

Table 6: Bolt selection for each interfacing component ....................................................................... 53

Table 7: Inlet Conditions in CFX-Pre ...................................................................................................... 76

Table 8: Outlet Conditions in CFX-Pre ................................................................................................... 76

Table 9: Payload Conditions in CFX-Pre ................................................................................................ 76

Table 10: Payload Conditions in CFX-Pre .............................................................................................. 77

Table 11: Pressure Transducer Calibration ........................................................................................... 83

Table 12: Theoretical Stagnation Pressures for Varying Mach Numbers ............................................. 85

Table 13: Theoretical Surface Pressures Calculated Using NACA Report 1135 .................................... 86

Table 14: Mesh Results for CFD ............................................................................................................ 91

Table 15: Test Data Using Different Pitch and Yaw Angles ................................................................... 92

Table 16: Raw CFD Data Obtained From CFX For P1, Pitch and Yaw Angles Kept at 0 ........................ 92Table 17: Linear Setup for CFD Results ................................................................................................. 93

Table 18: Percent Difference in Pressure Values Compared to Yaw = 0, for Change in Yaw Angle,

Pitch Angle Kept at 0 ............................................................................................................................ 95

Table 19: Error Percentage in CFD Compared to Theory .................................................................... 108

Table 20: Initial (Theoretical) Calibration Process Error ..................................................................... 110

Table 21: Approximation Error ............................................................................................................ 111

Table 22: Actual Calibration Process Error .......................................................................................... 111


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2 Scope of ProjectThe Air Data System that will be designed must be able to measure the overall flight

parameters of a Zuni rocket during the supersonic period of flight using a series of pressure

transducers. This essentially means the designed payload will be a pressure probe customised

for the Zuni rocket. Furthermore, as a benchmark for success, useable data should be obtainedfrom an in-flight experiment conducted at the Woomera launch range. Some major

parameters that must be determined from the Zuni test flight include the rockets angle of

attack (Pitch and Yaw angle), altitude and Mach number. The project can be divided into

three major sections.

2.1 Instrumentation and Nose Cone Design

In terms of the design, the nose cone needs to be modified into a pressure probe. This includes

the nose cone as well as the supporting components (i.e. transducers and payload casing). The

nose cones semi-vertex angle, mass and materials should be determined

The nose cone must be able to incorporate pressure transducers located at various positions;

one central transducer recording the total pressure and a determined amount of transducers

around the base to measure the static pressure on the cone surface. Furthermore, the design

must be able to use the Data Acquisition module named the F-Box, design by Franco Mario

Rabines Lara. This DAQ module will sit inside a payload case attached to the nose cone.

The pressure transducers used in-flight must be able to operate between the expected pressure

ranges. They must also be able to interface with the nose cone either by screwing into the

nose cone or via some sort of hosing.

The end product needs be a fully assembled payload from the supplied separation module

(payload/parachute separation interfacing plate) and up.

2.2 Computational Fluid Dynamics

The Computational Fluid Dynamics (CFD) section of the project involves the use of a CFD

language to simulate the flight of the payload at various Mach numbers and angles of attack.

The CFD language used is CFX, which is part of the simulation software ANSYS. The use of

CFD allows for quick and easy estimations of possible pressure readings at the rockets

expected flight conditions. This is to be done over the conventional wind tunnel test and

calibration. The conventional wind tunnel testing and calibration process involves simulating

real flow effects for short periods of times. However due to the hundreds of combinations that

must be performed, the wind tunnel testing is too time consuming. In order to have an


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effective CFD model the simulation is to be set up as realistically as possible. This involves

reducing the amount of approximations and assumptions made by the solver. This is

important so the solver does not over or under estimate the results which are to be used as a

comparison to real world data.

2.3 Pressure Probe CalibrationThe calibration section utilises both the recorded data from the instrumentation and the CFD

sections in order to obtain useful data that can represent the flight attitude of the Zuni rocket.

This process will take the voltage readings from the pressure transducers and convert them

into the rockets angle of attack, Mach number and altitude. To have a successful and accurate

model, the calibration process must include a detailed error analysis, working calibration

software and the data must be presented in a clear and concise format.

Some other considerations include a detailed risk analysis of the cone and payload

manufacturing and further detailing the risks involved during the launching process.

Furthermore a strict time line must be followed in order for all manufacturing, CFD

simulations and calibration software to be ready prior to launch.


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3 Literature Review

3.1 Pressure Probes

Almost all aircraft utilise some form of pitot-static system. It is common for aircraft,

particularly commercial and light-wing aircraft to utilise up to ten components to make up a

pitot-static system (Gavin Gillett). These components consist of; pitot tubes, static vents, static

drains, static lines, pitot lines, secondary static sources, airspeed indicators, altimeters and

vertical speed indicator. These usually determine in flight characteristics such as Mach

number, altitude and velocity. However, a simplified instrument for measuring flow speeds

and more importantly flow angularity, is a pressure probe. A simple pitot tube by itself is

insufficient to measure the angle of attack (flow angularity). Rather a modified pitot tube

consisting of multiple pressure transducers is used.

An example of pressure probes being used in aerospace applications is NASAs Ares-X

rocket. Its a large 5 hole pressure probe designed to record the mach number, altitude and

angle of attack.

Figure 1: 5-hole Pressure Probe on Ares-X Rocket (Space Fellowship 2009)

As outlined by the Cambridge engineering department, pressure probes can be found in many

forms. The most, common of the pressure sensitive direction probes are the cobra, the

wedge, the five-hole and cylindrical probes (Hodson).

3.1.1 4 hole (Cobra Probe):

The 4 hole pressure probe is a simpler, smaller design that reduces any redundant information

being collected (less pressures need to be calculated). It has a triangular shaped head as it is

relatively easy to manufacture, accurate location of the side holes is less critical because of

the absence of steep pressure gradients over most of the flat area in which the hole is located


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and the positive location of flow separation at the junctions of the flat surfaces insures

minimal sensitivity to Reynolds number (Shepard, I.C, 1981)

Figure 2: Cobra Probe (Chen, J et al 2000)

3.1.2 5 hole pressure probes:

The 5 hole pressure probe has more pressure calculations involved in the calibration technique

than the 4-hole pressure probe. However, the axial-symmetric design allows for a more

simplistic calibration process.

Figure 3: 5-hole pressure probe (Porro 2010)

In either case, the probes can be used to calculate the stagnation pressure, the static pressure

and the flow angularity. However, when designing a pneumatic probe that is to be used in

flow measurements, the effects of blockage, frequency response, pressure hole size and

geometry, the local Mach and Reynolds numbers and the relative scale of the phenomena

under investigation must be addressed (Porro 2010)

Five hole angularity pressure probes are manufactured by some companies such as Aerolab.

These require shock tunnel calibration before any practical application. They are also quite

expensive and can price around US$1200.


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An alternative to the pressure probe is a common vane which acts as a small airfoil. These are

located on the front of the fuselage before the incoming airflow is disturbed.

Figure 4: Devices for measuring angles of attack (allstar 2008)

3.2 Response Time:

In order to achieve the most accurate results, fast response times for the pressure transducers

are to be desired. In similar experiments traducers with nominal frequency response of 225

kHz(Porro 2010) were used.

However, it was also discovered that the response time of a pressure measurement system

would be influenced by a connecting tube. The following graph shows the expected settling

time for various set ups

Figure 5: Variation of the settling time as a function of the length of the connecting tube, for different internal diameters

(Bajsi, et al 2007)


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3.3 Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) is the use of computational software to analyse fluid

flows. The software used can range from simple codes, to complex programs with advanced

Graphical User Interfaces (GUI). These GUIs are most commonly used as they are able to

create complex geometries, and set up a flow around the model quite easily to analyse.

The use of CFD as an experimental tool has many advantages over conventional tests such as

a wind tunnel test. This is due to being able to change geometry or flow properties quite easily

using the CFD software. Whereas to undertake a wind tunnel test, the geometry needs to be

manufactured and instrumentation set up inside the tunnel, and then tests run. If it is found the

geometry is not satisfactory for the application it is needed for, the process needs to be started

again with the manufacture of another model and testing.

The use of CFD has increased dramatically over the past decade as a tool to optimise and

analyse flow before a model is manufactured, as well as saving on time and money.

3.3.1 Experimental Validation of Computational Fluid Dynamic Results

However, the results of the CFD calculations for the pressure probe need to be assessed for

their validity and accuracy before they are used in real world applications. This is because

there are a number of assumptions the CFD code makes to be able to calculate the results

more efficiently. These assumptions can either over-estimate the results, or significantly

under-estimate the results. Neither of these results are ideal. This is because to accurately

model an unknown flow exact values for pressures at specific velocities and angles are

needed.

The journal article Computational Fluid Dynamics: A Two Edged Sword (Baker, AJ et al,

1997) talks about these issues in depth. It looks at the legitimacy of using CFD to model air

flow in a room. It states that CFD is a good visual tool, and can be used to help understand

how a flow interacts with an environment. It is also able to measure miniscule values that

would normally be too small to measure experimentally. However, due to the many

assumptions and approximations that are originally made by the solver, the values obtained

using CFD are not the correct values that would be found in a real life scenario.

This means that to use CFD effectively, great care must be taken in the modeling, and set up

of the flow parameters, so that the flow is modeled as realistically as possible. The main

assumptions made by CFD solvers involve the turbulence models, as well as viscous effects

for analysing boundaries in high velocity profiles. The turbulence model is a major

contributing factor for all CFD flows. This can be because realistically there can be sections


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of local turbulence in a flow, with the majority of the flow laminar. However, the CFD

assumes that due to the small amount of turbulence that the entire flow is turbulent. This

severely affects the quantitative results of the flow.

Research papers have been written that are interested in determining the validity of CFD

based on experimental data that is already possessed. These papers cover a broad range offields, including medical, manufacturing, and the aerospace industry. However the

conclusions made for the validity of CFD results compared to experimental results can be

used across any application.

Mylavarapu, G (et al, 2009) investigated the use of CFD as a non-invasive method to model

the human upper airways to help determine the unsteady air flow in Obstructive Sleep Apnea

(OSA) patients. CFD is used due to the ability to easily change flow parameters and

determine the effects that these have on people who have OSA.

Magnetic Resonance (MR) and Computed Tomography (CT) imaging are used to create a 3D

virtual model of a persons upper airways. This model is then analysed using CFD simulations

to determine why there are problems, or where further problems could occur if the condition

is exacerbated.

The CFD experiment was conducted using various CFD flow models, and compared with

experimental results, both for the same airway. The comparison showed that the CFD was

able to model the trend of the experimental results, however, depending on the model, over-

estimated or under-estimated the result, compared to the experimental values. The closest

CFD result measured within 20% of the experimental results. This is a significant error

margin, with the model used both overestimating and underestimating the flow at different

times. However Mylavarapu, G (et al, 2009) concluded that CFD could be used to analyse the

flow, but use some experimental data to back up the CFD.

Oberkampf and Trucano (2002) talk about the process of experimentally validating CFD data

according to the AIAA Guide in the article Verification and Validation in Computational

Fluid Dynamics(2002). This process is shown in the Figure 6.


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Figure 6: The AIAA method for the validation of a particular CFD solver

This shows the relationship between how a computational model can be used to accurately

predict experimental results using the results of CFD simulations and experimental results. A

series of experiments are performed, and then replicated in the CFD. The results from both of

these are then compared and the differences assessed for a range of different experiments. A

general inference can then be made from these comparisons. This inference is then made for

every simulation run using this solver.

However, Oberkampf and Trucano also state that it needs to be acknowledged that this

inference is much weaker than actual experimental result. This is because even though CFDrelies on theoretical solutions, it also has other issues involving cell sizes, discretisation, and

etc. Due to this, there can be a significant error that the inference derived cannot predict,

unless exactly the same CFD conditions are kept each time. However this is an unlikely

scenario.

Computational Fluid Dynamics is an extremely useful tool for qualitatively analysing flows as

well as determining the best possible geometry of a model before being manufactured.

However, to accurately analyse a flow over a model and gain quantitative results, the flowparameters need to be carefully set with as little assumptions and approximations made as

possible to ensure a reasonably accurate result. The results gained from CFD should also be

checked with theoretical results, as well as experimental results to determine the validity of

the CFD for that particular model.


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3.4 Calibration

The calibration of the five-hole pressure probe in supersonic conditions involves collating the

recorded data from a flight and converting it into the total and dynamic pressure ahead of the

shock and hence finds the flight Mach number, angle of pitch, roll and yaw. Through the

literary review two main methods of calibration emerged, they are; the most commonly used

conventional method and the relatively new Neural method.

The conventional method outlined by Centolanzi (1957) involves finding calibration curves

relating to potential fluid flow theory. This process is the simplest and evidence from other

journal articles suggests that it is the most widely used method. The main advantage of this

process is that it is widely used meaning that it is a refined process and there are numerous

examples available. However, some disadvantages are that it can be a slow computing process

for a large set of collated pressure values, due to the need for large amounts of initial

calibrating data and the constant interpolation of those sets of data. Interpolation also leads toapproximation error, which if done numerous times in a single process could lead to

significant uncertainties in the final product. A brief outline of the process is as follows:

1. Find the ratio of the static pressure to total pressure behind the shock:

a..

2. Assuming that angles of pitch and yaw are zero, we interpolate a plot determined by

testing data to obtain the Mach number.

3. Using the mach number we interpolate the tables provided by Ames Research Staff(1953) to get the total pressure ratio,

and the dynamic pressure ratio

4. Total Pressure before the shock can then be found: 5. The dynamic pressure before the shock is then given by: 6. Using the dynamic pressure the coefficients of pitch and yaw can be obtained:

a. b. 7. Using the coefficients of pitch and yaw, interpolate the test data in order to gain an

approximation for the angles of pitch, yaw and roll.

8. In order to correct the initial assumption that the angle of attack was zero, a correction

factor must be applied to the initial ratio of static and total pressure. The new ratio is

found by the following equation:


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10

a.

9. The process is then repeated until the values of total and dynamic pressure before the

shock, and respectively have converged

The second method found was the neural method (Hui-Yuan et al. 2003), which is acomputational strategy that aims to simulate the biological processes that take place in the

human brain. The code is made from a series of interconnected processing elements that

individually seem insignificant, however, combined they can be used as a powerful tool for

approximation of arbitrary or non-linear functions such as pressure probe calibration. It is a

somewhat new method, but from previous tests it has been found to be quite accurate and

unlike the conventional method, it is not a slow process nor does it compound error by

continuously interpolating initial data sets. The code forms a good approximation for pressure

calibrations by first being 'trained', this is done by simply importing a series of input andoutput values (Figure 7). The software will slowly find a pattern in the imported values and

once 'training' is complete, it will be able to accurately output the data needed. In this case, the

sets of initial collated pressure values will be imported and the program will output, the

overall flight attitude and Mach number. Some advantages of this process includes a

theoretically accurate result and a quick computing time. However, some disadvantages

include; it is a fairly new and therefore untested method, the code needed to run this process

would be incredibly complex, training the program would be time consuming and accurate

methods of training are relatively unknown, which will lead to variable unknown errors in thefinal product.

Figure 7: Neural Network Calibration Method


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11

Therefore, taking both methods into consideration, the conventional method was chosen as

the process that will adequately suit the needs of this project. Although it is a slower

computing process that will potentially produce larger error, it is much simpler to set up and

in this case the error will be able to be quantified, giving a better indication of overall

accuracy. The neural method would be a faster process to run and possibly more accurate, but

the complexity of writing the code, training the program and the unquantifiable final error

makes the option unfeasible.


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4 Background Theory

4.1 Supersonic Flow and Shock Relations

The payload design attached to the Zuni rocket will experience speeds that are much higher

than the speed of sound.

The speed of sound can be defined as:

(1)

Where a is the speed of sound, k is the ratio of specific heats, R is the universal gas constant,

and T is the temperature of the flow.

At speeds higher than the speed of sound, shockwaves are formed at the front of the body.These shockwaves have a significant effect on the properties of the flow, changing the static

temperature and pressure of the flow behind the shock as well as the overall flow velocity.

We use a non-dimensional term to make calculating these flow parameters much easier. This

term is the Mach number, where:

(2)M is the Mach number, and V is the flow velocity. With shocks starting to form at M=1.

The flow properties after a shock wave for a specific Mach number can be calculated using

the isentropic flow relations, as well as the Compressible Flow Relations Tables found in

Fluid Mechanics (White, 2008).

4.1.1 Types of Shocks

There are two main types of shockwaves that can be formed in supersonic flow, a bow shock,

or an oblique shock.

4.1.1.1 Bow ShockA bow shock is defined as a strong shock with is not attached to the body in the flow,

however it sits in front of the body as a broad curved shock as shown on the right of Figure 8.

As the flow passes through the bow shock, from a speed of M>1, it is slowed down to a speed

of M


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Figure 8: Figure showing the differenc

4.1.1.2 Oblique ShockAn oblique shock wave is de

causes the flow to deflect at a

main difference between a bo

body and the other isnt, is t

sonic or subsonic dependin

completely parallel to the surf

4.1.1.3 Prandtl-Meyer ExpaThere is a case where there

oblique shock waves as flow

the body is at an angle of pitc

top of the body, or compresse

flow expands around the corn

as the flow compresses.

between Oblique shocks on the Left and Bow shocks on the

ined as a weak shock that is attached to the fr

n angle , relative to the body that the shock is

w shock and an oblique shock, other than one i

at the flow behind an oblique shock wave ca

g on the incoming Mach number. This fl

ace of the body as shown above on the left in Fi

nsion Waves

is an isentropic expansion or compression t

moves around a corner or a bend. This effect c

h or yaw to the flow, and the flow expands as i

s as it moves underneath the body, as shown in

r, the Mach number increases, with a decrease

13

Right. (White, 2008)

ont of a body. It

attached to. The

is attached to the

n be supersonic,

ow is deflected

ure 8.

hrough multiple

an happen when

t moves over the

Figure 9. As the

in Mach number


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14

Figure 9: The Definition of Prandtl-Meyer Expansion Waves (White, 2008)

4.1.2 Calculating Maximum Angle

Ideally, it is required that there is an oblique shockwave formed at all Mach numbers

experienced so that the flow is deflected instantly along the body. There is a maximum angle

that the flow can be deflected for a specific Mach number, before an attached oblique shock

can no longer be formed, but instead forms a strong bow shock, as shown in Figure 8. To

ensure that an oblique shock is formed, we need to consider the maximum Mach number that

the body could experience.

The maximum angle for a specific Mach number is defined as:

/ / (3)

Where:

(4)

The values for V are obtained from the Compressible Flow Relation Tables for specific Mach

numbers. (White, 2008)

4.1.3 Shock Relation Equations

To calculate the flow conditions downstream of an oblique shock we need to consider the

isentropic flow relations for a normal shock. This is because we can separate the components


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15

of the incoming flow, to the normal and tangential components of the flow relative to the

oblique shock, as shown in Figure 10.

Figure 10: How the velocity profile changes as it passes through an oblique shock, (White, 2008)

From this we can see that the tangential component of velocity is constant across the shock,

however the normal component of velocity changes as it passes through the shock.

The Mach Number Relations for the change in pressure and Mach number behind a normal

shock are defined as: 1 1 2 1 (5)

1

22 1 (6)

Where k is the ratio of specific heats for a perfect gas, is the Mach number before theshock, with the Mach number after the shock. is the ratio of the pressures, where p2 isthe static pressure after the shock, and p1 the static pressure before the shock.


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16

However, an oblique shock has an angle associated with it, as shown in Figure 10. This

requires the angle of the shock to be known to calculate the ratio of pressures as well as the

new Mach number. The normal component is related to the free-stream Mach number by:

(7)

sin (8)

is an arbitrary value for the angle of the shock and is the deflection angle of the flowparallel to the body. To find the pressure ratio, we substitute into the above pressureratio equation:

1 1 2 1 (9)

To determine the Mach number after the shock, we need to use:

1

22 1 (10)

And then sub this into:

sin (11)

This will determine the total Mach number of the flow after the shock.

can be determined from the following figure, knowing the Mach number and angle ofdeflection, for a value of 1.4 for specific heat ratio.


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17

Figure 11: Plot used to calculate the value for oblique shocks, (White, 2008)The figure above shows two possible values for for each value of. The dotted line in thegraph represents , the point in which the oblique shock moves from a weak shock (onthe left), where the Mach number behind the shock is greater than 1, to a strong shock (on the

right), where the Mach number behind the shock is less than 1. Ideally we will be looking at

weak oblique shocks with

less than

.

Another way to check the pressure along the cone surface is to use Chart 6 from the NACA

Report 1135 (Appendix D). These tables show pressure coefficient versus the semi-vertex

angle for varying Mach numbers of the cone where the pressure coefficient is,

(12)


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The following image indicates the necessary parameters required in order for this chart to be

useable.

Figure 12: Conditions for calculating surface pressure (NACA1135)

4.1.4 Calculating Pressures for Yaw and Pitch Angles

To determine the angle of deflection when there are angles of pitch and yaw, we can add, or

subtract this angle from the deflection angle, depending on the direction of the flow. For

example, if there is a pitch angle of, with a deflection angle of when there is no pitch, theresultant deflection angle is defined as:

(13)

(14)

This results in a non symmetrical oblique shock wave forming about the body, with a smaller

value for the bottom deflection angle, and larger for the top. Using these new values for

we can determine the static pressures on the top and bottom of the body.

However, if there is no yaw angle involved when there is a pitch angle, or vice versa, the

angle of deflection to calculate those pressures not affected by the added angle, is normal.


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4.1.5 Stagnation Temperature and Pressure

The stagnation temperature and pressure are also very important, in designing a body to

handle high speed flows, as well as record the pressure.

The stagnation pressure can be defined as:

1 12

(15)

Where the stagnation is pressure before the shock and is the static pressure of the flowbefore the shockwave.

We can also determine the stagnation temperature using the following relation:

(16)

is the stagnation temperature and is the static temperature.However, the stagnation pressure behind the shock is required. This can be calculated byfinding the value for / in the normal shock relation tables found in (White, 2008).

4.2 Multi-hole Pressure Probe and Pitot-Static Tubes

The multi-hole pressure probe uses the above theory for shockwaves in supersonic flow, to act

as a regular pitot-static tube.

A pitot-static tube is used in many different fields to find the velocity of an unknown flow. It

has an opening at the front of a tube which records the stagnation pressure of a flow. Around

the edges of the tube, there are also holes, which feed back to pressure sensors to measure the

average static pressure of the flow. As shown in Figure 13.

The flow velocity can then be computed using the following equation:

2 (17)


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is the density of the flow, V is the velocity, is the stagnation pressure and is the staticpressure of the flow.

Figure 13: A Pitot-Static Tube (eFunda, 2010)

A multi-hole pressure probe, acts in exactly the same way as a pitot-static tube. However the

shape is different. This is because as shown above, for supersonic flows, the flow is deflected

from its original path. This means that a conventional pitot-static tube will not be effective, as

it will be unable to measure the static pressure of the flow over the holes on the side, as the

flow is directed away from the body shown above.

However, due to the nature of oblique shocks, a conical shaped pressure probe can be

developed, which will allow the pressure probe to act exactly like a pitot-static tube. This isbecause the flow is deflected parallel along the surface of the cone, so the average static

pressure can be obtained. As shown in Figure 13.

4.3 Turbulence Effects over Cone

Ideally, for a flow interacting with a body with an angle of pitch or yaw the flow will instantly

separate into two streams based on which oblique shock is passes through. However, even for


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small angles of pitch and yaw, some of the flow does separate. At the front of the cone on the

windward side, there is a build up of pressure similar to that of the stagnation point, with the

leeward side having an absence of flow, and a significant decrease in pressure.

This is a similar effect as to that seen for aerofoils for increasing angle of attack, creating a

cavitation behind the aerofoil as seen in Figure 14.

Figure 14: Cavitation Effect (Stanford University, 2000)

This cavitation effect can significantly affect the results of the pressure measurements if the

sensors are positioned too close to this area. Therefore to accurately measure the pressure onthe sides of the probe, it is necessary to position the sensors a significant distance away from

the effects caused by possible pitch and yaw angles.

4.4 Reflection of Pressure Waves

As flow enters the inlet of a duct that is blocked at one end, there can be reflections which can

affect the incoming flow. This effect usually causes a decrease in pressure as the waves

interact, however, if there is a build up of waves there can be a dramatic increase in pressure.

This concept is much like acoustic waves interacting, with positive and negative amplitudes

interacting.

The length of the duct is a significant contributor to the whether there are severe pressure

wave reflections. This is because the longer the pressure waves spend reverberating in the

closed end duct; the longer it is affecting the results as pressure waves are absorbed causing

readings at the end of the ducts to be inaccurate.


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To avoid this something can be used to break up the pressure waves down the duct. This can

be a permeable medium inside the duct that will not allow for the transfer of the pressure

waves, however the pressure is still able to increase through the medium so the pressure

transducer is able to measure the pressures accurately.

4.5 Computational Fluid Dynamics Usage in the Calibration of Pressure ProbesThe use of CFD to calibrate the pressure probes involves determining the pressures at each

pressure sensor, depending on the flow velocity and the angle of attack. Using these obtained

values we are able to determine the velocity and angle at which the probe is in an unknown

flow, such as on a rocket, or aircraft.

Each pressure probe has a different set of calibration data, based on its geometry, number of

sensors, and positions of sensors. Therefore each different pressure probe needs to be

calibrated individually to ensure that it is accurately modeling the unknown flow.

Generally, calibration of pressure probes is performed in a wind or shock tunnel, depending

on the application. This process involves placing the probe into the tunnel, and simulating

different flow conditions, including mean flow velocity and angle of attack. This is done to

obtain pressures at each of the pressure sensors, and is used as a reference for when the probe

is in use.

However this is a very time demanding process. It involves having to place the model inside

at the exact required angle of attack, start the wind tunnel and allow the flow to reach the

desired flow velocity. Once the pressure sensors are reading a steady state flow, record the

data, turn the wind tunnel off, and start all over again. This needs to be done for every

possible scenario that the pressure probe may encounter while in use (all angles and all

velocities), which, depending on the range of velocities, and angles, as well as the number of

data points observed over the ranges. This number can become very large very quickly, over a

factor 106 combinations quite easily. As each different combination takes time to set up, this

process takes a very long time if not completely automated.

Therefore there is a need to reduce this calibration time. A reduction in calibration time willspeed up the process between the design and implementation phase of a pressure probe.

CFD is able to be used to speed up this process. The overall geometry and boundary

conditions only need to be set up once. From this point the flow conditions can be easily

changed, depending on the angle or the velocity. The pressure distribution about the probe can


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23

also be seen, and pressures can be obtained for the points where the pressure sensors are

located on the probe.

4.5.1 Reducing the Computation Time

Calculating a large number of data points in CFD can be extremely time consuming.

However, there are some simplifications that can be made to reduce the amount of data pointsthat need to be calculated. This is done by using simple mathematical relations to show that a

lot of the data is the same or very similar to that of other data points. Thus determining which

data points can be extrapolated from others. The following theory explains how this can be

done.

4.5.2 Separating Velocity Components

The velocity of a flow can be broken up into 3 separate velocity components using the

directional vectors x, y, and z. Knowing the angle of the flow it is possible to use basic

trigonometry to correctly determine these velocities. These velocity components are

extremely important in setting up the flow conditions in CFD. The following equations can be

used to determine the velocities in thex andy directions where there is no velocity component

in thez-direction.

(18)

(19)

(20)Where V is the actual velocity of the flow, and is the angle between the direction of theVelocity vector and thex-axis.

The velocity component inz can be calculated the same way as in y, with the angle betweenthe direction of the velocity vector and thex-axis. is the same value as above.4.5.3 Similarities in Pitch and Yaw Pressures

For a 5-hole pressure probe, there are 4 equidistant spaced positions around the cone where

the pressure is recorded. The opposite transducers are used to determine either the pitch or

yaw angles. This is done by determining the difference in pressure from the leading edge in


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the flow, to the trailing edge. This means that the transducer on the windward side would have

a higher pressure than that on the leeward side.

Using the above trigonometric theory, we can see that for the same value, and producethe same value, as does for both cases. It can be assumed that the component contributesto the pitch, and contributes to yaw, wherex is the direction of the flow.If this is the case, an angle of 5 yaw will produce the same pressures over the 4 sensors

around the cone, as an angle of 5 pitch. However, the values of pressure will be rotated by

90. For example, if the four pressure sensors are labelled, P2, P3, P4 and P5:

, , , ,

From this, we can extrapolate to say that for calculating pitch and yaw values ranging

between and , we only need to look at between 0 and , for either pitch or yaw, while

leaving the other variable at 0.

We can then use these results to determine what the pressure values are at every combination

of pitch and yaw. This is because, if looking at 5 pitch and 5 yaw, there are 2 points in the

leading edge and 2 points in the trailing edge. Knowing the pressure values for both these

scenarios, we can correctly assume what the pressure values are. The full list of Pressure

Values for every scenario can be found in Appendix K.

4.5.4 Roll

To calculate roll we need to look at how the pressures change on each pressure sensor. For a

constant angle of pitch and yaw, as the payload rolls, the pressures stay constant at the spatial

positions; however, the sensors oscillate between these values. If we consider four points of

roll, we can look at 0, 90, 180 and 270. Between 0 and 90, there is a curve that defines

the transition between the two pressures at those points. Figure 15 below is an extract from

the NASA Technical Note 3967, showing the effects of roll on the pressure coefficient for a

Mach number of 1.95.


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Figure 15: Roll Data vs. Pressure Coefficient for different Pitch Angles (NACA TN3967)

Each plot is for a different pitch angle. It can be seen that for large pitch angles, there is a

definitive curve between each major point as defined above. However for low pitch angles,

the progression from one point to the next is linear. Due to this we can assume that between

0 and 90, 90 and 180, 180 and 270, 270 and 0 it is entirely linear. This will make

interpolating results much easier, as well as cutting back the number of CFD calculations

required, as values for the four major points above can be easily defined using the data

already obtained.

, , , , 4.6 Bolt Calculations

As expected, flight conditions can be quite demanding on the mechanical system especially

during launch, landing and the deployment of the parachute. A Zuni rocket can be expected to

experience forces of up to 70 times that of normal gravity, the failure and design calculations

for the mechanical fittings must be taken into consideration.

The following equations should be applied to the proposed design.


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Table 1: Bolt Calculations (RoyMech 2008)

Shear stress 4FD

Compressive Stress F

Dt

Plate Shear Stress F2ct

Furthermore to design for maximum shear stress the shear yield strength needs to be

determined

The Maximum Distortion Energy Theorem suggests that the shear yield strength =

0.577*normal yield strength.

Table 2: Properties of Carbon Steel Bolts (Euler 2003)

Properties of carbon steel bolts

Grade Description Proof Load

Stress, MPa

Tensile Yield

Strength, MPa

Tensile Ultimate

Strength, MPa

4.6 low or medium carbon steel 225 240 400

4.8 low or medium carbon steel,

fully or partially annealed

310 340 420

5.8 low or medium carbon steel,cold worked

380 420 520

8.8 medium carbon steel,

quenched and tempered

600 660 830

9.8 Low or medium carbon

steel, quenched and

650 720 900


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tempered

10.9 medium carbon

quenched and temp

12.9 alloy steel, quenc

tempered

4.7 Calibration

The objective of this section i

use the CFD data to calibr

supersonic speeds. The varia

angle of pitch, angle of yaw

shock relations a good estima

flight attitudes for every data

4.7.1 Determination of Ma

The first step in the calibratio

(23). It was observed that at v

vary across the four transduce

good indication of the actual s

the estimated Mach number.

steel,

red

830 940 1

ed and 970 1100 1

s to take the pressure values recorded from a Z

te those values and return a model of the

les which will be describing the flight are; th

and flight altitude (Figure 16). Using a series

e of these variables can be found. The process

oint recorded over the flight were as follows:

Figure 16: Angles of Pitch and Yaw

ch Number

process was to find the ratio of static pressure

arying angles of pitch and yaw, the static pressu

rs around the base; however, averaging those v

tatic pressure and enables the value to be essen

Next an assumption was made that the angles

27

040

220

ni rocket flight ,

light attitude at

e Mach number,

f fluid flow and

s for finding the

to pitot pressure

re would largely

alues out gives a

ially invariant at

f pitch and yaw


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28

of the rocket were equal to zero. This assumption will later be corrected, however, it allows

for the initial determination of the Mach number by interpolating the CFD data and the ratio

of static pressure to pitot pressure (Figure 18). Using this initial Mach number the flow angles

can be estimated, the process for doing so is described in section 4.7.2Determination of Flow

Angles. Once the flight angles have been found a correction factor is reapplied to the ratio of

static to pitot pressure, which will then re-estimate the Mach number and hence re-evaluate all

other values. The process is continued until all values have converged. However, it must be

noted that the initial assumption of the flight angle equalling zero will not adversely affect the

end results due to the fact that the static and pitot pressures hardly vary at the calculated Mach

number. This can be seen in Appendix D Correction Factors, where at supersonic mach

numbers there is minimal variation of ratio of total and static pressures due to pitching.

Further evidence that the flight angle has little dependence on the resulting Mach numbers can

be seen in the low variance of pitot pressure due to varying speeds and pitch angles (Figure

17). This therefore provides enough evidence that Equation (23) which defines Mach number

in this calibration process has little dependence on the flight angles. Thus, only a small

correction factor will need be applied to find the 'true' Mach number.

Figure 17: Effect of Pitch on Total Pressure

0

0.2

0.4

0.6

0.8

1

1.2

-8 -6 -4 -2 0 2 4 6 8

pitotpressureratio

angle of pitch

Effect of pitch on pitot pressure

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4


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Figure 18: Variation of Mach Number With Respect to Ratio of Average Static Pressure to Total Pressure

4.7.2 Determination of Flow Angles

For the flight angles of a supersonic vehicle to be found, initially the total pressure before the

shock, and the dynamic pressures, had to be calculated. The total pressure is a functionof the pitot pressure, angle of attack and Mach number and therefore follows a similar process

to that of the determination of the Mach number where the angle of attack is initially ignored

and a correction factor will be later applied, but as mentioned, this assumption is not

detrimental to the end results. Furthermore, ongoing from the assumption that the angle of

attack is zero, results reported from Gracey et al. (1951), show that at any supersonic Mach

number the shock relations associated with a supersonic nose cone can be related to normal

shock theory. Thus the total pressure ratio (25) can be found by interpolating the tables

located in the NACA Report 1135 (1953). The tables were interpolated by finding a

polynomial relationship that would input the Mach number and output the corresponding total

pressure ratio, a method to complete this task can be seen in 8.4.5 Total and Dynamic

Pressure. The total pressure can then be calculated using the relationship seen in Equation

(26). The dynamic pressure is determined by a similar method, in that it utilises the

polynomial relationship which exists between the Mach number and the ratio of dynamic

pressure to total pressure to return the dynamic pressure ratio needed. The resulting dynamic

pressure can then be calculated using Equation (28). Utilising and the pressure differencesacross the sets of opposed transducers, the coefficients of pitch and yaw ( C and Crespecitely) can be calculated (Equation). The matrix plots (4.7.4 Probe Calibration Matrix)

generated with CFD data can then be interpolated with the coefficients of pitch and yaw at

each Mach number in order to find the angles of pitch and yaw.

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2 2.5 3

Pa

/Pt2

Mach Number

Mach number


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4.7.3 Correction Factor

As mentioned, in order to correct the initial assumption that flight angles were equal to zero a

correction factor is introduced. It simply measures the deviation of the ratio of static to pitot

pressure at different angles to the zero angle point. As can be seen in Appendix D Correction

Factors, the deviation due to pitching at high Mach numbers tends to be minimal, indicating

that the initial error was not large. Once the correction factor is applied to the static to pitot

pressure ratio, the process is repeated until the value of Mach number has converged. By

applying this correcting factor it continuously minimises the deviation of the static to pitot

pressure ratio from its actual value at the specified angle, therefore continuously improving

the solution.

4.7.4 Probe Calibration Matrix

The probe calibration matrix is a plot of the variables obtained (C, C, ,) from the CFDmodelling. An example of the plot can be seen in Figure 19(All other plots are located inAppendix E Probe Calibration Matrices. The probe calibration matrix was obtained by

initially finding the coefficients of pitch and yaw, found by the processes outlined in 8.4.5

Total and Dynamic Pressure. These data points were then plotted using simple plotting

software. The matrix forms a good representation of the flow fields at varying Mach numbers

and provides a good reference for quickly determining the angles of pitch and yaw once the

corresponding coefficients have been calculated. As can be seen in Appendix E Probe

Calibration Matrices the data points seem equidistant apart, with lower variance levels at high

supersonic speeds. The consistent plotting pattern is what should be expected from a CFDcalibration due to the fact that computer simulations have constant ambient values, unlike real

life testing which would have various inconsistencies due to experimental losses.


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Figure 19: Example of Probe Calibration Matrix

4.7.5 Determination of Altitude

Located inside the payload was a sixth pressure transducer which was utilised to record the

atmospheric pressures as the altitude of the rocket changed over time. The US standard

atmosphere (1976) and the Earth Atmospheric Model (Glenn Research Centre, 2010)

Equation were utilised in order to calibrate the ambient pressure values to obtain flight

altitude. The resulting calibration plots and function relating ambient pressure to altitude for

the US Standard (1976) model can be seen in Figure 20. As a further comparison of the data,

the same models were applied to the calculated average static pressure; this was simply done

in order to check the accuracy of the pressure values recorded and consistency in the results.

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

CoefficientofYaw

Coefficient of Pitch

Mach 2.2


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Figure 20: US Standard Atmosphere Model

, 101.29

. 288.08273.115.040.00649

(21)

y = -6978ln(x) + 32471

R = 0.9994

-10000

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 20 40 60 80 100 120

Altitude(m)

Pressure (kPa)

US Standard Atmosphere Model (Pressure vs.

Altitude)

Series1

Log. (Series1)


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5 Assumptions

- Maximum speed payload can reach is M=2.6, however, M=3 is used to calculate

optimum angles and pressures

- Flight time at supersonic speeds ends between 6-10 seconds

- The range of pitch and yaw angles experienced are between -7 and 7

- Acceleration forces can reach 70g

- Viscous effects are negligible when performing CFD calculations

- The payload will experience a roll effect. For a constant angle of pitch and yaw there

is a linear progression between pressures at 0 and 90, 90 and 180, etc.

- Pressures on surface of cone are the same as pressure at the end of tubing

- Due to small length of tubing there is a negligible response time reading the pressure

from the surface to the pressure transducer

- An oblique shock is created at all times when the payload is at speeds above M=1

- Heat transfers and thermal expansion are neglected due to the short flight time

- CFD results are comparable to real world applications

- Data is recorded by the DAQ at a rate of 1kHz for approximately 20 seconds

6 Limitations

6.1 Zuni

- 10 kg minimum weight of the payload for attachment to the Zuni

- The Zuni has a radius of 130mm

6.2 Manufacturing

- Length of drill bits capable to drill through long sections of the cone limited to greater

than 200mm

- Minimum diameter for drill bits capable of drilling to 200mm is limited to 63.5mm

()

- Copper Tubing outer diameter is limited to

- Hosing has to fit onto transducer flange (4.92mm) and be able to be molded to fit ontothe copper tubing

- All designed sections must be able to be manufactured in the workshop or instrument

lab.

- Finances are to be minimized. Transducers should be inexpensive. Design should

avoid the need to order anything else a part from transducer (i.e. Swaglok

connections).


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6.3 Assembly

- Make assembly as easy as possible while still meeting design requirements

- Must be able to physically connect plastic tubing to copper tubing by hand

- Lengths of tubing, and cables from pressure sensors are limited in length due to the

space available in the payload case

- Due to small space, need to be able to install the components into the payload case

with all cables and tubing completely attached together

6.4 CFD Simulations

- Restricted to using CFX within ANSYS to calculate CFD results

- Limited maximum number of elements in CFD Mesh due to processing power and

allowable computational time

- Limited time to perform excessive amount of pitch, yaw, mach combinations


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7 Previously Designed Components

7.1 Data Acquisition

7.1.1 Overview

The in-flight data acquisition module is Franc

asri flight packages

Documents