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Research & Development
Wind Tunnel Testing– Needs to be applicable for subsonic, transonic, and supersonic
velocities– Scaled down model
• Associated costs• Dimensions to minimize error due to scale effects, flow blockage, and wall boundary layers
– Possible testing locations• NASA Glenn Research Center – Cleveland, OH• NASA Langley Research Center - Hampton, VA• Purdue’s Mach-6 supersonic tunnel – West Lafayette, IN
AAE 450 Spring 2008Aerothermal
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Drag Model:Historical Data
SubsonicCD = 0.55
TransonicCD = 0.65
SupersonicCD = 0.60
•Correct Historical Data
•“Normal” Geometry
•Smaller Diameter than the Vanguard
Assumptions:Assumptions:
-Used Historical Values for large variety of similar shaped rockets and scaled the drag coefficient accordingly to determine CD at α=0.
-Also attempted CFD to determine CD at α=0.
-Then used CD at α=0 in order to generate plots of CD versus AoA.
-”Normal” Geometry indicates all upper stages are smaller in diameter than their predeceasing lower stage and only a total of 1 to 2 shoulders.
AAE 450 Spring 2008Aerothermal
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Drag Model:Geometric Data
Axial Force Coefficient = Drag Coefficient
(at α=0°)
•Linear Perturbation Theory(Linearized Supersonic Theory)(Linearized Subsonic Theory)
Assumptions:
Drag Coefficient:CD=N ∙ sin(α) + A ∙cos(α)
-Used pressure coefficient to calculate the axial and normal force coefficients.
-Used the axial and normal force coefficients to calculate the drag coefficient.
Coefficient of Drag
2
Plot Authors: Woods, Zott
AAE 450 Spring 2008Aerothermal
Vanguard Check – subsonic case using Fluent
Velocity VectorsRed – 401 m/sGreen – 225 m/s
Static PressureRed – 1.18 atmBlue – .364 atm
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Vanguard Check – subsonic case using Fluent
Static TemperatureRed – 300 KBlue – 220 K
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1 kg launch vehicle – Mach 1 case using Fluent
PressureRed – 1.56 atmBlue – .373 atm
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1 kg launch vehicle – Mach 1 case using Fluent
VelocityRed – 411 m/s
Green – 208 m/s
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200 g Aerodynamic LoadsTable 4.1.4.2.1 Summary of Maximum Aerodynamic Loading 200 g.
Aerodynamic Load Subsonic Supersonic
Bending Moment [Nm] -1850.7 -1133.1
Pitching Moment [Nm] 626.6 383.6
Normal Force [N] 146.6 89.8
Axial Force [N]Shear Force [N]Center of Pressure [% length]Coefficient of Drag CD
Dynamic Pressure [Pa]CD % error [%]
486.9 -99.4 38.3 1.38 54
298.1 -60.8 38.3 0.85 279 17
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1 kg Aerodynamic LoadsTable 4.1.4.2.1 Summary of Maximum Aerodynamic Loading 1 Kg.
Aerodynamic Load Subsonic Supersonic
Bending Moment [Nm] -773.0 -388.7
Pitching Moment [Nm] 357.8 179.9
Normal Force [N] 94.2 47.3
Axial Force [N]Shear Force [N]Center of Pressure [% length]Coefficient of Drag CD
Dynamic Pressure [Pa]CD % error [%]
335.7 -43.0 40.0 1.44 63
168.9 -21.6 40.0 0.81 240 21
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5 kg Aerodynamic LoadsTable 4.3.4.2.1 Summary of Maximum Aerodynamic Loading 5 Kg.
Aerodynamic Load Subsonic Supersonic
Bending Moment [Nm] -6505.0 -3346.0
Pitching Moment [Nm] 1246.0 640.9
Normal Force [N] 215.9 111.0
Axial Force [N]Shear Force [N]Center of Pressure [% length]Coefficient of Drag CD
Dynamic Pressure [Pa]CD % error [%]
760.0 -407.4 38.2 1.31 62.5
390.9 -209.6 38.2 0.78 225 19.5
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Creation of the Pressure Distribution
, 2
2
1p upperC
M
, *cos( )p p lowerC C
, 2
2
1p lowerC
M
AAE 450 Spring 2008
Aerothermal12
Linear Perturbation Forces are found by an integration of
pressure distribution over the launch vehicle exterior
Integrations are done numerically within the code
Phi is the geometric angle w/respect to the freestream
S is a reference area, taken to be the area of the base of the launch vehicle
Validated by comparison to Vanguard results and other related geometries
2
2
1pC
M
2
0 0
1cos
L
N pC r dz C dS
2
0 0
1cos
L
M pC r z dz C dS
2
0 0
1(2 ) cos
L
A pC r dy C dS
MCP
N
CX
C
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Important Assumptions in Theory Small changes in geometry Small angle of attack
~ 0 – 14 degrees Valid for subsonic or supersonic flow
0 < M < 0.88
1.12 < M < 5
Axial force neglects viscous effects
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Stresses due to Aerodynamic Force Shear Stress
– Differential of Normal Force between stages
Axial Loading– A*q∞*S
Bending Moment
Picture by Jayme Zott and Alex Woods
Bending Moment vs. Mach Number for the 5 kg case at 0 aoa
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Mach Number
Ben
din
g M
om
ent (
N*m
)
Bending Moment
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Pictures
Normal Loading vs. Mach Number for a family of Launch Vehicles at 0 aoa
0100200300400500600700
0 1 2 3 4 5
Mach Number
No
rmal
Fo
rce i
n
New
ton
s
5 kg
1 kg
200 g
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PicturesPitching Moment Vs. Mach Number for a family of
Launch Vehicles at 0 aoa
0
500
1000
1500
2000
0 1 2 3 4 5
Mach Number
Pit
chin
g M
om
ent
in
New
ton
Met
ers
5 kg
1 kg
200 g
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Heating Rate
Heating Rate Analysis– Primarily done to design a TPS (Thermal Protection System) – Stagnation Point
• Theoretical analysis using methods outlined by Professor Schneider• Nose cone heating• Determine best material and thickness for the structure of the nose cone
– Alternative methods and materials• SODDIT (Sandia One-Dimensional Direct and Inverse Thermal)• Ablative materials
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Heating Rate
Lumped Heating at Solid Nosetip Method
0
12
400 2 0
1( )
2w p n
dTc r q q T
dt
3
Assumptions– Constant specific heats– No heat transfer within the body– Treat whole nosetip as one solid heat sink– Laminar flow at point 2– No convective heating at point 3, only radiative– Wall temperature is the same at all 4 points
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Equations
N Mabsq C v
1-8 2
n wC = (1.83e )r (1-g )
w pw wh = c T
M = 3, N = 0.5 for fully catalytic surfaceM2 = 3.2 for laminar, flat
plate
2o ah = h + 0.5V
a pa ah = c T
nr
4( )p w r w
dTc V q q T dA
dt
ww
o
h wall enthalpyg = =
h total enthalpy
V
= nose body radius
= volume of solid nosetip
22 1
MNabsq C v
1 19 2 2
1 (2.53 )(cos ) (sin )( )(1 )wC e x g
Heating rate at point 2 on the nose cone
rq = radiation from fluid to surface
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Heating RateMatlab code: *help from Vince Teixeira
AAE450_Stag_heat_analysis.mUses trajectory outputs (.mat files)
Input: d - diameter (m) v - velocity (m/s) r - position from the
center of the earth (m) c_p - specific heat of material (J/kg*K) rho_w - density of material (kg/m3) emiss - emissivity of material
Output: q_dot - heating rate (W/m2) tw - thickness (mm) Tw - wall temperature (K)
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Heating Rate
0 20 40 60 80 100 120 140-100
0
100
200
300
400
500
600Heating rate vs. time, 1 kg payload
time (s)
Hea
ting
rate
(W
/m2 )
Titanium
SteelAluminum
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Backup Slides- Sizing Code Tables
Initial Sizing Code Table of Results450R
Payload Mass 1 (kg): 0.2Payload Mass 2 (kg): 1Payload Mass 3 (kg): 5
PM 1 PM 2 PM 3Overall Length (m, scale 1): 0.48298 2.4149 12.0745Overall Length (m, scale 2) 0.5112 2.556 12.78
First Stage Length (m): 0.25268 1.2634 6.317First Stage Diameter (m, scale 1): 0.02836 0.1418 0.709First Stage Diameter (m, scale 2): 0.6953 0.7357 0.9377
Second Stage Length (m): 0.11404 0.5702 2.851Second Stage diameter (m, scale 1): 0.02034 0.1017 0.5085Second Stage Diameter (m, scale 2): 0.38582 0.4271 0.6335
Third Stage Length (m): 0.05532 0.2766 1.383Third Stage Diameter (m, scale 1): 0.01158 0.0579 0.2895Third Stage Diameter (m, scale 2): 0.11524 0.1502 0.325
Table Created by Chris Strauss
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Backup Slides-CFD Models to be used for GAMBIT griding of project rocket
•Initial models of project rocket
•Model would have been used to simulate each stage of flight in Fluent
Models Created by Chris Strauss
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Backup Slides-CFD CMARC Model
•Model of aircraft launched rocket initially conceived
•Model was flexible enough so that multiple configurations could be made quickly
•Model was scrapped after it was discovered CMARC results are only valid to Mach 0.9
Model Created by Chris Strauss
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Drag Coefficient Standard Deviation
Method– Create a randomizer that produces random
values of angle of attack from 0-10 degrees
– Fed angles of attack into Cd code to obtain values for Cd
• Cd code created by Jayme Zott
– Entered values for Cd into Excel to calculate standard deviation with standard deviation function
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Top Down View
Fig. by Kyle Donohue
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Though an aircraft launch was not put into operation. A wing would be beneficial if it were.
A wing creates an additional nose up pitching moment allowing the launch vehicle to pitch from an initial horizontal configuration (α=0°) into a final vertical configuration (α=90°).
Wing Moment Coefficient versus AoA
Fig. by Brian Budzinski
Shear on Launch Vehicle from Wing
Fig. by Brian Budzinski
Shear on Launch Vehicle from Fins
Fig. by Brian Budzinski
Shear Coefficient on Launch Vehicle from Wing
Fig. by Brian Budzinski
The shear created through the addition of a wing or fins is assumed
to be equal to the normal force caused by the corresponding part.
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Wing Normal Force Coefficient versus AoA
Fig. by Brian Budzinski
Wing Axial Force Coefficient versus AoA
Fig. by Brian BudzinskiASSUMPTIONS:
Initial Horizontal Launch Configuration
Final Vertical Configuration
Newtonian Model
Delta Wing
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Wing Lift Coefficient versus AoA
Fig. by Brian Budzinski
Wing Drag Coefficient versus AoA
Fig. by Brian Budzinski
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ASSUMPTIONS:
Initial Horizontal Launch Configuration
Final Vertical Configuration
Newtonian Model
Delta Wing
Drag Coefficient versus Lift Coefficient
Fig. by Brian Budzinski
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ASSUMPTIONS:
Initial Horizontal Launch Configuration
Final Vertical Configuration
Newtonian Model
Delta Wing
Once the lift and drag coefficients are determined, the lift versus drag curve can be created.
Side View
Fig. by Kyle Donohue
Launch vehicle with a pair of fins.
Beneficial for:
•Stability Control
•Ground Launch
•Aircraft Launch
•Balloon Launch
Fins were not implemented because D&C was able to successfully control the launch vehicle without them.
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cossin AND CCC
coscoscossin3
4
eLELELE
N kS
lRC
2coscoscoscos23
4
eLELELE
A
k
S
lRC
c
zC
c
xCC LE
LEALE
LENm ,,
sincos ANL CCC
Wing Analysis
Divide the wing up into two sections: leading edge and lower surface.
These two are chosen because they are the two portions exposed to the relative wind once given an angle of attack.
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2sin
S
SkC LSLSN
2.0
5.125.2 sincos000,1070.05.4sin048.0
cV
V
S
SGC w
A
c
zC
c
xCC LS
LSALS
LSNm ,,
Wing Analysis Continued
Lower Surface Eqns.
A similar analysis can be done for a pair of fins.
AAE 450 Spring 2008Aerothermal
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References
Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp. 303-312
Anderson, John D., Fundamentals of Aerodynamics, Mcgraw-Hill Higher Education, 2001
Professor Colicott, in reference to linearized theory applications
AAE 450 Spring 2008Aerothermal
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References
Barrowman, James and Barrowman, Judith, "The Theoretical Prediction of the Center of Pressure" A NARAM 8, August 18, 1966. www.Apogeerockets.com
Klawans, B. and Baughards, J. "The Vanguard Satellite Launching Vehicle - an engineering summary" Report No. 11022, April 1960
Morrisette, E. L., Romeo D. J., “Aerodynamic Characteristics of a Family of Multistage Vehicles at a Mach Number of 6.0”, NASA TN D-2853, June 1965
Professor Williams, concerning the use of pressure coefficients to determine aerodynamic forces
The entire Aerothermodynamics group for their invaluable help and support
Anderson Jr., John D., “Hypersonic and High-Temperature Gas Dynamics”, 2nd ed., AIAA, Reston, VA, 2006.
Schneider, Steven P., “Methods for Analysis of Preliminary Spacecraft Designs”, AAE450, Spacecraft Design, Purdue University
Schneider, Steven P., personal conversation
http://www.omega.com/literature/transactions/volume1/emissivitya.html http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080005052_2008005
139.pdf http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19740009531_1974009
531.pdf
References
References
Wade, M., “Vanguard”, 1997-2007.
[http://www.astronautix.com/lvs/vanguard.htm]
Tsohas, J., “AAE 450 Spacecraft Design Spring 2008: Guest Lecture Space Launch Vehicle Design”, 2008
“The Vanguard Report”, The Martin Company, Engineering Report No. 11022, April 1960
38AAE 450 Spring 2008Aerothermal
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References
Hankey, Wilbur L., Re-Entry Aerodynamics, AIAA, Washington D.C., 1988, pp. 70-73
Rhode, M.N., Engelund, W.C., and Mendenhall, M.R., “Experimental Aerodynamic Characteristics of the Pegasus Air-Launched Booster and Comparisons with Predicted and Flight Results”, AIAA Paper 95-1830, June 1995.
Anderson, John D., Fundamentals of Aerodynamics, Mcgraw-Hill Higher Education, 2001
Ashley, Holt, Engineering Analysis of Flight Vehicles, Dover Publications Inc., New York, 1974, pp. 303-312
The Martin Company, “The Vanguard Satellite Launching Vehicle”, Engineering Report No. 11022, April 1960.
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