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 2008
Aerothermal
1
Drag Model:
Historical Data
Assumptions:
Assumptions:
•Correct Historical
Data
•“Normal” Geometry
•Smaller Diameter
than the Vanguard
Subsonic
CD = 0.55
Transonic
CD = 0.65
Supersonic
CD = 0.60
-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 2008
Aerothermal
2
Drag Model:
Geometric Data
Assumptions:
•Linear Perturbation Theory
(Linearized Supersonic Theory)
(Linearized Subsonic Theory)
Axial Force Coefficient
= Drag Coefficient
(at α=0°)
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.
AAE 450 Spring 2008
Aerothermal
3
200 g
Coefficient of Drag
1.5
1.3
1.1
Cd
0.9
1 Kg
1.5
0.5
1.3
0.3
1.1
0.1
0.9
Cd (historical)
0.7
-0.1 0
1
2
Cd
(dimensional)
0.5
4
5
5 Kg
1.5
1.3
1.1
0.9
0.7
0.5
0.3
0.1
-0.1 0
0.3
0.1
-0.1 0
3
Mach
1
2
3
4
5
Cd
Cd
0.7
Mach
1
2
3
4
5
Mach
Plot Authors: Woods, Zott
AAE 450 Spring 2008
Aerothermal
2
Vanguard Check – subsonic case using Fluent
Velocity Vectors
Red – 401 m/s
Green – 225 m/s
AAE 450 Spring 2008
Aerothermal
Static Pressure
Red – 1.18 atm
Blue – .364 atm
5
Vanguard Check – subsonic case using Fluent
Static Temperature
Red – 300 K
Blue – 220 K
AAE 450 Spring 2008
Aerothermal
6
1 kg launch vehicle – Mach 1 case using Fluent
Pressure
Red – 1.56 atm
Blue – .373 atm
AAE 450 Spring 2008
Aerothermal
7
1 kg launch vehicle – Mach 1 case using Fluent
Velocity
Red – 411 m/s
Green – 208 m/s
AAE 450 Spring 2008
Aerothermal
8
200 g Aerodynamic Loads
Table 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
AAE 450 Spring 2008
Aerothermal
9
1 kg Aerodynamic Loads
Table 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
94.2
47.3
335.7
-43.0
40.0
1.44
63
168.9
-21.6
40.0
0.81
240
21
Normal Force [N]
Axial Force [N]
Shear Force [N]
Center of Pressure [% length]
Coefficient of Drag CD
Dynamic Pressure [Pa]
CD % error [%]
AAE 450 Spring 2008
Aerothermal
10
5 kg Aerodynamic Loads
Table 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
AAE 450 Spring 2008
Aerothermal
11
Creation of the Pressure Distribution
C p ,upper 
C p ,lower 
2    
M 2 1
2    
M 2 1
AAE 450 Spring 2008
Aerothermal
C p  C p ,lower *cos( )
12
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
Cp 
M 2 1
1
CN 
S
CM
1

S
L
2
  r  dz  C
0
p
cos  d
0
2
L
  r  z  dz  C
0
L
p
cos  d
0
2
1
C A   (2 r )dy  C p cos  d
S0
0
X CP
AAE 450 Spring 2008
Aerothermal
CM

CN
13
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
AAE 450 Spring 2008
Aerothermal
14
Stresses due to Aerodynamic Force
Bending Moment vs. Mach Number for the 5 kg case at 0 aoa
 Shear Stress
0
0
– Differential
of Normal
Force
between
stages
– A*q∞*S
 Bending
Moment
 Picture by
Jayme Zott
and Alex
Woods
1
1.5
2
2.5
3
3.5
4
4.5
5
-2000
-4000
-6000
Bending Moment (N*m)
 Axial Loading
0.5
-8000
-10000
Bending Moment
-12000
-14000
-16000
-18000
-20000
Mach Number
AAE 450 Spring 2008
Aerothermal
15
Pictures
Normal Force in
Newtons
Normal Loading vs. Mach Number for a family of
Launch Vehicles at 0 aoa
700
600
500
400
300
200
100
0
5 kg
1 kg
200 g
0
1
2
3
4
5
Mach Number
AAE 450 Spring 2008
Aerothermal
16
Pictures
Pitching Moment in
Newton Meters
Pitching Moment Vs. Mach Number for a family of
Launch Vehicles at 0 aoa
2000
1500
5 kg
1000
1 kg
200 g
500
0
0
1
2
3
4
5
Mach Number
AAE 450 Spring 2008
Aerothermal
17
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
AAE 450 Spring 2008
Aerothermal
18
Heating Rate
3
0
1
2
 wc p
 Assumptions
–
–
–
–
–
–
dT0
1
rn  (q0  q2 )   T0 4
dt
2
Lumped Heating at Solid Nosetip Method
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
AAE 450 Spring 2008
Aerothermal
19
Equations
dT
cp
 wV   (q  qr   Tw4 )dA
dt
qr = radiation from fluid to surface
q   C  N vabs M
-8

1
2
1
2
rn
= nose body radius
V
= volume of solid nosetip
gw =
C = (1.83e )rn (1-g w )
q2  C1  N vabs M 2
M = 3, N = 0.5
for fully catalytic surface
M2 = 3.2 for laminar, flat
plate
1

2
C1  (2.53e9 )(cos  ) (sin  )( x )(1  g w )
Heating rate at point 2 on the nose cone
AAE 450 Spring 2008
Aerothermal
hw
wall enthalpy
=
ho
total enthalpy
h w = cpw Tw
h o = h a + 0.5V 2
h a = cpa Ta
20
Heating Rate
Matlab code:
*help from Vince Teixeira
AAE450_Stag_heat_analysis.m
Uses trajectory outputs (.mat files)
Input: d
v
r
- diameter (m)
- velocity (m/s)
- 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
tw
Tw
AAE 450 Spring 2008
Aerothermal
- heating rate (W/m2)
- thickness (mm)
- wall temperature (K)
21
Heating Rate
Heating rate vs. time, 1 kg payload
600
500
Heating rate (W/m 2)
400
300
200
100
Titanium
Steel
Aluminum
0
-100
0
20
40
60
80
100
120
140
time (s)
AAE 450 Spring 2008
Aerothermal
22
Backup Slides- Sizing Code Tables
 Initial Sizing Code Table of Results
450R
Payload Mass 1 (kg):
Payload Mass 2 (kg):
Payload Mass 3 (kg):
0.2
1
5
Overall Length (m, scale 1):
Overall Length (m, scale 2)
PM 1
0.48298
0.5112
PM 2
PM 3
2.4149 12.0745
2.556
12.78
First Stage Length (m):
First Stage Diameter (m, scale 1):
First Stage Diameter (m, scale 2):
0.25268
0.02836
0.6953
1.2634
0.1418
0.7357
6.317
0.709
0.9377
Second Stage Length (m):
Second Stage diameter (m, scale 1):
Second Stage Diameter (m, scale 2):
0.11404
0.02034
0.38582
0.5702
0.1017
0.4271
2.851
0.5085
0.6335
Third Stage Length (m):
Third Stage Diameter (m, scale 1):
Third Stage Diameter (m, scale 2):
0.05532
0.01158
0.11524
0.2766
0.0579
0.1502
1.383
0.2895
0.325
Table Created by Chris Strauss
AAE 450 Spring 2008
Aerothermal
23
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
AAE 450 Spring 2008
Aerothermal
24
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
AAE 450 Spring 2008
Aerothermal
25
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
AAE 450 Spring 2008
Aerothermal
26
Wing Moment Coefficient versus AoA
Top Down View
Fig. by Brian Budzinski
Fig. by Kyle Donohue
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°).
AAE 450 Spring 2008
Aerothermal
27
Shear on Launch Vehicle from Wing
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.
Shear on Launch Vehicle from Fins
Fig. by Brian Budzinski
AAE 450 Spring 2008
Aerothermal
28
Wing Axial Force Coefficient versus AoA
Wing Normal Force Coefficient versus AoA
Fig. by Brian Budzinski
Fig. by Brian Budzinski
ASSUMPTIONS:
Initial Horizontal Launch Configuration
Final Vertical Configuration
Newtonian Model
Delta Wing
AAE 450 Spring 2008
Aerothermal
29
Wing Lift Coefficient versus AoA
Wing Drag Coefficient versus AoA
Fig. by Brian Budzinski
Fig. by Brian Budzinski
ASSUMPTIONS:
Initial Horizontal Launch Configuration
Final Vertical Configuration
Newtonian Model
Delta Wing
AAE 450 Spring 2008
Aerothermal
30
Once the lift and drag coefficients
are determined, the lift versus drag
curve can be created.
Drag Coefficient versus Lift Coefficient
ASSUMPTIONS:
Fig. by Brian Budzinski
Initial Horizontal Launch Configuration
Final Vertical Configuration
Newtonian Model
Delta Wing
AAE 450 Spring 2008
Aerothermal
31
Launch vehicle with a
pair of fins.
Beneficial for:
•Stability Control
•Ground Launch
•Aircraft Launch
•Balloon Launch
Side View
Fig. by Kyle Donohue
Fins were not implemented because D&C was able to
successfully control the launch vehicle without them.
AAE 450 Spring 2008
Aerothermal
32
Wing Analysis
C L  C N  cos   C A  sin 
CD  CN  sin   C A  cos 
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.
 4  RLE  l LE 
CN  
  k LE  sin  cos  e  cos   cos  
3 S


 4  RLE  l LE  k LE
2
CA  
 cos cos  e  cos   cos  

3 S

 2
C m  C N , LE
x LE
c
 C A, LE
z LE
c
AAE 450 Spring 2008
Aerothermal
33
Wing Analysis Continued
Lower Surface Eqns.
C N  k LS
 S LS 

  sin 2 
 S 
2.25
1.5
 S w  0.048 sin 4.5   0.70V 10,000 cos   sin 
CA  G   
V  c   0.2
 S 
C m  C N , LS
x LS
c
 C A, LS
z LS
c
A similar analysis can be done for a pair of fins.
AAE 450 Spring 2008
Aerothermal
34
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 2008
Aerothermal
35
References

Barrowman, James and Barrowman, Judith, "The Theoretical
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
Prediction of
References

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
 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
AAE 450 Spring 2008
Aerothermal
38
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.
AAE 450 Spring 2008
Aerothermal
39