Research & Development

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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2

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.


3

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


Vanguard Check – subsonic case using Fluent

Velocity VectorsRed – 401 m/sGreen – 225 m/s

Static PressureRed – 1.18 atmBlue – .364 atm


5

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.







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.







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


Shear on Launch Vehicle from Fins


Shear Coefficient on Launch Vehicle from Wing


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


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


Wing Drag Coefficient versus AoA



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ASSUMPTIONS:



Newtonian Model

Delta Wing

Drag Coefficient versus Lift Coefficient



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ASSUMPTIONS:



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.


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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


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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

http://www.apogeerockets.com/

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

http://www.omega.com/literature/transactions/volume1/emissivitya.html

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080005052_2008005139.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

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.

Documents

Research & Development