Interactions between Flight Dynamics and Propulsion ...dalle/presentations/defense-dalle.pdf · Introduction Motivation Modeling SAMURI Ram mode Fight Dynamics Ram-Scram Transition

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart

Design andOptimization

Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Interactions between Flight Dynamics andPropulsion Systems of Air-Breathing

Hypersonic VehiclesDefense Presentation

Derek J. Dalle

Chair: James F. DriscollCognate: David J. Singer

Members: Joaquim R. R. A. Martins and Michael A. Bolender

March 21, 2013

Hypersonic Couplings, Defense 1/41

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Motivation: Use the oxygen from the atmosphereEven at really high speeds

Compression Expansion

Compressor work

AIR AIR+PRODUCTS(faster)(fast)

Energy added

Air-breathing engine

Combustor


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Motivation: Use the oxygen from the atmosphereEven at really high speeds

Inlet compression

Nozzle expansion

AIR AIR+PRODUCTS(faster)(fast)

Energy added

Air-breathing engine

Combustor


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Scramjets could be a transformational technologyOr possibly not. . .

Flight Mach number, M

Spec

ific

Impu

lse,

I sp [

s]

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

00 2 4 6 8 10

Turbofan

Turbofan with afterburner Ramjet

ScramjetRocket

Theoretical maximumHydrocarbon fuel in air

Theoretical maximumHydrogen fuel in air


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Movie of shocks in the inletFrom Mach 6 to Mach 12, zero angle of attack


inlet-movie.mp4Media File (video/mp4)

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Vehicle ConceptHighlights of the dynamic components

Exterior compression

Internal compression Internal combustion Expansion

Control surfaces


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Vehicle ConceptHighlights of the dynamic components

Exterior compression

Internal compression Internal combustion Expansion

Control surfaces

Diffuser

Internal compressionInternal combustion

Turbine

Expansion

Image credit: Wikimedia Commons user Boeing 757 maya


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Example of Tight CouplingAccelerate and maintain level flight

1. Increase the equivalence ratio 2. More lift from nozzle

3. Lower ; lower drag 4. TE-up elevon deflection

Starting from a steady, level flight condition, we want to accelerate

The first step is to increase the thrust

This increases the nozzle lift; reduces angle of attack ()

Lower drag due to angle of attack (usually . . . )

Net lower nose-up moment; change elevon setting


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions


1. Increase the equivalence ratio

2. More lift from nozzle








HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions










HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions



3. Lower ; lower drag

4. TE-up elevon deflection







HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions










HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

GOALS

Develop a tip-to-tail vehicle model that can be evaluated in about asecond (with a single processor)

MASIV: Michigan/AFRL Scramjet In VehicleSAMURI: Supersonic Aerodynamic Method Using RiemannIinteractionsMASTrim: Michigan/AFRL Scramjet Trim

Understand ram-to-scram transition and unstart

Collaborate with control design and control evaluation efforts

Model and describe ascent trajectories

Investigate effects of various design variables


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Example SAMURI solutionsA sample inlet solution (temperature in K)

0 2 4 6 8 10 12 14

3

2

1

0

x [m]

y[m

]

300400

500600700

8009001000

11.5 12 12.5 13 13.5 14

2.6

2.4

2.2

x [m]

y[m

]

300400

500600700

8009001000


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

SAMURISupersonic Aerodynamic Method Using Riemann Interactions

Something needed to solve for supersonic flows . . .

. . . with strong shocks, expansion fans, shock interactions, etc.

Two diamond airfoils, M = 2, = 0

A

B

C

D

A A

A

D

A

A

C

D

C

D

B = C

shock

wave

expansion fan

slip line / contact discontinuity

Sketch of two interacting waves

Hopefully it will apply to a wide variety of geometries.Hypersonic Couplings, Defense 9/41

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

SAMURIcomparison with CFDM = 10, h = 16 km, static temperature contours

Solution from CFD++

Solution from SAMURI


domain

physical geometry

initial conditions: p, , T, M

1

initial direction

shock

Mach wave

21

21

4

3

expansion fan

shock (continuation)

Mach wave (continuation)

21

4

3

5

6

7 shock

shockslip line

expansion fan(continuation)

2

4

1

3

5

7

6

89

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Dual-mode combustionMASIV and the ram mode solution method

1.0

2.0

3.0M

ach

num

ber, M

0.0

2 3 4


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions


1.0

2.0

3.0M

ach

num

ber, M

0.0

2 3 4

Increase the fuel until M4 = 1


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions


1.0

2.0

3.0M

ach

num

ber, M

0.0

2 3 4

Adding more fuel causesthe scram solution to choke.


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions


1.0

2.0

3.0M

ach

num

ber, M

0.0

2 3 4

Try a normal shock isolator; M4 < 1


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions


1.0

2.0

3.0M

ach

num

ber,

M

0.0

2 3 4

Find correct M3 value such that M4 = 1


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Equations of motion at hypersonic speeds

Zero speed: Ball drops.

Orbit!

Hypersoniccase:

more complicated

General nonlinear equations of motion:

x = f(x,u)

State variables:

x = [ L h V P Q R ]T

Control variables:

u = [ ER CE DE CR ]T

Trim:Now I want to pick some of the states () and all of thederivatives (x), and I want to use the controls and theremaining states () to satisfy the equations of motion.

Example: Fix h, V , and =. Now find , ER, and CEto trim the vehicle.


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Fuel consumption map, a = 0 m/s2Higher dynamic pressure is always better?

Flight Mach number, M7 8 9 10 11 12

26

28

30

32

34

36

5 kg/s

4 kg/s

6 kg/s

m f =

7 kg/s

.minim

um fuel

consum

ption

Alti

tude

, h [

km]

q = 100 k

Pa

q = 50 k

Pa


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Fuel comsumption map, a = 1 m/s2Higher dynamic pressure is always better?

11


Alti

tude

, h [k

m]

7 8 9 10 11 12

26

28

30

32

34

36

mf = 8 kg/s

.

5 kg/s

6 kg/s

7 kg/s

minimum fu

el consumpt

ion

q = 100 k

Pa

q = 50 k

Pa


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Why did this happen?That is, dynamic pressure and the engine

Well, first the lift is approximately independent of the dynamic pressure,

L = qSCL (1)

and so higher dynamic pressure means lower lift coefficient. This almostalways results in less drag.

D = qSCD qSCD0 +KL2

qS(2)

For steady, level flight, this is also the thrust (approximately).

CT (ER,M,) =T

qS CD0 +

KL2

q2S2(3)

A very low angle of attack is bad for CT , so there is a best q.

ma qS(CT CD) (4)


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Why did this happen?That is, dynamic pressure and the engine

Well, first the lift is approximately independent of the dynamic pressure,

L = qSCL (1)

and so higher dynamic pressure means lower lift coefficient. This almostalways results in less drag.

D = qSCD qSCD0 +KL2

qS(2)

High acceleration favors higher dynamic pressures

CT (ER,M,) =T

qS CD0 +

KL2

q2S2+

maq2S2

(3)

But acceleration is like thrust minus drag.

ma qS(CT CD) (4)


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Ram-to-Scram Transition

1.0

2.0

3.0M

ach

num

ber, M

0.0

2 3 4


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Ram-scram transition on the flight corridor mapEffect of acceleration

4.5 5.0 5.5 6.0 6.5 7.018

20

22

24

26

28


Alti

tude

, h [k

m]

q = 100 k

Pa90 kP

a80 kPa

70 kPa

60 kPaq

= 50 kP

a

a =

0 m

/s2

2 m/s

2

a = 6

m/s2

4 m/s

2


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Ram-scram transition on the flight corridor mapEffect of acceleration

4.5 5.0 5.5 6.0 6.5 7.018

20

22

24

26

28


Alti

tude

, h [k

m]

q = 100 k

Pa90 kP

a80 kPa

70 kPa

60 kPaq

= 50 kP

a

a =

0 m

/s2

2 m/s

2

a = 6

m/s2

4 m/s

2

This has the same explanationas the fuel consumption maps.

Reason for positive slope:Lower dynamic pressure Higher CL More dragLower slopes at higheraccelerations:Higher acceleration Thrust greater than drag Greater effect of q

ma qA(CT CD)


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Comparison to experiment

Experimental data from Fotia and Driscoll1

900 1000 1100 1200 1300 14000.0

0.1

0.2

0.3

0.4

0.5

Isolator stagnation temperature, T02 [K]

Equi

vale

nce

ratio

, ER

scram mode

ram mode

ram mode measuredscram mode measured

normal sh

ock limit

scram limit

ram limit

overfueling instability region

Comparison between experimentaldata and MASIV predictions. Soliddots are measured ram cases.

Experimental geometry

nozzle

fuel injection port

constant-area isolator

static pressure taps

combustor

1Fotia, M. L. and Driscoll, J. F., Ram-Scram Transition and Flame/Shock-Train Interactions in a ModelScramjet Experiment, Journal of Propulsion and Power , 2012Hypersonic Couplings, Defense 18/41

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

MASIV results at the jump

10 5 0 5 100.5

1.0

1.5

2.0

2.5

3.0

3.5

Axial coordinate, (x xF ) / H

Mac

h nu

mbe

r, M

scram mode, ER = 0.4487

ram mode, ER = 0.4489

0

2

4

6

8

10

10 5 0 5 10

Axial coordinate, (x xF ) / H

Stat

ic p

ress

ure,

p /p

2

scram mode, ER = 0.4487

ram mode, ER = 0.4489

Sudden jump for very smalldifference in equivalence ratio(as expected)

Pressures almost identical inthe downstream area

Mach numbers a little different

Big change in acceleration

ram: a = 2.00 m/s2

scram: a = 0.53 m/s2

Why?


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Is thrust continuous across ram-scram transition?Lets look at a control volume before and after transition

2 3 4

Scram case just before transition (M4 = 1+):

2 3 4

Now add a tiny bit more fuel:


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Evidence for this interpretation

Heiser and Pratt2 noticed a problem before:

. . . any further increment in [heat addition] unstarts the engine inlet, and any decrement in[heat addition] causes reversion to scramjet operation . . .

Experiments at Michigan3 suggest a different picture (with similarities):

0.0 0.1 0.2 0.3 0.4

0.7

0.8

0.9

1.0

Pressure recovery, (p 3 p2)/p02

Cor

e ar

ea ra

tio, A

3c/A

2

ram mode

scram mode

normal shock limit, M3 = 0.542

observed ram casesfuel off

observed scram

Isolator compression:

p3p2

= 1+M22M2M3

1+ 12 M

22

1+ 12 M23

Separated boundary layer area:

A3cA2

=1

M23

(p2p3

(1+M22)1)

2Heiser, W. H. and Pratt, D. T., Hypersonic Airbreathing Propulsion, AIAA Ed. Series, Washington, DC, 1994, pp. 358359

3Fotia, M. L. and Driscoll, J. F., Experimental Investigation of Ram-Scram-mode Transition Mechanics, 18thAIAA/3AF International Space Planes and Hypersonic Systems and Technologies Conference, 2012, AIAAPaper 2012-5835 Hypersonic Couplings, Defense 21/41

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Engine UnstartUnstarted is not the same as stopped

Definition of unstart margin: Distance from frontof shock train to the front of the isolator (normalized)

=LISOLST

LISO= 1 LST

LISO

Weak shock train: > 0

LISO

LISO

LST

2 3 4


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions



=LISOLST

LISO= 1 LST

LISO

Stronger shock train: > 0, decreases

LISOLST

2 3 4

LISO


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions



=LISOLST

LISO= 1 LST

LISO

Strong shock train: < 0, unstart

LISOLST

2 3 4

LISO


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Flight corridor map for steady flight (a = 0 m/s2)Unstart margin on flight envelope

4.4 4.6 4.8 5.0 5.2 5.4

18

20

22

24

26


Alti

tude

, h [

km]

q = 50 kPa

60 kPa

70 kPa

80 kPa

90 kPa

100 kPa

unstart

ram scram

= 0.4

= 0.

1

= 0.0 (unstart)

ram-scram transition

0.2

0.3

A

BC


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Unstart marginAll q = 100 kPa conditions considered

4.5

0.5


Uns

tart

mar

gin,

=

1

LST

/LIS

O

5.0 5.5 6.0 6.5

0.2

0.1

0.0

0.1

0.2

0.3

0.4

normal shock limit

a = 0

m/s2

1 m/s

2

2 m/s

2

3 m

/s2

4 m

/s2

5 m/s

2

6 m/s2

unstart line

ram-scram transition

1.0

~~

scram solutions ( = 1)

A

D

B

C


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Flight corridor map for varying accelerationThis is how unstart shows up on the flight envelope

4.518

Alti

tude

, h [

km]


5.0 5.5 6.0 6.5 7.0

20

22

24

26

28

q = 50 k

Pa 2 m/s

2

a = 4 m

/s2

amax < 0 m/s20 m/s2 < amax < 2 m/s22 m/s2 < amax < 4 m/s2

60 kPa

70 kPa

A

B

0 m/s

2

q = 100

kPa90 k

Pa80 k

Pa


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Framework for improving the design of MAX-1

EX

ISTIN

G K

NO

WL

ED

GE

BA

SE

Pick objective functions Fuel consumption Specific impulse

Stability Constraint

"Co-optimization" Trajectory variables Design variables

Optimization approach Conclusions?

IMPR

OV

ED

KN

OW

LE

DG

E B

ASE

Trajectory optimization Acceleration profile Effects of dynamic pressure

Optimization General guidelines

Sensitivity analysis Changes to design variables

Measure objectives

Identify most important vars Design Mach number Design Mach range


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Objective functions

If we just pick total fuel mass consumed (mf ), we might get

Alternative 1: Fix the payload mass. . .

Alternative 2: Use a rocket-equivalent specific impulse

V = gIsp lnm1

m1mfIsp =

V2V1g ln(m1/(m1mf ))

This almost eliminates the effect of mass, as we will see.


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Center of mass shiftno change in mass

center of volumecenter of mass

center of pressure

Lvehiclexcg

weight

aero forces


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Effect of moving the center of gravitySurprise! Moving the center of gravity forward improves stability

4 2 0 2 45

0

5

Real part [1/s]

Imag

inar

y pa

rt [1

/s] xcg = 0.05

xcg = 0.025

xcg = 0

M = 5

M = 12

M = 9.2

M = 12


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

What if I make the vehicle heavier?Well, the angle of attack increases, and then. . .

0.6 0.5 0.4 0.3 0.2 0.1 05

0

5

Real part [1/s]

Imag

inar

y pa

rt [1

/s]

M = 12

M = 12

M = 5

M = 5

rf = 0.6 ( )

rf = 0.5 ( )


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Dihedral angleView of vehicle from front

E

dihedral effectfrom body

Actual head-on view of MAX-1:


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Dihedral angleAffects lateral-directional stability and little else

0.20 0.15 0.10 0.05 05

0

5

Real part [1/s]

Imag

inar

y pa

rt [1

/s]

M = 5

M = 12

M = 12

E = 2.86 ( )

E = 2.86 ( )

E = 5.73 ( )


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Performance, selection of design variables, andtakeaways from the sensitivity analysis

xcg = 0

5 6 7 8 9 10 11 12

0.2

0

0.2

0.4

0.6

0.8

Mach number, M

Ang

le o

f atta

ck,

MAX-1

rf = 0.6

range = 0

rp = 75

Mdesign = 8

Changes in stabilityalmost completelydescribed usingangle of attack

Fuel consumptionclosely related to

Dihedral angleisolates Dutch-rollmode

Most effective design variables

Design Mach number (Mdesign) and Mach number range (Mrange)

Also important: angle of attack range (range) and inlet compressionratio (rp)


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Trajectory optimization


Acc

eler

atio

n, a

[m

/s2 ]

7 8 9 10 11 12 130

1

2

3

4

5

mf = 5.0 kg/s.

2.5

7.5

10.0

12.5

15optimum trajectory

initialized with a = 2 m/s2

7 8 9 10 11 12 130.00

0.02

0.04

0.06

0.08

0.10

0.12


0 m/s2

optimum trajectory

1 m/s2

a = 2 m/s2

3 m/s2

4 m/s2

Exha

ust O

2 m

ass f

ract

ion,

YO

2 ,5

Two rules for (scram-mode) trajectory planning

Accelerate at almost the maximum acceleration

Whichever is lower of these two:Equivalence ratio that causes scram-to-ram transitionEquivalence ratio that causes all the O2 to be used


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Optimization: contours of fuel efficiencyOriginal, coarse surrogate (purple points)

Design Mach number, Mdesign

Des

ign

Mac

h w

indo

w w

idth

, Mra

nge

6 7 8 9 10 11 12 130

1

2

3

4

5

6 constraint: Mupper 13

Isp = 750 s

700 s

600 s

500 s

400 s

300 s

constraint: amax > 0

Mupper = 1211

97


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Optimization: contours of fuel efficiencyWith additional points (green) added

Isp = 750 s

700 s

600 s

500 s

400 s

300 sconstraint: Mupper 13

constraint: amax > 0Mupper = 12

119

7Design Mach number, Mdesign

Des

ign

Mac

h w

indo

w w

idth

, Mra

nge

6 7 8 9 10 11 12 130

1

2

3

4

5

6

MAX-1

optimum


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Comparsion of MAX-1 to optimized result

MAX-1

Optimized design, Mdesign = 9.5, Mrange = 0

MAX-1

Optimized design, Mdesign = 9.5, Mrange = 0


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Artificial neural networksFlamelet table data reduction

00.2

0.40.6

0.81

00.2

0.40.6

0.810

0.2

0.4

0.6

0.8

1

fmeansmix

H2

smix fmean00.2

0.40.6

0.81

00.2

0.40.6

0.81

0.2

0

0.2

0.4

0.6

0.8

1

H2

Concept: Approximate species reaction rates() with a combination of simple functions.Currently they are interpolated from a hugetable.

fmean

smix H2

1

2

3st

4

5

6

7

8

9.

Previous work4 has been very closely related.

4Ihme, M., Marsden, A. L., and Pitsch, H., Generation of optimal artificial neural networks using a patternsearch algorithm: Application to approximation of chemical systems, Neural Computation, Vol. 20, No. 2, 2008,pp. 573601 Hypersonic Couplings, Defense 37/41

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Improved modeling of the combustor


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Generic hypersonic vehicles

1u1H1

2u2H2

1 + d1u1 + du1H1 + dH1

2 + d2u2 + du2H2 + dH2

dm12.

dm21.1

2

dx

1212 + d12

w1

w2

dq2

dq1

i

j3

j1

j2

j4

dm. j3,idm. i,j2

dm. j4,i

dm. j1,i

pTuvw

j2j2

j2

j2

j2

j2

dx x

zy


HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Conclusions

MASIV and MASTrim models are a significant improvement forcontrol-oriented hypersonic vehicle modeling

Predictions of unstart and ram-to-scram transition were plotted onthe Flight Corridor Map

Unstart: too high, too slow, or at too great of an accelerationRam-to-scram transition: higher Mach number, lower altitude,decreased acceleration

Strategies for sram-mode ascent trajectory optimizationHigh dynamic pressure (agrees with convention)Near maximum acceleration, limited by either thermal choking oravailable oxygen

Effects of changes to vehicle design

14% reduction in fuel consumption for Mach 7 to Mach 13 trajectoryHypersonic Couplings, Defense 40/41

HypersonicCouplings

Derek J. Dalle

Introduction

Motivation

Modeling

SAMURI

Ram mode

Fight Dynamics

Ram-Scram

Transition

Jumps

Unstart


Objectives

Sensitivities

Trajectories

Cooptimization

Future Work

Conclusions

Acknowledgments

Thank you to my committee!

My parents, who drove in from Iowa

This research was supported by U.S. Air Force ResearchLaboratory grant FA 8650-07-2-3744 for the Michigan Air ForceResearch Laboratory Collaborative Center for Control Science.

Special thanks to Sara Spangelo

Thank you for your time and attention!


IntroductionMotivationModelingSAMURIRam mode

Fight DynamicsRam-ScramTransitionJumps

UnstartDesign and OptimizationObjectivesSensitivitiesTrajectoriesCooptimization

Future WorkConclusions

Documents

Interactions between Flight Dynamics and Propulsion ...dalle/presentations/defense-dalle.pdf · Introduction Motivation Modeling SAMURI Ram mode Fight Dynamics Ram-Scram Transition