Optimization in the MASIV Scramjet Model - AERO 714dalle/presentations/AERO-714-masiv-and... · Jet...

MASIVOptimization

Dalle et al.

MASIVOverviewMotivation

Inlet model

Combustor model

OptimizationPrevious work

Further work

IntegerprogrammingRelaxation

Mixed-integernonlinearprogramming

Software

Optimization in the MASIVScramjet Model

AERO 714

Derek J. Dalle and Sean M. TorrezAdvisor: James F. Driscoll

April 28, 2011

CCCS

MASIV Optimization, AERO 714 1/23

MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Canonical Vehicle

8 1a 1b1c

1d 2a 3a 4a 4b 5a 6a

Several inlet ramps for compression efficiencyArbitrarily shaped, variable-area ductFuel injection trough any number of portsJet mixing in combustorNozzle with recombination and external expansion

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

The Michigan/AFRL Scramjet In Vehicle code

InletWave interactions solved using exact solution toRiemann problemsExpansions discretizedUp to 10,000 distinct regions tracked

CombustorRealistic fuel-air mixing from jet lawsFinite-rate chemistry pre-tabulated from flameletsolutionsVariable fuel injection and duct area change

Isolator/nozzleNeither of these is finishedInlet model can be applied to nozzleNeeds to handle subsonic/supersonic transitions

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Control design and evaluation

Control of air-breathinghypersonic vehicles notwell studiedCFD not yetappropriate for thisproblemImportant for our viewof optimizationRequires very fastmodel

Pole-zero diagram for previous MASIVvehicle model

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Previous work and motivation

Inlet optimizationCFD-based inletoptimization3D inward-turninggeometryDifficult to chooseobjective functions.

Inward-turning inlet geometry, Peterson et al.a

aD. M. Peterson, G. V. Candler, and T. W.Drayna. “Detached Eddy Simulation of a GenericScramjet Inlet and Combustor”.

Control designSimple models for manyhypersonic vehiclephenomenaQualitatively inaccurate

Control-oriented scramjet architectureb

bM. A. Bolender and D. B. Doman. “NonlinearLongitudinal Dynamical Model of an Air-BreathingHypersonic Vehicle”. Journal of Spacecraft andRockets. 44.3

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Aerodynamic model (SAMURI)

Uses oblique shock theory

Discrete expansion waves

Arbitrary number of waveinteractions

Accounts for caloricallyimperfect gas

Any geometry with nodetached waves

Figure: Two diamond airfoilsin M∞ = 2, α = 0 flow

Figure: Sample inlet geometry at M∞ = 8

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Riemann problem

Discontinuous regionscome in contact whenshocks intersectRegions B and C musthave the same pressureDensity andtemperature may differFlow matches directionWaves separate regionsA from B and D from C

Zoom in on a generic flow

A

B

C

D

ΘB

ΘA

ΘD

ΣA

ΒA

ΣD

ΣC

ΜD

ΜC

Sketch of two interacting waves.

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Inlet geometry

Inlets have a certainnumber of ramps tocompress the flow andthen a certain numberof cowl turns to returnthe flow to horizontalWeaker shocks and lessloss of total pressurewith more shocksWave interactions playa huge roleIntroduces integervariables into theoptimization problem

H1z

x

M¥

Α

x1a x1b x1c x1dx1e x2a

z1az1b

z1c

z1dz1e

Sample inlet geometry with threeramps and one cowl turn

H1z

x

M¥

Α

L1

Sample inlet geometry with threeramps and two cowl turns

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Comparison to CFD

Results from CFD++.

Results from reduced-order model.

Darker colors represent higher pressures, blackcorresponds to p/p∞ = 90

Maximum error is about 6%CFD model included viscosity

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Flow along outflow plane

Inviscid inlet model

CFD

20 25 30 35 40 45 501.00

0.98

0.96

0.94

0.92

0.90

p � p¥

Hz -

z1a

L� H

1

Comparison of pressure along the downstream edge ofthe inlet

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Stationary Laminar Flamelet Model

Turbulent flame is represented as small regions oflaminar flame wrinkled by turbulenceFlame is portrayed in the mean, with a variance anda probability density function for fluctuations

Fuel

AirFlam

e

Progress

Fuel

Air

Flame

Progress

MeanContour

Sandia National Labs Flame “d”

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Three-dimensional mixing

Mixing in real engines is a fundamentally 3D process

Mixing occurs in a horseshoe pattern of acounter-rotating vortex pairVortices and turbulence cause the fuel stream to mixwith the air streamAverage mixing can be computed using similaritysolutions and PDFs

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Similarity solution

Hasselbrink and Mungal (2001) provideexperimentally chosen parameters for scaling lawMean quantities are mapped onto domain based ongeneralized scaling lawCircular jet spreading and fuel mixing, Guassianradial decay

Typical plane slices of mixture fraction showing effects of jet mixing

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Vehicle optimization

8 1a 1b1c

1d 2a 3a 4a 4b 5a 6a

Optimization goalsMaximize thrustControllable vehicleReasonable control surfaces and deflectionsHigh specific impulseThermal vehicle closure

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Previous inlet optimization

Pressure recovery factorSingle-condition designRatio of stagnation pressure,p0,2/p0,∞, decreased by strongshocksWeak indicator of thrustOptimization can be solvedanalyticallyc

UnrealisticTemperature and pressureseem to be more important

cM. K. Smart. “Optimization of Two-DimensionalScramjet Inlets”. Journal of Aircraft. 36.2

One-turn inlet at ideal conditions

Two-turn inlet at ideal conditions

Three-turn inlet at optimum pressurerecovery factor

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Robust inlet optimization

Single-condition designApparently excellentperformance at one conditionDifficult/impossible to control(high sensitivities)Performance curve is jaggedNarrow operating range

Range of conditionsOperating range specified as partof designPerformance curves smoothwithin that range

improved design

single-condition design

6 7 8 9 100.3

0.4

0.5

0.6

0.7

0.8

M¥

p 0,2

�p 0

,¥

single-condition design

improved design

6 7 8 9 10

40

50

60

70

M¥

p 2�p ¥

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Future design optimization

Multi-disciplinary optimizationNumber of rampsFuel injectionNozzle geometryAerothermoelastic considerationsTrajectory

Multi-objective optimizationThrust and dragControllability and operatingrangeTrajectory considerationsThermal considerations

8 1a 1b1c

1d 2a 3a 4a 4b 5a 6a

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

General integer optimization

Nonlinear integer program

min f (x)

s.t. g(x)≤ 0

x ∈ X ⊆ Zn

ApproachesTry every x ∈ Zn

Genetic optimizationRelaxation

Solve continuous alias of the programPick an integer that is “near” the continuous optimum

Well-known problem if f (x) is linearAlso some tools if X ⊆ {0,1}n

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Relaxation

Nonlinear integerprogram

min f (x)

s.t. g(x)≤ 0

x ∈ X ⊆ Zn

Relaxation ofnonlinear integerprogram

min f (y)

s.t. g(y)≤ 0

y ∈ conv(X)⊆ Rn

Hopefully f : Rn→ Rmakes senseSame for g : Rn→ Rm

Otherwise construct analias function

f̂ : conv(X)→ Rf̂ (y) = f (x) for all y ∈ XUse interpolation forany y 6∈ X

How to find x∗ given y∗

Just try all the options if Xis small

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Example of relaxation problem

Examplef (x) = (x− x0)

TQ(x− x0)

0≤ x1 ≤ 7

0≤ x2 ≤ 6

x0 = [3.1 2.5]T

Q =

[42.67 −49.41−49.41 57.38

]Solutionx∗ = [6 5]T

f (x∗) = 1.0347f (3,2) = 9.8307f (4,3) = 4.4387

Contour plot of example problem

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

General mixed-integer nonlinear program

MINLP

min f (x,y)

s.t. g(x,y)≤ 0

x ∈ X ⊆ Zn

y ∈ Y ⊆ Rm

Separated MINLP

min F(x)

x ∈ X ⊆ Rn

F(x0) = min f (x0,y)

s.t. g(x0,y)≤ 0

y ∈ Y ⊆ Rm

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Parameter-dependent dimension

Variable-dimension MINLP

min f (x,y)

s.t. g(x,y)≤ 0

x ∈ X ⊆ Zn

y ∈ Y ⊆ Rh(x)

h : X→ Z

Very common engineering problemPrevious approaches all apply, but no need to usebranch and bound on y

Interpolations lose their meaningSeparating problem recommended; hopefully X issmall

CCCS


MASIVOptimization

Dalle et al.


Inlet model

Combustor model


Further work



Software

Numerical function project

If f happens to be linear and X ⊆ {0,1}n, Matlab hasa function (bintprog)For functions of limited complexity, MATHEMATICAhas a function (Minimize or NMinimize)I have a function freely available

Not sophisticated (implements “try everything”method for general problem)Programmed in Matlab with similar syntax tofminconCan easily be found on AFS (or mfile) at/afs/umich.edu/user/d/a/dalle/Public/MATLABToolsOther tools available, too (including a dramaticupgrade of fsolve)

CCCS


Optimization in the MASIV Scramjet Model - AERO 714dalle/presentations/AERO-714-masiv-and... · Jet...

Documents

Transcript of Optimization in the MASIV Scramjet Model - AERO 714dalle/presentations/AERO-714-masiv-and... · Jet...