optimization in the masiv scramjet model - aero 714dalle/presentations/aero-714-masiv-and... · jet...
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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.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 2/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 3/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 4/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 5/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 6/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 7/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 8/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 9/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 10/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 11/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 12/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 13/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 14/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 15/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 16/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 17/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 18/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 19/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 20/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 21/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 22/23
MASIVOptimization
Dalle et al.
MASIVOverviewMotivation
Inlet model
Combustor model
OptimizationPrevious work
Further work
IntegerprogrammingRelaxation
Mixed-integernonlinearprogramming
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
MASIV Optimization, AERO 714 23/23