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1.
CFD in Aeronautics and Aerospace
Numerical Computation and Modeling of Internal and External Flows
Progress in Aerospace Planes, Aerodynamics, and High-Speed Combustion
Mario Felipe Campuzano Ochoa
Terra Global Energia Investments Ltd.
NASA Fellow ’95 -’98
mfc27@cornell.edu
Cornell Workshop on Large-Scale Wind Generated Power
June 12-13, 2009
Cornell University
Ithaca, New York 14853
1
External Flows - Aerodynamics
Samples of Flows – Subsonic and Separation
Flow Separation
Turbulence
Design is
MULTIDISCIPLINARY
(everything is related and
dependent)
2
2.
The Fluid Dynamics Equation (Navier-Stokes)
dw + dfi = dfvi
dt dxi dxi
r rui 0
ru1 ru1ui si1
w = ru2 fi = ru2ui fvi = si2
ru3 ru3ui si3
rE ruiH sijuj + k dT/dxi
p = (g -1) r {E - 1/2(ui ui)}
Equation solved numerically using optimal and iterative algorithms
3
CFD Stages of Design and Testing
Automatic Modeling
State of the Art Aerodynamic Design
• Integrate the capabilities into an automatic method that
incorporates computer optimization.
Interactive Calculation
Rapid Prediction of Flows
• Can be done when flow calculation can be performed fast enough
• But does NOT provide any direction on how to change the
conditions if performance is not desirable.
Flow Modeling w/ “complex” Boundary Conditions
• Predict the flow past an aerodynamic body or its components in
different flight regimes and paths such as take-off or cruise and
off-design conditions.
Inflatable Reentry Vehicle Concept
4
3.
Design by Numerical Finite Modeling
The method is to define the geometry as
f(x)
f ( x) i bi ( x)
where i weight,
bi ( x) set of shape functions
The finite difference method, translates to a function
I I ( w, ) (such as C D at constant C L )
I I ( i i ) I ( i )
has parameters
i i
I
If the geometry change is n 1 n (small positive )
i
I T I T I
The resulting solution is I I I I I
More complex search may be modeled, such as quasi - Newton.
Issues with the Discretization Models
The number of aerodynamic calculations is proportional to the
number of design variables
Using 2016 grid points
on the wing surface as design variables
2016+ flow calculations
~ 2-5 minutes each (Euler not Viscous
Flow)
Boeing 747 Cost Prohibited for
Industrial Design
4.
System and Feedback Theory in Aero Design
GOAL : Reduction of Computational Costs
Minimization of Drag Optimal Control of Aerodynamic
Equations subject to body changes
Cost function defined
I I ( w, S ) e.g. Minimize CD
change in S gives a change in
I I
T T
I w S
w S
Supposing that the equation R expresses
the dependence of w - S
R ( w, S ) 0
and
R R
R w S 0
w
S
System and Feedback Theory in Aero Design II
The change R is zero, we can multiply by a Lagrange Multiplier
and subtract from the variation I with no changing in result.
I T I T R R
I w S T w S
w F w S
I T R I T R
T w T S
w w S S
Pick to satisfy adjoint equation (Adjoint)
R I
T
w w
first term is canceled, and we find that (Gradient)
I T
R
I T S
S S
2016 variables
In grid
Flow Physics Solution + Ad-joint Solution
5.
Ad-joint Method Characteristics:
• Gradient for N variables
with cost equal to 2 flow solutions
• Minimal memory needs in
comparison with auto differentiation
• Shapes can be designed as free surface
• No need for specific shape function
• No constraints on the design space
2016 variables
Design Loop
Final Solution
Ad-joint solution
Iterate to Convergence
and Optimum Shape
Gradient/PDE Calc.
Sobolev Solution
Contour/Grid Modification
6.
Summary Flow and Ad-joint Modeling
With grid coordinate s i
Flow equations :
(1) S ij f j ( w) 0
i
where S ij are metrices, f j ( w) the fluxes.
Ad - joint :
f j
(2) Ci 0, Ci S ij
i w
BC' s for the Inverse problem
1
(3) I ( p pt ) 2 ds
2
2 n x 3 n y 3 n z p pt
Change of Flow (gradient)
T
(4) I S ij f j d D S 21 2 S 22 3 S 23 4 pd1d 3
D w
i
Sobolev Modeling
Key issue for implementation of Continuous adjoint solution.
The gradient w ith respect to the Sobolev product
I g , f gf g ' f 'dx
Set
f = g , I g , g
This approximat es a continuous descent class of solution
df
g
dt
The Sobolev gradient g comes from simple gradient
g and by the smoothing of the equation
g
g g.
x x
Continuous descent trajectory
7.
Computational Costs - N Variables
Cost of Algorithm
Steep Descent (N2)
Quasi-Newton (N )
Sobolev Grad. (K )
(K independent of N)
Total Computational Cost
Fin. Diff. Gradients (N3)
+ Steepest Descent
Fin. Diff. Gradients (N2)
+ Quasi-Newton Search or Response surface - N~2000
- Huge Savings
Ad-joint Grad. (N ) - Enables Calculations
+ Quasi-Newton Search on a small PC or
Adjoint Gradient (K ) iPAD
+ Sobolev Grad.
(K independent of N)
Design of Boeing 747 Wing at its Cruise Mach Number
Constraint: : Fixed CL = 0.42
: Fixed load distribution
Euler Calc. : Fixed thickness for wing 14% wing drag saves
(7 minutes cpu time - 1proce.)
~5% aircraft drag saving
baseline
New design
8.
Planform and Aero-Structural Optimization
Boeing 747 at CL ~ .47 (fuselage lift ~ 16%)
Item CD Cumulative CD
Wing Pressure 125 counts 125 counts
(15 shock, 100 induced)
Wing friction 45 160
Fuselage 55 215
Tail 22 235
Nacelles 22 255
Other 15 275
___
Total 270
Drag (the) largest component
Comments
• Aerodynamic wing design is complex due to complexity of
flow around the wing.
• The adjoint method, aerodynamic wing design is carried out
quick and cost effective
Pay-Off
• Aerodynamic design by a small team of engineers
focusing on design issues.
• Significant reduction time and cost.
• Superior and unconventional aero designs.
9.
Airbreathing Propulsion CFD
Dual Mode Scramjet
- Cooled Structure for long flight
X-43A
- Integrated Vehicle
- Scramjet Engine Design X-51A
- Short Duration Test (Heat Sink Tech.)
Long Duration
Durable Combustor Set
Combined Cycle
Turbine Combined Cycle Rig
Flight Experimentation
HIFiRE 17
Test Cases for CFD
Objective: Duplicate hydrocarbon scramjet acceleration and performance during flight
NASA data analysis and CFD code validation using full-scale X-51 test data
X-51 in the NASA Langley X-51A flight hardware at Edwards Air Force
8’ High Temperature Tunnel Base
18
10.
Turbine Combined Cycle Propulsion
Objective: Demonstrate transition between turbine and simulated scramjet
NASA finished the design of a large scale inlet
Turbine
Dual Inlet
Simulated Scramjet
Assembled Inlet hardware at manufacturer
Drawing of full TBCC Test Rig
Rotating Doors
Scramjet Flowpath
Dual Inlet Turbine Flowpath
Centerline view of inlet
19
Turbine-Based Combined Cycle Propulsion
Objective: Validate tools for Mach 4 stage with/without distortion
NASA finished evaluation of Mach 4 stage
Inlet Distortion Screens
RTA: GE 57 / NASA Mach 4 capable Turbine Engine
Turbo Code Calculation
Fan Rotor Blisk
20
11.
Combustion in High-Speed Flows - SCRAMJET
• CFD usage in scramjet engine design/analysis
– Why is it a critical tool?
– How is it used and developed?
• CFD practices in scramjet analysis and design
– Reynolds stress tensor closure
– Reynolds flux vector closure
– Turbulence-chemistry interactions (i.e. internal and external)
– Unsteady formulation (e.g. turbulence models)
• Concluding Remarks
• Sample FAP NRA projects currently underway
– Hybrid RAS/LES
– FDF and PDF (Filtered/Probability Density Function) development
– Reduced chemical kinetics model development (MS thesis @ Syracuse
University – NASA LaRC)
Role of CFD in Scramjet Development
• CFD role in scramjet development
– Not possible to exactly reproduce hypersonic flight conditions at ground test
facilities
i. CFD used to extrapolate/approximate results to flight
ii. CFD used to examine effects of “modeled-conditions”
– Not possible to measure all relevant properties at ground test facilities
i. CFD used to complete gaps due to lack of measurements and instrumentation
(overcome maybe by nanotechnology in near future)
ii. CFD used to model outcomes from perturbations made from a calibrated
condition
– Not possible to copy from designs of existing vehicles and engines
i. CFD used to examine candidate configurations
ii. CFD used to build databases
iii. Sensitivity studies performed on most designs
12.
Scramjet Propulsion System
Scramjet Flow Dynamics
• NASP Model Space Plane
13.
CFD in Scramjet Design & Development
• Current CFD
– 3-D steady-state RAS (parabolized versions for some analyses)
– Turbulence models use eddy viscosity/gradient diffusion concepts
– Chemical reactions handled via reduced finite rate kinetics
– Turbulence-chemistry interactions typically ignored (but some
studies have been done by Givi @ SUNY Buffalo for example).
– Acceptable turn-around time for solutions is measured in days
• Limitations of current methodology
– Uncertainty related to turbulence model is often unacceptable
– Crude chemistry Flame-holding limits can not be obtained
– Unsteady effects (very important) are ignored and/or “poorly
modeled”
Reynolds Averaged Equations
14.
Reynolds Turbulence Stress Model
• Most common closure is the Boussinesq assumption:
• Typical eddy viscosity models:
– Zero-equation models (e.g. Baldwin-Lomax)
– One-equation models (e.g. Spalart-Allmaras)
– Two-equation models (e.g. k-ε, k-ω)
– Three-equation models (e.g. Durbin k-ε-v2)
• LEVMs are deficient in several areas:
– Unable to capture stress-induced secondary flow structures
(Reynolds-stress anisotropies)
– No direct avenue to incorporate pressure-strain correlation effects
– No rigorous accounting for streamline curvature effects
Con’t - Reynolds Stress
• Second order models can address these deficiencies:
• Cost of solving these equations is significant (i.e. computational time)
– Algebraic models extracted by enforcing equilibrium assumptions
– These models retain much of the information from the full Reynolds stress
equation
– When recast as explicit relationships, the cost is comparable to LEVMs
15.
Reynolds Stress Comparison Models
• Mach 3.0 flow through a symmetric square duct
• Linear k-ω model unable to predict secondary flow
• EARS k-ω predicts anisotropy secondary motions
Measured Linear k-ω Measured EARS k-
ω
X/h = 40
Scalar Flux Models
• Closure used is the gradient diffusion model:
• Diffusion is tested by the specification of σt
16.
Vector Flux Models
• Scramjet Flow Path
Scalar Flux Models
• Scalar flux transport equation:
• The cost of solving the additional equations is prohibitive
(3*ns additional transport equations)
• Algebraic models have been explored, but not to a level
that compares with algebraic closures for the Reynolds
stress tensor
17.
Turbulence - Chemistry Models
• Common closures are for laminar-chemistry situations, i.e.
• Turbulent fluctuation effects on the chemistry can be modeled
using PDF’s (i.e. Givi SUNY @ Buffalo):
• The form of the PDF can be assumed before test, or an evolution
equation can be integrated for it
• To date, results from various turbulence-chemistry combinations
modes had small changes than results obtained from variations of
turbulent models
Supersonic Axi-symmetric Burner
• New Injector Design
18.
Turbulence - Chemistry Models
CFD
Hybrid RAS and LES
• Real Concept: LES far from walls, RAS near walls
• Hybrid RAS/LES value (relative to flow-state RAS)
– Temporal accuracy requires 4-8 times more work per
iteration
– Flow must be integrated to a stationary state (N) followed by
more iterations (on the order of N) to gather meaninful data
– Spatial resolution increase
– Nearly isotropic grid regions in LES spaces
– Cost of a hybrid RAS/LES is roughly 100 to 500 times that of
steady-state RAS
– Time history data dumps hundreds of GB’s to tens (even
hundreds) of TB’s in future
19.
Hybrid RAS and LES
Concluding Remarks
• Steady-state RAS will be the primary governing
equation - for some time - for high-speed internal flows
studies
• RAS models must focus on the scalar transport
closures
• Closures of higher-order for the Reynolds stress
equations can be used ideally for the shock-dominated
scramjet flows
• Turbulence-chemistry interactions may be a secondary
(BUT IMPORTANT) issue for high-speed flows
• Hybrid RAS/LES can be the next step for CFD analysis
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