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CFD in Aeronautics and AerospaceNumerical 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 -’98mfc27@cornell.edu

Cornell Workshop on Large-Scale Wind Generated PowerJune 12-13, 2009

Cornell UniversityIthaca, New York 14853

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External Flows - Aerodynamics

Samples of Flows – Subsonic and Separation

Flow Separation

Turbulence

Design is MULTIDISCIPLINARY

(everything is related and dependent)

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The Fluid Dynamics Equation (Navier-Stokes)

dxidxidt

dfvi=dfi+dw

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ru3

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ru1

r

p = (g -1) r {E - 1/2(ui ui)}

Equation solved numerically using optimal and iterative algorithms

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CFD Stages of Design and Testing

Inflatable Reentry Vehicle Concept

Flow Modeling w/ “complex” Boundary Conditions

Automatic ModelingState of the Art Aerodynamic Design

Interactive CalculationRapid Prediction of Flows

• Integrate the capabilities into an automatic method that incorporates computer optimization.

• 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.

• 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.

Design by Numerical Finite Modeling

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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

Boeing 747

2016+ flow calculations ~ 2-5 minutes each (Euler not Viscous Flow)

Cost Prohibited for Industrial Design

System and Feedback Theory in Aero Design

Minimization of Drag Optimal Control of Aerodynamic Equations subject to body changes

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GOAL : Reduction of Computational Costs

e.g. Minimize CD

System and Feedback Theory in Aero Design II

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Flow Physics Solution + Ad-joint Solution

(Adjoint)

(Gradient)

2016 variables In grid

Ad-joint Method Characteristics:

• Gradient for N variableswith 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

Gradient/PDE Calc.

Sobolev Solution

Contour/Grid Modification

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Summary Flow and Ad-joint Modeling

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Key issue for implementation of Continuous adjoint solution.

Computational Costs - N Variables

(K independent of N)

(K )Sobolev Grad.

(N ) Quasi-Newton

(N2)Steep Descent

Cost of Algorithm

(N )Ad-joint Grad.

+ Quasi-Newton Search

(K independent of N)

(K )Adjoint Gradient

+ Sobolev Grad.

(N2) Fin. Diff. Gradients

+ Quasi-Newton Search or Response surface

(N3)Fin. Diff. Gradients

+ Steepest Descent

Total Computational Cost

- N~2000- Huge Savings- Enables Calculationson a small PC or iPAD

Design of Boeing 747 Wing at its Cruise Mach Number

Constraint: : Fixed CL = 0.42: Fixed load distribution: Fixed thickness for wing 14% wing drag saves

(7 minutes cpu time - 1proce.)

~5% aircraft drag saving

baseline

New design

Euler Calc.

Planform and Aero-Structural Optimization

270Total

___

27515Other

25522Nacelles

23522Tail

21555Fuselage

16045Wing friction

(15 shock, 100 induced)

125 counts125 countsWing Pressure

Cumulative CDCDItem

Boeing 747 at CL ~ .47 (fuselage lift ~ 16%)

Drag (the) largest component

Comments

• Aerodynamic design by a small team of engineers focusing on design issues.

• Significant reduction time and cost.

• Superior and unconventional aero designs.

• 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

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Airbreathing Propulsion CFD

X-43A- Integrated Vehicle- Scramjet Engine Design- Short Duration Test (Heat Sink Tech.)

Dual Mode Scramjet- Cooled Structure for long flight

Turbine Combined Cycle Rig

X-51A

Durable Combustor Set

HIFiRE

Flight Experimentation

Long Duration

Combined Cycle

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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 8’ High Temperature Tunnel

X-51A flight hardware at Edwards Air Force Base

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Turbine Combined Cycle Propulsion

Objective: Demonstrate transition between turbine and simulated scramjet

NASA finished the design of a large scale inlet

Turbine Flowpath

Scramjet Flowpath

Dual Inlet

Rotating Doors

Drawing of full TBCC Test Rig

Centerline view of inlet

Assembled Inlet hardware at manufacturer

Turbine

Dual Inlet

Simulated Scramjet

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Fan Rotor Blisk

Turbine-Based Combined Cycle Propulsion

Objective: Validate tools for Mach 4 stage with/without distortion

NASA finished evaluation of Mach 4 stage

RTA: GE 57 / NASA Mach 4 capable Turbine EngineInlet Distortion Screens

Turbo Code Calculation

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

Scramjet Propulsion System

Scramjet Flow Dynamics

• NASP Model Space Plane

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 EquationsReynolds Averaged Equations

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

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

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

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 ofturbulent models

Supersonic Axi-symmetric Burner

• New Injector Design

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

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