Mario Felipe Campuzano Ochoa (Cornell Energy Workshop)

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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  pd1d 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    gf   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