High Reynolds Number Computational Aero-Optics Edwin Mathews Kan - PowerPoint PPT Presentation

High Reynolds Number Computational Aero-Optics Edwin Mathews Kan Wang, Meng Wang, Eric Jumper Research made possible by the Blue Waters Graduate Fellowship

What is Aero-Optics? • In short: The distortion of an optical beam caused by turbulent compressible flow • Distortions are caused by non-uniform index-of-refraction field resulting from turbulent density fluctuations and small amplitude distortions in the near field can cause severe performance degradation in beam intensity and fidelity • Major impediment to applications of airborne optical systems for communication, imaging, targeting, and directed energy systems

Current Work • Want to use Computational Fluid Dynamics (CFD) to improve our understanding and our predictive capability of aero-optics systems at realistic Reynolds and Mach numbers Ma  V c • Simulate the optical turret used on Notre Dame’s Airborne Aero- Optical Laboratory (AAOL) using wall-modeled Large-Eddy Simulation (LES) at the actual flight Reynolds number of 2,300,000 and Mach number of 0.4 • Largest aero-optics calculation and highest Reynolds number wall- modeled LES to date, using over 200M control volumes

Challenges for Computational Aero-Optics • Prediction of aero-optical distortions requires the capturing of optically relevant flow scales • Mani et al. (2008) showed that this requirement can be fulfilled by adequately resolved Large-Eddy Simulation (LES) • LES solves the spatially filtered Navier-Stokes, continuity, and energy equations and provides modeling to account for the scales smaller than those resolved by the computational grid • Resolving the turbulence near a wall in high Reynolds number flows is cost prohibitive in high-fidelity CFD (Choi and Moin, 2012) 37/14 for DNS N total  Re L • 13/7 for wall resolved LES N total  Re L • N total  Re L to resolve outer scales of boundary layer in LES •

Wall Model Method • By solving the simplified Thin Boundary Layer equations on an embedded mesh, the wall shear stress τ wm and heat flux q w are imposed as approximate boundary conditions to the near-wall cell for LES calculations LES Mesh Wall-Model Mesh • In only resolving the outer scales of the boundary layer, LES at the Reynolds numbers of some engineering systems becomes possible where it was previously cost prohibitive

Flow Solver • Unstructured mesh, compressible LES code CharLES developed at Cascade Technologies Inc. (Khalighi et al. 2011) • Low-dissipative finite volume for spatial discretization • Non-dissipative central flux blended with a dissipative upwind flux to provide computational stability when the mesh quality is not ideal • The amount of upwind dissipation is minimized and determined by local mesh skewness Formally 2 nd order but is 4 th order in uniform Cartesian mesh • • Third-order Runge-Kutta in time • Vreman model for subgrid-scale stress (Vreman 2004, You & Moin 2007) • Parallelized using MPI

Simulation Domain 1.5 D Sponge Region 3.5 D 0.5 D 0.1 D 0.375 D 3.5 D 1 D 5.5 D 5 D • Computational domain: 15 D × 10 D × 5 D, 200.5 million CV’s • 0.1D Mean turbulent boundary layer profile provided at inlet • Wall model applied on turret surface and bottom wall • Sponge layer at the top and outlet damps out turbulent structures and acoustic waves • Running average is employed in sponge region and acts as boundary condition on both surfaces • In spanwise direction, flow is periodic

Optics Solver • To compute the optics, separate beam grids are embedded in the computational mesh and computed using geometric optics • Each grid extends approximately 2 D from the turret surface encompassing the entire optically active region of the flow • At each time step when the optics are calculated, the density is interpolated from the LES mesh using a second- order method, and the index of refraction is calculated and integrated along the beam propagation path • Parallelized by integrating segments on each processor and compiling at the end using a collective communication

Optics Solver • With Blue Waters, able to solve for nearly 300 viewing angles encompassing the entire turret viewing area. • Each beam contained 5.4 million points – each time optics are calculated, ~1.5 billion points are interpolated and integrated. Generated ~1 TB of optical data in all.

Flow Field Results - λ 2 in Turret Wake Vortex structures visualized using λ 2 . Blue structures denote strong coherent vortices (lower values of λ 2 ), red structures represent weaker vortices (higher values of λ 2 ).

Fluctuating Pressure in Turret Wake Isosurface of the fluctuating component of pressure, 0.7% lower than the local mean value. Surface colored by value of fluctuating density, -2.5% (blue) – +0.5% (red) above local average.

Streamlines of Time-Averaged Velocity Gordeyev and Jumper. “Fluid dynamics and aero-optics of turrets.” Progress in Aerospace Sciences. 2010.

Pressure Coefficient in Turret Centerline Coefficient of pressure along the turret centerline compared with wind tunnel measurements.

Density Fluctuations in Turret Wake Contours of fluctuating component of density responsible for aero-optic effects. Red and blue regions are 1.25% larger and smaller than the local mean, respectively.

Optical Results – Centerline in Wake Aberrated Wavefront Nearfield Intensity Pattern Increasing Lookback Angle 110˚ Initial Beam 130˚ Distribution 150˚ Z = 16000D

Optical Distorsion Measurements Comparison with wind tunnel measurements of the normalized OPD RMS , a measure of optical distortion, along the centerline of the turret.

Optical Distorsion Measurements Comparison with wind tunnel measurements of the normalized OPD RMS , a measure of optical distortion, along the centerline of the turret. 3 Malley Probe, Vukasinovic et al. 2010 2.5 Shack-Hartmann WFS, Gordeyev et al. 2010 Shack-Hartmann WFS, Gordeyev et al. 2007 WMLES, 200M - Actual Reynolds Number 2 WMLES, 41M - Reduced Reynolds Number 1.5 1 0.5 0 90 100 110 120 130 140 150

Future Work • Processing the over 40 TB of flow field and optical data to extract information that can be used to guide the design of aero-optics mitigation strategies • Beyond classical statistical approaches, looking to use data mining techniques like Proper Orthogonal Decomposition (aka PCA) and Dynamic Mode Decomposition • A scalable set of data mining tools specifically for fluid dynamics would be useful for experimentalists and CFD users

Extra Slides

Separation Structures

Resolution of near wall mesh / Shear Stress W al ls c al i ng of1s twal lnor m alc e l lhe i ght W al ls c al i ng ofs t r e am wi s e c e l ll e ngt h 140 400 350 120 300 100 250 age y+ age x+ 80 200 r r Ave 60 Ave 150 40 100 20 50 0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Thet a Thet a N or m al i z e d She arSt r e s s ,Tur r e tCe nt e r l i ne # 10 -4 8 7 s s e 6 r arSt 5 d She 4 e z i m al 3 age N or 2 r A ve 1 0 -1 0 20 40 60 80 100 120 140 160 180 The t a

CharLES Scaling on Blue Waters M e an t i m e t o s ol ve 25 s t e ps-192M CV M e s h Ac t ual ) s I de al ps( 10 2 e t ve 25 s ol o s m e t i an t M e 10 1 10 3 10 4 Cor e s