Development of Simulation Methodologies for Forced Mixers Anastasios

Development of Simulation Methodologies for Forced Mixers Anastasios Lyrintzis School of Aeronautics & Astronautics Purdue University

Acknowledgements • Indiana 21 st Century Research and Technology Fund • Prof. Gregory Blaisdell • Rolls-Royce, Indianapolis (W. Dalton, Shaym Neerarambam) • L. Garrison, C. Wright, A. Uzun, P-T. Lew

Motivation • Airport noise regulations are becoming stricter. • Jet exhaust noise is a major component of aircraft engine noise • Lobe mixer geometry has an effect on the jet noise that needs to be investigated.

Methodology • 3 -D Large Eddy Simulation for Jet Aeroacoustics • RANS for Forced Mixers • Coupling between LES and RANS solutions • (Semi-empirical method)

3 -D Large Eddy Simulation for Jet Aeroacoustics

Objective • Development and full validation of a Computational Aeroacoustics (CAA) methodology for jet noise prediction using: § A 3 -D Large Eddy Simulation (LES) code working on generalized curvilinear grids that provides time-accurate unsteady flow field data § A surface integral acoustics method using LES data for far-field noise computations

Numerical Methods for LES • 3 -D Navier-Stokes equations • 6 th-order accurate compact differencing scheme for spatial derivatives • 6 th-order spatial filtering for eliminating instabilities from unresolved scales and mesh non-uniformities • 4 th-order Runge-Kutta time integration • Localized dynamic Smagorinsky subgrid-scale (SGS) model for unresolved scales

Computational Jet Noise Research • Some of the biggest jet noise computations: § Freund’s DNS for Re. D = 3600, Mach 0. 9 cold jet using 25. 6 million grid points (1999) § Bogey and Bailly’s LES for Re. D = 400, 000, Mach 0. 9 isothermal jets using 12. 5 and 16. 6 million grid points (2002, 2003) • We studied a Mach 0. 9 turbulent isothermal round jet at a Reynolds number of 100, 000 • 12 million grid points used in our LES

Computation Details • Physical domain length of 60 ro in streamwise direction • Domain width and height are 40 ro • 470 x 160 (12 million) grid points • Coarsest grid resolution: 170 times the local Kolmogorov length scale • One month of run time on an IBM-SP using 160 processors to run 170, 000 time steps • Can do the same simulation on the Compaq Alphaserver Cluster at Pittsburgh Supercomputing Center in 10 days

Mean Flow Results • Our mean flow results are compared with: § Experiments of Zaman for initially compressible jets (1998) § Experiment of Hussein et al. (1994) Incompressible round jet at Re. D = 95, 500 § Experiment of Panchapakesan et al. (1993) Incompressible round jet at Re. D = 11, 000

Jet Aeroacoustics • Noise sources located at the end of potential core • Far field noise is estimated by coupling near field LES data with the Ffowcs Williams–Hawkings (FWH) method • Overall sound pressure level values are computed along an arc located at 60 ro from the jet nozzle • Cut-off Strouhal number based on grid resolution is around 1. 0

Jet Aeroacoustics (continued) • OASPL results are compared with: § Experiment of Mollo-Christensen et al. (1964) Mach 0. 9 round jet at Re. D = 540, 000 (cold jet) § Experiment of Lush (1971) Mach 0. 88 round jet at Re. D = 500, 000 (cold jet) § Experiment of Stromberg et al. (1980) Mach 0. 9 round jet at Re. D =3, 600 (cold jet) § SAE ARP 876 C database

Conclusions • Localized dynamic SGS model stable and robust for the jet flows we are studying • Very good comparison of mean flow results with experiments • Aeroacoustics results are encouraging • Valuable evidence towards the full validation of our CAA methodology has been obtained

Near Future Work • Simulate Bogey and Bailly’s Re. D = 400, 000 jet test case using 16 million grid points § 100, 000 time steps to run § About 150 hours of run time on the Pittsburgh cluster using 200 processors • Compare results with those of Bogey and Bailly to fully validate CAA methodology • Do a more detailed study of surface integral acoustics methods

Can a realistic LES be done for Re. D = 1, 000 ? • Assuming 50 million grid points provide sufficient resolution: • 200, 000 time steps to run • 30 days of computing time on the Pittsburgh cluster using 256 processors • Only 3 days on a near-future computer that is 10 times faster than the Pittsburgh cluster

Future Work • Extend methodology to handle: – Noise from unresolved scales – Supersonic flow – Solid boundaries (lips) – Complicated (mixer) geometries multi-block code

RANS for Forced Mixers

Objective • Use RANS to study flow characteristics of various flow shapes

What is a Lobe Mixer?

Nozzle Internally Forced Mixed Jet Bypass Flow Mixer Exhaust Flow Core Flow Tail Cone Lobed Mixer Mixing Layer Exhaust / Ambient Mixing Layer

Forced Mixer H H: Lobe Penetration (Lobe Height)

3 -D Mesh

WIND Code options • • • 2 nd order upwind scheme 1. 7 million/7 million grid points 8 -16 zones 8 -16 LINUX processors Spalart-Allmaras/ SST turbulence model Wall functions

Grid Dependence Density Contours 1. 7 million grid points Density Contours 7 million grid points

Grid Dependence 1. 7 million grid points Density Vorticity Magnitude

Spalart-Allmaras and Menter SST Turbulence Models Spalart-Allmaras Menter SST

Spalart-Allmaras and Menter SST at Nozzle Exit Plane SST Spalart Density Vorticity Magnitude

Mean Axial Velocity at x = 2. 88” (High Penetration) experiment Spalart Allmaras ¼ Scale Spalart at x = 2. 88/4”

Mean Axial Velocity at x = 2. 88” (High Penetration) experiment Menter SST ¼ Scale Menter SST at x = 2. 88/4”

Spalart-Allmaras vs. Menter SST • The Spalart-Allmaras model appears to be less dissipative. The vortex structure is sharper and the vorticity magnitude is higher at the nozzle exit. • The Menter SST model appears to match experiments better, but the experimental grid is rather coarse and some of the finer flow structure may have been effectively filtered out. • Still unclear which model is superior. No need to make a firm decision until several additional geometries are obtained.

Geometry at Mixer Exit Low Penetration Mid Penetration High Penetration

DENSITY CONTOURS (¼ Scale) Low Penetration Mid Penetration

Vorticity Magnitude at Nozzle Exit (¼ Scale Geometry) Low Penetration Mid Penetration High Penetration

Turbulent Kinetic Energy at Nozzle Exit (¼ Scale Geometry) Low Penetration Mid Penetration High Penetration

Preliminary Conclusions • 1. 7 million grid is adequate • Further work is needed comparing the turbulence models and results for different penetration lengths

Future Work • Analyze the flow fields and compare to experimental acoustic and flow-field data for additional mixer geometries. • Further compare the two turbulence models. • If possible, develop qualitative relationship between mean flow characteristics and acoustic performance.

Implementing RANS Inflow Boundary Conditions for 3 -D LES Jet Aeroacoustics

Objectives • Implement RANS solution and onto 3 -D LES inflow BCs as initial conditions. • Investigate the effect of RANS inflow conditions on: – Reynolds Stresses – Far-field sound generated

Implementation Method LES RANS • RANS grid too fine for LES grid to match. • Since RANS grid has high resolution, linear interpolation will be used.

Issues and Challenges • • • Accurate resolution of outgoing vortex with LES grid. Accurate resolution of shear layer near nozzle lip. May need to use an intermediate Reynolds number eg. Re = 400, 000

Final Conclusion • Methodologies (LES, RANS, coupling) are being developed to study noise from forced mixers