Noise from Forced Mixers Funded by the Indiana 21 st Century Research and Technology Fund

Correlating RANS Computed Mean Flow with Forced Mixed Jets C. Wright, G. Blaisdell, A. Lyrintzis School of Aeronautics & Astronautics Purdue University

Goals of Project The primary goal is to develop a greater understanding of the how noise from forced mixed jets may be correlated to the RANS calculated mean flow field. The ultimate goal is to develop quantitative correlations that could be used as input for a semi-empirical model

Approaches Careful selection of numerical tools such as the turbulence model and CFD code are very important. Validation should concentrate on a detailed comparison of flow contours rather than integrated quantities. Grid development and validation should likewise concentrate on the details of the flow. Qualitative trends and observations regarding the relationship between noise data and CFD results should be investigated before attempting to quantify the results.

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

Forced Mixer H Lobe Penetration (Lobe Height) H:

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 1.7 million grid points7 million grid points Density Vorticity Magnitude

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

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

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

High Penetration Mixer Flowfield Case is for a high throttle setting at Mach 0.2 Used Menter SST Turbulence Model Good overall agreement with experiment. TKE is a little low for X/D = 1.0 and X/D = 2.0. CFD results tend to be overly sharp and defined. CFD and experiment both show a substantial amount of interaction between the free shear layer and the streamwise vortices.

Medium Penetration Mixer Flowfield Case is for a high throttle setting at Mach 0.2 Used Menter SST Turbulence Model The agreement between the CFD and the experiment is about the same as for the high penetration case. The free shear layer and the streamwise vortices exist as separate and distinct flow structures through at least X/D = 1.0.

Experimental Results (1/4 Scale Model)

Current State of Project Finishing up CFD runs. Using WIND and Menter SST turbulence model. Currently studying noise data along with RANS results and PIV experiments (including low penetration case not shown). Have identified some interesting trends, and are preparing more CFD runs to finalize these comparisons. Specifics of research is being published in a paper for the AIAA Reno conference (Jan. 2004).

Development of a Semi-Empirical Jet Noise Model for Forced Mixer Noise Predictions L. Garrison, Purdue University W. Dalton, Rolls-Royce Indianapolis A. Lyrintzis and G. Blaisdell Purdue University

Four-Source Model Comparisons –Four-Source method implementation –Predictions for the confluent mixer Two-Source Model –Formulation –Optimization procedure –Optimized results for the 12 lobe mixers –Optimized parameter correlations Outline

Four-Source Coaxial Jet Noise Prediction VsVs VsVs VpVp Initial Region Interaction Region Mixed Flow Region Secondary / Ambient Shear Layer Primary / Secondary Shear Layer

Practical Configuration Geometry Secondary Flow Primary Flow Flow Mixer Nozzle Wall Tail Cone (Bullet) Final Nozzle Exit

Dual Flow Configurations Four-Source method developed for a coplanar, coaxial jet The configuration for the practical case has a buried primary flow in a convergent nozzle with a center body (tail cone or bullet)

Based on an ‘Equivalent Coaxial Jet’ –Approach developed by B. Tester and M. Fisher Define primary and secondary jets at the final nozzle exit plane Assumptions –Isentropic flow in the nozzle –Primary and secondary flows do not mix in the nozzle –Static pressure of the two flows at the exit plane are equal Single Jet Property Calculation

Jet Areas at the Final Nozzle Exit –Guess A p –Calculate A s –Calculate M exit –Calculate P static –Iterate until the primary and secondary static pressures are equal

Four-Source Method Implementation Primary and Secondary Jet Properties –Calculated at the final nozzle exit Mixed Jet and Effective Jet Properties

Current Prediction Method Comparisons Four-Source / Single Jet / Experimental Data Comparisons –Confluent Mixer, Low Power Operating Point –ARP876C Method used for all single jet noise predictions Bass and Sutherland correction for atmospheric attenuation –Four-Source coaxial jet prediction Based on equivalent coaxial jet properties –Single jet prediction Based on fully mixed flow at the final nozzle exit

Current Prediction Method Comparisons

Forced Mixer Experimental Data Four Mixer Configurations –Confluent Mixer (CFM) –Low Penetration 12 Lobe Mixer (12CL) –Mid Penetration 12 Lobe Mixer (12UM) –High Penetration 12 Lobe Mixer (12UH) Low Power Operating Point H

Forced Mixer Experimental Data

Objective: –Match the experimental data SPL spectrum at all angles and all frequencies using two single stream jet sources. Formulation: Single Jet Prediction Source Strength Spectral Filter Variable Parameters : Two-Source Model

 dB fcfc fcfc Variable Parameters 1/3 Octave Band Number 1/3 Octave SPL [dB] Effects of Variations in  dBEffects of Variations in f c

Optimization Procedure –For a given geometry and operating condition, optimize the source strength parameters (  db s,  db m ) for a range of cut-off frequencies –Find the set of optimized parameters that minimize the prediction error for all operating conditions –Correlate the final set of parameters to the changes in the mixer design Two-Source Model Optimization

Optimization Challenges –Optimum Criterion Maximum Error Average Error Weighted Error –Solution Non-Uniqueness –Local Minima –Non-Linear Behavior Optimization Tools –Nonlinear Least Squares M ATLAB : lsqnonlin (Levenberg–Marquadt Optimization Method ) Two-Source Model Optimization

15Microphone locations (90 º to 160 º in 5º increments) 1Sound Pressure Level (SPL) spectrum per microphone 27Frequency Bands per spectrum (1/3 Octave Bands) 405SPL values per data point Microphone Locations Jet

Two-Source Model Optimization Optimum Criterion –Based on a ‘OASPL type’ weighting –At each observer angle: –Weighted error values:

Two-Source Model Results Test Case –Low Penetration Mixer –Low Power Operating Point Two-Source Model –Upstream Source: Secondary Jet –Downstream Source: Mixed Jet

Optimized Two-Source Results

Current jet noise predictions do not accurately model the noise from jets with internal forced mixers Forced mixer jet noise can be modeled by a combination of two single jet sources Optimized Two-Source model source strengths and cut-off Strouhal numbers appear to correlate linearly with the amount of lobe penetration Summary

Fisher, M.J., Preston, G.A., and Bryce, W.D., “A Modelling of the Noise from Simple Coaxial Jets Part I: With Unheated Primary Flow,” Journal of Sound and Vibration, 209(3): , 1998 Fisher, M.J., Preston, G.A., and Mead, C.J., “A Modelling of the Noise from Simple Coaxial Jets Part II: With Heated Primary Flow,” Journal of Sound and Vibration, 209(3): , 1998 “ARP87C: Gas Turbine Jet Exhaust Noise Prediction,” Society of Automotive Engineers, Inc., November, Bass, H.E., Sutherland, L.C., Zuckerwar, A.J., Blackstone, D.T., and Hester, D.M., “Atmospheric Absorption of Sound: Further Developments,” Journal of the Acoustical Society America, 97(1): , 1995 References

Two-Source Model Optimization SPL exp - SPL pred SPL exp – SPL exp max