On the Development of Semi-Empirical Noise Models for Jets With Forced Mixers

1. On the Development of Semi-Empirical Noise Models for Jets With Forced Mixers L.A. Garrison Purdue University School of Aeronautics and Astronautics W.N. Dalton Rolls-Royce Corporation A.S. Lyrintzis and G.A. Blaisdell Purdue University School of Aeronautics and Astronautics Funding provided by the 21st Century Research and Technology Fund Purdue University School of Aeronautics and Astronautics

2. Overview of Four-Source Method Application to an Axisymmetric Mixer Forced Mixer Jet Noise Two-Source Model for Forced Mixer Predictions Outline Purdue University School of Aeronautics and Astronautics

3. Secondary / Ambient Shear Layer Primary / Secondary Shear Layer Vs Vp Vs Initial Region Interaction Region Mixed Flow Region Four-Source Coaxial Jet Noise Prediction (Fisher et.al. 1998) Purdue University School of Aeronautics and Astronautics

4. Four-Source Coaxial Jet Noise Prediction (Fisher et.al. 1998) • Secondary Jet: • Effective Jet: • Mixed Jet: • Total noise is the incoherent sum of the noise from the three jets Purdue University School of Aeronautics and Astronautics

5. Confluent Mixer / Nozzle Geometry Secondary Flow Primary Flow Flow Mixer Nozzle Wall Tail Cone Final Nozzle Exit Purdue University School of Aeronautics and Astronautics

6. Coaxial 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) Purdue University School of Aeronautics and Astronautics

7. 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 Purdue University School of Aeronautics and Astronautics

8. Confluent Mixer Predictions • Four-Source / Single Jet / Experimental Data Comparisons • Experimental Data • NASA Glenn Aeroacoustic Propulsion Laboratory • One-foot lossless sound pressure level spectra • Three power settings (Set Points 1, 2,and 3) • Four-Source coaxial jet prediction • Based on ‘equivalent coaxial jet’ properties • Single jet prediction • Based on fully mixed flow at the final nozzle exit • ARP876C Method used for all single jet noise predictions Purdue University School of Aeronautics and Astronautics

9. Confluent Mixer Predictions Set Point 1 Purdue University School of Aeronautics and Astronautics

10. Forced Mixer / Nozzle Geometry Secondary Flow Primary Flow Flow Mixer Nozzle Wall Final Nozzle Exit Tail Cone Purdue University School of Aeronautics and Astronautics

11. Forced Mixer Flow Field Vortex Interactions with the Cold Secondary Flow Vortex Pair Interactions Vortex Interactions between Adjacent Lobes Vortex Interactions with the Hot Primary Flow Purdue University School of Aeronautics and Astronautics

12. H Forced Mixer Experimental Data • Four Mixer Configurations • Confluent Mixer • Low Penetration 12 Lobe Mixer • Mid Penetration 12 Lobe Mixer • High Penetration 12 Lobe Mixer Purdue University School of Aeronautics and Astronautics

13. Forced Mixer Experimental Data Set Point 1 Purdue University School of Aeronautics and Astronautics

14. Motivation: Work by B. Tester and M. Fisher shows the elimination of the effective jet region for jets with forced mixers Formulation: Single Jet Prediction Spectral Filter Source Strength Two-Source Model Variable Parameters: Purdue University School of Aeronautics and Astronautics

15. Model 1: Upstream Jet Source: Fully Mixed Jet Downstream Jet Source: Fully Mixed Jet Model 2: Upstream Jet Source: Secondary Jet Downstream Jet Source: Fully Mixed Jet Two-Source Model Purdue University School of Aeronautics and Astronautics

16. Two-Source Model • Variable Parameters DStc DStc DdB DdB Purdue University School of Aeronautics and Astronautics

17. Objective: Match the experimental data SPL spectrum at all angles and all frequencies using two single stream jet sources. Optimization Procedure: For a given geometry and operating condition, optimize the source strength parameters (Ddbu, Ddbd) for a range of cut-off Strouhal numbers For a given geometry, 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 Purdue University School of Aeronautics and Astronautics

18. Two-Source Model Parameter Optimization Parameter Correlation Apply a Linear Curve Fit Low Penetration Opt Parameters Intermediate Penetration Opt Parameters High Penetration Opt Parameters Evaluate Average Weighted Errors Low Penetration Set Point 1 Low Penetration Set Point 2 Low Penetration Set Point 3 Purdue University School of Aeronautics and Astronautics

19. Optimization Challenges Optimum Criterion Maximum Error / Average Error / Weighted Error 405 Error Values per Data Point Non-Linear Behavior Solution Non-Uniqueness Local Minima Optimization Tools Nonlinear Least Squares MATLAB: lsqnonlin (Levenberg–Marquadt Optimization Method) Two-Source Model Optimization Purdue University School of Aeronautics and Astronautics

20. Two-Source Model Optimization • Optimum Criterion • Based on a ‘OASPL type’ weighting • At each observer angle: • Weighted error values: Purdue University School of Aeronautics and Astronautics

21. Parameter Optimization Process Model 1 Purdue University School of Aeronautics and Astronautics

22. Model 1 Performance Purdue University School of Aeronautics and Astronautics

23. Model 1 Results Low Penetration Set Point 1 Model 1 Purdue University School of Aeronautics and Astronautics

24. 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 appear to correlate linearly with the amount of lobe penetration Optimized Cut-off Strouhal numbers vary little with respect to the amount of mixer penetration Summary Purdue University School of Aeronautics and Astronautics

25. Investigate relations between the source strengths and the turbulent properties in the jet plume Using experimental aerodynamic data (PIV) Using RANS solutions with turbulence models Future Directions Purdue University School of Aeronautics and Astronautics

26. Backup Slides Purdue University School of Aeronautics and Astronautics