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STUDY OF A LOW-DISPERSION FINITE VOLUME SCHEME IN ROTORCRAFT NOISE PREDICTION

A PhD Thesis Defense Presented to The Faculty of the Division of Graduate Studies By Gang Wang Advisor: Dr. Tim C. Lieuwen April 4, 2002. STUDY OF A LOW-DISPERSION FINITE VOLUME SCHEME IN ROTORCRAFT NOISE PREDICTION. Background LDFV Scheme Objectives Results Contributions & Conclusions

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STUDY OF A LOW-DISPERSION FINITE VOLUME SCHEME IN ROTORCRAFT NOISE PREDICTION

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  1. A PhD Thesis Defense Presented to The Faculty of the Division of Graduate Studies By Gang Wang Advisor:Dr.Tim C. Lieuwen April 4, 2002 STUDY OF A LOW-DISPERSION FINITE VOLUME SCHEME IN ROTORCRAFT NOISE PREDICTION

  2. Background LDFV Scheme Objectives Results Contributions & Conclusions Recommendations OUTLINE

  3. Helicopter has a wide range of military and civil applications. However, the high noise level associated with it greatly restricts its further applications. BACKGROUND

  4. Three categories of rotor noise: Rotational noise: steady or harmonically varying forces, volume displacements Broadband noise: random disturbances Impulsive noise High-Speed-Impulsive (HSI) noise Blade-Vortex-Interaction (BVI) noise Rotorcraft Noise

  5. Rotorcraft Noise High-Speed-Impulsive noise

  6. Rotorcraft Noise Blade-Vortex-Interaction noise

  7. Great efforts have been spent on quantifying and minimizing rotorcraft noise. Two noise prediction techniques: Fully computational aerodynamics and acoustics; High resolution CFD calculation in the near field coupling with acoustic analogy or Kirchhoff method in the far field; Noise Prediction

  8. Noise Prediction Far Field Observer Acoustic calculation Region Blade  CFD calculation Region

  9. Near-field CFD calculation is critical to the accuracy of far-field noise prediction. Much progress has been made on understanding and predicting rotorcraft noise characteristics with the aid of CFD methods. Special attention is needed to simulate acoustic wave propagation with CFD methods. Noise Prediction

  10. Differences between aerodynamic and aeroacoustic problems: Relative Magnitude Length and Frequency Scale Dispersion and dissipation errors generated by conventional CFD methods can easily change the observed noise characteristics. Noise Prediction

  11. Noise Prediction T=50 T=100 T=0 Magnitude drops as wave propagates… Dissipation Dispersion Errors - some waves travel slower than the rest.

  12. These errors must be reduced to give correct traveling-wave profile. Dispersion error minimization methods: Dispersion-Relation-Preserving (DRP) Scheme, by Dr. Tam and Web; Compact Scheme, by Dr. Lele; Low Dispersion Finite Volume (LDFV) Scheme, by Dr. Nance and Sankar; Noise Prediction

  13. The spatial derivative is approximated by the difference of the numerical fluxes evaluated at the adjacent half points. LDFV SCHEME

  14. The general interpolation formulations for the left and right physical fluxes are: The approximation of spatial derivative becomes: LDFV SCHEME

  15. Expand uj+l about xj using classical Taylor series expansion, like: Specific spatial order scheme can be obtained by comparing corresponding coefficients of each term at both sides of the approximation equation. LDFV SCHEME

  16. A further restriction is imposed to match the Fourier transform of the approximation of spatial derivative with its exact transform. The Fourier transform of the spatial difference approximation is: LDFV SCHEME Non-dimensional Wave Number F. T.

  17. The least square error: should be minimized with respect to coefficients and . LDFV SCHEME Optimization Equations

  18. Study dispersion and dissipation characteristics of LDFV scheme Apply LDFV scheme to rotorcraft noise prediction OBJECTIVES

  19. Analysis of dispersion and dissipation characteristics of LDFV scheme High-Speed-Impulsive or shock noise prediction Spherically symmetric wave propagation study RESULTS

  20. The one-dimensional advection equation: Semi-discretization of advection equation: Discrete operator A is of the form: Analysis of LDFV Scheme

  21. Full-discretization of advection equation written in operator notation: Z is time shift operator: Define an amplification factor: which satisfies characteristic equation Analysis of LDFV Scheme

  22. The phase velocity of full-discretization: The amplitude error: Analysis of LDFV Scheme

  23. Analysis of LDFV Scheme Phase Velocity, CFL=0.01

  24. Analysis of LDFV Scheme Amplitude Error, CFL=0.01

  25. The phase difference between predicted results and exact solution: The predicted amplitude: Analysis of LDFV Scheme

  26. Analysis of LDFV Scheme Phase Difference Comparison at t=50 Fourier Transform Comparison at t=50

  27. Analysis of LDFV Scheme Phase Difference Comparison at t=400 Fourier Transform Comparison at t=400

  28. Both MUSCL and LDFV schemes can accurately capture low non-dimensional wave number components. LDFV scheme generates lower numerical errors for high non-dimensional wave number components than MUSCL scheme. The above observations are still kept as propagation distance increases although low error generation ranges are reduced. Comments on LDFV Scheme Analysis

  29. 1/7 scale model of untwisted rectangular UH-1H blades in hover condition NACA0012 airfoil Non-lifting case Shock Noise Prediction

  30. Shock Noise Prediction C-H Computational Grid

  31. Shock Noise Prediction

  32. Shock Noise Prediction Shock Noise Measurement Locations and Method

  33. Grid Independence Study Acoustic Pressure Time History, MTip=0.90, r/R=3.09

  34. Grid Independence Study

  35. Acoustic Pressure Time HistoryMTip = 0.9, r/R=1.111

  36. Acoustic Pressure Time HistoryMTip = 0.9,r/R=3.09

  37. MUSCL and LDFV scheme results are very similar. Two factors to be investigated: Flux Limiter Error generation Shock Noise Prediction

  38. Flux limiter switches higher order schemes back to first order scheme in the large flux gradient regions. Different flux limiters will give different results in those regions. Flux Limiter Effects

  39. Acoustic Pressure Time HistoryMTip = 0.9,r/R=3.09

  40. What’s the non-dimensional wave number range of shock noise signal? Is the simulated domain large enough to see difference between the results of two schemes? Error Generation Issues

  41. The spherically symmetric wave equation: Shock noise signal at sonic cylinder is chosen as initial condition. Spherically Symmetric Wave Propagation Study

  42. Spherically Symmetric Wave Propagation Study kr=0.0614 Initial Acoustic Signal Distribution Spectrum of Initial Signal

  43. Wave Distribution at r=3.229m(Without Limiter)

  44. Spherically Symmetric Wave Propagation Study Phase Difference at r=3.229m (Without Limiter) Fourier Transform of Signal Distributions at r=3.229m (Without Limiter)

  45. Wave Distribution at r=20.0m(Without Limiter)

  46. Spherically Symmetric Wave Propagation Study Phase Difference at r=20.0m (Without Limiter) Fourier Transform of Signal Distributions at r=20.0m (Without Limiter)

  47. Negative Pressure Peak Under-prediction Ratio (Without Limiter)

  48. Wave Distribution at r=3.229m(With Limiter)

  49. Spherically Symmetric Wave Propagation Study Phase Difference at r=3.229m (With Limiter) Fourier Transform of Signal Distributions at r=3.229m (With Limiter)

  50. Wave Distribution at r=20.0m(With Limiter)

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