Aero-Acoustic Computation of Wind Turbines Using High-Order Schemes

1
Aero-Acoustic Computation of Wind Turbines Using
High-Order Schemes

• Wei Jun Zhu
• Dept. of Mechanical Engineering,
• Fluid Mechanics Section, Building 403,
• Technical University of Denmark,
• DK-2800 Lyngby, Denmark
•  

Second PhD Seminar on Wind Energy in Europe ,
4th-5th October 2006 ,Roskilde
2
Introduction

• CAA is a common tool for predicting
  aerodynamically generated noise.
• The goal is to find the sound pressure p, that
  is the difference between the instantaneous value
  of the total pressure and the static pressure.
• Sound waves have small amplitude. (Noise level of
  75 dB corresponds to p10-6 P0)
• To propagate waves accurately for long distance
  over long periods of time the numerical schemes
  are expected to have low dispersion and
  dissipation.
• Grid size depends on the shortest wavelength to
  be solved.

3
The acoustic Equations

• The sound field can be simulated using DNS of the
  compressible NS equations. However, the
  computational cost is too expansive since the
  speed of the sound restricts the size of the time
  step so much.
• In our study, a technique proposed by Hardin and
  Pope is used. The compressible variables are
  decomposed as
• u U u, v V v,
• ? ?0 ?, p P p.
• The approach involves two steps comprising an
  incompressible flow part and an acoustic part.

4
Numerical method

• Optimized finite difference schemes
  (Dispersion-Relation-Preserving scheme)
• Finite difference scheme can be written as
• The Fourier transform of function f(x) and
  its inverse are
• The Fourier transform of finite difference
  scheme is

5
Numerical method

• Optimized finite difference schemes
• Compare the two sides, we can define the
  modified wave number
• The modified wave number is required to be
  as close to the exact wave number as possible.
• The condition that E is a minimum is that
  , aj is one of the coefficient.
• For example, to achieve 4th-order accuracy
  we use NM3. After some arrangement by doing
  traditional Taylor expansion, we have one free
  coefficient left which can be used to minimize
  the error integral E.

6
Numerical method

• Optimized finite difference schemes

7
Numerical method

• Optimized compact finite difference schemes
• Consider a tridiagonal system based on a
  five-point stencil. The scheme has 6th-order
  accuracy. We may use the same method to optimize
  the scheme.

fi-2
fi2
8
Numerical method

• Optimized compact finite difference schemes

9
Numerical method
Block 1

• Block 2

Block 3
10
Airfoil Noise
11
Airfoil Noise

• 4th-order RK time advancing scheme
• 4th-order DRP scheme (7-point), 8th-order Compact
  scheme, 6th-order CompactDRP scheme
• 8th-order filter scheme (applied after 4th step
  of RK)
• Radiation outflow boundary condition
• NACA 0012 airfoil, Re200, M0.2, a20deg

12
Airfoil Noise

13
Airfoil Noise
14
Current work and near future

• Currently Working on 3D computation at high
  Reynolds number.
• Noise from 3D blade is the future work.

15
Thank you!