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					University of Greenwich
Computing and Mathematical Sciences


    Experience of using a CFD code for
   estimating the noise generated by gusts
         along the sunroof of a car
                        by Liang Lai
              Supervisors: Professor C- H Lai,
                   Dr. G S Djambazov,
                 Professor K A Pericleous
            Sponsored by University of Greenwich
                                                                                Introduction

  Solution strategies for Computational Aeroacoustics




                             Decreasing cost
  DNS/LES/RANS                                   1. Direct Numerical Simulation (DNS)
(Near field + far field)                         2. Large Eddy Simulation (LES or DES)
source                                           3. Reynolds-Averaged Navier-Stokes (RANS)
              +
      Propagation
                           ¤ High-order schemes in space and time
                                               ( Truncation error ~ x m  t n ,   m, n  3 )

       ¤ Different length scales and time scales for aeroacoustic
          simulation in turbulent flows
               ¤ Computational cost is very high even for
                  using RANS with high-order schemes !
                                                   Introduction
Coupling Methods ?
            The unsteady near-field is solved directly by LES or
            unsteady RANS, but acoustic solutions obtained by
            solving a set of simpler equations (e.g. wave equation,
            Euler equations, and other perturbation equations).

        LES/RANS                            +
        (near field)                       Simpler equations *
                                             (near field + far field)
                                +
          source                                 Propagation



                        • non-linearised Euler equations
  Simpler equations *   
                        • Decomposition + source-retrieval techniques
                        • Other methods, e.g. Helmholtz equation?
                        
Automobile Application Examples
CAA in the automotive industry
             The Car Sunroof Problem

• Buffeting noise is due to shear-layer instability in the opening
  of the cavity subjected to tangential flow.
• Shear-layer vortices are produced and are convected
  downstream of the opening, eventually hitting the rear edge.
• When the vortex breaks, a pressure wave is produced which
  enters into the cavity.
• At a certain speed, the vortex shedding frequency in the
  shear layer will match an acoustic mode of the cavity leading
  to resonance is in the form of a standing wave.
• Resonance is in the form of a Helmholtz mode
  Problem setup and external excitation
Car as a Helmholtz Resonator

                          1.2m          0.4m   0.5m    1.1m            0.8m




       25m/s




          A sinusoidal disturbance                                   0.4m
                                               0.03m

                                                              0.9m


                         0.5m




    Time step:                       Wave amplitude:    Wave time per cycle:
    dt = 0.00124 s                    P0= -0.1 kg/s             ta= 10 dt
Car as a Helmholtz Resonator
• Basic procedure with PHOENICS

                                                         


            

                                                             time
  The pressure fluctuation along the open sun-roof can be calculated,
                           Pf ( x, t )  P( x, t )  P( x)

  where P is the pressure distribution obtained by using the CFD
  calculation and P is the background pressure distribution due to the
  upstream velocity.
Car as a Helmholtz Resonator
• Analyse Acoustic Response by using FFT
                                                                                         2nd point along the sun-roof
                                                                                         4th point along the sun-roof
                                               20000


                      Power spectral density   15000


                                               10000


                                               5000


                                                  0
                                                       0                         10                                     20
                                                                             Frequency


• Comparison to a Helmholtz Resonator
                                                           c : speed of sound                                l : neck length
    f  (c / 2 ) A /(leff V )                             A : cross sectional area of the neck              l cor : neck length correction
                                                           l eff : effectivelength of the neck               : empirical coefficient
     l eff  l  l cor  l  r
                                                           V : volume of the cavity                          r : the radius of the neck

  therefore, resonant frequency ( = 1.45) f = 6.32Hz
Alternative Problem Description
• A hypothetical car with an open sun-roof                        ###Mesh


                1.28m   0.52m   0.3m   0.6m     1.35m   0.35m



    25m/s


                        0.05m




                                              1.2m
                                                                0.85m
       0.52m




• *The vortex strength W = A0 sin(ωt), where A0 = 1.2 m/s
• t = 10-3 s , wave time per cycle ta = 20 t, f = 50 Hz
Use of nested sub-grids
Geometry and Observation points




                                        7 points along sun-roof




          9 observation points within computational domain
Differencing Schemes Affect Disturbance Decay

          ------------------------------------------------------------------------------------------------------------
          |                                  |                                   |                                   |
          |                W                 w                 P                 |                 E                 |
          |                          --------------                             |                                   |
          |                                  |                                   |                                   |
          ------------------------------------------------------------------------------------------------------------

               r  (P  W ) /(W  WW )

     UDS : w  W                                                                         Hybrid scheme
     CDS : w  (P  W ) / 2                                                                 UDS, if Pe  2
                  3      3       1                                                         or  CDS, if Pe  2
     QUICK : w  P  W  WW
                  8      4       8                                                                     u x
                                                                                           where Pe  n
     SMART : w  W  0.5B(W  WW )                                                                                   
              B  max(0, min(2r ,0.75r  0.25r ,4))
     HQUICK : r  0,  w  W
                                                  2(P  W )(W  WW )
                  r  0,  w  W 
                                                     P  2W  3WW
Effect of Differencing Scheme: (a) Hybrid
                                      Pressure Fluctuation_Hybrid

                25

                                                                                                                            Source Input
                20
                                                                                                                            (fs=50Hz)
                15


                10
                                                                                                                                     Pdas at i1 k16
                                                                                                                                     Pdas at i10 k16
                 5                                                                                                                   Pdas at i40 k16
pressure (Pa)




                                                                                                                                     Pdas at i57 k16
                 0                                                                                                                   Pdas at i64 k16
                      0   0.1   0.2         0.3                              0.4                    0.5                   0.6        Pdas at i67 k16
                                                                                                                                     Pdas at i69 k16
                 -5
                                                                                                                                     Pdas at i71 k16
                                                                                                                                     Pdas at i77 k16
                -10
                                                                                     Pressure Fluctuation on top of sunroof_Hybrid

                -15                                                    3
                                                                       2
                                                      pressure (Pa)




                                                                       1                                                             Pdas at i67 k16
                -20                                                    0                                                             Pdas at i69 k16
                                                                      -1 0         0.1    0.2     0.3       0.4    0.5     0.6       Pdas at i71 k16
                                                                      -2
                -25                                                   -3

                                          time (s)                                              tim e (s)
                  Effect of Differencing Scheme: (b) QUICK
                                      Pressure Fluctuation_QUICK_528dt

                25
                                                                                                                                                                Source Input
                20
                                                                                                                                                                (fs=50Hz)
                15
                                                                                                                                                                           i1
                10                                                                                                                                                         i10
                                                                                                                                                                           i40
                 5                                                                                                                                                         i57
pressure (Pa)




                                                                                                                                                                           i64
                                                                                                                                                                           i67
                 0
                      0   0.1   0.2                 0.3                        0.4                                         0.5                                    0.6      i69
                                                                                                                                                                           i71
                 -5
                                                                                                                                                                           i77

                                                                                     P r e ssur e Fl uc t ua t i on on t op of sunr oof _ QU I C K _ 5 2 8 dt
                -10                                                     12
                                                                        10
                                                                                                                                                                          i65
                                                                         8
                -15                                                      6                                                                                                i66
                                                             pressure (Pa)




                                                                         4                                                                                                i67
                                                                         2                                                                                                i68
                -20                                                      0                                                                                                i69
                                                                        -2 0   0.1                0.2                    0.3                  0.4               0.5     0.6
                                                                                                                                                                          i70
                                                                        -4
                -25                                                     -6                                                                                                i71

                                                  time (s)              -8
                                                                                                                    tim e (s)
 Pressure time history at the sunroof LE
By QUICK scheme.




        6.7m
                           lx   6.7 m
                      t                 0.0197 s
                           c 0 340 m / s
FFT of Pressure Fluctuation – Resonance at 13Hz

 ---- Analyse Acoustic Response
                           500
                                                             i65
                                                             i66
                           400
  Power Spectral Density




                                                             i67
                           300                               i68
                                                             i69
                           200                               i70
                                                             i71
                           100

                             0
                                  0   5   10     15       20       25   30   35
                           -100
                                                 Frequency

                                               f = 13Hz
Helmholtz Equation, the FT of the Wave Equation

Homogeneous Wave equation

                                   2u
                                        c 2  2 u  0,
                                  t 2
Integrate with respect to time --- taking Fourier transform of the wave
equation
                                             
                           2 u it
                         2
                         t
                               e dt  c 2   2 ue it dt 0
                                         


finally, one gets
                                                          
             c    0,              where           ue it dt
              2       2       2

                                                         


  Apply inside car cavity – neglecting convective effects
                   Acoustic Pressure




x-axis direction
                Conclusion
•Coupling techniques offer a realistic alternative
to a full CAA simulation
•A complete acoustic response can be obtained
by the coupling of RANS and Helmholtz
equation
• High order schemes are necessary to avoid
numerical diffusion of fluctuations.
                 Acknowledgement
The Helmholtz Equation program is coded by Professor Frederic Magoules.
Supported by The British Council Franco-British Alliance Programme.



                         References
[1] Z. K. Wang, “A Source-extraction Based Coupling Method for
Computational Aeroacoustics”, PhD Thesis, University of Greenwich
(2004)
[2] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, (Hemisphere,
1980)
[3] G. S. Djambazov, “Numerical Techniques for Computational
Aeroacoustics”, PhD Thesis, University of Greenwich (1998)
[4] E. Avital, “A Computational and Analytical Study of Sound Emitted by
Free Shear Flows”, PhD Thesis, Queen Mary and Westfield College (1998)

[5] CFD Code PHOENICS, www.CHAM.co.uk

[6] CFD Code PHYSICA, www.physica.co.uk
50Hz Disturbance Velocity
  Vectors [u(x,t)* - u(x,t)]