The synthesized isotropic turbulent fluctuations are generated at the inlet plane with a prescribed turbulent length scale and energy spectrum. A large number of independent realizations are generated. When running the unsteady CFD code a correlation in time between these realization is introduced via an asymmetric, non-truncated time filter. In this way the turbulent time scale of the synthesized isotropic turbulent fluctuations is prescribed.

Isotropic fluctuations are generated above. However, turbulence is generally anisotropic, The method can be summarized by the following steps.

• A Reynolds stress tensor, ⟨v'_i v'_j ⟩ is taken from DNS data for turbulent channel flow.
• The principal directions (the eigenvectors), are computed for the ⟨v'_i v'_j ⟩ tensor. The eigenvalues are normalized so that their sum is equal to three. This ensures that the kinetic energy of the synthetic fluctuations does not change during transformation.
• Isotropic synthetic fluctuations are then generated in the principal directions.
• The isotropic synthetic fluctuations in the principal directions are multiplied by the square-root of the normalized eigenvalues. This gives a new field of fluctuations.
• The new fluctuations are transformed to the computational coordinate system; the transformation matrix consists of the three eigenvectors.
• The Python and Matlab/Octave codes for generating the anisotropic fluctuations can be downloaded below.

Downloads
Here Python and Matlab/Octave Matlab files can be downloaded to generate isotropic and anisotropic synthetic fluctuations described above. The method is described in detail in the PDF files (see References below).

• The theory is described in my eBook
• readme
• Python files
  • synt_main.py, isotropic
  • synt_main_aniso.py, anisotropic
  • synt_main_earsm.py, anisotropic defined from EARSM
  • rans.py
  • angles.py
  • randf_1.py
  • randf_2.py
• Matlab/Octave files
  • synt_main.m, isotropic
  • synt_main_aniso.m, anisotropic
  • synt_main_earsm.m, anisotropic defined from EARSM
  • rans.m
  • rans_wallfunctions.m
  • angles.m
  • randf_1.m
  • randf_2.m
• yp_u_k_om_vist_uv_yc_PDH_8000.dat
• zp.dat
• set_inlet_bc.f

Integral time scale=0.015, computational time step=0.000625 (a=0.95, b=0.3)
Integral length scale=0.40
Colors show u'.

movie (6.2MB)
 

1. BILLSON, M
   "Computational Techniques for Turbulence Generated Noise", PhD thesis, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Göteborg, 2004.
     View PDF file
     Errata: View PDF file
    
   
2. M. Billson, L.-E. Eriksson and L. Davidson
   Jet Noise Modeling Using Synthetic Anisotropic Turbulence", 10th AIAA/CEAS Aeroacoustics Conference, AIAA 2004-3028, Manchester, United Kindom, 2004.
   View PDF file
    
   
3. L. Davidson
   "Using Isotropic Synthetic Fluctuations as Inlet Boundary Conditions for Unsteady Simulations" Advances and Applications in Fluid Mechanics, Vol. 1(1), pp. 1-35, 2007.
   View PDF file
    
   
4. L. Davidson
   "HYBRID LES-RANS: Inlet Boundary Conditions for Flows Including Recirculation", 5th International Symposium on Turbulence and Shear Flow Phenomena, Vol. 2, pp. 689-694, 27-29 August, Munich, Germany, 2007.
   View PDF file
    
   
5. Appendix: "Computation of wavenumber vector and angles"
   View PDF file
    
   
6. L. Davidson
   "Inlet fluctuating boundary conditions for 3D Hill Flow"
   View PDF file
    
   
7. L. Davidson and S.-H. Peng
   "Embedded LES Using PANS", I6th AIAA Theoretical Fluid Mechanics Conference, AIAA paper 2011-3108 27 - 30 Jun 2011, Honolulu, Hawaii.
   View PDF file
    
   
8. L. Davidson
   "Large Eddy Simulation of Heat Transfer in Boundary Layer and Backstep Flow Using PANS", Turbulence, Heat and Mass Transfer 7 Hanjalic, Y. Nagano, D. Borello and S. Jakirlic (Editors), Begell House, Inc., 2012
   View PDF file
    
   
9. L. Davidson and S.-H. Peng
   "Embedded Large-Eddy Simulation Using the Partially Averaged Navier-Stokes Model", AIAA J, Vol. 51(5), pp. 1066-1079, 2013. DOI
    
   
10. L. Davidson
    Fluid mechanics, turbulent flow and turbulence modeling, course material in MSc courses, Division of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology, Göteborg, 2010
    View PDF file