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Analysis for cell restriction at the wall

  • Now we wonder what should be the size of the near wall cells
  • We consider theory based on flat plate analysis
  • Using the wall functions it may be sufficient to put   
  • We look for  meeting () for 
  • Friction coefficient  of turbulent boundary layer on the flat plate is known (correlation of measurements and DNS simulations)
  • For fast estimation: 
  • More accurate estimation is:

    (7.5)

  • For   ,               
  • So, finally the minimal cell height (the wall normal direction size) is $ 1.9 mm$