Fluids

Fluids

Closure problem associated with the RANS equations

    • Karthik R
      Administrator

      I am reading up on the Reynolds averaging of the Navier-Stokes equations. I was wondering if someone can shed light on the closure problem associated with the RANS equations? ?


    • prajput
      Ansys Employee

      Hello,

      The equations obtained from the Reynolds averaging of the Navier Stokes equations contain terms called the Reynolds stresses that are dependent on the velocity fluctuations in the flow. Since the idea of Reynolds averaging is to separate the mean and fluctuating parts of the turbulent flow and identify the equations governing the mean fluid flow behavior, these Reynolds stress terms need to be expressed in terms of mean flow quantities rather than the velocity fluctuations. This is called the closure problem.

    • Karthik R
      Administrator
      Thank you very much @prajput . That helps. I have a follow-up question. So, how is the problem avoided?

    • prajput
      Ansys Employee

      You are very welcome @Kremella  ! ?

      In order to tackle the closure problem you can use the Boussinesq approach. The Reynolds stresses are set to be proportional to the mean flow using a variable called the eddy viscosity. This resembles how the effect of molecular motion on fluid flow is described by molecular viscosity.

    • Karthik R
      Administrator
      aha, I see. I appreciate your help @prajput ?
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