2.5. Governing Equations

Try these first

1. 1.

   What does Reynolds shear stress represent?

   Hint

   Think about the fluctuating part of fluid velocity.

2. 2.

   State what the closure problem involves.

   Hint

   Look for where we relate unknowns back to known quantities.

3. 3.

   What is the primary purpose of the closure problem in turbulence modeling?

   • To simplify equations
   • To relate unknowns to known values
   • To define flow direction

   Hint

   Focus on how turbulent flow terms are connected.

4. 4.

   True or False: The k-epsilon model only considers the velocity field in turbulent flows.

   • True
   • False

   Hint

   Reflect on what parameters the k-epsilon model uses.

5. 5.

   Given a turbulent flow with a Reynolds number of 10^5, estimate the number of grid points needed for DNS and discuss the computational challenges involved.

   Hint

   Use the power relationship to scale the number of required grid points.

6. 6.

   Explain how the k-epsilon model can be applied to a real-world scenario like airflow in a tunnel. Discuss the benefits and limitations.

   Hint

   Consider aspects like flow conditions and scales when relating it to the k-epsilon model.