Turbulence Modelling — Lesson 3

This lesson covers the concept of turbulence models in fluid dynamics, focusing on the Reynolds average Navier Stoke equations and the unknown Reynolds stress. The lesson explains how to model turbulent viscosity and discusses various turbulence models such as Prandtl's mixing length hypothesis, Spallard Almaras model, and two-equation models like standard K epsilon, RN GK epsilon, realizable K epsilon and K Omega model. The lesson also explains how to derive the equation for turbulent kinetic energy and the dissipation rate of this energy. It concludes by discussing the applications and advantages of different turbulence models in various fields like aerospace engineering.

Video Highlights

00:07 - Explanation of the Reynolds average Navier Stokes equations and the additional term Reynolds stress.
01:58 - Discussion on the zero equation model.
04:03 - Explanation of the standard K epsilon model and derivation of the expressions for turbulent kinetic energy and dissipation rate.
27:09 - Discussion on the significane of the terms of the equation for turbulent kinetic energy and equation for Eddy viscosity.
31:21 - Explanation of the RNG K epsilon model.
32:39 - Explanation of the K Omega model and its empirical constants.

Key Takeaways

- The Reynolds average Navier Stoke equations are used to model turbulent viscosity.
- Different turbulence models are used depending on the specific requirements of the flow being modeled.
- The Prandtl's mixing length hypothesis is a zero equation model that does not require solving any extra equations.
- Two-equation models like the standard K epsilon and K Omega model require solving additional equations to find the unknown Eddy viscosity.
- The standard K epsilon model is a versatile model used for industrial internal flows and aerospace applications.
- The RNG K epsilon model is suitable for transitional flows, while the K Omega model is used for rotational flows with high strain rates.