VL XI - Eddy viscosity modeling

With which quantity does the cost for a Turbulent Simulation Scale

Reynolds number

What scales are needed for Modeling RANS

• Velocity/Time scale

• Length scale

Ananlogy Turbulent fluctuations to molecular diffusion

• Eddies exchange momentum with another

Formel Normal Stress

With what does molecular viscosity differ

With different fluids

With what does turbulent viscosity differ

With different flows

Problems of Mixing length model

• Dominant flow direction and wall distance need to be known

• Potential overestimation of mixing layer

  • turbulent viscosity

    • momentum transfer at wall

      • delayed detachment prediction

• Main Problem is prediction of turbulent viscosity in outer flow domain

Pros and Cons of Algebraical Models

Pros:

• Mathematical simplicity

• Numerical robustness

• Suitable for 2D boundary layers without detachment or pressure gradients

Cons:

• Insufficient for complex flows with significantly curved mean streamlines

• Works fors small groups of flows only with proper parameter calibration

• No robust generalization

Modeling Problem of Algebraic Models

For algebraic Models: Eddie viscosity = 0 for mean velocity at core, which is a problem

» Solution: two equation models

Whats dissipation in regards to Turbulence

Change of TKE over Time

Pros and Cons One equation model

Pros:

• Mathematical simplicity

• No Transport eq. required for dissipation

• Includes knowledge on TKE transport

• Calibrated for shear dominated flows

Cons:

• Extra-effort of additional transport equation

• Empirical relations for lentgh-scale, therefore often failing for complex flows

Concept of Eddy-Viscosity Transport model

• Directly model transport of eddy-viscosity as derived quantity

• Note, such a tranport equation is not derived from conservation law

Pros and Cons of Transport models

Pros:

• Robustness and effeciency similar to simple on-eq. models

• no length scale required

• Good results for simple shear flows including detachment

Cons:

• No physical justification

• Unsuitable for complex flows and free jets