In the previous modeling, the momentum equation includes the term Reynolds stress, which is modeled. One commonly used modeling approach is the Boussinesq hypothesis, which connects Reynolds stress with velocity gradients:
(6.5)
The Boussinesq hypothesis is used in the Spalart-Allmaras, κ-ε, and κ-ω models.
One advantage of this approach is its low computational effort, especially in calculating turbulent viscosity, miu,t, which only requires solving an additional transport equation.
From the explanation above, κ, ε, and ω respectively represent turbulence kinetic energy, turbulent dissipation rate, and specific dissipation rate.
However, the Boussinesq approach has a drawback in assuming miu,t as a scalar isotropic, which sometimes isn’t entirely accurate but remains sufficiently accurate for flows dominated by shear, such as boundary layers, mixing layers, jets, and others.
Another approach is Reynolds Stress Transport (RSM), which solves transport equations for the Reynolds stress tensor, requiring five to seven additional transport equations.
The RSM model is superior to Boussinesq for flows dominated by turbulent anisotropy, such as swirling flows or stress-driven secondary flows.
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