Towards a calibration of the length-scale equation

Behaviour of turbulence models near a turbulent/non-turbulent interface revisited

“…The power law solution found by Cazalbou et al (1994) is retrieved together with a second power law solution which was already pointed out by Catris (1999) and Catris and Aupoix (2000), to be discussed later. As the transformed eddy viscosity g is linear, it must be pointed out that the length scale determining variable and turbulent kinetic energy evolutions are linked, as pointed out by Daris (2002) and Aupoix et al (2003), as:…”

“…The present analysis holds as well for two-equation models, whatever the constitutive relation (eddy viscosity, non-linear eddy viscosity or explicit algebraic Reynolds stress model) as for differential Reynolds stress models. For that, generic models, following Catris and Aupoix (2000), are introduced.…”

“…Compared to the generic form proposed by Catris and Aupoix (2000), a diffusion term was dropped in the turbulent kinetic energy transport equation for the sake of simplicity. These transport equations have to be coupled with a constitutive relation, of the eddy viscosity form, either linear or non-linear.…”

Assessment of Reynolds-stress models for aeronautical applications

“…The SSG/LRR-ω and the SSG-ω-Aup models both use the specific dissipation rate ω as the lengthscale providing quantity, due to its improved performance in adverse-pressure-gradient (APG) flow, and thus in aeronautical applications. This behavior, observed for the two-equation k − ω models, has been explained by Huang and Bradshaw (1995) and Catris and Aupoix (2000) by the mathematical ability of the ωequation to preserve the log-law prediction in APG, compared to the ε-equation. The SSG-ω-Aup model also uses a specific nearwall approach to correctly reproduce the asymptotic behavior of the turbulent quantities at the wall, including the near-wall model of Manceau and Hanjalić (2002) developed for the EB-RSM.…”

“…where y corresponds to the wall distance. The clipping corresponds to a Yap-type correction to prevent the deviation of the log-law slope in APG flows (see for instance Catris and Aupoix, 2000), whereas the damping function ensures the correct asymptotic behavior of k close to the wall.…”