A New “λ2” Term for the Spalart–Allmaras Turbulence Model, Active in Axisymmetric Flows

Abstract The new term belongs in the “basic,” free-shear-flow part of Spalart–Allmaras (SA) model, and extends an idea Secundov team, incorporated ν t -92 model. It detects transverse curvature distribution eddy viscosity $$ \tilde{\nu } ν ~ , so that it is passive two-dimensional thin shear flows but potent especially round jets. eliminates large over-prediction growth rate such jets by SA first detected Birch 1993. originality proportional to middle eigenvalue λ 2 Hessian operator . This course empirical concept, discriminating rises when distance r from cylindrical axis becomes comparable with length scale δ variations direction. inverted parabola a prime example distribution, not unlike jet. quantity infinitely differentiable, free singularities, version, dependent on two quantities cancelling. core added Lagrangian derivative D\tilde{\nu }/Dt D / t simply c b3 where constant. computing cost calculating ordering eigenvalues moderate. We have no proof well-posedness for equation set, evidence far favorable, both structured unstructured grids. calibrated fully-developed jet, tested nine other cases, either 2D or which » δ, finding latter negligible as expected. although constant rather large, namely 6. strong enough make mature vortex fully relaminarize would be desirable, drops 74%. raw reduces pipe flow, detrimental; therefore, final multiplied function parameter measure wall proximity. appears safe addition its application different codes variety desirable.