A Comparison of Algebraic and Differential Second-Moment Closures for Axisymmetric Turbulent Shear Flows With and Without Swirl

Computations are reported for three axisymmetric turbulent jets, two of which are swirling and one containing swirl-induced recirculation, obtained with two models of turbulence: a differential second-moment (DSM) closure and an algebraic derivative thereof (ASM). The models are identical in respect of all turbulent processes except that, in the ASM scheme, stress transport is represented algebraically in terms of the transport of turbulence energy. The comparison of the results thus provides a direct test of how well the model of stress transport adopted in ASM schemes simulates that of the full second-moment closure. The comparison indicates that the ASM hypothesis seriously misrepresents the diffusive transport of the shear stress in nonswirling axisymmetric flows, while in the presence of swirl the defects extend to all stress components and are aggravated by a failure to account for influential (additive) swirl-related stress-transport terms in the algebraic modelling process. The principal conclusion thus drawn is that in free shear flows where transport effects are significant, it is advisable to adopt a full second-moment closure if turbulence modelling needs to proceed beyond the eddy-viscosity level.