One-Equation Turbulence Model based on ε-Equation

M. M. Rahman, R. K. Agarwal, T. Siikonen

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


A one–equation variant of a two–equation k-ϵ turbulence model based on the mean dissipation–rate ϵ–equation is constructed to account for the distinct effects of low–Reynolds number (LRN) and wall proximity. The turbulent kinetic energy k is evaluated with an algebraically prescribed length scale having only one adjustable coefficient. The stress–intensity ratio Ra = uv/k is devised as a function of local variables without resorting to a constant √Cμ = 0.3. An anisotropic function fk is embedded with Ra to reduce its magnitude in the near–wall region. Consequently, the parameter Ra entering the turbulence production Pk is supposed to prevent the overestimation of Pk in flow regions where non–equilibrium effects may result in a misalignment between turbulent stress and mean strain–rate with a linear eddy–viscosity model. The Bradshaw–relation Ra and the coefficients of length-scale determining terms are calibrated against the fully developed turbulent channel flow; they yield good predictions. A comparative assessment of the present model with the Spalart–Allmaras (SA) one–equation model and the shear stress transport (SST) k–ω model is provided for well–documented simple and non–equilibrium turbulent flows.

Original languageEnglish
Title of host publication46th AIAA Fluid Dynamics Conference
Number of pages18
ISBN (Print)9781624104367
Publication statusPublished - 2016
MoE publication typeA4 Article in a conference publication
EventAIAA Fluid Dynamics Conference - Washington, United States
Duration: 13 Jun 201617 Jun 2016
Conference number: 46


ConferenceAIAA Fluid Dynamics Conference
CountryUnited States


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