An integral criterion for turbulence suppression in swirling flows

Abstract

AbstractA numerical study of flow in rotating pipes was conducted to elucidate the relative importance of convection and turbulence. CFD (Computational Fluid Dynamics) simulations of flow inside a rotating pipe (D = 2 cm and L/D = 20) were carried out, using the Reynolds Stress Model, for four different Reynolds numbers and a range of rotation numbers. The objective was to gain a deeper understanding of the interaction between fluid forces in swirling flows. This widely‐studied model problem was used to ascertain the conditions under which computationally cheaper turbulence models such as the k‐ϵ model should be accurate.We identified a dimensionless rotation parameter that delineates the condition at which decreasing turbulence force equals increasing convective force as rotational speed increases. This dimensionless number establishes a criterion for knowing which forces are dominant, and thereby a rational basis for choosing turbulence models that are both cost‐effective and accurate. We found a universal, critical threshold that determines when convective forces dominate over turbulence forces. This threshold determination is based on an ‘integral measure criterion’ of local forces in the radial direction. The threshold itself is defined by a dimensionless rotation number, N, based on the ratio of the circumferential and axial flow velocities. The critical value was found to be Ncr = 0.45. Above this, convection dominates; below it, turbulence dominates. This finding will facilitate selection of CFD models to optimize cost and accuracy for modelling swirling flows. For example, k‐ϵ models suffice when Ncr < 0.45, but more complex models are required for higher values.