Results are presented from a numerical investigation of turbulent source flow between two discs, both of which are stationary or corotating. Parabolic flow was assumed and the Box Method used to obtain marching solutions of the governing equations. Turbulence modelling was based on extensions of classical eddy-viscosity/mixing-length concepts which reflect the influences of divergence of the mean-flow streamlines and non-isotropic Reynolds stresses due to disc rotation. The predictions for the rotating case are the first local results available. For the stationary case, earlier work has been extended by the use of empirical formulae for reverse transition and inclusion of the influence of streamline divergence. Comparisons with limited data for stationary and corotating discs show reasonable agreement. Although the turbulence models are probably not optimum, they provide an adequate basis for engineering studies of turbulent source flow between corotating and stationary discs until more extensive and reliable empirical information is available.

The development of turbulent shear layers on rotating or curved surfaces is usually characterized by strong effects of streamline curvature on the turbulence structure. The present contribution deals with the calculation of these effects with a model of turbulence which solves transport equations for the turbulence kinetic energy and its local rate of dissipation. The direct effect of curvature in the model is limited to a single empirical coefficient whose magnitude is directly proportional to a Richardson number based on a time scale of the energy-containing eddies. (In the absence of significant streamline curvature the model reduces to a form that has earlier been extensively tested in various thin shear flows.) Finite difference computations are reported of the following turbulent flows: the boundary layer on concave and convex surfaces; fully developed flow in a curved channel; axisymmetric flow over a spinning cylinder; and heat and mass transfer due to spinning cones of various vertex angles. Agreement with experiment is satisfactorily close in all these cases.

Technical Briefs Prediction of Local Heat Transfer on a Rotating Disk By a Two-Equation Model of Turbulence B. I. Sharma B. I. Sharma Department of Mechanical Engineering, Imperial College of Science and Technology, London, England Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information B. I. Sharma Department of Mechanical Engineering, Imperial College of Science and Technology, London, England J. Heat Transfer. Feb 1977, 99(1): 151-152 (2 pages) https://doi.org/10.1115/1.3450643 Published Online: February 1, 1977 Article history Received: September 10, 1976 Online: August 11, 2010

Numerical predictions are presented of fully-developed turbulent flow through a concentric annulus in which the core tube rotates about its axis. Comparisons are drawn with the extensive experimental data of Kuzay and Scott [1] which span Reynolds numbers from 1.7 to 104 to 6.5 × 104 and with rotational speeds of the core tube varying from zero to nearly 2.8 times the bulk axial velocity. Predictions have been obtained by means of an adapted version of the Patankar-Spalding [5], numerical procedure employing, as turbulent transport model, the version of the mixing length hypothesis applied by Koosinlin, Sharma and Launder [2] to flows on spinning cones and cylinders. Agreement with experiment is generally close at the higher relative swirl rates but the predictions of the swirling velocity profile deteriorate as the bulk flow rate is increased. The discrepancy seems to be due to the experimental data requiring a greater development length as the magnitude of the rotational velocity is reduced relative to that of the mean flow. Demonstrative developing-flow predictions are provided which exhibit closer agreement with the experimental data.

This note compares the finite difference predictions of local Nusselt number on a rotating disc in still air with the very recent experimental data of Popiel and Bogulawski (1). Their measurements include laminar, transitional and turbulent regimes up to spin Reynolds number of 6.5∗105. The model of turbulence employed in the calculations is a “swirl flow” version of the Prandtl's mixing length hypothesis. Agreement with the experimental data is satisfactorily close.

The paper presents the outcome of finite-difference calculations of turbulent flow near spinning cones, disks, and cylinders. The turbulence model used is a version of the mixing-length hypothesis in which the mixing length which would prevail in the absence of swirl is made a linear function of the local “swirling flow” Richardson number. Agreement with available experimental data for these geometries is generally good. At high swirl rates, however, a few systematic differences between experiment and calculation become evident which are probably attributable to the nonisotropic nature of the effective viscosity in such complex strain fields.