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DOI: 10.1016/S1001-6058(14)60019-6

Direct numerical simulation of Open Von Kármán Swirling Flow*


Department of Mechanical Engineering, College of Engineering, University of Idaho, Idaho 83844-0902, USA, E-mail:

(Received January 15, 2014, Revised April 10, 2014)

Abstract: Direct numerical simulations are used to investigate the Open Von Kármán Swirling Flow, a new type of unsteady three-dimensional flow that is formed between two counter-rotating coaxial disks with an axial extraction enclosed by a cylinder chamber. Solution verification shows that monotonic convergence is achieved on three systematically refined grids for average pressure at the disk periphery with a small grid uncertainty at 3.5%. Effects of the rotational speeds and flow rates on the flow field are examined. When the disks are rotating at the lowest speed, 100 RPM, only circular vortices are formed regardless of the flow rates. When the disks are rotating at 300 RPM and 500 RPM, negative spiral vortex network is formed. The radial counterflow concept for such spiral vortex network is verified by examining various horizontal cuts and radial velocity component, which show radial outflows in two bands near the two disks and radial inflow in one band between them. Overall, the flow is similar to the Stewartson type flow but with significant differences for all three velocity components due to the axial suction at the upper disk center and gap between the disk periphery and chamber wall.

Key words: direct numerical simulation, Open Von Kármán flow, swirling, radial counterflow



Fluid motion between two coaxial disks/plates

has been studied extensively for decades due to their importance to industrial applications. Applications of such flows in practice include heat and mass excha- ngers[1], disk reactor for intensified synthesis of bio- diesel[2], open clutch system[3,4], lubrication[5], rotating packed beds[6], and internal cooling-air systems of most gas turbines[7], etc. The two disks/plates may co- rotate, counter-rotate, or one disk is stationary and the other rotates (rotor-stator system), which creates dra- matically different flow patterns.

Limited number of studies used analytical metho- ds, likely due to the strong viscous effect within the boundary layers near the disk surfaces and strong three-dimensional features of the flow. Batchelor[8] so- lved the steady rotationally-symmetric viscous lami- nar flow between two infinite disks. When the two disks are exactly counter-rotating, the distribution of

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tangential velocity is symmetrical about the mid-plane and exhibits five distinct regions: two disk boundary layers, a transition shear layer at mid-plane, and two rotating cores on either side of the transition layer. Stewartson[9] draw controversial conclusions on the flow structure as he found that the flow is divided into only three zones when the Reynolds number ReH =

H2 / 100, where H is the disk spacing,  is the rotational speed of the disk and  is the fluid ki- nematic viscosity. The three regions are two boundary layers on the two disk surfaces separated by a region that has zero tangential velocity and uniform radial in- flow. The work by Wilson and Schryer[10] numerically solved the steady viscous flow between two coaxial infinite disks with one stationary and the other rota- ting. The effects of applying a uniform suction throu- gh the rotating disk are determined. At large Reynolds numbers, the equilibrium flow approaches an asymp- totic state in which thin boundary layers exist near both disks and an interior core rotates with nearly con- stant angular velocity. The flow field is assumed to be axisymmetric. This study also demonstrates that more than one steady (equilibrium) solution exist for the

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