Fluid motion in a rotating sliced cylinder

1970 ◽  
Vol 68 (1) ◽  
pp. 203-212
Author(s):  
J. A. Durance
Keyword(s):  
Boundary Layer ◽  
Viscous Incompressible Fluid ◽  
Fluid Motion ◽  
Steady Motion ◽  
Side Wall ◽  
Rotating Circular Cylinder ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Interior Flow ◽  
Sloping Bottom

AbstractSteady motion of a viscous incompressible fluid in a rotating circular cylinder with a sloping bottom is investigated at low Ekman number. The flow is driven by a lightly faster rotation of the top, and non-linear inertia terms are neglected.A solution is found for a shallow container of small bottom slope. The side-wall boundary layer is shown to have an almost axi-symmetric component as well as the asymmetric layer found by Pedlosky and Greenspan (3). A further asymmetry in the interior flow is produced by the presence of the second component of the side-wall boundary layer.

The axisymmetric convective regime for a rigidly bounded rotating annulus

1968 ◽  
Vol 32 (4) ◽  
pp. 625-655 ◽  
Author(s):  
Michael E. Mcintyre
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Axisymmetric Flow ◽  
Side Wall ◽  
Boundary Layer Equations ◽  
Wall Boundary Layer ◽  
Ekman Layers ◽  
Interior Flow ◽  
Side Walls ◽  
Annular Container

The axisymmetric flow of liquid in a rigidly bounded annular container of heightH, rotating with angular velocity Ω and subjected to a temperature difference ΔTbetween its vertical cylindrical perfectly conducting side walls, whose distance apart isL, is analysed in the boundary-layer approximation for small Ekman numberv/2ΩL2, withgαΔTHv/4Ω2L2K∼ 1. The heat transfer across the annulus is then convection-dominated, as is characteristic of the experimentally observed ‘upper symmetric regime’. The Prandtl numberv/kis assumed large, andHis restricted to be less than about 2L. The side wall boundary-layer equations are the same as in (non-rotating) convection in a rectangular cavity. The horizontal boundary layers are Ekman layers and the four boundary layers, together with certain spatialaveragesin the interior, are determined independently of the interior flow details. The determination of the latter comprises a ‘secondary’ problem in which viscosity and heat conduction are important throughout the interior; the meridional streamlines are not necessarily parallel to the isotherms. The secondary problem is discussed qualitatively but not solved. The theory agrees fairly well with an available numerical experiment in the upper symmetric regime, forv/k[bumpe ] 7, after finite-Ekmannumber effects such as finite boundary-layer thickness are allowed for heuris-tically.

Computational modeling of the flow in a wind tunnel

2018 ◽  
Vol 90 (1) ◽  
pp. 175-185 ◽  
Author(s):  
Mahmood Khalid ◽  
Khalid A. Juhany ◽  
Salah Hafez
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Computational Modeling ◽  
Stokes Equations ◽  
Side Wall ◽  
Simultaneous Application ◽  
Content Type ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Solid Walls

Purpose The purpose of this paper is to use a computational technique to simulate the flow in a two-dimensional (2D) wind tunnel where the effect of the solid walls facing the model has been addressed using a porous geometry so that interference arriving at the solid walls are duly damped and a flow suction procedure has been adopted at the side wall to minimize the span-wise effect of the growing side wall boundary layer. Design/methodology/approach A CFD procedure based on discretization of the Navier–Stokes equations has been used to model the flow in a rectangular volume with appropriate treatment for solid walls of the confined volume in which the model is placed. The rectangular volume was configured by stacking O-Grid sections in a span-wise direction using geometric growth from the wall. A porous wall condition has been adapted to counter the wall interference signatures and a separate suction procedure has been implemented for reducing the side wall boundary layer effects. Findings It has been shown that through such corrective measures, the flow in a wind tunnel can be adequately simulated using computational modeling. Computed results were compared against experimental measurements obtained from IAR (Institute for Aerospace, Canada) and NAL (National Aeronautical Laboratory, Japan) to show that indeed appropriate corrective means may be adapted to reduce the interference effects. Research limitations/implications The solutions seemed to converge a lot better using relatively coarser grids which placed the shock locations closer to the experimental values. The finer grids were more stiff to converge and resulted in reversed flow with the two equation k-w model in the region where the intention was to draw out the fluid to thin down the boundary layer. The one equation Spalart–Allmaras model gave better result when porosity and wall suction routines were implemented. Practical implications This method could be used by industry to point check the results against certain demanding flow conditions and then used for more routine parametric studies at other conditions. The method would prove to be efficient and economical during early design stages of a configuration. Originality/value The method makes use of an O-grid to represent the confined test section and its dual treatment of wall interference and blockage effects through simultaneous application of porosity and boundary layer suction is believed to be quite original.

scholarly journals Viscous Flow Field Calculations in High-Loaded Centrifugal Compressor Diffusers

1990 ◽  
Author(s):  
Ingolf Teipel ◽  
Alexander Wiedermann
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Sheet Thickness ◽  
Side Wall ◽  
Flow Fields ◽  
Wall Boundary Layer ◽  
Wall Boundary

The topic of this paper is the computation of transonic turbulent flow fields in high-loaded centrifugal compressor diffusers with a time-marching scheme. A thin-layer approximation is introduced into the time-dependent Navier-Stokes equations and the turbulent quantities are provided by a zero-equation eddy-viscosity model due to Baldwin and Lomax. For solving the governing equations an explicit-implicit MacCormack scheme is applied. The effect of the side wall boundary layer can be employed globally by variable stream sheet thickness. The present code has been verified by comparison of calculated and measured data. Pressure and velocity fields as well as global results like diffuser efficiency have been considered. The code is very efficient at a CRAY-XMP vector computer. Hence, two-dimensional and quasi-three-dimensional turbulent flow fields can be obtained with a reasonable effort. However, one has to be very careful concerning the modelling of the effect of the side-wall boundary layer by variable stream sheet thickness.

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