scholarly journals On the viscous core boundary layer of the injection and suction driven channel flows with expanding or contracting walls

2018 ◽  
Vol 98 (6) ◽  
pp. 969-980
Author(s):  
Joseph Majdalani ◽  
Li-Jun Xuan
Keyword(s):  
Boundary Layer ◽  
Channel Flows ◽  
Core Boundary ◽  
Viscous Core ◽  
Expanding Or Contracting Walls

scholarly journals Strongly nonlinear vortices in magnetized ferrofluids

1998 ◽  
Vol 40 (2) ◽  
pp. 146-170 ◽  
Author(s):  
Craig L. Russell ◽  
P.J. Blennerhassett ◽  
P.J. Stiles
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Layer Structure ◽  
Vortex Motion ◽  
Thin Layers ◽  
Marginal Stability ◽  
Weakly Nonlinear ◽  
Boundary Layer Equations ◽  
Conduction State ◽  
Core Boundary

AbstractNonlinear convective roll cells that develop in thin layers of magnetized ferrofluids heated from above are examined in the limit as the wavenumber of the cells becomes large. Weakly nonlinear solutions of the governing equations are extended to solutions that are valid at larger distances above the curves of marginal stability. In this region, a vortex flow develops where the fundamental vortex terms and the correction to the mean are determined simultaneously rather than sequentially. The solution is further extended into the nonlinear region of parameter space where the flow has a core-boundary layer structure characterized by a simple solution in the core and a boundary layer containing all the harmonics of the vortex motion. Numerical solutions of the boundary layer equations are presented and it is shown that the heat transfer across the layer is significantly greater than in the conduction state.

A Note on a Generalized Eddy-Viscosity Hypothesis

1992 ◽  
Vol 114 (3) ◽  
pp. 463-466 ◽  
Author(s):  
P. Andreasson ◽  
U. Svensson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Eddy Viscosity ◽  
Channel Flows ◽  
Length Scale ◽  
Asymmetric Channel ◽  
Boundary Layer Flows ◽  
Turbulent Length Scale ◽  
Model Predictions

The standard eddy-viscosity concept postulates that zero velocity gradient is accompanied by zero shear stress. This is not true for many boundary layer flows: wall jets, asymmetric channel flows, countercurrent flows, for example. The generalized eddy-viscosity hypothesis presented in this paper, relaxes this limitation by recognizing the influence of gradients in the turbulent length scale and the shear. With this new eddy-viscosity concept, implemented into the standard k–ε model, predictions of some boundary layer flows are made. The modelling results agree well with measurements, where predictions with the standard eddy-viscosity concept are known to fail.

Friction velocity and power law velocity profile in smooth and rough shallow open channel flows

2002 ◽  
Vol 29 (2) ◽  
pp. 256-266 ◽  
Author(s):  
R Balachandar ◽  
D Blakely ◽  
J Bugg
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Froude Number ◽  
Power Law ◽  
Friction Velocity ◽  
Open Channel ◽  
Rough Surfaces ◽  
Channel Flows ◽  
Open Channel Flows ◽  
Log Law

This paper examines the mean velocity profiles in shallow, turbulent open channel flows. Velocity measurements were carried out in flows over smooth and rough beds using a laser-Doppler anemometer. One set of profiles, composed of 29 velocity distributions, was obtained in flows over a polished smooth aluminum plate. Three sets of profiles were obtained in flows over rough surfaces. The rough surfaces were formed by two sizes of sand grains and a wire mesh. The flow conditions over the rough surface are in the transitional roughness state. The measurements were obtained along the centerline of the flume at three different Froude numbers (Fr ~ 0.3, 0.8, 1.0). The lowest Froude number was selected to obtain data in the range of most other open channel testing programs and to represent a low subcritical Froude number. For each surface, the Reynolds number based on the boundary layer momentum thickness was varied from about 600 to 3000. In view of the recent questions concerning the applicability of the log-law and the debate regarding log-law versus power law, the turbulent inner region of the boundary layer is inspected. The fit of one type of power law for shallow flows over a smooth surface is considered. The appropriateness of extending this law to flows over rough surfaces is also examined. Alternate methods for determining the friction velocity of flows over smooth and rough surfaces are considered and compared with standard methods currently in use.Key words: power law, open channel flow, velocity profile, surface roughness.

A Numerical Computation of a Confined Rotating Flow

1970 ◽  
Vol 37 (2) ◽  
pp. 480-487 ◽  
Author(s):  
Hsien-Ping Pao
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Bottom Boundary Layer ◽  
Navier Stokes ◽  
Bottom Boundary ◽  
Small Reynolds Numbers ◽  
Viscous Core ◽  
High Reynolds

A numerical investigation of a viscous incompressible fluid confined in a closed circular cylindrical container is made. The top and side wall are in rotation with a constant angular velocity, and the bottom is held fixed. A numerical scheme using the full Navier-Stokes equations is developed. For small or moderate Reynolds numbers (Re = ΩL2/ν), the convergence of iteration is quite rapid. When the Reynolds number increases, the flow in the bottom boundary layer and the viscous core is intensified. An initial value problem is also investigated for Re = 1000 and 5000. The flow development of the bottom boundary layer and the viscous core is clearly exhibited. Some experimental investigation is also made. The numerical solution agrees very well with the analytic solution for small Reynolds numbers and with the experimental observation for moderate and high Reynolds numbers.

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