Jet Impingement of a Non-Newtonian Fluid

2006 ◽  
Author(s):  
Jiangang Zhao ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Hydraulic Jump ◽  
Similarity Solutions ◽  
Surface Velocity ◽  
Free Surface Velocity ◽  
Viscous Boundary Layer ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Viscous Boundary

The similarity solutions are presented for the wall flow which is formed when a smooth planar jet of power-law fluids impinges vertically on to a horizontal plate, and spreads out in a thin layer bounded by a hydraulic jump. This problem is formulated analogous to radial jet flow problem and the solution procedure is accounted for by means of similarity solution of the boundary-layer equation [1] for Newtonian fluids. For the convenience of analysis, the flow may be divided into three regions, namely a developing boundary-layer region, a fully viscous boundary-layer region, and a hydraulic jump region. The similarity solutions of the film thickness and free surface velocity in fully viscous boundary-layer region include unknown constant L, which is solved numerically and approximately in the developing boundary-layer flow region. Comparison between the numerical and approximate solutions leads generally to good agreement, except for severely shear-thinning fluids. The boundary-layer solution depends on two parameters: power-law index n and α, the dimensionless flow parameters. The effect of α on film thickness and free surface velocity is investigated. The relations between the position of the hydraulic jump and dimensionless flow parameter are obtained and the effect of α on the position of the jump is presented.

Mass transport in water waves over an elastic bed

1995 ◽  
Vol 450 (1939) ◽  
pp. 371-390 ◽  
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Mass Transport ◽  
Water Waves ◽  
Viscous Boundary Layer ◽  
Curvilinear Coordinate ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Orthogonal Curvilinear Coordinate System ◽  
Viscous Boundary

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

scholarly journals CONTRA-ROTATING PROPELLER AERODYNAMICS SOLVED BY A 3D PANEL METHOD WITH COUPLED BOUNDARY LAYER

2017 ◽  
Vol 57 (5) ◽  
pp. 355 ◽  
Author(s):  
Vít Štorch ◽  
Jiří Nožička
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Panel Method ◽  
Vortex Wake ◽  
Viscous Boundary Layer ◽  
Free Vortex ◽  
Operational Conditions ◽  
Equation Boundary ◽  
Layer Region ◽  
Viscous Boundary

The aerodynamics of contra-rotating propellers is a complex three-dimensional problem of an unsteady flow, which is often approached by assuming numerous simplifications. Presented computational model combines a 3D panel method with a force-free vortex wake and a two-dimensional two-equation boundary layer model in an attempt to capture all the main contributing elements of the flow physics. An emphasis is placed on the interaction of the viscous boundary layer region with the inviscid region and the development of a portable method of their coupling. The kinematics of a force-free vortex wake is supplemented with a vortex aging due to a diffusion. Extra attention is paid to the process of the blade passing through the wake of another blade. To demonstrate the ability of the numerical model, several test cases are presented, illustrating the reaction of the system to various operational conditions.

Flow of Moving Wall Jet Near Channel Exit at Moderate Reynolds Number

2010 ◽  
Author(s):  
Rizwana Amin ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Equations Of Motion ◽  
Outer Region ◽  
Moving Wall ◽  
Moderate Reynolds Number ◽  
Boundary Layer Region ◽  
Asymptotic Development ◽  
Layer Region

The two-dimensional jet flow of a Newtonian fluid at moderate Reynolds Number emerging from a channel where the upper plate is moving is examined theoretically in this study. In this case, the equations of motion are reduced by expanding the flow field about the basic Couette flow. Inertia is assumed to be large enough, allowing asymptotic development in terms of the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow in the free surface and the moving wall. The influence of this boundary layer is investigated with the aid of the method of matched asymptotic expansions. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface and the flow both in the inner (boundary-layer) region and in the outer region of the core. The influence of wall velocity on the shape of the free surface, the velocity and stress is emphasized. The formulation allows for the determination of the steady state flow and free surface profiles analytically. The present work provides the conditions near exit, with the help of Higher-order boundary-layer effects (i.e. the cubic term of the inverse Reynolds number), to determine the jet structure further downstream.

Sign in / Sign up

Export Citation Format

Share Document