Experiments on Laminar Flow about a Rotating Sphere in an Air Stream

1987 ◽  
Vol 201 (6) ◽  
pp. 427-438 ◽  
Author(s):  
M A I El-Shaarawi ◽  
M M Kemry ◽  
S A El-Bedeawi
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Separation Angle ◽  
Governing Equations ◽  
Rotating Sphere ◽  
Axis Of Rotation ◽  
Air Stream ◽  
Uniform Stream

Laminar flow about a rotating sphere which is subjected to a uniform stream of air in the direction of the axis of rotation is investigated experimentally. Measurements of the velocity components within the boundary layer and the separation angle were performed at a Reynolds number, Re, of 10 000 and Ta/Re 2 of 0, 1 and 5. These measurements are compared with the numerical solutions of the same problem where either theoretical potential or actual experimental boundary conditions are imposed on the governing equations.

Numerical Solution of Laminar Boundary Layer Flow About a Rotating Sphere in an Axial Stream

1985 ◽  
Vol 107 (1) ◽  
pp. 97-104 ◽  
Author(s):  
M. A. I. El-Shaarawi ◽  
M. F. El-Refaie ◽  
S. A. El-Bedeawi
Keyword(s):  
Boundary Layer ◽  
Present Scheme ◽  
Rotating Sphere ◽  
Boundary Layer Equations ◽  
Meridional Velocity ◽  
Axis Of Rotation ◽  
Stress Components ◽  
Layer Flow ◽  
Momentum Integral ◽  
Uniform Stream

A finite-difference scheme is developed for solving the boundary layer equations governing the laminar flow about a rotating sphere which is subjected to a uniform stream in the direction of the axis of rotation. Numerical results are presented for the meridional and azimuthal velocities and for the wall-shear-stress components. Also, the angle at which the meridional velocity gradient normal to the wall vanishes is given at values of the parameter Ta/Re2 ranged from zero (the stationary sphere case) to 10000. As compared with the momentum integral technique of Schlichting [8], the present scheme succeeded in obtaining solutions for very considerably larger values of the parameter Ta/Re2.

Heat Transfer in the Laminar Boundary Layer Over an Impulsively Started Flat Plate

1975 ◽  
Vol 97 (3) ◽  
pp. 482-484 ◽  
Author(s):  
C. B. Watkins
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Constant Temperature ◽  
Laminar Boundary Layer ◽  
Temperature Difference ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Prandtl Numbers

Numerical solutions are described for the unsteady thermal boundary layer in incompressible laminar flow over a semi-infinite flat plate set impulsively into motion, with the simultaneous imposition of a constant temperature difference between the plate and the fluid. Results are presented for several Prandtl numbers.

Viscous shear flow past small bluff bodies attached to a plane wall

1975 ◽  
Vol 69 (4) ◽  
pp. 803-823 ◽  
Author(s):  
Masaru Kiya ◽  
Mikio Arie
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Major Axis ◽  
Plane Wall ◽  
Local Boundary ◽  
Flow Past ◽  
Viscous Shear

Numerical solutions of the Navier-Stokes equations are presented for two-dimensional viscous flow past semicircular and semielliptical projections attached to a plane wall on which a laminar boundary layer has developed. Since the major axis is in the direction normal to the wall and is chosen to be twenty times as long as the minor axis in the present case, the flow around the semielliptical projection will approximately correspond to that around a normal flat plate. It is assumed that the height of each obstacle is so small in comparison with the local boundary-layer thickness that the approaching flow can be approximated by a uniform shear flow. Numerical solutions are obtained for the range 0·1-100 of the Reynolds number, which is defined in terms of the undisturbed approaching velocity at the top of the obstacle and its height. The geometrical shapes of the front and rear standing vortices, the drag coefficients and the pressure and shear-stress distributions are presented as functions of the Reynolds number. The computed results are discussed in connexion with the data already obtained in the other theoretical solutions and an experimental observation.

scholarly journals Effects of Suction and Blowing on Flow Separation in a Symmetric Sudden Expanded Channel

2008 ◽  
Vol 13 (4) ◽  
pp. 451-465 ◽  
Author(s):  
G. C. Layek ◽  
C. Midya ◽  
S. Mukhopadhyay
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Finite Difference ◽  
Recirculation Zone ◽  
Critical Reynolds Number ◽  
Governing Equations ◽  
Flow Asymmetry ◽  
Suction And Blowing ◽  
Finite Difference Techniques

A numerical simulation has been carried out to study the laminar flow in a symmetric sudden expanded channel subjected to a uniform blowing/suction speed placed at the lower and upper porous step walls. The governing equations for viscous flow have been solved using finite-difference techniques in pressure-velocity formulation. The results obtained here have been compared with the available experimental and numerical results of similar problems. It is noted that the recirculating region formed near the step walls diminishes in its length for increasing values of blowing speed applied at the porous step walls. For a suitable blowing speed, the recirculation zone disappears completely. The critical Reynolds number for the flow bifurcation (i.e. flow asymmetry) is obtained and it increases with the increase of the blowing speed. The critical Reynolds number for symmetry breaking of the flow decreases with the increasing values of suction speeds. The primary and the secondary recirculating regions formed near the channel walls are controlled using blowing.

Correlated unsteady and steady laminar trailing-edge flows

1981 ◽  
Vol 108 ◽  
pp. 171-183 ◽  
Author(s):  
S. N. Brown ◽  
H. K. Cheng
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Small Amplitude ◽  
Frequency Parameter ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Sinusoidal Oscillations ◽  
Steady Laminar ◽  
Uniform Stream

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of small amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. It is shown that if the frequency parameter is of any order less than R¼ the viscous correction to the Kutta condition and hence to the lift and moment may be determined from the results for the steady case. Justification of this correlation requires discussion of the flow in an additional region not encountered in previous studies.

Analysis of the Convergent Channel as an Extensional Rheometer

1999 ◽  
Author(s):  
P. R. Souza Mendes ◽  
R. L. Thompson ◽  
A. O. Nieckele
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Numerical Solutions ◽  
Mechanical Energy ◽  
Flow Characteristics ◽  
Channel Length ◽  
Geometrical Parameters ◽  
Inlet Section ◽  
Convergent Channel ◽  
Number Range

Abstract An important aspect while designing an “R2 z = constant” convergent channel as an extensional rheometer is the appropriate choice of the geometrical parameters and of the Reynolds number range of operation. The higher is the Reynolds number value, the thinner will be the boundary layer where the undesirable no-slip effect is confined, as discussed in the literature. However, if the Reynolds number, Re, is too large, then shear-related pressure losses become important, which is also undesirable in rheometry. Therefore, one design task is to find a range of Re within which the boundary layer is thin enough, and the velocity field in most of the domain is reasonably close to the desired kinematics. In this work we obtained numerical solutions for the flow of Newtonian and viscoelastic fluids through a convergent channel, for representative ranges of Re, dimensionless channel length, L, and dimensionless axial coordinate of inlet section, z0. For all cases, we determined fields of flow type, where regions of shear and of extension can be visualized. Among other findings, it is shown that, depending on the geometrical and flow characteristics, most of the mechanical energy dissipated can be due to shear effects, so that the extensional viscosity cannot be determined via pressure drop measurements.

Mathematical Modelling of Hydromagnetic Convection from a Rotating Sphere with Impulsive Motion and Buoyancy Effects

2006 ◽  
Vol 11 (3) ◽  
pp. 227-245 ◽  
Author(s):  
O. Anwar Bég ◽  
H. S. Takhar ◽  
G. Nath ◽  
A. J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Chemical Engineering ◽  
Numerical Solutions ◽  
Forced Flow ◽  
Impulsive Motion ◽  
Rotating Sphere ◽  
Linear Partial Differential Equations ◽  
Layer Flow

The convective heat transfer on a rotating sphere in the presence of magnetic field, buoyancy forces and impulsive motion is examined theoretically and numerically in this paper. We apply a boundary layer model comprising the balance equations for x and y direction translational momentum and heat transfer, and solve these coupled non-linear partial differential equations using Blottner’s finite-difference method [1]. The numerical solutions are benchmarked with the earlier study by Lee [2] on laminar boundary layer flow over rotating bodies in forced flow and found to be in excellent agreement. The effects of magnetic field, buoyancy parameter, Prandtl number and thermal conductivity parameter on translational velocities and temperature and other variables (shear stress etc) are presented graphically and discussed at length. The problem finds applications in chemical engineering technologies, aerodynamics and planetary astrophysics.

A Simple Device for Preventing Turbulent Contamination on Swept Leading Edges

1965 ◽  
Vol 69 (659) ◽  
pp. 788-789 ◽  
Author(s):  
M. Gaster
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Leading Edge ◽  
Critical Value ◽  
Stagnation Line ◽  
Naturally Occurring ◽  
Swept Wings ◽  
Laminar State ◽  
Attachment Line

On unswept wings, or wings with small amounts of sweep, the favourable pressure gradient round the leading edge, where the flow is rapidly accelerated away from the stagnation line, ensures a certain amount of laminar flow, provided the wing surface is sufficiently smooth. On highly swept wings, however, it has been found that turbulent flow can exist on the attachment line itself and there are therefore no naturally occurring regions of laminar flow. This trouble arises from the turbulence at the root of the wing, which sweeps along the attachment line. If the Reynolds number of this turbulent attachment line boundary layer is greater than some critical value, the whole attachment line boundary layer remains turbulent and the complete wing is contaminated. But if the Reynolds number is below the critical value, the turbulence decays along the leading edge and the boundary layer on the attachment line reverts back to the laminar state. This situation arises when the leading edge radius is small and the wing is only slightly swept. The attachment line boundary layer Reynolds number, Rθ, is given by the following equation:

The Flow of a Laminar, Incompressible Jet Along a Parabola

1972 ◽  
Vol 39 (1) ◽  
pp. 13-17 ◽  
Author(s):  
A. Plotkin
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
External Flow ◽  
Boundary Layer Theory ◽  
Second Order ◽  
Wall Jet ◽  
Governing Equations ◽  
Displacement Effect ◽  
First Order ◽  
External Stream

The flow of a laminar, incompressible jet along a parabola in the absence of an external stream is analyzed using the techniques of second-order boundary-layer theory. The first-order solution is the Glauert wall-jet solution. Second-order corrections in the jet due to the effects of curvature and displacement are obtained numerically after the external flow is corrected to account for the displacement effect. The shear stress at the wall is calculated and it appears that for values of the Reynolds number at which the governing equations are valid the jet does not separate from the parabola.

On the impulsively started rotating sphere

1967 ◽  
Vol 27 (4) ◽  
pp. 779-788 ◽  
Author(s):  
K. E. Barrett
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Field ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Series Solutions ◽  
Rotating Sphere ◽  
Boundary Layer Equations ◽  
Small Times ◽  
3 Omega

The velocity field generated in a fluid of viscosity, v, by impulsively starting at time t = 0, a sphere of radius a spinning with angular velocity Ω about a diameter is described using a new expansion variable 2 √vt/r. It is first shown how the standard time-dependent boundary-layer equations can be modified to give series solutions satisfying all the boundary conditions. Next, that these new solutions are relevant when the Reynolds number R = a2Ω/v goes to infinity in such a way that $R^{\frac{1}{3}} \Omega t$ is large. Lastly, solutions are given, applicable at small times for non-zero Reynolds numbers. These last expansions show that the velocity components decay algebraically rather than exponentially at large distances.

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