Laminar Flow over a Backward Facing Step: Numerical Solutions for a Test Problem

1984 ◽  
pp. 140-161
Author(s):  
K. A. Cliffe ◽  
I. P. Jones ◽  
J. D. Porter ◽  
C. P. Thompson ◽  
N. S. Wilkes
Keyword(s):  
Laminar Flow ◽  
Test Problem ◽  
Numerical Solutions ◽  
Backward Facing Step

Uncertainty Estimation for Numerical Solutions of Wall Bounded Turbulent Flows

2006 ◽  
Author(s):  
Francisco Elizalde-Blancas ◽  
Ismail Celik ◽  
Suryanarayana Pakalapati
Keyword(s):  
Laminar Flow ◽  
Turbulent Flows ◽  
Numerical Solutions ◽  
Turbulence Models ◽  
Grid Size ◽  
Gradient Term ◽  
True Error ◽  
Flow Solver ◽  
Solution Convergence ◽  
Manufactured Solution

In this study numerical solutions are presented for a steady state, incompressible, 2-D turbulent flow near a wall. For this specific problem a manufactured (exact) solution was provided by the organizers of the 2006 Lisbon Workshop [6]. With the help of manufactured solution, assessment of the true error and other relevant uncertainty measures are possible. The calculations were performed using the commercial flow solver FLUENT along with some user defined functions to define source terms and velocity profiles at boundaries. Though the flow regime is turbulent; the numerical solution is carried out for pseudo-laminar flow. This was done in order to avoid the errors implicit in turbulence models. The transformation from turbulent to laminar flow was done by defining a momentum source term which precludes the pressure gradient term. A detailed grid convergence analysis was performed. Using three-grid triplets the limiting values of the variables solved as the grid size tends to zero were calculated using different extrapolations. The L2 norms of the true error obtained from various extrapolations are assessed. These results exhibit solution convergence as the grid size decreases. It was also shown that cubic spline extrapolation perform the best among the methods considered.

Some numerical experiments on developing laminar flow in circular-sectioned bends

1985 ◽  
Vol 154 ◽  
pp. 357-375 ◽  
Author(s):  
J. A. C. Humphrey ◽  
H. Iacovides ◽  
B. E. Launder
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Numerical Predictions

The paper reports numerical solutions to a semi-elliptic truncation of the Navier–Stokes equations for the case of developing laminar flow in circular-sectioned bends over a range of Dean numbers. The ratios of bend radius to pipe radius are 7:1 and 20:1, corresponding with the configurations examined experimentally by Talbot and his co-workers in recent years. The semi-elliptic treatment facilitates a much finer grid than has been possible in earlier studies. Numerical accuracy has been further improved by assuming radial equilibrium over a thin sublayer immediately adjacent to the wall and by re-formulating the boundary conditions at the pipe centre.Streamwise velocity profiles at Dean numbers of 183 and 565 are in excellent agreement with laser-Doppler measurements by Agrawal, Talbot & Gong (1978). Good, albeit less complete, accord is found with the secondary velocities, though the differences that exist may be mainly due to the difficulty of making these measurements. The paper provides new information on the behaviour of the streamwise shear stress around the inner line of symmetry. Upstream of the point of minimum shear stress, our numerical predictions display a progressive shift towards the result of Stewartson, Cebici & Chang (1980) as the Dean number is successively raised. Downstream of the minimum, however, in contrast with the monotonic approach to an asymptotic level reported by Stewartson, the numerical solutions display a damped oscillatory behaviour reminiscent of those from Hawthorne's (1951) inviscid-flow calculations. The amplitude of the oscillation grows as the Dean number is raised.

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.

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.

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