Numerical Studies of Transition From Laminar to Turbulent Flow Over a Flat Plate

1962 ◽  
Vol 10 (4) ◽  
pp. 569-595 ◽  
Author(s):  
Daniel F. De Santo ◽  
Herbert B. Keller
Author(s):  
R. E. Mayle ◽  
K. Dullenkopf

A theory for transition from laminar to turbulent flow as the result of unsteady, periodic passing of turbulent wakes in the free stream is developed using Emmons’ transition model. Comparisons made to flat plate boundary layer measurements and airfoil heat transfer measurements confirm the theory.


1967 ◽  
Vol 89 (4) ◽  
pp. 362-370 ◽  
Author(s):  
M. Soliman ◽  
H. A. Johnson

An approximate analysis and experimental data are presented for the transient mean wall temperature of a flat plate of appreciable thermal capacity, heated by a step in the heat generation rate and cooled on both sides by a steady, incompressible turbulent flow with a Prandtl number of unity. Theory and experiments are in agreement over a range of Reynolds numbers 5 × 105 ≤ ReL ≤ 2 × 106. The experimental mean heat transfer coefficient is observed to go through a dip to a minimum before reaching the steady state. This dip is found to be due to the conjunction of a large wall thermal capacity and a sufficiently high flow velocity.


1976 ◽  
Vol 77 (3) ◽  
pp. 473-497 ◽  
Author(s):  
L. J. S. Bradbury

This paper describes an investigation into the response of both the pulsed-wire anemometer and the hot-wire anemometer in a highly turbulent flow. The first part of the paper is concerned with a theoretical study of some aspects of the response of these instruments in a highly turbulent flow. It is shown that, under normal operating conditions, the pulsed-wire anemometer should give mean velocity and longitudinal turbulent intensity estimates to an accuracy of better than 10% without any restriction on turbulence level. However, to attain this accuracy in measurements of turbulent intensities normal to the mean flow direction, there is a lower limit on the turbulent intensity of about 50%. An analysis is then carried out of the behaviour of the hot-wire anemometer in a highly turbulent flow. It is found that the large errors that are known to develop are very sensitive to the precise structure of the turbulence, so that even qualitative use of hot-wire data in such flows is not feasible. Some brief comments on the possibility of improving the accuracy of the hot-wire anemometer are then given.The second half of the paper describes some comparative measurements in the highly turbulent flow immediately downstream of a normal flat plate. It is shown that, although it is not possible to interpret the hot-wire results on their own, it is possible to calculate the hot-wire response with a surprising degree of accuracy using the results from the pulsed-wire anemometer. This provides a rather indirect but none the less welcome check on the accuracy of the pulsed-wire results, which, in this very highly turbulent flow, have a certain interest in their own right.


The boundary-layer equations for an incompressible fluid in motion past a flat plate are examined, numerically and analytically, in the special case when the pressure gradient vanishes and there is a uniform injection of fluid from the plate. In the numerical study the principal properties of the boundary layer are computed as far as separation ( x ═ x δ ≑ 0.7456) with a high degree of accuracy. In the analytic study the structure of the singularity at separation is determined. It is of a new kind in boundary layer theory and its elucidation requires the division of the boundary layer into three zones—an outer zone in which the non-dimensional velocity u is much larger than x * (the non-dimensional distance from separation), a central zone in which u ~ x * and an inner zone in which u ≪ x *. A match is effected between solutions in the central and inner zones from which it is inferred that the skin friction τ 0 ~ ( x * / In (1/ x *) 2 as x * → 0. A completely satisfactory agreement between the numerical and analytic studies was not possible. The reason is that the analytic study is only valid when ln ( 1 / x *) ≫ 1 which means that for the analytic and numerical studies to have a common region of validity, the numerical integration must be extended to much smaller values of x * than is possible at present. It was also not possible to effect a match between the central and outer zones in the analytic solution due to the difficulty of finding the properties of the stress τ in the central zone as u / x * →∞.


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