The Turbulence Characteristics of Two-Dimensional Wall-Jet and Wall-Wake Flows

1971 ◽  
Vol 38 (1) ◽  
pp. 239-252 ◽  
Author(s):  
S. C. Kacker ◽  
J. H. Whitelaw

Measurements of mean and fluctuating hydrodynamic properties of two-dimensional, constant property, wall-jet and wall-wake flows are reported. The mean properties include static pressure, velocity and wall shear stress; the fluctuating properties include the three fluctuating components of velocity, the local turbulent shear stress, uv, and u-spectra. The measurements were carried out for four values of the velocity ratio, UC/UG, viz. 0.75, 0.91, 1.33, and 2.3; for values of the ratio of lip thickness to slot height, t/yC, of 0.126 and 1.14; and for values of nondimensional distance, x/yC, between zero and 150. The results demonstrate the difficulties involved in deriving a satisfactory prediction procedure for flows of this type. In the upstream region, normal pressure gradients and separated flow regimes imply the need for elliptic equations. Also in the upstream region, the u-spectra measurements reveal preferred frequencies although the energy contained at the preferred frequency is never more than 25 percent of the total energy. Prandtl mixing length and the Prandtl-Kolmogorov turbulence length scale are deduced from measurements and shown to be very nonsimilar for all values of x/yC. The measurements are reported in sufficient detail to permit the detailed testing of prediction procedures.

1970 ◽  
Vol 12 (6) ◽  
pp. 404-420 ◽  
Author(s):  
S. C. Kacker ◽  
J. H. Whitelaw

An existing numerical procedure for solving the steady, two-dimensional, constant property form of the Navier–Stokes equations, has been used to obtain predictions of mean and fluctuating properties downstream of a two-dimensional wall jet. The Prandtl–Kolmogorov model of turbulence, with a simple empirical expression for the length scale, is shown to permit satisfactory predictions over a wide range of flow situations. These flow situations are relevant to the design of film-cooling slots.


2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.


1975 ◽  
Vol 70 (1) ◽  
pp. 127-148 ◽  
Author(s):  
B. Van Den Berg ◽  
A. Elsenaar ◽  
J. P. F. Lindhout ◽  
P. Wesseling

First a three-dimensional turbulent boundary-layer experiment is described. This has been carried out with the specific aim of providing a test-case for calculation methods. Much attention has been paid to the design of the test set-up. An infinite swept-wing flow has been simulated with good accuracy. The initially two-dimensional boundary layer on the test plate was subjected to an adverse pressure gradient, which led to three-dimensional separation near the trailing edge of the plate. Next, a calculation method for three-dimensional turbulent boundary layers is discussed. This solves the boundary-layer equations numerically by finite differences. The turbulent shear stress is obtained from a generalized version of Bradshaw's two-dimensional turbulent shear stress equation. The results of the calculations are compared with those of the experiment. Agreement is good over a considerable distance; but large discrepancies are apparent near the separation line.


1986 ◽  
Author(s):  
H. Pfeil ◽  
M. Göing

The paper presents an integral method to predict turbulent boundary layer behaviour in two-dimensional, incompressible flow. The method is based on the momentum and moment-of-momentum integral equations and a friction law. By means of the compiled data of the 1968-Stanford-Conference, the results show that the integral of the turbulent shear-stress across the boundary layer, which appears in the moment-of-momentum integral equation, can be described by only two basic assumptions for all cases of flow.


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