THE BOUNDARY LAYER IN TURBULENT FLOW OVER A PLATE

0 THE BOUNDARY LAYER IN TURBULENT FLOW OVER A PLATE 

Turbulent flow over a flat plate is characterized by three re-gions f l (a) a viscous sublayer often called the laminar sublayer, which exists right next to the plate, (b) an adjacent turbulent boundary layer, and (c) the turbulent core. Viscous forces dominate inertial forces in the viscous sublayer, which is relatively quiescent compared to the other regions and is therefore also called the laminar sublayer. This is a bit of a misnomer, since it is not really laminar. It is in this viscous sublayer that the velocity changes are the greatest, so that the shear is largest. Viscous forces become less dominant in the turbulent boundary layer. These forces are not controlling factors in the turbulent core. 

In the supercritical region, the kinematic viscosity of carbon dioxide is Z) 10 cm so that even for a low flow speed u of 100 cm/s, the Reynolds number Re = u slD is 10, 5 being the typical length scale chosen here to be 1 cm. At such Reynolds numbers we 

The transition between the laminar region and the turbulent region is made by demanding continuity, which yields a self-consistent equation to be solved  

We notice from Eq. (1) that the wall shear stress x is constant within the laminar boundary layer, and for this case is 0.25 dyne/ cm. As far as calculation of the wall shear stress for a known stream velocity is concerned, we point out that the use of Fanning s factor alone suffices to determine its value, and we do not need all the formulas stated above. 

FigHre3. This figure is similar to Fig. 2, excq t that the pressure used is 400 bars. Notice the coneqMiidingly higher velocities required to attain the same viscous sublayer thidcnesses (100 microns and 200 microns). 

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