Page 79 - Mechanical Engineers' Handbook (Volume 4)

68 Fluid Mechanics

numbers. High speeds and low viscous forces are associated with turbulent flow and high
Reynolds numbers. Turbulence is a characteristic of flows, not of fluids. Typical fluctuations
of velocity in a turbulent flow are shown in Fig. 21.
The axes of eddies in turbulent flow are generally distributed in all directions. In iso-
tropic turbulence they are distributed equally. In flows of low turbulence, the fluctuations are
small; in highly turbulent flows, they are large. The turbulence level may be defined as (as
a percentage)
2
2
2
(u v w )/3
T 100
u
where u , v , and w are instantaneous fluctuations from mean values and u is the average
velocity in the main flow direction (x, in this instance).
Shear stresses in turbulent flows are much greater than in laminar flows for the same
velocity gradient and fluid.

9.2 Boundary Layers
The growth of a boundary layer along a flat plate in a uniform external flow is shown in
Fig. 22. The region of retarded flow, , thickens in the direction of flow, and thus the velocity
changes from zero at the plate surface to the free stream value u in an increasingly larger
s
distance normal to the plate. Thus, the velocity gradient at the boundary, and hence the
shear stress as well, decreases as the flow progresses downstream, as shown. As the laminar
boundary thickens, instabilities set in and the boundary layer becomes turbulent. The tran-
sition from the laminar boundary layer to a turbulent boundary layer does not occur at a
well-defined location; the flow is intermittently laminar and turbulent with a larger portion
of the flow being turbulent as the flow passes downstream. Finally, the flow is completely
turbulent, and the boundary layer is much thicker and the boundary shear greater in the
turbulent region than if the flow were to continue laminar. A viscous sublayer exists within
the turbulent boundary layer along the boundary surface. The shape of the velocity profile
also changes when the boundary layer becomes turbulent, as shown in Fig. 22. Boundary
surface roughness, high turbulence level in the outer flow, or a decelerating free stream causes
transition to occur nearer the leading edge of the plate. A surface is considered rough if the
roughness elements have an effect outside the viscous sublayer, and smooth if they do not.
Whether a surface is rough or smooth depends not only on the surface itself but also on the
character of the flow passing it.
A boundary layer will separate from a continuous boundary if the fluid within it is
caused to slow down such that the velocity gradient du/dy becomes zero at the boundary.
An adverse pressure gradient will cause this.

Figure 21 Velocity at a point in steady turbulent flow.