Pressure Gradient Effects on Boundary Layers http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
9.6 Pressure Gradient Effects on Boundary Layers
In the preceding sections the features of a boundary layer on a flat plate where the external pressure gradient is
zero have been presented. The boundary layer begins as laminar, goes through transition, and becomes turbulent
with a  fuller velocity profile and an increase in local shear stress. The purpose of this section is to present
some features of the boundary layer over a curved surface where the external pressure gradient is not zero.
The flow over an airfoil section is shown in Fig. 9.13. The variation in static pressure with distance, s, along the
surface is also shown on the figure. The point corresponding to s = 0 is the forward stagnation point where the
pressure is equal to the stagnation pressure. The pressure then decreases toward a minimum value at the
midsection. This minimum pressure corresponds to the location of maximum speed as predicted by the Bernoulli
equation. The pressure then rises again as the flow accelerates toward the trailing edge. When the pressure
decreases with increasing distance (dp/ds < 0), the pressure gradient is referred to as a favorable pressure
gradient as introduced in Chapter 4. This means that the direction of the force due to the pressure gradient is in
the flow direction. In other words, the effect of the pressure gradient is to accelerate the flow. This is the
condition between the forward stagnation point and the point of minimum pressure. A rise in pressure with
distance (dp/ds > 0)is called an adverse pressure gradient and occurs between the point of minimum pressure
and the trailing edge. The pressure force due to the adverse pressure gradient acts in the direction opposite to the
flow direction and tends to decelerate the flow.
Figure 9.13 Surface pressure distribution on airfoil section.
The external pressure gradient effects the properties of the boundary layer. Compared to a flat plate, the laminar
boundary layer in a favorable pressure gradient grows more slowly and is more stable. This means that the
boundary-layer thickness is less and the local shear stress is increased. Also the transition region is moved
downstream, so the boundary layer becomes turbulent somewhat later. Of course, free-stream turbulence and
surface roughness will still promote the early transition to a fully turbulent boundary layer.
The effect of external pressure gradient on the boundary layer is most pronounced for the adverse pressure
gradient. The development of the velocity profiles for the laminar and turbulent boundary layers in an adverse
pressure gradient are shown in Fig. 9.14. The retarding force associated with the adverse pressure gradient
decelerates the flow, especially near the surface where the velocities are the lowest. Ultimately there is a reversal
of flow at the wall, which gives rise to a recirculatory pattern and the formation of an eddy. This phenomenon is
called boundary-layer separation. The point of separation is defined where the velocity gradient "u/"y becomes
zero as indicated on the figure. The separation point for the turbulent boundary layer occurs farther downstream
because the velocity profile is much fuller (higher velocities persist closer to the wall) than the laminar profile,
and it takes longer for the adverse pressure gradient to decelerate the flow. Thus the turbulent boundary layer is
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Pressure Gradient Effects on Boundary Layers http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
less affected by the adverse pressure gradient.
Figure 9.14 Velocity distribution and streamlines for boundary layer separation.
(a) Laminar boundary layer.
(b) Turbulent boundary layer.
Even though shear stresses on a body in a flow may not contribute significantly to the total drag force, the effect
of boundary-layer separation can be very important. When boundary-layer separation takes place on airfoils at a
high angle of attack,  stall occurs, which means the airfoil loses its capability to provide lift. A photograph
illustrating boundary-layer separation on an airfoil section is shown in Fig. 4.26. Boundary-layer separation on a
cylinder was discussed and illustrated in Section 4.8 on page 111. Understanding and controlling boundary-layer
separation is important in the design of fluid dynamic shapes for maximum performance.
Copyright © 2009 John Wiley & Sons, Inc. All rights reserved.
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