Have you ever stood under a waterfall and seen the water jump ahead of you?
Why would that happen? – Flow separation. This is a common phenomenon occurring in both external
as well as internal flows. Flow separation occurs as air flow around an object: the cliff,
an aircraft wing, over high-rise buildings, and even around a soccer
ball. In wall-bounded internal flows, when a fluid flow is expanding along a pipe
or when it is taking a 90 degree turn around the corner of an elbow pipe, we see flow separation.
The physics responsible for this phenomenon is the same for internal and external flows
and, in this lesson, we will learn about flow separation and its consequences.
Let us first understand why fluid flow separates. A thin viscous region, called the boundary layer,
is created when a viscous fluid moves over a stationary solid. In most external flows,
the flow outside this viscous region can be regarded as inviscid. In these boundary layers,
the velocity of the fluid at the surface of the object is equal to the object velocity.
For instance, if the object is stationary, the fluid velocity on the surface is equal to zero.
This is called the no-slip boundary of the fluid. The fluid velocity continues to grow away from
this boundary until it nearly becomes equal to the free-stream velocity. For the flow over a
horizontal flat plate, the pressure gradient along the plate is continuously decreasing and remains
favorable. Fluid flow cannot separate under these conditions and remains attached to the surface.
However, for certain boundary layer flows, the fluid encounters adverse pressure gradients.
This means that the pressure is locally increasing in the direction of flow.
Under such conditions, the flow is struggling and the local velocity gradient approaches zero.
At this point, the fluid detaches from the surface and this detachment of fluid flow
from the surface is referred to as flow separation. Beyond this separation point,
a reversed flow occurs near the surface and the velocity gradient becomes negative.
The streamlines following the surface of the body are now deflected away from the surface.
The separation point is defined using the wall shear stress profile along the flow. The location
along the surface where the wall shear stress becomes zero is regarded as the point of
separation. Beyond this point, owing to local flow reversal, the wall shear stress changes direction.
The relatively low-pressure region behind the body is commonly referred to as a wake.
Flow separation over a body induces wakes behind the body. The interaction between
these forward and reversed flows in the region generates fluid rotation or vortex structures.
Depending on the Reynolds number of the fluid and the shape of the geometry,
we can have either laminar or turbulent vortices.
The shape of the solid body greatly influences flow separation.
For example, in the flow over any backward facing step, the momentum of the flow is
so large in the fluid direction that the flow cannot remain attached to the surface.
In these cases, unless the fluid is acted upon by external forces, we observe flow separation.
This is a representation of a waterfall – given the right conditions,
you can sometimes find a dry zone behind the waterfall.
From an engineering perspective, in external flows, flow separation is detrimental to both lift
and drag forces; it decreases lift and increases drag. Streamlining a body helps delay this flow
separation and streamlined bodies are employed in most external flow applications.
Flow Reynolds number is another critical parameter that dictates whether flow separation occurs
over a body. Reynolds number also influences the magnitude of flow separation. Despite
its engineering importance, there is no concise analytical definition to measure flow separation.
However, we have several analytical models to determine its exact location.
In the case of laminar boundary layer flows, Thwaites correlation uses the zero-shear stress
criterion to estimate the separation point. Based on his correlation, Thwaites was able to calculate
the momentum boundary layer thickness and the skin friction within plus or minus 10 % accuracy.
Stratford obtained a more accurate estimation of the location of separation point for laminar
flows. His analysis is based on the fact that the pressure should be minimum where the flow velocity
is maximum. He matched the velocities between the inner and outer layers of the separating region
to show that the coefficient of separation, which is defined as follows, satisfies this relation.
In this relationship, x’ = 0 if Vmax occurs at x = 0. If the maximum velocity occurs at a point
‘m’ downstream, then x’ is the momentum thickness at xm based on the Blasuis layer over xm – x’.
This solution can be extended to turbulent boundary layers.
In this case, at the minimum pressure point x = xm, the velocity profile is approximated to that
of a turbulent flat plate starting from a false origin x’. Determining the value of x’ is tricky
and requires additional correlations depending on whether the flow in the boundary layer is laminar,
transitional, or turbulent. A more precise way of predicting flow separation
is to solve the boundary layer equations numerically under adverse pressure conditions.
The point where the wall shear stress becomes zero is the location where flow separates.
This numerical solution, however, requires some level of computer programming.
Having said that, obtaining a numerical solution to the boundary layer equation is far
easier and faster compared to solving the entire set of Navier Stokes equation. These numerical
predictions are far more accurate compared to the approximate analytical solutions.
Flow separation causes interesting stable patterns in nature, especially in clouds. Satellites have
captured these swirling cloud patterns formed near the Guadalupe Island, which is a volcanic island
rising from the Pacific Ocean. Physicists have replicated these periodic flow patterns
in laboratories on simple external flows around cylinders. At a certain range of Reynolds numbers,
periodic pairs of vortices are generated from the top and bottom surfaces of the cylinder.
This stable periodically repeating trail of vortices is referred to as Karman Vortex Street,
named after the famous physicist Theodore Von Karman. The frequency of these vortices is
expressed using a dimensionless number called the Strouhal Number. As the Reynolds number increases,
the vortex street transitions into a turbulent wake which is more complex to study.
However, we can still identify these periodic fluctuations as well as their
tonal frequencies until a Reynolds number of 105. These periodic fluctuations lead to two important
effects on the surface of the body. For starters, if the flow field is compressible,
these fluctuations can generate acoustic sound waves. Secondly,
if the frequency of these fluctuations coincides with the natural frequency of the structure,
we see resonant effects on such structures. One disastrous example of this is the Tacoma Narrows
Bridge which was known to oscillate in windy conditions and finally collapsed in 1940.
In certain flow scenarios, the separated flow reattaches back on to the surface.
This happens primarily when the effect of adverse pressure gradient,
which was originally responsible for separation, dies out and a favorable pressure gradient
returns in the flow configuration. However, the return of the favorable pressure gradient
sometimes is not sufficient. When the separated portion transitions from laminar to turbulent,
the flow tends to reattach. This happens because turbulent flows have
larger momentum to overcome these adverse pressure gradients, thereby leading to the reattachment.