This video from The Efficient Engineer is
sponsored by Brilliant. One of the very first things you learn in
fluid mechanics is the difference between laminar and turbulent flow. And for good reason - these two flow regimes
behave in very different ways and, as we’ll see in this video, this has huge implications
for fluid flow in the world around us Here we have an example of the laminar flow
regime. It's characterised by smooth, even flow. The fluid is moving horizontally in layers,
and there is a minimal amount of mixing between layers. As we increase the flow velocity we begin
to see some bursts of random motion. This is the start of the transition between
the laminar and turbulent regimes. If we continue increasing the velocity we
end up with fully turbulent flow. Turbulent flow is characterised by chaotic
movement and contains swirling regions called eddies. The chaotic motion and eddies result in significant
mixing of the fluid. If we record the velocity at a single point
in steady laminar flow, we'll get data that looks like this. There are no random velocity fluctuations,
and so in general laminar flow is fairly easy to analyse. For turbulent flow we’ll get data that looks
like this. This flow is much more complicated. We can think of the velocity as being made
up of a time-averaged component, and a fluctuating component. The larger the fluctuating component, the
more turbulent the flow. Because of its chaotic nature, analysis of
turbulent flow is very complex. Since laminar and turbulent flow are so different
and need to be analysed in different ways, we need to be able to predict which flow regime
is likely to be produced by a particular set of flow condition We can do this using a parameter which was
defined by Osborne Reynolds in 1883. Reynolds performed extensive testing to identify
the parameters which affect the flow regime, and came up with this non-dimensional parameter,
which we call Reynolds number. It's used to predict if flow will be laminar
or turbulent. Rho is the fluid density, U is the velocity,
L is a characteristic length dimension, and Mu is the fluid dynamic viscosity. The equation is sometimes written as a function
of the kinematic viscosity instead, which is just the dynamic viscosity divided by the
fluid density. The characteristic length L will depend on
the type of flow we are analysing. For flow past a cylinder it will be the cylinder
diameter. For flow past an airfoil it will be the chord
length. And for flow through a pipe it will be the
pipe diameter. Reynolds number is useful because it tells
us the relative importance of the inertial forces and the viscous forces. Inertial forces are related to the momentum
of the fluid, and so are essentially the forces which cause the fluid to move. Viscous forces are the frictional shear forces
which develop between layers of the fluid due to its viscosity. If viscous forces dominate flow is more likely
to be laminar, because the frictional forces within the fluid will dampen out any initial
turbulent disturbances and random motion. This is why Reynolds number can be used to
predict if flow will be laminar or turbulent. If inertial forces dominate, flow is more
likely to be turbulent. But if viscous forces dominate, it’s more
likely to be laminar. And so smaller values of Reynolds number indicate
that flow will be laminar. The Reynolds number at which the transition
to the turbulent regime occurs will vary depending on the type of flow we are dealing with. These are the ranges usually quoted for flow
through a pipe, for example. Under very controlled conditions in a lab
the onset of turbulence can be delayed until much larger Reynolds numbers. Most flows in the world around us are turbulent. The flow of smoke out of a chimney is usually
turbulent. And so is the flow of air behind a car travelling
at high speed. The
flow of blood through vessels on the other hand is mostly laminar, because the characteristic
length and velocity are small. This is fortunate because if it were turbulent
the heart would have to work much harder to pump blood around the body. To understand why this is, let's look at how
the flow regime affects flow through a circular pipe. The flow velocity right at the pipe wall is
always zero. This is called the no-slip condition. For fully developed laminar flow, the velocity
then increases to reach the maximum velocity at the centre of the pipe. The velocity profile is parabolic. For turbulent flow the profile is quite different. We still have the no-slip condition, but the
average velocity profile is much flatter away from the wall. This is because turbulence introduces a lot
of mixing between the different layers of flow, and this momentum transfer tends to
homogenise the flow velocity across the pipe diameter. Note that I have shown the time-averaged velocity
here. The instantaneous velocity profile will look
something like this. In pipe flow one thing we are particularly
interested in is pressure drop. Across any length of pipe there will be a
drop in pressure due to the frictional shear forces acting within the fluid. The pressure drop in turbulent flow is much
larger than in laminar flow, which explains why the heart would have to work harder if
blood flow was mostly turbulent! We can calculate Delta-P along the pipe using
the Darcy-Weisbach equation. It depends on the average flow velocity, the
fluid density and a friction factor f. For laminar flow the friction factor can be
calculated easily. It is just a function of the Reynolds number. If we combine these two equations we can see
that the pressure drop is proportional to the flow velocity. But for turbulent flow calculating f is more
complicated. It is defined by the Colebrook equation. f appears on both sides of the equation, so
it needs to be solved iteratively. Unlike laminar flow, for which the pressure
drop is proportional to the flow velocity, it turns out that for turbulent flow it is
proportional to the flow velocity squared. And it also depends on the roughness of the
pipe surface. Epsilon is the height of the pipe surface
roughness, and the term Epsilon/D is called the relative roughness. Surface roughness is important for turbulent
flow because it introduces disturbances into the flow, which can be amplified and result
in additional turbulence. For laminar flow it doesn't have a significant
effect because these disturbances are dampened out more easily by the viscous forces. Since the Colebrook equation is so difficult
to use, engineers usually use its graphical representation, the Moody diagram, to look
up friction factors for different flow conditions. Where flow is laminar the friction factor
is only a function of Reynolds number, so we get a straight line on the Moody diagram. For turbulent flow you select the curve corresponding
to the relative roughness of your pipe, and you can look up the friction factor for the
Reynolds number of interest. So we know that if Reynolds number is large,
inertial forces dominate, and the flow is turbulent. But even for turbulent flow viscous forces
can be significant in the boundary layers that develop at solid walls. Because of the no-slip condition, shear stresses
are large close to a wall. This means that in a turbulent boundary layer
there remains a very thin area close to the wall where viscous forces dominate and flow
is essentially laminar. We call this the laminar, or viscous, sublayer. Its thickness decreases as Reynolds number
increases. Above the laminar sublayer there is the buffer
layer, where both viscous and turbulent effects are significant. And above the buffer layer turbulent effects
are dominant. If the roughness of a surface is contained
entirely within the thickness of the laminar sublayer, the surface is said to be hydraulically
smooth, because the roughness has no effect on the turbulent flow above the sublayer. This is important in pipe flow because, as
can be seen from the Moody diagram, flow in smooth pipe has a lower friction factor and
so smaller pressure drop than flow in rough pipe. We can see that for a given roughness the
friction factors converge to a constant value to the right of this dashed line, meaning
that at high Reynolds number the friction depends only on the relative roughness. At these high Reynolds numbers the thickness
of the laminar sublayer is extremely thin, and so the effect of the surface roughness
is governing. Modelling turbulent flow through a pipe is
fairly simple, but most scenarios are far more complex. It’s worth talking more about why analysis
of turbulent flow is so complicated, and a lot of it has to do with the turbulent eddies
we saw at the start of the video. Large eddies contain a lot of kinetic energy. Over time the energy in these large eddies
feeds the creation of progressively smaller eddies, until at the smallest scale the turbulent
energy in minuscule eddies dissipates as heat, due to frictional forces caused by the fluid
viscosity. We can think of the energy in the flow as
cascading from the largest to the smallest eddies, and so this concept is called the
energy cascade. The energy cascade was summarised in a very
elegant way by the physicist Lewis Fry Richardson, who wrote that "Big whirls have little whirls
that feed on their velocity, and little whirls have lesser whirls, and so on to viscosity". Because of this behaviour, turbulence involves
a huge range of length and time scales. This makes analysis of turbulent flow very
complex, to the point that it is probably the most significant challenge facing the
field of Fluid Mechanics. For complex scenarios like flow past an airfoil,
we can't accurately describe the fluid behaviour using simple equations. So to analyse the flow we have to use either
experimentation or numerical methods, or a combination of the two. Modelling flow using numerical methods is
the field of Computational Fluid Dynamics. It essentially involves using computational
power to solve the Navier-Stokes equations, which is a system of partial differential
equations that describes the behaviour of fluids, but is difficult to solve. To do this we model the fluid domain around
the airfoil as a mesh of discrete elements, define boundary conditions and fluid properties,
and apply an appropriate assessment technique to find a solution. I mentioned earlier that one of the main challenges
when dealing with turbulence is capturing the wide range of length scales associated
with the turbulent eddies. There are three main techniques which are
used to simulate flow in CFD, and they differ mainly in how they treat turbulence on these
different scales. First we have Direct Numerical Simulation. This involves solving the Navier-Stokes equations
down to even the smallest scales, and so all turbulent eddies are fully resolved, meaning
that they are simulated explicitly. This is very computationally expensive, and
isn’t a practical solution for the vast majority of fluid flow problems. Next we have Large Eddy Simulation. This technique resolves the large scale eddies
explicitly, but small scale eddies are filtered out and are modelled, using what is known
as a subgrid-scale model. LES is much less computationally expensive
than DNS. Finally we have the Reynolds-Averaged Navier-Stokes
technique, which is the least computationally expensive of the three techniques. This is a time-averaged method which doesn’t
resolve eddies explicitly at all. Instead it models the effect of eddies using
the concept of turbulent viscosity. Several different turbulence models exist,
like the K-Epsilon or K-Omega models, with different models being better suited to different
problem types. As is so often the case in engineering, experience
and intuition will need to be used to determine which techniques and models are best suited
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link will get 20% off the annual Premium subscription. That's it for this look at laminar and turbulent
flow. Thanks for watching.
