Understanding Laminar and Turbulent Flow
Summary
TLDRThe video from The Efficient Engineer, sponsored by Brilliant, explores the fundamental difference between laminar and turbulent flow in fluid mechanics. It explains how these flow regimes impact fluid behavior and their analysis, using the Reynolds number to predict flow types. The video also delves into the implications of flow regimes on pressure drop in pipes and the challenges of turbulent flow analysis, including the energy cascade and various Computational Fluid Dynamics techniques. It concludes by highlighting the importance of engineering intuition and the resources offered by Brilliant for developing problem-solving skills.
Takeaways
- 🔬 The fundamental difference between laminar and turbulent flow is crucial in fluid mechanics due to their distinct behaviors and implications in real-world fluid flow.
- 🌀 Laminar flow is characterized by smooth, even movement with minimal mixing between fluid layers, while turbulent flow is marked by chaotic motion and the presence of swirling eddies.
- 📈 The transition from laminar to turbulent flow occurs as flow velocity increases, leading to more complex and difficult-to-analyze fluid dynamics.
- 📊 Reynolds number, introduced by Osborne Reynolds, is a non-dimensional parameter that predicts the flow regime (laminar or turbulent) based on fluid properties and flow characteristics.
- 🧮 The Reynolds number is calculated using fluid density, velocity, characteristic length, and dynamic viscosity, and it helps to understand the balance between inertial and viscous forces in fluid flow.
- 🛠️ In engineering, the flow regime affects design considerations, such as the pressure drop in pipes, which is significantly higher in turbulent flow due to increased frictional forces.
- 🩸 The flow of blood through vessels is mostly laminar, which is advantageous as it reduces the workload on the heart, contrasting with the turbulent flow seen in larger-scale fluid dynamics like smoke from a chimney.
- 🔍 Computational Fluid Dynamics (CFD) is used to model complex fluid flows, particularly when dealing with turbulence, and it involves solving the Navier-Stokes equations using various numerical methods.
- 🌐 The concept of the energy cascade in turbulence describes how energy moves from larger to smaller eddies, influencing the analysis and modeling of turbulent flows.
- 💡 Engineering intuition plays a vital role in troubleshooting fluid flow problems, highlighting the importance of understanding concepts beyond just mathematical calculations.
Q & A
What is the primary difference between laminar and turbulent flow?
-Laminar flow is characterized by smooth, even flow with minimal mixing between layers, while turbulent flow is characterized by chaotic movement, swirling regions called eddies, and significant mixing of the fluid.
How does the flow velocity affect the transition from laminar to turbulent flow?
-As flow velocity increases, the flow starts with laminar characteristics but begins to show bursts of random motion as it transitions. If the velocity continues to increase, the flow becomes fully turbulent.
What is Reynolds number and how is it used in fluid mechanics?
-Reynolds number is a non-dimensional parameter used to predict if flow will be laminar or turbulent. It is calculated using the fluid density, velocity, a characteristic length dimension, and fluid dynamic viscosity. It helps determine the relative importance of inertial forces and viscous forces in a flow.
What are inertial forces and viscous forces, and how do they influence the flow regime?
-Inertial forces are related to the momentum of the fluid and cause it to move, while viscous forces are frictional shear forces between layers due to fluid viscosity. If viscous forces dominate, the flow is more likely to be laminar; if inertial forces dominate, it's more likely to be turbulent.
What is the significance of the no-slip condition in pipe flow?
-The no-slip condition states that the flow velocity at the pipe wall is always zero. This condition affects how the flow velocity profile develops: it's parabolic for laminar flow and flatter for turbulent flow due to the mixing caused by turbulence.
How does turbulent flow affect the pressure drop in a pipe compared to laminar flow?
-The pressure drop in turbulent flow is much larger than in laminar flow due to the increased frictional shear forces acting within the fluid. This is described by the Darcy-Weisbach equation, which includes a friction factor that depends on the flow regime.
What is the energy cascade in the context of turbulent flow?
-The energy cascade refers to the transfer of kinetic energy from larger to smaller turbulent eddies. Energy in large eddies is transferred to create smaller eddies, eventually dissipating as heat at the smallest scales due to fluid viscosity.
Why is analyzing turbulent flow considered a significant challenge in fluid mechanics?
-Analyzing turbulent flow is challenging because it involves a wide range of length and time scales, making it complex to model accurately. Turbulence requires either experimentation, numerical methods, or a combination of both for analysis.
What are the three main techniques used to simulate flow in Computational Fluid Dynamics (CFD)?
-The three main techniques are Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and Reynolds-Averaged Navier-Stokes (RANS). DNS resolves all scales, LES resolves large scales and models small scales, and RANS uses time-averaging and models the effect of eddies with turbulent viscosity.
How does the relative roughness of a pipe surface affect turbulent flow?
-Surface roughness introduces disturbances into the flow, which can lead to additional turbulence. For laminar flow, it has less effect due to the damping action of viscous forces. In turbulent flow, the friction factor and thus the pressure drop are influenced by the roughness.
What is the significance of the laminar sublayer in turbulent flow near a wall?
-The laminar sublayer is a thin area close to the wall where viscous forces dominate and the flow is essentially laminar, despite the overall flow being turbulent. Its thickness decreases as Reynolds number increases, affecting the shear stress near the wall.
Outlines
🌀 Understanding Laminar and Turbulent Flow
This paragraph introduces the fundamental concepts of fluid mechanics, specifically focusing on the differences between laminar and turbulent flow. Laminar flow is characterized by smooth, even movement of fluid layers with minimal mixing, while turbulent flow is marked by chaotic motion and the presence of swirling eddies that cause significant fluid mixing. The transition from laminar to turbulent flow is triggered by increasing the flow velocity. The video also explains how to analyze these flows, with laminar flow being more straightforward due to its consistent velocity profile, whereas turbulent flow involves a complex interplay of time-averaged and fluctuating velocity components. The Reynolds number, a non-dimensional parameter, is introduced as a tool to predict the flow regime based on the balance between inertial and viscous forces.
🛠️ Analyzing Flow in Pipes
This section delves into the specifics of fluid flow within pipes, contrasting fully developed laminar flow, where velocity increases parabolically from the pipe wall to the center, with turbulent flow, which exhibits a flatter average velocity profile due to increased mixing. The 'no-slip condition' at the pipe wall is a constant, regardless of flow type. The paragraph discusses the implications of flow type on pressure drop, with turbulent flow causing a larger pressure drop due to higher frictional forces. The Darcy-Weisbach equation is mentioned for calculating pressure drop, with the friction factor being dependent on the Reynolds number for laminar flow and requiring iterative solutions for turbulent flow. The concept of surface roughness and its impact on flow, particularly in turbulent conditions, is also explored, leading to the introduction of the Moody diagram for determining friction factors in different flow scenarios.
🌐 Complexity of Turbulent Flows
The final paragraph addresses the complexity of analyzing turbulent flows, particularly due to the wide range of length scales involved with turbulent eddies. It introduces the concept of the energy cascade, where energy from large eddies is transferred to smaller ones, eventually dissipating as heat due to viscosity. The paragraph outlines three main Computational Fluid Dynamics (CFD) techniques for simulating flow: Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and Reynolds-Averaged Navier-Stokes (RANS), each with its own approach to handling turbulence. The importance of engineering intuition and experience in selecting appropriate techniques for fluid flow analysis is emphasized, concluding with a recommendation for the Brilliant platform as a resource for developing problem-solving skills and engineering intuition.
Mindmap
Keywords
💡Laminar Flow
💡Turbulent Flow
💡Reynolds Number
💡Inertial Forces
💡Viscous Forces
💡Characteristic Length
💡No-slip Condition
💡Pressure Drop
💡Darcy-Weisbach Equation
💡Moody Diagram
Highlights
The difference between laminar and turbulent flow is fundamental in fluid mechanics.
Laminar flow is characterized by smooth, even flow with minimal mixing between layers.
Turbulent flow features chaotic movement and eddies, leading to significant fluid mixing.
The transition from laminar to turbulent flow occurs with increasing flow velocity.
Laminar flow is easier to analyze due to its predictable velocity profile.
Turbulent flow analysis is complex, involving time-averaged and fluctuating velocity components.
Reynolds number, a non-dimensional parameter, predicts if flow will be laminar or turbulent.
The characteristic length dimension varies depending on the type of flow being analyzed.
Reynolds number indicates the balance between inertial and viscous forces in a fluid.
Laminar flow is dominated by viscous forces, while turbulent flow is dominated by inertial forces.
The onset of turbulence in flow through a pipe can be delayed under controlled lab conditions.
Most real-world flows are turbulent, such as smoke from a chimney or air behind a fast-moving car.
Blood flow in vessels is mostly laminar due to small characteristic length and velocity.
The no-slip condition at the pipe wall is a key factor in flow velocity profiles.
Turbulent flow in pipes has a flatter average velocity profile due to increased mixing.
Pressure drop in turbulent flow is much larger than in laminar flow due to increased friction.
The Darcy-Weisbach equation is used to calculate pressure drop along a pipe.
Friction factors for laminar flow are easily calculated based on Reynolds number.
The Colebrook equation and Moody diagram are used for turbulent flow friction factor calculations.
The laminar sublayer in turbulent flow is a thin area near the wall where viscous forces dominate.
Hydraulically smooth surfaces have roughness within the laminar sublayer, affecting flow minimally.
Modeling turbulent flow is complex due to the wide range of length scales involved.
Computational Fluid Dynamics (CFD) uses numerical methods to solve the Navier-Stokes equations.
Different CFD techniques handle turbulence on varying scales, including DNS, LES, and RANS.
Engineering intuition is crucial for troubleshooting real-world fluid flow problems.
Brilliant.org offers courses to develop problem-solving intuition and support the channel.
Transcripts
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 to a particular problem.
When it comes to troubleshooting problems in the real world, the importance of engineering
intuition can’t be overstated.
And that’s why I’d like to introduce you to Brilliant.
Brilliant is a math and science learning website and app that has courses covering a wide range
of topics, including differential equations, energy, momentum, and even dimensional analysis,
to name just a few which are relevant to Fluid Mechanics.
But the Scientific Thinking course in particular is great for engineers.
We know all too well that traditional engineering teaching tends to be very math-heavy, which
can make even relatively simple topics seem complex, and can get in the way of true understanding.
And that’s what I love about this course - it intentionally ditches the math and puts
the emphasis on concepts, using fun puzzles to help you develop your engineering intuition.
So if you’d like to start having fun actively developing your problem-solving intuition,
and support this channel at the same time, head over to brilliant.org/EfficientEngineer
and sign up for free.
The first 200 people to sign up using this link will get 20% off the annual Premium subscription.
That's it for this look at laminar and turbulent flow.
Thanks for watching.
関連動画をさらに表示
Peristiwa Perpindahan - Bilangan tak Berdimensi
Reynolds Experiment | Fluid Mechanics
LECTURE NOTES: AIRCRAFT AERODYNAMICS I, CHAPTER I, PART 1
Heat Transfer (27) - Heat transfer in internal flows in tubes
Form, Lift, Drag and Propulsion
Pumps Types - Types of Pump - Classification of Pumps - Different Types of Pump
5.0 / 5 (0 votes)