Understanding Laminar and Turbulent Flow

Summary

The 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

00:00

🌀 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.

05:04

🛠️ 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.

10:06

🌐 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.

Keywords

💡Laminar Flow

Laminar flow is characterized by smooth, orderly movement of fluid particles in parallel layers with minimal disruption between them. In the context of the video, laminar flow is introduced as one of the two primary flow regimes in fluid mechanics, contrasting with turbulent flow. The video script uses the example of fluid moving horizontally in layers to illustrate laminar flow, emphasizing its predictability and ease of analysis due to the absence of random fluctuations in velocity.

💡Turbulent Flow

Turbulent flow is marked by chaotic, irregular motion of fluid particles with significant mixing between layers. The video explains that turbulent flow is more complex than laminar flow due to the presence of eddies and random velocity fluctuations. This complexity makes turbulent flow more difficult to analyze and is illustrated in the script by the example of smoke coming out of a chimney or air flow behind a fast-moving car.

💡Reynolds Number

The Reynolds number is a dimensionless quantity used to predict the onset of turbulence in fluid flow. It is defined as the ratio of inertial forces to viscous forces and is calculated using the fluid's density, velocity, a characteristic length, and dynamic viscosity. In the video, the Reynolds number is highlighted as a critical parameter for determining whether a flow will be laminar or turbulent, with different flow conditions leading to different critical Reynolds numbers for the transition.

💡Inertial Forces

Inertial forces in fluid mechanics are the forces that cause the fluid to continue moving due to its momentum. The video script explains that when inertial forces dominate, the flow is more likely to be turbulent. This is because the fluid's momentum pushes it to move in a disordered manner, leading to the chaotic motion characteristic of turbulent flow.

💡Viscous Forces

Viscous forces are the internal frictional forces that resist the relative motion of fluid layers and are related to the fluid's viscosity. The video emphasizes that when viscous forces are dominant, flow tends to be laminar because these forces dampen out disturbances and maintain an orderly flow. This is why, in the script, flows with lower Reynolds numbers are more likely to be laminar.

💡Characteristic Length

The characteristic length is a specific dimension of a system that is used in the calculation of the Reynolds number. It varies depending on the type of flow being analyzed, such as the diameter of a pipe or the chord length of an airfoil. In the video, the characteristic length is mentioned as an essential factor in determining the flow regime, as it influences the balance between inertial and viscous forces.

💡No-slip Condition

The no-slip condition is a fundamental principle in fluid dynamics stating that the velocity of a fluid at the boundary with a solid surface is equal to the velocity of that surface. The video uses this concept to explain the flow velocity profile near a pipe wall, where the flow velocity is zero at the wall and increases towards the center for both laminar and turbulent flow.

💡Pressure Drop

Pressure drop refers to the decrease in pressure that occurs as a fluid flows through a pipe or around an object due to frictional forces. In the video, the script discusses how the pressure drop is much larger in turbulent flow compared to laminar flow, which is significant for applications like blood flow in the human body, where a large pressure drop would require the heart to work harder.

💡Darcy-Weisbach Equation

The Darcy-Weisbach equation is used to calculate the pressure drop in a fluid flow due to friction. It involves the average flow velocity, fluid density, and a friction factor. The video script explains how this equation is applied differently for laminar and turbulent flow, with the friction factor being a function of the Reynolds number for laminar flow and requiring iterative solutions for turbulent flow.

💡Moody Diagram

The Moody diagram is a graphical representation used by engineers to determine the friction factor for different flow conditions in pipes. It is particularly useful for turbulent flow where the friction factor depends on both the Reynolds number and the relative roughness of the pipe. The video script mentions that the Moody diagram allows engineers to look up friction factors for various conditions, simplifying the analysis of fluid flow in pipes.

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.

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That's it for this look at laminar and turbulent flow.

Thanks for watching.