## Fluid Mechanics – Boundary Layer

Fluid mechanics is the field that studies the properties of fluids in various states.  Fluid dynamics studies the forces on a liquid or a gas during motion.  Osborne Reynolds, an Irish innovator, popularized this dynamic with a dimensionless number, Re. This number determines the state in which the fluid is moving; laminar, transitional, or turbulent.  For compressed air, a value of Re < 2300 will indicate a laminar air flow while the value of Re > 4000 will be in the range of turbulent flow.  Equation 1 below shows the relationship between the inertial forces of the fluid as compared to the viscous forces.

Equation 1:

Re = V * Dh / u

Re – Reynolds Number (no dimensions)

V – Velocity (feet/sec or meters/sec)

Dh – hydraulic diameter (feet or meters)

u – Kinematic Viscosity (feet^2/sec or meter^2/sec)

To dive deeper into this, we can examine the boundary layer.  The boundary layer is the area that is near the surface of the object.  This could refer to a wing on an airplane or a blade in a turbine.  In this blog, I will target the boundary layer inside pipes, tubes, and hoses that are used to transport fluids.  The profile across the area (reference diagram below) is a velocity gradient.  The boundary layer is the distance from the wall or surface to 99% of the maximum velocity of the fluid stream.  At the surface, the velocity of the fluid is zero because the fluid is in a “no slip” condition.  As we move away from the wall, the velocity starts to increase.  The boundary layer thickness measures that area where the velocity is not uniform.  If you reach 99% of the maximum velocity very close to the wall of the pipe, the air flow is turbulent.  If the boundary layer reaches the radius of the pipe, then the velocity is fully developed, or laminar.  Mathematically, laminar flow equations can be calculated, but turbulent flows require theories and experimental data to determine.

As an analogy, imagine an expressway as the velocity profile, and the on-ramp as the boundary layer.  If the on-ramp is long and smooth, a car can reach the speed of traffic and merge without disrupting the flow.  This would be considered Laminar Flow.  If the on-ramp is curved but short, the car has to merge into traffic at a much slower speed.  This will disrupt the flow of some of the traffic.  I would consider this as the transitional range.  Now imagine an on-ramp to be very short and perpendicular to the expressway. As the car goes to merge into traffic, it will cause chaos and accidents.  This is what I would consider to be turbulent flow.

In a compressed air system, similar things happen within the piping scheme.  Valves, tees, elbows, pipe reducers, filters, etc. are common items that will disrupt the flow.  Let’s look at a scenario with the EXAIR Digital Flowmeters.  In the instruction manual, we require the flow meter to be placed 30 pipe diameters from any disruptions.  The reason is to get a laminar air flow for accurate flow measurements.  In order to get laminar flow, we need the boundary layer thickness to reach the radius of the pipe.

Why is this important to know?  In many compressed air applications, the laminar region is the best flow to generate a strong force; efficiently and quietly.  Allowing the compressed air to have a more uniform boundary layer will optimize your compressed air system.  And for the Digital Flowmeter, it helps to measure the flow accurately and consistently.  If you would like to discuss further how to reduce “traffic jams” in your process, an EXAIR Application Engineer will be happy to help you.

John Ball
Application Engineer
Email: johnball@exair.com
Twitter: @EXAIR_jb

## Boundary Layer: Laminar and Turbulent flow

Fluid mechanics is the field that studies the properties of fluids in various states.  Fluid dynamics studies the forces on a fluid, either as a liquid or a gas, during motion.  Osborne Reynolds, an Irish innovator, popularized this dynamic with a dimensionless number, Re. This number determines the state in which the fluid is moving; either laminar flow, transitional flow, or turbulent flow.  For compressed air, Re < 2300 will have laminar flow while Re > 4000 will have turbulent flow.  Equation 1 below shows the relationship between the inertial forces of the fluid as compared to the viscous forces.

Equation 1:

Re = V * Dh / u

Re – Reynolds Number (no dimensions)

V – Velocity (feet/sec or meters/sec)

Dh – hydraulic diameter (feet or meters)

u – Kinematic Viscosity (feet^2/sec or meter^2/sec)

To dive deeper into this, we will need to examine the boundary layer.  The boundary layer is the area that is near the surface of the object.  This could refer to a wing on an airplane or a blade from a turbine.  In this blog, I will target pipes, tubes, and hoses that are used for transporting fluids.  The profile across the area (reference diagram below) is a velocity gradient.  The boundary layer is the distance from the wall or surface to 99% of the maximum velocity of the fluid stream.  At the surface, the velocity of the fluid is zero because the fluid is in a “no slip” condition.  As we move away from the wall, the velocity starts to increase.  The boundary layer distance measures that area where the velocity is not uniform.  If you reach 99% of the maximum velocity very close to the wall of the pipe, the air flow is turbulent.  If the boundary layer reaches the radius of the pipe, then the velocity is fully developed, or laminar.

The calculation is shown in Equation 2.

Equation 2:

d = 5 * X / (Re1/2)

d – Boundary layer thickness (feet or meter)

X – distance in pipe or on surface (feet or meter)

Re – Reynolds Number (no dimensions) at distance X

This equation can be very beneficial for determining the thickness where the velocity is not uniform along the cross-section.  As an analogy, imagine an expressway as the velocity profile, and the on-ramp as the boundary layer.  If the on-ramp is long and smooth, a car can reach the speed of traffic and merge without disrupting the flow.  This would be considered Laminar Flow.  If the on-ramp is curved but short, the car has to merge into traffic at a much slower speed.  This will disrupt the flow of some of the traffic.  I would consider this as the transitional range.  Now imagine an on-ramp to be very short and perpendicular to the expressway. As the car goes to merge into traffic, it will cause chaos and accidents.  This is what I would consider to be turbulent flow.

In a compressed air system, similar things happen within the piping scheme.  Valves, tees, elbows, pipe reducers, filters, etc. are common items that will affect the flow.  Let’s look at a scenario with the EXAIR Digital Flowmeters.  In the instruction manual, we require the meter to be placed 30 pipe diameters from any disruptions.  The reason is to get a laminar air flow for accurate flow measurements.  In order to get laminar flow, we need the boundary layer thickness to reach the radius of the pipe.  So, let’s see how that number was calculated.

Within the piping system, high Reynold’s numbers generate high pressure drops which makes the system inefficient.  For this reason, we should keep Re < 90,000.  As an example, let’s look at the 2” EXAIR Digital Flowmeter.  The maximum flow range is 400 SCFM (standard cubic feet per min).  In looking at Equation 2, the 2” Digital Flowmeter is mounted to a 2” Sch40 pipe with an inner diameter of 2.067” (52.5mm).  The radius of this pipe is 1.0335” (26.2 mm) or 0.086 ft (0.026m).  If we make the Boundary Layer Thickness equal to the radius of the pipe, then we will have laminar flow.  To solve for X which is the distance in the pipe, we can rearrange the terms to:

X = d * (Re)1/2 / 5 = 0.086ft * (90,000)1/2 / 5 = 5.16 ft or 62”

If we look at this number, we will need 62” of pipe to get a laminar air flow for the worse-case condition.  If you know the Re value, then you can change that length of pipe to match it and still get valid flow readings.  From the note above, the Digital Flowmeter will need to be mounted 30 pipe diameters.  So, the pipe diameter is 2.067” and at 30 pipe diameters, we will need to be at 30 * 2.067 = 62”.  So, with any type of common disruptions in the air stream, you will always get good flow data at that distance.

Why is this important to know?  In many compressed air applications, the laminar region is the best method to generate a strong force efficiently and quietly.  Allowing the compressed air to have a more uniform boundary layer will optimize your compressed air system.  And for the Digital Flowmeter, it helps to measure the flow correctly and consistently.  If you would like to discuss further how to reduce “traffic jams” in your process, an EXAIR Application Engineer will be happy to help you.

John Ball
Application Engineer
Email: johnball@exair.com
Twitter: @EXAIR_jb

## What’s So Great About Air Entrainment?

Air entrainment is the phenomenon that occurs when air (or any gas) under pressure is released from a device in such a way that a low pressure is generated in the immediate area of the air (or gas) discharge.  Air (or gas) from the surrounding environment is then pulled (or entrained) into the discharged air stream, increasing its volumetric flow rate.  EXAIR Corporation has been engineering & manufacturing compressed air products to take maximum advantage of this phenomena since 1983…and we’ve gotten better & better at it over the past 36 years.

Obviously, the first thing that’s so great about air entrainment is…free air flow.  Every cubic foot that’s entrained means that’s a cubic foot that your compressor didn’t have to spend energy compressing.  Considering the EXAIR Super Air Knife’s entrainment ratio of 40:1, that makes for a VERY efficient use of your compressed air.

Another thing that’s so great about air entrainment is…it’s quiet.  As you can see from the graphic at the top of this blog, the Super Air Knife entrains air (the lighter, curved blue arrows) into the primary compressed air stream (the darker, straight blue arrows) from above and below.  The outer layers of the total developed flow are lower in velocity, and serve as a sound-attenuating boundary layer.  The sound level of a Super Air Knife (any length…here’s why) is only 69dBA.  That means if you’re talking with someone and a Super Air Knife is running right next to you, you can still use your “inside voice” and continue your conversation, unaffected by the sound of the air flow.

I always thought it would be helpful to have more than just a graphic with blue arrows to show the effect & magnitude of air entrainment.  A while back, I accidentally stumbled across a stunning visual depiction of just that, using a Super Air Knife.  I had the pleasure of talking with a caller about how effective a Super Air Knife might be in blowing light gauge paperboard pieces.  So I set one up in the EXAIR Demo Room, blowing straight upwards, and tossed paper plates into the air flow.  It worked just as expected, until one of the paper plates got a little closer to the Super Air Knife than I had planned:

As you can see, the tremendous amount of air flow being entrained…from both sides…was sufficient to pull in lightweight objects and ‘stick’ them to the surface that the entrained air was being drawn past.  While it doesn’t empirically prove the 40:1 ratio, it indisputably demonstrates that an awful lot of air is moving there.

If you’re looking for a quiet, efficient, and OSHA compliant solution for cleaning, blow off, drying, cooling…anything you need an even, consistent curtain of air flow for – look no further than the EXAIR Super Air Knife.  If you’d like to discuss a particular application and/or product selection, give me a call.

Russ Bowman
Application Engineer
EXAIR Corporation
Visit us on the Web
Follow me on Twitter
Like us on Facebook

## Fluidics, Boundary Layers, And Engineered Compressed Air Products

Fluidics is an interesting discipline of physics.  Air, in particular, can be made to behave quite peculiarly by flowing it across a solid surface.  Consider the EXAIR Standard and Full Flow Air Knives:

If you’ve ever used a leaf blower, or rolled down the car window while traveling at highway speed, you’re familiar with the power of a high velocity air flow.  Now consider that the Coanda effect can cause such a drastic redirection of this kind of air flow, and that’s a prime example of just how interesting the science of fluidics can be.

EXAIR Air Amplifiers, Air Wipes, and Super Air Nozzles also employ the Coanda effect to entrain air, and the Super Air Knife employs similar precision engineered surfaces to optimize entrainment, resulting in a 40:1 amplification ratio:

As fascinating as all that is, the entrainment of air that these products employ contributes to another principle of fluidics: the creation of a boundary layer.  In addition to the Coanda effect causing the fluid to follow the path of the surface it’s flowing past, the flow is also affected in direct proportion to its velocity, and inversely by its viscosity, in the formation of a boundary layer.

This laminar, lower velocity boundary layer travels with the primary air stream as it discharges from the EXAIR products shown above.  In addition to amplifying the total developed flow, it also serves to attenuate the sound level of the higher velocity primary air stream.  This makes EXAIR Intelligent Compressed Air Products not only as efficient as possible in regard to their use of compressed air, but as quiet as possible as well.

If you’d like to find out more about how the science behind our products can improve your air consumption, give me a call.