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.     

Hot Tap DFM

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

Photo: Smoke by SkitterphotoPixabay license

Laminar Flow vs Turbulent Flow for Compressed Air Blowoff

You’ll often hear us refer to laminar vs turbulent flow when discussing our blowoff products. In any blowoff process or application, laminar airflow is going to be much more effective at cooling or drying than the turbulent airflow delivered by commonly found homemade blowoff devices or cheap knockoffs. To read more about the math behind it, check out my colleague John Ball’s previous post here.

Allow me to use the Super Air Knife to help illustrate the benefit of laminar vs turbulent flow. When a wide, even, laminar flow is necessary there isn’t a better option available on the market than EXAIR’s Super Air Knife. What really sets EXAIR’s Super Air Knife above the competition is the ability to maintain a consistent laminar flow across the full length of the knife compared to similar compressed air operated knives. This is even more evident when compared against blower operated knives or fans. A fan “slaps” the air, resulting in a turbulent airflow where the airflow particles are irregular and will interfere with each other. A laminar airflow, by contrast, will maintain smooth paths that will never interfere with one another.

visual representation of a turbulent flow on top and laminar flow on bottom

The effectiveness of a laminar airflow vs turbulent airflow is particularly evident in the case of a cooling application for automotive computers coming out of a wave soldering machine. The chart below shows the time to cool computers to ambient temperatures for an automotive electronics manufacturer. They used a total of (32) 6” axial fans, (16) across the top and (16) across the bottom as the computers traveled along a conveyor. The computers needed to be cooled down before they could begin the testing process. By replacing the fans with just (3) Model 110012 Super Air Knives at a pressure of just 40 psig, the computers were cooled from 194°F down to 81° in just 90 seconds. The fans, even after 300 seconds still couldn’t remove enough heat to allow them to test.

While the fans no doubt made for large volume air movement, the laminar flow of the Super Air Knife resulted in a much faster heat transfer rate.

Utilizing a laminar airflow is also critical when the airflow is being used to carry static eliminating ions further to the surface. Static charges can be both positive or negative. In order to eliminate them, we need to deliver an ion of the opposite charge to neutralize it. Since opposite charges attract, having a product that produces a laminar airflow to carry the ions makes the net effect much more effective. As you can see from the graphic above showing a turbulent airflow pattern vs a laminar one, a turbulent airflow is going to cause these ions to come into contact with one another. This neutralizes them before they’re even delivered to the surface needing to be treated. With a product such as the Super Ion Air Knife, we’re using a laminar airflow pattern to deliver the positive and negative ions. Since the flow is laminar, the total quantity of ions that we’re able to deliver to the surface of the material is greater. This allows the charge to be neutralized quickly, rather than having to sit and “dwell” under the ionized airflow.

With lengths from 3”-108” and (4) four different materials all available from stock, EXAIR has the right Super Air Knife for your application. In addition to shipping from stock, it’ll also come backed up by our unconditional 30-day guarantee. Test one out for yourself to see just how effective the Super Air Knife is on a wide variety of cooling, cleaning, or drying applications.

Tyler Daniel
Application Engineer
E-mail: TylerDaniel@exair.com
Twitter: @EXAIR_TD

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. 

Boundary Layer Concept

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.      

EXAIR Digital Flowmeter

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

Video Blog: Laminar and Turbulent Flows

I have written blogs about laminar and turbulent flows as related to the Reynold’s number.  Now, let’s demonstrate the difference between the two flows and the advantages of laminar flow from EXAIR’s engineered air nozzles; as demonstrated by our VariBlast Safety Air Gun.

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