Centrifugal Compressor: Absolute Velocity Calculation

In summary, the calculation of absolute velocity in a centrifugal compressor involves determining the velocity of fluid as it moves through the compressor's components. This process typically requires understanding the relative velocity of the fluid, the rotational speed of the impeller, and the geometrical configuration of the compressor. By applying principles of fluid dynamics and vector analysis, engineers can calculate the absolute velocity, which is crucial for optimizing compressor performance and efficiency.
  • #1
MysticDream
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TL;DR Summary
Seeking insight on how to calculate the absolute velocity
How can I calculate the absolute velocity of air at the outlet of a centrifugal compressor if I have:

Diameter of impeller
RPM
Slip factor

I've been reading for weeks and cannot seem to find the answer to this question. For anyone who is familiar with the subject, I'm sure you know about the blade angle, slip factor, radial and tangential components of flow velocity, and absolute flow angle. It's the absolute flow angle that I cannot find any formulas for. Knowing this, I'd be able to calculate the absolute velocity if I know the tangential velocity of the gas, which is a function of the slip factor and tip speed. I can find nothing that relates the radial component of the flow velocity to the RPM or tip speed of the impeller. Any help would be appreciated.
 
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  • #2
Assuming that your term "centrifugal compressor" refers to a high speed blower as in the simplified diagram below:
Blower.jpg

The velocity of the air at the outlet is a function of flow rate and outlet flow area. The flow rate is a function of the back pressure, where the function is shown by the fan curve. Search that term, the Aerovent link is a particularly good introduction: https://www.aerovent.com/wp-content/uploads/2018/12/Understanding-Fan-Curves-FE-2000.pdf.

What is the "slip factor"? Air flow around impeller vanes is analyzed using velocity triangles, such as are found using search terms blower velocity triangle. The book Centrifugal and Axial Flow Pumps, 2nd Edition, by A. J. Stepanoff has an entire chapter on the subject. It is a good resource if you want to get deeper into the subject than a simple internet search. The analysis of a blower is identical to the analysis of a pump until you get into compressible flow. Air, or any gas, is merely a low density fluid.
 
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  • #3
jrmichler said:
Assuming that your term "centrifugal compressor" refers to a high speed blower as in the simplified diagram below:
View attachment 339348
The velocity of the air at the outlet is a function of flow rate and outlet flow area. The flow rate is a function of the back pressure, where the function is shown by the fan curve. Search that term, the Aerovent link is a particularly good introduction: https://www.aerovent.com/wp-content/uploads/2018/12/Understanding-Fan-Curves-FE-2000.pdf.

What is the "slip factor"? Air flow around impeller vanes is analyzed using velocity triangles, such as are found using search terms blower velocity triangle. The book Centrifugal and Axial Flow Pumps, 2nd Edition, by A. J. Stepanoff has an entire chapter on the subject. It is a good resource if you want to get deeper into the subject than a simple internet search. The analysis of a blower is identical to the analysis of a pump until you get into compressible flow. Air, or any gas, is merely a low density fluid.
Thanks for the book suggestion. Yeah, I'm interested in a compressor specifically. The slip factor is the ratio between the tip speed (tangential) of the impeller and the actual tangential component of the absolute velocity of the gas. Again, I don't have a mass or volumetric flow rate. I want to be able to determine that from the impeller geometry and angular velocity (RPM). I'm familiar with the velocity triangles, but just like with any right triangle, you need at least two sides or an angle and a side to determine the other sides. The slip factor can give you the tangential component of the absolute velocity based on the RPM and impeller tip velocity, but the angle of the fluid exit and/or the radial component of the velocity is still not known, therefore no absolute velocity can be determined and no flow rate or pressure. The flow rate is based on the radial component of the absolute velocity. The absolute velocity of the gas at the outlet of the impeller has to be known to determine the performance.
 
  • #4
I did not do this for a long time and I don't have a lot of time to study this problem at this time, so it would be easier for me - and others I'm sure - if you develop the problem here for us. We may help out better this way.

If I understand what you want to do, You have to go with the velocity triangles as @jrmichler mentioned. This will give you a set of equations and unknowns. You may have other equations that would join in regarding desired pressure, mass air flow, and power. You must have one equation for each unknown. That is the way to start a problem like that.

Do the work - write the equations, identify the unknowns, make the drawings, etc. - and come back to us as you go along if needed.
 
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  • #5
I must make a correction, the slip factor is the ratio between ideal whirl velocity and the actual whirl velocity, also called tangential component of the absolute velocity. Apparently I can't edit my reply above.
 
  • #6
jack action said:
I did not do this for a long time and I don't have a lot of time to study this problem at this time, so it would be easier for me - and others I'm sure - if you develop the problem here for us. We may help out better this way.

If I understand what you want to do, You have to go with the velocity triangles as @jrmichler mentioned. This will give you a set of equations and unknowns. You may have other equations that would join in regarding desired pressure, mass air flow, and power. You must have one equation for each unknown. That is the way to start a problem like that.

Do the work - write the equations, identify the unknowns, make the drawings, etc. - and come back to us as you go along if needed.
Yes, the velocity triangle is the problem. At this point, most of it is unknown so I'll have to do some more reading.
 
  • #7
MysticDream said:
TL;DR Summary: Seeking insight on how to calculate the absolute velocity

How can I calculate the absolute velocity of air at the outlet of a centrifugal compressor if I have:

Diameter of impeller
RPM
Slip factor

I've been reading for weeks and cannot seem to find the answer to this question. For anyone who is familiar with the subject, I'm sure you know about the blade angle, slip factor, radial and tangential components of flow velocity, and absolute flow angle. It's the absolute flow angle that I cannot find any formulas for. Knowing this, I'd be able to calculate the absolute velocity if I know the tangential velocity of the gas, which is a function of the slip factor and tip speed. I can find nothing that relates the radial component of the flow velocity to the RPM or tip speed of the impeller. Any help would be appreciated.
Turbomachinery design involves lots of initial assumption, iteration and then validation.

Assuming you have you mass flow rate and inlet and outlet condition from your thermodynamic anaysis. Then you can evaulate the axial exit velocity from continuity equation. From slip factor you can evaluate your velocity triangle because you have the blade speed at the exit.
SmartSelect_20240509_190037_Samsung Notes.jpg
 
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  • #8
harsh_raj said:
Turbomachinery design involves lots of initial assumption, iteration and then validation.

Assuming you have you mass flow rate and inlet and outlet condition from your thermodynamic anaysis. Then you can evaulate the axial exit velocity from continuity equation. From slip factor you can evaluate your velocity triangle because you have the blade speed at the exit.View attachment 344830
I don't have my mass flow rate. That is the problem. I need to know the radial component of the velocity through the impeller to calculate the mass flow rate from the density, velocity, and cross sectional area. All I have is my impeller geometry and the RPM. I would imagine the radial component of the velocity could be approximated by an equation using centrifugal force but I haven't seen any information about it.
 
  • #9
MysticDream said:
I don't have my mass flow rate. That is the problem.
Go back and read Post #2 VERY CAREFULLY. Especially the part about fan curves, including the link.

Hint: You calculate the fan curve, then superimpose the system curve. The intersection is where it will operate.
 
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  • #10
Will have another look at it.
 
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FAQ: Centrifugal Compressor: Absolute Velocity Calculation

What is a centrifugal compressor and how does it work?

A centrifugal compressor is a type of dynamic compressor that increases the pressure of a gas by converting kinetic energy into potential energy through the use of a rotating impeller. The gas enters the impeller at the eye and is accelerated outward by the centrifugal force generated by the rotation. As the gas moves through the diffuser, its velocity decreases while its pressure increases, resulting in a higher pressure output.

What is absolute velocity in the context of centrifugal compressors?

Absolute velocity refers to the actual velocity of the gas as it moves through the compressor, taking into account both the rotational speed of the impeller and the flow direction. It is an important parameter for determining the performance of the compressor and is calculated by combining the tangential velocity of the impeller with the axial velocity of the gas.

How do you calculate absolute velocity in a centrifugal compressor?

The absolute velocity can be calculated using vector addition of the tangential and axial components of the velocity. The tangential velocity (Vt) is derived from the impeller's rotational speed and radius, while the axial velocity (Va) can be measured or estimated based on the flow conditions. The absolute velocity (V) is then obtained using the formula: V = √(Vt² + Va²).

What factors affect the absolute velocity in a centrifugal compressor?

Several factors can influence the absolute velocity in a centrifugal compressor, including the impeller design (such as blade angle and geometry), rotational speed, inlet conditions (such as temperature and pressure), and the properties of the gas being compressed. Changes in these parameters can lead to variations in the absolute velocity and overall compressor performance.

Why is understanding absolute velocity important for centrifugal compressor design?

Understanding absolute velocity is crucial for optimizing the design and performance of centrifugal compressors. It helps engineers predict the flow behavior, efficiency, and stability of the compressor under various operating conditions. Accurate calculations of absolute velocity also aid in minimizing losses, enhancing reliability, and improving the overall energy efficiency of the compressor system.

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