Quantifying the swirl in CFX, Swirl Number/Swirl Angle
 

[Note: It might be the case that this information has already been shared on the CFX forum but this is an effort to bring it under one thread.]

Quantifying swirl becomes very important in some situations where you would like to reduce it or even sometimes when requirement of design is to increase the swirl.

Swirl Number:

The degree of swirl in the flow can be quantified by the dimensionless parameter, Sn, known as the swirl number which is defined as the ratio of the axial flux of angular momentum to the axial flux of axial momentum:

http://www.cfd-online.com/Forums/att...1&d=1331804552

To calculate in the CFX, create the following CEL expression;

Swirl Number [non dimensional] = areaInt(Density*sqrt(Velocity v*Velocity v)*sqrt((Velocity u*Velocity u)+(Velocity w*Velocity w))*sqrt((X*X)+(Z*Z)))@Plane 1/(maxVal(sqrt((X*X)+(Z*Z)))@Plane 1*areaInt(Density*Velocity v*Velocity v)@Plane 1)

Where
areaInt = Area Integral
sqrt = Square Root
Velocity v = Velocity in mean flow direction i.e. Y-axis in this case
Velocity u = Velocity in X-axis
Velocity w = Velocity in Z-axis
maxVal = Maximum Value
Y-axis is perpendicular to Plane 1, while X-axis and Z-axis are parallel to the Plane1 in this case.

For centrifugal pump impeller design it should be between 0.05-0.1 for good suction performance or 0.01 for excellent suction performance.

Swirl Angle:
This is again very important for specifying the blade angles in centrifugal pumps.

Use following CEL expression;

Swirl Angle[radians] = atan2(sqrt(Velocity u^2+Velocity w^2), sqrt(Velocity v^2))
Where
atan2 = arctangent
sqrt = Square Root
Velocity v = Velocity in mean flow direction i.e. Y-axis in this case
Velocity u = Velocity in X-axis
Velocity w = Velocity in Z-axis
Y-axis is perpendicular to Plane 1, while X-axis and Z-axis are parallel to the Plane1 in this case

Then create a variable SwirlAngleVariable to calculate an area average over the plane, this would give you a value in degrees.

Hi Raja_Bhai.....
As I know that the results from cfx is in x,y,z coordiantion, and the velocity component into the above expression is in r, tetha, z coordiante. your expresion can make unaccurate estiamtion of swrling no.

You know some times the horizontal plane which include the two component of the velocity, (in r and theta direction or in x&z direction ( considering Z is vertical) is inclined with angule. so the unaccurate estiamtion can come from.

If any one has any knowledge about this issue, please share it with us.:rolleyes:

Best Regards

Hi again
does your celexpression is for the swirl coming from rotating configuration or even for the natural induced?
Regards

Safia,

I normally use these expressions for the calculation of swirl at pump suction (i.e. stationery frame of reference), to adjust the blade angles. Never used them for the rotating frames.

it seems to me that the swirl number as defined above is not dimensionless.

Did you check it in CFX or is it a guess?

Hi,
no I didn't check it in CFX, i just looked at the expression.
Probably the correct expression includes a r^2 in the integrand on top:

correct expression
 

yes, I agree with you I check with many references that r^2 instead of r. see Snegireve et al. (2004).
Regrads

Also be aware that there are different definitions of swirl. For internal combustion engines, swirl inside a combustion chamber is usually defined as the angular momentum of the gas divided by the angular momentum of the same gas if it was in solid body rotation at the crank angular velocity. This results in a unitless number as it is the ratioes of angular momentums.

Agreed the correct equation is http://www.cfd-online.com/Forums/att...1&d=1335348574

areaInt(Density*(sqrt(X^2+Z^2))^2*sqrt(Velocity v^2)*sqrt((Velocity u^2)+(Velocity w^2))*sqrt(X^2+Z^2))@Plane 1/(maxVal(sqrt(X^2+Z^2))@Plane 1*areaInt(Density*(sqrt(X^2+Z^2))*Velocity v^2)@Plane 1*1 [m])

Any comments!

questions
 

yes, where 1[m] comes from where you represent r as sqrt(X^2+Z^2)? as well as, I why you take square root of v^2 or u^2 instead of taking direct variable ( v or u)?

You have to divide the equation by 1[m] to make it dimensionless because when you take max value of the radius; the output you get is dimensionless in CFX. If you do not divide by the unit 1[m], the value of Swirl Number that you get is in meters.
Secondly you take root of squares of velocities to get absolute values, otherwise you might get a negative swirl number.

Then why not use the abs() function?

Most definitions of swirl numbers can be positive or negative so you get the direction of the swirl. If you want the absolute swirl number then you should calculate it including sign, and take the abs value once at the end.

Why take the square root then square it again?

Your comment about units is puzzling. The equation seems to have the units cancelling giving a unitless number. If you have to put a divide by 1[m] at the end to get the correct units then you have a mistake in the CEL.

Agree that abs() function would do the same thing. As regards square of radius, it comes from the formula quoted earlier and I have used sqrt(X^2+Z^2) to calculate radius. Also sqrt((Velocity u^2)+(Velocity w^2) to calculate radial velocity components.

That is obvious. So why write "(sqrt(X^2+Z^2))^2" when this obviously becomes (X^2+Z^2)?

But my key point is about the units - your formula is almost certainly wrong if you have to add a divide by 1[m] at the end to get the units to check out.

Thank you Ghorrocks, please find the corrected formula below;

areaInt(Density*(X^2+Z^2)*sqrt(Velocity v^2)*sqrt((Velocity u^2)+(Velocity w^2)))@Plane 1/(maxVal(sqrt(X^2+Z^2))@Plane 1*areaInt(Density*(sqrt(X^2+Z^2))*Velocity v^2)@Plane 1)

to know the direction of swirling flow
 

As I read through fluid flow books, I learnt that the sign of vortisity (omiga) provides the researcers with the direction of swirling if it was anticlockwise or clockwise:D.

So this means we can use Swirl Number to quantify the flow and Vortisity to predict the direction?

swirl no. use to know the strenght of swirling flow and yes the vorticity is useful to know swirling flow direction.

Mr Glen Horrocks, your comment above has confused me! I just read through a research paper titled "Swirl Control of Combustion Instabilities is a Gas Turbine Combustor" by C. Stone and and S. Menon - Proceedings of the Combustion Institute, Vol 29 / 2002, pg 155-160.

This paper calls out the exact (corrected) formula for swirl number that tariq wrote down in post# 10. Would this formula still be valid, given the alternate definition that you posted for swirl for a gas inside a combustion chamber??

I am a student and relatively new to CFD so please excuse my ignorance.

Have a look in my PhD thesis - http://hdl.handle.net/2100/248

See page 74, in the literature review.

Thanks. The formula is for combustion within the cylinder of an IC engine, and includes "omega" - the crankshaft velocity. Would this relate to a gas turbine engine combustor, where there is no rotating component? The swirl could be introduced in the gas by means of swirl vanes around the inlet nozzle of the gas?

I mentioned this because I wanted to make the point that there is no universal definition of swirl number. It is defined based on what makes sense in the application.

In IC engines it makes a lot of sense to normalise against crankshaft velocity as it is the scaling factor on all engine flows. But for a GT this may not be the case, so an equivalent swirl number normalised by shaft speed may be meaningless.

Hello tauqirnawaz
I confused for CEL equation.
The W in the swirl number equation is tangential velocity. So, why you use sqrt((Velocity u^2)+(Velocity w^2)) for the W ?
Why isn't velocity u or velocity w used for W?