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March 15, 2012, 05:56 
Quantifying the swirl in CFX, Swirl Number/Swirl Angle

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[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: 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. Yaxis in this case Velocity u = Velocity in Xaxis Velocity w = Velocity in Zaxis maxVal = Maximum Value Yaxis is perpendicular to Plane 1, while Xaxis and Zaxis are parallel to the Plane1 in this case. For centrifugal pump impeller design it should be between 0.050.1 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. Yaxis in this case Velocity u = Velocity in Xaxis Velocity w = Velocity in Zaxis Yaxis is perpendicular to Plane 1, while Xaxis and Zaxis 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. Last edited by tauqirnawaz; March 16, 2012 at 04:48. 

March 15, 2012, 22:50 

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Quote:
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. Best Regards 

March 15, 2012, 23:59 

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

March 16, 2012, 05:20 

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Quote:
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. Last edited by tauqirnawaz; March 16, 2012 at 10:58. 

April 12, 2012, 04:03 

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


April 12, 2012, 07:52 

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April 13, 2012, 05:05 

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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: 

April 13, 2012, 23:03 
correct expression

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April 15, 2012, 18:24 

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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.


April 25, 2012, 06:10 

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Agreed the correct equation is
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! Last edited by tauqirnawaz; April 25, 2012 at 08:49. 

April 25, 2012, 21:54 
questions

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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)?


April 26, 2012, 03:29 

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Quote:
Secondly you take root of squares of velocities to get absolute values, otherwise you might get a negative swirl number. 

April 26, 2012, 06:22 

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Quote:
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. Quote:
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. 

April 26, 2012, 10:49 

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Quote:


April 26, 2012, 18:45 

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Quote:
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. 

April 27, 2012, 07:03 

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Quote:
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) 

April 27, 2012, 20:00 
to know the direction of swirling flow

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April 28, 2012, 06:25 

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


April 28, 2012, 23:44 

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swirl no. use to know the strenght of swirling flow and yes the vorticity is useful to know swirling flow direction.
Last edited by happy; April 30, 2012 at 22:48. 

April 30, 2012, 23:43 

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Quote:
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. 

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