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Quantifying the swirl in CFX, Swirl Number/Swirl Angle

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Old   May 1, 2012, 01:06
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Glenn Horrocks
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Have a look in my PhD thesis - http://hdl.handle.net/2100/248

See page 74, in the literature review.
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Old   May 2, 2012, 22:35
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Originally Posted by ghorrocks View Post
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?
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Old   May 2, 2012, 23:48
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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.
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Old   July 24, 2016, 22:28
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Originally Posted by tauqirnawaz View Post
[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. 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.
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?
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