| Description | The laminar fully developed velocity profile in a pipe is usually defined as u(r) = 2*Umean*(1-(r/R)^2) where Umean is average velocity, r is the distance from center, R is the radius.
OpenFOAM implements this one by "operator==(avgU*profile*patch().nf()) which basically results in avgU = 2*Umean and profile = (1-(r/R)^2) according to the above formula.
However, as I analyzed, it could be wrong because of the following reason:
* The profile is defined in laminarBLI.H as follows:
profile = t*(2 - t) where t is the normalized distance to the wall. t is calculated in setWallDist() function as t = pwd/gMax(pwd) = point to wall distance / maximum point to wall
distance. In terms of pipe properties, it can be re-interpreted as t = (R-r)/R = 1-(r/R). Therefore, the profile can be re-interpreted in terms of pipe properties as follows:
profile = t*(2-t) = (1-(r/R)^2) (you can find the full derivation in the attachment)
* The average velocity avgU is calculated based on volumetric flow rate as follows:
avgU = -(scale*flowRate_->value(db().time().userTimeValue()))
/gSum(alpha*rho*profile*patch().magSf());
As I understand, it basically divides the flowrate by the area of the patch so avgU = Umean.
* Following the above reason, I suggest that OpenFOAM implements the laminar fully developed flow as u(r) = Umean*(1-(r/R)^2) so there is a factor of 2 missing here. |
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