Previously, I have used Reynolds number for dimensionless analysis for optimizing orifice shape (Article Computational study of fluid flow in tapered orifices for ne...
). I was hoping to do a similar analysis for more complex geometries. In that, the calculation of Re at the exit surface is tricky due to the curved exit surface (see attached figure).Re= (ρ∗v∗Dh)/μ = (4∗ρ∗Q)/(μ∗p)
Where, Dh = Hydraulic diameter, v = Mean exit velocity, Q = Flow rate, p = Wetted perimeter.
Would it be more accurate to consider the wetted perimeter of the projected surface rather than a curved surface? (see figure)
There is no issue about "accuracy" in the evaluation of the Reynolds number. It has different values depending on the choice you do for lenght and velocity. I would define in a very simple way as Q/ni where Q is the volumetric flow rate you can compute.
In such computations I always compute the Re number based on the projected area.
This problem is interesting when considering the meaning of the Reynolds number. The Reynolds number arises from dimensional analysis and the mathematics of self-similarity. The quantity you are attempting to estimate for Re is a characteristic length, if it exists, of the flow field at the outflow of your geometry. Your outflow is bounded longitudinally by no-slip surfaces that are also curved at the exit. For this reason, the fluid stream will be released from the no-slip traction at the sides of the exit before the center. For this reason, I suspect the stream velocity will change some across the arc of the exit. Hence, the characteristic length would also change. From this standpoint, the curved surface across the stream seems preferable.
Thank you all for your answers. For clarification, Filippo Maria Denaro , what do you mean by "ni" in "Q/ni"
Yatish Rane
ni = kinematic viscosity
Q = Int [A] n.v dS (A is the outflow surface)
R= radius
Re= (Q/R)/ni
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