I assume that at lower Re numbers those vorteces are not regularely generated or they are not stable, disappearing quickly.

   Although I'm not familiar with what you would term "low flow rates" as opposed to "high flow rates", this is the first thought that occurs to me. At low flow rates the noise  in the flow is of the same order of magnitude as the eddy amplitude.
   Consider a flow barely moving, but, because it is not perfect, the flow at any point has a small velocity deviation. The flow velocity change induced by the vortex is about the same as the inherit velocity deviation.  A larger flow rates, the velocity change induced by the vortex is much larger than the inherit velocity deviation.
   It just occured to me that you specified flow rate. Do you mean:
      a) different velocities for a given pipe diameter, or
      b) different pipe diameters for a given velocity, or
      c) any combination. (Assuming the flow acts incompressible).
   Also have you checked the accuracy against the Reynold number. Look out for big jumps at around Re 3e5.

   Timbo

I was making a CFD simulation for such device once, so I can guess it's because for low flow rates the dependance between frequency and flow rate is non-linear (Strouhal number changes with Reynolds number) and there is some "critical" flow rate when it becomes linear (Strouhal number is constant).

davedun,

A vortex flowmeter works because the frequency of the vortices that are shed is directly proportional to velocity, over the speed range for which vortices are shed.  At very low speeds, no vortices are shed at all, since the fluid has a tendency to simply stay attached to any obstruction, flowing around it and rejoining.  As the velocity increases, the flow will separate, and some unpredictable, nonperiodic, unsteadiness will occur.  As the velocity increases further, the flow will become strongly perodic, and will be in the range over which a vortex flowmeter can be used.  The short answer is that as the flow regime approaches potential flow ( very low velocity ), the phenomenon that causes periodic vortices does not occur.

vortexman

How low is very low velocity?


At what Reynolds number do vortices appear?
At what Reynolds number are they periodic?

samv,

Two nearly steady counter-rotating vortices will be seen in the wake of a circular cylinder for Reynold's numbers from about 4 to about 60.  Above 60 or so, the vortices begin to shed periodically.  I'm not sure at what Reynold's number the periodic shedding stops.  This is for a circular cylinder, in external flow.  I'm not sure how the behavior changes for other shapes or for internal flow.

vortexman

I don't think there is a Reynold's number where vortex shedding stops.  The frequency just increases.

Do a search on "Strouhal number" and stuff that comes up will indicate that once vortex shedding starts, the Sn remains roughly constant up to Re=200,000.  Sn governs the frequency of shed vortices, but 200,000 isn't an upper limit, just the point where the Sn stops being constant.  Vortex shedding causes smokestacks and aircraft struts to oscillate if they're not designed properly - Reynold's numbers can get very high.

STF

SparWeb,

I did a little more searching on the web.  For a circular cylinder, the nominal Reynold's number at which the periodic vortex shedding stops is about 400.  It does seem odd to me that a flowmeter relying on this phenomenon could be feasible, considering this fairly narrow range of Reynold's numbers over which it occurs.  I don't know how different the vortex shedding is for other shapes, or for confined flow.

Right - you meant periodic vortex shedding, not the turbulent type.  A good reference on this is Hoerner's Fluid Dynamic Drag; several pages devoted to the topic which really doesn't have an analytical solution (yet).  Empirical charts may help davedun figure out the process.

STF