Hydrodynamic Entry Length of Flow Through Circular Annulus

[Disquoveri]

I might be going crazy or searching at the wrong places. Is there an empirical formula for solving the hydrodynamic entry length of laminar flow through a circular annulus? Thanks!

 

[Chestermiller]

If the gap between the cylinders is small compared to the radii of the cylinders, then you can treat it as flow between parallel plates. Do you have an estimate of the hydrodynamic entry length for flow between parallel plates? If the inner radius is much smaller than the outer radius, then you are essentially dealing with flow in a circular tube. Do you have an estimate of the hydrodynamic entry length for flow in a circular tube?

Chet

 

[Disquoveri]

Thanks for your help, Chet. (Also, thanks for answering my question on displacement, momentum, enthalpy, etc. thicknesses in circular pipes.)

The gap between the cylinders is not small compared to the inner cylinder though. I have the gap to be 0.015 m, the the inner cylinder radius is 0.012 m, but the outer cylinder radius is 0.027 m. Can I still use the estimate of entry length for flow between parallel plates? The estimation of entrance length is given as L_e = Re*D/K, where K = 20 for circular tube and K = 100 for parallel plates. From simulations done on COMSOL, I know that fully developed velocity profile is achieved within the tube length. The entry length for a circular tube overestimates the entry length/point of fully developed velocity profile.

 

[Chestermiller]

Thanks for your help, Chet. (Also, thanks for answering my question on displacement, momentum, enthalpy, etc. thicknesses in circular pipes.)

The gap between the cylinders is not small compared to the inner cylinder though. I have the gap to be 0.015 m, the the inner cylinder radius is 0.012 m, but the outer cylinder radius is 0.027 m. Can I still use the estimate of entry length for flow between parallel plates? The estimation of entrance length is given as L_e = Re*D/K, where K = 20 for circular tube and K = 100 for parallel plates. From simulations done on COMSOL, I know that fully developed velocity profile is achieved within the tube length. The entry length for a circular tube overestimates the entry length/point of fully developed velocity profile.

The entry length for a circular tube is going to be longer than for an annulus if the Re is defined in terms of the outer diameter for both. So, to be conservative, why not just use the value K=20.

In the entrance region, irrespective of whether it's an annulus or just a tube, the boundary layer growth is initially going to be that for the Blasius solution. This is because the inlet velocity profile is flat, and the boundary layer thickness is negligible compared to the radius of curvature. So it's the same as for flow over a flat plate. So I would determine a nominal boundary layer thickness from the Blasius solution, and divide that by the tube radius (or half the gap between the cylinders in the case of an annulus). When that number is about equal to unity, this would give a reasonable approximation to the entry length. I guess this is how they came up with the values of the entry length for a tube or for parallel plates. Try this, and see what you get.

Chet