Adaptation of ASME PTC 19.3 (2010) to other types of Pipe-intrusions û The vibrational part

[rvivac]

Hello all!

I have an interesting issue here about the interaction between mechanical engineering and instrumentation engineering.

It came to my hands the ASME PTC 19.3 (2010) which scope is just about designing thermowells against resonance and fatigue. It is a really interesting norm that involves the mechanical engineering side of the instrumentation engineering. But the scope is restricted to hollow cylindrical wells of some sets of geometries on pipelines where they insert the thermo-sensor.

I have the task to try to adapt the calculation of these hollow cylindrical forms to other forms like fixed-one-end-simply-supported-other-end beam of various forms like vortex sensors and others as well.

The restriction to hollow cylinders comes clear with the factors involving the area moment of inertia: Izz=π.(D ⁴)/32 like the coefficients of oscillating-drag, oscillating-lift, many corrections factors, as well as the mounting compliance factor to correct the ideal natural frequency according to the dimensions, geometry and mounting set of the TW and the Scruton Number as well.

It is not so difficult to calculate the ideal natural frequency of a simple beam at many conditions. This is definitely not a huge problem.

At the end of the process, they determine a dimensionless quantity G as a relation between the bending moment and the drag pressure in order to combine it with a resonance magnification factor and determine the point of maximum stress.

They go further and calculate the hollow cylinder subjected to external pressure.

But to do all I have to stop on the issues bellow:

1) The 6.5.2 formula for the correction of the natural frequency for the deviation of solid beams (eq. 6-5-2). Someone know from where does it come?

2) For a squared like well, the eq. 6-5-5, have someone any idea how it would be?

3) How do they determine the eq. 6-6-4: the rotational stiffness of the support? I believe it is by F.E. analysis, but I am not sure if it can be done analytically.

Thanks.

 

[hacksaw]

do a search on Brock, he had advocated an early attempt to extend the original design code. The report is freely available.

his report deals with the support flexibility that uses analytical estimate that originated in the mid 1800's, later adapted to square beams and circular shafts and identifed how simple cantilever resonance formulas could be correlated to practical thermowells.

you are right finite elements are the way to go, but it is not a trival problem even for those with all the proper software and extensive computing resources. To extend it as you indicate is noble enough, but it will require major funding and staffing