Mud Siren Torque and Erosion Analysis - Measurement While Drilling Signal Analysis, Optimization and Design - page 204

Run G. We now reverse the annular geometry and allow the flow area to
diverge instead. The computed results show a significant reduction in the force
acting on the downstream lobe.
Run H. In this simulation, the gap distance is decreased significantly, as
we had allowed in going from Run A to Run B. Aside from this change, the
geometry is identical to that in Run B, where the force range was -28 lbf to +28
lbf. Here we allow the annular area to converge again, and as in Run F, we
obtain some decrease in the upstream force.
Run I. We allow the annular area to diverge instead, and the effect is a
sharply reduced force (about 25%) on the downstream lobe.
Run J. Finally, we allow both a diverging annular area and a 15 o outward
taper on the downstream lobes. The result is a sharply reduced force range, now
falling in a -16 lbf to +14 lbf band. This combination of design tapers appears
to offer the potential for fast modulations in high-data-rate MWD transmissions.
7.5 Conclusions
In this chapter, a three-dimensional inviscid flow formulation for MWD
mud siren torque prediction is justified and developed. The computational
model is not applicable to pressure drop determination in the downstream
viscous wake. The numerical algorithm hosts a stable and rapidly converging
finite difference solution of the governing fluid-dynamical equations. Column
relaxation methods are used which provide diagonally dominant intermediate
matrices, which allow for robust simulation and numerical convergence by
practicing engineers, without intervention from specialists in numerical analysis.
This combination of fluid mechanics, software design and integrated color
graphics permits the depth-averaged model to be used in real-time engineering
design, guiding the formulation of test matrices and the interpretation of flow
data. The basic operational problems associated with mud siren design, and
their implications in high-data-rate MWD telemetry, have been discussed and
addressed both experimentally and numerically. Considerations related to
“stable-open,” “stable-closed,” “self-rotating,” “low torque,” and “erosion”
issues were in particular discussed in detail.
7.5.1 Software reference.
The Fortran simulation engine for the three-dimensional model are found
in C:\MWD-01\siren-22.for while the graphics module is embedded in the
Visual Basic 6.0 program sfline.vbp. Note that a complementary three-
dimensional model for 'p signal generation is possible for periodic rotor
turning. This model, solving a Helmholtz-type formulation derived from the
more general wave equation, would require a greater degree of complexity and
more computing resources.