Mud Siren Torque and Erosion Analysis - Measurement While Drilling Signal Analysis, Optimization and Design - page 191

details of the method, we introduce three additional design variables not
discussed in Section 1.
First consider the siren configuration shown in Figure 7.8. This diagram
indicates still another design variable - a swirling upstream flow that can be
induced by the presence of deflection vanes located just upstream of the lobed
pair, as suggested in U.S. Patent No. 3,867,714. The degree of imposed swirl
can be introduced by prescribing the value of 1/R m ) T as a boundary condition.
Figure 7.9 illustrates the downstream central hub, which is always present in
existing designs; it also shows an upstream hub, which may or may not be
present. Although it is natural to design the associated annular passages with
surfaces that are completely aligned with the direction of the oncoming flow,
this is not necessary or recommended. In fact, the right side of Equation 7.3.10
shows that local geometric curvatures will affect computed torques, velocity and
pressure fields, although their consequences are not immediately evident.
Possible choices for the annular passages leading up to the siren and away
from it are shown in Figure 7.10. By no means are these the most general.
Streamwise surface slopes shown in the individual diagrams here only increase
or decrease monotonically, but they can increase and decrease, decrease and
increase, or for that matter, take on the “wavy wall” form studied in aerospace
literature. The sign of {R i V i - R o V o } in Equation 7.3.10 is seen to be an
important design parameter. For instance, referring to Figure 7.10.1, it is
positive for the converging case and negative for the diverging case. Figure
7.10.2 shows one possibility (of several) tested for its influence on torque and
signal. We emphasize again that the three-dimensional character of typically
small hub radii is modeled in the integral approach leading to Equation 7.3.10.
Figure 7.8. Basic mud siren with upstream swirl.
Figure 7.9. Three-dimensional mud siren with annular passages.