Mud Siren Torque and Erosion Analysis - Measurement While Drilling Signal Analysis, Optimization and Design - page 184

C L NACA 4412 Airfoil

2.0

Theory

1.0

Experiment

Inclination D (deg)

-16 - 8 0 + 8 +16 + 24

-1.0

Figure 7.4. Typical inviscid lift coefficient versus inclination.

By analogy, we expect that the torque acting on siren rotors and stators -
controlled principally by the upstream attached flow - can be calculated
accurately using inviscid theory. (As in airfoil analysis, torque is perpendicular
to the direction of the oncoming flow.) This is motivated by laboratory and field
experience: the stable-closed or stable-open character of any particular siren
design is independent of flow rate, viscosity, mud weight, or water versus oil
mud type, i.e., it is largely unaffected by rheology. This is borne out by
qualitative and quantitative experimental comparisons to be discussed. Here,
because the work focuses on torque at low oncoming speeds, or more precisely,
low Mach numbers, fluid compressibility is neglected. Compressibility, of
course, is important to signal generation and propagation, subjects already
treated in this topic. To simplify torque analysis, we restrict ourselves to steady
flow and examine its “static stability” as stationary siren rotor and stator sections
are altered with varying degrees of closure. This philosophy is adopted from the
classical approach used in airplane stability analysis and design.
We emphasize that separated viscous downstream flows and streamwise
pressure drops are not described adequately in this approach. Highly empirical
methods are instead needed. These flows are affected by rheology, and pressure
drops at high flow rates can range in the hundreds of psi's (numbers quoted are
qualitative and intended to convey “ballpark” estimates only). Engineers new to
mud siren design often equate large pressure drops or “delta-p's” with strong
MWD signals. This is not the case. A localized static pressure drop does not
propagate and transmit information. Only dynamic, acoustic components of
time-dependent pressures - water hammer signals, for instance - are useful in
data transmission. For positive and negative pulsers, this propagating signal can
exceed 200-300 psi at high flow rates, although the power needed to generate
such signals are enormous. Sirens typically create acoustic 'p's or peak-to-peak