Mud Siren Torque and Erosion Analysis - Measurement While Drilling Signal Analysis, Optimization and Design - page 199

left, closed at right” appears on the horizontal axis, referring to the azimuthal
coordinate. All torque trends indicated qualitatively agree with experimental
results. In all the runs considered, a specific gravity of 1.0 assuming pure water
is taken. The inner hub radius at the siren lobe base is 1 inch, the outer lobe
radius is 2 inch, so that the blade height is 1 inch. The effective moment arm is
approximately 1.5 inch. Also, the volume flow rate is fixed at 1,200 gpm. Both
sets of siren lobes were centered in the computational box. For brevity, detailed
gridding information and tabulated torques are not discussed and we focus on
fundamental physical effects instead.
Run A. The geometry in the cascade plane assumes square rotor and stator
lobes having 1 in u 1 in dimensions, separated by a gap of 0.25 inches. This is
considered large by MWD standards and will not generate significant signal,
however, the run was performed to furnish baseline numbers for comparison.
Again, neither lobe possesses tapers, so that the run corresponds to the sirens
shown in Figures 7.1 and 7.3. Also, there is no streamwise annular taper. The
upper (red) curve corresponds to forces obtained for the upstream lobe, while
the lower (green) curve corresponds to forces on the downstream lobe. The
forces peak at -19 lbf and +19 lbf for downstream and upstream lobes. The
straight line behavior of the force curves versus the inclination of the lobe pair is
consistent with inviscid aerodynamics, as seen in Figure 7.4 for computed lift
coefficients. Note that the force varies linearly with closure and therefore acts
like a linear spring. The corresponding spring constant can be used to estimate
mechanical response times. To estimate the maximum torque acting on the siren
system, consider the outer radius of 2.0 inch, having a circumference of about 12
inches. This fits to a six lobe system in the cascade plane (six solid lobes
combined with six port spaces, each space being 1 inch). The moment arm is
about 1.5 inch. Thus, the torque is approximately 6 lobes u

20 lbf/lobe u 1.5

inch or about 180 in-lbf, in rough agreement with mud loop experiments.
Run B. Here, the geometry in Run A is altered by decreasing the gap from
0.25 inches to 0.1 inches. This distance represents the small gap that might be
used in siren-type tools. Note how computed forces increase approximately
50% to the -28 lbf to +28 lbf range, a trend that agrees with experiment. Also,
the green curve shifts to left, indicating a decreased stable-open character.
Run C. In this simulation, we change the geometry in Run B by adding an
outward taper of 10 o to the downstream lobe, consistently with the shape in
Figure 7. 2. The -28 lbf to +28 lbf range obtained previously is significantly
reduced to -21 lbf to + 18 lbf, again consistently with experiment. In addition,
there is a noticeable shift of the green curve to the right, indicating improved
stable open characteristics for the downstream lobe, also observed empirically.
Run D. We now repeat Run C, and increase the taper angle from 10 o to
15 o . The force range is narrowed, now falling in the -20 lbf to 11 lbf band.