Siren Design and Evaluation in Mud Flow Loops and Wind Tunnels - Measurement While Drilling Signal Analysis, Optimization and Design - page 246

Note that the dynamic torque in Figure 9.5 does not vanish at Z = 0
because asymmetric rotor tapers were evaluated in the test. The following
observation from Figures 9.5 is crucial from a testing perspective. In order to
determine the dimensionless torque curve, it is not necessary to use all of the
data points shown. The same straight line can be constructed from a wind
tunnel dynamometer test using two widely separated test points only, say those
corresponding to “southwest” and “northeast.” These two test points are
selected as follows: fix the value of Q and perform tests at wide-apart rotation
rates Z 1 and Z 2 . The resulting curve, normalized as shown, applies to all flow
and rotation rates and to all mud densities. These results are well known in
aircraft turbine flow analysis and result from fundamental consequences of
dynamic similarity. Again we emphasize that tests for dynamic torque are less
important relative to those for static torque. It is also important to emphasize a
physical consequence of Figure 9.5. The straight line dependence means that we
can write (R x Torque)/(UQ 2 ) = D (ZR 3 /Q) + E where D and E are constant
dimensionless slope and intercept values. Thus, Torque = (U/R)(EQ 2 + DZR 3 Q).
This shows that, unlike the simple quadratic dependence of force on flowrate in
static problems, a dynamic correction proportional to the first power of flowrate
and rotation speed is obtained. It is not quadratic, but the dependence on fluid
density is still linear.
9.2.3 Erosion considerations.
Figure 9.6 shows eroded metal prototype parts (for a design concept not in
commercial use) with obvious gouging of the metal very apparent. This is
caused by intense, high speed, swirling, sand-carrying “vortex” flows which
continuously remove metal. Advanced and expensive engineering measurement
methods include hotwires and laser anemometers, but these are not necessary for
our purposes. The “ball in cage” in Figure 9.7a can be constructed from flexible
copper wires soldered in place. This cage contains a white plastic or styrofoam
ball painted white on one hemisphere and black on the other. This device is
introduced into the flow. A straight oncoming flow presses the ball against the
back of the cage, as shown in Figure 9.7a, but a recirculating flow as in Figure
9.7b will impart an obvious spin. The higher the spin rate, the greater the
implied erosion. The erosion design objective is reduction of rotation velocity
or a complete elimination of the recirculation zone. “Ball in cage” test devices
have been developed in different sizes, e.g., over diameters from 0.1 to 0.5
inches in order to characterize different scales of recirculating vortex motion.
The author cautions against “common sense” approaches when redesigning
blunt body flows. Very often, the results are unpredictable, but fortunately,
reliable test results can be obtained inexpensively.