Siren Design and Evaluation in Mud Flow Loops and Wind Tunnels - Measurement While Drilling Signal Analysis, Optimization and Design - page 226

aircraft in the air, almost always are corrected for “displacement thickness”
effects because Reynolds numbers do not exactly match. Wind tunnel usage in
the petroleum industry is not completely new. Forces and unsteady loads (due
to vortex shedding) acting on offshore platforms are also routinely obtained
from wind tunnel measurements extrapolated to hydrodynamic environments.
Here, dimensionless Reynolds and Strouhal numbers enter the picture. In any
event, which parameters are more important and how are results to be
interpreted in any given application constitute difficult questions. Answering
these is often more of an art form than a precise science.
9.1.1 Basic ideas.
In low speed viscous flow, typical of many downhole petroleum
applications, the dimensionless “Reynolds number” Rey of the model test should
be almost that of the full-scale problem. Let U be the oncoming speed of the
flow, and L be a characteristic length of the model, say, the diameter; also, let Q
denote the kinematic viscosity, which is simply the quotient “viscosity/density.”
Then, the Reynolds number is given by Rey = UL/Q. If we keep the mud and
wind speeds U identical, and the scales L for test and full-scale geometries the
same, both of which are easily accommodated for most downhole tools in wind
tunnel analysis, then dynamic similarity is guaranteed if the kinematic
viscosities are close.
In Figure 8.5, the kinematic viscosity is plotted versus temperature for
different types of fluids. In the chart, the red dots show the kinematic viscosities
of air (for wind tunnel application) and then water for reference. It may seem, at
least superficially, that water should model drilling mud accurately, since they
are equally dense and just as wet ! The kinematic viscosity of water, indicated
by the lower red dot, is “0.00001.” But water is not drilling mud. Drilling mud
is about 20-30 times more viscous and approximately twice as dense. Thus, the
kinematic viscosity is about fifteen times more than that of water. If the lower
red dot is followed upward vertically (along the 70 o F room temperature line), it
is seen to occupy the “0.00015” position occupied by the red dot for air, exactly
fifteen times as much, as required !
In fluid mechanics, “close” Reynolds numbers need not be too close - a
factor of five to ten difference might suffice for closeness. But the closeness in
Reynolds number just demonstrated - and the fact that wind tunnel testing is just
as applicable when both wind and mud scenarios are turbulent - are significant
from the testing point of view. These suggest that wind tunnel tests are the best
substitute for drilling mud - and the fact that air is convenient, clean, free and
safe, and testing is fast, does not hurt. Only one other fluid works, namely,
methane at room temperature and pressure; methane, of course, is difficult to
work with, being explosive and toxic, not to mention its higher cost. These
reasons explain why clever use of the wind tunnel analysis for hydraulics and
acoustics enables rapid progress to be made.