Downhole Turbine Design and Short Wind Tunnel Testing - Measurement While Drilling Signal Analysis, Optimization and Design - page 210

flow is found, then the argument of Gavignet et al applies. We do emphasize
that, in the laminar case, Reynolds numbers need not be too close; in fluid
dynamics, Reynolds numbers that differ by, say, a factor of ten, may be close
enough. For both turbine and siren testing, we are actually more than fortunate
- the effects of viscosity (that is, Reynolds number) on torque are secondary, as
viscosity primarily affects only the thrust acting in the direction of flow.
An unanticipated benefit is the use of wind tunnel analysis in compressible
flow, that is, in MWD sound transmission modeling. While high turbine
rotation speeds will result in very short wavelength sound which will not travel
to the surface, the opposite is true of siren valves which typically operate at low
frequencies. Although this chapter deals with turbine flows, it is important to
digress temporarily to study siren acoustic modeling which, after all, forms the
main subject of this topic. In a downhole situation, mud sound speeds vary from
3,000-5,000 ft/sec. In the most optimistic case, consider a carrier frequency of
100 Hz. The associated wavelength is 30-50 ft, which greatly exceeds a typical
drillpipe diameter; thus, our waves are acoustically long.
Now consider sound wave propagation in a very long wind tunnel. The
sound speed is approximately 1,000 ft/sec. For the same 100 Hz, the
wavelength is now 10 ft, which still greatly exceeds a typical pipe diameter.
Since MWD transmissions in air are also long waves, the wind tunnel can be
used to study important problems in transmission, reflection, and constructive
and destructive interference, provided results are properly scaled and
interpreted. Interestingly, thermodynamic attenuation is also amenable to such
modeling. As we have discussed elsewhere in this topic, acoustic pressure
decays like P 0 e - D x where P 0 is an initial value, x is the distance traveled by the
wave and D is the attenuation rate D = (Rc) -1 — {(PZ)/(2U)} = (Rc) -1 — {(QZ)/2}.
The effects of viscosity appear only through the kinematic viscosity and not
viscosity or density individually - and since kinematic viscosity values of air
and mud are comparable, air as a working medium is again justified.
We will develop the foundations underlying wind tunnel analysis
thoroughly in Chapter 9, where we introduce techniques for short, intermediate
and long wind tunnels in the context of siren design. Again, short wind tunnels
are used to evaluate torque and erosion; intermediate wind tunnels are used to
determine siren 'p, while long wind tunnels are used to develop telemetry
concepts. In this chapter, we work with the short wind tunnel exclusively for
turbine design. In the next section, we assume that turbine “stall torque” and
“no-load rotation rate” are both available from short wind tunnel modeling, that
is, from constant density, incompressible air flow measurements about the very
complicated geometries described early in this chapter. We then demonstrate
how performance curves can be developed for muds of arbitrary density at any
downhole flow rate using simple wind tunnel data and aerodynamic conversion
formulas. For more detailed discussions on turbine design, the reader is referred
to Hawthorne (1964) and Oates (1978).