Geology Reference
In-Depth Information
7.4 Typical Computed Results and Practical Applications
In this section we discuss typical qualitative and quantitative computed
results. Figure 7.14 shows streamline patterns obtained as relative siren rotor
and stator lobe positions are changed from opened to closed. The tapers clearly
indicated in Figure 7.13 could not be plotted by the graphical software used to
generate Figure 7.14; only shown are the mean lobe box boundaries where taper
boundary conditions are applied. The streamlines correspond to the radially
averaged flow obtained per Equation
7.
3.2. Similar comments apply to Figure
7.15, which illustrates the absolute value of the velocity magnitude in the flow
domain and at solid surfaces; to visually enhance the color scheme, its logarithm
is plotted instead. Red zones in the velocity plots identify areas of high fluid
and surface speed that are susceptible to sand erosion.
Erosion concerns are paramount to practical mud siren design. Very often,
a poorly shaped mud siren will not survive more than several hours in heavy
weight muds flowing at high speeds, e.g., 12 ppg muds with gpm's exceeding
700. Mechanical engineers new to siren design often quote a nominal 100 ft/sec
as
the
dangerous critical velocity to avoid, that is, it is the velocity at which
erosion is incipient. However, this rule-of-thumb is not completely accurate.
Every highway driver has witnessed bug impacts on windshields: the high
inertia of typical insects does not allow them to flow tangentially with the wind.
Consequently, they collide into the automobile. Sand particle convection by
flowing mud follows similar principles. Solids collide into the surfaces of mud
sirens, not to mention turbines, strainers, and other downhole equipment. The
speed of impact is, of course, important. However, the impingement angle and
the impact velocity together dictate the predominant erosion mechanism, that is,
whether metal removal is controlled by brittle fracture, ductile shearing, or both.
While diagrams like Figures 7.14 and 7.15 do not predict particle impact
velocity vectors, they do provide a qualitative indicator that may be useful in
empirically correlating field and laboratory observed erosion patterns. In the
aerospace industry, particularly in jet engine design, computed results like those
shown in Figures 7.14 and 7.15 are actually used in particle-hydrodynamic
simulators to predict turbine blade erosion. These color plots are followed by
design calculations in which torque predictions are addressed. We again
emphasize that computed torque results are entirely consistent with the results of
detailed experiments in which key geometric design parameters were varied
systematically over different oncoming freestream velocities. Refer to Chapter
9 for descriptions of mud flow loops and wind tunnels used for validation of the
computed results obtained here.
7.4.1 Detailed engineering design suite.
In this section, an illustrative set of ten siren design calculations is
described, using our mathematical model and software implementation. In
Figures 7.16 to 7.25, “Lobe Force” appears on the vertical axis, while “Open at
Search WWH ::
Custom Search