Mud Siren Torque and Erosion Analysis - Measurement While Drilling Signal Analysis, Optimization and Design - page 187

I xx + I yy = 0

Tangent Flow

U f Kutta BC

Exact Model

I xx + I yy = 0

I y (x,0) / U f #Slope

U f Kutta BC

Thin Airfoil Theory

Figure 7.5. Exact model and thin airfoil theory.

The axisymmetric model was motivated by cylindrical coordinate methods
used to model flows past aircraft fuselages, rocket casings and projectiles. The
ideas have been extended to three-dimensional nacelle flows, solving Equation
7.3.1 below, which include the effects of lower “chin inlets” containing gear
boxes and azimuthal pressure variations accounting for wing-induced effects. A
schematic showing how a sub-grid nacelle model is embedded within the
framework of the complete rectangular-coordinate airplane model is given in
Figure 7.7. Iterations are performed between sub and major grid systems until
the computer modeling converges. The successful approaches in Figures 7.6
and 7.7 were developed by this author for Pratt and Whitney Aircraft Group,
United Technologies Corporation, in the late 1970s, and are described in the
aerodynamics literature; for example, see Chin et al (1980, 1982).

I xx + I rr + 1/r I r = 0

Tangent Flow

Kutta BC

U f

Exact Model

I xx + I rr + 1/r I r = 0

I r (x,R) / U f #Slope

Kutta BC

U f

Thin Engine Nacelle Theory

Figure 7.6. Exact model and approximate thin engine nacelle theory.