Page 216 - Computational Fluid Dynamics for Engineers

204 6. Inviscid Flow Equations for Incompressible Flows

6C.2 Subroutine COEF

This subroutine is modified according to Eqs. (6.5.2) and (6.5.4).

6C.3 Subroutine VPDIS
This subroutine is also modified to take into account the distribution of all the
sources and vorticities from each element.

6C.4 Subroutine CLCM

In this subroutine, the lift CL and pitching moment CM coefficients of each
element are first determined and then the total lift CLT and total pitching
moment CMT coefficients are calculated by adding together the coefficients of
each element.

R e f e r e n c e s

[1] Hess, J. L. and Smith, A. M. O.: "Calculation of Potential Flow About Arbitrary Bod-
ies," Progress in Aerospace Sciences, Vol. 5, Pergamon Press, N.Y., 1966.
[2] Anderson, J.D.: Fundamentals of Aerodynamics, McGraw Hill, Inc., N.Y., 1991.
[3] Abbott, J.H. and von Doenhoff, A.E.: Theory of Wing Sections, Dover, 1959.
[4] Cebeci, T., An Engineering Approach to the Calculation of Aerodynamic Flows, Hori-
zons Pub., Long Beach, Calif., and Springer, Heidelberg, 1999.

P r o b l e m s

6-1. Consider a two-dimensional, steady, fully-developed laminar flow in a chan-
nel of rectangular cross-section with a width of 2L in the ^-direction and the
distance between upper and lower surfaces zl. Determine the velocity distribu-
tion by the direct method discussed in subsection 4.5.1 by solving

\i dx I dx 2 dy 2 J

subject to the boundary conditions in one symmetric quadrant of the flow

du(0,z
= 0, u(l,z) = 0 (P6.1.2a)
dy
du(v,0)
= 0, u(y,L) = Q (P6.1.2b)
dz
Hint: First express the above equations in dimensionless form by defining