Determination of streamlines on stream surface with discretely defined geometry and velocity distribution

Numerical generation of streamlines along an arbitrary stream surface is discussed in the present work. Using a given set of nodal Cartesian coordinates, which define a stream surface, and the associated velocities at each node, a new nonorthogonal, curvilinear coordinate system (p,q) is devised along the surface. On the basis of this curvilinear system a piecewise, analytically defined surface is generated passing through the p and q coordinate lines. Using the velocity components at each nodal point, a piecewise, analytical representation of the velocity distribution (as a function of p and q), along the surface is determined. Using the differential geometry of the surface and velocity distribution along it, a set of streamlines is calculated along with an additional set of streamline orthogonal lines.