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An analytical method is presented for the solution of two-dimensional solidification of fluid in motion over a semi-infinite plate. The method is applicable to other two-dimensional free boundary problems involving convection of the liquid phase. The solution is based upon an instantaneous source method which transforms the moving free boundary problem to a stationary domain. The transformed problem is solved by a Laplace transformation which results in a two-dimensional elliptic problem in an irregularly shaped region. An approximate point matching method is employed to solve the elliptic problem. Interface motion is obtained from the solution of a nonlinear integrodifferential equation of the Volterra type. Numerical solutions are presented to verify the validity of the model used in the analytical method and to examine the accuracy of the analytical solution.

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A variable flow fan aircraft propulsion system offers the potential for achieving a low specific thrust with high flow and low jet velocity requirement as specified for takeoff, side-line noise, initial climb, and a high specific thrust requirement for climb and acceleration to supersonic cruise. These requirements are conflicting. To achieve this, the operating envelope of a variable flow fan has to be expanded over existing turbofan engines. The variable flow fan concept (i.e., the Variable Fan Exit or “VFX”) can efficiently operate beyond the usual fan (or compressor) stall operating line using novel methods of designing and scheduling the fan geometry as a function of flight Mach Number, fan pressure ratio and corrected speed. Fan geometry is altered by using variable inlet guide vanes (IGV’s), variable stators, and variable outlet guide vanes (OGV’s).

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