A basis for numerical modeling of fluid amplifiers

Laminar fluid flow in a simplified fluidic amplifier is analyzed using finite difference numerical techniques. Numerical solutions to the two dimensional incompressible Navier-Stokes equations are obtained in terms of stream function and vorticity. These solutions are presented as contour plots of lines of constant stream function. The effect of various flow parameters, such as Reynolds number, outlet port loading, and deflection of the power jet are examined. Finite difference solutions are also obtained for the pressure distribution. The problems associated with obtaining accurate numerical pressure solutions are discussed in detail. In particular, the problems associated with an inconsistent formulation of this Neumann problem are described. A large-scale laminar flow amplifier was designed and constructed so that the geometry matched that of the numerical simulation. Dye was injected into water flowing in the amplifier, and streamline photographs were obtained. Good agreement existed between the photographs and the numerically predicted streamlines. Extensions of the model aimed at producing a working tool for use in design of fluidic amplifiers are suggested.