The computer modelling and experimental study of confined jet mixing with application to jet pump design

As an, aid to jet pump design and performance analysis, a theoretical investigation on turbulent confined jet mixing in a non-uniform axisymmetric duct typically used in jet pumps and ejectors has been undertaken. A so-called Prandtl-Kolmogorov two-equation turbulence model, with turbulent kinetic energy k and turbulent energy dissipation rate E as the two parameters, is incorporated into the time-mean Navier-Stokes equations to form a complete set of partial differential equations which describes the turbulent flow mathematically. The equations are solved numerically via a primitive pressure-velocity finitedifference procedure using a digital computer. The timemean static pressure, velocities, turbulent kinetic energy and dissipation rate are predicted directly throughout the whole flow field. To validate the computer model, predicted time-mean static pressure and velocity as well as turbulent shear stress for flow in a uniform bore mixing tube are compared with the published results. The method is then extended to predict flows in conical diffusers and typical jet pumps. The predictions are also compared with the available experimental data. A laser Doppler anemometer is used to measure the mean and fluctuating velocities of water jet mixing in a uniform perspex mixing tube with a centrally located nozzle. The measured data which enable turbulent kinetic energy to be evaluated, are compared with the computer predictions to further consolidate the theoretical model. Finally, the computer model is used to predict the performance of a proposed jet pump and to investigate the influence of various geometrical parameters on jet pump performance. The capability of the computer model as a useful design tool is also demonstrated via an optimization procedure to give the optimum geometry for a given design specification.