An Explicit Numerical Method for the Solution of Jet Flows

Abstract

The parabolic momentum and energy equations for axisymmetric compressible jet flows in zero pressure gradient can be expressed as first-order difference equations which relate the velocity and enthalpy at any downstream point to the velocities and enthalpies at upstream points. Using this relation, a numerical scheme is developed in such a way that the velocity, enthalpy, density, and effective viscosity at each location are expressed as Fourier cosine series thus satisfying the condition of vanishing gradients at the axis and allowing solution of the difference equations at downstream points by direct substitution of values at upstream points. The stability and accuracy are investigated by solving the momentum equations for laminar compressible flow of a hot primary jet into a colder secondary stream and for a laminar incompressible free jet at constant temperature. There is good agreement in the first case with published finite difference solutions and with experimental data in the second case. The method displays good stability and permits the prediction of velocity profiles and the axis velocity decay from known profiles at the nozzle without the use of excessive computing time.