Numerical solution of periodically pulsed laminar free jets

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A LTHOUGH the behavior of a steady, two-dimensional, laminar free jet has been treated in detail by many workers such as Pai and Schlichting, there is still limited information on the flow development region near the nozzle exit, the effect of exit conditions on flow characteristics, the location of the virtual origin, and the location at which the velocity profile becomes very nearly self-preserving. Few detailed experimental studies have been reported, mainly because the laminar free jet has limited applications. Numerical solutions have been sought by Pai and Hsieh and Hornbeck. Velocity profiles fluctuating about a mean are common in practice. However, unsteady, two-dimensional, laminar free jets issuing into a stationary medium have scarcely been explored either experimentally or theoretically. This is mainly because unsteady laminar jets normally become turbulent shortly after leaving the nozzle. Closed form solutions always entail certain assumptions which limit their range of validity. For instance, McCormack et al. obtained a closed solution for the mean velocity of a gas jet in the near-field region with a source of periodicity at the orifice by employing the method developed by Lin. However, the solution is only valid for high frequencies. The problem of unsteady mixing of compressible fluid has been studied by Pai with perturbation techniques. Recently, Kent computed the unsteady laminar axisymmetric jet by using an integral method which reduces the number of spatial coordinates from two to one. This greatly reduces computation in terms of space and time but suffers from the drawback that accurate velocity profile information cannot be obtained. The objectives of this study are to use the case of a laminar free jet to develop an efficient transformation technique which is applicable to the computation of unsteady turbulent jets, to study the mean flow development of steady and unsteady laminar free jets, and to examine the unsteady effects.