Prediction of Turbulent Forced Plumes Issuing Vertically Into Stratified or Uniform Ambients

Abstract

A finite difference calculation method is used to solve the conservation equations of mass, momentum, and energy in differential form for a buoyant turbulent forced plume discharging vertically into both a uniform and a stratified quiescent ambient. This flow configuration is of interest relative to the discharge of thermal or sewage effluents into the ocean and the discharge of effluents from chimneys and cooling towers into a still atmosphere. The effects buoyancy on the turbulent transport model are discussed. The predictions, including the predicted maximum height of rise for the stratified ambient case, are compared with available experimental data and the results of other prediction methods.

Measurements in Vertical Plane Turbulent Plumes

“…Early methods of prediction of buoyant jets were based on the well-known integral techniques [1][2][3][4] using empirical physical assumptions about the flow (e.g., the value of an entrainment coefficient). More recent methods [5][6][7][8] involve solution of the complete set of governing partial differential equations using turbulence models of varying degrees of complexity.…”

Calculation of whole field for vertical round buoyant jets in static linearly stratified environment

“…In the past, a number of turbulence models have been used for the prediction of turbulent buoyant jets. Madni and Pletcher [6] used a mixing-length model, while a large number of other workers have employed buoyancy-extended versions of the k-z two-equation turbulence model [7]. The k-e model involves the solution of transport equations for the turbulence energy k and its dissipation rate £.…”

“…The Finite Difference Procedure of Patankar and Spalding [20] was used to solve the parabolic equation in refs. [6]- [10]. The Hybrid Finite Analytic (HFA) Method [21] is used to solve the convective-diffusion type equation in this study.…”

An Analysis of the Two-Dimensional Turbulent Buoyant Jet

“…Since this analysis, several investigators have published results that deal with the integral relations and empirical representations for the centerline data ([2]- [6]). Madni and Pletcher [7] present an eddy viscosity solution for the mean flow equations, but this study is restricted to centerline data. Baker [8] and Baker et al [9], [10] developed a set of transformed equations which were used to obtain an eddy viscosity solution to the axisymmetric turbulent buoyant jet.…”