The effect of the nonlinearity of the equation of state on a turbulent buoyant jet

Abstract

In most theoretical treatments of turbulent buoyant jets, a linearized equation of state is used. This simplifies work as well as removes the dependence of the density variations of the jet with respect to the ambient on the nature of the fluid and on the type of property causing the density difference–once the linearized equation of state is non-dimensionalized.

Also, in this study, in the process of fitting the predictions of a turbulent buoyant jet model to a set of laboratory data for a hot water jet, a momentum-dilution tradeoff is persistently observed, i.e., when the velocity predictions fitted the data, the dilution (concentration) curves were too low. implying too much entrainment, while if the entrainment were reduced so that the dilution curves fitted the data, the calculated velocities were much too high.

The above two observations motivate this investigation of the effect of using the nonlinear equation of state as a possible solution to the momentum-dilution tradeoff and to determine criteria under which the nonlinear equation of state should be used.

Therefore, combining the mass, momentum, and thermal energy (concentration) flux equations that govern the fully developed turbulent flow of axially symmetric buoyant jets of various types (e.g. hot water jets, saline water jets, hot air jets) with the corresponding nonlinear or linearized equations of state, this investigation concludes that criteria to determine whether a nonlinear or linearized equations of state should be used depends on (a) the fluid medium involved (b) the jet property causing the buoyancy and (c) the value of the initial density parameter, d₀. As an example, to fit the predictions of a hot water jet model to laboratory data, one must match the initial density defect d₀, the initial Fronde number F₀ and the ambient temperature at the jet exit T_∞ and use the nonlinear equation of state even for values of d₀ less than 0.005.

Consequently, the observed momentum-dilution tradeoff mentioned earlier tends to be eliminated using the nonlinear equation of state.