Vertical Round Jet Research Articles

Flow and heat transfer in round vertical buoyant jets

The application of the algebraic stress modeling method (ASM) for calculating the flow in a turbulent vertical round jet is described. The ASM method yields algebraic equations for Reynolds stresses 〈 u' iu' j 〉 and turbulent heat flux components 〈 u' iT' 〉. Transport equations are solved for the turbulent kinetic energy k, its dissipation rate ε. and mean square of temperature fluctuations 〈 T' 2〉. A new version of the model has been used allowing one to account for the effect of normal Reynolds stresses on energy redistribution in the spectrum of turbulent fluctuations. To model these effects, an additional term has been included into the equation for ε. A new effective approach to solving the governing system of partial differential equations is suggested based on the introduction of mathematical variables. Examples of numerical calculations are presented which are compared with the available experimental data of other authors. It has been found that they agree satisfactorily with the results of measurements.

Buoyant Jets in Density‐Stratified Crossflow

Analysis is performed to predict the maximum and equilibrium heights‐of‐rise for vertical round jets discharged into a linearly stratified crossflow. Approximate relations for minimum dilution at the maximum height of rise is also presented. Length scales describing the interaction of a buoyant jet with the crossflow and stratification are presented. Various asymptotic solutions can be developed with the use of dimensional analysis and physical reasoning; their applicability depends upon the relative magnitudes of the different length scales. Experimental results were obtained to determine the values of the appropriate coefficients in the various asymptotic solutions. These were obtained by towing a buoyant jet discharge at constant velocity through a stagnant, stratified fluid. Measurements of maximum and equilibrium rise heights were obtained along with concentration profiles at the maximum height‐of‐rise. The results indicate that the approximate solutions can be applied if the coefficients in the various expressions are allowed to vary; this variation may be small enough to neglect for many practical applications.

Closure to “ Vertical Round Buoyant Jet in Shallow Water ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Closure to “ <i>Vertical Round Buoyant Jet in Shallow Water</i> ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Discussion of “ Vertical Round Buoyant Jet in Shallow Water ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Discussion of “ <i>Vertical Round Buoyant Jet in Shallow Water</i> ” by Joseph H. W. Lee and Gerhard H. Jirka (December, 1981)

Vertical Round Buoyant Jet in Shallow Water

The stability and bulk mixing characteristics of an axisymmetric turbulent buoyant jet discharging vertically into a stagnant waterbody of large horizontal extent is studied theoretically and experimentally. A stable discharge configuration is defined as one in which a buoyant surface layer is formed which spreads radially from the source and does not communicate with the initial buoyant jet region. On the other hand, the discharge configuration is unstable when recirculation cells exist around the jet efflux. A semi-empirical theory shows the discharge stability is only dependent on the dynamic interaction of three near-field regions—the buoyant jet region, surface impingement region, and radial internal hydraulic jump region. A series of laboratory experiments were performed with a half-jet, using heat as source of buoyancy, and inserting a plane of symmetry in a large model basin. The experimental results are in good agreement with the theoretical predictions, both as regards the stability criterion and the near field mixing characteristics.

Closure to “Dilution in a Vertical Round Buoyant Jet”

Closure to “Dilution in a Vertical Round Buoyant Jet”

Discussion of “Dilution in a Vertical Round Buoyant Jet”

Discussion of “Dilution in a Vertical Round Buoyant Jet”

The Effect of Buoyancy on the Turbulence Structure of Vertical Round Jets

The paper presents an application of the algebraic stress modeling (ASM) technique to the prediction of the flow in a turbulent round buoyant jet. In the ASM approach, algebraic formulas are obtained for the Reynolds stresses, uiuj, and for the components of the turbulent heat flux, tui. In the model used here, transport equations are solved for the turbulence kinetic energy, k, its dissipation, ε, and the mean square temperature fluctuations, g. The study shows that buoyancy increases the rate of dissipation of g above the values indicated by previous recommendations for the modeling of that quantity. As a possible explanation for this result it is suggested that buoyancy introduces anisotropy in the fluctuations at the dissipation scale. The study shows that the contribution from the secondary components of the strain tensor to the production of k is non-negligible. In addition, between 12 and 17 percent of the longitudinal enthalpy flux is contributed by the turbulent fluctuations. Finally, it is observed that the modeling of buoyant flows still presents uncertainties and that additional work is necessary to properly account for the effect of buoyancy on the production of ε and the dissipation of g.

Dilution in a Vertical Round Buoyant Jet

A round, vertical, turbulent buoyant jet is defined here as a source of fluxes per unit mass of mass μ o , momentum m o , and buoyancy β o , issued through an orifice of diameter D into a nonflowing fluid of uniform density ρ a . Such flows occur often in hydraulic engineering and the time average mean concentration along the axis of the buoyant jet is often needed. The purpose of this note is to present an explicit, easy to use formula that gives the mean center line dilution in a vertical buoyant jet for a wide range of the initial densimetric Froude number. This note assumes that the reader is familiar with basic results of jets and plumes.