Forced Plumes Research Articles

Countergradient turbulent transport in a plume with a crossflow

AbstractDirect numerical simulation of a turbulent forced buoyant plume in a crossflow is performed at a source Reynolds number $${\text{ Re }}_0=1000$$ Re 0 = 1000 , Richardson number $$\mathrm{{Ri}}_0=1$$ Ri 0 = 1 , Prandtl number $$\mathrm{{Pr}}=1$$ Pr = 1 and source-to-crossflow velocity ratio $$R_0=1$$ R 0 = 1 . The instantaneous and temporally averaged flow fields are assessed in detail, providing an overview of the flow dynamics. The velocity, temperature and pressure fields are used together with enstrophy fields to describe qualitatively the evolution of the plume as it is swept downstream by the crossflow, and the mechanisms involved in its evolution are outlined. The plume trajectory is determined quantitatively in a number of ways, and it is shown that the central streamline and the centre of buoyancy of the plume differ significantly—as with jets in crossflow, the central streamline is seen to follow the top of the plume, whereas the centre of buoyancy, by definition, describes the plume as a whole. We then investigate the turbulence properties inside the plume; in particular the eddy viscosity and diffusivity are presented, which are significant parameters in turbulence modelling. Assessment of turbulence production demonstrates the presence of regions where turbulence kinetic energy is redistributed to the kinetic energy of the mean flow, implying a negative eddy viscosity within certain regions of the domain. Similarly, the observation that the buoyancy flux and buoyancy gradient are anti-parallel in specific regions of the flow implies a negative eddy diffusivity in said regions, which must be realised in models of such flows in order to capture the countergradient transport of thermal properties. A characteristic eddy viscosity and diffusivity are presented, and shown to be approximately constant in the fully developed regime, resulting in a constant characteristic turbulent Prandtl number, in turn signifying self-similarity.

Large eddy simulations of a forced plume subjected to volumetric heating in a stratified medium

Large eddy simulations of a forced plume subjected to volumetric heating in a stratified medium

Study on the development of a laminar buoyant starting plume following a thermal

Direct numerical simulations are conducted to study the dynamics of a laminar forced plume with sudden removal of the momentum source. The pinch-off process dependent on two non-dimensional parameters (Richardson number and injection duration) is analyzed, and the effects of the two parameters on the catching time when the pure plume catches up with the thermal ahead and the corresponding catching height are investigated. Four stages of the flow development, i.e., initial accelerating stage, transition and pinch-off stage, approaching stage, and interaction stage, are observed. It is found that with the Richardson number increasing, the thermal cap ascends to a higher height and the temperature near the heat source becomes lower. The increase of the Richardson number can cause the accumulation of heat beneath the thinnest stem, and the increase of injection duration can accelerate the accumulation of heat in the stem. It is observed that the fresh pure plume may catch up with the thermal ahead. The increase of injection duration can cause the increase of the catching time and catching height, while the increase of the Richardson number leads to the decrease of the catching time for a short injection duration.

Lattice-Boltzmann modeling of buoyancy-driven turbulent flows

The pressure-based hybrid lattice-Boltzmann method presented by Farag et al. [“A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows,” Phys. Fluids 32, 066106 (2020)] is assessed for the simulation of buoyancy driven flows. The model is first validated on Rayleigh–Benard and Rayleigh–Taylor two-dimensional cases. A large-eddy simulation of a turbulent forced plume is then carried out, and results are validated against experiments. Good overall agreement is obtained, both for mean and fluctuation quantities, as well as global entrainment. The self-similarity characteristic of the plume in the far-field is also recovered.

Assessment of RANS-based turbulence model for forced plume dynamics in a linearly stratified environment

We present a computational study on the dynamics of a forced plume released in a linearly stratified medium for a range of buoyancy frequencies N∞=0 - 0.7 s−1. Three dimensional unsteady Reynolds-Averaged Navier–Stokes (RANS) simulations are performed using the standard k−ε turbulence model. The mean flow parameters such as the maximum height Zm, mean centerline velocity 〈wc〉, mean axial velocity 〈w〉, and turbulence parameters such as shear production (P), buoyancy production (B), and dissipation rate (ε) are compared with the experimental results of Mirajkar et al. (2020) and a good agreement is found. The validated model is then used to study the forced plume characteristics and energetics at various values of N∞. The passive scalar contours reveal that the plume reaches a maximum height in a stratified medium where the momentum becomes zero, then falls back to the neutral buoyancy height before spreading in the lateral direction. We also found that the maximum height reached by the plume decreases with increasing value of N∞, consistent with the previous studies. Quantification of turbulence parameters reveal that the production flux, P, and viscous dissipation, ε, from the RANS computation are in reasonable agreement with the experimental values at N∞ = 0.4 s−1. Further, the residual, given by 〈〈P〉〉 + 〈〈B〉〉 - 〈〈ε〉〉, is found to be larger for higher N∞, indicating more non-homogeneity in the flow at higher stratification. Overall, the RANS modeling is found to accurately predict the mean flow quantities, such as mean centerline velocity and maximum height reached by the plume. The comparison of the modeled turbulence quantities with experimental data seems satisfactory, but indicates a need for some improvement at high values of N∞.

Global and local spreading rate estimation in forced plumes

A new methodology is proposed to study turbulent axisymmetric plume behaviour based on the analysis of dye forced plume images. The methodology is based on the plume geometrical information deduced from the frames and allows us to obtain measurements in all the axial and radial extensions of the plume (vertical and radial profiles) and its use in a sequence of consecutive frames allows the analysis of the time evolution of the vertical and radial measurements.The time evolution of the vertical and radial measurements allows us to study the spreading rate coefficient in detail. We define the concept of the local spreading rate (βlocal) and its maximum value frequently used in the studies reported in the literature and named here the classical spreading rate (βclassic).As a case study, two experiments were carried out, with two values of Atwood number (0.001 and 0.01) and a fixed source distance Ho(2 cm). The results confirm the variability of the spreading rate with distance from the source (axial evolution) and show a complex time evolution depending on the z-coordinate. In addition, an asymptotic trend was observed but the asymptotic behaviour was not a constant value also depending on the z-coordinate.This methodological approach has the advantage of being noninvasive and easily exportable and requires only the recording of fluid flows (for example, volcanic plumes). Generally, it is not possible to directly control and/or measure a real fluid flow (a geophysical or pollution flow) and the only thing that can be done is its recording and analysis it, which our method allows.

Asymptotic approximations for swirling turbulent plume rising from circular sources

Swirling turbulent plumes are investigated with the Morton, Taylor, and Turner model (MTT) and the $\mathrm{\ensuremath{\Gamma}}$-approach. We derive the asymptotic solutions using regular perturbation methods, and discuss the influence of swirling motions on the plume properties for lazy and forced plumes, respectively. Specially and intriguingly, by introducing a swirl, a forced plume can even be turned into a lazy one in the near field during the vertical evolution.

Reynolds-Averaged Navier-Stokes modeling of a turbulent forced plume in a stratified medium

We present here a computational study of turbulent forced plume released in a varying density environment. The buoyancy frequency N∞ and the Richardson number (Ri) considered in this study are 0.4 s-1 and 0.1, respectively. The Unsteady Reynold-Averaged Navier-Stokes simulations are conducted to evaluate the capabilities of different turbulence models. First, a grid independence study is performed to finalize the grid parameters. Then, simulations were performed using various k-ε turbulence models. The passive scalar contours reveal that the plume reaches a maximum height before it spreads laterally. The velocity contours for the standard k-ε model were compared with a reported experimental study and a good agreement is observed. The mean centerline vertical velocity profile throughout the plume height is compared using different k-ε turbulence models and similar trends are observed for different turbulence models. Overall, we observed that all the variants of k-ε turbulence models capture the macroscale physics accurately, however, the r.m.s. error is the least for the standard k-ε model when compared with the reported experimental study.

Vortex formation in starting buoyant jets at moderate Richardson numbers

In this paper, the formation process of the leading vortex ring in positively and negatively buoyant starting jets with moderate Richardson number in the range of 0.06 < |Ri| ≤ 0.321 has been investigated numerically and theoretically. Using the similarity variables |Ri| and |Ri|2/5 for the positively and negatively buoyant starting jets, respectively, fitting equations can be obtained to predict the buoyant jet penetration rate. Based on these fitting equations, a revised circulation model is proposed by incorporating the effects of both over-pressure and buoyancy. The revised model is well consistent with the numerical results for all positively buoyant starting jets. However, for the negatively buoyant starting jets, this model can predict well only during the initial period. The over-pressure has little influence on the vortex ring characteristics of the starting jets with positive buoyancy, whereas it can significantly affect the vortex ring formation of the negatively buoyant starting jets at moderate Richardson numbers. As the positive Richardson number increases, the instabilities of the trailing shear layer occur earlier. At moderately negative Richardson numbers, a “double plume” structure (an inner sinking circular forced plume and an outer rising annular plume) can be observed. The outer negative vorticity layers develop gradually due to the baroclinic effect. Consequently, the size and strength of the leading vortex progressively decrease. As the negative Richardson number decreases, the negative vorticity layers occur earlier and grow faster.

Analytical solutions and virtual origin corrections for forced, pure and lazy turbulent plumes based on a universal entrainment function

Previous measurements and numerical simulations of buoyant turbulent plumes that develop from area sources provide convincing evidence that entrainment varies locally in response to an imbalance from the asymptotic state of equilibrium, a state referred to as a pure plume. Across the wide spectrum of possible source conditions, that span forced and lazy plume releases, this variation of entrainment has been successfully captured by a single, or universal, description in which the entrainment function $\unicode[STIX]{x1D6FC}$ varies linearly with the local Richardson number. Herein, an analytical solution for the virtual origin of forced, pure and lazy turbulent plumes from circular sources in unstratified environments is derived based on this universal description of entrainment. Prior to this, the analytical solutions reported were limited to those based on the simplifying assumption of invariant entrainment, so-called constant- $\unicode[STIX]{x1D6FC}$ solutions of the plume conservation equations. Analytical solutions for the fluxes of volume and specific momentum are first developed. These solutions highlight the deficit in near-field entrainment in forced plumes and enable the general imbalance from the equilibrium state to be predicted via the streamwise variation of the local Richardson number. Focus then turns to the virtual origin due to the practical benefits that a knowledge of this location offers experimentalists (e.g. in comparing measurement with theory) and theoretical modellers (e.g. in incorporating a turbulent plume within a broader modelling framework).

A general definition of formation time for starting jets and forced plumes at low Richardson number

As an important dimensionless parameter for the vortex formation process, the general form of the formation time defined by Dabiri (Annu. Rev. Fluid Mech., vol. 41, 2009, pp. 17–33) is refined so as to provide better normalization for various vortex generator configurations. Our proposed definition utilizes the total circulation over the entire flow domain rather than that of the forming vortex ring alone. It adopts an integral form by considering the instantaneous infinitesimal increment in the formation time so that the effect of temporally varying properties of the flow configuration can be accounted for properly. By including the effect of buoyancy, the specific form of the general formation time for the starting forced plumes with negative and positive buoyancy is derived. A theoretical prediction based on the Kelvin–Benjamin variational principle shows that the general formation time manifests the invariance of the critical time scale, i.e. the formation number, under the influence of a source–ambient density difference. It demonstrates that the general formation time, based on the circulation production over the entire flow field, could take into account the effect of various vorticity production mechanisms, such as from a flux term or in a baroclinic fluid, on the critical formation number. The proposed definition may, therefore, serve as a guideline for deriving the specific form of the formation time in other types of starting/pulsatile flows.

Integral model for multiple forced plumes arranged around a circle in a linearly stratified environment

An integral model is developed to predict the mixing of multiple forced plumes evenly spaced around a circle in a stratified environment, e.g., buoyant plumes in nature. The model reasonably captures the significant plume boundary distortion caused by plume interactions at the touching height.

Numerical simulation of two coalescing turbulent forced plumes in linearly stratified fluids

A computational fluid dynamic model that can solve the Reynolds-averaged Navier-Stokes equations and the species transport equation is developed to simulate two coalescing turbulent forced plumes, which are released with initial momentum and buoyancy flux into a linearly stable stratified environment. The velocity fields, turbulence structures, and entrainment of two plumes with different source separations and source buoyancy fluxes are analyzed quantitatively, in comparison with a series of physical experiments. An empirical parameterization is proposed to predict the amplification of the maximum rise height of two coalescing forced plumes caused by superposition and mutual entrainment. The maximum values of both turbulent kinetic energy and turbulence dissipation rate decrease monotonically with the increase in source separation of the two turbulent plumes. However, the trajectory of the maximum turbulent viscosity attained in the plume cap region presents two notable enhancements. This variation may be attributed to the turbulence transported from the touching region and the strong mixing around the neutrally buoyant layer between two plumes, while the mixing is caused by the lateral convection and the rebound after overshooting. The plume entrainment coefficient in near vent stems has a positive relationship with the source Richardson number. A transition of flow regimes to plume-like flows would occur when the contribution of initial momentum is important. The entrainment coefficient will decrease in the touching region of two plumes due to mutual entrainment, while the superposition of plumes can lead to distortion of the boundary of plume sectors.

Dynamic Interaction and Mixing of Two Turbulent Forced Plumes in Linearly Stratified Ambience

The hydrodynamics of a two-vent turbulent forced plume propagating in a linear stratification has been studied by a series of laboratory experiments using the two-tank method and the particle image velocimetry (PIV) technique. The velocity fields and turbulence characteristics of a two-vent plume under different source buoyancy flux, ambient stratification, and nozzle distance are analyzed quantitatively. The increase of maximum penetration of a two-vent plume is mainly due to the attenuation of buoyancy gradient caused by less entrainment of ambient fluid in the region between the two vents. The energy spectra do not exhibit a sizable range of the Kolmogorov −5/3 slope, indicating that no substantial inertial subrange is present in this small-scale plume in a linear stratification generated in the laboratory. Both turbulent kinetic energy and dissipation increase with the decrease of distance between the two plumes, indicating that the interaction, entrainment, and mixing in a two-vent plume stem greatly enhance energy production and dissipation. The maximum turbulent viscosity in a two-vent plume, however, presents a three-stage variation. An increase of viscosity in the second stage appears in the mixing region of the neutral buoyancy layer between the two plumes when the normalized distance L/Zmax is in the range of 0.3–0.6; this increase is attributed to flow rebound after overshooting and a strong entrainment and mixing in this region due to lateral flow convection. A new semiempirical formula for the maximum penetration and new scaling relationships for the maximum turbulent viscosity of a two-vent plume are proposed and verified by the PIV experimental data.

Role of dispersed particles on the dynamics of an umbrella cloud of a forced plume in a linearly stratified environment

The vertical release of a lighter buoyant fluid, commonly referred to as a forced plume, into dense environment is a common occurrence in ocean and atmosphere. Such releases may have heterogeneity in them in form of particles with varied size, shape, and volume fraction. Normally in field conditions, the particle size ranges from a few microns to millimetres, and the volume fraction ranges from $$\phi _{v}=0.1{-}10$$ %. In this study, the effects of low values of $$\phi _{v}$$ (corresponding to a two-way coupled system) on the dynamics and structure of a plume umbrella cloud formed in a linearly stratified ambient were examined. Spherical particles with mean diameter $$d_{p}=100\, \upmu \hbox {m}$$ , density, $$\rho _{p}=2500\, \hbox {kg}\,\hbox {m}^{-3}$$ , and $$\phi _{v}=0{-}0.7\%$$ were injected along with the lighter plume fluid. Due to the phenomena of “particle fall-out” and “particle re-entrainment”, it was observed that a plume trough characterized by radius, $$R_{c}$$ , and depth, $$L_p$$ , forms below the neutral buoyant layer of an umbrella cloud. The plume trough formation is linked to the draw-down of the fluid from the neutral buoyant layer by the sedimenting particles. This trough either sustains or collapses depending on the plume conditions at the source, namely, the diameter $$d_{0}$$ , fluid buoyancy, $$g^{\prime }_{0}$$ , vertical velocity, $$W_{0}$$ , and $$\phi _{v}$$ . In all the experiments, $$g^{\prime }_{0}$$ and $$d_{0}$$ were kept constant while $$\phi _{v}=0{-}0.7\%$$ and $$W_{0}=0.2{-}0.65 \,\hbox {m}\,\hbox {s}^{-1}$$ were varied. The experiments revealed that the sustaining and collapsing trough regimes could be qualitatively demarcated based on a source effective Richardson number, $$Ri^{*}_{0}$$ , that accounts for the combined effect of $$\phi _{v}$$ and $$W_{0}$$ . It was found that when $$Ri^{*}_{0}<0.018$$ , the plume trough collapses, otherwise it is sustained. However, $$Ri^{*}_{0}$$ failed to predict the variations in $$R_{c}$$ and $$L_{p}$$ and hence was unsuitable for quantifying the plume trough. Therefore, it was established that the characteristics of a plume trough (i.e. $$R_{c}$$ and $$L_{p}$$ ) depend independently on the particle volume fraction $$(\phi _{v})$$ and source Richardson number $$(Ri_{0})$$ , while the demarcation of the trough regimes could be done using $$Ri^{*}_{0}$$ . For a constant $$Ri_{0}= \frac{-g^{\prime }_{0}d_{0}}{W_{0}^{2}}$$ , with an increase in $$\phi _{v}$$ the trough radius, $$R_{c}$$ , was found to decrease. In contrast, $$L_p$$ increases for a sustaining trough and decreases for a collapsing trough. For a constant $$\phi _{v}$$ , a decrease in $$Ri_{0}$$ caused both $$R_{c}$$ and $$L_{p}$$ to increase irrespective of a sustaining or collapsing plume trough. Using equations of motion for sedimenting particles, an analytical expression for the trough radius, $$R_{c}$$ , was formulated that accurately explains the experimental results. A relation for trough radius, $$R_{c}$$ , that elucidates the dynamics of particle re-entrainment was also obtained. If a particle is within the value of $$R_{c}$$ it is re-entrained into the plume, otherwise settles at the bottom. These results provide useful information needed for modeling particle-laden forced plumes.

An entrainment model for lazy turbulent plumes

An entrainment model for lazy turbulent plumes is proposed, the resulting solutions of the plume conservation equations are developed and the implications for plume behaviour are considered and compared with the available experimental data. Indeed, the applicability of the classic solutions of the conservation equations subject to source conditions that produce lazy plumes, i.e. those with suitably high source Richardson number, contains an essential weakness: the underlying assumption of a constant entrainment coefficient. While entrainment models prescribing the dependence of the entrainment coefficient on the local Richardson number have been proposed for forced plumes, corresponding formulations for lazy plumes have not until now been considered. In the context of saline plumes, the model is applied directly. For hot gaseous plumes, we use a modified definition of buoyancy flux to recover a constant buoyancy flux in a non-stratified environment, despite the specific heat varying with the temperature. After a brief review of existing forced-plume formulations of entrainment, a power-law variation is adopted for the lazy plume. The plume equations are solved for the parameter $0\leqslant \unicode[STIX]{x1D714}&lt;1$, where $\unicode[STIX]{x1D714}$ denotes the exponent of the power law. The cases of pure plumes and lazy plumes are then analysed in more detail; to the best of our knowledge this represents the first modelling of variable entrainment for lazy plumes. Specifically, it is shown that classic plume theory is recovered for $\unicode[STIX]{x1D714}=0$, while for $\unicode[STIX]{x1D714}=1/5$ the plume equations may be solved using usual functions (notably polynomials) only. The results of the models for these cases are very similar, which advocates the idea of selecting systematically $\unicode[STIX]{x1D714}=1/5$, instead of $\unicode[STIX]{x1D714}=0$, for cases where the effect of variation of entrainment is weak, since the new model leads to simple calculations. In the case of very lazy plumes, it is shown that, provided that a relevant value of $\unicode[STIX]{x1D714}$ is chosen, the new model reproduces the available experimental results well.

Vortex ring formation in starting forced plumes with negative and positive buoyancy

The limiting process of vortex ring formation in starting forced plumes, with Richardson number in the range of −0.06 ≤ Ri ≤ 0.06, was studied numerically under the Boussinesq approximation. The examination of the dynamics of the starting flow evolution reveals that the plume-ambient density difference affects the vortex ring pinch-off mainly through three mechanisms, i.e., the baroclinic production of vorticity, the buoyancy acceleration (or deceleration) on the vortical structures, and its effect on the trailing shear layer instability. As Ri increases from negative to positive values, three regimes can be identified in terms of the vortex interaction patterns during the pinch-off process, i.e., the weak-interaction regime (−0.06 &amp;lt; Ri &amp;lt; − 0.02), the transition regime (−0.02 ≤ Ri &amp;lt; 0), and the strong-interaction regime (0 ≤ Ri &amp;lt; 0.06). By eliminating the influence of the baroclinic vorticity production, the circulation method proposed for the starting jets is revised to determine the buoyant formation number F in the starting forced plumes. Besides the formation number F, another dimensionless time scale (dubbed as the separation number S), which corresponds to the end of the pinch-off process, is identified by the time of vanishment of the vorticity flux feeding the leading vortex ring. The numerical results show that the variation trends of formation number and separation number against Ri change near the critical value of Ric ≈ − 0.02. In the weak-interaction regime, both formation number and separation number increase rapidly against Ri. While in the transition and strong-interaction regimes alike, the formation number increases at a much slower rate than in the weak-interaction regime, and the separation number declines dramatically as Ri increases. Finally, a qualitative explanation on the variation patterns of formation number and separation number is proposed based on the buoyancy effects on the dynamic properties of the leading vortex ring and the vortex interaction patterns.

ASHEE-1.0: a compressible, equilibrium–Eulerian model for volcanic ash plumes

Abstract. A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas–particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid dispersed particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low-concentration regimes (particle volume fraction less than 10−3) and particle Stokes number (St – i.e., the ratio between relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium Eulerian), is significantly faster than the N-phase Eulerian model while retaining the capability to describe gas–particle non-equilibrium effects. Direct Numerical Simulation accurately reproduces the dynamics of isotropic, compressible turbulence in subsonic regimes. For gas–particle mixtures, it describes the main features of density fluctuations and the preferential concentration and clustering of particles by turbulence, thus verifying the model reliability and suitability for the numerical simulation of high-Reynolds number and high-temperature regimes in the presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce the averaged and instantaneous flow properties. In particular, the self-similar Gaussian radial profile and the development of large-scale coherent structures are reproduced, including the rate of turbulent mixing and entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of the important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal and maximum plume height. For very fine particles (St → 0, when non-equilibrium effects are negligible) the model reduces to the so-called dusty-gas model. However, coarse particles partially decouple from the gas phase within eddies (thus modifying the turbulent structure) and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the concurrent effect of gravity. By these mechanisms, gas–particle non-equilibrium processes are able to influence the large-scale behavior of volcanic plumes.

An examination of the high-order statistics of developing jets, lazy and forced plumes at various axial distances from their source

In this study, direct numerical simulations of a turbulent free jet (Re = 2000), a lazy plume (), and a forced plume (Re = 1684, Ri = 0.025) are compared. The evolution of the various fluxes and the so-called source parameter, Γ, are examined as a function of distance from the source. The first-, second-, and third-order statistics of the flows are calculated and discussed. The radial profiles of such statistics, as well as that of the turbulent kinetic energy balance and other second-order transport equations are examined at two axial distances, one axial distance before the flows have adjusted to their similarity solution, and the other beyond the similarity adjustment length scale. Vortical structures are visualised and discussed along with entrainment. The source term Γ was not found to monotonically decrease with axial distance from the source as predicted by past researchers. While the mean flow and turbulent velocity statistics of the simulated lazy and forced plumes took on similar behaviour far from the sources turbulent statistics which involve buoyancy did not.

Numerical and experimental study of horizontal round turbulent forced plume in a static homogeneous environment

This paper investigates a numerical and experimental study about horizontal round turbulent forced plume injected into a static homogeneous environment. Helium–air plume is an example of non-Boussinesq forced plume in which a low-density binary gas mixture is injected into a high density ambient of air. Since the domain temperature is assumed to be constant, the density of the mixture is a function of the concentration only. Numerical model is based on the finite volume method and reports on an application of standard k–e model for steady flow with densimetric Froude numbers of 30–300 and Reynolds numbers of 2000–6000. The basic features of the model are: the conservation of mass, momentum and concentration. The boundaries of plume body, the centerline trajectory, the radius plume and the centerline mixture density are determined. It is found that the plume spreading and behavior depend on the ratio between buoyancy flux and momentum, i.e. Froude number. Laboratory experiments have been conducted for photographic observations of plumes trajectories for different mixture (helium–air) densities with different velocities and injection nozzle diameters. Numerical results are described and compared with the experiments and good agreement has been achieved.