Pure Plume Research Articles

A compact open boundary treatment for a pure thermal plume by direct numerical simulation

This study introduces a novel open boundary treatment method for simulating thermal plumes in natural convection, utilizing a combination of the Perfectly Matched Layer (PML) and local one-dimensional inviscid (LODI) methods within a compressible flow solver for Direct Numerical Simulation (DNS). This innovative approach significantly reduces the size of the computational domain yet effectively captures the complex transition from laminar to turbulent flow. Validation of the proposed methodology includes comparisons with existing empirical formulations, experimental data, and well-resolved DNS results, incorporating both time-averaged and spectral analyses. Additionally, the buoyancy-induced laminar-turbulent transition is investigated to enhance understanding of the dynamics and behaviors of thermal plumes. The findings offer insights into optimizing computational efficiency without compromising the accuracy needed to analyze intricate fluid dynamics in thermal engineering applications.

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.

Predicting radial profiles for jets with arbitrary buoyancy

The present study investigates the profiles of statistically axisymmetric turbulent jets with arbitrary buoyancy. Analytical expressions for the shape of the radial velocity, Reynolds stress and radial scalar flux profiles are derived from the governing equations by assuming self-similar Gaussian mean velocity and scalar profiles. Previously these have only been derived for the special cases of pure jets and plumes, whereas the present study generalises them to arbitrary buoyancies. These are then used to derive analytical expressions for the turbulent Schmidt/Prandtl numbers, which, along with the mean profiles, are shown to give predictions in agreement with existing literature.

Energetics of buoyancy-generated turbulent flows with active scalar: pure buoyant plume

A framework for the budget of Reynolds stress, temperature and density variations, turbulent mass flux and turbulent heat flux is presented for buoyancy-generated turbulent flows with a focus on turbulent plumes. The dynamical interactions between the turbulence generated from the velocity and thermodynamic fluctuations in thermal and heated gas plumes is studied. A large-eddy simulation tool has been used to simulate heavier and lighter than air plumes released from a circular heated source for high Reynolds number (Re). The budget equations are developed using a Favre-averaging approach. Both heated air plumes and heated gas plumes, namely, heated ${\rm SO}_2$ and heated ${\rm CH}_4$ plumes, are included in the study. The study focuses on addressing key questions – does the turbulence kinetic energy (TKE) spectrum follow the classical inertial $-5/3$ spectrum or is there a $-3$ buoyancy regime with a different scaling law? Fundamental pathways for generation of turbulence through velocity fluctuations, and temperature and density fluctuations are discussed. Analysis of the TKE and scalar variance budget equations has demonstrated that multiple mechanisms dominate the transport of Reynolds stresses, and in particular that correlations between the density and the velocity dominates the turbulence production mechanisms. Entrainment is connected to the turbulent transport and pressure-dilation processes.

Experimental investigation on the characteristics of pressure oscillations for sonic steam-air jet in subcooled water

To investigate the characteristics of pressure oscillations for sonic steam-air jets in subcooled water, a series of experiments are conducted, and pressure oscillations are recorded and analyzed. The results indicate the occurrence of the back-attack phenomenon for steam-air jets. The back-attack phenomenon is the result of the necking of the steam-air plume, which hinders the flow of gas downstream, thereby causing some gas to expand in the opposite direction and back attack the nozzle. When the back-attack phenomenon occurs, a pressure pulse occurs at the nozzle outlet simultaneously. Regarding jet pressure oscillation, the intensity of pressure oscillation increases with the increase of temperature and air mass fraction. The dominant frequency of pressure oscillation decreases with the increase of water temperature and air mass fraction when the water temperature is lower than 80 °C. The pressure oscillation frequency increases initially and then decreases with the increase of air mass fraction when the water temperature is 80 °C. An empirical equation for predicting the radius of the steam bubble separated from the end of the pure steam plume is proposed, and the deviation is within the error band of ±15%. In addition, a prediction equation for the oscillation frequency of steam-air jets is proposed based on bubble oscillation theory, which can predict the dominant frequency when the air mass fraction is 0.01–0.5, the water temperature is 25–80 °C, and the inlet pressure is 0.3–0.7 MPa.

1.79–1.75 Ga mafic magmatism of the Siberian craton and late Paleoproterozoic paleogeography

The paper presents new geological, geochronological, geochemical, and Nd isotopic data on the late Paleoproterozoic dolerites of the Siberian craton. U-Pb baddeleyite ages of the Doros dolerites (Aldan shield, south-eastern Siberia) and East Anabar dolerites (Anabar shield, northern Siberia) are 1757 ± 4 and 1774 ± 6 Ma, respectively. This new geochronological data together with published 1.76–1.75 Ga ages for Timpton-Algamay dolerites of the Aldan shield and Chaya dolerites of the Baikal uplift (southern Siberia) revealed a 20 my difference between this magmatism in the north and south Siberia. The Doros dolerites in their chemical compositions correspond to sub-alkaline basaltic andesites, but the East Anabar dolerite is chemically close to basaltic trachyandesite. The Doros dolerites demonstrate negative and close to zero ɛNd(t) values (from −7.0 to +0.1), which correlate well with SiO2 and Mg#. All Doros dolerites have Nb–Ta and Ti anomalies in multielement spectra. The geochemical and Nd isotopic data suggest that the Doros dolerites have been formed by the mixing of mantle and crustal material. The East Anabar dolerites are characterized by a negative ɛNd(t) value of −3.7, negative Nb–Ta anomaly in multielement spectra, high concentrations of TiO2 and P2O5. The 1775 Ma East Anabar dolerites could be generated from a subcontinental lithospheric mantle source, possibly with some mantle plume interaction (possibly centred at the convergence with the 1.76–1.75 Ga fanning Aldan swarm). Geochemistry and Nd isotope systematics of all 1.78–1.75 Ga mafic dykes and intrusions of the Siberian craton indicate the subcontinental lithospheric mantle source or mantle source contaminated by crustal material. Geochronological data from the 1.79–1.75 Ga magmatic rocks of Siberia and other continents suggest continuous magmatism over this interval in some continents, but a series of short magmatic events/pulses (from one to four) separated by intervals of quiescence in other continents. We locate the analysed dykes and sills on new 1750 Ma and 1790 Ma global paleogeographic reconstructions. Analysis of 1.79–1.75 Ga geochemical data on mafic intrusions from Late Paleoproterozoic continents suggests the prevalence of subcontinental lithospheric mantle source for the mafic intrusions over the pure mantle plume source.

What is the entrainment coefficient of a pure turbulent line plume?

Despite its pivotal role in the classic theory of turbulent line plumes, there has been no consensus on the value of the entrainment coefficient $\alpha$ suitable for a pure plume. Reported measurements vary by 100 %, from $\alpha =0.1$ to $\alpha =0.2$, hindering the predictive capabilities of plume theory. Following our theoretical developments, measurements of plume entrainment using a new approach and a rigorous assessment of reported values for $\alpha$, we conclude that ${\alpha =0.11\pm 15\,\%}$ should be adopted as the consensus value. Our theoretical framework demonstrates how $\alpha$ is determined from underlying plume measurements, and places an emphasis on the link between measurement uncertainty and uncertainty in $\alpha$. This framework inspired our experimental design, intentionally conceived to precisely determine $\alpha$. From measurements of the plume scalar width and the entrainment velocity outside the plume, we determine that $\alpha =0.108\pm 2\,\%$ ($95\,\%$ confidence interval). Complementing our experiments is an evaluation of the historical data which, after we explain why some reported values of $\alpha$ are erroneous, supports the range $0.095\lesssim \alpha \lesssim 0.13$. The proposed consensus value thus represents both our precisely determined value and the variation in the published data. The significance of a consensus value for $\alpha$ can be summarised as follows: (i) it enhances confidence in the application of plume theory to practical situations and (ii) it permits more detailed comparison of entrainment between pure line plumes and related turbulent flows, including forced and lazy line plumes and wall plumes.

Two-dimensional buoyant plumes in a uniform co-flow

The behaviour of turbulent, buoyant, planar plumes is fundamentally coupled to the environment within which they develop. The effect of a background stratification directly influences a plumes buoyancy and has been the subject of numerous studies. Conversely, the effect of an ambient co-flow, which directly influences the vertical momentum of a plume, has not previously been the subject of theoretical investigation. The governing conservation equations for the case of a uniform co-flow are derived and the local dynamical behaviour of the plume is shown to be characterised by the scaled source Richardson number and the relative magnitude of the co-flow and plume source velocities. For forced, pure and lazy plume release conditions the co-flow acts to narrow the plume and reduce both the dilution and the asymptotic Richardson number relative to the classic zero co-flow case. Analytical solutions are developed for pure plumes from line sources, and for highly forced and highly lazy releases from sources of finite width in a weak co-flow. Contrary to releases in quiescent surroundings, our solutions show that all classes of release can exhibit plume contraction and the associated necking. For entraining plumes, a dynamical invariance spatially only occurs for pure and forced releases and we derive the co-flow strengths that lead to this invariance.

Determination of the entrainment coefficient of a pure plume using the salt-bath technique

Determination of the entrainment coefficient of a pure plume using the salt-bath technique

New findings in vorticity dynamics of turbulent buoyant plumes

The vorticity dynamics of turbulent, buoyant, and pure plumes released into the quiescent ambience has been investigated using large-eddy simulations with plume Reynolds number in the range of 6 × 107 to 108. The plume is generated by a circular heat source and sustained by buoyancy forcings generated by heating. As the starting plume rises vertically, it expands radially, entraining ambient fluid into the plume and two distinct stages of evolution are evident. During stage one (initial stage), in the near-source region the plume is accelerating characterized by developing turbulence. During the next stage (mixing stage), the plume is significantly altered by turbulence resulting in significant entrainment and expansion in the radial direction. As turbulent intensities decay during the mixing stage, the enstrophy decays in an exponential manner with height with an exponent of −7/4. The turbulent kinetic energy budget analysis reveals—baroclinic torque, stretching, and compression—as the three dominant mechanisms for the plume growth. The probability distribution function (PDF) of vorticity shows that vorticity is mainly aligned along the transverse direction near the source and slowly reaches to a quasi-isotropy state downstream. Turbulence spectra demonstrate the presence of a buoyancy-regime with a −3 spectral slope. The PDF of vorticity further shows extreme dominance of the strain rate rather than rotation within the plume. Consistent with studies in the literature, the vorticity fluctuations align with the intermediate eigen-vector of strain-rate tensor.

Vertical Round Buoyant Jets and Fountains in a Linearly, Density-Stratified Fluid

Turbulent round buoyant jets and fountains issuing vertically into a linearly density-stratified calm ambient have been investigated in a series of laboratory experiments. The terminal (steady-state) height of rise and the mean elevation of subsequent horizontal spreading have been measured in positively buoyant jets (at source level), including pure momentum jets and plumes, as well in momentum-driven negatively buoyant jets (fountains). The results from experiments confirmed the asymptotic analysis that was based on dimensional arguments. The normalized terminal height and spreading elevation with respect to the elevation of injection of momentum-driven (positively) buoyant jets and fountains attained the same asymptotic values. The numerical results from the solution of entrainment equations, using an improved entrainment coefficient function, confirmed the results related to buoyancy dominant flows (plumes), while their predictions in momentum-driven flows were quite low if compared to measurements.

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).

Structure of the natural convective flow above to the horizontal surface with localized heating

Pure thermal plumes have been the subject of study for the past decades. The active development of experimental and numerical research methods allowed to identify the flow characteristics in the entire region of the plume formation. Nevertheless, the bifurcation discovered in the last ten years remains to be studied, in the authors' opinion, poorly. Until now, there is no general conception of the existence of several stable flow regimes and the key features of the unsteady regime. In this paper results of an experimental and numerical study of pure thermal plume structure in the near-hot-wall region at moderate Grashof numbers are presented. Experimental data on the general flow structure and temperature field are supplemented by the results of numerical simulation. The analysis of changes in instantaneous and average values is carried out, in particular, the geometric characteristics of the near-wall layer are determined. Additionally, data on the characteristics of heat transfer, information on which in modern studies is usually limited and is fragmentary, are presented.

One-dimensional model of hydrogen distribution in confined space based on Froude number

Some hydrogen mitigation study programs have been conducted to figure out the hydrogen distribution characteristics and provide useful information for codes development and validation. However, there is a lack of models with direct relations between hydrogen distribution and a non-dimensional parameter which governs the hydrogen flow, such as Froude number. This deficiency will lead to lack of understandings of the dominated force regimes. Therefore, in this paper, one-dimensional model of hydrogen distribution is built, based on Froude number. With theoretical study and fitting method, a semi-empirical formula is given, which is verified by experimental data obtained from pure plume conditions and buoyant jet conditions. Finally, this newly-built model is employed in typical accidents analysis. Three typical Froude numbers which are based on PANDA and TOSQAN study, are selected to get much closer to the real accidents. According to the evolution of helium concentration and concentration distinction, it can be found that obvious stratification may take place in the middle part and lower part of the containment model, while it turns to be more uniform in the top, corresponding to these three Froude numbers of 3.8, 17 and 280. Moreover, the higher the buoyancy is (Fr = 3.8), the more uniform the helium distribution throughout the containment model will be. The medium momentum will lead to significant stratification, which needs to be paid much attention in reactor design and accident mitigation.

Ground wind generated near the base by the massive convective column of very large-scale mass fires

In large-scale mass fires generated in forests or by a nuclear event, the area of the fire is large (diameter 1 or more kilometers) whereas the flame height is relatively small (less than 10 m) creating a large turbulent buoyant plume. This paper determines a correlation for the magnitude of velocity such a flow generates near above the ground at the edges of the mass fire. This induced wind velocity is due primarily to the total cumulative buoyant plume above the mass fire. Therefore, this situation can be simulated by using a pure buoyant plume (for example of helium) representing the buoyant flow above the flame height and having a diameter representing that of the mass fire. A similarity and numerical study of turbulent buoyant helium plumes is presented to determine and correlate the induced velocity near the ground in terms of the total buoyancy or equivalent heat release rate and the diameter of the source fire. The similarity analysis is based on relations for large buoyant plumes which have also been recently supported by experiments. Simulations for validation using the fire dynamics simulator (FDS) were performed for literature data for a 1 m helium plume source. Subsequently, simulations were carried out for various source sizes and for a range of helium flow rates to deduce a correlation between the maximum horizontal velocity with the buoyancy rate and the fire plume diameter. Finally, additional simulations were performed for a 2D case where the fire source length was set the same as the computational domain in that direction with varying fire source widths and flow rates and it is found that similar relation as that deduced for a 3D plume also applies to the 2D case with the characteristic length being the length of the fire source. In this work, we do not address asymmetric fire source load conditions, which may or may not generate fire whirls.

Visualization of instability processes in pure thermal plume

In the paper, the results of physical and numerical simulation of a natural convective flow formed over a heated horizontal disk are presented. The main purpose of this study is to analyze the occurrence of various stable states of a free-convection plume depending on the temperature of the heated surface. The presented flow patterns make it possible to determine the critical value of the temperature factor at which a change of stable states is observed. The visualization data obtained in the framework of physical modeling are compared and supplemented with data on flow patterns obtained numerically. A mechanism for the formation of separate air masses (“puffs”), which destroy both the near-wall layer and the formed upward flow is proposed. It was found that the emerging soft bifurcation is characterized by a sharp increase in the amplitude of perturbations with a slight increase in the value of the temperature factor: initial fluctuations of the plume boundary lead to further disruption of the heat balance and formation of puffs.

A second-order integral model for buoyant jets with background homogeneous and isotropic turbulence

Buoyant jets or forced plumes are discharged into a turbulent ambient in many natural and engineering applications. The background turbulence generally affects the mixing characteristics of the buoyant jet, and the extent of the influence depends on the characteristics of both the jet discharge and ambient. Previous studies focused on the experimental investigation of the problem (for pure jets or plumes), but the findings were difficult to generalize because suitable scales for normalization of results were not known. A model to predict the buoyant jet mixing in the presence of background turbulence, which is essential in many applications, is also hitherto not available even for a background of homogeneous and isotropic turbulence (HIT). We carried out experimental and theoretical investigations of a buoyant jet discharging into background HIT. Buoyant jets were designed to be in the range of $1<z/l_{M}<5$, where $l_{M}=M_{o}^{3/4}/F_{o}^{1/2}$ is the momentum length scale, with $z/l_{M}<\sim 1$ and $z/l_{M}>\sim 6$ representing the asymptotic cases of pure jets and plumes, respectively. The background turbulence was generated using a random synthetic jet array, which produced a region of approximately isotropic and homogeneous field of turbulence to be used in the experiments. The velocity scale of the jet was initially much higher, and the length scale smaller, than that of the background turbulence, which is typical in most applications. Comprehensive measurements of the buoyant jet mixing characteristics were performed up to the distance where jet breakup occurred. Based on the experimental findings, a critical length scale $l_{c}$ was identified to be an appropriate normalizing scale. The momentum flux of the buoyant jet in background HIT was found to be conserved only if the second-order turbulence statistics of the jet were accounted for. A general integral jet model including the background HIT was then proposed based on the conservation of mass (using the entrainment assumption), total momentum and buoyancy fluxes, and the decay function of the jet mean momentum downstream. Predictions of jet mixing characteristics from the new model were compared with experimental observation, and found to be generally in agreement with each other.

Collapse of particle-laden buoyant plumes

Particle loading affects the dynamics of buoyant plumes, since the difference between particle and fluid densities is much greater than that in the fluid alone. In stratified environments, plume rise is density limited; after initial overshoot, the plume reaches a terminal level and spreads radially. Particles dropping from this horizontal intrusion may be re-entrained. This recycling of dense matter reduces plume buoyancy and intrusion height and, for sufficient load, can lead to plume collapse. Entrainment-based formulae yield a steady-state plume rise. We identify a new conserved quantity for such plumes. Integrating paths of particles dropping from the intrusion yields the fraction re-entrained. A simple mathematical model predicts from buoyancy ratio at source ($P=$ negative particle buoyancy divided by positive fluid buoyancy) whether a particle-laden plume will collapse. Under this model, for small settling velocity, a particle-laden plume will not collapse if $P<0.368$. Above this, collapse depends also on the amount of particle-free ambient fluid entrained in the overshoot region. For pure plumes, experimental evidence suggests that this is small. For forced plumes, more substantial overshoot and entrainment is shown to increase the critical ratio. An extension, based on successive recycling, estimates time to collapse. To investigate further we develop a simple computational model, coupling a ‘top-hat’ plume model, an analytical formula for radially decaying concentrations in the intrusion and an axisymmetric finite-volume solution for time-dependent settling and entrainment. The model can predict the impact of particle load on final rise, as well as the occurrence and time scales of plume collapse.

On the effects of buoyancy on higher order moments in lazy plumes

ABSTRACTJets and plumes are shear flows created by momentum and buoyant sources. They can be classified as either pure jets, forced plumes, pure plumes, or lazy plumes. Lazy plumes are characterised as having a high source buoyancy flux relative to the momentum flux. We use direct numerical simulations to simulate lazy plumes to ascertain the effects of increasing plume ‘laziness’ on the higher order moments, such as Reynolds stresses, third order moments and turbulent kinetic energy budgets. The mildly lazy plumes behaved like most plumes in terms of higher order statistics: a self-similar collapse some distance downstream and peak values comparable to previous experiments and simulations. The highly lazy plumes did not show a self-similar collapse and, in most cases, had higher peak values in all moments. The highly lazy plumes had higher levels of turbulence intensities due to the high buoyancy flux, leading to significant buoyancy-induced turbulence production downstream.

Ship-borne aerosol profiling with lidar over the Atlantic Ocean: from pure marine conditions to complex dust–smoke mixtures

Abstract. The multi-wavelength Raman lidar PollyXT has been regularly operated aboard the research vessel Polarstern on expeditions across the Atlantic Ocean from north to south and vice versa. The lidar measurements of the RV Polarstern cruises PS95 from Bremerhaven, Germany, to Cape Town, Republic of South Africa (November 2015), and PS98 from Punta Arenas, Chile, to Bremerhaven, Germany (April/May 2016), are presented and analysed in detail. The latest set-up of PollyXT allows improved coverage of the marine boundary layer (MBL) due to an additional near-range receiver. Three case studies provide an overview of the aerosol detected over the Atlantic Ocean. In the first case, marine conditions were observed near South Africa on the autumn cruise PS95. Values of optical properties (depolarisation ratios close to zero, lidar ratios of 23 sr at 355 and 532 nm) within the MBL indicate pure marine aerosol. A layer of dried marine aerosol, indicated by an increase of the particle depolarisation ratio to about 10 % at 355 nm (9 % at 532 nm) and thus confirming the non-sphericity of these particles, could be detected on top of the MBL. On the same cruise, an almost pure Saharan dust plume was observed near the Canary Islands, presented in the second case. The third case deals with several layers of Saharan dust partly mixed with biomass-burning smoke measured on PS98 near the Cabo Verde islands. While the MBL was partly mixed with dust in the pure Saharan dust case, an almost marine MBL was observed in the third case. A statistical analysis showed latitudinal differences in the optical properties within the MBL, caused by the down-mixing of dust in the tropics and anthropogenic influences in the northern latitudes, whereas the optical properties of the MBL in the Southern Hemisphere correlate with typical marine values. The particle depolarisation ratio of dried marine layers ranged between 4 and 9 % at 532 nm. Night measurements from PS95 and PS98 were used to illustrate the potential of aerosol classification using lidar ratio, particle depolarisation ratio at 355 and 532 nm, and Ångström exponent. Lidar ratio and particle depolarisation ratio have been found to be the main indicator for particle type, whereas the Ångström exponent is rather variable.