Vertical Plume Research Articles

Numerical Simulation of Vertical Forced Plume in a Crossflow of Stably Stratified Fluid

In this study, an investigation using a three-dimensional numerical model, which treats conservation of mass, momentum, and salinity simultaneously, was carried out to study the character of a vertical forced plume in a uniform cross-stream of stably linear stratified environment. A k-ε turbulence model was used to simulate the turbulent phenomena and close the solving problem. The performance of the three-dimensional model is evaluated by comparison of the numerical results with some available experimental measurements. Results indicate that the numerical computation simulates satisfactorily the plume behavior in a stratified crossflow. The secondary vortex pairs in the cross section induced by the primary one change as the plume flows downstream. This denotes the transformation of entrainment mechanism in stratified crossflow.

Effect of Ambient Stratification on Buoyant Jets in Cross-Flow

A numerical technique for integrating the fully elliptic Reynolds-averaged Navier-Stokes and diffusion equations has been used to investigate the effect of ambient density stratification on the flow characteristics of a vertical force plume in a cross-flow of a stably linear stratified environment. A two-equation \ik-ϵ turbulence model is employed to simulate the turbulent transport quantities and to close the solving problem. Some basic flow features and a structure for the interaction of the buoyant jets with a density-stratified cross-flow are obtained. The results show that the ambient stratification tends to inhibit the flow development of the buoyant source and to encourage the formation of secondary and third vortex pairs in the jet cross section as a plume flowing downstream. It then results in causing the jet-flow oscillation from its maximum height-of-rise.

Estimate of diffusion parameters of aircraft exhaust plumes near the tropopause from nitric oxide and turbulence measurements

Horizontal and vertical plume scales and respective diffusivities for dispersion of exhaust plumes from airliners at cruising altitudes are determined from nitric oxide (NO) and turbulence data measured with the DLR Falcon research aircraft flying through the plumes. Ten plumes of known source aircraft were encountered about 5 to 100 min after emission at about 9.4 to 11.3 km altitude near the tropopause in the North Atlantic flight corridor at 8°W on three days in October 1993. The ambient atmosphere was stably stratified with bulk Richardson numbers greater than 10. The measured NO peaks had half widths of 500 to 2000 m with maximum concentrations up to 2.4 parts per billion by volume (ppbv), clearly exceeding the background values between 0.13 and 0.5 ppbv. For analysis the measured plumes are approximated by an analytical Gaussian plume model which accounts for anisotropic diffusion in the stably stratified atmosphere and for shear. Two methods are given to obtain diffusivity parameters from either the individual plume data or the set of all plume measurements. Using estimates of the emitted mass of NO per unit length, the vertical plume width is found to be 140 m on average. This width is related to mixing in the initial trailing vortex pair of the aircraft. The range of the plume data suggests vertical diffusivity values between 0 and 0.6 m2 s−1. The turbulence data exhibit strong anisotropic air motions with practically zero turbulent dissipation and weak vertical velocity fluctuations. This implies very small vertical diffusivities. The horizontal diffusivity is estimated as between 5 and 20 m2 s−1 from the increase of horizontal plume scales with time. For constant diffusivities, shear dominates the lateral dispersion after a time of about 1 hour even for the cases with only a weak mean shear of 0.002 s−1.

95/02046 Numerical study of the influence of the ambient pressure field on free plane turbulent vertical jets and plumes

95/02046 Numerical study of the influence of the ambient pressure field on free plane turbulent vertical jets and plumes

NUMERICAL STUDY OF THE INFLUENCE OF THE AMBIENT PRESSURE FIELD ON FREE PLANE TURBULENT VERTICAL JETS AND PLUMES

Abstract To help resolve the inconsistencies observed when examining measured properties of free plane jets and plumes, a numerical study was performed to determine the influence of a weak ambient motion and of the associated pressure field on the flows of free plane vertical turbulent jets and plumes. A nested grid control volume technique with the buoyancy-extended k-e model plane was used to model turbulent jets and plumes issuing into open spaces as veil as into two-dimensional rooms of various sizes. The results indicate that slight variations in the ambient pressure distribution affect jet and plume development and similarity relationships.

Large-scale measurements of the physical characteristics of round vertical bubble plumes in liquids

The hydrodynamics of air/water plumes in a large-scale model of a metallurgical ladle were investigated. The dimensions of the cylindrical vessel were 1600-mm ID and 2250-mm total height. The air was injected through a centered nozzle. Axial and radial profiles of gas concentration, bubble frequency, and liquid and gas velocities were measured using electrical resistivity probes and a propeller flowmeter. It was found that the bubble plume is not at a fixed position but wanders away from the vertical vessel axis. This causes difficulties in the measurements, and special methods have to be designed to define and deduce reproducible values for the characteristic plume quantities. In the analysis of the data, the various physical characteristics were related toz 0, the distance from the nozzle where the axial gas concentration is 50 Pct. The maximum values of the radial profiles are presented in nondimensional correlations.

Acoustical scattering from plumes of sediment suspended in open waters

Acoustical data from a field survey at a disposal site for dredged materials near Mobile Bay, Alabama, are analyzed. During the survey, two independent acoustical instruments provided measurements of echo strength from vertical plumes of suspended sediments. Particulate concentrations and grain size distributions were determined from insitu water samples. Quantitative analysis of the measurements indicates that the acoustical echoes from the suspended sediments are dominated by Rayleigh backscattering. The best fit to data is achieved when the measured decrease of grain size with decreasing concentration is explicitly accounted for. Attenuation appears to play a significant role at high concentrations (i.e., within the dense part of the plume). For the grain sizes studies here (1–200 m), viscous effects account for at least 90% of the attenuation. When the theoretical estimates are subtracted from the data, the residual echo strength is seen to increase with decreasing concentration; some possible causes of this are beam-to-beam variability, effects of grain shape, and factors related to experimental design. One of the instruments measured echo strength on four beams simultaneously; the average beam-to-beam variability was about 3 dB, corresponding to a precision of about 50% in the measured concentration. [Work supported by U.S. Army, Corps of Engineers, Dredging Research Program.]

NUMERICAL COMPUTATION OF CONVECTIVE DISPERSION IN TURBULENT BUOYANT JETS

Numerical predictions of mean and turbulent characteristics of the axisymmetric vertical jet and plume are reported. An algebraic stress and flux model is used to close the time-averaged Navier-Stokes and energy equations. Special attention was given to the numerical model, which is based on a finite-volume discretization of the elliptic form of flow equations. A special procedure is used to treat free boundaries and to compute the flow up to the similarity regime. The model was applied to the prediction of the flow for the momentum-dominated (jet) and buoyancy-dominated (plume) regime. The results show that the essential characteristics of the flows, especially for the plume, are correctly reproduced. However, some discrepancies arise from the comparison of predicted and experimental levels.

Small-scale hydromagnetic flow in the Earth's core: Rise of a vertical buoyant plume

Abstract The steady and transient flow induced by a vertical cylinder of buoyant electrically conducting fluid immersed in an infinite extent of slightly denser fluid in the presence of a horizontal magnetic field is investigated, with the aim of elucidating the small-scale flow within the Earth's core. The evolution from a state of rest may be divided into three regimes. For short times [t O(L 2/v)] lateral viscous diffusion also becomes important and a quasi-steady state is reached...

Dispersion and deposition of smoke plumes generated in massive fires

Massive fires resulting from the uncontrolled burning of crude oil from spills or industrial accidents produce large smoke-laden buoyant plumes which rise in the wind direction before they equilibrate within a stably stratified atmosphere. Beyond this point, the plume material cools by entrainment and the plume becomes negatively buoyant due to the heavy smoke loading. The trajectory of the descending plume, which determines the ground distribution of smoke, is the subject of this paper. A computational model for the simulation of large-scale smoke plumes resulting from such fires is developed and applied to investigate the effects of the plume initial properties on its trajectory and smoke deposition patterns. Attention is focused on the descent and dispersion of wind-driven plumes in a homogeneous atmosphere, and the smoke deposition on flat terrain. Results show that the plume dynamics in the cross-wind direction are dominated by two buoyantly generated, coherent, streamwise vortices which distort the plume cross section into a kidney-shaped structure. The strength of the two vortices and their separation increase as the plume falls. The plume width grows under the action of these vortices at a rate which increases as the plume settles on the ground, leading to a smoke footprint which does not resemble the prediction of Gaussian dispersion models. The effects of the injection altitude and the initial shape of the plume cross section on the transport and dispersion of the negatively buoyant smoke plume are investigated. Plumes falling from higher elevations disperse more in the vertical direction while those falling from lower elevations disperse further in the horizontal cross-wind direction. Plumes with circular cross-sections reach the ground faster and disperse horizontally further than plumes with elliptical cross-sections with the minor axes in the vertical direction. Vertical plume dispersion is weakly dependent on the shape of its initial cross-section.

Tracing fly ash emitted from a coal-fired power plant with enriched rare-earth isotopes: An urban scale test

Artificially enriched isotopes of neodymium (Nd) were released from a 100 MW(e) coal-fired power plant at rates ranging from 40 to 61 mg h −1 in an experiment designed to test a new intentional particulate tracer technique. During each release, ambient samples of airborne particles with diameters < 2.5 μm were collected for 6 h at 13 locations along a 72° arc 20 km from the plant on 47-mm diameter Teflon filters operated at nominal flow rates of 130 l min −1. Samples collected when estimates of the meteorological dispersion parameter, X/ Q, ranged from 0.3 × 10 −10 to 350 × 10 −10 s m −3, were analysed for total Nd mass and excess 148Nd, the tracer isotope, by thermal-ionization mass spectrometry. Measured concentrations were in good agreement with predictions of ambient tracer concentrations made with a Gaussian plume model in which lateral and vertical plume dispersion parameters were derived from the standard deviation of the horizontal wind direction. The observed tracer concentrations correspond to signal-to-noise ratios ( S: N) of 150–450. The concentration of 148Nd measured in particles <0.65 μm in diameter corresponds to an S: N in excess of 4500.

Numerical and Physical Modeling of Air Diffuser Plume

A drift‐flux formulation that accounts for multiple bubble interactions is applied to describe the mean water velocity, air fraction, and plume growth for a vertical air diffuser plume that is bound on one side. A coarse‐bubble line‐diffuser source in a rectangular mixing tank is considered. Physical velocity and plume width measurements are used to calibrate the numerical model. The model is shown to be sensitive to the initial plume width and the entrainment coefficient. A dimensionless equation for the ambient water velocity at the outer edge of the plume is developed from physical measurements. The water velocity and air fraction are assumed to be uniform over the plume width. Four ordinary differential equations are developed and solved simultaneously to obtain the changes in significant plume variables with fluid depth. To reproduce the observed plume characteristics, the entrainment coefficient was 30‐60% higher than the single‐phase jet entrainment coefficient. The effect of the wall friction was minor for depths less than 1 m.

A three‐dimensional field study of solute transport through unsaturated, layered, porous media: 1. Methodology, mass recovery, and mean transport

A field experiment is reported which monitored the three‐dimensional movement of cubic solute plumes through an unsaturated, loamy sand soil. The plumes were created with one of two methods, a two‐dimensional flux application and an initial resident distribution. Soil coring was used to sample resident concentrations for the three solutes studied. The data were analyzed using the method of moments. In addition to the solute transport experiments, a detailed set of physical properties of the field was obtained by excavating three pits to a depth of 5.0 m and also by taking soil cores throughout the study area. This paper explains the experimental methodology, summarizes the relevant site characteristics, and describes the observed transport based on the zeroth and first order spatial moments. Mass balance varied between 78 and 138%. The field‐averaged gravimetric water content and dry bulk density were used to accurately predict the mean vertical plume displacements. The plumes spread relatively little in the horizontal direction.

ALGEBRAIC STRESS MODEL PREDICTION OF A PLANE VERTICAL PLUME

A finite-volume prediction is obtained for a plane vertical plume using nonequilibrium algebraic turbulence models for the Reynolds stress and turbulent heat flux. Vie turbulence models include approximations for convection and diffusion. Unlike previous studies, the full two-dimensional form of the model equations is retained, and the transport equations are solved elliptically. A major conclusion of this work is that the nonequilibrium algebraic stress model (ASM), when solved in an elliptic framework, yields a realistic prediction for a vertical plume. This result resolves the difficulty encountered by previous workers who solved the parabolic equations.

Calculation of turbulent buoyant plumes with a Reynolds stress and heat flux transport closure

A differential Reynolds stress and heat flux closure is adopted for modelling the turbulent transport of heat and momentum in vertical buoyant free plumes. Modelled transport equations are solved for the turbulent stresses and heat fluxes, the turbulence energy dissipation rate, and the mean-square temperature fluctuations. Closure at this level permits the turbulent transport processes to be treated more exactly than with Boussinesq-type two-equation models which are based on the notion of an effective viscosity and diffusivity. The solution of a transport equation for the thermal dissipation rate, which avoids the need to empirically prescribe the ratio of the thermal and mechanical time scales, is also investigated. The model is applied to the calculation of both self-similar plumes and forced plumes. The results are compared with existing experimental data and are found to be in reasonable agreement with the measured behaviour.

Effect of homogeneous and heterogeneous surface roughness on heavier-than-air gas dispersion

The effect of homogenous and heterogenous roughness on entrainment and dispersion rates was assessed by collecting experimental data in a boundary-layer wind tunnel. Point and area sources were simulated at a 1:100 model scale with homogenous surface roughness configurations ranging from flat grass land to an urban area. Heterogenous roughness was simulated in the form of a typical refinery tank farm and typical process unit. Relative gas densities (source gas to ambient air) varied from 1 to 4. Concentrations of a tracer gas were measured and analyzed to determine the horizontal and vertical plume spread rates, rate of air entrainment as well as the variation of maximum ground-level concentration with roughness size. The results of the study demonstrated that large roughness elements can significantly reduce the concentrations and that the entrainment relations presently in use for homogenous roughness configurations do adequately model the process. For heterogenous roughness configurations, the entrainment and dispersion rates appeared to be site specific and not well modeled using existing techniques.

Analysis of Inclined Wall Plume by the k-ε Turbulence Model

The similarity solution of inclined wall plume is obtained analytically. The mathematical model used herein consists of the continuity equation of flow, the momentum balance equation in the flow direction, the diffusion equation of concentration, the equation of kinetic energy of turbulence and the equation of viscous dissipation rate of turbulence. It is shown that this set of equations has the similarity solution which can be solved numerically for each angle of the inclined wall. This numerical model is applied to the wide range of the slope angle, which includes the vertical wall plume as the special case and the nearly horizontal wall plume. The velocity and concentration profiles of the inclined wall plume are explained well by the similarity solutions.

Diffusion Behavior of Vertical Forced Plume in Linear-Stratified Cross Flow

The characteristics of vertical forced plume in a uniform cross flow of stably linear stratified environment are studied both numerically and experimentally. The empirical formulas for the diffusion characteristics of vertical forced plume (trajectory, dilution, etc.) are presented experimentally. The three-dimensional numerical model is used to quantitatively simulate the behavior of the vertical forced plume in these ambient conditions. The performance of the three-dimensional model is evaluated by comparison of numerical results with experimental measurements. By using numerical model, the production and disappearance of vortex pairs are discussed as plume flow downstream.

Low-wavenumber signatures of time-dependent mantle convection

Spectral analysis is applied to idealized two-dimensional numerical models of mantle convection. Examining the spectral signature of known model temperature fields represents the forward problem corresponding to the inverse problem of inferring the unknown temperature field in the mantle from the spectral components of lateral heterogeneity obtained by seismic tomography. Previous two-dimensional Fourier analyses of steady convection cells indicate that, with current levels of resolution, tomographic techniques have a much better chance of detecting horizontal boundary layers than vertical plumes. From an examination of the shape of the spectral envelopes of the power spectrum of lateral heterogeneity at various depths in steady convection cells, it has been suggested that evidence for thermal boundary layers in the mantle may be contained in the published spectral amplitudes of lateral heterogeneity. This possibility is expanded on in the present study. Here we examine the effects, on the spectral signature of lateral heterogeneity, of averaging the model temperature field over vertical intervals of a few hundred kilometers, of large amounts of internal heating, of time-dependent flow and of aspect ratios greater than unity. The vertical averaging is an attempt to mimic the finite vertical resolution of tomographic inversions. The various complications considered here are found to render the distinction between the spectra of lateral heterogeneity, inside and outside of thermal boundary layers, less clear than in the simpler models considered previously. Nevertheless, the boundary layer spectra continue to contain significant information on the dominant scale of the model flow solutions.

Building wake dispersion at an Arctic industrial site: Field tracer observations and plume model evaluations

Ten multi-hour atmospheric dispersion SF 6 tracer experiments were conducted during October and November of 1987 near a large oil gathering facility in the Prudhoe Bay, Alaska, oilfield reservation. The purpose of this study was to investigate dispersion under arctic conditions and in situations where building-generated airflow disturbances dominate downwind distributions of ground level pollutant concentrations. This was accomplished with a network of micrometeorological instruments, portable syringe tracer samplers, continuous tracer analyzers, and infrared visualization of near source plume behavior. Atmospheric stability and wind speed profiles at this arctic site are influenced by the smooth (surface roughness = 0.03 cm), snow covered tundra surface which receives negligible levels of solar isolation in winter. The dispersion of pollutants emitted from sources within the oil gathering facility, however, is dominated by the influence of nearby buildings when high winds generate elevated ground level concentrations. An order of magnitude increase in maximum ground level concentration was observed as wind speeds increased from 5 to 8 m s −1 and another order of magnitude increase was observed as winds increased from 8 to 16 m s −1. Variation in maximum concentrations was also observed with changes in wind direction. Vertical plume diffusion ( σ z ) near the buildings was a factor of 2–3 greater than that observed in open terrain and was dependent on both wind speed and the projected building width and location of nearby buildings. Wind tunnel tracer distributions for east winds agree with field observations but also indicate that a significant increase in plume downwash occurs with other wind directions. Concentration distributions were calculated using several versions of the Industrial Source Complex (ISC) model. Model estimates of ground level concentrations were within a factor of three depending on wind direction. The model predictions are extremely sensitive to the ratio of plume height to vertical plume diffusion which is significantly influenced by a complex aerodynamic wake in the field.