Laminar Plume Research Articles

A note on mixed convection of laminar plane water plumes at temperatures around the density extremum

In all studies concerning mixed convection in plane laminar plumes a linear relationship between fluid density and temperature has been used. However, it is known that the water density-temperature rela- tionship is non-linear at low temperatures with a density maximum at 3.98 ◦ C for pure water. In this note the problem of plane laminar water plume in a coflowing vertical free stream has been investigated taking into account the non-linearity between density and temperature. This is the first work in the literature which treats plane mixed convection plumes with nonlinear relation between density and temperature. Both rising and descending plumes have been investigated. It was found that the ambient water temperature plays an important role on the results. When the ambient temperature is greater than maximum density temperature (Ta > Tm), the water plume behavior is similar to that of the classical plume with linear density-temperature relationship. However, when the ambient temperature is equal or lower than the maximum density temperature the water plume behavior is completely different from the classical plume with linear density-temperature relationship. The centerline velocity shows a series of maxima and minima which are produced by the combination of the nonlinear density-temperature relation and the free stream.

Formulations and Direct Numerical Simulation Methods for Effects of Coriolis Force, Latitude, and Stably Stratified Ambient on a Large-Scale Thermal Plume

A thermal plume with (1) the Coriolis force depending on the latitude of the earth, (2) turbulence, (3) varying density and properties, (4) hydrostatic pressure of air column weight placed above a heated square, and (5) stably stratified ambient is first elucidated. The earth model is employed as an analytical model, time-dependent three-dimensional governing equations are formulated, and a direct numerical simulation (DNS) methodology is obtained. Then, the plume without the Coriolis force is computed, the grid dependence is discussed, and the computed results are compared with previous results. As a result, the formulations, numerical methods, and computed results are validated. At the North Pole, a laminar plume with the Coriolis force rises spirally with the earth's rotation in an anticlockwise direction. However, the turbulent plume with the Coriolis has a thin column rotating very quickly and spirally in the clockwise direction. The rotations and heights of laminar and turbulent plumes are suppressed by a stably stratified ambient and/or a decrease of latitude. With increasing Rayleigh number, the rotation direction in the plume is varied to clockwise in the turbulent state from anticlockwise in the laminar state. Whether the thermal flow is turbulent or not is determined by the slopes of power spectrum density (PSD) of time-series data of computed temperature, and a sufficient number of grids and time steps exist in the Kolmogorov microscale.

A206 背景パターンシュリーレン法を用いた浮力プルームの三次元温度計測

The three-dimensional temperature measurement was carried out using the background oriented schlieren method in combination with the tomographic image reconstruction technique. This technique allows a non-invasive optical measurement without any tracers, and is applied for the temperature measurement in a laminar buoyant plume in still water surroundings. The measured temperature distribution shows a top hat profile, which is in rough agreement with the thermocouple measurement.

The effect of radiation on the laminar natural convection induced by a line heat source

PurposeTo show the effect of radiation from the heat source and the variation of fluid properties on the laminar natural convection induced by a line heat source.Design/methodology/approachThe governing equations – Navier‐Stokes and energy equation are discretized in a staggered grid by a control volume approach, and they are solved using a segregated technique. The equations for the fluid and solid (line heat source) phases are solved simultaneously. The three sides of the computational domain are open boundary. Some of the physical and thermo‐physical properties of the fluid (air) such as density, thermal conductivity and viscosity were considered to vary with temperature.FindingsThe present predictions are compared with those using the Boussinesq approximation, with the results for the boundary layer equations, and with the experimental results. The present predictions reveal considerable departure from the Boussinesq‐based solution and from the boundary layer results. This study also shows the radiation exchange between the heat source and surrounding has major effect in the results. Thus, the departure between the experimental and analytical results can be explained by the effect of radiation exchange.Research limitations/implicationsIn this work, just studied steady‐state laminar thermal plume with the effects of radiation from heat source and the variation of air properties with temperature while it is propose to extend this work to transient and/or turbulent flow.Originality/valueThe effect of radiation from a line heat source on the flow filed around the source and offers enhancement of design to thermal engineers.

Experimental determination of preferred instability modes in a mechanically excited thermal plume by ultrasound scattering

Ultrasound scattering is used to characterize instability modes in a laminar axisymmetric thermal plume subjected to controlled axisymmetric (“varicose”) disturbances. A scattered signal is detected as soon as vortical structures appear in the flow, whereas temperature inhomogeneities have almost no effects on scattering. In the absence of any disturbances, the flow remains laminar and quite stable, which was corroborated with Schlieren visualizations. Scattering peaks exhibited maxima around forcing frequencies of f = 2 Hz. By increasing the mechanical forcing frequency, the amplitude of the scattering peak decreases and disappears for higher forcing frequencies, revealing a relaminarization process. For frequencies around f = 1 Hz and lower, no scattering is observed, like without forcing. The study of the normalized amplitude of the scattering peak at different structure sizes enables the identification of two ranges of preferred wavelengths of instability modes: the first ranges from l = 80 mm to l = 54 mm and the second from l = 20 mm to l = 16 mm. These preferential space modes can be attributed to natural frequencies of the flow. The levels of vorticity of the preferential modes depend on the frequency of the mechanical disturbance, being maximum around f = 2 Hz. The position of the maximum of vorticity moves to higher values of frequency as the temperature is increased. When the mechanical forcing frequency increases away from the resonance frequency, vorticity decays gradually reaching very low values. High frequency disturbances do not destabilize the thermal plume, which acts as a filter.

Penetration of mantle plumes through depleted lithosphere

Laboratory experiments and numerical calculations are used to study how a laminar thermal plume deforms and penetrates a buoyant and viscous layer, which serves as an analog for continental lithosphere. The viscosity contrast between the two liquids and the buoyancy ratio B (the ratio between the intrinsic chemical density contrast and the thermal density contrast due to temperature differences) are varied by 3 orders of magnitude and 1 order of magnitude, respectively. The manner of plume‐lithosphere interaction is not sensitive to the viscosity contrast, which sets the timescale for displacement of the interface, and depends mostly on the B value, which sets the magnitude and shape of interface deformation. Heating of the upper layer by plume material plays an important role. For B > 0.6, plume material spreads beneath the interface and applies a buoyancy force which deforms the interface. For B < 0.6, true plume penetration into the upper layer occurs with a significant vertical velocity component. With time, the upper layer may become unstable and develop an active upwelling which entrains material from the lower layer. Approximate scaling laws allow prediction of interface displacement as a function of time for the whole parameter range studied. Applied to the continental lithosphere, these results show that true plume penetration through Archean lithosphere requires thermal anomalies larger than 300 K corresponding to buoyancy fluxes in excess of those determined today for the Hawaiian plume. Mantle plumes have different effects on lithospheres of different ages and composition, which precludes diagnosis of a single “typical” plume signature.

Observation of preferred instability modes in a mechanically excited thermal plume using Schlieren visualizations

An experimental study of the instability modes of a laminar axisymmetric thermal plume under symmetrical controlled disturbances of varicose type was carried out. The Schlieren technique was used to investigate the considered flow. The range of excitation frequencies over which the studied plume became unstable was determined. The size of the corresponding induced large-scale structures was analyzed in function of the disturbance frequency. The results obtained throughout this work confirmed the ability of a plume to behave like a frequencies filter.

Check of OH rotational temperature using an interferometric method

This paper presents an interferometric method used to check the rotational temperature of the OH free radical obtained using emission spectroscopy. The temperature is extracted from an interferogram via the phase shifting introduced by the refractive index of the studied medium. The refractive index is related to the temperature through the Gladstone–Dale equation and the ideal gas law.The method is tested on the laminar premixed flame of an oxy-acetylene burner and on the laminar plume of a dc argon plasma torch. The results obtained are compared with those obtained from the UV OH band at 306.357 nm (transition A2Σ, ν = 0 → X2Π, ν′ = 0) by emission spectroscopy using the Boltzmann plot method and using a method based on numerical simulated spectra with the amplitude ratios of groups of unresolved rotational lines.

From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection

We report an experimental study on the onset of the large-scale coherent mean flow in Rayleigh–Benard turbulent convection. Shadowgraph and particle image velocimetry techniques are used to visualize the motion of thermal plumes and measure the velocity of the plumes and of the ‘background’ flow field, as the fluid motion evolves from quiescent to steady state. The experiment reveals the dynamical origin of the initial horizontal motion required by the large-scale flow: the fluid entrainment caused by the plume's vertical motion generates vortices surrounding the plume itself. These vortices in turn generate the initial horizontal motion of the flow field. Two types of interactions have been identified: (i) direct plume–vortex interaction; and (ii) plume–plume interaction via vortices. These interactions and the interaction and merging of the vortices from neighbouring plumes lead to groupings and/or merging of plumes, which in turn generate vortices of even larger scale. As a result of these interactions, the convective flow evolves into a coherent rotatory motion consisting of mainly the plumes themselves and spanning the whole convection box. This study clearly demonstrates that it is the thermal plumes that initiate the horizontal large-scale flow across the top and bottom conducting plates.

Mixed convection in a laminar axisymmetric water plume in a vertical coflowing stream at temperatures around the density extremum

In all studies concerning mixed convection in round laminar plumes a linear relationship between fluid density and temperature has been used. However, it is known that the density-temperature relationship for water is nonlinear at low temperatures. In this study the problem of a round laminar water plume in a coflowing vertical free stream has been investigated in the temperature range between 20 °C and 0 °C taking into account the nonlinearity between density and temperature. The results are obtained with the numerical solution of the boundary-layer equations. The paper deals mainly with assisting mixed convection and with some special cases of opposing and assisting mixed convection at the same plume flow. For the assisting mixed convection it was found that the plume behavior depends on the temperature difference between the plume orifice and the ambient water due to the nonlinear relationship between water density and temperature. This dependence weakens and finally diminishes as the buoyancy parameter ξ increases and the mixed convection becomes pure forced convection.

Laminar axisymmetric pure and saline water plumes

In most studies concerning round laminar plumes in a uniform environment a linear relationship between fluid density and temperature has been used. However it is known that the density-temperature relationship for water is non-linear at low temperatures. In this study the problem of round laminar plume of pure and saline water has been investigated in the temperature range between 20 °C and 0 °C taking into account the nonlinearity between density and temperature. The results are obtained with the numerical solution of the boundary layer equations. It was found that the plume behavior is dependent on ambient temperature and the centerline axial velocity at maximum density temperature is approximately 10% lower than the corresponding value based on linear relation between density and temperature.

Dynamics of electrohydrodynamic laminar plumes: Scaling analysis and integral model

In this paper electrohydrodynamic plumes are examined in the region far from the injecting electrode and the collector plate, for both two-dimensional and axisymmetric geometries. The relative importance of the conduction mechanisms (convection, drift and diffusion of electric charge) is analyzed. Diffusion turns out to be negligible compared to convection and drift for the experimental conditions. But the transverse drift (Coulomb repulsion) is of the same order of magnitude than convection. We find a set of three differential equations giving the evolution of the velocity at the center of the plume and the widths of the plume and the charged core inside.

Direct and large-eddy simulation of the transition of two- and three-dimensional plane plumes in a confined enclosure

We investigate here, the free convection flow induced by a line heat source in a confined geometry. The buoyancy forcing of this flow can be characterized by a Rayleigh number, Ra, which is chosen in the range where an intermittent spatial transition from laminar to turbulent flow takes place. The objective of the study is to explore this flow with help of numerical simulations. We restrict ourselves to the case of an air flow with Ra=1010. For the numerical simulation techniques, we employ Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). With help of DNS we consider first, a 2D representation of this flow at a resolution of 1952 which is found to be sufficient to represent the heat source and its resulting flow. Next, we consider the 3D case at a resolution of 1953. The 3D simulation reveals a symmetrical time mean recirculation which covers the domain above the heat source. This large scale circulation is driven by the small scale laminar plume generated by the heat source and which breaks down into turbulence. The flow is found to be essentially 3D, especially near the top wall. No clear turbulent inertial range is present. A LES for the same flow has been carried out at a resolution of 453. The comparison of the les results with the DNS data has been used to investigate the performance of several sub-grid models. It turns out that simple equilibrium sub-grid models perform fairly well in estimating the statistics of the flow.

Experimental analysis of a confined transitional plume with respect to subgrid-scale modelling

Free convection flow of water induced by a small prismatic heat source in a confined space is studied in the present paper. The forcing of the flow is in the range of Rayleigh numbers where a spatial transition from laminar to turbulent flow can be observed.Velocity measurements were performed by means of Particle Tracking Velocimetry (PTV ) . From the velocity data a resolved and a subgrid field is obtained by means of spatial filtering. These data are analysed with respect to modelling consequences in Large-Eddy Simulation (LES) , constituting an a priori test.Astatistically steady flow has been obtained with a converged temporal mean and standard deviation as function of space. A low correlation of time mean model stresses with exact stresses is found. In the transitional region the inter-scale kinetic energy transfer, taken over a wavenumber corresponding to the laminar plume width, is found to possess a relative large standard deviation. In this region backscatter and forward scatter of kinetic energy, with respect to the mentioned wavenumber, are of equal importance. Application of a dynamic model to the filtered data yields a qualitative good representation of the exact inter-scale kinetic energy transfer.

A model for near-wall dynamics in turbulent Rayleigh–Bénard convection

Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh–Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh–Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

Electrohydrodynamic plumes in point-plane geometry

We examine the flow organization induced by charge injection from a needle of small radius of curvature into an insulating dielectric liquid. Experimental results are presented for the electrical current as a function of the point-plane distance and of the applied voltage. Schlieren visualization reveals the existence of very thin plumes which are slightly vacillating. An approximate analysis of the laminar plume is developed which takes into account the finite but very thin axial region where charge is confined. A classical type of asymptotic treatment results in a set of ordinary differential equations, provided the current and the field distribution are known. A new expression for the order of magnitude of the liquid velocity is proposed which leads to estimates of the radius a of the charge core and the typical radial scale /spl delta/ of the velocity profile. For a gap spacing d, these estimates are of the order of 10/sup -3/ d and 10/sup -2/ d which confirm the thinness of such charge plumes.

Observations on transition in plane bubble plumes

Flow visualization studies of plane laminar bubble plumes have been conducted to yield quantitative data on transition height, wavelength and wave velocity of the most unstable disturbance leading to transition. These are believed to be the first results of this kind. Most earlier studies are restricted to turbulent bubble plumes. In the present study, the bubble plumes were generated by electrolysis of water and hence very fine control over bubble size distribution and gas flow rate was possible to enable studies with laminar bubble plumes. Present observations show that (a) the dominant mode of instability in plane bubble plumes is the sinuous mode, (b) transition height and wavelength are related linearly with the proportionality constant being about 4, (c) wave velocity is about 40% of the mean plume velocity, and (d) normalized transition height data correlate very well with a source Grashof number. Some agreement and some differences in transition characteristics of bubble plumes have been observed compared to those for similar single-phase flows.

An experimental study of laminar plumes

We present an experimental study of the scaling laws for the front (or cap) of an isolated, laminar starting plume. The scaling relations are formulated and measured experimentally over a range of power, fluids, and heaters. The results are that the cap rises at constant velocity, grows diffusively in width, and its temperature depends inversely on height. This extends analytic results by Batchelor (1954) for the column (stem) below the front. The source size determines initial conditions for the cap, but does not affect it in the far field. The shape of the front is fitted by a model of potential flow. The interaction between plume caps is complex, but with simple underlying dynamics. We conjecture that some of our conclusions can be applied to a distribution of plumes, as in soft turbulent convection.

Comprehensive correlations for laminar mixed convection line plume and wall plume

Comprehensive correlations for laminar mixed convection line plume and wall plume

Use of vector Bragg wave-number scattering condition in bistatic scattering experiments

Applying the Born approximation to a buoyant plume yields the Bragg scattering condition that determines along with knowledge of the scattering potential, the scattered wave at any given scattering angle. The Bragg scattering condition allows for information obtained from the same Bragg direction albeit different scattering angles to be pieced together to form an entire Bragg wave-number spectrum of the scatterer. Data are taken in a multiple bistatic configuration whose geometry is predetermined via knowledge of the bandwidth of the transducers and the desired overlap of the resulting Bragg phase space. Results are given for a buoyant axisymmetric laminar plume. As an aside of the Bragg scattering condition an empirical formula derived from the far-field expressions for the Green’s function solution to the Hemholtz equation given the scattering dimensionality of the plume, which is acoustically measured and shown to give expected results.