Round Plume Research Articles

Formation of coronae topography and fractures via plume buoyancy and melting

Coronae are volcanic-tectonic features seemingly unique to the surface of Venus. As such they offer potential insights into differences in geodynamic processes on Venus and Earth. Largely due to limitations in processing power and computational complexity, models of corona formation generally ignore the effect of melt and magmatism despite the presence of volcanic features like domes and lava flows. Here we present a new model of corona formation integrating visco-plastic rheology with two-phase flow melt migration. Additionally, we model brittle failure of surface material, viscous flow of partially molten material at depth, and cracking of solid rock from fluid pressure in one model. The model consists of a two-dimensional half space with a round plume body ascending through an asthenosphere and interacting with a Venusian lithosphere and crust. The size and temperature of the plume body, lithosphere thickness, crustal thickness, and regional strain rate are all varied over 20 model runs. Most models show deflection of the plume as it rises due to the increased viscosity of the base of the lithosphere. As the plume spreads and rises against the base of the lithosphere, melting occurs. Melt rises and accumulates in the lithosphere which supports surface topography. Brittle failure occurs at the surface due to the induced stress of the migrating plume body and rising melt. Increased temperatures and sizes of initial plumes result in larger topographies occurring over smaller timescales. Decreased temperatures and sizes of initial plumes result in smaller topographies over larger timescales. Increased lithosphere thickness generates smaller topographies. Thinner crusts result in more viscous lithosphere and more strain accumulation, creating surface depressions seen in approximately half of real corona. Both thicker crusts and increased regional strain result in lower viscosities at the base of the lithosphere, preventing the deflection of the plume body, which instead rises through the lithosphere relatively unimpeded. The varied model parameters generally result in an evolutionary sequence of topographies and fracture patterns which resemble actual corona, without requiring a collapsing dome to create outer rims, as is often invoked for corona formation via upwelling plumes. Corona rim topography is generally created within 105 and 106 year timescales, while multiple rims or central depressions are generally observed over 106 year timescales. Observed topography is actively supported by partially molten regions in the lithosphere, supporting the notion of an active squishy-lid Venus. These partially molten regions are not centrally located and may provide a source for observed lava flows away from corona centers.

Experimental investigation and integral simulation of a thermal annular plume

Thermal plumes issued with mean exit velocities of 0.527 and 0.702 m/s from internally closed annular nozzles are investigated experimentally, theoretically, and numerically. The experimental setup and the measurement and analysis methodologies for flow and mixing are described in detail. The experimental setup consists of an air heating box with an annular slot of 0.12-m mean diameter and 0.01-m width, accompanied by equipment for setup operation and measurement of mean velocities and temperatures. The trajectory of maximum velocities and the isovelocity contours indicate reattachment due to plume self-merging at z_{textrm{P0}}= 0.161 m and around 0.20 m in correspondence to exit velocities. It was found that z_{textrm{P0}} depends mainly upon initial Froude number and annulus equivalent diameter. Experiments detected a vortex ring right after the exit followed by a stagnation point at z_{textrm{P1}}cong 0.055 m on the plume centreline. The annular plume core obtains almost uniform temperature and on average 15 times higher dilutions than bulk dilutions of the equivalnt round plume. To predict the self-merging trajectory, a novel integral model was developed named self-merging approach (SMA). SMA is based on the solution of the ordinary differential equations of momentum and buoyancy applied to an infinitesimal sector of the annular plume, which is equivalent to two identical slot plumes. These plumes are reattached due to outer entrainment, inner entrainment starvation, and a series of sinks along the annular plume centreline with strengths calculated by an original relationship. SMA predictions agree very well with the observations. The present findings contribute to a better understanding of the phenomenon and offer new ideas for designing buoyancy-operating disposal systems with low momentum, using annular- or rosette-type diffusers mainly in shallow water bodies.

The transition of a line plume to round plume

The transition of a line plume to round plume

Evolution: why all plumes and jets evolve to round cross sections.

Turbulent curtains of smoke rise initially as flat plumes and, above a certain height, they become round plumes. The same evolution of cross-sectional shape is exhibited by jets issuing from flat nozzles. Here we predict based on principle that all such flows should evolve their cross-sectional shapes from flat to round (and not the other way) at a critical distance downstream, which is predictable. The principle is that the prevailing flow architecture provides greater access to the flow of momentum from the moving core (plume, jet) to the still surroundings. For turbulent plumes and jets, the transition distance scales with the long dimensions (L) of the two-dimensional (flat) heat sources and nozzles that drive them. For laminar jets, the transition distance scales with L Re, where Re is the Reynolds number based on nozzle velocity and the smaller dimension of the nozzle cross section. These predictions are confirmed by full numerical experiments of the three-dimensional flow fields of turbulent and laminar jets covering the Re range 10–104.

Analytical exact solutions for unsteady collisionless plume flows in a vacuum

This paper presents a set of gaskinetic solutions to the problem of unsteady collisionless round plume development: startup and development to a steady flow; steady flow; and shutting down from a steady flow. This can find applications in studying similar transient plume flows from space propulsion devices. Different from many past studies, here we consider the general situation that the average exit gas speed can be larger than zero, and detailed geometry of the nozzle exit radius is included. A fundamental space–velocity–time relation is adopted in this study and it plays a crucial role to obtain the complete flowfield properties of density, velocity, pressure and temperature. This study reveals that there are some internal complementary relations on density and momentum among these three processes. The results involve complex integrations involving factors of time, geometry, and specific speed ratio. Several numerical simulations with the direct simulation Monte Carlo method validate these analytical exact results.

Inviscid and viscous models of axisymmetric fluid jets or plumes

The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free- boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume. doi:10.1017/S1446181112000156

INVISCID AND VISCOUS MODELS OF AXISYMMETRIC FLUID JETS OR PLUMES

AbstractThe vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free-boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume.

Quantification of turbulence properties in bubble plumes using vortex identification methods

Turbulence characteristics within bubble plumes are quantified in the laboratory using particle image velocimetry (PIV) data and postprocessing techniques to identify continuous phase vortices and their properties. Experiments are conducted using a single, high-speed Phantom camera (frame rate 250 Hz); images are preprocessed to eliminate signatures from the bubbles, resulting in high temporal and spatial resolution PIV data for the continuous phase only. The local swirl strength is used to identify vortices in the flow field. By combining the velocity fields and identified vortex maps, the vortex size probability distribution and the relationship of the vortex size, circulation and enstrophy with respect to the position in the plume are quantified. Results demonstrate that these quantities are self-similar when nondimensionalized by the plume radius and center line velocity. A direct relationship is also identified between vortex size and the corresponding average circulation and enstrophy. Modulation of the turbulent energy spectrum compared to a single-phase plume is noted and is attributed to the presence of the bubbles in the flow. Vortex size and energy density are greatest in the shear layers at the edge of the round plume, indicating that shear instability, and not bubble wakes, is the dominant process of large-scale turbulent and coherent structure generation in bubble plumes.

Review of Turbulent Jets and Plumes—A Lagrangian Approach by Joseph H. W. Lee and Vincent H. ChuTurbulent Jets and Plumes—A Lagrangian ApproachKluwer Academic Publishers$135

The authors attempt “to give a consistent and unified development of a Lagrangian approach for the prediction of free jets and plumes, including effects of crossflow and ambient density stratification. The authors believe that the integral approach plays a pivotal role in explaining important and practically useful concepts to the engineer and that the subject can best be understood by observation of simple experiments,” and this reviewer shares this view. A practical Lagrangian modeling tool in the form of an interactive virtual reality software VISJET is offered to the readers to solve their problems. The text includes many worked examples and provides problems for the reader to solve. This book is intended for senior undergraduates and first-year graduate students in water and environmental engineering programs. It can also serve as an introduction to environmental fluid mechanics for students in mechanical and chemical engineering as well as earth and environmental sciences. The first chapter provides a general introduction to turbulent jets and plumes, with some pictures of jets and plumes in the environment. Chapter 2 presents a detailed treatment of plane and circular turbulent jets. It develops the integral equations from the Reynolds equations and the continuity equation and shows good correlation of the different scales along with some details of turbulence properties from experiments. On page 28, p / y is wrongly given the order of zero, and it would be logical to add a minus sign on the left-hand side of Eq. 2-30. Chapter 3 deals with turbulent plumes and buoyant jets. It considers in detail the round plume, the relevant equations of motion, as well as integral equations and extends this treatment to plumes with initial momentum buoyant jets . This chapter also introduces a discussion of the

Fire dynamics simulations of buoyant diffusion flames stabilized on a slot burner

In recent years fire dynamics simulator (FDS) [1,2], a CFD model for buoyancy-driven flames developed at the National Institute of Standards and Technology (NIST), has been used in simulations of numerous fire scenarios and buoyancy-driven flows. FDS is based on a set of equations describing the behavior of thermally driven buoyant flows proposed by Rehm and Baum [3]. Validation of the various submodels in FDS has been performed using small-scale round plumes [4], small and large round pool fires [4–7], rectangular pool fires [8,9], and vertical wall fires [8]. Based on the confidence gained in these validation studies and also by a rapidly growing practical applications base, FDS has been applied to practical considerations of room airflows [10], fire and smoke behavior in large building fires including the World Trade Center fires [11], compartment fires [12,13], oil pool fire in a containment test facility [14], and tunnel fires [15]. To the best of our knowledge, FDS has not been used to simulate linear buoyant fire sources like line fires and slot burner flames. Fires above twodimensional fuel sources are important in some practical fires scenarios such as forest fires and wall fires. For round plumes and flames, 3D simulations were found to be necessary for capturing the mixing behavior, which was grossly underpredicted by the 2D simulations [4]. Given the two-dimensional source geometry, whether two-dimensional mixing considerations are adequate is an interesting question.

Similarity solutions of round jets and plumes

The k-e turbulence model, considering the effect of buoyancy on turbulent kinetic energy and its dissipation rate, is adopted to present a mathematical model for round plumes and jets. There are similarity solutions in the uniform environment. Taking into account the conservation of momentum and heat flux. Finite Analytic Method is applied to obtain the similarity functions of velocity, temperature and turbulent kinetic energy. The agreement between the calculated and experimental data is good.

Turbulence spectra in free convection flow

The results of a laboratory experiment to study the spectral density of temperature fluctuations in a fully developed round plume are presented. It is found that there is a range of low wave numbers K (the next to inertial subrange) where the spectra of temperature are proportional to K−3. The modification of turbulent spectrum at small wave numbers due to buoyancy forces in free convection flow is discussed.

The geometric similarity of the laminar sections of boundary layer-type flows

Experimental observations of the shape of the laminar and transition sections of a confined coaxial jet show that the laminar length (L) is always approximately ten times greater than the wavelength of the first sinusoidal deformation of the flow (λ). This discovery coincides with the L∼ 10 λ proportionality noted in an earlier study of the laminar sections of air plumes rising above concentrated heat sources. A search of the literature shows that the L∼ 10 λ proportionality characterizes other boundary layer-type flows, for example the flow over a flat plate and the plane mixing layer. Using the confined jet and the round plume as examples, it is shown also that the L∼ 10 λ proportionality can be derived theoretically.

Temperature measurements in a turbulent round plume

The basic objective of this paper is to present and analyze some experimental information regarding the structure of the mean and fluctuating temperature field in a turbulent, vertical round water plume issuing into non-stratified, non-moving ambient water. The focus of this study is the transition of plume-like flows to fully developed self-preserved plumes. One interesting result of this paper is that self preservation of the turbulent field is accomplished at approximately twice the normalized axial distance required for self-preservation of the mean temperature field. It is found that the normalized centerline intensity of temperature fluctuations has an asymptotic value of 44% in the fully developed region.

Round buoyant laminar and turbulent plumes

Two approximate solutions, which become exact for Prandtl numbers 1 and 2, are given for laminar round plumes for arbitrary Prandtl number σ. The first of these gives a very accurate solution for laminar found plumes in air, for which σ = 0.73, and the second provides a good solution for laminar round plumes in water, for which σ = 6.7. Two approximate solutions, which become exact for turbulent Prandtl numbers 1.1 and 2, respectively, are given for turbulent round plumes. The one which becomes exact at σ = 1.1 is used to give a highly accurate solution for σ = 1, which, for an eddy-viscosity coefficient λ equal to 0.0156, provides a remarkably good agreement with the experimental data of Beuther, Capp, and George, Jr.

Turbulent buoyant plumes

The velocity and temperature distributions in turbulent buoyant induced by a line source or point source of heat are calculated by assuming the eddy viscosity and eddy diffusivity to be constant in any cross section of the plume. Two solutions in closed forms are obtained for the two-dimensional plume, corresponding to turbulent Prandtl number σ equal to 2/3 and 2. Two such solutions are also obtained for the round plume, corresponding to σ equal to 1.1 and 2. The solution for σ=2/3 is compared with previous measurements for two-dimensional plumes, and the solution for σ=1.1 is compared with previous measurements for the axisymmetric plume. The analytical and experimental results agree well in the two-dimensional case, and satisfactorily in the axisymmetric case.

The round plume due to a falling point source of heat

The natural convection due to a point source of heat, which falls with constant velocity, is given in the form of an asymptotic series.