Imaging of Turbulent Buoyant Jet Mixing

2006 ◽  
Author(s):  
David B. Helmer ◽  
Lester K. Su
Keyword(s):  
Mole Fraction ◽  
Rayleigh Scattering ◽  
Quantitative Imaging ◽  
Mean Field ◽  
Jet Flows ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Scaling Properties ◽  
Jet Mixing ◽  
The Mean

This paper presents quantitative imaging measurements of jet fluid mole fraction fields in turbulent buoyant jets of helium issuing into air. The measurements use planar laser Rayleigh scattering. Signal levels are low, necessitating a novel approach to background subtraction in the signal processing. The jet flows considered are classified as momentum-driven, meaning that buoyancy effects are presumed to be confined to the small scales of the flow. We focus here on the near-nozzle, developing region of the jet, which is of particular interest to flows with combustion. The results suggest that buoyancy affects the details of the evolution of the mixing field even while the mean field maintains scaling properties consistent with non-buoyant jets. Specifically, the mean jet fluid mole fraction profiles show a sharper jet/ambient fluid interface relative to non-buoyant jets. The mole fraction fluctuations within the jet are also weaker than those reported in non-buoyant jets. These results will inform ongoing efforts to model the mixing process in flows with density differences, such as combustion systems.

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

2019 ◽  
Vol 871 ◽  
pp. 271-304 ◽  
Author(s):  
Adrian C. H. Lai ◽  
Adrian Wing-Keung Law ◽  
E. Eric Adams
Keyword(s):  
Isotropic Turbulence ◽  
Second Order ◽  
Integral Model ◽  
Length Scale ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Jet Mixing ◽  
Mixing Characteristics ◽  
Background Turbulence ◽  
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.

SCALING LAWS OF REVERSIBLE AGGREGATION IN COMPACT CLUSTER SYSTEMS

2000 ◽  
Vol 14 (09) ◽  
pp. 983-991
Author(s):  
GUOCE ZHUANG ◽  
JIAFU WANG ◽  
WEI WANG
Keyword(s):  
Scaling Laws ◽  
Mean Field ◽  
Cluster Systems ◽  
Scaling Properties ◽  
Cluster Aggregation ◽  
Reversible Aggregation ◽  
A Value ◽  
Aggregation Processes ◽  
The Mean ◽  
Compact Cluster

The reversible cluster–cluster aggregation processes in compact cluster systems are studied via a scaling argument and Monte Carlo simulations. To describe the detail effects of fragmentations from tree-like fractal to compact clusters a relative breakup probability [Formula: see text] with an exponent β is introduced. The mean-field rate equation and numerical simulation results indicate that the critical exponent y, which is defined as <s (k, ∞)> ~ k-y, has a value of (α + ξ - β + 2)-1. It is shown that the scaling properties of the cluster size distributions are determined by the selections of the exponents α, β and ξ.

scholarly journals On the Nearest-Neighbor Algorithm for the Mean-Field Traveling Salesman Problem

2014 ◽  
Vol 51 (01) ◽  
pp. 106-117
Author(s):  
Antar Bandyopadhyay ◽  
Farkhondeh Sajadi
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Traveling Salesman ◽  
Nearest Neighbor Algorithm ◽  
Scaling Properties ◽  
Limiting Behavior ◽  
Total Length ◽  
The Mean

In this work we consider the mean-field traveling salesman problem, where the intercity distances are taken to be independent and identically distributed with some distribution F. We consider the simplest approximation algorithm, namely, the nearest-neighbor algorithm, where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all possible cases of general F.

Quantitative planar imaging of turbulent buoyant jet mixing

2009 ◽  
Vol 643 ◽  
pp. 59-95 ◽  
Author(s):  
L. K. SU ◽  
D. B. HELMER ◽  
C. J. BROWNELL
Keyword(s):  
Mass Fraction ◽  
Rayleigh Scattering ◽  
Near Field ◽  
Outer Boundary ◽  
Turbulent Transport ◽  
Scalar Dissipation ◽  
Planar Imaging ◽  
Buoyant Jet ◽  
Jet Mixing ◽  
Dissipation Rates

Planar Rayleigh scattering provides quantitative mixing measurements in the developing region of axisymmetric turbulent helium jets issuing into air. The measurements focus on the relatively near field, in which the jets are primarily momentum driven. The imaging parameters are specified to ensure high spatial resolution. The mean jet fluid concentration fields attain self-similarity within the measurement region, though the forms of the mole fraction profiles indicate a reduction in turbulent transport at the jet outer boundary, arising from the reduced jet fluid density. Nevertheless, jet-like scaling pertains for the concentration fields. Mass fraction fluctuations on the jet centreline attain the expected asymptotic value of ≈23% of the centreline mass fraction values. The scalar dissipation rates, however, show an axial decay rate that is slower than theoretical predictions. The two-dimensional extent of the measurements also allows spatial filtering similar to that inherent in large-eddy simulations (LESs). The results confirm that fluctuation levels and scalar dissipation rates determined for the filtered fields are reduced as the effective resolution is reduced, but while the fluctuation profiles for the filtered fields are similar for the different filter sizes, the forms of the scalar dissipation profiles are highly dependent on filter size. These latter results in particular are of a form that will be useful for grid-dependent assessments of LES results.

scholarly journals Curvilinear Coordinate System for Mathematical Analysis of Inclined Buoyant Jets Using the Integral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Aristeidis A. Bloutsos ◽  
Panayotis C. Yannopoulos
Keyword(s):  
Coordinate System ◽  
Integral Method ◽  
Two Dimensional ◽  
Mean Flow ◽  
Buoyant Jet ◽  
Cross Sectional ◽  
Buoyant Jets ◽  
Curvilinear Coordinate ◽  
The Mean ◽  
Cartesian Coordinate

The development of a local system of orthogonal curvilinear coordinates, which is appropriate to monitor the flow of an inclined buoyant jet with reference to the basic Cartesian coordinate system is presented. Such a system is necessary for the correct application of the integral method, since the well-known Gaussian profiles should be integrated on the cross-sectional area of inclined buoyant jet, where they are valid. This is the major advantage of the present work compared to all other integral methods using Cartesian coordinate systems. Consequently, the flow and mixing governing partial differential equations (PDE), i.e., continuity, momentum, buoyancy, and/or tracer conservation, are written in the local orthogonal curvilinear coordinate system and, then, the Reynolds substitution regarding mean and fluctuating components of all dependent variables is applied. After averaging with respect to time, the mean flow PDEs are taken, omitting second-order terms, as the dynamic pressure and molecular viscosity, compared to the mean flow and mixing contributions of turbulent terms. The latter are introduced through empirical coefficients. The Boussinesq’s approximation regarding small density differences is taken into consideration. The system of PDEs is closed by assuming known spreading coefficients along with Gaussian similarity profiles. The methodology is applied in the inclined two-dimensional buoyant jet; thus, PDEs are integrated on the jet cross-sectional area resulting in ordinary differential equations (ODE), which are appropriate to be solved by applying the 4th order Runge-Kutta algorithm coded in either FORTRAN or EXCEL. The numerical solution of ODEs, concerning trajectory of the inclined two-dimensional buoyant jet, as well as longitudinal variations of the mean axial velocity, mean concentration, minimum dilution, and entrainment velocity or entrainment coefficient, occurs quickly, saving computer memory and effort. The satisfactory agreement of results with experimental data available in the literature empowers the usefulness of the proposed methodology in inclined buoyant jets.

scholarly journals On the Nearest-Neighbor Algorithm for the Mean-Field Traveling Salesman Problem

2014 ◽  
Vol 51 (1) ◽  
pp. 106-117
Author(s):  
Antar Bandyopadhyay ◽  
Farkhondeh Sajadi
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Traveling Salesman ◽  
Nearest Neighbor Algorithm ◽  
Scaling Properties ◽  
Limiting Behavior ◽  
Total Length ◽  
The Mean

In this work we consider the mean-field traveling salesman problem, where the intercity distances are taken to be independent and identically distributed with some distribution F. We consider the simplest approximation algorithm, namely, the nearest-neighbor algorithm, where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all possible cases of general F.

scholarly journals Revisiting Mean Flow and Mixing Properties of Negatively Round Buoyant Jets Using the Escaping Mass Approach (EMA)

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 131
Author(s):  
Aristeidis A. Bloutsos ◽  
Panayotis C. Yannopoulos
Keyword(s):  
Numerical Models ◽  
Gaussian Model ◽  
Uniform Density ◽  
Mean Flow ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Mixing Properties ◽  
Flow Phenomena ◽  
The Mean ◽  
Return Point

The flow formed by the discharge of inclined turbulent negatively round buoyant jets is common in environmental flow phenomena, especially in the case of brine disposal. The prediction of the mean flow and mixing properties of such flows is based on integral models, experimental results and, recently, on numerical modeling. This paper presents the results of mean flow and mixing characteristics using the escaping mass approach (EMA), a Gaussian model that simulates the escaping masses from the main buoyant jet flow. The EMA model was applied for dense discharge at a quiescent ambient of uniform density for initial discharge inclinations from 15° to 75°, with respect to the horizontal plane. The variations of the dimensionless terminal centerline and the external edge’s height, the horizontal location of the centerline terminal height, the horizontal location of centerline and the external edge’s return point as a function of initial inclination angle are estimated via the EMA model, and compared to available experimental data and other integral or numerical models. Additionally, the same procedure was followed for axial dilutions at the centerline terminal height and return point. The performance of EMA is acceptable for research purposes, and the simplicity and speed of calculations makes it competitive for design and environmental assessment studies.

Numerical Solutions of Single and Multiple Laminar Jets

2005 ◽  
Author(s):  
D. Prasanna ◽  
K. Aung
Keyword(s):  
Power Plants ◽  
Numerical Solutions ◽  
Waste Heat ◽  
Electrical Energy ◽  
Theoretical Work ◽  
Jet Flows ◽  
Published Data ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Finite Distance

Modern power plants discharge approximately 1.5 to 2kWhr of waste heat for every kWhr of electrical energy produced. Modern power plants discharge approximately 1.5 to 2kWhr of waste heat for every kWhr of electrical energy produced. Usually this heat is discharged to an adjacent water body which increases the water temperature near the outfall. In order to assess the ecological consequences of waste heat discharge one must first know the physical changes (temperature, velocity, salinity) induced by these discharges. It is with this later aspect, prediction of physical properties, that the current work is primarily concerned. Existing theoretical work on axisymmetric buoyant jets is confined to integral techniques developed by Morton in the early 1950’s. From these techniques only centerline velocities and temperatures can be calculated. Experimental data for this type of flow are essentially confined to centerline temperature measurements except for pure jet or plume data which constitute the extremes for a buoyant jet. The present work addresses the problem of developing a theoretical model for an axisymmetric laminar buoyant jet. The governing equations for an axisymmetric buoyant jet in rectangular co-ordinates are transformed into an orthogonal curvilinear co-ordinate system which moves along the length of the jet axis. The complete partial differential equations governing steady, incompressible laminar flow are solved in the new curvilinear co-ordinates using finite-difference techniques. This method is applicable to a much wider range of jet flows issued at arbitrary angles into quiescent or flowing ambience. This method is also applied to the case for multiple jets spaced by a finite distance apart. Results for the momentum jet, axial and radial distribution of velocity and temperature, show good agreement with published data.

Escaping mass approach for inclined plane and round buoyant jets

2012 ◽  
Vol 695 ◽  
pp. 81-111 ◽  
Author(s):  
P. C. Yannopoulos ◽  
A. A. Bloutsos
Keyword(s):  
Present Model ◽  
Curvilinear Coordinates ◽  
Integral Model ◽  
Uniform Density ◽  
Mean Flow ◽  
Buoyant Jet ◽  
Inclined Plane ◽  
Buoyant Jets ◽  
Integral Forms ◽  
The Mean

AbstractAn integral model predicting the mean flow and mixing properties of inclined plane and round turbulent buoyant jets in a motionless environment of uniform density is proposed. The escaping masses from the main buoyant jet flow are simulated, and the model can be successfully applied to initial discharge inclinations ${\theta }_{0} $ from 90 to $\ensuremath{-} 7{5}^{\ensuremath{\circ} } $ with respect to the horizontal plane. This complementary approach introduces a concentration coefficient, which is calibrated using experimental evidence. The present model has incorporated the second-order approach and, regarding the jet-core region, a jet-core model based on the advanced integral model for the production of more correct transverse profiles of the mean axial velocities and mean concentrations than the common Gaussian or top-hat profiles. The partial differential equations for momentum and tracer conservation are written in orthogonal and cylindrical curvilinear coordinates for inclined plane and round buoyant jets, respectively, and they are integrated under the closure assumptions of (a) quasi-linear spreading of the mean flow and mixing fields, and (b) known transverse profile distributions. The integral forms are solved by employing the Runge–Kutta algorithm. Since the most important contribution in the present model is the simulation of the escaping masses, the model has been called the escaping mass approach (EMA). Herein EMA is applied to predict the mean flow properties (trajectory characteristics, mean axial velocities and mean concentrations) for inclined plane and round buoyant jets. The results predicted are compared with experimental data available in the literature, and the accuracy obtained is more than satisfactory. The performance of the EMA is up to 56 % better than using classical integral procedures. EMA can be used for design purposes and for environmental impact assessment studies.

scholarly journals On the Nearest-Neighbor Algorithm for the Mean-Field Traveling Salesman Problem

2014 ◽  
Vol 51 (01) ◽  
pp. 106-117
Author(s):  
Antar Bandyopadhyay ◽  
Farkhondeh Sajadi
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Traveling Salesman ◽  
Nearest Neighbor Algorithm ◽  
Scaling Properties ◽  
Limiting Behavior ◽  
Total Length ◽  
The Mean

In this work we consider the mean-field traveling salesman problem, where the intercity distances are taken to be independent and identically distributed with some distribution F. We consider the simplest approximation algorithm, namely, the nearest-neighbor algorithm, where the rule is to move to the nearest nonvisited city. We show that the limiting behavior of the total length of the nearest-neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all possible cases of general F.

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