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 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.

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.

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.

Non-Boussinesq Integral Model for Horizontal Turbulent Strongly Buoyant Plane Jets

2008 ◽  
Author(s):  
Jianjun Xiao ◽  
John R. Travis ◽  
Wolfgang Breitung
Keyword(s):  
Power Plants ◽  
Boussinesq Approximation ◽  
Density Variation ◽  
Integral Model ◽  
Buoyant Jet ◽  
Boussinesq Model ◽  
Buoyant Jets ◽  
Jet Trajectory ◽  
Plane Jets ◽  
Hydrogen Safety

Horizontal buoyant jets are fundamental flow regimes for hydrogen safety analyses in the nuclear power plants. Integral model is an efficient, fast running engineering tool that can be used to obtain the jet trajectory, centerline dilution and other properties of the flow. In the published literature, most of the integral models that are used to predict the horizontal buoyant jet behavior employ the Boussinesq approximation, which limits the density range between the jets and the ambient. CorJet, a long researched, developed, and established commercial model, is such a Boussinesq model, and has proved to be accurate and reliable to predict the certain buoyant jet physics. In this study, Boussinesq and non-Boussinesq integral models with modified entrainment hypothesis were developed for modeling horizontal turbulent strongly buoyant plane jets. All the results and data where the Boussinesq model is valid will collapse to CorJet when they are properly normalized, which implies that the calculation is not sensitive to density variations in Boussinesq model. However, non-Boussinesq results will never collapse to CorJet analyses using the same normalized scaling, and the results are dependent on the density variation. The reason is that CorJet employs the Boussinesq approximation in which density variations are only important in the buoyancy term. For hydrogen safety analyses, the large density variation between hydrogen and the ambient, which is normally the mixture of air and steam, will make the Boussinesq approximation invalid, and the effect of the density variation on the inertial mass of the fluid can not neglected. This study highlights the assumption of the Boussinesq approximation as a limiting, simplified theory for strongly buoyant jets. A generalized scaling theory for horizontal strongly buoyant jet seems not to exist when the Boussinesq approximation is not applicable. This study also reveals that the density variation between jets and the ambient should be less than 10% to accurately model horizontal buoyant jets when the Boussinesq approximation is applied. Verification of this integral model is established with available data and comparisons over a large range of density variations with the CFD codes GASFLOW and Fluent. The model has proved to be an efficient engineering tool for predicting horizontal strongly buoyant plane jets.

Measurements in Two-Dimensional Plumes in Crossflow

1989 ◽  
Vol 111 (2) ◽  
pp. 130-138 ◽  
Author(s):  
B. R. Ramaprian ◽  
H. Haniu
Keyword(s):  
Experimental Data ◽  
Short Distance ◽  
Two Dimensional ◽  
Mean Flow ◽  
Buoyant Jets ◽  
Laser Velocimetry ◽  
Buoyancy Forces ◽  
The Mean

The mean-flow and turbulent properties of two-dimensional buoyant jets discharged vertically upward into a crossflowing ambient have been measured in a hydraulic flume, using laser velocimetry and microresistance thermometry. The trajectory of the resulting inclined plume is found to be nearly straight, beyond a short distance from the source. The flow is essentially characterized by the presence of buoyancy forces along (s-direction) and perpendicular (n-direction) to the trajectory. While the s-component buoyancy tends to destabilize the flow and hence raise the overall level of turbulence in the flow, the n-component buoyancy tends to augment turbulence on the upper part of the flow and inhibit turbulence on the lower part. The experimental data are used to examine these effects quantitatively.

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.

Influence of a Coflowing Ambient Stream on a Turbulent Axisymmetric Buoyant Jet

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
S. Habli ◽  
N. Mahjoub Said ◽  
H. Mahmoud ◽  
H. Mhiri ◽  
G. Le Palec ◽  
...  
Keyword(s):  
Flow Field ◽  
Numerical Data ◽  
Algebraic Model ◽  
Numerical Results ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Free Jet ◽  
Discharge Velocity

This paper reports numerical results on turbulent buoyant axisymmetric jets in a coflowing ambient stream. The objective of this study is to compare the performance of the Reynolds stress algebraic model (ASM) with that of the k-ε turbulence model in predicting the flow field. A finite difference method has been used to solve a system of coupled partial differential equations. A comparison has been carried out between the numerical results obtained in the present work and experimental and numerical data reported in the literature. It has been found that the two investigated models reasonably predict the mean flow properties of the flow field. Nevertheless, the ASM proves to be better than the k-ε method to predict the effects of buoyancy and the turbulence structure. It has been found that the increase of the coflow can slow the development of the jet to the state of similarity of mean characteristic profiles. A jet with a ratio of coflow velocity u¯∞ to jet discharge velocity u¯0 less than 0.05 has developed to closely approximate a free jet in a stagnant medium while a jet with higher u¯∞∕u¯0 ratio never reaches a similarity state. In buoyant jets, only a flow with u∝∕u0⩽0.05 reaches a similarity state. Buoyancy ensures that the similarity region begins at a distance closer to the nozzle exit than if the medium is stagnant.

A vertical buoyant jet with high momentum in a long ventilated tunnel

1993 ◽  
Vol 252 ◽  
pp. 279-300 ◽  
Author(s):  
S. J. Barnett
Keyword(s):  
Steady State ◽  
Small Radius ◽  
High Momentum ◽  
Mean Flow ◽  
Buoyant Jet ◽  
Flow Models ◽  
The Mean ◽  
Flow Variables ◽  
Mean Concentration ◽  
Theoretical Results

In this paper the flow resulting from the release of buoyant material within a long tunnel is investigated. The source fluid is discharged through a nozzle of small radius with sufficiently high flow rate to ensure that the axial lengthscale of the buoyant jet (subsequently called the ‘jet-length’) is several times the depth of the tunnel, d. The ends of the tunnel may be either open or closed and a number of ventilation points may exist along it. Consideration of a source with high momentum is an important development in confined jet flow models, as most previous models have assumed that the source has little or no initial momentum. It is found that circulation cells are driven near to the source and that the concentration within them increases to a steady-state maximum. At a distance of about 2.5d from the source the buoyancy forces are then sufficiently strong to drive a two-layered stratified counterflow. The steady-state conservation equations are analysed in order to calculate the mean flow variables. The flow past a ventilation point and the characteristics of the secondary outflow are derived, enabling the calculation of the total number of vents needed to vent the buoyant layer. The time dependence of the mean concentration in the circulation cell near to the source is also deduced. This could be used to calculate time-dependent solutions for the other mean flow variables. All of the theoretical results are compared with experimental measurements.

Roles of surface tension and Reynolds stresses on the finite amplitude stability of a parallel flow with a free surface

1970 ◽  
Vol 40 (2) ◽  
pp. 307-314 ◽  
Author(s):  
S. P. Lin
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Gravity Waves ◽  
Wave Amplitude ◽  
Finite Amplitude ◽  
Parallel Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Inclined Plane ◽  
The Mean

Subcritically stable motion of long gravity waves of finite amplitude in a liquid layer flowing down an inclined plane is shown to be impossible. However, super-critically stable wave régimes for such flows are found and curves of constant wave amplitude in such régimes are obtained. The mechanism of non-linear stability is investigated by considering the energy transfer between the mean flow and the disturbances. The results obtained show that the mechanism of stability in a parallel flow with a free surface is quite different from that in a parallel flow without a free surface.

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