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.

Three-Dimensional Buoyant Wall Jets Released Into a Coflowing Turbulent Boundary Layer

1990 ◽  
Vol 112 (2) ◽  
pp. 356-362 ◽  
Author(s):  
J. R. Sinclair ◽  
P. R. Slawson ◽  
G. A. Davidson
Keyword(s):  
Three Dimensional ◽  
Ground Level ◽  
Turbulent Shear ◽  
Wall Jet ◽  
Turbulent Shear Flow ◽  
Streamwise Vorticity ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Jet Trajectory ◽  
Model Predictions

Experiments have been conducted in a water flume to simulate finite-length line sources of heat that issue horizontally at ground level into a coflowing turbulent shear flow. The downstream development of each buoyant jet is documented by detailed mean temperature measurements, which are analyzed to determine the jet trajectory, spread rates, and distance to the point of liftoff from the surface. In addition, a three-dimensional, parabolic, numerical model based on the fundamental conservation equations is developed. Model predictions of several buoyant jets compare reasonably with the experimental data and suggest that the strength of the streamwise vorticity plays an important role in governing liftoff of a buoyant wall jet from the surface.

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.

scholarly journals Non-Boussinesq Integral Model for Horizontal Turbulent Buoyant Round Jets

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
J. Xiao ◽  
J.R. Travis ◽  
W. Breitung
Keyword(s):  
Experimental Data ◽  
Flow Regime ◽  
Large Range ◽  
Safety Analysis ◽  
Power Industry ◽  
Integral Model ◽  
Engineering Model ◽  
Buoyant Jet ◽  
Round Jets ◽  
Hydrogen Safety

Horizontal buoyant jet is a fundamental flow regime for hydrogen safety analysis in power industry. The purpose of this study is to develop a fast non-Boussinesq engineering model the horizontal buoyant round jets. Verification of this integral model is established with available experimental data and comparisons over a large range of density variations with the CFD codes GASFLOW. The model has proved to be an efficient engineering tool for predicting horizontal strongly buoyant round jets.

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.

Dynamic interaction of multiple buoyant jets

2012 ◽  
Vol 708 ◽  
pp. 539-575 ◽  
Author(s):  
Adrian C. H. Lai ◽  
Joseph H. W. Lee
Keyword(s):  
Stokes Equations ◽  
Dynamic Pressure ◽  
Unit Length ◽  
Iterative Solution ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Dynamic Interaction ◽  
Ambient Conditions ◽  
Buoyant Jet ◽  
Buoyant Jets

AbstractAn array of closely spaced round buoyant jets interact dynamically due to the pressure field induced by jet entrainment. Mutual jet attraction can result in a significant change in jet trajectories. Jet merging also leads to overlapping of the passive scalar fields associated with the individual jets, resulting in mixing characteristics that are drastically different from those of an independent free jet. A general semi-analytical model for the dynamic interaction of multiple buoyant jets in stagnant ambient conditions is proposed. The external irrotational flow field induced by the buoyant jets is computed by a distribution of point sinks with strength equal to the entrainment per unit length along the unknown jet trajectories and accounting for boundary effects. The buoyant jet trajectories are then determined by an iterative solution of an integral buoyant jet model by tracking the changes in the external entrainment flow and dynamic pressure fields. The velocity and concentration fields of the jet group are obtained by momentum or kinetic energy superposition for merged jets and plumes, respectively. The modelling approach is supported by numerical solution of the Reynolds-averaged Navier–Stokes equations. The model shows that jet merging and mixing can be significantly affected by jet interactions. Model predictions of the multiple jet trajectories, merging height, as well as the centreline velocity and concentration of the buoyant jet group are in good agreement with experimental data for: (i) a clustered momentum jet group; (ii) a turbulent plume pair; and (iii) a rosette buoyant jet group. Dynamic interactions between a jet group are shown to decrease with the addition of an ambient cross-flow.

Flow patterns of vertical plane thermal buoyant jet in shallow water

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840041
Author(s):  
Li-Qing Zhao ◽  
Jian-Hong Sun ◽  
Yang Lu
Keyword(s):  
Flow Pattern ◽  
Vertical Plane ◽  
Free Water ◽  
Simulation Method ◽  
Boussinesq Approximation ◽  
Flow Patterns ◽  
Buoyant Jet ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Impinging Flow

A heated plane water jet impinging vertically onto free water surface has been numerically studied based on large eddy simulation method coupled with the volume of fluid approach. The Boussinesq approximation is adopted to simulate the effect of buoyancy. Results showed that there exist two flow patterns for the plane thermal buoyant jet, which are the stable impinging flow pattern and the flapping impinging flow pattern. Distinct temperature stratification can be found in the stable impinging flow pattern, while it disappears in the flapping impinging flow pattern.

Natural Convection in a Horizontal Cavity Partially Occupied by a Porous Media Saturated by a Coolant Liquid

2006 ◽  
Author(s):  
Fakhreddine S. Oueslati ◽  
Rachid Bennacer ◽  
Habib Sammouda ◽  
Ali Belghith
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Natural Convection ◽  
Flow Structure ◽  
Boussinesq Approximation ◽  
Density Variation ◽  
Heat Fluxes ◽  
Complex Flow ◽  
Coupled Equations ◽  
Complex Flow Structure

The natural convection is studied in a cavity witch the lower half is filled with a porous media that is saturated with a first fluid (liquid), and the upper is filled with a second fluid (gas). The horizontal borders are heated and cooled by uniform heat fluxes and vertical ones are adiabatic. The formulation of the problem is based on the Darcy-Brinkman model. The density variation is taken into account by the Boussinesq approximation. The system of the coupled equations is resolved by the classic finite volume method. The numerical results show that the variation of the conductivity of the porous media influences strongly the flow structure and the heat transfer as well as in upper that in the lower zones. The effect of conductivity is conditioned by the porosity which plays a very significant roll on the heat transfer. The structures of this flow show that this kind of problem with specific boundary conditions generates a complex flow structure of several contra-rotating two to two cells, in the upper half of the cavity.

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