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.

Flow Field Analysis Around the Ship Fin Stabilizer Including Free Surface

2009 ◽  
Author(s):  
Fatemah Hoseini Dadmarzi ◽  
Hassan Ghassemi ◽  
Parviz Ghadimi ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Numerical Data ◽  
Numerical Results ◽  
Field Analysis ◽  
Hydrodynamic Performance ◽  
Pressure Distributions ◽  
Flow Field Analysis ◽  
Ship Roll ◽  
Fin Stabilizer

Fin stabilizers are very important device for controlling the ship roll motion against the external moments due to wave. This paper presents numerical results for flow field simulation and the hydrodynamic performance of fin stabilizer attached to a ship hull with free surface effects. Combination of CFD and RANS method has been used for this study. The fin is non-rectangular NACA0015 profile section with a finite aspect ratio. The numerical results include pressure distributions and flow field around the fin which are used to calculate lift coefficients and free surface elevation as the main interest. Some results are compared with available experimental and numerical data in literature and they show good agreement.

Boundary Effects on Dilution of Buoyant Jets

1973 ◽  
Vol 8 (1) ◽  
pp. 168-177
Author(s):  
James J. Sharp ◽  
Chung-su Wang
Keyword(s):  
Experimental Study ◽  
Boundary Effects ◽  
Shear Stresses ◽  
Wall Jet ◽  
Practical Case ◽  
Buoyant Jet ◽  
Momentum Exchange ◽  
Buoyant Jets ◽  
Free Jet ◽  
Analytical Studies

Abstract Most studies of buoyant jet phenomena have been conducted with the outfall pipe remote from the bed. This situation idealises the practical case because, over a period of time, it is likely that the diffuser pipeline will settle some way into the bed due to the scour action of prevailing currents. Thus, the dilution achieved in the rising jet may be affected to some extent by the proximity of the ocean bed. This paper describes an experimental study conducted to determine the effect of a bed immediately below the outfall mozzle. The results indicated generally that the effect of the floor was to considerably increase the surface dilution above the value predicted by current theories and other experiments, in which the nozzle is remote from the floor. The magnitude of the increase varied but could be as high as 1000%. Although no analytical studies were undertaken visual observations indicated some reasons for the increase of dilution. As the jet was discharged shear stresses between the floor and the jet caused the effluent to cling to the floor in a manner somewhat similar to that of a wall jet. This caused greater momentum exchange at the interface between the jet and receiving fluid and thereby increased dilution beyond that obtained with a free jet. It has been known for some time that studies of buoyant jets undertaken in quiescent homogeneous receiving fluid considerably underestimate the dilution which will be achieved in practice because of prevailing currents at the outfall site and the possibility of stratification in the receiving fluid. This study indicates that existing theories for buoyant jet dilution may be even more conservative than was previously thought.

Tidally induced jet in Koombana Bay, Western Australia

1985 ◽  
Vol 36 (4) ◽  
pp. 453 ◽  
Author(s):  
CJ Hearn ◽  
JR Hunter ◽  
J Imberger ◽  
Senden D Van
Keyword(s):  
Aspect Ratio ◽  
Coastal Waters ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Low Aspect Ratio ◽  
Discharge Velocity ◽  
Alongshore Current ◽  
New Criterion ◽  
Shallow Coastal Waters ◽  
Axial Speed

A study is made of a coastal tidal jet, based on a field program together with numerical and analytical modelling of the tidal discharge and jet dynamics. A new criterion is demonstrated for bottom attachment of low-aspect-ratio buoyant jets. The slightly buoyant jet is attached to the seabed over the initial 2 km of its trajectory, which lies in shallow coastal waters of less than 10 m depth. The jet is about 200 m in width and so its ratio of depth to half-width (aspect ratio) is much lower than for previously reported bottom-attached jets. The longitudinal retardation of the axial speed of the jet is due to bottom friction and entrainment. The jet widens only slowly with distance along its trajectory because entrainment is limited to its sides and is compensated by bathymetric deepening. The jet attaches to the coastline by turning, without loss of speed, to move parallel to the shore. The coastal attachment width is found to be a simple function of the ratio of the jet discharge velocity to the speed of the prevailing alongshore current.

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 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.

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.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

Study of the Standard k-ε Model for Tip Leakage Flow in an Axial Compressor Rotor

2016 ◽  
Vol 33 (4) ◽  
Author(s):  
Yanfei Gao ◽  
Yangwei Liu ◽  
Luyang Zhong ◽  
Jiexuan Hou ◽  
Lipeng Lu
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Axial Compressor ◽  
Leakage Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Compressor Rotor

AbstractThe standard k-ε model (SKE) and the Reynolds stress model (RSM) are employed to predict the tip leakage flow (TLF) in a low-speed large-scale axial compressor rotor. Then, a new research method is adopted to “freeze” the turbulent kinetic energy and dissipation rate of the flow field derived from the RSM, and obtain the turbulent viscosity using the Boussinesq hypothesis. The Reynolds stresses and mean flow field computed on the basis of the frozen viscosity are compared with the results of the SKE and the RSM. The flow field in the tip region based on the frozen viscosity is more similar to the results of the RSM than those of the SKE, although certain differences can be observed. This finding indicates that the non-equilibrium turbulence transport nature plays an important role in predicting the TLF, as well as the turbulence anisotropy.

Turbulence structure and flow field of shallow water with a submerged eel grass patch

2014 ◽  
Vol 69 ◽  
pp. 201-205 ◽  
Author(s):  
Cui-chao Pang ◽  
Di Wu ◽  
Xi-jun Lai ◽  
Shi-qiang Wu ◽  
Fang-fang Wang
Keyword(s):  
Flow Field ◽  
Shallow Water ◽  
Turbulence Structure ◽  
Grass Patch
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