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.

scholarly journals Dependence of the non-stationary form of Yaglom’s equation on the Schmidt number

2002 ◽  
Vol 451 ◽  
pp. 99-108 ◽  
Author(s):  
P. ORLANDI ◽  
R. A. ANTONIA
Keyword(s):  
Dynamic Equation ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Second Order ◽  
Order Moment ◽  
Length Scale ◽  
Stationary Form

The dynamic equation for the second-order moment of a passive scalar increment is investigated in the context of DNS data for decaying isotropic turbulence at several values of the Schmidt number Sc, between 0.07 and 7. When the terms of the equation are normalized using Kolmogorov and Batchelor scales, approximate independence from Sc is achieved at sufficiently small r/ηB (r is the separation across which the increment is estimated and ηB is the Batchelor length scale). The results imply approximate independence of the mixed velocity-scalar derivative skewness from Sc and underline the importance of the non-stationarity. At small r/ηB, the contribution from the non-stationarity increases as Sc increases.

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.

Second-order integral model for a round turbulent buoyant jet

2002 ◽  
Vol 459 ◽  
pp. 397-428 ◽  
Author(s):  
HONGWEI WANG ◽  
ADRIAN WING-KEUNG LAW
Keyword(s):  
Mass Flux ◽  
Richardson Number ◽  
Momentum Flux ◽  
Second Order ◽  
Integral Model ◽  
Width Ratio ◽  
Buoyant Jet ◽  
Turbulent Characteristics ◽  
Momentum Fluxes ◽  
Local Mean

The development of a second-order integral model for a round turbulent buoyant jet is reported based on new experimental data on turbulent mass and momentum transport. The mean and turbulent characteristics of a round vertical buoyant jet covering the full range from jets to plumes were investigated using a recently developed combined digital particle image velocimetry (DPIV) and planar laser-induced fluorescence (PLIF) system. The system couples the two well-known techniques to enable synchronized planar measurements of flow velocities and concentrations in a study area. The experimental results conserved the mass and momentum fluxes introduced at the source accurately with closure errors of less than 5%. The momentum flux contributed by turbulence and streamwise pressure gradient was determined to be about 10% of the local mean momentum flux in both jets and plumes. The turbulent mass flux, on the other hand, was measured to be about 7.6% and 15% of the mean mass flux for jets and plumes respectively. While the velocity spread rate was shown to be independent of the flow regime, the concentration-to-velocity width ratio λ varied from 1.23 to 1.04 during the transition from jet to plume. Based on the experimental results, a refined second-order integral model for buoyant jets that achieves the conservation of total mass and momentum fluxes is proposed. The model employs the widely used entrainment assumption with the entrainment coefficient taken to be a function of the local Richardson number. Improved prediction is achieved by taking into account the variation of turbulent mass and momentum fluxes. The variation of turbulent mass flux is modelled as a function of the local Richardson number. The turbulent momentum flux, on the other hand, is treated as a fixed percentage of the local mean momentum flux. In addition, unlike most existing integral models that assume a constant concentration-to-velocity width ratio, the present model adopts a more accurate approach with the ratio expressed as a function of the local Richardson number. As a result, smooth transition of all relevant mean and turbulent characteristics from jet to plume is predicted, which is in line with the underlying physical processes.

Surface Dilution of Round Negative Buoyant Jets–A Comparison with Other Jets

1982 ◽  
Vol 14 (4-5) ◽  
pp. 13-20
Author(s):  
G Noutsopoulos ◽  
J Demetriou
Keyword(s):  
Free Surface ◽  
Salt Water ◽  
Water Solution ◽  
Experimental Results ◽  
Common Salt ◽  
Internal Diameter ◽  
Length Scale ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Small Depth

Experimental results, concerning surface dilutions of round turbulent jets with negative buoyancy, are presented and discussed. Fresh water jets, of density ρo, discharging from a vertical pipe, of internal diameter do, placed in the middle of the experimental tank, at a depth H from the free surface of a quiescent ambient liquid, consisting of common salt water solution, of density ρs, slightly larger than ρo, have been studied. Dilution measurements, made with a conductivity probe, have been performed, along radial traverses, at a small depth of 5do, below the free surface. The experimental results were analyzed and presented in terms of dimensionless dilution scale gl versus the dimensionless length scale zl. In this form they are directly compared to axial dilution results of the positive buoyant jet. With the proper definition of length scale, they are expressed satisfactorily by the well established semiem-pirical expressions, concerning the axial dilution of positive buoyant jets. Semiem-pirical relationships, concerning the axial dilution distribution of the horizontal buoyant jet, are also presented. Thus, a direct comparison is made possible for surface dilutions in the three round buoyant jet cases, namely the positive, the negative and the horizontal jet, which will be very useful in engineering design.

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.

On the time scales and structure of Lagrangian intermittency in homogeneous isotropic turbulence

2019 ◽  
Vol 867 ◽  
pp. 438-481 ◽  
Author(s):  
R. Watteaux ◽  
G. Sardina ◽  
L. Brandt ◽  
D. Iudicone
Keyword(s):  
Time Scales ◽  
Isotropic Turbulence ◽  
Flow Characteristics ◽  
Residence Times ◽  
Particle Trajectories ◽  
Local Flow ◽  
Available Energy ◽  
Homogeneous And Isotropic Turbulence ◽  
History Of ◽  
Optimum Manner

We present a study of Lagrangian intermittency and its characteristic time scales. Using the concepts of flying and diving residence times above and below a given threshold in the magnitude of turbulence quantities, we infer the time spectra of the Lagrangian temporal fluctuations of dissipation, acceleration and enstrophy by means of a direct numerical simulation in homogeneous and isotropic turbulence. We then relate these time scales, first, to the presence of extreme events in turbulence and, second, to the local flow characteristics. Analyses confirm the existence in turbulent quantities of holes mirroring bursts, both of which are at the core of what constitutes Lagrangian intermittency. It is shown that holes are associated with quiescent laminar regions of the flow. Moreover, Lagrangian holes occur over few Kolmogorov time scales while Lagrangian bursts happen over longer periods scaling with the global decorrelation time scale, hence showing that loss of the history of the turbulence quantities along particle trajectories in turbulence is not continuous. Such a characteristic partially explains why current Lagrangian stochastic models fail at reproducing our results. More generally, the Lagrangian dataset of residence times shown here represents another manner for qualifying the accuracy of models. We also deliver a theoretical approximation of mean residence times, which highlights the importance of the correlation between turbulence quantities and their time derivatives in setting temporal statistics. Finally, whether in a hole or a burst, the straining structure along particle trajectories always evolves self-similarly (in a statistical sense) from shearless two-dimensional to shear bi-axial configurations. We speculate that this latter configuration represents the optimum manner to dissipate locally the available energy.

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.

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