Second-order integral model for plane turbulent buoyant jets in stratified environments

2010 ◽  
pp. 137-142
Keyword(s):  
Second Order ◽  
Integral Model ◽  
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.

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.

A modified integral model for negatively buoyant jets in a stationary ambient

2014 ◽  
Vol 15 (5) ◽  
pp. 939-957 ◽  
Author(s):  
I. K. Nikiforakis ◽  
A. I. Stamou ◽  
G. C. Christodoulou
Keyword(s):  
Integral Model ◽  
Buoyant Jets ◽  
Negatively Buoyant ◽  
Negatively Buoyant Jets

A Numerical Study of Swirling Buoyant Laminar Jets at Low Reynolds Numbers

2009 ◽  
Author(s):  
Gordon N. Taub ◽  
Hyungoo Lee ◽  
S. Balachandar ◽  
S. A. Sherif
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Second Order ◽  
Step Method ◽  
Fractional Step Method ◽  
Central Difference ◽  
Buoyant Jets ◽  
Low Reynolds Numbers ◽  
Low Reynolds

The effect of swirl on laminar buoyant jets with low Reynolds numbers is explored. Three dimensional direct numerical simulations are performed to solve the time-dependent, incompressible Navier-Stokes equations. We use a body fitted grid system and employ the finite volume method to discretize the governing equations. A second-order central difference scheme is employed for all spatial derivative terms. The numerical simulation is advanced in time by a fractional step method with the second-order Adams-Bashforth scheme for explicit-convection terms and the Crank-Nicholson scheme for implicit-diffusion terms. The amount of swirl and buoyancy is varied from zero to very large values and the effect on the velocity field, jet width, entrainment and vortex are examined. Comparisons with analytical and experimental models are discussed.

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