Theoretical Analysis of A Buoyant Jet Interacting with Small Amplitude Waves

A new theoretical solution is presented here for the dynamic characteristics of a buoyant jet due to opposing small amplitude waves. The conservation equations of mass, tangential moment^n and vertical momentum are solved by the integral method which encompasses the Gaussian profiles of velocity and density. The action of waves is incorporated into the equations of motion as an external force and a new exact solution is obtained to predict the trajectory, velocity distribution and boundary thickness of the buoyant jet over an arbitrary lateral cross section. It is found that the velocity along the centerline is inversely proportional to the ratio of the momentum of the wave to the buoyant jet. The averaged bound- ary width varies with the fluctuation of the boundary width, the distance from the orifice and the velocity correction function. Owing to the motion of waves, the fluctuation of the boundary width is proportional to the wave steepness.

NUMERICAL STUDY ON THE STABILITY AND MIXING OFVERTICAL ROUND BUOYANT JET IN SHALLOW WATER

The k-epsilon model was applied to establish the mathematical model of vertical round buoyant jet discharging into confined depth, and it was solved using the Hybrid Finite Analytic Method (HFAM). The numerical predictions demonstrate two generic flow patterns for different jet discharge and environmental parameters: (ⅰ)a stable buoyant flow discharge with the mixed fluid leaving the near-field warm in a surface warm water layer; (ⅱ)an unstable buoyant flow discharge with recirculation and re-entrainment of warm water in the near field. Furthermore, the mixing characters of vertical round buoyant jet were numerically predicted. Both the stability criterion and numerical predictions of bulk dilutions are in excellent agreement with Lee and Jirka's experiments and theory.

Behavior of near-field dilution of thermal buoyant jet discharged horizontally in compound open-channel

The RNG κ-ε model considering the buoyancy effect, which is solved by the hybrid finite analytic method, is used to simulate the mixture of the horizontal round thermal buoyant jet in compound open channel flow. The mixing features near the spout and flowing characteristic of the secondary currents are studied by numerical simulation. Meanwhile, （1） the distribution of the measured isovels for stream-wise velocity, （2） secondary currents, （3） the distribution of the measured isovels for temperature of typical cross-section near the spout, were obtained by the three-dimensional Micro ADV and the temperature measuring device. Compared with experimental data, the RNG κ-ε model based on buoyancy effect can preferably simulate the jet which performs the bifurcation phenomenon, jet reattachment （Conada effect） and beach secondary currents phenomenon with the effect of ambient flow, buoyancy, and secondary currents of compound section and so on.

Numerical Study of A Round Buoyant Jet Under the Effect of JONSWAP Random Waves

This paper presents a numerical study on the hydrodynamic behaviours of a round buoyant jet under the effect of JONSWAP random waves. A three-dimensional large eddy simulation （LES） model is developed to simulate the buoyant jet in a stagnant ambient and JONSWAP random waves. By comparison of velocity and concentration fields, it is found that the buoyant jet exhibits faster decay of centerline velocity, wider lateral spreading and larger initial dilution under the wave effect, indicating that wave dynamics improves the jet entrainment and mixing in the near field, and subsequently mitigate the jet impacts in the far field. The effect of buoyancy force on the jet behaviours in the random waves is also numerically investigated. The results show that the wave effect on the jet entrainment and mixing is considerably weakened under the existence of buoyancy force, resulting in a slower decay rate of centerline velocity and a narrower jet width for the jet with initial buoyancy.

Model-scale tests to examine water pressures acting on potentially buoyant underground structures in clay strata

Throughout the service life, underground structures are subjected to transient and sustained hydrostatic pressures. The reservoir impoundment results in an increase in water level, as well as hydraulic gradient,which can endanger the uplift performance of infrastructure. In uplift design, a reduction factor is often suggested for buoyant force acting on underground structures in clays due to the time lag effect.However, the mechanism of pore pressure generation in clays is not fully understood. This investigation presents a novel U-shaped test chamber to assess the pore pressure generation with time in the horizontal branch subjected to an increase in reservoir level in the left vertical branch. A mathematical model is developed to explain the time lag effect of pore pressure generation. The test program also involves the evaluation of uplift pressure acting on foundation model in the right vertical branch due to adjacent reservoir impoundment. It is found that the time lag effect of pore pressure generation in clays can be observed irrespective of hydraulic gradient, but a higher hydraulic gradient can lead to a faster response in pore pressure sensors. A reduction factor of 0.84-0.87 should be considered to reduce the conservatism of uplift design.

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT (Ⅰ)-VERIFICATION OF MATHEMATICAL MODEL AND NUMERICAL METHOD

Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation were substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant ver- tical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross-sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.

Steady thermocapillary-buoyant convection in a shallow annular pool.Part 2:Two immiscible fluids

This work is devoted to the study of steady thermocapillary-buoyant convection in a system of two horizontal superimposed immiscible liquid layers filling a lateral heated thin annular pool.The governing equations are solved using an asymptotic theory for the aspect ratios ε→ 0.Asymptotic solutions of the velocity and temperature fields are obtained in the core region away from the cylinder walls.In order to validate the asymptotic solutions,numerical simulations are also carried out and the results are compared to each other.It is found that the present asymptotic solutions are valid in most of the core region.And the applicability of the obtained asymptotic solutions decreases with the increase of the aspect ratio and the thickness ratio of the two layers.For a system of gallium arsenide （lower layer） and boron oxide （upper layer）,the buoyancy slightly weakens the thermocapillary convection in the upper layer and strengthens it in the lower layer.

An experimental research on surface oscillation of buoyant-thermocapillary convection in open cylindrical annuli

An experiment is carried out on the surface oscillation of buoyant-thermocapillary convection in an open cylindrical annulus. When the radial temperature difference AT reaches a critical value △Tc, a regular oscillation appears and soon disappears on the open surface, which varies when the liquid layer＇s thickness h and temperature difference △T are varied. With growth of △T, dominant frequency of the visible oscillation will grow too but is found within certain frequencies. Driving forces, buoyance and thermocapillarity, are responsible for this phenomanon and the ＂balance＂ point is considered to exist when h is between 4.5-5.0 mm. Surface oscillation region is also found restricted within a narrow gap when Bo is smaller than 3.7.

Dilution characteristics of dual buoyant jets in wavy cross-flow environment

Due to the difference in density between the discharge effluent and coastal water,partially treated wastewater is often discharged into the marine environment as a buoyant jet via submarine outfalls with multiport diffusers.The dilution characteristics of effluent discharge(dual buoyant jets)in a wavy cross-flow environment were studied in a laboratory.The planar laser-induced fluorescence technique was used to obtain the concentration data of the jets.The effects of different environmental variables on the diffusion and dilution characteristics of the jets were examined through physical experiments,dimensional analysis,and empirical formulations.It was found that the dilution process of the dual jets could be divided into two components:the original jet component and the effluent cloud component.The jet-to-current velocity ratio was the main parameter affecting the concentration levels of the effluent cloud.The merging of the two jets increased the jet concentration in the flow field.When the jets traveled further downstream,the axial dilution increased gradually and then increased significantly along the axis.Under the effects of strong waves,the concentration contours branched into two peaks,and the mean dilution became more significant than under the effects of weak waves.Therefore,the dilution of the effluent discharge was expected to be significant under strong wave effects because the hydrodynamic force increased.A dilution equation was derived to improve our understanding of the dilution process of buoyant jets in a wavy cross-flow environment.This equation was used to determine the influences of the jet-to-current velocity ratio,wave-to-current velocity ratio,and Strouhal number on the minimum jet dilution.It revealed that the wave and buoyancy effects in effluent discharges were significant.

Steady thermocapillary-buoyant convection in a shallow annular pool. Part 1:Single layer fluid

This paper examines the steady thermocapillarybuoyant convection in a shallow annular pool subjected to a radial temperature gradient. A matched asymptotic theory is used to obtain the asymptotic solutions of the flow and thermal fields in the case of small aspect ratios,which is defined as the ratio of the layer thickness to the gap width. The flow domain is divided into the core region away from the cylinder walls and two end regions near each cylinder wall. Asymptotic solutions are obtained in the core region by solving the core and end flows separately and then joining them through matched asymptotic expansions. For the system of silicon melt,the asymptotic solutions are compared with the results of numerical simulations. It is found that the two kinds of solutions have a good agreement in the core region for a small aspect ratio. With the increase of aspect ratio,the applicability of the present asymptotic solutions decreases gradually.

ROUNDED FLOWING STATES OF OBSTRUCTED BUOYANT JET

The mutual relationships of three effective factors, the diameter D/d （d is the diameter of exit） of obstructed plate, exit densimetric Froude number and the distance Hid of the plate from jet orifice for obstructed buoyant jet in static ambient, are analyzed to explain normal and abnormal rounded flowing （reverberated and bifurcated flowing）. The critical Froude numbers for obstructed buoyant jets with H/d=2, 4, 6, 8 which distinguished normal and abnormal flowing pattern are obtained. Normal rounded flowing is found only for a plate under a special value of H/d. A fitted formula of critical Froude numbers with H/d and D/d is presented to distinguish rounded flowing types. The occurring of reverberated or bifurcated flowing in abnormal rounded flow is analyzed. Based on the results of obstructed buoyant jets with D/d=1, normal rounded flowing occurred only for all conditions and axial dilution behind the plate under different H/D is obtained.

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT (Ⅱ)-ANALYSIS ON BEHAVIOR OF FLOW FIELD

Based on a series of numerical calculations, the behavior of flow field in obstructed square buoyant vertical jet is summarized and analyzed. Based on the axial line velocity distribution, the flow after the disc can be divided into three regions, i.e., recirculation region, transitional region and self-similar region The characteristic of selfsimilarity of upright velocity was validated. The three regions can also be distinguished based on the axial velocity. The axial velocity in self-similar region was found to obey the same law and the formula presented by introducing the velocity expression used by Chen and Rodi. The isolines of pressure on cross-sections of different heights were displayed and the production, expansion, breaking and disappearing of negative pressure regions were found.

STUDY ON ANISOTROPIC BUOYANT TURBULENCE MODEL

By analyzing the components of Reynolds stresses of implicit algebraic stress model(IASM) in this paper, that Reynolds stresses in buoyant turbulent flows were produced by both strain and buoyancy is considered. Consequently, a nonlinear anisotropy buoyant turbulence model was developed by applying linearity of equilibrium hypothesis to Reynolds stress transports. The model avoids numerical singularity and its reliability is verified by the comparisons between predictions and experimental data.

LIF Measurement of the Diluting Effect of Surface Waves on Turbulent Buoyant Plumes

In this paper, the diluting effect of surface waves on a buoyant plume has been measured using a Laser Induced Fluorescence (LIF) technique. The resulting time-averaged, full field concentration maps have allowed quantification of enhanced mixing due to surface waves as well as measurement of other plume parameters.

A Buoyant Export Market For Yangzi Company's Petrochemical Products

In face of the rapid fall in prices on theworld petrochemical product market, ChinaPetrochemical International Business YangziCorporation (CPIBYZC) took active meas-ures to regulate its product mix, and by theend of November 1996, it had earned foreignexchange through the export of US＄76 mil-lion, emerging from the quagmire of foreigntrade. The import and export operations ofthe very large Yangzi Petrochemical Corpo-

Explicit Algebraic Stress Model for Three-Dimensional Turbulent Buoyant Flows Derived Using Tensor Representation

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.

MEAN BEHAVIOR OF THREE DIMENSIONAL LINE BUOYANT JETS IN CROSS FLOWS

This paper presents the results of a numerical calculation on the meanbehavior of finite length line buoyant jets from slot with width B , discharged perpendicularly intorelatively deep cross-flows in the mixing region. The length of diffuser was varied from 4 to 20times the width of diffuser. The calculations were performed with the standard K-ε model and HybridFinite Analytic Method (HFAM) with staggered grid. The phenomenon and development of vortex pairsare simulated successfully and the influence of diffuser length and buoyant on turbulent buoyantjets are analyzed.

STABILITY AND MIXING CHARACTER FOR BUOYANT JETS IN QUIESCENT SHALLOW WATER

The near field stahility and mixing characteristics of buoyant jets produced by thermal diffuse in quiescent shallow water are inw.stigated numerically to predict under what combinations of discharge and ambient characteristics the near field will be stable or unstable, Analyses for different discharging types show that the discharge stability is purely dependent on the near-field hehavior of the jets, or the dynam ic interaction of the buoyant jet region, the surface impinge ment region and the internal hydraulic jump region, and is independent of the far-field geometry of the receiving water. The stability criterion is a function of the relative submerged depth, and source densimetrie Froude number.

Flow instability of buoyant-Marangoni convection in the LEC GaAs melt

Flow transitions and instabilities have significant effects on the quality of the crystals. The flow and heat transfer in the LEC GaAs melt are numerically studied by a time-dependent and three-dimensional turbulent flow model. The effects of the change of the buoyancy and Marangoni force on the flow state are analyzed by changing the temperature difference between the crystal and the crucible walls. The results show that the flow will transform from axisymmetric steady flow to non-axisymmetric oscillatory flow when the temperature difference exceeds the critical value, and that the mechanism of the transition is attributed to the Marangoni instability. The critical temperature differences for the flow transitions corresponding to different melt depth H are numerically predicted. Several important characteristics of the non-axisymmetric buoyant-Marangoni convection are numerically observed and compared with that of the non-axisymmetric mixed convection coupled with crystal rotation.

Effects of three positively buoyant dietary supplements on the buoyancy of feces,growth and intestinal health of Tilapia,Oreochromis niloticus
O.aureus

Two trials were conducted to evaluate the effects of positively buoyant dietary materials on growth,intestinal health,and fecal properties of tilapia.In trial 1,ten diets containing 0(control)1%,2%or 3%cork,expanded and vitrified microball or expanded vermiculilite fine particles(250e450 mm)were fed to tilapia fry(5.0±0.1 g)for 30 days to evaluate the effects on the growth and feeding efficiencies.In trial 2,the three buoyant materials with coarse particles(450e830 mm)were included in diets at 0(control),3%,4%or 5%supplementation levels to feed tilapia juveniles(55.0±1.0 g),and the growth,feed efficiencies,evacuation velocity,fecal floatability and intestinal histology were examined after 21 days feeding.In trial 1,the weight gain(WG)of the fish significantly decreased with the supplementation of 2%,3%cork,3%microball or 3%vermiculite(P<0.05),and the feed conversion ratio(FCR)was significantly increased by 3%cork and 3%vermiculite(P<0.05)when compared to the control.In trial 2,cork-fed groups were observed to have more floating feces than microball-and vermiculite-fed groups.Dietary cork significantly decreased the sinking velocity of diets and feces(P<.05),but microball only decreased the sinking velocity of diets,and vermiculite(4%,5%)decreased the sinking velocity of feces(P<0.05).All buoyant materials supplemented groups showed lower WG and higher FCR than the control(P<.05).The intestine evacuation velocity and villus height,crypt depth,muscle thickness of intestinal walls were decreased by the increasing buoyant materials in diets,and 5%microball group showed the lowest values among all groups.In conclusion,dietary cork,microball and vermiculite(3%e5%)negatively affect the growth performance and intestinal histology of tilapia,and diets with cork supplementation could decrease the density of feed and feces to produce floating feces.