Influence of Downstream Control and Limited Depth on Flow Hydrodynamics of Impinging Buoyant Jets

Much study has been performed on the mixing properties of submerged, turbulent buoyant jets. It is safe to say that the problem of estimating dilution rates in vertical buoyant jets spreading in an `infinitely deep' ambient water has been more than adequately resolved by previous researchers. However, the majority of environmental applications involve discharges into ambient waters of finite depths in which a bounding surface serves to re-direct the impinging buoyant jet horizontally into a radial spreading layer. Previous research indicates that this impinging jet undergoes additional mixing before buoyancy stabilizes vertical mixing and confines the spreading layer to the vicinity of the bounding surface. Unfortunately, the conceptualization and subsequent mathematical modeling of this additional mixing phenomenon is surrounded by considerable amount of disagreement between researchers. The purpose of this study is to provide, by means of velocity and concentration profile measurements, independent experimental evidence for the existence of a critical flow state immediately downstream of the active mixing zone in the horizontally flowing, radial flow that forms after impingement. It is further shown that this critical flow state must be expressed in terms of a composite Froude Number that takes into account the possibility of a non-zero exchange layer flow. Finally, the influence of the presence of a sill-like topographic downstream control on the criticality of the radial flow immediately downstream of the active mixing zone is also investigated.     

Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects

In hydraulic structures, free-surface aeration is commonly observed: i.e., the white waters. The air bubble entrainment may be localised (hydraulic jumps, plunging jets) or continuous along an interface (water jets, chutes). Despite recent advances, there are some basic concerns about the extrapolation of laboratory results to large size prototype structures. Herein the basic air bubble entrainment processes are reviewed and the relevant dynamic similarities are discussed. Traditionally, physical studies are conducted using a Froude similitude which implies drastically smaller laboratory Reynolds numbers than in the corresponding prototype flows. Basic dimensional analyses are developed for both singular and interfacial aeration processes. The results are discussed in the light of systematic investigations and they show that the notion of scale effects is closely linked with the selection of relevant characteristic air–water flow properties. Recent studies of local air–water flow properties highlight that turbulence levels, entrained bubble sizes and interfacial areas are improperly scaled based upon a Froude similitude even in large-size models operating with the so defined Reynolds numbers ρ _w × q _w/μ _w up to 5 E+5. In laboratory models, the dimensionless turbulence levels, air–water interfacial areas and mass transfer rates are drastically underestimated.     

外立面作用下水平湍流浮力射流火焰的附壁研究

用防火板模拟建筑外立面,设计了可控流速和开口尺寸的气体燃烧器产生水平湍流浮力射流火焰,系统研究了外立面抑制火焰卷吸所导致的水平湍流浮力射流火焰附壁规律。将火焰流场演变分为两个阶段:(1)出口到流场水平动量衰减为零(等价点)的阶段;(2)火焰附壁或不附壁的阶段。其中,火焰附壁与否很大程度上取决于等价点到出口的水平距离LE。通过分析,我们发现雷诺应力是导致流场水平动量衰减和火焰附壁的主要原因。由此,我们基于普朗特混合长度理论推导了雷诺应力的近似表达式并结合动量控制方程,获得了LE与修正弗洛德数Fr*的线性关系,从理论上解释了出口宽高比n(n=B/H,B是开口宽度;H是开口高度)越大,火焰越容易附壁的现象,并确定了不同开口及流速条件下,火焰附壁的临界条件。     

On Disturbances Introduced by Impulse Source into Stratified Two-Component Media

The paper considers the problem concerning the response of a stably stratified two-component medium (salt water, moist air) in the presence of a stationary source of vertical impulse. For a homogeneous vertical distribution of the impulse source (i.e., the applied vertical force), due to the symmetry of the problem, one succeeded in finding the explicit analytical solution of the stationary problem for arbitrary source amplitude. The solution is expressed through Kelvin’s cylindrical functions and represents the stationary vertical jet. The two-component character of the medium can influence substantially the quality of the properties of the solution. In particular, the jet parameters are not defined uniquely by the buoyancy frequency (density stratification). In the solution, the stratifications of the two hydrodynamic components have the distinctive influences that are defined by values of corresponding exchange coefficients. For example, in salt water the solution dependence on salinity stratification may be much more than on temperature stratification.     

Vertical Buoyant Jets in a Linearly Stratified Ambient Cross-Stream

In this study a numerical simulation is performed to investigate the effect of ambient density stratification on the characteristic of a vertical buoyant jet in a stably linearly stratified ambient cross-stream. Based on the ensemble integral method, the theoretical formulation for such a flow field consists of a set of elliptic Reynolds-averaged equations incorporating with the k– transport equations for the turbulence closure. An oscillating motion can be observed in the computed jet trajectory, and the corresponding alternative variation of dominant quantities for the induced momentum and buoyancy of the jet are examined by direct integration on a cross-section along the jet axis. The influences on the jet development both by the ambient cross-stream and the stratification are investigated. The oscillation characteristic shows that a linear relation holds between the wavenumber of jet trajectory, crossflow velocity and the Brunt–Väisälä frequency of ambient stratification. Computational results indicate that the formation of the secondary and a third pairs of vortices, which are not induced in the unstratified environment, causes the jet flow oscillation from its maximum height-of-rise in the flowing direction. The ambient stratification prohibits the growth of the plume radius and reduces the mixing rate as well as the plume rise. The developed flow indicates the transformation of entrainment mechanism in stratified crossflow.     

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.     

Rain-out investigation: Initial droplet size measurement

Droplet size distribution inside water flashing jets and corresponding rain-out fraction were measured. Mass distribution showed that a few droplets are ‘large’ (d>150 μm) and count for more than 85% of the liquid mass in the jet because of their large individual mass. This could be due to incomplete thermal fragmentation. It could explain the rain-out falling near the orifice or pipe exit.