The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation

The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.

Parameterization of Sheared Entrainment in a Well-developed CBL.PartⅡ:A Simple Model for Predicting the Growth Rate of the CBL

Following the parameterization of sheared entrainment obtained in the companion paper, Liu et al. （2016）, the present study aims to further investigate the characteristics of entrainment, and develop a simple model for predicting the growth rate of a well-developed and sheared CBL. The relative stratification, defined as the ratio of the stratification in the free atmosphere to that in the entrainment zone, is found to be a function of entrainment flux ratio （Ae）. This leads to a simple expression of the entrainment rate, in which Ae needs to be parameterized. According to the results in Liu et al. （2016）, Ae can be simply expressed as the ratio of the convective velocity scale in the sheared CBL to that in the shear-free CBL. The parameterization of the convective velocity scale in the sheared CBL is obtained by analytically solving the bulk model with several assumptions and approximations. Results indicate that the entrainment process is influenced by the dynamic effect, the interaction between mean shear and environmental stratification, and one other term that includes the Coriolis effect. These three parameterizations constitute a simple model for predicting the growth rate of a well-developed and sheared CBL. This model is validated by outputs of LESs, and the results show that it performs satisfactorily. Compared with bulk models, this model does not need to solve a set of equations for the CBL. It is more convenient to apply in numerical models.

Experimental investigation on debris flow resistance and entrainment characteristics:effects of the erodible bed with discontinuous grading

Debris flow deposits in natural channels typically have a wide grain size distribution(GSD).The effects of bed sediment GSD on the basal entrainment rate are neglected in current debris flow erosion models.Field investigations have detected three different vertical graded bedding structures:normal,inverse,and mixed-gradation,characterized by discontinuous gradation sediment and almost without intermediate-sized particles.This study conducted small-scale flume experiments to investigate the debris flow resistance forces and entrainment characteristics by incorporating the effects of discontinuous grading bed sediments.Discontinuous graded bed sediments with varying fine particle content,volumetric water content(VWC),and roundness were designed for comparison.Debris flow resistance in erodible beds generally increased in the group with gravel of larger-sized coarse particle,lower roundness,and higher bed sediment VWC.For discontinuous grading bed sediment,the entrained depths increased in the group with gravel of smaller coarse particle sizes,larger amounts of fine particles,and higher sediment roundness,and decreased with larger VWCs.This abnormality may be attributed to the disproportionately large effects of viscous flow resistance in our small-scale flume tests.The maximum erosion rates of the continuous bed sediment were higher than those of the corresponding discontinuous bed sediment with the same maximum coarse gravel size.This is because,for discontinuous grading bed sediments,localized failure of intermediate-sized sediment grains may cause a large-scale collapse of the solid grain skeleton and enhance basal entrainment rates.A revised formula for calculating the debris flow entrainment rate is proposed by incorporating the kurtosis coefficient,which describes the distribution of discontinuous bed sediments and fine particle content.Our revised formula could facilitate an elaborate estimation of basin erosion and sediment runoff and reveal the development and recession of debris flow fans.

Gustiness and Coherent Structure of Strong Winds and Their Role in Dust Emission and Entrainment

After the passage of a cold front, spring in northern China, the outbreak of strong wind is often accompanied by dust emissions. Through analyses of data in the atmospheric boundary layer during a typical case, it is revealed there are rather regular gust wave packets superimposed on the basic strong wind flow. The gust-wind wave packets have a period equal to around 3 6 rains and possess coherent structure. As the vertical transport of momentum is decomposed into separate parts by （a） basic flow, （b） gust-wind, and （c） turbulence, they are all in a downwards direction at the lower levels of the atmospheric boundary layer during strong wind periods. However, （a） is the largest, while （b） and （c） are comparable. All these are very different from the case of normal weather. Besides, the friction velocity at the ground surface is also much larger than that of normal weather and should be corrected by taking the contributions of the basic flow and gust-wind into account.The strong basic flow with descending motion is very favorable for soil erosion and sand/dust emissions, but suppresses the entrainment of dust particles by keeping them within the bottom levels of the atmospheric boundary layer. Owing to the coherent structure of gust-wind, dust particles can effectively overcome the systematic descending air motion and penetrate into the middle and upper levels of the atmospheric boundary layer, and then propagate further and diffuse into the troposphere where ascending air motion prevails.

Statistical evaluation of flotation and entrainment behavior of an artificial ore

The role of several parameters on gangue recovery in froth was investigated. Effects of frother type and collector dosage on flotation performance were tested at pH 10. The results were evaluated statistically by two-way analysis of variance without replicates, sample range and sample standard deviation. Hydrophilic mineral was recovered mainly by entrainment through hydrophobization of Ca＋2-activated quartz from tap-water in the presence of Na-oleate as collector; entrapment and slime coating were also proposed as recovery mechanisms in minority. Degree of gangue-entrainment in froth product increases by reduction in liberation size. The experimental results state that selectivity would be improved by increasing collector concentration and reducing the flotation time.

Parameterization of Sheared Entrainment in a Well-Developed CBL.Part I:Evaluation of the Scheme through Large-Eddy Simulations

The entrainment flux ratio Ae and the inversion layer （IL） thickness are two key parameters in a mixed layer model. Ae is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of Ae is derived from the TKE budget in the first- order model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness, The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized Ae and IL thickness agree well with the LES outputs.

Experimental Study on Aqueous Phase Entrainment in a Mixer-settler with Double Stirring Mode

The mixer-settler is a core device of solvent extraction for separating rare earth elements. There are some adverse effects like high rare earth accumulation and poor production efficiency during industrial production. Current researches usually focus on changing the structure of the mixer-settler without making a breakthrough towards gravity clarification. In this paper, in order to improve the efficiency of clarification, a mixer-settler with double stirring mode was designed and manufactured by adding a stirring device in the settler after reducing the volume of the settler. The innovation of this research involves adopting the ultraviolet-visible spectrophotometer to investigate the quantity of aqueous phase entrainment at the settler outlet in order to measure the clarification degree. Experimental results show that the clarification effect with stirring is better than that without stirring. The clarification effect is ameliorated as the stirring speed increases. Generally, the clarification effect shows a best condition when the offset distance is 12.5 cm, making the phase entrainment reduced to less than 0.1%. When the clearance over the tank bottom is 7 cm and 10 cm, respectively, the quantity of aqueous phase entrainment is better than the case with a clearance of 4 cm. The results show that the stirring paddle close to the mixed phase zone can better promote the two-phase separation.

Simulation study on factors influencing the entrainment behavior of liquid steel as bubbles pass through the steel/slag interface

In this study, a water/silicone oil interface was used to simulate the steel/slag interface in a converter. A high-speed camera was used to record the entrainment process of droplets when air bubbles were passed through the water/silicone oil interface. Motion parameters of the bubbles and droplets were obtained using particle kinematic analysis software, and the entrainment rate of the droplets was calculated. It was found that the entrainment rate decreased from 29.5% to 0 when the viscosity of the silicone oil was increased from 60 mPa.s to 820 mPa.s in the case of bubbles with a 5 mm equivalent diameter passing through the water/silicone oil interface. The results indicate that in- creasing the viscosity of the silicone oil is conducive to reducing the entrainment rate. The entrainment rate increased from 0 to 136.3% in the case of silicone oil with a viscosity of 60 mPa.s when the equivalent diameter of the bubbles was increased from 3 mm to 7 ram. We there- fore conclude that small bubbles are also conductive to reducing the entrainment rate. The force analysis results for the water colmnn indicate that the entrainment rate of droplets is affected by the velocity of the bubble passing through the water/silicone oil interface and that the en- trainment rate decreases with the bubble velocity.

Parameterization for the Depth of the Entrainment Zone above the Convectively Mixed Layer

It has been noted that when the convective Richardson number Ri* is used to characterize the depth of the entrainment zone, various parameterization schemes can be obtained. This situation is often attributed to the invalidity of parcel theory. However, evidence shows that the convective Richardson number Ri* might be an improper characteristic scaling parameter for the entrainment process. An attempt to use an innovative parameter to parameterize the entrainment-zone thickness has been made in this paper. Based on the examination of the data of water-tank experiments and atmospheric measurements, it is found that the total lapse rate of potential temperature across the entrainment zone is proportional to that of the capping inversion layer. Inserting this relationship into the so-called parcel theory, it thus gives a new parameterization scheme for the depth of the entrainment zone. This scheme includes the lapse rate of the capping inversion layer that plays an important role in the entrainment process. Its physical representation is reasonable. The new scheme gives a better ordering of the data measured in both water-tank and atmosphere as compared with the traditional method using Ri*. These indicate that the parcel theory can describe the entrainment process suitably and that the new parameter is better than Ri*.

Air entrainment in a vertical dropshaft with limited air supply

Dropshafts are vertical structures widely used in urban drainage systems and buildings for water transportation.In this paper,a physical model study was conducted to investigate the air entrainment in the dropshaft under various flow regimes with and without air ventilation.Observed from the experiments,the air entrainment mechanisms varied with the water flow regimes in the dropshaft.When there was no water plug formed in the dropshaft,air could be supplied directly from downstream.Once the water plug was formed,while without venting,the air was replenished only from downstream intermittently and then in the form of large air bubble traveling upwards to the airspace at the top;while with venting,air was mainly replenished from the dropshaft top and no large air bubble was observed.The experimental results also showed that the amount of entrained air in the dropshaft with venting was greater than that without venting.

Bubble entrainment, spray and splashing at hydraulic jumps

The sudden transition from a high-velocity, supercritical open channel flow into a slow-moving sub-critical flow is a hydraulic jump. Such a flow is characterised by a sudden rise of the free-surface, with some strong energy dissipation and air entrainment, waves and spray. New two-phase flow measurements were performed in the developing flow region using a large-size facility operating at large Reynolds numbers. The experimental results demonstrated the complexity of the flow with a developing mixing layer in which entrained bubbles are advected in a high shear stress flow. The relationship between bubble count rates and void fractions was non-unique in the shear zone, supporting earlier observations of some form of double diffusion process between momentum and air bubbles. In the upper region, the flow consisted primarily of water drops and packets sur-rounded by air. Visually significant pray and splashing were significant above the jump roller. The present study is the first com-prehensive study detailing the two-phase flow properties of both the bubbly and spray regions of hydraulic jumps, a first step towards understanding the interactions between bubble entrainment and droplet ejection processes.

Entrainment effects and the dynamical evolution of debris avalanche/flow on substrate materials

A pair of flumes with variable inclinations were employed to investigate the entrainment mechanics and dynamical evolution of a debris avalanche/flow. A fixed quantity of solid and water mixture was released from a constant elevation and accelerated along a higher chute to impact substrate materials with different water contents and particle size distributions in the lower chute. Two high-speed cameras, pore and earth pressure detecting devices, were placed in the substrate materials where severe scouring occurs in order to collect multiple measurements of dynamical and mechanical parameters. The entrainment dynamics were verified by geometrical analysis and quasi-static simulation. The results show that wet and fine materials that are placed in the lower chute with steeper slopes are easily entrained during debris flow initiation, the pattern of which can be described by Coulomb friction and the Mohr-Coulomb law. Elaborate measurements of dynamical parameters enable the results of an elementary computational framework to predict the time-dependent scouring depth ht, which provides insight into rapidly determining debris flow propagation. Finally, the post-entrainment dynamics were studied. The results indicate that the propagation and the amplification of debris flows along erodible beds are dominated by the velocity and the solid volume fraction of the mixed substrate, and the coarse particle group of the substrate is a key feature affected by momentum changes.

Comparison of the entrainment rate of debris flows in distinctive triggering conditions

Debris flows can be extremely destructive because they can increase in magnitude via progressive entrainment. In this paper, a total of 18landslide-type debris flows and 268 channelized debris flows in Wenchuan earthquake and Taiwan region, as well as other regions were collected to analyze the entrainment rate of debris flows in each triggering condition. Results show that there is a power relationship between volume of initial triggered mass and final deposited debris for landslide type debris flow. The debris flows during2008 and 2013 in Wenchuan earthquake-region have smaller entrainment rate than that from 2001 t02009 in Taiwan. The entrainment rate of debris flow events from 2001 to 2009 in Taiwan shows a decaying tendency as elapsed time. Comparison of the entrainment rate in the two earthquake-hit regions with other regions proves that entrainment rate has a close relation with major sediment availability and secondary rainstorm conditions.

Experimental study of entrainment behavior of debris flow over channel inflexion points

On-spot observation and field reconnaissance of debris flows have revealed that inflexion points in the longitudinal profile of a movable channel may easily become unstable points that significantly affect their entrainment behavior.In this study,small-scale flume experiments were performed to investigate the entrainment characteristics of debris flows over two types of inflexion points,namely,a convex point,which has an upslope gradient that is less than the downslope gradient,and a concave point,which has an upslope gradient that is greater than the downslope gradient.It was observed that when debris flowed over a convex point,the entrainment developed gradually and progressively from the convex point in the downstream direction,and the primary control factors were the slope gradient and friction angle.Conversely,when debris flowed over a concave point,the entrainment was characterized by impacting and impinging erosion rather than traditional hydraulic erosion,and the impingement angle of the flow significantly determined the maximum erosion depth and outflow exit angle.An empirical relationship between the topography change and the control factors was obtained from the experimental data.

Effect of carrier gases on the entrainment defects within AZ91 alloy castings

An entrainment defect(also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres(i.e., SF6/CO2, SF6/air).The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.

Mold flux entrainment mechanisms

This paper presents a comprehensive and critical review of mold flux entrainment mechanisms in continuous casting of steel.Entrainment introduces inclusions into the final product,and thus greatly hinders clean steel production.By understanding the mechanisms that cause entrainment,the operating conditions of casters can be tuned to reduce the number of defects.Nine different mechanisms have been proposed over the last three decades,including vortex formation around the submerged entry nozzle(SEN),argon bubble interactions with the slag layer,shear-layer instability at the slag-steel interface,excessive upward flow impingement upon the meniscus, top surface level fluctuations,meniscus freezing and hook formation,top surface "balding",top surface standing wave instability,and slag crawling down the SEN.The previous work done for each of these mechanisms is presented,including both quantitative and qualitative descriptions of their behavior.

Air Entrainment and Pressure Fields over Stepped Spillway in Skimming Flow Regime

This paper deals with some aspects of the air entrainment process along the chute of spillway and study of pressure fluctuations. The experimental study has been carried out using stepped spillway model located in the campus of Government College of Engineering, Amravati (India). It is observed that air concentration is increasing with discharge as well as with number of step. Air concentration is increasing along the length of spillway. It is also observed that the bottom mean air concentration increases with step height in the upstream reach of stepped spillway, which is prone to cavitation. The pressure profiles exhibit a wavy pattern down the stepped chute and pressure on each step increases with ratio of critical depth to step height (yc/h).

Entrainment range affected by the heterogeneity in the amplitude relaxation rate of suprachiasmatic nucleus neurons

Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has been found that the SCN neurons differ in the amplitude relaxation rate, which represents the rigidity of the neurons to the external amplitude disturbance. Thus far, the appearance of that difference has not been explained. In the present study, an alternative explanation based on the Poincare′ model is given which takes into account the effect of the difference in the entrainment range of the SCN. Both our simulation results and theoretical analyses show that the largest entrainment range is obtained with suitable difference in the case that only a part of SCN neurons are sensitive to the light information. Our findings may give an alternative explanation for the appearance of that difference(heterogeneity) and shed light on the effects of the heterogeneity in the neuronal properties on the collective behaviors of the SCN neurons.

Investigation on balcony plume entrainment

An investigation on the scenarios of the spill plume and its equation was presented,including two aspects,i.e.,the small-scale experiment and the numerical simulation. Two balcony spill plume models are assessed by comparing with the fire dynamic simulation (FDS) and small scale model experiment results. Besides validating the spill model by experiments,the effect of different fire locations on balcony plume is also discussed. The results show that the balcony equation in NFPA gives good predictions on the mass flow rate. And the balcony plume entrainment coefficient is independent of the fire location. This investigation is useful for the fire engineers in designing smoke control systems.

Entrainment range affected by the difference in sensitivity to light-information between two groups of SCN neurons

The mammals can not only entrain to the natural 24-h light–dark cycle, but also to the artificial cycle with non 24-h period through the main clock named suprachiasmatic nucleus in the brain. The range of the periods of the artificial cycles which the suprachiasmatic nucleus(SCN) can entrain, is called entrainment range reflecting the flexibility of the SCN. The SCN can be divided into two groups of neurons functionally, based on the different sensitivities to the light information. In the present study, we examined whether the entrainment range is affected by this difference in the sensitivity by a Poincaré model. We found that the relationship of the entrainment range to the difference depends on the coupling between two groups. When the coupling strength is much smaller than the light intensity, the relationship is parabolic-like, and the maximum of the entrainment range is obtained with no difference of the sensitivity. When the coupling strength is much larger than the light intensity, the relationship is monotonically changed, and the maximum of the entrainment range is obtained when the difference is the largest. Our finding may provide an explanation for the exitance of the difference in the sensitivity to light-information as well as shed light on how to increase the flexibility of the SCN represented by widening the entrainment range.