Investigation of scalar measurement error in diffusion and mixing processes

In variable density, multi-fluid and reacting flows, the degree of molecular mixing is a critical component of turbulent transfer and mixing models. Also, in many microflows and low Reynolds number flows, scalar diffusion length- and time-scales play a significant role in the mixing dynamics. Characterization of such molecular mixing processes requires scalar measurement devices with a small probe volume size. Spatial averaging, which occurs due to finite probe volume size, can lead to errors in resolving the density or scalar gradients between pockets of unmixed fluids. Given a probe volume size and a priori knowledge of the functional profile of the diffusion layer being measured, we obtain an estimate for the measurement error due to spatial averaging and make the corrections accordingly. An analytical model for the measure of scalar mixing is developed as a predictor for the growth of scalar gradients in a variable scalar flow. The model is applied to a buoyancy-driven mixing layer with a Prandtl number of 7. Measurements within the mixing layer have shown that initial entrainment of unmixed fluid causes a decrease in the measured amount of molecular mixing at the centerplane. Following this period of initial entrainment, the fluids within the mixing layer exhibit an increase in the degree of molecular mixing.     

A model for droplet entrainment in heated annular flow

The ability to accurately predict droplet entrainment in annular two-phase flow is required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. Most annular flow entrainment models in the open literature are formulated in terms of dimensionless groups, which do not directly account for interfacial instabilities. However, many researchers agree that there is a clear presence of interfacial instability phenomena having a direct impact on droplet entrainment. The present study proposes a model for droplet entrainment, based on the underlying physics of droplet entrainment from upward co-current annular film flow that is characteristic to light water reactor safety analysis. The model is developed based on a force balance and stability analysis that can be implemented into a transient three-field (continuous liquid, droplet, and vapor) two-phase heat transfer and fluid flow systems analysis computer code.     

An experimental study of unsteady natural convection in a reservoir model subject to periodic thermal forcing using combined PIV and PIT techniques

The present experimental investigation is concerned with the transient flow response in a reservoir model to periodic heating and cooling at the water surface. The experiment reveals a stable stratification of the water body during the heating phase and an unsteady mixing flow in the reservoir during the cooling phase. It is shown that thermal instabilities play an important role in breaking up the residual circulation and initiating a reverse flow circulation in deep waters after the switch of thermal forcing from heating to cooling. Moreover, the heating from the water surface results in a stable large-scale convective roll that is clearly observed in the experiment. The present flow visualization is carried out with the application of thermo-chromic liquid crystals. Quantitative temperature and velocity fields are extracted using Particle Image Thermometry and Particle Image Velocimetry techniques. Understanding of the flow mechanisms pertinent to this problem is important for predicting the transport of nutrients and pollutants across reservoirs.     

Modeling of droplet entrainment phenomena at a quench front

The phenomena of droplet entrainment at a quench front is of practical importance as a clear understanding of the underlying mechanisms required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. The present study proposes a model for droplet entrainment at a quench front that is based on the best-understood physics related to the Lagrangian quenching phenomenon characteristic to light water reactor (LWR) safety analysis. The model is based on a film boundary layer and stability analysis that attempts to match the characteristic time and length scales of the entrainment phenomenon. This model has been developed such that direct implementation can be made into any two-phase flow simulation code with a three-field (continuous liquid, droplet, and vapor) flow model. Comparisons with integrated transient test data independent of those used for model development have been performed to verify the applicability of the proposed model for the prediction of the entrainment rate of liquid droplets at a quench front under typical reflood conditions envisioned in LWRs.     

Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part I: Subsonic Flow

The mixing and flowfield of a complex geometry, similar to a rearward-facing step flow but with injection, is studied. A subsonic top-stream is expanded over a perforated ramp at an angle of 30°, through which a secondary stream is injected. The mass flux of the second stream is chosen to be insufficient to provide the entrainment requirements of the shear layer, which, as a consequence, attaches to the lower guidewall. Part of the flow is directed upstream forming a re-entrant jet within the recirculation zone that enhances mixing and flameholding. A control-volume model of the flow is found to be in good agreement with the variation of the overall pressure coefficient of the device with variable mass injection. The flowfield response to changing levels of heat release is also quantified. While increased heat release acts somewhat analogously to increased mass injection, fundamental differences in the flow behaviour are observed. The hypergolic hydrogen-fluorine chemical reaction employed allows the level of molecular mixing in the flow to be inferred. The amount of mixing is found to be higher in the expansion-ramp geometry than in classical free-shear layers. As in free-shear layers, the level of mixing is found to decrease with increasing top-stream velocity. Results for a similar configuration with supersonic flow in the top stream are reported in Part II of this two-part series.     

A multiphase model for the hydrodynamics and total dissolved gas in tailraces

Elevated supersaturation of total dissolved gas (TDG) has deleterious effects in aquatic organisms. To minimize the supersaturation of TDG at hydropower dams, spillway flow deflectors redirect spilled water horizontally forming a surface jet that prevents bubbles from plunging to depth in the stilling basin.     

A semi-implicit lagrangian scheme for 3D shallow water flow with a two-layer turbulence model

A semi-implicit Lagrangian finite difference scheme for 3D shallow water flow has been developed to include an eddy viscosity model for turbulent mixing in the vertical direction. The α-co-ordinate system for the vertical direction has been introduced to give accurate definition of bed and surface boundary conditions. The simple two-layer mixing length model for rough surfaces is used with the standard assumption that the shear stress across the wall region at a given horizontal location is constant. The bed condition is thus defined only by its roughness height (avoiding the need for a friction formula relating to depth-averaged flow, e.g. Chezy, used previously). The method is shown to be efficient and stable with an explicit Lagrangian formulation for convective terms and terms for surface elevation and vertical mixing handled implicitly. The method is applied to current flow around a circular island with gently sloping sides which produce periodic recirculation zones (vortex shedding). Comparisons are made with experimental measurements of velocity using laser Doppler anemometry (time histories at specific points) and surface particle-tracking velocimetry.     

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.     

Liquid and gas entrainment to a small break hole from a stratified two-phase region

A theoretical and experimental study has been conducted for liquid and gas entrainment to a small break hole from a stratified two-phase region. Theoretical correlations previously obtained for top, side and bottom entrainment were modified to express the relation between break flow rate, break quality and bulk water level so that they can be used easily for any break geometry. The modified correlations were assessed with experimental data obtained under room temperature and low pressure conditions using air and water. The experiment results were predicted well with the present model without using any adjustment coefficient when the upstream flow was symmetrical around the break. The effects of vortex, crossflow and wavy flow, observed in the experiment but not taken into account in the model, were empirically correlated based on the present correlation. By using the empirically modified correlations, the data in the literature, including high-pressure steam-water conditions, were reasonably predicted.     

Convective transport of air bubbles in strong hydraulic jumps

A hydraulic jump is a flow singularity characterised by a significant amount of air entrainment in the shear zone. The air is entrapped at the jump toe that is a discontinuity between the impinging flow and the roller. The impingement point is a source of air bubbles, as well as a source of vorticity. Herein the convective transport of air bubbles in the jump roller is re-visited. Some analytical extension is presented and the theoretical results are compared with some laboratory experiments conducted in a large-size facility operating at large Froude numbers. The turbulent air bubble mixing coefficient was found to increase linearly with increasing distance and be independent of the Froude and Reynolds numbers. Overall the study highlighted some seminal features of the air–water shear layer in hydraulic jumps with large Froude numbers (5.1 < Fr₁ < 11.2). The air bubble entrainment in the mixing zone was a convective transport process, although there was some rapid flow de-aeration for all Froude numbers.     

Numerical modeling of downslope flows of different rheology

Naturally occurring flow along a long homogeneous slope is numerically simulated. It is taken into account that the flow is able to capture the slope material and to entrain it into motion. The flow depth and velocity increase with time at the expense of the capture. The medium in motion is simulated using different rheological models including those of Herschel & Bulkley and Cross, as well as the power-law fluid model. For all the models the time dependences of the total depth and the mean flow velocity are obtained. The slope inclination effect on the dynamic flow parameters is studied. For the Herschel–Bulkley model the yield strength effect is also investigated. On the basis of the numerical calculations some assumptions are made and then used to derive asymptotic formulas for the bottom material entrainment rate at large times from the entrainment onset for all the above-listed rheological models.     

Experimental investigation and theoretical modeling of liquid entrainment in a horizontal tee with a vertical-up branch

This article describes a comprehensive literature review of liquid entrainment in horizontal pipes with vertical-up branches. Deficiencies in the available data and correlations were identified. The Air–water Test Loop for Advanced Thermal–hydraulic Studies (ATLATS) was constructed and entrainment onset and steady-state data were collected for a wide range of flow conditions. Using new insights gained from experimental testing, the authors developed a model for predicting the onset of entrainment and steady-state entrainment rate. Previously published correlations, along with the new model, are compared against all available data. The new model shows very good agreement with the onset data, but is not very good at predicting branch quality at high liquid flow rates.     

A study of thin water film flow down an inclined plate without and with countercurrent air flow

Characteristics of thin water film flow down an inclined plane surface without as well as with superposed countercurrent air flow were studied experimentally. Three different angles of inclination of the channel with horizontal were investigated. At each inclination angle, five film Reynolds numbers were studied. Experiments were performed beginning at zero air flow and then increasing the air flow rate in steps until water entrainment occurred. Visual observation of the film surface was carried out as were film thickness measurements by means of capacitance probes. Results presented include mean film thickness and distribution, frequency spectra and propagation velocities of interfacial disturbances, and the incipience condition for entrainment of water from the film into the air stream.     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part II: Analysis and comparison to models

Film thickness distributions in upward vertical air–water annular flow have been determined using planar laser-induced fluorescence (PLIF). Film thickness data are frequently used to estimate interfacial shear and pressure loss. This film roughness concept has been used in a number of models for annular flow of varying complexity. The PLIF data are presently applied to the single-zone interfacial shear correlation of Wallis; the more detailed model of Owen and Hewitt; and the two-zone (base film and waves) model of Hurlburt, Fore, and Bauer. For the present data, these models all under-predict the importance of increasing liquid flow on pressure loss and interfacial shear. Since high liquid flow rates in annular flow induce disturbance wave and entrainment activity, further modeling in these areas is advised.     

A preliminary laboratory study of the lateral entrainment of non-local waters by a subsurface mesoscale eddy

Most previous studies of mesoscale variability in the ocean have emphasized that rings and eddies are isolated vortices embedded in relatively homogeneous water. Recent observations of eddy systems in the California Current System (CCS), however, show that at least some CCS eddy systems continue to dynamically interact with inshore coastal (cold) and offshore (warm) waters of the California Current through the process of lateral vortex entrainment. Oceanic data suggest that lateral vortex entrainment of non-local waters with significantly different temperature and salinity characteristics may partially account for the presence of high shear mixing regimes, double diffusive phenomenon and secondary circulations at depth in the vicinity of the eddies. Two different sets of laboratory experiments were conducted to assess the kinematic possibility of lateral vortex entrainment as a generation mechanism for these oceanic phenomena. The results of the laboratory studies qualitatively support the conclusion that lateral vortex entrainment could produce at least some of the observed oceanic phenomena.     

Die Wirkung von Polymerzusätzen auf die Turbulenzstruktur in der ebenen Mischungsschicht zweier Ströme

The plane mixing layer formed between two parallel streams moving with different velocities is one of the simplest types of free turbulent boundary layers and has frequently been studied for Newtonian fluids. As a result of this and because of its good experimental accessibility this type of flow provides a good opportunity for obtaining information about the influence of drag reducing additives on the structure of free turbulence. This is all the more so because of the presence of a characteristic vortex structure which can be clearly distinguished from the overlying statistical fine turbulence. The turbulence field was investigated using an existent laser Doppler anemometer system that had been designed for space-time correlation measurements. This enabled measurements to be made of the mainstream velocity as well as of the longitudinal and transversal turbulent fluctuations and, after a simple modification, also of the Reynolds shear stresses and the cross correlation coefficients. The main result of the addition of 50 ppm of the polymer used (Separan AP30) was found to be an intensification of the Reynolds shear stresses. The resulting substantially more rapid increase (than in water) in the thickness of the shear layer can be explained theoretically; such behaviour has also been observed in free jets. On the other hand, the reduced thickness of the mixing layer in the initial region and the associated enhancement of the longitudinal fluctuations and damping of the transversal fluctuations indicate that the main shear flow induces a flow anisotropy by uncoiling and aligning the polymer molecules. The increase in the spreading angle suggests that the entrainment process at the edges of the mixing layer is intensified. This can be explained by the enhancement of the large energy carrying vortices in the turbulence spectrum. This is probably also the reason for the general increase in the correlation coefficients observed at all positions along the centreline of the flow field. However, a complete discussion of the energy transfer mechanism present here, in particular with inclusion of the fine turbulence responsible for dissipation, is only possible with the help of a detailed analysis of the vortex structure in the mixing layer. This is presented in a following paper. The relation between the degree of drag reduction and the intensity of the Reynolds shear stresses enables the direct influence of the rheological properties of the fluid on the turbulent momentum transfer to be clearly recognized.     

水下欠膨胀高速气体射流的实验研究

采用实验途径研究了下水高速气体射流的动力学特性,研制了水下高速气体射流实验系统并发展了相应的测试手段。实验中,用插入式静压探针测量了射流轴线静压分布;用γ射线衰减法测量了径向空隙率分布,从而揭示了水下高速气体射流均压和掺混两个过程的基本规律。测量结果表明：水下高速气体射流在欠膨胀工况下运行时,近场将出现含有复杂波系结构的膨胀压缩区域,由于气水的掺混作用,水下欠膨胀气体射流均压化过程比空气中衰减得快。测量结果还表明,水下射流在近场区的混合层由气水两相占据,其流态从靠近气体侧的液滴流型过渡到靠近液体侧的气泡流型。