Physical modelling and scale effects of air-water flows on stepped spillways

During the last three decades, the introduction of new construction materials (e.g. RCC (Roller Compacted Concrete), strengthened gabions) has increased the interest for stepped channels and spillways. However stepped chute hydraulics is not simple, because of different flow regimes and importantly because of very-strong interactions between entrained air and turbu- lence. In this study, new air-water flow measurements were conducted in two large-size stepped chute facilities with two step heights in each facility to study experimental distortion caused by scale effects and the soundness of result extrapolation to pro- totypes. Experimental data included distributions of air concentration, air-water flow velocity, bubble frequency, bubble chord length and air-water flow turbulence intensity. For a Froude similitude, the results implied that scale effects were observed in both facilities, although the geometric scaling ratio was only Lr=2 in each case. The selection of the criterion for scale effects is a critical issue. For example, major differences (i.e. scale effects) were observed in terms of bubble chord sizes and turbulence levels al- though little scale effects were seen in terms of void fraction and velocity distributions. Overall the findings emphasize that physical modelling of stepped chutes based upon a Froude similitude is more sensitive to scale effects than classical smooth-invert chute studies, and this is consistent with basic dimensional analysis developed herein.

PARALLEL ADAPTIVE SIMULATION OF A PLUNGING LIQUID JET

This paper is concerned with three-dimensional numerical simulation of a plunging liquid jet. The transient processes of forming an air cavity around the jet, capturing an initially large air bubble, and the break-up of this large toroidal-shaped bubble into smaller bubbles were analyzed. A stabilized finite element method （FEM） was employed under parallel numerical simulations based on adaptive, unstructured grid and coupled with a level-set method to track the interface between air and liquid. These simulations show that the inertia of the liquid jet initially depresses the pool＇s surface, forming an annular air cavity which surrounds the liquid jet. A toroidal liquid eddy which is subse- quently formed in the liquid pool results in air cavity collapse, and in turn entrains air into the liquid pool from the unstable annular air gap region around the liquid jet.

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.

A numerical investigation in buoyancy effects on micro jet diffusion flame

The buoyancy effect on micro hydrogen jet flames in still air was numerially studied.The results show that when the jet velocity is relatively large(V≥0.2 m/s),the flame height,width and temperature decrease,whereas the peak OH mass fraction increases significantly under normal gravity(g=9.8 m/s^2).For a very low jet velocity(e.g.,V=0.1 m/s),both the peak OH mass fraction and flame temperature under g=9.8 m/s^2 are lower than the counterparts under g=0 m/s^2.Analysis reveals that when V≥0.2 m/s,fuel/air mixing will be promoted and combustion will be intensified due to radial flow caused by the buoyancy effect.However,the flame temperature will be slightly decreased owing to the large amount of entrainment of cold air into the reaction zone.For V=0.1 m/s,since the heat release rate is very low,the entrainment of cold air and fuel leakage from the rim of tube exit lead to a significant drop of flame temperature.Meanwhile,the heat loss rate from fuel to inner tube wall is larger under g=9.8 m/s^2 compared to that under g=0 m/s^2.Therefore,the buoyancy effect is overall negative at very low jet velocities.

Effect of air bubble size on cavitation erosion reduction

Over the past 60 years, the air concentration in water has been considered as a control index of cavitation erosion reduction and widely used in the designs of hydraulic structures. However, the mechanism of air entrainment against cavitation erosion has been paid good attention to. In the present work, the effect of air bubble size on cavitation erosion reduction was experimentally investigated. A device with micron-scale orifice diameters(10, 20 and 50 μm in size) was specially designed to introduce air bubbles into water. The experiments about the effect of air bubble size were conducted by means of a vibratory apparatus, including the behavior of formation and movement for single air bubble, the characteristics of cavitation erosion reduction at different air entrainment conditions. The findings demonstrate that high air concentration has significant effects on cavitation erosion reduction.But, a notable problem was that the size of air bubbles is of outstanding effect on cavitation erosion reduction. Small air bubbles support to alleviate cavitation erosion, even at same air concentration.

EFFECTS OF ENTRAINED AIR MANNER ON CAVITATION DAMAGE

Early in 1953 the experiments by Peterka proved that air entrainment has effects on decreasing cavitation damage. This technology has been widely used in the release works of high dams since the inception of air entrainment in the Grand Goulee Dam in 1960. Behavior, mechanism and application of air entrainment for cavitation damage control have been investigated for over half century. However, severe cavitation damage happened due to complex mechanism of air entrainment. The effects of air entrainment are related to many factors, including geometric parameters, hydraulic parameters and entrained air manners. In the present work an experimental set-up for air entrainment was specially designed, the behavior of reducing cavitation damage was experimentally investigated in the three aspects of entrained air pressure, air tube aera and air tube number. The results show that magnitude of reduction of cavitation damage is closely related to the entrained air tube number as well as entrained air pressure, air tube aera, and that the effect through three air tubes is larger than that through single air tube although the entrained air tubes have the same sum of tube aera, that is, 1 ＋ 1 ＋ 1 〉 3. Therefore, it is important to design an effective manner of air entrainment.

Two-phase air-water flows: Scale effects in physical modeling

Physical modeling represents probably the oldest design tool in hydraulic engineering together with analytical approaches. In free surface flows, the similitude based upon a Froude similarity allows for a correct representation of the dominant forces, namely gravity and inertia. As a result fluid flow properties such as the capillary forces and the viscous forces might be incorrectly reproduced, affecting the air entrainment and transport capacity of a high-speed model flow. Small physical models operating under a Froude similitude systematically underestimate the air entrainment rate and air-water interfacial properties. To limit scale effects, minimal values of Reynolds or Weber number have to be respected. The present article summarizes the physical background of such limitations and their combination in terms of the Morton number. Based upon a literature review, the existing limits are presented and discussed, resulting in a series of more conservative recommendations in terms of air concentration scaling. For other air-water flow parameters, the selection of the criteria to assess scale effects is critical because some parameters （e.g., bubble sizes, turbulent scales） can be affected by scale effects, even in relatively large laboratory models.

Collapse of cavitation bubbles near air bubbles

The cavitation erosion is one of the common damage modes in water engineering.The study of the interaction among cavitation bubbles,air bubbles and the wall is of great significance for understanding the mechanism of the air entrainment to alleviate the cavitation and to enhance the cavitation erosion mitigation effect of aeration.By using the high-speed camera,the regular patterns of the collapse of cavitation bubbles in the vicinity of the wall and the air bubbles are studied in this paper.It is shown that in the vicinity of air bubbles,the cavitation bubbles may only collapse towards or from air bubbles,while under the dual impacts of air bubbles and the wall,the direction of collapse of the cavitation bubbles depends on the combined vector of the impact forces of the air bubbles and the wall.When the air bubbles are very close to the cavitation bubbles,the air bubbles will be penetrated and stretched by the cavitation bubbles,when the distance between them is short enough,the cavitation bubbles and the air bubbles will connect to form gas-type cavitation bubbles,and the collapse strength will be significantly decreased,when there are two air bubbles near the cavitation bubbles,they may even be penetrated successively by the cavitation bubbles.Thus it can be concluded that during the air entrainment to alleviate the cavitation,the number of air bubbles is more important than the total air concentration.

Preliminary control of the air entrainment in bow wave based on the Liutex force method

Trails induced by air entrainment of bow wave breaking can be observed clearly around an advancing ship,making it prong to be detected and causing reduction in hydrodynamic performance.In breaking bow wave region,different scale of coherent vortex structures related closely to the air entrainment are generated.The formation and evolution of bubble clouds can be accounted partly by the swirling vortex flow of the jet plunging.In this work,high-fidelity simulation of the bow wave breaking around a rectangular thin plate is performed with the in-house code BAMR-SJTU.A Liutex force model is constructed to investigate the interaction between the free surface and vortices,and to explore the possibility of alleviating or controlling the air entrainment.This study is the first attempt to manipulate vortices corresponding to the air entrainment of the bow wave breaking.Some typical vortex structures based on the Liutex vortex identification method and the distribution of the vortex force are presented.Comparison of the vortex structures and the entrapped bubbles is conducted to illustrate the efficiency of Liutex force model in air entrainment control.

Inception point of air entrainment over stepped spillways

The location of the inception point of the air entrainment directly affects the energy dissipation ratio, the cavitation damage control, and the training wall height designs for a stepped spillway and a stilling basin. In this paper, the boundary layer theory of plates is used to predict the location of the inception point of the air entrainment over the stepped spillways by assuming the steps on the spillways as a kind of roughness. An empirical formula is presented based on the physical model experiments, with the maximum error less than 1% except at one point where the error is 1.6%, as compared to the experimental data. Meanwhile, it is shown that the location of the inception point of the air entrainment for the stepped spillway is much nearer to the top of the spillway than that for a smooth spillways, which explains why the high ratio of the energy dissipation is provided for the stepped spillway.

Air entrainment of hydraulic jump aeration basin

In order to avoid the cavitation damage and the decrease of the energy dissipation of the stepped spillways with a large unit discharge, the air entrainments of the hydraulic jump aeration basin （HJAB） are theoretically and experimentally investigated for the hydraulic-jump-stepped spillway developed by the authors. It is shown that the submerged degree of the hydraulic jump and the air concentration in the measuring section are all functions of the dimensionless discharge, the length and the end sill height of the H JAB. The submerged degree odecreases with the increase of the dimensionless discharge or the dimensionless length of the H JAB, but increases with the increase of the dimensionless height of the end sill of the HJAB. The flow regimes near the critical hydraulic jump, namely, at or= 1.0, have the best effect of the air entrainment for the flow at the measuring section and then that of the stepped spillway.

INCEPTION OF AIR ENTRAINMENT ON STEEP SLOPE

Based on the momentum integral equation of boundary layer on the steep slope and the equation of water depth deduced form both the equation of continuity including the effect of the boundary layer and the energy equation outside the boundary layer on the steep slope, and with the aid of the function of velocity profile in the boundary layer, the water depth and boundary layer were numerically computed by Runge-Kutta method. The method determine parameters in the preceding equation were also discussed in detail for the laminar and turbulent flows. The water depth boundary layer and point of inception of air entrainment calculated by above method agree well with the data obtained by prototype.

Design of the Airbag Inflation System Applicable to Conventional and Autonomous Vehicles

The emergency transformation of various aspects of life and business these days requires prompt evaluation of autonomous vehicles.One of the primary reassessments deals with the applicability of the vehicle passive safety system to the protec-tion of arbitrarily positioned passengers.To mitigate possible risks caused by the simultaneous deployment of several big airbags,a new principle of their operation is required.Herein,the aspirated inflator for a driver airbag is developed that can provide 50L-airbag inflation within 30-40 ms.As a result,about 3/4 of the air is to be entrained into an airbag from the vehicle compartment.The process is initiated by a supersonic pulse jet(1/3 air volume)generated pyrotechnically.Then the Prandtl-Meyer problem formulation enables guiding linear and angular dimensions of the essential parts of the device.Accordingly,a family of experimental models of varied geometry is fabricated and tested to determine their operational effectiveness in a range of motive pressure within~3-7 MPa.Experiments are performed on a specially designed facility equipped with compressed-air tanks and a high-speed valve to mimic the inflator operation with the pyrotechnic gas generator.The aspirated inflator operability is characterized using multivariate measurements of pressure fields,high-speed video-recording of the airbag inflation process,and evaluation of aspiration(entrainment)ratio.The average volume aspiration ratio measured at 300 K is found to reach 2.8 and it’s expected to almost double at 1200 K.

Numerical simulation of air entrainment and suppression in pump sump

The dynamics of air entrainment and suppression schemes in a pump sump are investigated. Four different turbulence models(standard k-ε model, realizable k-ε model, renormalization group(RNG) k-ε model and shear-stress transport(SST) k-ω model) and the volume of fluid(VOF) multiphase model are employed to simulate the three-dimensional unsteady turbulent flow in a pump sump. The dynamic processes of air entrainment are simulated under conditions of relatively high discharge and low submergence; the mechanism of air entrainment is discussed in detail. Then suppression means for air entrainment is adopted by placing a circular plate on the intake pipe at three different heights. The results show: the position and structure of the free-surface vortices, sidewall-attached vortices, back wall-attached vortices, and floor-attached vortices calculated by SST k-ω turbulence model agree well with the experimental data. The two main contributors for air entrainment are pressure difference and vortex strength. By placing a circular plate in the middle of the intake pipe under water, air entrainment is suppressed because vortex strength is reduced.

EXPERIMENTAL STUDY ON A NEW TYPE OF AERATOR IN SPILLWAY WITH LOW FROUDE NUMBER AND MILD SLOPE FLOW

Experimental study on aeration characteristics of various aeration devices was conducted in the spillway tunnel of the Pubugou hydropower project, Sichuan Province, China. It is shown by comparison that the new type of aeration device, namely, the aerator with a trapezoidal-shaped slot and a steep-slope section（ATSS）, can avoid water accumulation in the cavity of the aeration device in the project, thus can effectively solve the backwater problems arising from this project and be used for a wide range of different water levels, without any drain facilities. Above the water level of 840 m, the water contained in the cavity can be eliminated completely, which means that the recommended new type of aerator can meet the aeration demands in the spillway of the project with low Froude number and may be of practical significance and of interest to other projects with similar types of aeration devices.

Cavity flow regime for spillway aerators

It is well known that the effect of air entrainment for cavitation damage controls is related not only to the air discharge into aerator devices but also the flow regime of the cavity below them.On the basis of the hydraulic characteristics of the flow,the aerator devices were for the first time classified.The theoretical considerations were performed about the jet length and cavity flow regime with the influencing factors.Comparing with the behavior of the flow through the aerator of discharge tunnels,the flow regimes of the cavity below spillway aerators were experimentally investigated,and the empirical expressions were presented to identify the conversions of the cavity flow regimes,including fully filled cavity,partially filled cavity,and net air cavity.Some issues of the design of the aerator devices were suggested in the present work.

THEORETICAL AND EXPERIMENTAL INVESTIGATIONS OF ENTRAINED AND TRANSPORTED CHARACTERISTICS OF SUBMERGED JET

This paper presents entrainment mechanism, and transported and diffusioncharacteristics at the point of entry of submerged jet. The profiles of both velocity andconcentration within the air-water mixing layer were theoretically deduced. And the comparisonsbetween theoretical values and measured data were made. Results show that the velocity profilewithin the air-water mixing layer exhibits a form of error function. The concentrations of airentrainment in the internal and external regions of air-water mixing layer correspond to Gaussiandistribution.

Inverse problem of bottom slope design for aerator devices

Air entrainment is an effective approach to protect release works from cavitation damage. The traditional method of aerator device designs is that, for given flow conditions, the geometries of the aerator device are designed and then the effec（s are experimentally tested for cavitation damage control. The present paper proposes an inverse problem method of determining the bottom slopes in front of and behind an aerator if the requirements of air entrainment, flow conditions and some of aerator geometric parameters are given. An RBF neural network model is developed and the relevant bottom slopes are calculated in different conditions of flow and geometry on the basis of the data of 19 aerator devices from different discharge tunnels with safe operation. The case study shows that the methodology provides an effective way to design aerator devices under given target conditions.

A method of determining flame radiation fraction induced by interaction burning of tri-symmetric propane fires in open space based on weighted multi-point source model

The interaction of multiple fires may lead to a higher flame height and more intense radiation flux than a single fire,which increases the possibility of flame spread and risks to the surroundings.Experiments were conducted using three burners with identical heat release rates(HRRs)and propane as the fuel at various spacings.The results show that flames change from non-merging to merging as the spacing decreases,which result in a complex evolution of flame height and merging point height.To facilitate the analysis,a novel merging criterion based on the dimensionless spacing S/z_(c) was proposed.For non-merging flames(S/z_(c)>0.368),the flame height is almost identical to a single fire;for merging flames(S/z_(c)≤0.368),based on the relationship between thermal buoyancy B and thrust P(the pressure difference between the inside and outside of the flame),a quantitative analysis of the flame height,merging point height,and air entrainment was formed,and the calculated merging flame heights show a good agreement with the measured experimental values.Moreover,the multi-point source model was further improved,and radiation fraction of propane was calculated.The data obtained in this study would play an important role in calculating the external radiation of propane fire.

Solution of analytical model for fuel spray penetration via homotopy perturbation method

The present paper attempts to solve equations in the initial stage and the two-phase flow regime of fuel spray penetration using the HPM-Padétechnique,which is a combination of the homotopy perturbation method(HPM)and Padéapproximation.At the initial stage,the effects of the droplet drag and the air entrainment were explained while in the two-phase flow stage,the spray droplets had the same velocities as the entrained air.The results for various injection pressures and ambient densities are presented graphically and then discussed upon.The obtained results for these two stages show a good agreement with previously obtained expressions via successive approximations in the available literature.The numerical result indicates that the proposed method is straight forward to implement,efficient and accurate for solving nonlinear equations of fuel spray.