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This paper presents an experimental study of the liquid disintegration process on an atomizer with two counter-rotating wheels by high-speed imaging. The process was investigated for a wide range of wheel rotational speeds, liquid flow rates and impingement positions. Compared to flat disc and cup atomizers operating at similar Weber numbers, proposed atomizer design is capable of producing much finer droplets in the ligament formation mode (mean diameter under 0.15 mm when We = 106) and at a significantly larger liquid throughput. Despite the atomizer gap flow complexity, approximation of mean liquid trajectories with tangent lines proved to be fairly accurate. We were able to identify two main challenges in atomizer operation, namely the occurrence of hydraulic jump upon liquid impingement causing the formation of large droplets, and escaping of the liquid spray through the wheel gap. Nevertheless, both issues can be largely mitigated by optimization of atomizer geometry and operating parameters.

This study investigates the capacities of chute spillway and stilling basin under multiple flow discharge scenarios. Thirteen cases, categorised as low, medium, and high flow discharges were experimentally conducted, with a 100% increase of Probable Maximum Flood (PMF) as the modified maximum flow. An analysis is extended to flood and scour potential at the Type II and III stilling basin. Low and medium discharge scenarios have no significant impact on the spillway but posed insufficient capacity to confine efficiently the hydraulic jump within the stilling basin. Types II and III basins reduced the length of hydraulic jump up to 50% and 73%, respectively at PMF. Similarly, potential of severe scour particularly at the spillway exit increases to 5 times more than the cases for low discharge. Similarly, potential of severe scour at PMF, particularly at the spillway exit increases to 5 times more than the cases for low discharge. High discharge not only compromises the spillway integrity due to overflow but also increases flood and scour potential at the stilling basin. An up-to-date evaluation of the existing dam appurtenances capacities to withstand the future flow pattern is crucial to ensure smooth dam operations and avoiding catastrophic events such as dam breach, jeopardising the river environmental flow and water resources.

Supercritical flows are ubiquitous in natural environments; however, there is rare 3D anatomy of their deposits. This study uses high-quality 3D seismic datasets from the world’s largest submarine fan, Bengal Fan, to interpret 3D architectures and flow processes of Pliocene undulating bedforms that were related to supercritical flows. Bengal undulating bedforms as documented in this study were developed in unconfined settings, and are seismically imaged as strike-elongated, crescentic bedforms in plan view and as rhythmically undulating, upstream migrating, erosive, discontinuous reflections in section view. Their lee sides are overall 3 to 4 times steeper (0.28° to 1.19° in slope) and 3 to 4 times shorter (117 to 419 m in length) than their stoss flanks and were ascribed to faster (high flow velocities of 2.70 to 3.98 m/s) supercritical flows (Froude numbers of 1.53 to 2.27). Their stoss sides, in contrast, are overall 3 to 4 times gentler (0.12° to 0.27° in slope) and 3 to 4 times longer (410 to 1139 m in length) than their lee flanks and were related to slower (low velocities of 2.35 to 3.05 m/s) subcritical flows (Froude numbers of 0.58 to 0.97). Bengal wave-like features were, thus, created by supercritical-to-subcritical flow transformations through internal hydraulic jumps (i.e., cyclic steps). They have crests that are positive relative to the surrounding region of the seafloor, suggesting the predominant deposition of draping sediments associated with net-depositional cyclic steps. Turbidity currents forming Bengal wave-like features were, thus, dominated by deposition, resulting in net-depositional cyclic steps. Sandy deposits associated with Bengal net-depositional cyclic steps are imaged themselves as closely spaced, strike-elongated high RMS-attribute patches, thereby showing closely spaced, long and linear, strike-elongated distribution patterns.

This study used a 3D coupled CFD-DEM model to study velocity and porosity relationships within horizontal dense phase pneumatic conveying. Inlet velocities, initial layer fractions and initial slug lengths were varied for a total of 72 single slug simulations. The linear relationship between particle velocity and slug velocity was examined and the origins and contributions of individual variables were looked at in detail. It was found that the slug velocity to particle velocity relationship can be defined using slug to bulk density ratio and propagation velocity. It was also found that within a single slug system, slugs tend to their ‘preferred’ steady-state length which is a function of inlet velocity and stationary layer ahead of the slug. Another finding is that hydraulic jump can be used as an analogy to the interaction between slug front and the stationary layer. This analogy can be used to define a boundary for slug flow as well as help predict slug porosity.

In this research, the effect of curvature radius of convex target plates on the radius of formed circular hydraulic jump is investigated using experimental investigation and numerical modeling. Ethylene glycol with constant density and viscosity is used as the working fluid. In order to simulate the hydraulic jump, the volume of fluid (VOF) method is applied using a continuous surface force model (CSF) and geometric reconstruction for determining the interface of the two fluids. The results of experimental studies and numerical simulation indicate that the hydraulic jump is a function of three important parameters, including the vertical jet radius, the curvature radius of the target plate and the volumetric flow rate. Subsequently, an empirical relation for the hydraulic jump radius formed on convex target plates is proposed. Comparing the radius of the hydraulic jump on the convex and flat target plates it is observed that the jump radius increases with increasing the volumetric flow rate and significantly decreases with increasing the curvature radius of the convex target plate and impinging jet radius.

In this study, heat transfer and hydrodynamics of air-assisted free water jet impinging a flat plate surface are experimentally investigated. The effects of the nozzle-to-surface distance (H/d = 0.02–0.51) and volumetric quality (β = 0.3–0.8) on the stagnation Nusselt number, stagnation pressure, and hydraulic jump diameter are considered. The results show that the normalized stagnation Nusselt number and hydraulic jump diameter drastically increase with decreasing the nozzle-to-surface distance, since the stagnation pressure increases due to the jet deflection effect. Based on the experimental results, new correlations for the stagnation Nusselt number and pressure are developed as a function of the nozzle-to-surface distance.

Hydraulic jumps, transitions from supercritical to subcritical flows, tend to maintain suspended particles in the water column and enhance biological productivity near the surface. Transitions occur from flow adjustments as the flow moves through a cross-section reduction, such as a reef crest. Hydraulic jumps can also inhibit the settlement of coral larvae and bivalve mollusks, but could favor connectivity among reefs by dispersing planktonic organisms to surrounding areas. The Veracruz Reef System (VRS) was chosen as a case study of hydraulic jumps produced over reef crests. This system is located in the southwestern part of the Gulf of Mexico (GoM) and features 50 coral reef structures. The area is influenced by vertical stratification that modifies its dynamics. Hydrographic and yearlong current data collections in the area during 2009 identified fronts and a cyclonic recirculation. On the other hand, the presence of a hydraulic jump weakened the cyclonic recirculation on the leeward side of the reefs. The vertical gradient of the horizontal velocity suggested the influence of vertical eddies at least 35% of the time throughout the entire year. Moreover, the current velocity profiles showed a bidirectional behavior in spring and summer conditions of stratified waters. These bidirectional flows contrasted the unidirectional structure caused by frictional dynamics during northerly winds.

A flume study using a surge-type flow produced by quickly lifting a gate was conducted to simulate a tsunami the height of which is larger than level 1 (prevention level) by a hybrid system comprising a forest, an embankment, and a moat while changing the layout of the components. The overflow volume, tsunami arrival time, fluid force, and moment by fluid force were measured, and the tsunami reduction effects in each model were compared. The hybrid defense system in the order of vegetation, a moat, and an embankment (Case V40ME) from the sea side showed the highest reduction in overflow volume, moment index, and tsunami delay effect. In terms of the fluid force index, Case V40ME performed best up to a certain tsunami height. For higher tsunamis, a hybrid system in the order of vegetation, an embankment, and a moat from the sea side (Case V40EM) performed better, although Case V40ME had a large advantage in total when there was a space landward of the existing forest. Suitable structures when there is space seaward and on both sides of a forest were also clarified for different wave heights through the mechanism of reflection, hydraulic jump, and vegetation resistance.

The measurement of turbulent velocity in highly aerated flow is difficult because of the presence of air bubbles. The characterisation of three-dimensional velocity field in highly aerated flows is even more challenging using existing phase-detection techniques. This paper presents an attempt on a quantification of transverse velocity and velocity fluctuations in quasi-two-dimensional hydraulic jumps with relatively high Froude and Reynolds numbers. A four-sensor phase-detection probe array was developed to measure the bubble convection in both streamwise and spanwise directions. A characteristic instantaneous transverse velocity component was derived together with a measure of its fluctuations. The transverse velocity component characterised the three-dimensional turbulent structures, although the time-averaged flow pattern was two-dimensional and the average transverse velocity was zero. Both the transverse velocity and velocity fluctuations were smaller than the longitudinal time-averaged velocity and velocity fluctuations in the shear flow, and were quantitatively comparable to those in the free-surface region, revealing different turbulent structures in the lower and upper roller regions. The approximate of Reynolds stresses was discussed together with the limitation of the method. The present work also provided some guidelines for the use of phase-detection probe array and correlation signal processing techniques in complex turbulent two-phase flows.

Local scour downstream of spillways due to hydraulic jump is considered the most complicated and tedious problems which threats the overall stability of the spillway. Throughout this paper, eighty experimental runs were carried out to investigate the effect of using cylinder blocks fixed on the back slope of the spillway on the scour hole dimensions downstream of spillway under different flow conditions. Case of smooth spillway was included to estimate the influence of the considered modifications. Experiments were performed using different diameters, lengths, and arrangements of cylinder blocks with different discharges. Data collected from the experiments were analyzed and graphically introduced. Furthermore, experimental data for smooth spillway were compared with scour formulae for other researchers. Finally simple formulae were predicted to estimate the different scour and deposition parameters. Use of concrete cylinder blocks will assist engineers in the design of spillways. Keywords: Experimental, Spillway, Local scour, Hydraulic structures, Staggered blocks

In this work, the influence of constant background vorticity on the properties of shock waves in a shallow water system are considered. It is shown that the flow-depth ratio of stationary shocks can be written as a function of two non-dimensional parameters: the Froude number, suitably defined in the presence of the shear flow, and a non-dimensional vorticity. Some properties of these hydraulic jumps are explored, and it is shown that stronger background vorticity has the effect of moderating the strength of the hydraulic jump.

Air entrainment and air-water mixing by a flow impingement are enhanced by the turbulent shear layer and associated instabilities in the receiving waterbody. This paper presents an experimental study aiming at a quantitative description of bubble-turbulence interplay in two-dimensional supported plunging water jets. In addition to the basic air-water flow properties, the turbulence intensity in the highly-aerated plunging pool was estimated based on void fraction and total pressure fluctuation measurements, while the turbulent time and length scales were recorded systematically. The coupling of bubble convection and formation of macroscopic turbulent structures was characterised in terms of bubble clustering behaviours and turbulent length and time scales of the bubbly flow eddy structures. The effects of jet impact velocity were investigated for a fixed jet length. These advanced data analyses were applied to plunging jet two-phase flow for the first time. The results would provide new benchmark data for numerical modelling of intense air-water flow at a higher level than the basic two-phase flow dynamic properties. A discussion was developed at the end on the turbulent length scales and the Schmidt number in the bubbly flow regions of horizontal hydraulic jump and vertical supported plunging jet.

The rotation of polygons in a Type-II hydraulic jump prompts us to look for a rotational feature in the Type-I hydraulic jump. Coupling the radial and azimuthal flows breaks the azimuthal symmetry of the shallow-water circular jump. An unstable rotating wave along the circumference of the jump is possible with a kinematic viscosity of very small order, whose upper threshold value is less than the kinematic viscosity of water.

The present work proposes to investigate the impact of a turbulent round jet on a disk. The disk diameter is one order of magnitude larger than the jet diameter but small enough to avoid the formation of a circular hydraulic jump. The case of a smooth disk is first studied as the reference case. We then report results obtained with a disk engraved along its circumference by a number N of radial grooves. The grooves are used to split the liquid sheet into multiple jets. According to the incoming flow rate Q and to the geometry of the groove, the number of jets n can be stable and corresponds to 2 N jets and N jets, or variable, i.e. merged jets (mixed zone). Phase diagrams ( Q , n ) are deduced from measurements for different lengths of the groove. Finally, the obtained droplets are characterized in terms of diameters and velocities.

Determining water surface profiles of steady open channel flows in a one-dimensional bounded domain is one of the well-trodden topics in conventional hydraulic engineering. However, it involves Dirichlet problems of scalar first-order quasilinear ordinary differential equations, which are of mathematical interest. We show that the notion of viscosity solution is useful in thoroughly describing the characteristics of possibly non-smooth and discontinuous solutions to such problems, achieving the conservation of momentum and the entropy condition. Those viscosity solutions are the generalized solutions in the space of bounded measurable functions. Generalized solutions to some Dirichlet problems are not always unique, and a necessary condition for the non-uniqueness is derived. A concrete example illustrates the non-uniqueness of discontinuous viscosity solutions in a channel of a particular cross-sectional shape.

A high resolution computational fluid dynamics model is used to simulate a steady air entraining laboratory scale hydraulic jump. A detailed examination of shear layer instabilities reveals the dynamic relationship between spanwise vortices, free surface fluctuations, and air–water spatial patterns. Spanwise vortices generated at the toe roll-up under a variable depth roller, creating large free surface fluctuations through high velocity water ejections in the roller. The mean shear layer elevation and free surface elevations periodically alternate between positive and negative correlation throughout the roller, driven by dynamic vortex transport. Vortices descending towards the lower wall create an upwelling of non-bubbly fluid into the shear layer that contributes to regions of decreased bubble concentration between vortices. The position of a strong shear layer at the location of maximum air entrainment, directly above the jump toe, leads to highly aerated vortices that influence bubble behavior. Bubbles breakup quickly after entrainment at the toe and bubble clusters are observed most frequently below and at the end of the roller where bubble breakup and energy dissipation are diminished. The dominant separation angle of clustered bubbles is independent of downstream distance and aligns closely with the direction of initial shear, suggesting bubble clustering is a remnant of bubble breakup.

A disposal system for low- and medium-level nuclear waste in Hungary is being constructed inside the fractured rock body of the Lower Carboniferous Moragy Granite. Previous studies proved that the granitoid massif is rather heterogeneous in terms of lithological composition, brittle structure and hydrodynamic behaviour. A significant part of the body consists of monzogranite, while other portions are more mafic in composition and are monzonites. As a result of at least three significant brittle deformation events, the area is at present crosscut by wide shear zones that separate intensively fractured zones and poorly deformed domains among them. Due to late mineralization processes, some of these fractured zones are totally sealed and cannot conduct fluids, while others are excellent migration pathways. The spatial distribution of these two types nevertheless does not show any systematics. Hydrodynamic behaviour clearly reflects this heterogeneous picture; in some places, hydraulic jumps as great as 25 m at compartment boundaries can be detected. In this study, the fracture network of the Moragy Granite body is evaluated from a geometric aspect using datasets measured at a wide range of scales. 2D digitized images of a hand specimen, one large (20 × 60 m) and 12 smaller subvertical wall rocks (outcrops) and 120 images from tunnel faces representing the ground level of the underground repository site were analysed. Moreover, 1D data from 13 wells that all penetrate the granitoid massif were studied. Based on measured geometric data (spatial position, length, orientation, and aperture) fracture networks are simulated to study connectivity relations and for computing the fractured porosity and permeability at different scales. The results prove the scale-invariant geometry of the fracture system. Geostatistical calculations indicate that measurable fracture geometry parameters behave as regionalized variables and so can be extended spatially. Estimated localities of connected subsystems fit very well with fault zones mapped previously. Moreover, the spatial position of regimes of different hydrodynamic behaviours can be explained by connectivity relations both regionally and within wells.

Circular hydraulic jump (CHJ) and its deviation from the azimuthal symmetry due to non-orthogonal impingement of liquid jet on a solid surface are studied using finite volume based numerical framework. Asymmetric interfacial jump has been modelled from volume of fluid (VOF) prediction for a different angle of inclination of a jet from normal of the surface. The extent of asymmetry is found to be increasing as the jet becomes more and more horizontal, deviation from orthogonal impingement. To understand the role of wall adhered jet on jump, flow physics has been studied which reveals back flow in the jump region causing circulation. Moreover, equipotential and heterogeneous jump–jump interactions are studied to predict fluidic features like fountain formation and upwash. Numerical simulations reveal that strength of interacting wall jets play a major role in the formation of a pattern as consequence of neighbouring twin jet impingement. A vertical flat liquid protrusion is observed at equidistant stagnation line from the impingement points of equipotential jets. On the other hand, a curvilinear upwash film has been found out as characteristics of the interaction between heterogeneous strengths of interacting jets. At a higher ratio of jet strengths, complete engulfment of a smaller hydraulic jump as an eye of larger one has been obtained from careful numerical simulation. Physical insights of these rich fluidic phenomena are described using well-resolved velocity vectors in the wall jet and upwash.

A shallow water model was applied to study the hydraulic jump and Bernoulli equation across the jump. On a flat terrain, when a supercritical flow plunges into a subcritical flow, discontinuity develops on velocity and Bernoulli function across the jump. The shock generated by the obstacle may propagate downstream and upstream. The latter reflected from the inflow boundary, moves downstream and leaves the domain. Before the reflected wave reaching the obstacle, the short-term integration (i.e., quasi-steady) simulations agree with Houghton and Kasahara’s results, which may have unphysical complex solutions. The quasi-steady flow is quickly disturbed by the reflected wave, finally, flow reaches steady and becomes critical without complex solutions. The results also indicate that Bernoulli function is discontinuous but the potential of mass flux remains constant across the jump. The latter can be used to predict velocity/height in a steady flow.

Hydraulic jumps are a complex hydraulic phenomenon characterised by a water surface discontinuity from supercritical to subcritical flows. Along the jump roller, high turbulence, flow aeration and three-dimensional motions are key characteristics which are associated with jump toe oscillations and free-surface fluctuations. Previous studies have provided significant insights into the characterisation of the free-surface and jump toe characteristics in hydraulic jumps. However, a continuous observation of the time-varying free-surface has been so far limited to fixed data points along the hydraulic jump. Herein, novel experiments were conducted with a LIDAR measuring the continuous free-surface profiles in aerated hydraulic jumps providing detailed spatial and temporal free-surface characteristics of aerated hydraulic jumps. The free-surface observations provided basic statistics of the free-surface including mean profiles and standard deviations of the free-surface fluctuations as well as their characteristic frequencies. The effect of the jump toe oscillations on the free-surface properties was analysed for two conditions using a free moving jump toe and a fixed jump toe position. The results showed a strong effect of the jump toe oscillations on the free-surface features close to the jump toe. Based upon the characteristic frequencies, three characteristic regions in hydraulic jumps were identified. Overall the comparison with previous studies showed good agreement highlighting that a LIDAR is a suitable instrument to measure the free-surface characteristics in aerated hydraulic jumps.

The discharge and the velocity field of the delivery system in the top side-pouring twin-roll casting (TSTRC) were investigated combined with numerical simulation and water model experiment. The Renormalization Group k-e model (RNG) and Reynolds Stress Model (RSM) were employed in the simulation, both showing high reliability and accuracy under various opening of the sluice gate. The variation trend of the outflow velocity and the flow rate fluctuation were explained with the development of the hydraulic jump and vortices in the flow fluid, with the analysis of the velocity field of the flow fluid in the canal of the delivery system. A formula was derived to predict the discharge with regard to the gate opening, showing good agreement with the experiment results. Compared to RNG, RSM performed better in predicting the discharge of the delivery system.

A systematic assessment of morphometric parameters of over 200 plunge pools along the steep escarpment base of western Great Bahama Bank and ~ 2000km2 of sediment wave fields of upslope migrating cyclic steps documents the importance of cascading density currents for sedimentation on the slope. The abrupt downslope termination of the Holocene mud wedge with the cyclic steps shows that strike parallel bottom currents interacting with the off-bank currents are responsible for slope sediment distribution. The plunge pools and sediment waves were generated by density-cascading and both are related to a hydraulic jump caused by two gradient changes along the slope profile. The bedforms highlight both the erosional and depositional nature of this current regime, which is controlled by slope gradient and the directional confinement by either grooves on the steep escarpment or gullies on the middle to lower slope. The > 20 m deep plunge pools are ellipsoidal, with an average width of 211 m and length of 283 m, but variations between 80–360 m and 100–650 m for width and length occur. They are caused by an average gradient break of 16° on the cemented upper slope. Gradient breaks of as low as 2° are reported to be sufficient to scour a plunge pool like the ones in the study area, but higher gradient breaks between 10 and 20° are quite common for consistent plunge pool development. A second gradient break further down slope changes flow conditions for the generation of cyclic steps, with asymmetric waveforms of 4 m high (average) in large wave fields in the entire the study area. Orientation is mainly orthogonal to the main slope direction but wave lengths and sinuosity vary, depending on the morphologic location of the wave field. The comparison with sediment wave fields with similar geometries or in similar environments shows that flow reconstruction based on the wave height and wave length alone along with a characterization of sediment grain size, however, yields non-unique results and is site specific.

Typhoon Khanun caused over 226 mm of accumulated rainfall for 6 h (0700 to 1300 UTC), localized around the summit of Mt. Halla (height 1950 m), with a slanted rainfall pattern to the northeast. In this study, we investigated the enhancement mechanism for precipitation near the mountains as the typhoon passed over Jeju Island via dual-Doppler radar analysis and simple trajectory of passive tracers using a retrieved wind field. The analysis of vertical profiles of the mountain region show marked features matching the geophysical conditions. In the central mountain region, a strong wind (≥ 7 m s− 1) helps to lift low-level air up the mountain. The time taken for lifting is longer than the theoretical time required for raindrop growth via condensation. The falling particles (seeder) from the upper cloud were also one of the reasons for an increase in rainfall via the accretion process from uplifted cloud water (feeder). The lifted air and falling particles both contributed to the heavy rainfall in the central region. In contrast, on the leeward side, the seeder-feeder mechanism was important in the formation of strong radar reflectivity. The snow particles (above 5 km) were accelerated by strong downward winds (≤−6 m s− 1). Meanwhile, the nonlinear jumping flow (hydraulic jump) raised feeders (shifted from the windward side) to the upper level where particles fall. To support these development processes, a numerical simulation using cloud-resolving model theoretically carried out. The accreting of hydrometeors may be one of the key reasons why the lee side has strong radar reflectivity, and a lee side weighted rainfall pattern even though lee side includes no strong upward air motion.

The hydraulic jump is an economical alternative to dissipate energy in the conduit and to reduce erosion at the culvert outlet. In the literature, very limited studies have been reported on the performance of hydraulic jump in a closed conduit. The innovation of this research is to employ a numerical method for the estimation of the hydraulic jump characteristics in a closed conduit with different positive slopes (S0). The analytical method was used to develop several equations for hydraulic jump and the provided results were compared with the numerical method. The results indicate that the numerical method predicts the flow depth ratio after conduit with higher accuracy (error less than 5%) in comparison to the analytical method (error less than 10%). Furthermore, in the slope of 0.00, the energy loss increases by 16% with increasing the Froude number from 4.617 to 5.562 while this value is 23% and 22% for slopes of 0.01 and 0.02, respectively. Finally, several equations were developed for the prediction of hydraulic jump characteristics in terms of Fr1, S0, and conduit depth (D).

The effect of the Hutze (a secondary ECC injection pipe within the hot leg pipe of a Konvoi-type PWR) upon CCFL was experimentally investigated at COLLIDER test facility of the Technical University Munich (TUM). COLLIDER represents a PWR hot leg with a large dimeter of 190 mm and ~¼ scale. A Hutze pipe was built into COLLIDER’s hot leg according to a German Konvoi-type PWR reactor design data. The effect of the Hutze upon CCFL are shown through comparisons with previous investigations at COLLIDER without a Hutze. Visual observations using high-speed recordings are presented at different flow conditions: supercritical conditions at low air velocities, transition into subcritical flow, and the onset of CCFL with comparison against previous recording without a Hutze. Limits of: the onset of hydraulic jumps, onset of CCFL (flooding), and most importantly CCFL characteristics are also shown and compared. The Hutze was found to induce a large impact upon these limits: two hydraulic jumps are observed prior to the onset of CCFL instead of only one (in case without a Hutze), the limits of the onset of hydraulic jumps and onset of CCFL occur at much lower air velocities, and the hysteresis effect (difference between limits of flooding and deflooding) disappears. CCFL characteristics curve is also shifted toward lower values of gas velocities and less liquid flows into the reactor vessel at same air velocities in the case with a Hutze which means a less cooling potential during the reflux condensation mode. Ohnuki correction of the Hutze effect upon CCFL characteristics of 1988 is tested and it seems to work well at small diameter but it overestimates CCFL characteristics for COLLIDER data. The previous agreement between CCFL characteristics obtained from downscaled experiments with D > 50 mm without a Hutze (including COLLIDER data and other large scale facilities) with UPTF data (at full scale) is found to happen because of the Hutze effect which shifts the CCFL characteristics downwards in Wallis diagram and not because of the correct representation of occurring CCFL phenomena. The actual CCFL characteristics for the 1:1 scale without a Hutze are expected to be higher than those reported from data with Hutze at UPTF facility. This indicates that there is still a scale effect even at a large diameter channel, and that most previous downscaled experiments have underestimated CCFL characteristics at full scale. Based upon obtained results, a correlation of CCFL characteristics at full scale excluding the Hutze effect is given. This correlation is of a special interest for the design of new PWR reactors as most new designs does not include a Hutze.

This study uses 3D reflection seismic data to investigate how sediment gravity flows contribute to the evolution of the lower continental slope of the Myanmar margin that is part of the Bengal Fan, the largest deep-water fan system in the world. Seafloor and subseafloor data show large sediment wave fields that developed on both flanks of an extensive submarine canyon. The sediment waves exhibit asymmetric stoss and lee sides, wave lengths and heights of 850–3000 m and 25–70 m, respectively, and an upslope direction of migration. Seismic data reveals the presence of multiple fields of vertically stacked sediment waves, interbedded with units characterised by a chaotic seismic facies that accumulate mainly in the troughs of the sediment waves and can be tracked laterally to the adjacent canyons. According to their seismic facies, geometry, and internal architecture these chaotic units are interpreted as debrites. Seismic attributes extracted from different horizons indicate that the sediment waves are dominated by fine-grained sediment, while the debrites are probably associated with coarser-grained deposits. The debrites fill the troughs of the sediment waves, as well as the downstream portions of canyon thalweg, thus flattening the paleo-seafloor. The sediment waves are interpreted as cyclic steps formed by low-density turbidity currents flowing across the slope down to the basin floor, where the change in gradient favours the formation of hydraulic jumps and the transition from supercritical to subcritical flow conditions. A conceptual model for the sediment wave evolution was proposed for the study area, in the transitional environment on the lower slope, with low-density gravity flow deposits and high-density debris flow deposits alternatively accumulating on the major gravity flow conduits.

Electrolyte jet machining (EJM) is an innovative form of electrochemical machining (ECM) with excellent machining flexibility and accuracy. Recently, the nozzle inclination is introduced into EJM to further expand its machinability. In this work, to clearly reveal the mechanism behind this EJM process, a three-dimensional (3-D) multiphysics model of the stationary EJM process accounting for two-phase flow field and electric field was developed for the first time and experiments were also performed for validation. With the inclined nozzle, the distribution of flow velocity and thickness of electrolyte film around the jet exhibits uneven, thus resulting in non-circular hydraulic jump and non-axisymmetric anodic current density distribution, respectively. Besides, the effects of nozzle inclination angle and electrolyte ejecting flow velocity were investigated. Larger inclination angle leads to increased asymmetry of flow velocity and current density distribution, which results in more seriously non-circular hydraulic jump and asymmetric machined dimple shape. The electrolyte ejecting flow velocity affects the jet shape and current density distribution that eventually influences the machined results with the inclined nozzle, but this effect does not exist with the conventional vertical nozzle. Moreover, this work was extended to the translating EJM process to study the effect of nozzle translating direction with the inclined nozzle. It is demonstrated that through selecting translating directions, grooves with different shapes and surface finish can be machined even using a certain nozzle inclination. The mechanism for these phenomena was clarified by simulation, paving the way for design of the EJM process with the inclined nozzle.

Estimation of turbulence intensity within a highly-aerated turbulent flow is challenging. A possible way is to record bubble arrival information using intrusive phase-detection probes, but the derivation of velocity variation is subject to the correlation and de-correlation of the signals, especially in highly-turbulent and rapidly-varied flows with complex bubble transport such as in hydraulic jumps. Although attempts have been devoted to the improvement of data processing, it is difficult to assess the existing approaches in strong hydraulic jumps due to the lack of alternative measurement techniques applicable to the internal air-water flow region. In this letter, a substantial amount of work is devoted to manual analysis of instantaneous interfacial velocity in strong hydraulic jumps, and the velocity variation results are compared with the results of full-signal cross-correlation and adaptive-window cross-correlation approaches, to evaluate their performance in approximating the velocity turbulence. The manual results are validated in terms of the time-averaged velocity. The interfacial turbulence intensity is suggested to be greater than the water-phase velocity turbulence, typically between 20% and 40% in the unidirectional jet-shear region. Overall the manual results agree better with the calculation of adaptive-window cross-correlation technique. The relevance of the signal decomposition processing is also discussed, and it is emphasized that the phase-detection-based approaches are subject to the limitations of one-dimensional measurements in a complex three-dimensional flow.

Weirs may be used to control the discharge, decrease the water slope in canals and to distribute water between canals for irrigation, etc. The objective of this research was to investigate the influence of using one opening or more in weirs on discharge coefficient (Cd), the hydraulic jump characteristics and velocity distribution downstream of these structures. This study is based on an experimental program. Three cases of openings arrangements were included, one, two and three openings. Different diameters of openings (D) and different heights from the bed (Z) were tested. The experiments showed that decreasing (D/Z) for weirs which have the same openings numbers and diameters decreases the discharge coefficient (Cd) and the ratio between the length of the submerged hydraulic jump (Lj) and the water tail depth (yt). Also, decreasing (D/Z) leads to make the maximum velocity near the bed tends to be lifted upward. Moreover, Comparing weirs with different openings numbers but have the same openings area leads to that, weirs with one opening have a bigger (Cd) than weirs with two or three openings but the maximum velocity near the bed of the weir with three openings is less than that with one opening. Also, the hydraulic jump length downstream weir with three openings is less than that downstream weir with one opening. Finally, equations were developed to deduce the value of the coefficient of discharge for the composite structure.

Cyclic steps are long-wave (the ratio of wavelength to height is ≫ 1), upstream-migrating, upper-flow-regime bedforms bounded by internal hydraulic jumps (i.e., transition from densimetric Froude supercritical to subcritical flow) in turbidity currents. They commonly occur in regions with high gradients and slope breaks. Here we review the morphodynamic evolution and depositional products of cyclic steps and related supercritical bedforms (e.g., antidunes). We present examples from high-resolution geophysical surveys and monitoring of continental margins in western North America integrated with physically based numerical modeling of turbidity currents and associated bedforms. We compare numerical modeling results to direct monitoring of turbidity currents in the Squamish prodelta, British Columbia, Canada. Cyclic steps and antidunes influence phases of canyon-channel evolution, levee-overbank deposition, and channel-lobe-transition-zone sedimentation, thereby advancing channels and lobes into the basin. Bedforms range from relatively small cyclic steps and antidunes within active submarine canyons and channels (~ 10 1 m wavelength; ~ 10 0 m height) to large cyclic steps in less confined levee-overbank environments and the channel-lobe transition zone (~ 10 3 m wavelength; ~ 10 2 m height). Cyclic steps and related supercritical bedforms are important to the morphodynamic evolution of architectural elements of some deep-water depositional systems, especially those located along tectonically active margins with high gradients and slope breaks that can promote internal hydraulic jumps in turbidity currents.

Two-phase gas-liquid slug flow is the prevailing flow regime in many processes in the petroleum and chemical industries. This flow regime is the result of the growth of wavelike instabilities at the gas-liquid interface. The main characteristic of slug flow is the presence of liquid slugs that span the entire pipe diameter separated by gas bubbles. The rear end of these gas pockets can exhibit a staircase shape (also known as plug flow) or a hydraulic jump that reaches the top of the pipe when the flow rate is increased. In this paper, an experimental investigation of the statistical properties of slug flow is presented for flow initiation. A gas-liquid circuit made of acrylic tubes with a 26 mm ID was used to make these measurements. The test facility was composed of two sections: the first corresponded to a downward flow of −3 degree inclination where the prevalent flow regime was stratified flow, and the second was a horizontal section where the prevalent flow regime was slug flow. Resistive sensors located at three different positions in the horizontal section were used to acquire the liquid holdup, and the time series were processed and analyzed. Statistics for slug initiation position, slug and bubble lengths, bubble velocity, slug and unit-cell frequencies are presented. Further, the length and probability of occurrence of the bubble tail were also analyzed in the cases where the bubbles exhibited a staircase shape. Ultimately, data are provided for the validation and development of mathematical models and numerical codes for the simulation of two-phase slug flow.

Cyclic steps are ubiquitous in modern sedimentary environments, yet their recognition remains sparse in the rock record. Here, we interpret three sets of undulating backsets (1 to 3) recognized in the late Miocene-early Pliocene Latrania Formation in the Anza-Borrego Desert, the Fish Creek-Vallecito Basin, southern California, USA as the first cm- to dm-scale outcrop record of cyclic steps, based on asymmetrical cross-sections, upstream migration, and inversely graded laminae. Upstream migration and asymmetrical cross-sections of backsets and concomitant backset laminae are attributed to supercritical-to-subcritical flow transitions through weak hydraulic jumps, which are composed of: (i) thin (tens of centimetres) and slower (reported as flow velocities (Ū) of 0.45 to 1.45 m s− 1, with mean value of Ū = 0.89 m s− 1) subcritical (represented by internal Froude numbers (Fr) of 0.67 to 0.99, with mean value of Fr = 0.84) turbidity currents on the stoss sides, and (ii) thin (tens of centimetres) and faster (reported as Ū of 0.99 to 4.03 m s− 1, with mean value of Ū = 2.24 m s− 1) supercritical (represented by Fr of 1.84 to 3.07, with mean value of Fr = 2.42) turbidity flows on the lee sides. The inversely graded laminae in the troughs of backsets are 2 to 5 cm thick, and consist of two discrete divisions: (i) 1 to 2 cm thick, lower finer-grained divisions made up of parallel laminated siltstones, overlain by very fine- to fine-grained sandstones, and (ii) 2 to 3 cm thick, upper divisions composed of medium- to coarse-grained sandstones, with sporadic occurrence of subrounded pebbles. These inversely graded laminae are related to stratified, collisional and/or frictional traction carpets under conditions of high fall-out rates. Due to the poor preservation potential of cyclic steps, the rock record of cyclic steps is generally considered to be rare. The present outcrop-based study presents a detailed analysis of sedimentary facies, growth patterns, and flow dynamics of marine cyclic steps, thereby contributing to better understand architectural styles and lithological properties of cyclic steps in the geological record.

Inferred supercritical structures and bedforms, including sediment waves and backset-bedded sets, are identified as components of coarse-grained siliciclastic and bioclastic, high-gradient clinoform wedges (Plio-Pleistocene of southern Italy) and canyon head infills (Tortonian of Venetian pre-Alps), showing evidence of having been built out in a setting influenced by shallow-marine hydrodynamics. The facies identified are dominated by a range of traction carpets, formed after segregation of coarser particles in the lower part of bipartite density underflows. The generation of backset-bedded sets is thought to imply scouring due to impact of a submerged hydraulic jump on the bed, and upstream migration of the jump, concomitant with the deposition of backset beds on the stoss side of the developing bedform. Submerged hydraulic jumps apparently formed spontaneously and in any position on the foreset and toeset, without requiring any precursor bed defect. The mostly solitary, non-cyclical character of the bedforms prevents their attribution to cyclic steps. The sets of backset beds are locally underlain by chaotic infills of deep, steep-sided scours attributed to vigorous erosion at the hydraulic jump, accompanied by instantaneous loss in transport capacity which results in rapid plugging of the scour (hydraulic jump facies of Postma et al., 2014). Gravel waves have a distinct internal stratigraphy, and their length to amplitude ratios show lower mean values and higher variability when compared to sediment waves consisting of sand. The presence of supercritical bedforms on steep foreset slopes of the studied clinoform systems, even in proximity to the topset-foreset rollover, is believed to reflect high inefficiency of mud-poor and short run-out bipartite underflows episodically transporting relatively small volumes of coarse-grained sediment. This may also account for common solitary, non-cyclical bedforms. It is proposed that during intense oceanographic events, such as coastal storms, seaward sediment entrainment, assisted by gravity, was very effective on the gently sloping subaqueous topset, and that, beyond the topset-foreset rollover, the flows evolved to high-concentration turbidity underflows with supercritical Froude numbers. The flows are inferred to have been sustained, probably lasting for the duration of the meteorological events, and to have commonly been unsteady in discharge, fluctuating in concentration and size of transported sediments, and subject to peaks in velocity. The characteristics of the structures are regarded as typical of the systems fed by oceanographic processes, and may fall into the class of coarse-grained “small sediment waves with mixed relief” of Symons et al. (2016), formed from a combination of erosion and deposition, and by the action of stratified flows depositing from denser basal layers, and typically restricted to small-scale shallow-marine slope systems.

International audience; Surface wave breaking induces strong turbulence in the two-phase flow region. Detailed turbulence statistics were experimentally obtained using non-intrusive optical techniques in a breaking bore roller, at relatively large scale, with a bore Froude number Fr1 = 2.15 and Reynolds number Re = 2.3 × 105. These novel velocity data were ensemble-averaged based upon an instantaneous dataset of 24,320 images. In terms of the velocity field, the breaking bore roller was classified into three regions: the impinging jet, developing shear layer and flow reversal region. The vertical profiles of the longitudinal velocity data exhibited some self-similarity. The Reynolds stress data showed an anisotropic turbulent flow immediately downstream of the roller toe, and tended towards isotropy away from the roller toe. The vorticity data suggested that the breaking at the roller toe was responsible for the generation of vortices. The turbulent structures in the shear layer presented significantly smaller length and time scales with higher dissipation rate than other regions. A discussion between present turbulence statistical data and bubble dynamics from literature was developed. The comparison between present and past studies suggested a similarity in two-phase physical processes in the breaking roller region between the tidal bore, hydraulic jump, swash zone bore and breaking wave.

To countermeasure the scouring and tsunami energy reduction, this study conducted a series of laboratory experiments where vertically double layered vegetation (VDLV) was introduced behind the seaward embankment on a gravel bed. The experimental results demonstrated that the overtopping flow from the embankment experienced a submerged hydraulic jump over the embankment, against all the considered cases. The dense VDLV i.e. dense (G/d = 0.041, where G is the clear gap between the cylinders in the cross-stream direction, and d is the cylinder diameter) short submerged vegetation (L1) incorporated within a sparse (G/d = 2.125) tall emergent vegetation (L2) influenced the scour phenomena. It reduced the relative scoured depth by approximately 29 − 41% at the embankment toe, the maximum scoured depth by approximately 29 − 37%, and the scoured length by approximately 28 − 34%, as compared to that of single embankment system. Furthermore, dense VDLV provided the maximum i.e. 49 − 53%, loss to the total flow energy. The increase in the density of L1 in VDLV offered a larger drag to the flow by shifting the position of the submerged hydraulic jump more towards the embankment top; hence, consequently resulted in significant reduction of scoured depth, scoured length and energy of the tsunami flow.

This paper presents a newly-designed experimental setup based on the interaction of a dam-break flow with an elastic sluice gate in the context of the hydroelasticity problems. As the experimental measurement, displacements of the elastic sluice gate and water level evolutions at various points, calculated from the digital video images, are used. The present phenomenon includes violent free-surface motions with the rotational flow, hydraulic jump, and spilling type wave break, and both the static and dynamic impacts of that motions on the boundaries. Therefore, the experiment was repeated two times for testing the stability of the experimental process and measurements and, the obtained results were compared. The present phenomenon also was modeled numerically using the coupled SPH-FEM model and, the numerical computations were compared with experimental measurements.

The dynamics of slosh induced wave systems in shallow water tanks is analyzed for various excitation conditions. Shake table experiments have been systematically performed to understand the complex interaction of multi-wave system under harmonic excitation. From the experiments, it was observed that, for relatively large excitation amplitudes, the hydraulic jumps emanated around the resonance region. The hydraulic jump phenomenon is further explored for different tank aspect ratios, i.e, 2.5 ≤ L ∕ B ≤ 4.038. To establish the frequency bounds for hydraulic jumps, excitation amplitude and frequency are demarcated over the range of 0.841 ≤ β ≤ 1.628 and liquid depth range of 0.034 ≤ h ∕ L ≤ 0.069. The experimental bounds are juxtaposed with the theoretical bounds to analyze the margins present in hydraulic jumps. Although, the theoretical bound is independent of liquid depth, experimental observations clearly indicate a strong dependency.

A hydraulic jump is an abrupt transition between subcritical and supercritical flows which is associated with energy dissipation, air entrainment, spray, splashing, and surface waves. Both physical and numerical modeling were largely applied to study hydrodynamics, turbulence and air-entrainment in the hydraulic jump, while the literature about the application of classifier models is quite limited. Determining air-flow parameters and turbulent intensity has been merely performed by costly and time-consuming experimental methods, while this study is the first attempt to estimate the mentioned parameters using a computer-based methodology with desired precision. In the present study, air-flow parameters including void fraction (C) and bubble count rate (F), as well as turbulent intensity (Tu) on rough bed were estimated using Bayesian model averaging (BMA) and three multilayer perceptron (MLP), support vector regression (SVR) and generalized regression neural network (GRNN) as classifier models. To develop the stated models, the experimental data from Felder and Chanson (2016) were divided into four classes based on longitudinal distance from the jump toe. Results highlighted that the MLP and GRNN models have more accurate results compared to the SVR model. For F and Tu, the GRNN model and for C, the MLP model showed better performance than other models in four classes. The average acceptance rate between 15 and 30% of the BMA model performance for all classes proved the accuracy and efficiency of the proposed methodology. The average RMSE value of BMA results and the bests classifier models were 0.41 and 0.42, respectively, for the estimation of all three parameters. Results revealed that the BMA model by weighting individual classifier models could be able to estimate parameters with better accuracy than the best classifier model in each class. The significant outcome of this study is that the proposed model is able to render accurate results in a complex system such as hydraulic jump.

A non-hydrostatic model is developed to predict internal wave generations and propagations. The model employs a semi-implicit, fractional step algorithm to solve the governing equations based on the Cartesian grid system. Immersed boundary method is incorporated to deal with the complex geometry of uneven bottoms. The combination of the z -level vertical coordinate and the immersed boundary method enables the model to treat uneven bottoms and meanwhile to avoid numerical errors in the calculation of the baroclinic pressure force. To consider the effect of stratification, a variant of the Smagorinsky sub-grid scale model is employed to calculate the eddy viscosity and diffusivity. The capability of the model in resolving internal wave generation by tidal forcing over an idealized Gaussian-shaped topography is firstly validated by comparing the developed model with a terrain-following non-hydrostatic model. Then, two laboratory-scale test cases involving internal solitary wave propagations over variable topographies are considered. It can be found that the model captures the main characteristics of waveform evolution including internal hydraulic jump, wave breaking and waveform inversion. Thus, the proposed model provide an alternative to simulate internal wave generations and propagations.

Floods resulting from extreme events like tsunamis may inundate widespread inland areas, but vegetation can act as a natural buffer zone to reduce the inundation area and dissipate the energy of flowing water. This paper summarizes a series of laboratory experiments in which the energy loss through emergent vegetation in a steady subcritical flow was investigated. The energy loss was determined against vegetation of variable thickness (dn, where d = diameter of cylinder, n = number of cylinders in a stream-wise direction per unit of cross-stream width), density (G/d, where G = spacing of each cylinder in cross-stream direction, d = diameter of cylinder), and initial Froude number. On the upstream side of vegetation, the backwater rise increased by increasing both vegetation thickness and density. Contrarily, on the downstream side a breaking undular jump with a lateral shock wave was observed for a dense vegetation arrangement (G/d = 0.25), whereas a non-breaking undular jump with and without air bubbles was identified for intermediate (G/d = 1.09) and sparse (G/d = 2.13) vegetation conditions, respectively. Under these conditions, the maximum energy reduction due to a jump reached 6.4% for dense vegetation, and was reduced to 1.7% and 1.4% for intermediate and sparse vegetations, respectively. Hence, denser vegetation offers larger resistance, thus causes significant energy loss.

In this work, we present an experimental study on the re-aeration of a biological effluent coming from a wastewater treatment plant located at sea level. The oxygen transfer efficiency has been calculated for a hydraulic structure characterized by three different weirs jumps (Bazin type). The experimental results have been compared with those obtained by two (and well known) empirical equations (Avery-Novak equation (Avery and Novak, 1978) and Thene equation (Thene, 1988)). These equations did not allow a well fitting of the experimental data. We proposed a modification of the Thene equation by inserting of the Weber number of the jet. By this new correlation, we obtained a good fitting of re-aeration data obtained for the studied hydraulic structure.

In this study, an upwinding SPH model with a non-symmetric kernel function is proposed to predict one-dimensional open channel flows. Due to the application of non-symmetric kernel function biased in favor of the upstream side, numerical diffusion is intrinsically added into the discretized momentum equation using SPH. The proposed model thus has shown to have good potential to resolve steep gradient or discontinuous solutions without the need of exactly adding artificial viscosity to the discretized equation. Furthermore, an upwinding coefficient for the determination of the degree of upwinding is derived to accommodate the dispersion-relation-preserving (DRP) property. In wave number space, the error between the discretized SPH equations and the original partial differential equations is minimized, thereby yielding the optimized upwinding coefficient. The proposed model has been validated by solving four benchmark problems involving non-rectangular cross section, varying channel width, non-uniform bed slope and hydraulic jump. Comparison of the numerical and exact solutions shows that the proposed model has the ability of accurately predicting various open channel flows involving complicated transcritical flows. The consistency condition of the proposed model is also analyzed theoretically for the sake of completeness.

The characteristics of three-dimensional vortical flow structures in submerged hydraulic jumps (generated downstream of a sluice gate) are analyzed in this paper. Results of a careful experimental investigation of the mean flow as well as turbulence statistics obtained with the use of Acoustic Doppler Velocimetry (ADV) and Particle Tracking Velocimetry (PTV) are presented and discussed. Experiments encompass incident Froude numbers ( Fr 1 ) of 3, 4 and 5, and submergence factors ( S ) ranging from 0.18 to 1.04. First, distributions in three vertical planes of values of the stream-wise velocity component and turbulent kinetic energy (TKE) are shown. With this information, the influence of Fr 1 and S on turbulence statistics is assessed. For the first time to the best of our knowledge, an approximately self-similar behavior of the profiles of TKE in the fully-developed region of the submerged jump is reported herein. A “climb effect” in the TKE is identified, very much in agreement with what occurs with the velocities. Then, the analysis focuses on the zone located near the gate, aiming at explaining the physical mechanisms which are responsible for the vorticity of vertical axis in that area. A relationship between the length scale of the roller of horizontal axis ( L rsj ) and that of the vortices of vertical axis ( L v ) is introduced, revealing that the dynamics of the two vortices are strongly linked. Compelling evidence sustaining that vorticity of vertical axis appears as a consequence of boundary-layer separation associated with the lateral walls is also provided. Finally, the anisotropy of turbulence in the outskirts of the vertical vortices is addressed, finding that such anisotropy is a consequence rather a cause of the presence of the vortices.

Transition of plug to slug flow is associated with bubble detachment from elongated bubble tail or bubble entrainment inside the liquid slug. The mechanism responsible for this transition was earlier identified by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) based on the shape of the hydraulic jump observed at elongated bubble tail region. The transition mechanism reported by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) was only based on their flow visualization study. Plug to slug transition and associated dynamics of bubble detachment from the elongated bubble is analysed in the present paper using flow visualization and local velocity measurements. Experiments are reported for 13 different inlet flow conditions of air and water phases. Images of plug/slug flow structures are captured at a rate of 4000 FPS using FASTCAM Photron camera and the local values of axial liquid velocity are measured using LDV system synchronised with a 3D automated traverse system. LDV measurement of local liquid velocity in the liquid slug and liquid film establishes the reason for detachment of bubbles from the slug bubble tail.

In this study, heat transfer and hydrodynamics of a free water jet impinging a flat plate surface are experimentally investigated. The effects of the nozzle-to-plate spacing, which is equal to or less than one nozzle diameter ( H / d = 0.08–1), on the Nusselt number, hydraulic jump diameter, and pressure at the stagnation point are considered. The results show that the normalized stagnation Nusselt number, pressure, and hydraulic jump diameter are divided into two regions: Region (I) jet deflection region ( H / d ⩽ 0.4) and Region (II) inertia dominant region (0.4 H / d ⩽ 1). In region I, the normalized stagnation Nusselt number and hydraulic jump diameter drastically increase with decreasing the nozzle-to-plate spacing, since the stagnation pressure increases due to the jet deflection effect. In region II, the effect of the nozzle-to-plate spacing is negligible on the normalized stagnation Nusselt number and hydraulic jump diameter since the average velocity of the jet is constant, which means the jet deflection effect disappears. Based on the experimental results, new correlations for the normalized hydraulic jump diameter, stagnation Nusselt number, and pressure are developed as a function of the nozzle-to-plate spacing alone.

The shallow-water equations for two-dimensional hydrostatic flow over a bottom bathymetry b ( x ) are h t + ( u h ) x = 0 , u t + ( g h + u 2 / 2 + g b ) x = 0 . It is shown that the combination of discontinuous free-surface solutions and bottom step transitions naturally lead to singular solutions featuring Dirac delta distributions. These singular solutions feature a Rankine–Hugoniot deficit, and can readily be understood as generalized weak solutions in the variational context, such as defined in [13] , [22] . Complex-valued approximations which become real-valued in the distributional limit are shown to extend the range of possible singular solutions. The method of complex-valued weak asymptotics [22] , [23] is used to provide a firm link between the Rankine–Hugoniot deficit and the singular parts of the weak solutions. The interaction of a surface bore (traveling hydraulic jump) with a bottom step is studied, and admissible solutions are found.

The flow characteristics over vertical drops equipped with a grid roof, namely the “grid drop-type dissipator”, were investigated using model experimentation. To study the flow patterns and hydraulic characteristics, all three velocity components were measured. Moreover, a flow visualization technique was used to examine the flow structure of the falling jet through the grid roof, mixing zone, and the pool. The trends of the hydraulic and geometrical flow characteristics, the length scales of distributed/deflected jets, and aspects of the hydraulic jump in the pool were examined. The results indicate that the proposed hydraulic structure eliminates unfavorable flow conditions and forms the basis of a more effective flow control system compared with a plain vertical drop. Some 70% of the experimental data were randomly selected to calibrate the derived empirical equations. The remaining 30% of the data were used to validate these equations. Estimations compare well with the test data, indicating that the proposed empirical equations provide reliable estimates for the main flow characteristics. It is demonstrated that the dispersion/diffusion mechanism in the pool increases the velocity gradient as well as the momentum exchange and consequently, increases the energy dissipation relative to a plain vertical drop.

This experimental study was aimed at turbulence researches in ECC T-junction structure and it was conducted on ECC condensation heat transfer in a horizontal T-junction pipe. By using sub-cooled water in different flow rates, various flow patterns had a comparison with saturate steam in the cold leg. In the researches, the first part is dedicated to obtain the effects of hydraulic jump and back flow on T-junction thermal mixing. This research, which was based on momentum method, tries to find the influence of different flow patterns on the temperature distribution and capture the flow patterns' picture as reference. The equations, which can be employed to analyze temperature change, have been deduced after the research. And the second part of the researches focused on two-phase flow status after SI coolant mixed. The conclusion was deduced according to the pure steam SI injected condition. With some reasonable assumptions, the analysis included both steam Reynolds number and liquid Reynolds number correlations. The length of downstream is longer than that of the scaled-down distance from SI line to downcomer in PWR. And this could contribute to PWR safety analysis and find the relation between the flow status and mixed length. In addition, the test also figured out the relative velocity changes in T-junction thermal mixing following the Reynolds number research on mixed two-phase flow. This correlation could contribute to structure design improvement in PWR and prevent excessive steam from rushing to downcomer. All equations and correlations show good agreement within experiment data.

Hydrodynamic and heat transfer characteristics of the circular hydraulic jump by air-assistant water jet impingement was experimentally investigated using water and air as the test fluid. The effects of volumetric quality ( β = 0–0.9) on the hydraulic jump radius, local Nusselt number and, pressure at the stagnation point were considered under fixed water-flow-rate condition. The results showed that the dimensionless hydraulic jump radius increased with volumetric quality, attained a maximum value at around 0.8 of the volumetric quality, and then decreased. The hydraulic jump of two phase impinging jet is governed by the stagnation pressure and the lateral variation of Nusselt number is governed by hydraulic jump radius. Based on the experimental results, a new correlation for the normalized hydraulic jump radius of the impinging jet are developed as a function of the normalized stagnation pressure alone.