Free Surface Fluctuations Research Articles

Physical Simulation on the Liquid Metal Flow in FC-Mold of Slab Continuous Casting

The flow state and velocity distribution of liquid metal in the FC-Mold and the influence rules by the magnetic flux density have been investigated when electromagnetic brake adopted, applying mercury as medium to simulate molten steel in the continuous casting process. The velocity measurement has been completed by the Ultrasonic Doppler Velocimeter (UDV) under various magnetic distribution and the influence laws of magnetic flux density on the liquid metal flow in the mold has been analyzed. The experimental results indicate that, when the upper and lower magnetic flux density is 0.18T and 0.5T respectively, a preferable control effect can be obtained, not only the free surface fluctuation can be compressed, but also a plug flow can be rapidly formed.

Flow over sills by the MPS mesh-free particle method

A particular flow structure and the behaviour of free surface complicate flow modelling over sills, especially if the free surface is highly deformed and made up of spray. Mesh-free particle methods have recently been developed to increase the flexibility and accuracy of numerical methods to deal with these boundaries and interfaces. This research aims to develop, apply, and evaluate the capabilities of one of the particle methods, the moving particle semi-implicit method, for modelling flow over sills under various flow regimes. The model developed, along with modifications in its pressure calculation and boundary definition techniques, is applied to predict the free surface and the velocity profiles of sill flow. These results are compared with experimental measurements and results from other numerical techniques. They are demonstrated to agree well with the experiments, indicating that the model simulates velocity profiles and free surface fluctuations reasonably.

RADINS equations for aerated shallow water flows over rough beds

Depth-averaged equations describing turbulent free-surface flows are usually derived assuming that the free surface is constant over a statistical ensemble of realizations. This work presents the derivation of the Reynolds-Averaged-Depth-Integrated Navier–Stokes (RADINS) equations obtained if this assumption is removed. These equations are applied to transient turbulent open-channel flow over a rough bed with an aerated free surface containing air bubbles. The RADINS equations contain terms which explicitly include the contribution of turbulent free-surface fluctuations to the large-scale volume and momentum transfer. These terms are evaluated in a laboratory experiment which involves a turbulent bore climbing up a rough slope. The new RADINS equations are compared with the conventional depth-integrated-Reynolds-averaged Navier–Stokes (DIRANS) equations. The RADINS and DIRANS equations are identical only for flows with negligible depth fluctuations. If this condition is not satisfied, the equations are different and the terms in the RADINS equations have a clearer physical meaning.

Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers

The transition from supercritical to subcritical open channel flow is characterised by a strong dissipative mechanism called a hydraulic jump. A hydraulic jump is turbulent and associated with the development of large-scale turbulence and air entrainment. In the present study, some new physical experiments were conducted to characterise the bubbly flow region of hydraulic jumps with relatively small Froude numbers (2.4 < Fr 1 < 5.1) and relatively large Reynolds numbers (6.6 × 10 4 < Re < 1.3 × 10 5). The shape of the time-averaged free-surface profiles was well defined and the longitudinal profiles were in agreement with visual observations. The turbulent free-surface fluctuation profiles exhibited a peak of maximum intensity in the first half of the hydraulic jump roller, and the fluctuations exhibited some characteristic frequencies typically below 3 Hz. The air–water flow properties showed two characteristic regions: the shear layer region in the lower part of the flow and an upper free-surface region above. The air–water shear layer region was characterised by local maxima in terms of void fraction and bubble count rate. Other air–water flow characteristics were documented including the distributions of interfacial velocity and turbulence intensity. The probability distribution functions (PDF) of bubble chord time showed that the bubble chord times exhibited a broad spectrum, with a majority of bubble chord times between 0.5 and 2 ms. An analysis of the longitudinal air–water structure highlighted a significant proportion of bubbles travelling within a cluster structure.

Free-surface fluctuations and turbulence in hydraulic jumps

A hydraulic jump is the highly turbulent transition between a high-velocity impinging flow and a turbulent roller. The jump flow is characterised by some substantial air bubble entrainment, spray and splashing. In the present study, the free-surface fluctuations and air–water properties of the hydraulic jump roller were investigated physically for relatively small Froude numbers (2.4 < Fr 1 < 5.1) and relatively large Reynolds numbers (6.6 × 10 4 < Re < 1.3 × 10 5). The shape of the mean free surface profile was well defined, and the time-averaged free-surface elevation corresponded to the upper free-surface, with the quantitative values being close to the equivalent clear-water depth. The turbulent fluctuation profiles exhibited a maximum in the first part of the hydraulic jump roller. The free-surface fluctuations presented some characteristic frequencies between 1.4 and 4 Hz. Some simultaneous free-surface measurements at a series of two closely located points yielded the free-surface length and time scales of free-surface fluctuations in terms of both longitudinal and transverse directions. The length scale data seemed to depend upon the inflow Froude number, while the time scale data showed no definite trend. Some simultaneous measurements of instantaneous void fraction and free-surface fluctuations exhibited different features depending upon the phase-detection probe sensor location in the different regions of the roller.

CFD simulation of free liquid surface motion in a pilot plant stirred tank

AbstractThe Volume of Fluid method together with the Large Eddy Simulation technique for turbulence flow was used for CFD prediction of liquid flow and free liquid surface motion in a pilot plant cylindrical flat‐bottomed stirred tank with an inner diameter of 1 m filled with tap water at room temperature. A pitched‐blade (45°) down pumping impeller (diameter of 0.33 m) with six blades was used for stirring. The impeller speed was 180 rpm. For simulation of the impeller motion, the sliding mesh method was adopted. The CFD simulations of the flow field predicted a highly complex, multi‐dimensional dynamic system exhibiting unstable, pseudo‐stationary behaviour. The main advantage of this CFD simulation is the prediction of the velocity flow patterns and the free surface elevation/depression in the whole system at one time. The results for the location and dimensions of the free liquid surface fluctuation correspond well with an experimental investigation by a conductivity method.

High bandwidth linear viscoelastic properties of complex fluids from the measurement of their free surface fluctuations

We present a new non-invasive optical method to measure the linear viscoelastic properties of materials, ranging from complex fluids to soft solids, within a large frequency range (about 0.1–104 Hz). The surface fluctuation specular reflection (SFSR) technique is based on the measurement of the thermal fluctuations of the free surfaces of materials at which a laser beam is specularly reflected. The propagation of the thermal surface waves depends on the surface tension, density, and complex viscoelastic modulus G*(ω) of the material. The SFSR signal results from the contribution of different surface modes, and we discuss the leading effect measured as a function of |G*| and frequency. For known surface tension and density, we show that the frequency dependent elastic and loss moduli can be deduced from the fluctuation spectrum. Using a viscoelastic solid (a cross-linked PDMS), which linear viscoelastic properties are known in a large frequency range from rheometric measurements and the time–temperature superposition principle, we show that there is a good agreement between the rheological characterization provided by rheometric and fluctuation measurements. We also present measurements conducted with a complex fluid: a supramolecular polymer solution, formed from H-bonded molecules. At low frequencies, the agreement with rheometric measurements is again very good. We further investigate the high frequency rheology of the supramolecular polymer solution, and show that it behaves very similarly to supramolecular polymer solutions formed by wormlike giant micelles.

Effect of Feeding Modes of Molten Steel on the Mould Metallurgical Behavior for Round Bloom Casting

Three kinds of modes for molten steel delivery have been studied in the paper for better understanding of their mould metallurgical effects during round bloom casting. The melt flow, free surface fluctuation, temperature field and solidification behavior in the mould region have been numerically analyzed upon the respective adoption of conventional straight single SEN, quad-furcated SEN with outlets in radial direction and a new type of quad-furcated SEN with outlets at tangential direction. For the latter, a strong horizontal swirling flow has been observed along with the upper and lower recirculation region in the mould. It is shown that the horizontal swirling flow in the mould can reduce the impingement depth of molten steel remarkably, inhibit the mould level fluctuation, and create an active bulk flow below the meniscus, which can also move the hot spot upward and promote superheat dissipation of the molten steel. Meanwhile, the temperature of molten steel near the free surface can be increased by 2.6 K to 4.4 K as compared with the two other normal nozzles. Moreover, compared with quad-furcated SEN with outlets in radial direction, the jet impingement on shell is much weaker, while the thickness of solidified shell at the cross-section of the mould is more even. Furthermore, the shell thickness at exit of the mould under the new type of SEN can reach approximately 18.6 mm, while that under quad-furcated SEN with outlets at radial direction is about 17.4 mm, which leave much allowance for the speed enhancement of present round bloom castings.

ICONE19-43893 EVALUATION OF STATISTICAL PROPERTIES OF FREE-SURFACE FLUCTUATION ON A HIGH-SPEED WATER JET USING LASER REFRACTION TECHNIQUE

Free-surface fluctuation on a high-speed water jet has been evaluated using a laser beam refraction technique. This technique employs two pulse laser diodes and one high-speed optic detector. By detecting the two dimensional (2D) trajectory of laser beams refracted at free surface, the local streamwise slope-angle fluctuation at two measuring locations 1.27 mm apart on a jet free surface can be evaluated. The experiments are conducted for several locations along the jet center axis within the range of average velocity up to 10 m/s. The wave speed is evaluated from dominant time lag of cross-correlation coefficient for individual wave period, which is divided from time-series slope-angle data according to the zero-up-crossing method. The shape of waves is also calculated by integrating the free-surface slope angle. The wavelength and wave height are evaluated from the individual waveform. The steepness of free surface wave takes a maximum at a certain distance from nozzle exit for U &le; 8 m/s. This suggests that the initial amplification of wave results in a wave breaking on the jet free surface for these velocity conditions.

Influence of the Development History of Nozzle Wall Boundary Layer upon Wave Generation on a Liquid Jet Free Surface

The relation between the development of the wall boundary layer in a convergent nozzle and free surface waves on the emanated liquid jet has been investigated experimentally. In the convergent nozzle, which forms a water jet along a flat back wall, the velocity profiles of the wall boundary layer were measured using a laser Doppler velocimeter with jet average velocities of U0 = 5, 10 and 15 m/s. The property of free-surface waves and the intermittency factor of free surface fluctuations were also determined by photography and an optical measurement technique, using laser beam refraction on the jet surface. For the lowest velocity case U0 = 5 m/s, the mean velocity profiles of the boundary layer under the pressure gradient in the convergent nozzle indicated an inverse transition from turbulent to laminar boundary layer, so-called relaminarization. On the other hand, for the higher velocity case U0 ≥ 10 m/s, the relaminarization in the convergent section became incomplete. For these cases, the turbulent intensity near the wall increased significantly and the nozzle-exit boundary layer was restored quickly to a turbulent profile for a short parallel section immediately upstream of the nozzle exit plane. The increase in the velocity fluctuation near the wall promotes wave generation downstream of the nozzle exit plane. Therefore, the intermittence of the wave packet almost disappeared and the jet free surface was covered with continuous capillary waves when the turbulent boundary layer was separated from the nozzle exit.

Evaluation of Streamwise Waveform on a High-Speed Water Jet by Detecting Trajectories of Two Refracted Laser Beams

Free surface fluctuations on a high-speed water jet were measured by a laser beam refraction technique. This method can be used to obtain quantitative time-series data on local surface fluctuations. The developed system employs two pulsed laser diodes, and it uses a high-speed optical sensor to detect the instantaneous positions of the laser beams that are refracted at the free surface. Fluctuations in the slope angle are measured at two locations separated by 1.27 mm. The wave speed of each free surface wave, which is determined by the zero-upcrossing method, is experimentally evaluated by the cross-correlation method. A two-dimensional waveform is obtained by integrating the slope angle data. The local mean wavelength and mean wave steepness are evaluated for average jet velocities up to m/s. Streamwise waveforms of the high-speed water jet at several locations exhibit appreciable asymmetry and have steep profiles.

Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: turbulence structure and correlation with the free surface

This paper is a companion paper to a study devoted to the analysis of experimental instantaneous fluid levels and three-component fluid velocity measurements in a stationary flow field generated by a Crump weir in a laboratory flume, using an ultrasonic distance sensor and a three-probe arrangement of an ultrasonic Doppler velocity profiler (UVP) (Longo in Exp Fluids, doi: 10.1007/s00348-010-0881-5, 2010). Whereas Longo (Exp Fluids, doi: 10.1007/s00348-010-0881-5, 2010) deals with a general overview of the problem, the description of the experiments and the analysis of the free surface statistics and relevant scales, the present manuscript is devoted to a detailed analysis of the turbulence and the correlation with the free surface. The data are elaborated by obtaining the macroturbulence Reynolds tensor, using conditional averages based on free surface–fluctuation statistics. We also compute the two-point correlations of fluid velocity, the micro-scale and the integral scale, the correlation between free surface and the turbulence beneath. A free surface–boundary layer was detected having a thickness proportional to the root mean square of the free surface–height series and with a velocity scale that correlates well with the free surface–elevation time gradient. Most of the relevant state variables, such as the mean velocity and Reynolds stress components, collapse to a single curve if scaled appropriately. There are many indicators that a specific regime occurs that has an optimal tuning between the free surface and turbulence. In this regime, the length scales are considered as an indicator.

光学測定法を用いた水噴流自由界面波の統計的性質評価(&lt;特集&gt;第14回動力・エネルギー技術シンポジウム)

Free surface fluctuations at the neighboring two locations on a water jet have been evaluated using the developed non-intrusive optical technique. The free-surface slope angles are measured by detecting the two dimensional trajectories of laser beams refracted at the jet free surface. The obtained time series data of slope angles are divided into each wave period in accordance with the zero-up-crossing method. Then, the individual wave speed is evaluated from the dominant time lag of cross-correlation coefficient. The spatial shape of each wave is reconstructed by integrating the slope angle data. By comparing the analysis of wave shape statistics and the visual observation of free-surface photograph, it is found that the wave steepness reaches a maximum in the free surface region where a periodic wave train breaks down into less regular three dimensional patterns. In addition, the probability density functions of non-dimensional wave height are close to the Rayleigh distribution in the downstream region of wave breaking.

Free-surface fluctuations in hydraulic jumps: Experimental observations

A hydraulic jump is the rapid and sudden transition from a high-velocity supercritical open channel flow to a subcritical flow. It is characterised by the dynamic interactions of the large-scale eddies with the free-surface. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 3.1 and 8.5 to investigate these interactions. The dynamic free surface measurements were performed with a non-intrusive technique while the two-phase flow properties were recorded with a phase-detection probe. The shape of the mean free surface profile was well defined and the turbulent fluctuation profiles highlighted a distinct peak of turbulent intensity in the first part of the jump roller, with free-surface fluctuation levels increasing with increasing Froude number. The dominant free-surface fluctuation frequencies were typically between 1 and 4 Hz. A comparison between the acoustic sensor signals and conductivity probe data suggested that the air–water “free-surface” detected by the acoustic sensor corresponded to about the boundary between the turbulent shear layer and the upper free-surface layer. Simultaneous measurements of free surface and bubbly flow fluctuations for Fr = 5.1 indicated that the frequency ranges of both sensors were similar ( F < 5 Hz) whatever the position downstream of the toe. The present results highlighted that the dynamic free-surface measurements can be conducted successfully using acoustic displacement meters, and the time-averaged depth measurements was a physical measure of the free-surface location in hydraulic jumps.

Experimental Study on the Amplitude of a Free Surface Fluctuation

An experimental study was performed to measure the fluctuation phenomena of a free surface in a vessel with or without an internal structure. A flow enters from the bottom and flows out of the side wall nozzles. Characteristics of the free surface fluctuation are investigated in terms of the geometry factors of the vessel and the flow rate. A modified Froude number is proposed to describe the amplitude of a free surface fluctuation. The fluctuation amplitude increases stably with an increase in the ratio of the vessel diameter to the water level in a vessel without an internal structure. When the ratio is greater than about 2, the fluctuation decreases suddenly with an increase in the ratio and it becomes unstable. The fluctuation amplitude is linearly proportional to the square of the Froude number. The amplitude of a free surface fluctuation increases with an increase in the height of an internal structure, but this increasing ratio is reduced when the height becomes higher. Two correlations were developed in terms of the Froude number and geometry factors to predict the amplitude of the free surface fluctuation in a vessel with or without an internal structure.

Effect of Sen Design on Surface Fluctuation and Solidifying Shell in Slab Mold and Its Optimization

Turbulent flow and heat transfer coupled with solidification in slab continuous casting mold was studied by numerical simulation method. Volume of fluid (VOF) model is used to solve steel-air two-phase flow problem and enthalpy-porosity scheme is introduced to solve the fluid flow problem involving solidification. Contributions of various nozzle port angles and port widths and heights on the free surface fluctuation and the thickness of solidifying shell in slab mold were particularly investigated, based on which the structure of submerged entry nozzle was optimized. Flow inside the common nozzle port cannot fill the entire outlet area, having a recirculation in the upper portion of the port, which is enlarged for the nozzle port with both larger height and width. Results show that the flow in mold cavity is mainly controlled by the nozzle port angle. The increase of the angle of upper face of the port to shape a roughly streamlined inner-wall improves the effective area fraction of the nozzle, resulting in less jet impingement, weaker free surface turbulence and thicker solidifying steel shell.

Turbulence measurements in the bubbly flow region of hydraulic jumps

A hydraulic jump is characterized by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air–water flow measurements were performed in a large-size facility using two types of phase-detection intrusive probes: i.e. single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent integral time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of Chanson [H. Chanson, Bubbly flow structure in hydraulic jump, Eur. J. Mech. B/Fluids 26 (3) (2007) 367–384], providing the turbulent scales of the eddy structures advecting the air bubbles in the developing shear layer. The length scale L xz is an integral air–water turbulence length scale which characterized the transverse size of the large vortical structures advecting the air bubbles. The experimental data showed that the dimensionless integral turbulent length scale L xz / d 1 was closely related to the inflow depth: i.e. L xz / d 1 = 0.2–0.8, with L xz increasing towards the free-surface.

Periodic Oscillation Caused by a Flow over a Vertical Drop Pool

The flow patterns of various dropping flows were investigated and classified experimentally for subcritical approach flows passing a vertical drop pool. A wave gauge was used to measure the free surface fluctuations in the pool. A flow visualization technique was employed to reveal the flow structure of the dropping flows qualitatively. It was discovered that, under certain conditions, the dropping flow forms a switching jet that oscillates up and down periodically and impinges on the bed and the downstream pool wall alternately. The switching jet switches between an impinging jet (a napped flow) and a sliding jet (a skimming flow), causing it to oscillate periodically with a unique period. The primary frequency of the periodic oscillation was determined by applying spectral analysis to the time series of the gauge measurements. Since a large number of air bubbles was entrained in the oscillatory flow, particle image velocimetry, and bubble image velocimetry were used for quantitative velocity determination in the liquid region and the aerated region, respectively. The mechanism causing the periodic oscillation in the pool was elucidated, and variables affecting the oscillation frequency were identified. An empirical relation between a weighted Strouhal number and a grouped dimensionless parameter was proposed to predict the primary frequency of the periodic oscillatory flow.

Investigation of free-surface fluctuations of liquid lithium flow for IFMIF lithium target by using an electro-contact probe

In the international fusion materials irradiation facility (IFMIF), 14 MeV neutrons will be generated by 40 MeV deuteron beam injection into a high-speed liquid lithium (Li) plane jet, flowing along a vertical concave wall in vacuum. The Li jet has to be stable to produce a stable neutron field, while a free surface flow is anticipated to be unstable. In order to ensure a reliable operation, a detailed knowledge of the Li flow is of conical importance. The experiment on the Li flow is conducted using the Li loop facility to qualify the magnitude of the surface oscillation. The test section of this loop, which is a 1/2.5 scale of the IFMIF design, produces a flat plane jet of 10 mm in depth and 70 mm in width with a free surface in the velocity range of up to 15 m/s. In the present study, a surface-detection apparatus called electro-contact probe, is employed. This apparatus allows us to measure the surface oscillation directly. By means of the electro-contact probe, the magnitude of the surface oscillation in this configuration was found to be in the range from 2.2 to 2.9 mm at the position of 175 mm downstream from the nozzle exit at a mean velocity of 15 m/s. This is the first time it was measured in detail. These values are considered to be improved in the case of the actual target of IFMIF. Estimation shows the present data of 2.9 mm could be transformed to be much smaller value, if the flow is free from the effect of surface wakes.

Air–water interface dynamic and free surface features in hydraulic jumps

Following previous experimental works (Mouaze et al., J. Fulids Engng. ASME 127(6) (2005) 1191–1193; Murzyn et al., Int. J. Multiphase Flow, 31(1) (2005) 141–154) on gas fraction characterisation in hydraulic jumps, the present paper aims to investigate free surface properties developing in these flows. Indeed, air–water interface exhibits a wide range of frequencies that free surface probes are not always enough accurate to follow. As a solution, two new free surface wire gauges (thin wires, φ = 0.05 mm, 1mm apart) have been built and calibrated. Accurate measurements of free surface fluctuations have been obtained with frequency resolution up to 12 Hz. Two sets of experiments have been made depending on Froude (Fr) and Weber (We) numbers. Experimental results showthat free surface mean and turbulent profiles exhibit discontinuities at the front of the toe characterized by a sudden high level of turbulence downstream followed by a zone of dissipation. Furthermore, free surface length scales have been estimated from correlation measurements. Similar features are found according to Fr andWe. Good agreement is shown with results deduced from a video analysis technique (Mouaze et al., J. Fulids Engng. ASME 127(6) (2005) 1191–1193). Lastly, comparison is made with Brocchini and Peregrine (Brocchini and Peregrine, J. Fluid Mech. 449 (2001a) 225–254; 449 (2001b) 255–290) depicting similar shapes for behaviour of vertical velocity fluctuations (w ′) as a function of longitudinal free surface length scale.