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.     

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 < Fr₁ < 5.1) and relatively large Reynolds numbers (6.6 × 10⁴ < Re < 1.3 × 10⁵). 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 < Fr₁ < 5.1) and relatively large Reynolds numbers (6.6 × 10⁴ < Re < 1.3 × 10⁵). 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.     

Simulating air entrainment and vortex dynamics in a hydraulic jump

The air entrainment characteristics of three separate Froude number hydraulic jumps are investigated numerically using an unsteady RANS, realizable k–ε turbulence model, with a Volume of Fluid treatment for the free surface. Mean velocity profiles, average void fraction, and Sauter mean diameter compare favorably with experimental data reported in literature. In all simulations, time-averaged void fraction profiles show good agreement with experimental values in the turbulent shear layer and an accurate representation of interfacial aeration at the free surface. Sauter mean diameter is well represented in the shear layer, and free surface entrainment results indicate bubble size remains relatively unchanged throughout the depth of the jump. Several different grid resolutions are tested in the simulations. Significant improvements in void fraction and bubble size comparison are seen when the diameter to grid size ratio of the largest bubbles in the shear layer surpasses eight. A three-dimensional simulation is carried out for one Froude number jump, showing an improvement in the prediction of entrained air and bubble size compared with two-dimensional results at a substantial increase in computation time. An analysis of three-dimensional vorticity shows a complex interaction between spanwise and streamwise vortical structures and entrained air bubbles. The jump is similar to a turbulent mixing layer, constrained by the free surface, with vortex pairing and subsequent fluctuations in free surface elevation. Downstream fluctuations of the toe are associated with a roll up of the primary spanwise vortex, fluctuations of the free surface, and counter-rotating streamwise vortex pairs. The action of these flow structures is likely responsible for the improvement in three-dimensional results.     

Skin friction reduction by large air bubbles in a horizontal channel flow

Microbubble and air film methods are believed to be applicable to skin friction reduction in ships. Small bubbles are dispersed into the turbulent boundary layer in the former case, and wide air layers cover the wall surface in the latter case. Previous studies did not specifically address the intermediate case between the microbubble and air film conditions. This study is concerned with the possibility and mechanism of drag reduction using relatively large air bubbles compared to the boundary layer thickness in a horizontal turbulent channel flow. The relationship between local skin friction and the bubble’s interfacial structure is investigated by synchronizing the measurement of wall-shear stress with the image acquisition of bubbles. The bubble sizes range from 2 to 90 mm approximately. As a result, a negative correlation between the local skin friction and the local void fraction is confirmed by the time-resolved measurement. A new observation is the fact that the local skin friction decreases drastically in the rear part of individual large bubbles, and rapidly increases after the bubble’s rear interface passes. This characteristic underlies the bubble-size dependency of the average skin friction in the intermediate bubble size condition.     

Dynamics of large turbulent structures in a steady breaker

The flow near the leading edge of a steady breaker has been studied experimentally using Bubble Image Velocimetry (BIV) with the aim of characterizing the dynamics of the large eddies responsible for air entrainment. It is well reported in the literature, and confirmed by our measurements of the instantaneous velocity field, that this flow shares some important features with the turbulent shear-layer formed between two parallel semi-infinite streams with different velocities. Namely, the formation of a periodic array of coherent vortices, the constant convective velocity of those vortices, the linear relation between their size and their downstream position and the self-similar structure of both mean velocity profiles and Reynolds shear stresses. Nonetheless, important differences exists between the dynamics of the large eddies in a steady breaker and those in a free shear-layer. Particularly, the convective velocity of these large structures is slower in a steady breaker and, consistent with this, their growth rates are larger. A physical interpretation of these differences is provided together with a discussion of their implications. To support our measurements and conclusions, we present a careful analysis of the accuracy of the BIV technique in turbulent flows with large bubbles.     

Numerical computation of fluid pressure transients in pumping installations with air entrainment

In pumping installations such as sewage pumping stations, where gas content and air entrainment exist, the computation of fluid pressure transients in the pipelines becomes grossly inaccurate when constant wave speed and constant friction are assumed. A numerical model and computational procedure have been developed here to better compute the fluid pressure transient in a pipeline by including the effects of air entrainment and gas evolution characteristics of the transported fluid. Free and dissolved gases in the fluid and cavitation at the fluid vapour pressure are modelled. Numerical experiments show that entrained, entrapped or released gases amplify the pressure peak, increase surge damping and produce asymmetric pressure surges. The transient pressure shows a longer period for down-surge and a shorter period for up-surge. The up-surge is considerably amplified and the down-surge marginally reduced when compared with the gas-free case. These observations are consistent with the experimental observations of other investigators. Numerical experiments also show that the use of a variable loss factor in the pressure transient analysis produces marginally higher maximum and lower minimum pressure transients when compared with the constant-loss-factor model for pipelines where the pressures are above the fluid vapour pressure.     

Momentum transport in a turbulent mixing layer

The turbulent momentum transport phenomena in a two-dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time-dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large-scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian-like, with only a few exceptions.     

Treatment of numerical diffusion in strong convective flows

A three-dimensional extension of the QUICK scheme adapted for the finite volume method and non-uniform grids is presented to handle convection-diffusion problems for high Peclet numbers and steep gradients. The algorithm is based on three-dimensional quadratic interpolation functions in which the transverse curvature terms are maintained and the diagonal dominance of the coefficient matrix is preserved. All formulae are explicitly given in an appendix. Results obtained with the classical upwind (UDS), the simplified QUICK (transverse terms neglected) and the present full QUICK schemes are given for two benchmark problems, one two-dimensional, steady state and the other three-dimensional, unsteady state. Both QUICK schemes are shown to give superior solutions compared with the UDS in terms of accuracy and efficiency. The full QUICK scheme performs better than the simplified QUICK, giving even for coarse grids acceptable results closer to the analytical solutions, while the computational time is not affected much.     

Simulation of proppant transport at intersection of hydraulic fracture and natural fracture of wellbores using CFD-DEM

Proppants transport is an advanced technique to improve the hydraulic fracture phenomenon, in order to promote the versatility of gas/oil reservoirs. A numerical simulation of proppants transport at both hydraulic fracture (HF) and natural fracture (NF) intersection is performed to provide a better understanding of key factors which cause, or contribute to proppants transport in HF–NF intersection. Computational fluid dynamics (CFD) in association with discrete element method (DEM) is used to model the complex interactions between proppant particles, host fluid medium and fractured walls. The effect of non-spherical geometry of particles is considered in this model, using the multi-sphere method. All interaction forces between fluid flow and particles are considered in the computational model. Moreover, the interactions of particle–particle and particle–wall are taken into account via Hertz–Mindlin model. The results of the CFD-DEM simulations are compared to the experimental data. It is found that the CFD-DEM simulation is capable of predicting proppant transport and deposition quality at intersections which are in agreement with experimental data. The results indicate that the HF–NF intersection type, fluid velocity and NF aperture affect the quality of blockage occurrence, presenting a new index, called the blockage coefficient which indicates the severity of the blockage.     

Numerical modelling and computation of fluid pressure transients with air entrainment in pumping installations

In pumping installations such as sewage pumping stations, where gas content and air entrainment exist, the computation of fluid pressure transients in pipelines becomes grossly inaccurate when a constant wave speed is assumed. An accurate numerical model with gas release and absorption has been developed in this paper and used to compute the fluid pressure transients in the pumping mains of selected pumping installations. Free and dissolved gases in the transported fluid and cavitation at vapour pressure are also modelled. When compared with the gas-free case, computations show that entrained, entrapped or released gases amplify the positive pressure peak, increase surge damping and produce asymmetric pressure surges. While the upsurge with air entrainment in the pipelines was considerably amplified, the downsurge was only marginally reduced. The computed results show good agreement with the data available.     

Experimental and numerical studies of rotational relaxation behind a strong shock wave in air

This paper describes the experimental and numerical investigations of unknown characteristics of the rotational nonequilibrium phenomena behind a strong shock wave in air. Experiments were carried out using a piston-driven shock tube with helium as driving gas and air as driven (test) gas, operated as a two-stage shock tube. In the experiments, emission spectra of NO were measured to evaluate the rotational temperature behind a strong shock wave. The numerical calculations use the computational code for the thermal and chemical nonequilibrium flow behind a strong shock wave developed by the present author's group, where 11 chemical species (N, O, NO, N, O, N, O, NO, N, O, e) and 48 chemical reactions of high-temperature air are considered. The thermal nonequilibrium is expressed by introducing an 8 temperature model composed of translational temperature, rotational and vibrational temperatures for N, O, NO, and electron temperature. The coupling of a rotation, vibration and dissociation (CRVD) model was incorporated to take sufficiently into account the rotational nonequilibrium. The calculations were conducted for the same conditions as the experimental ones. From the calculated flow properties, emission spectra were re-constructed using the code for computing spectra of high temperature air “SPRADIAN”. Furthermore, rotational and vibrational temperatures of NO (0,1) were determined from a curve fitting method and compared with the computed results. Received 12 September 2001 / Accepted 18 February 2002     

Orthogonal wavelet analysis of counter gradient transport phenomena in turbulent asymmetric channel flow

In this paper four families of orthogonal wavelets are applied to analyze the turbulent counter gradient transport phenomena in fully developed asymmetric channel flows. The results show that: (1) In the instance of counter gradient transport, the principal scale of the coherent structure is responsible for the strong local counter gradient transport; (2) Counter gradient transport phenomena have a strong effect on the intermittency of turbulence; (3) Non-Gaussian part of the principal coherent structure is essential for counter gradient transport phenomena.The project supported by the National Natural Science Foundation of China (10272071, 10472063)     

Turbulent transport of particles in a straight square duct

Turbulent flow through a duct of square cross-section gives rise to off-axis secondary flows, which are known to transfer momentum between fluid layers thereby flattening the velocity profile. The aim of this study is to investigate the role of the secondary flows in the transport and dispersion of particles suspended in a turbulent square duct flow. We have numerically simulated a flow through a square duct having a Reynolds number of Re_τ = 300 through discretization of the Navier–Stokes equations, and followed the trajectories of a large number of passive tracers and finite-inertia particles under a one-way coupling assumption. Snapshots of particle locations and statistics of single-particle and particle pair dispersion were analyzed. It was found that lateral mixing is enhanced for passive tracers and low-inertia particles due to the lateral advective transport that is absent in straight pipe and channels flows. Higher inertia particles accumulate close to the wall, and thus tend to mix more efficiently in the streamwise direction since a large number of the particles spend more time in a region where the mean fluid velocity is small compared to the bulk. Passive tracers tend to remain within the secondary swirling flows, circulating between the core and boundary of the duct.     

Large eddy simulation of turbulent statistical and transport properties in stably stratified flows

Three dimensional large eddy simulation （LES） is performed in the investigation of stably stratified turbulence with a sharp thermal interface. Main results are focused on the turbulent characteristic scale, statistical properties, transport properties, and temporal and spatial evolution of the scalar field. Results show that the buoyancy scale increases first, and then goes to a certain constant value. The stronger the mean shear, the larger the buoyancy scale. The overturning scale increases with the flow, and the mean shear improves the overturning scale. The flatness factor of temperature departs from the Gaussian distribution in a fairly large region, and its statistical properties are clearly different from those of the velocity fluctuations in strong stratified cases. Turbulent mixing starts from small scale motions, and then extends to large scale motions.     

送风方式对飞机座舱内污染物传播影响研究

采用数值模拟方法研究了波音737-200座舱模型内的气流场以及污染物传播过程,并通过实验数据加以验证;分析了天花板加侧壁送风(混合送风)、侧壁送风以及天花板送风三种送风方式下座舱内的速度场、涡量场、污染物浓度场和空气龄,并且解释了舱内流场结构对污染物传播过程的影响。研究结果表明:不同送风方式下飞机座舱内污染物的传播过程差异明显,这是由流场结构特征的差异造成的,特别是在小尺度范围内,涡结构十分复杂,严重影响污染物的传播规律;在聚集过程中,污染物更容易在漩涡范围内聚集,而变形主导的气流运动会阻碍污染物向更大范围传播;在排除过程中,天花板送风形式下污染物的排除效率最快,混合送风次之,侧壁送风最慢。这对于防控新冠肺炎是有参考价值的。     

Large-scale flow structures and heat transport of turbulent forced and mixed convection in a closed rectangular cavity

Results of an experimental study of flow structure formation and heat transport in turbulent forced and mixed convection are presented. The experiments were conducted in a rectangular cavity with a square cross section, which has an aspect ratio between length and height of Γ_xz = 5. Air at atmospheric pressure was used as working fluid. The air inflow was supplied through a slot below the ceiling, while exhausting was provided by another slot, which is located directly above the floor. Both vents extend over the whole length of the cell. In order to induce thermal convection the bottom of the cell is heated while the ceiling is maintained at a constant temperature. This configuration allows to generate and study mixed convection under well defined conditions. Results of forced convection at Re = 1.07 × 10⁴ as well as mixed convection at 1.01 × 10⁴ ? Re ? 3.4 × 10⁴ and Ra = 2.4 × 10⁸ (3.3 ? Ar ? 0.3), which were obtained by means of Particle Image Velocimetry and local temperature measurements, are presented. For purely forced convection a 2D mean wind, which can be approximated by a solid body rotation, is found. With increasing Archimedes number this structure becomes unstable, leading to a transition of the solid body rotation into additional smaller convection rolls. Proper orthogonal decomposition of the instantaneous velocity fields has been performed for further analysis of these coherent large-scale structures. Their fingerprint is found in the spatial temperature distribution of the out flowing air at the end of the outlet channel, which reveals a temporally stable profile with two maxima over the length of the outlet. Moreover a maximum in the global enthalpy transport by the fluid is found at Ar ≈ 0.6.