Dilution characteristics of dual buoyant jets in wavy cross-flow environment

Due to the difference in density between the discharge effluent and coastal water,partially treated wastewater is often discharged into the marine environment as a buoyant jet via submarine outfalls with multiport diffusers.The dilution characteristics of effluent discharge(dual buoyant jets)in a wavy cross-flow environment were studied in a laboratory.The planar laser-induced fluorescence technique was used to obtain the concentration data of the jets.The effects of different environmental variables on the diffusion and dilution characteristics of the jets were examined through physical experiments,dimensional analysis,and empirical formulations.It was found that the dilution process of the dual jets could be divided into two components:the original jet component and the effluent cloud component.The jet-to-current velocity ratio was the main parameter affecting the concentration levels of the effluent cloud.The merging of the two jets increased the jet concentration in the flow field.When the jets traveled further downstream,the axial dilution increased gradually and then increased significantly along the axis.Under the effects of strong waves,the concentration contours branched into two peaks,and the mean dilution became more significant than under the effects of weak waves.Therefore,the dilution of the effluent discharge was expected to be significant under strong wave effects because the hydrodynamic force increased.A dilution equation was derived to improve our understanding of the dilution process of buoyant jets in a wavy cross-flow environment.This equation was used to determine the influences of the jet-to-current velocity ratio,wave-to-current velocity ratio,and Strouhal number on the minimum jet dilution.It revealed that the wave and buoyancy effects in effluent discharges were significant.

Fluid Flow and Mixed Heat Transfer in a Horizontal Channel with an Open Cavity and Wavy Wall

Heat exchangers are utilized extensively in different industries and technologies.Consequently,optimizing heat exchangers has been a major concern among researchers.Although various studies have been conducted to improve the heat transfer rate,the use of a wavy wall in the presence of different types of heat transfer mechanisms has not been investigated.This study thus investigates the mixed heat transmission behavior of fluid in a horizontal channel with a cavity and a hot,wavy wall.The fluid flow in the channel is considered laminar,and the governing equations including continuity,momentum,and energy are all solved numerically.The numerical solution is stabilized by using a first-order multi-dimensional characteristic-based scheme in combination with a fifth-order Runge-Kutta method.The flow and heat transfer effects of varying Richardson numbers,Reynolds numbers,wave amplitude,wavelength,channel height,and cavity width are examined.The results indicate that the mean Nusselt number increases with an increase in Reynolds number,wave amplitude,and cavity width,while it decreases with an increase in Richardson number,wavelength,and channel height.The minimum Nusselt number is calculated to be 0.7,whereas the maximum Nusselt number is 27.09.The Nusselt number has only increased by 40%in the higher depths of the cavity,despite the Richardson number being 10,000 times larger.But this figure increases to 130%at lower depths.The mean Nusselt number is thus significantly influenced by channel height and cavity width.The influence of wave amplitude on the mean Nusselt number is twice that of wavelength.

Simulation of Natural Convection Flow with Magneto-Hydrodynamics in a Wavy Top Enclosure with a Semi-Circular Heater

Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approach is used to solve two-dimensional governing mass, momentum and energy-equations for natural convection flow in the presence of a magnetic field on a roof top with semi-circular heater. In the enclosure the horizontal lower wall was heated, the vertical two walls were adiabatic, inside the semi-circular heater, the wavy top wall cooled. The parameters Rayleigh number, Hartmann number and Prandtl number are considered. The effects of the Hartmann number and Rayleigh number on the streamlines, isotherms, velocity profiles and average Nusselt number are examined graphically. The local Nusselt number and the average Nusselt number of the heated portion of the enclosure with the semi-circular heater are presented in this paper. Finally, for the validation of the existing work, the current results are compared with published results and the auspicious agreement is achieved.

Modeling of Mixed Convection in a Lid Driven Wavy Enclosure with Two Square Blocks Placed at Different Positions

The purpose of this paper is to investigate the simulation of mixed convection in a lid-driven wavy enclosure with blocks positioned at various positions. This study also examined the impact of the longitudinal position of the heated block on heat transfer enhancement. The Galerkin weighted residual finite element method is employed to computationally solve the governing equations of Navier-Stokes, thermal energy, and mass conservation. The enclosure consists of two square heated blocks strategically placed at different heights—firstly, one set is closer to the bottom surface;secondly, one set is nearer to the middle area and finally, one set is closer to the upper undulating surface of the enclosure. The wavy top wall’s thermal insulation, along with active heating of the bottom wall and blocks, generates a dynamic convective atmosphere. In addition, the left wall ascends as the right wall falls, causing the flow formed by the lid. The study investigates the impact of the Richardson number on many factors, such as streamlines, isotherms, dimensionless temperature, velocity profiles, and average Nusselt numbers. These impacts are depicted through graphical illustrations. In all instances, two counter-rotating eddies were generated within the cage. Higher rotating speed consistently leads to improved performance, irrespective of other characteristics. Furthermore, an ideal amalgamation of the regulating factors would lead to increased heat transmission.

Scale-adaptive simulation of flow past wavy cylinders at a subcritical Reynolds number

The Xu ＆ Yan scale-adaptive simulation （XYSAS） model is employed to simulate the flows past wavy cylinders at Reynolds number 8 × 10 3.This approach yields results in good agreement with experimental measurements.The mean flow field and near wake vortex structure are replicated and compared with that of a corresponding circular cylinder.The effects of wavelength ratios λ/D m from 3 to 7,together with the amplitude ratios a /D m of 0.091 and 0.25,are fully investigated.Owing to the wavy configuration,a maximum reduction of Strouhal number and root-meansquare （r.m.s） fluctuating lift coefficients are up to 50% and 92%,respectively,which means the vortex induced vibration （VIV） could be effectively alleviated at certain larger values of λ/D m and a /D m.Also,the drag coefficients can be reduced by 30%.It is found that the flow field presents contrary patterns with the increase of λ/D m.The free shear layer becomes much more stable and rolls up into mature vortex only further downstream when λ/D m falls in the range of 5-7.The amplitude ratio a /D m greatly changes the separation line,and subsequently influences the wake structures.

Mechanism of wavy vortex and sign laws in flow past a bluff body:vortex-induced vortex

As reported in a previous work by Lin et al.(Acta Meeh Sin, 2018. https://doi.org/10.1007/s 10409-018-0758-z), an interesting phenomenon was discovered based on the analysis of wavy vortex and vorticity distribution in the shear layers and near wake of a peak-perforated conic shroud, and two sign laws were summarized. In the present paper, the theory of a vortex-induced vortex is introduced to explore mechanisms in a wavy vortex and applicable sign laws for uniform and incompressible flow past a fixed bluff body. Based on the analysis of the nearest-wall How, two vortex-induced models for streamwise and vertical vortex pairs, respectively, are proposed under two boundary cases, denoting the induced vorticity introduced or distributed on and near the walls. As a result, the first sign law, for only streamwise and vertical components of vorticity, and the second sign law, for three components of vorticity, are obtained under their own particular conditions. The first sign law reveals the intrinsic physical relationship between streamwise and vertical vorticities, independent of the distribution of spanwise vortices in the whole flow field. It is also confirmed that the spanwise vortices, as well as the shear layers and wake width, distributed wavily across the span, are attributed to the introduced streamwise or vertical vortices. The two sign laws for vorticity are independent of the disturbed spanwise wavelength and the Reynolds number. Through the analysis of flow past the conic shroud, the two sign laws are successfully used to summarize typical spacial distributions of vorticity in three flow regions: on and near the front cylinder surfaces, the separated shear layers and the near wake.

Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media

Magnetohydrodynamic （MHD） bioconvection of an incompressible electrically conducting nanofluid near a vertical wavy surface saturated porous medium containing both nanoparticle and gyrotactic microorganisms is investigated. The nanofluid is represented by a model that includes both Brownian motion and thermophoresis effects. A suitable set of non-dimensional variables are used to transform the governing boundary layer equations into a dimensionless form. The resulting nonlinear system is mapped to the vertical flat plate domain, and a non-similar solution is used to the obtained equations. The obtained non-similar system is then solved numerically using the fourth-order Runge-Kutta method. The influence of various physical parameters on the local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms, the dimensionless velocity, the dimensionless temperature, and the rescaled density of motile microorganisms is studied. It is found that the local Nusselt number, the local Sherwood number, and the local density number of the motile microorganisms decrease by increasing either the Grashof number or the magnetic field parameter.

Initial Dilution of A Vertical Round Non-Buoyant Jet in Wavy Cross-Flow Environment

The phenomenon of wastewater discharged into coastal waters can be simplified as a turbulent jet under the effect of waves and currents. Previous studies have been carried out to investigate the jet behaviors under the current only or the wave only environment. To obtain better understanding of the jet behaviors in a realistic situation, a series of physical experiments on the initial dilution of a vertical round jet in the wavy cross-flow environment are conducted. The diluted processes of the jet are recorded by a high-resolution camcorder and the concentration fields of the jet are measured with a peristaltic suction pumping system. When the jet is discharged into the wavy cross-flow environment, a distinctive phenomenon, namely ＂effluent clouds＂, is observed. According to the quantitative measurements, the jet width in the wavy cross-flow environment increases more significantly than that does in the cross-flow only environment, indicating that the waves impose a positive effect on the enhancement of jet initial dilution. In order to generalize the experimental findings, a comprehensive velocity scale ua and a characteristic length scale l are introduced. Through dimensional analysis, it is found that the dimensionless centerline concentration trajectories cy/l is in proportion to 1/3 power of the dimensionless downstream distance x/l, and the dimensionless centerline dilution 2c aS Q/（u l） is proportional to the square of the dimensionless centerline trajectory cy/l. Several empirical equations are then derived by using the Froude number of cross-flow Frc as a reference coefficient. This paper provides a better understanding and new estimations of the jet initial dilution under the combined effect of waves and cross-flow current.

Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel

The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das' nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls(wavy and undulation numbers)are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.

Characterization of wavy root 1,an agravitropism allele,reveals the functions of OsPIN2 in fine regulation of auxin transport and distribution and in ABA biosynthesis and response in rice(Oryza sativa L.)

Root system architecture is influenced by gravity.How the root senses gravity and directs its orientation,so-called gravitropism,is not only a fundamental question in plant biology but also theoretically important for genetic improvement of crop root architecture.However,the mechanism has not been elucidated in most crops.We characterized a rice agravitropism allele,wavy root 1(war1),a loss-of-function allele in OsPIN2,which encodes an auxin efflux transporter.With loss of OsPIN2 function,war1 leads to altered root system architecture including wavy root,larger root distribution angle,and shallower root system due to the loss of gravitropic perception in root tips.In the war1 mutant,polar auxin transport was disrupted in the root tip,leading to abnormal auxin levels and disturbed auxin transport and distribution in columella cells.Amyloplast sedimentation,an important process in gravitropic sensing,was also decreased in root tip columella cells.The results indicated that OsPIN2 controls gravitropism by finely regulating auxin transport,distribution and levels,and amyloplast sedimentation in root tips.We identified a novel role of OsPIN2 in regulating ABA biosynthesis and response pathways.Loss of OsPIN2 function in the war1 resulted in increased sensitivity to ABA in seed germination,increased ABA level,changes in ABA-associated genes in roots,and decreased drought tolerance in the seedlings.These results suggest that the auxin transporter OsPIN2 not only modulates auxin transport to control root gravitropism,but also functions in ABA signaling to affect seed germination and root development,probably by mediating crosstalk between auxin and ABA pathways.

Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al2O3-water nanofluid with discrete heating

We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid(Cu-Al2O3-water).The upper and bottom walls of the cavity have a wavy shape.The temperature of the vertical walls is lower,the third part in the middle of the bottom wall is kept at a constant higher temperature,and the remaining parts of the bottom wall and the upper wall are thermally insulated.The magnetic field is applied under the angleγ,an opposite clockwise direction.For the numerical simulation,the finite element technique is employed.The ranges of the characteristics are as follows:the Rayleigh number(10^3≤Ra≤10^5),the Hartmann number(0≤Ha≤100),the nanoparticle hybrid concentration(ϕAl2O3,ϕCu=0,0.025,0.05),the magnetic field orientation(0≤γ≤2π),and the Prandtl number Pr,the amplitude of wavy cavity A,and the number of waviness n are fixed at Pr=7,A=0.1,and n=3,respectively.The comparison with a reported finding in the open literature is done,and the data are observed to be in very good agreement.The effects of the governing parameters on the energy transport and fluid flow parameters are studied.The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement.When the Rayleigh number is raised,the Nusselt number is increased,too.For moderate Rayleigh numbers,the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid,followed by the Al2O3-nanofluid.The nature of motion and energy transport parameters has been scrutinized.

Simulation of the hydrodynamics and mass transfer in a falling film wavy microchannel

The flow in a liquid falling film is predominantly laminar,and the liquid-side mass transfer is limited by molecular diffusion.The effective way to enhance the mass transfer is to improve the liquid film flow behavior.The falling film behaviors of water,ethanol and ethylene glycol in nine different wavy microchannels were simulated by Computational Fluid Dynamics.The simulation results show that the falling film thickness exhibits a waveform distribution resulting in a resonance phenomenon along the wavy microchannel.The fluctuation of liquid film surface increases the gas-liquid interface area,and the internal eddy flow inside the liquid film also improves the turbulence of liquid film,the gas-liquid mass transfer in falling film microchannels is intensified.Compared with flat microchannel,the CO_(2) absorption efficiency in water in the wavy microchannel is improved over 41%.Prediction models of liquid film amplitude and average liquid film thickness were established respectively.

Heat Generation Effects on MHD Natural Convection Flow along a Vertical Wavy Surface with Variable Thermal Conductivity

The heat generation effects on magnetohydrodynamic(MHD) natural convection flow along a vertical wavy surface with variable thermal conductivity have been investigated. The governing boundary layer equations are first transformed into a non-dimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines as well as the isotherms are shown graphically for a selection of parameters set consisting of thermal conductivity variation parameter, heat generation parameter Q, magnetic parameter M and Prandtl number Pr. Comparison of numerical results of present work with other published data has been shown in table.

TRPIV investigation of space-time correlation in turbulent flows over flat and wavy walls

The present experimental work is devoted to in- vestigate a new space-time correlation model for the turbulent boundary layer over a flat and a wavy walls. A turbulent boundary layer flow at Reo = 2460 is measured by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated at 3 different wall-normal locations in logarithmic layer. It is found that the scales of coherent structure increase with moving far away from the wall. The growth of scales is a manifestation of the growth of prevalent coherent structures in the turbulent boundary layer like hairpin vortex or hairpin packets when they lift up. The resulting contours of the space-time correlation exhibit elliptic-like shapes rather than straight lines. It is suggested that, instead of Taylor hypothesis, the elliptic model of the space-time correlation is valid for the wallbounded turbulent flow over either a flat wall or a wavy wall. The elliptic iso-correlation curves have a uniform preferred orientation whose slope is determined by the convection velocity. The convection velocity derived from the space-time correlation represents the velocity at which the large-scale eddies carry small-scale eddies. The sweep velocity rep- resents the distortions of the small-scale eddies and is intimately associated with the fluctuation velocity in the logarithmic layer of turbulent boundary layers. The nondimensionalized correlation curves confirm that the elliptic model is more proper for approximating the space-time correlation than Taylor hypothesis, because the latter can not embody the small-scale motions which have non-negligible distortions. A second flow over a wavy wall is also recorded using TRPIV. Due to the combined effect of shear layers and the adverse pressure gradient, the space-time correlation does not show an elliptic-like shape at some specific heights over the wavy wall, but in the outer region of the wavy wallbounded flow, the elliptic model remains valid.

Wavy structures for stretchable energy storage devices:Structural design and implementation

The application of wavy structures in stretchable electrochemical energy storage devices is reviewed. First, the mechanical anaJysis of wavy structures, specific to flexible electronics, is introduced. Second, stretchable electrochemical energy storage devices with wavy structures are discussed. Finally, the present problems and challenges are reviewed, and possible directions for future research are outlined.

Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

The combined effects of thermal and mass convection of viscous incom- pressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed. The dimensionless governing equations are perturbed into a mean part （the zeroth-order） and a perturbed part （the first-order）. The first-order quantities are ob- tained by the perturbation series expansion for short wavelength, in which the terms of the exponential order arise. The analytical expressions for the zeroth-order, the first-order, and the total solutions are obtained. The numerical computations are presented graph- ically to show the salient features of the fluid flow and the heat transfer characteristics. Separate solutions are matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number are also analyzed for variations of the governing parameters. It is observed that the Grashof number, the viscosity ratio, the width ratio, and the conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.

A novel wavy non-uniform ligament chiral stent with J-shaped stress-strain behavior to mimic the native trachea

Tracheal stents are an important form of treatment for benign or malignant central airway obstruction.However,the mechanical behavior of current tracheal stents is significantly different from that of the native trachea,which leads to a variety of serious complications.In this study,inspired by the structure of the native trachea,a wavy non-uniform ligament chiral tracheal stent is proposed,in which J-shaped stress-strain behavior and negative Poisson's ratio response are achieved by replacing the tangential ligament of tetrachiral and anti-tetrachiral hybrid structure with a wavy non-uniform ligament.Through the combination of theoretical analysis,finite element analysis and experimental tests,a wide range of desired J-shaped stress-strain curves are explored to mimic the native porcine trachea by tailoring the stent geometry.Besides,the negative Poisson’s ratio and auxetic diameter curves versus axial strain of the stent are also studied in detail,thus contributing to the enhancement of cross-section ventilation and reducing the migration of the stent.This novel tracheal stent with a unique microstructure shows a potential to perfectly match the physiological activities of the native trachea and thereby reduce potential complications.

Reflection and Refraction of Gaussian Beam on Wavy Surface in Airborne Ocean Lidar

According to the statistical description of direction distribution on wavy surface by Cox, we have set up a physical model of reflection and refraction of Gaussian beam on wavy surface, derived that a beam reflected and refracted by wavy surface is also a Gaussian beam when the incident beam is a Gaussian beam, and set up the relationship between Gaussian beam's light spot size and wind speed over sea surface.

Prediction of Wavy Liquid Film Profile for Thin Film on a Falling Film Absorber

A hydrodynamic model of thin, laminar, gravity-driven, wavy-film flow over a vertical plate was considered. To make advantage of the cyclic boundary conditions and due to the nature of the wavy flow, a solution based on a Fourier series was implemented. Two representative cases of practical importance were studied;Re = 25, Re = 100. This range of Reynolds numbers is of the most practical importance in the process industry. Multiple solutions were obtained. Most of these solutions are mathematically correct but physically are not. It is observed that realistic wave profiles are always obtained once we approach the Froude number corresponding to thin film.