UNSTEADY WAVES DUE TO AN IMPULSIVE OSEENLET BENEATH THE CAPILLARY SURFACE OF A VISCOUS FLUID

The two-dimensional free-surface waves due to a point force steadily moving beneath the capillary surface of an incompressible viscous fluid of infinite depth were analytically investigated. The unsteady Oseen equations were taken as the governing equations for the viscous flows. The kinematic and dynamic conditions including the combined effects of surface tension and viscosity were linearized for small-amplitude waves on the free-surface. The point force is modeled as an impulsive Oseenlet. The complex dispersion relation for the capillary-gravity waves shows that the wave patterns are characterized by the Weber number and the Reynolds number. The asymptotic expansions for the wave profiles were explicitly derived by means of Lighthill’s theorem for the Fourier transform of a function with a finite number of singularities. Furthermore, it is found that the unsteady wave system consists of four families, that is, the steady-state gravity wave, the steady-state capillary wave, the transient gravity wave, and the transient capillary wave. The effect of viscosity on the capillary-gravity was analytically expressed.     

REFLECTION OF OBLIQUE INCIDENT WAVES BY PERFORATED CAISSONS WITH TRAVERSE WALL

The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons are close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.     

Kelvin-Helmholtz instability.with mass transfer through porous media： Effect of irrotational viscous pressure

This paper studies the effect of the irrotational viscous pressure on Kelvin-Helmholtz instability of the plane interface of two viscous and incompressible fluids in a fully saturated porous media with mass and heat transfers across the interface. In the earlier work, the instability of the plane interface of two viscous and streaming miscible fluids through porous media was studied by assuming that the motion and the pressure are irrotational and the viscosity enters the normal stress balance. This theory is called the viscous potential flow theory. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by considering viscous contributions of the irrotational pressure. The Darcy-Brinkman model is used in the investigation and the stability criterion is formulated in terms of a critical value of the relative velocity. It is observed that the heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.     

Couple stress fluid flow in a rotating channel with peristalsis

This article describes a new model for obtaining closed-form semi-analytical solutions of peristaltic flow induced by sinusoidal wave trains propagating with constant speed on the walls of a two-dimensional rotating infinite channel. The channel rotates with a constant angular speed about the z-axis and is filled with couple stress fluid. The governing equations of the channel deformation and the flow rate inside the channel are derived using the lubrication theory approach. The resulting equations are solved, using the homotopy perturbation method(HPM), for exact solutions to the longitudinal velocity distribution, pressure gradient, flow rate due to secondary velocity, and pressure rise per wavelength. The effect of various values of physical parameters, such as, Taylor's number and couple stress parameter, together with some interesting features of peristaltic flow are discussed through graphs. The trapping phenomenon is investigated for different values of parameters under consideration. It is shown that Taylor's number and the couple stress parameter have an increasing effect on the longitudinal velocity distribution till half of the channel, on the flow rate due to secondary velocity, and on the number of closed streamlines circulating the bolus.     

Analytical approach to entropy generation and heat transfer in CNT-nanofluid dynamics through a ciliated porous medium

The transportation of biological and industrial nanofluids by natural propulsion like cilia movement and self-generated contraction-relaxation of flexible walls has significant applications in numerous emerging technologies. Inspired by multi-disciplinary progress and innovation in this direction, a thermo-fluid mechanical model is proposed to study the entropy generation and convective heat transfer of nanofluids fabricated by the dispersion of single-wall carbon nanotubes(SWCNT) nanoparticles in water as the base fluid. The regime studied comprises heat transfer and steady, viscous, incompressible flow, induced by metachronal wave propulsion due to beating cilia, through a cylindrical tube containing a sparse(i.e., high permeability) homogenous porous medium. The flow is of the creeping type and is restricted under the low Reynolds number and long wavelength approximations. Slip effects at the wall are incorporated and the generalized Darcy drag-force model is utilized to mimic porous media effects. Cilia boundary conditions for velocity components are employed to determine analytical solutions to the resulting non-dimensionalized boundary value problem. The influence of pertinent physical parameters on temperature, axial velocity, pressure rise and pressure gradient, entropy generation function, Bejan number and stream-line distributions are computed numerically. A comparative study between SWCNT-nanofluids and pure water is also computed. The computations demonstrate that axial flow is accelerated with increasing slip parameter and Darcy number and is greater for SWCNT-nanofluids than for pure water. Furthermore the size of the bolus for SWCNT-nanofluids is larger than that of the pure water. The study is applicable in designing and fabricating nanoscale and microfluidics devices, artificial cilia and biomimetic micro-pumps.     

Motion and deformation of immiscible droplet in plane Poiseuille flow at low Reynolds number

Droplet migration in plane Poiseuille flow is numerically investigated with a dissipative particle dynamics method.The single droplet deformation in the channel flow is first studied to verify the current method and the physical model.The effect of the viscosity ratio between the droplet and the solvent and the effect of the confinement are systematically investigated.The droplet is in an off-centerline equilibrium position with a specific selection of the parameters.A large viscosity ratio makes the droplet locate in a near-wall equilibrium position,and a large capillary number makes the droplet migrate to the near-centerline region of the channel.For the droplet migration at the same Capillary number,there is a critical width of the channel,which is less than twice of the droplet diameter,and the droplet will only migrate to the channel centerline if the width is less than this critical value.     

Effects of variable fluid properties on the thin film flow of Ostwald-de Waele fluid over a stretching surface

We investigate, in this paper, the effects of thermo-physical properties on the flow and heat transfer in a thin film of a power-law liquid over a horizontal stretching surface in the presence of a viscous dissipation. The fluid properties, namely the fluid viscosity and the fluid thermal conductivity, are assumed to vary with temperature. Using a similarity transformation, the governing partial differential equations with a time dependent boundary are converted into coupled non-linear Ordinary Differential Equations (ODEs) with variable coefficients. Numerical solutions of the coupled ODEs are obtained by a finite difference scheme known as the Keller-box method. Results for the velocity and temperature distributions are presented graphically for different values of the pertinent parameters. The effects of unsteady parameter on the skin friction, the wall temperature gradient and the film thickness are presented and analyzed for zero and non-zero values of the temperature-dependent thermo-physical properties. The results obtained reveal many interesting features that warrant further study on the non-Newtonian thin film fluid flow phenomena, especially the shear-thinning phenomena.     

Diffusion of chemically reactive species in Casson fluid flow over an unsteady permeable stretching surface

In this paper we investigate the two-dimensional flow of a non-Newtonian fluid over an unsteady stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First-order constructive/destructive chemical reaction is considered. With the help of a shooting method, numerical solutions for a class of nonlinear coupled differential equations subject to appropriate boundary conditions are obtained. For the steady flow, the exact solution is obtained. The flow features and the mass transfer characteristics for different values of the governing parameters are analyzed and discussed in detail.     

INVESTIGATION OF THE FLOW IN FRACTAL RESERVOIR INCLUDING THE EFFECTS OF QUADRATIC GRADIENT TERM

According to the assumption of slightly compressible fluid, the quadratic gradient term in the nonlinear partial differential equations for the traditional well-test model is usually neglected. The linear partial differential equation is thus established. It is known that neglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flow model for fractal medium is constructed and the quadratic gradient term is considered. The exact solutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in a constant-rate and constant-pressure production for an infinitely large system. This paper addresses the variation of pressure with fluid compressibility coefficient and fractal reservoir parameters. The plots of the typical pressure curves are constructed, and the results can be applied to well-test analysis.     

APPLICATION OF TIME-VARYING VISCOUS GROUT IN GRAVEL- FOUNDATION ANTI-SEEPAGE TREATMENT

The time-varying viscosity of common grout and the controllable grout are measured with a rotation viscometer in experiments.The time-varying viscosity of grout is analyzed according to the characteristics in the process of anti-seepage treatment for gravel foundation.The principle of effective stress for porous medium is applied to analyzes the fluid-structure coupling in grouting.In the consideration of coupling physical variables,dynamic models of porosity,permeability and viscosity are constructed.The diffusion radius can thus be defined by the foundational porosity.The distribution of holes in field experiments is designed according to the diffusion radius of grout.Then,the permeability test is designed to verify the grout effect.The calculated diffusion radius coincides with experimental results,and the permeability meets the requirements of the project,which is valuable for the anti-seepage treatment in gravel foundation.     

一类非牛顿流体非线性渗流的压力波解析求解方法及波形分析

一类非牛顿流体渗流的视粘度依赖于压力梯度,且在不同的压力梯度区间内变化规律不同。其具有既不同于牛顿流体渗流,也不同于幂律流体渗流和宾汉流体渗流的非线性渗流特征。建立了该流体在多孔介质内部渗流的数学模型并利用行波法推导出了压力波的解析解。通过一系列算例分析了渗流方程控制参数对压力波形的影响,对比了该类流体与牛顿流体渗流的压力波差异。     

WAVE DISSIPATING PERFORMANCE OF AIR BUBBLE BREAKWATERS WITH DIFFERENT LAYOUTS

The wave dissipating performance of air bubble breakwaters with different layouts is studied by experimental and numerical methods in this article. Based on the assumpation that the mixture of air and water is regarded as a variable density fluid, the mathematical model of the air bubble breakwater is built. The numerical simulation results are compared with the experimental data, which shows that the mathematical model is reasonable for the transmission coefficient Ct_m. The influencing factors are studied experimentally and numerically, including the incident wave height H_i, the incidentt wave period T, the air amount Q_m, the submerged pipe depth D and the single or double air discharging pipe structure. Some valuable conclusions are obtained for further research of the mechanism and practical applications of air bubble breakwaters.     

Large transient waves generated through modulational instability in deep water

The long-term evolution of nonlinear wave train in deep water with varied initial wave steepness is investigated experimentally in a super wave flume (300 m long, 5 m wide, 5.2 m deep). The initial wave train is the combination of one carrier wave and a pair of imposed sideband components. Increasing modulation of wave train is observed due to sideband instability until a critical value which either initiates wave breaking or reaches the maximum modulation. The observed maximum local wave steepness increases rapidly with the increase of the initial wave steepness, and levels off at initial wave steepness roughly equal to 0.15 despites that the data exhibits a little scattering. The normalized crest elevation at peak modulation increases rapidly with initial wave steepness and approached a maximum value almost equal to 3.5 which corresponds to initial wave steepness around k_ca_c = 0.15. The results reveal that the large transient wave such as freak wave could be generated during the propagation of nonlinear wave trains in deep water through sideband instability.

     

Study of fluid resonance between two side-by-side floating barges

The hydrodynamic interaction between two vessels in a side-by-side configuration attracted research attentions in recent years. However, because the conventional potential flow theory does not consider the fluid viscosity, in the hydrodynamic results, the wave elevations were overestimated in the narrow gap under resonance conditions. To overcome this limitation and investigate the complex fluid flow around multiple bodies in detail, this study examines the fluid resonance between two identical floating barges using a viscous flow analysis program FLOW-3D. The volume of fluid method is implemented for tracking the free surface, and a porous media model is used near the outflow boundary to enhance the wave absorption. A three-dimensional numerical wave basin is established and validated by comparison with the waves generated using theoretical values. On this basis, a computational fluid dynamics(CFD) simulation of the two barges in a resonance wave period is performed, and the wave elevations, the fluid flow around the barges, and the motions of the barges are discussed. The numerical simulation is verified by comparison with results of corresponding experimental data.     

A Note to the Variable Sorptivity Infiltration Equation

A simplification for the variable sorptivity infiltration equation of Poulovassilis et al. (1989) is proposed. The resulting equation has three parameters S _x, c and K ₀. From these, S _x and c are considered as fitting parameters and K ₀ as a physical one. The new empirical infiltration equation is tested for precision, parameter time-dependence and applicability for soil surveys. The test was carried out by comparison with reference solutions i.e. infiltration data obtainedexperimentally, analytically or numerically for two different head conditionsat the infiltration surface. A good agreement is observed for all examinedcases. The dependence of the fitting parameters S _x and c on the initialand boundary conditions, as well as the error that arises by taking intoaccount different values of them, are examined. In fine textured soilsparameter c seems to be very small, so that one can easily suppose that the proposed equation reduces to the well-known Philip's infiltration equation (Philip, 1957).     

Estimation of Clark’s Instantaneous Unit Hydrograph Parameters and Development of Direct Surface Runoff Hydrograph

We present a method to estimate Time of Concentration (T _c) and Storage Coefficient (R) to develop Clark’s Instantaneous Unit Hydrograph (CIUH). T _c is estimated from Time Area Diagram of the catchment and R is determined using optimization approach based on Downhill Simplex technique (code written in FORTRAN). Four different objective functions are used in optimization to determine R. The sum of least squares objective function is used in a novel way by relating it to slope of a linear regression best fit line drawn between observed and simulated peak discharge values to find R. Physical parameters (delineation, land slope, stream lengths and associated drainage areas) of the catchment are derived from SPOT satellite imageries of the basin using ERDAS: Arc GIS is used for geographic data processing. Ten randomly selected rainfall–runoff events are used for calibration and five for validation. Using CIUH, a Direct surface runoff hydrograph (DSRH) is developed. Kaha catchment (5,598 km²), part of Indus river system, located in semi-arid region of Pakistan and dominated by hill torrent flows is used to demonstrate the applicability of proposed approach. Model results during validation are very good with model efficiency of more than 95% and root mean square error of less than 6%. Impact of variation in model parameters T _c and R on DSRH is investigated. It is identified that DSRH is more sensitive to R compared to T _c. Relatively equal values of R and T _c reveal that shape of DSRH for a large catchment depends on both runoff diffusion and translation flow effects. The runoff diffusion effect is found to be dominant.     

Influence of horizontal eddy viscosity and bottom friction coefficients on morphodynamic evaluations

The horizontal eddy viscosity (ε) and bottom friction coefficient (K_br) are important hydrodynamic parameters in the computation of flow fields that dictate the morphodynamics. The effect of the variations in ε and K_br as well as their combination on the prediction of hydrodynamics and morphodynamics in the Cochin harbor and adjoining nearshore area (9.9312° N, 76.2673° E) has been investigated in detail. A tidal circulation model to solve the shallow water equation is applied with the different parameterizations of ε and K_br. In order to understand its effect, ε is expressed as a function of depth averaged velocity and length scale of computation mesh, whereas K_br is expressed as a function of depth. The validation of the model is carried out with the measured currents. The improvement in the hydrodynamic and morphodynamic predictions is demonstrated by implementing the spatially and temporally varying ε The predictions are further improved by implementing a spatially varying K_br. It is seen that the simulations with varying ε and K_br predict the morphodynamic behavior close to the field values. The performance of the model predictions is discussed in terms of R², RMSE and BSS (Brier Skill Score).     

EXPERIMENTAL INVESTIGATION ON THE DRAG REDUCTION CHARACTERISTICS OF TRAVELING WAVY WALL AT HIGH REYNOLDS NUMBER IN WIND TUNNEL

Drag reduction experiments of the traveling wavy wall at high Reynolds number, ranging from 1.46×10⁶ to 5.83×10⁶ based on the free-stream velocity and the model length, were conducted. A suit of traveling wavy wall device was developed and its characteristics of drag reduction at high Reynolds number were investigated. The drag forces of the traveling wavy wall with various wave speeds (c) were measured at different wind speeds (U) in the FL-8 low-speed wind tunnel and compared with the drag force of the flat plate. The results show that the mean drag force of the traveling wavy wall decreases as the value of c/U increases, at different wind velocities, the values of c/U corresponding to minimal drag force of the traveling wavy wall are different, when the values of c/U are larger than 0.6, the mean drag forces of the traveling wavy wall are smaller than those of the flat plate, and the drag reduction can be up to 60%. The drag reduction effectiveness of traveling wavy wall is thus achieved. Furthermore, as the value of c/U increases, the traveling wavy wall can restrain the separation and improve the quality of flow field.     

Numerical simulation of scouring funnel in front of bottom orifice

The scouring funnel in front of a bottom orifice under the condition of fixed water levels is simulated by using an Eulerian two-phase model, with onsideration of the flow-particle and particle-particle interactions. The predictions of the scouring funnel shape agree well with laboratory measurements. The flow-field characteristics of the two phases and the influences of the hydraulic and geometric parameters on the shape of the scouring funnel are analyzed on the basis of the computation results. It is revealed that the non-dimensional maximum scour hole parameters, the depth d_m / d_o, the length l_m / d_o, and the half-width w_m / d_o, are linear with the densimetric Froude number Fr_o, the main parameter describing the scour hole, the centerline scour depth D_c and the half-scour width W_r vary according to a power law, and the transverse scour profiles exhibit strong similarities, the velocity distribution of the water is confined within the sink-like area near the orifice, and the mutual impact of the flows at the azimuthal sections and the resistances of the walls and the sand layer produce a vortex in the scour hole, that makes the sand particles to be suspended in the water, the exchanging water in the pore water is the main contributor in forcing the sand to move, and transporting the sand in the same direction as the pore water along azimuthal sections.     

洪涝灾害三参数损失函数的构建Ⅰ——基本原理

为把握快速城镇化、社会经济增长、防洪工程标准提高背景下暴雨洪涝灾害风险的演变趋势,基于洪水风险理论及城市洪涝灾害的连锁性与损失突变性特征,探讨了洪涝灾害风险演变驱动机制,构建了具有物理意义的三参数洪涝灾害损失-重现期(D-R)风险函数,明确了曲线形态中临界洪灾损失值Dc、临界重现期Rc、区域脆弱性综合指数k等控制参数的物理意义。该函数可作为洪涝灾害风险评估与预测的一种便捷手段,找到洪涝灾害风险演化的转折点,可为防灾减灾决策提供依据,同时也可应用于对防洪工程体系减灾效益的评估。