On optical flow techniques applied to breaking surges

Surface wave breaking is a challenging two-phase flow process which plays an important role in numerous physical processes. A highly-turbulent unsteady breaking surge was investigated experimentally in a large facility, and substantial aeration occurred in the roller. The application of three optical flow techniques (Lucas-Kanade, Horn-Schunck and Farnback) to the air-water region was tested. The results indicated that the Farnback technique provided most accurate results, although some misleading results could be obtained near the air-water boundaries of the roller. The bore generation by a rapid gate closure showed a highly-unsteady complicated velocity field, with substantial free-surface deformations, wave breaking and formation of large coherent structures before the surge detached from the gate. Further upstream, the surge propagated as a hydraulic jump in translation and the data showed a marked shear region with a recirculation zone above, showing air-water flow features comparable to stationary hydraulic jumps. The upper and lower bounds of air-water flow region yielded data implying an air-to-water velocity ratio about 4–5 for a Froude number Fr₁ = 2.1.     

Semianalytical Model for Drawdown due to Pumping a Partially Penetrating Large Diameter Well

A semianalytical model is developed for computing drawdowns in and around a partially penetrating large diameter well. The new model can take into account an unsteady pumping discharge and thus drawdowns during recovery can be computed. This model can also yield the unsteady contributions from well and aquifer storages to the pumped discharge. While developing the model, the flow from the bottom of the well is also accounted.     

Field Verification of Two-Dimensional Surface Irrigation Model

A two-dimensional (2D) model of unsteady shallow-water flow in surface irrigation was developed to evaluate the influence of field-grading precision on surface irrigation performance. This paper presents field data for verification of this 2D model. No attempt was made here to evaluate irrigation performance. Verification of such models relies on independent estimates of parameters for infiltration and roughness. To accomplish this, water surface elevations were measured at 26 points within a 3 ha level basin. A double-bubbler system was used to obtain relative water depths. Field surveys were used to convert these to water surface elevations and field water depths, from which surface water volumes over time were computed. The infiltration function was determined by matching inflow minus surface volume over time with computed subsurface volume. A value of Manning n (0.05) was found for which advance and water depth hydrographs were both well predicted with the 2D model. Differences in advance for a plane versus undulating field surface were minor, except near the end of advance.     

Shallow Turbulent Flows by Video Imaging Method

Shallow turbulent flows were produced in a tank of small thickness to study the friction effects on large-scale turbulent motion of small depth. The tank was constructed of two parallel walls. The space between the parallel walls (4.4, 1.57, and 0.59 cm) was small compared with the height (107 cm) and the width (212 cm) of the tank, and was varied during the experiments for different friction effects. Turbulent flows were produced by the injection of water in the form of starting jets into the tank filled with water. The large-scale turbulent flow in the small space between the walls of the tank is confined to essentially two-dimensional motion, and the motion is retarded by the force of friction. Dye was injected with the source fluid as the tracer for the highly unsteady and quasitwo-dimensional turbulent motion. From the initiation of the turbulent motion at the source to the final interaction of the jets with the tank bottom, the entire sequence of events was recorded by a pair of video cameras. The depth-averaged concentration of the dye was analyzed using the recorded video images.     

Stability of Periodically Unsteady Axisymmetric Jet

To date, the majority of studies on stability of axisymmetric jets have been completed under the assumption of steady mean flow. Yet, many of the natural and man-made flows that are modeled by these jets can have an inherent unsteadiness; the effects of which on the stability and transition have not been determined. Moreover, controlled unsteadiness can be used to control stability and possibly the transition to turbulence. In this note, the effects of periodic variations of the mean flow on the stability of axisymmetric jets are examined. The problem is treated analytically. The results show that the governing equations and dispersion relation for the unsteady jet can be reduced to those governing the steady jet with a time transformation. It is shown that the periodic variations in the mean flow cause amplitude and phase modulations of the unstable modes. The implications of the modulations on the subsequent transition stages are discussed.     

A CCD–ADI method for unsteady convection–diffusion equations

With a combined compact difference scheme for the spatial discretization and the Crank–Nicolson scheme for the temporal discretization, respectively, a high-order alternating direction implicit method (ADI) is proposed for solving unsteady two dimensional convection–diffusion equations. The method is sixth-order accurate in space and second-order accurate in time. The resulting matrix at each ADI computation step corresponds to a triple-tridiagonal system which can be effectively solved with a considerable saving in computing time. In practice, Richardson extrapolation is exploited to increase the temporal accuracy. The unconditional stability is proved by means of Fourier analysis for two dimensional convection–diffusion problems with periodic boundary conditions. Numerical experiments are conducted to demonstrate the efficiency of the proposed method. Moreover, the present method preserves the higher order accuracy for convection-dominated problems.     

High-order compact boundary value method for the solution of unsteady convection–diffusion problems

In this paper, we propose a new class of high-order accurate methods for solving the two-dimensional unsteady convection–diffusion equation. These techniques are based on the method of lines approach. We apply a compact finite difference approximation of fourth order for discretizing spatial derivatives and a boundary value method of fourth order for the time integration of the resulted linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. Also this method is unconditionally stable due to the favorable stability property of boundary value methods. Numerical results obtained from solving several problems include problems encounter in many transport phenomena, problems with Gaussian pulse initial condition and problems with sharp discontinuity near the boundary, show that the compact finite difference approximation of fourth order and a boundary value method of fourth order give an efficient algorithm for solving such problems.     

Pulsatile flow of blood using a modified second-grade fluid model

We study the unsteady pulsatile flow of blood in an artery, where the effects of body acceleration are included. The blood is modeled as a modified second-grade fluid where the viscosity and the normal stress coefficients depend on the shear rate. It is assumed that the blood near the wall behaves as a Newtonian fluid, and in the core as a non-Newtonian fluid. This phenomenon is also known as the Fahraeus–Lindqvist effect. The equations are made dimensionless and solved numerically.     

“网河”非稳定流模型在洪泛区洪流演进中的应用

将宽阔的溃口洪水行进范围概化成由河道水塘和联系河道组成的网河,用一维非恒定流方程组来描述主要的水充运动状态,通过简化和变换,改写成统一的四点线性隐式有限差的方程组形式,再用双消除法求解,全部计算在微机上实现,参数用实测资料率定,成果具有较好的精度,在一定程度上反映出横水流方向的水位流量变化,为防洪水利计算开辟一条新的途径。     

Upstream wake-secondary flow interactions in the endwall region of high-loaded turbines

A detailed experimental and numerical investigation of the unsteady interaction of secondary flow vortices in turbine endwall region was performed with the effect of upstream periodic wakes. The flow field was investigated respectively in a linear turbine cascade and a turbine rotor. The study revealed the physical mechanisms of unsteady interaction between upstream wake and secondary vortices. The influence of the upstream wake on the performance of turbine endwall region was also discussed.The flow field at the exit of the turbine blade row showed a decrease in passage vortex strength and loss due to the upstream wake transport. Two interaction mechanisms are proposed whereby passage vortex loss decreases. They are the upstream wake-pressure side leg of the horseshoe vortex interaction and the upstream wake-passage vortex interaction. The transport of upstream wake can suppress the development of pressure side leg of the horseshoe vortex and passage vortex because of the “negative jet” influence of the wake.