Comparison of oscillatory and stationary flow through porous media

Experiments were conducted in an oscillatory water tunnel to investigate what effects temporal inertia has on the resistance of a granular medium. The flow law governing stationary porous media flow is reasonably well accepted and understood but the effects of unsteady flow have commonly been neglected. The present research was designed to assess the magnitude of the acceleration effects on media of uniformly packed spheres of equal diameter and on one sample of randomly placed stone.Oscillatory flow tests were made in a large oscillatory flume tunnel with periods varying from 3 to 12 seconds. The influence of properties of the medium (grain size and porosity) were tested by using spheres with two different diameters and packing each size sphere in different geometric arrangements. Tests made on a stone sample provided a qualitative assessment of the effects of more random material properties.For the experiments described in this paper, the Forchheimer unsteady-stationary flow law described the oscillatory measurements well when velocities and energy losses were maximum. Empirical coefficients determined from steady-stationary flow were generally found to apply to the unsteady flow, however some evidence of dependency on the period of oscillation was noted.     

In-line response of a cylinder in oscillatory flow

The most widely used mathematical model to represent flow-induced in-line forces on structures is based on the Morison¹ equation. The present paper investigates the validity of using an extension of Morison's equation for non-stationary structures, by comparing predictions with results from a simple laboratory experiment. An elastically-mounted circular cylinder is placed in the sinusoidal flow of a U-tube, and responds in-line with the flow. Cylinder forces and responses are recorded over a range of Keulegan Carpenter numbers up to 35. An equation of motion is solved simply by using relative coordinates and by employing equivalent linearisation. The linear results are compared over a wide variation of parameters with solutions using the full nonlinear equation. Thereafter experimental results are compared with linear predictions.     

振荡流作用下圆柱体结构的水动力特性研究

圆柱绕流作为流体力学领域中的经典问题,近年来得到了广泛的关注和研究。开展振荡流下二维圆柱的水动力特性和漩涡发放形态研究将为认识和理解圆柱绕流特性提供重要参考。基于RANS方程,采用k-ωSST湍流模型,首先通过对比雷诺数10 000时均匀流下的受迫振动试验数据,验证了研究方法的可行性,进而开展了振荡流下圆柱绕流的数值模拟,对比讨论了5种KC数下流体力系数变化情况及漩涡脱落模式,并开展了升力系数时历分析。结果表明:在低振幅、低频率下,小KC数时激励力系数变化较大,大KC数时流态趋向于均匀流,激励力系数变化较小。在大KC数时可以观察到较为明显的2S脱落模式,升力系数在每一周期内出现两次振幅调制现象,小KC数时流体变化较快,规律性相对较弱。     

The inception of sheet flow in oscillatory flow

A simple model is developed to study the inception of sheet flow in oscillatory flow based on the available experimental data. The inception of sheet flow in oscillatory flow is well defined by the simple model: A/d=KA²ω/ν+B, where A is the semi-excursion of wave orbital motion near the bed, d is the grain size, ω is the angular frequency, ν is the kinematic viscosity of water, and K and B are the coefficients and dependent on sediment properties only. The inception velocity of sheet flow derived from the model is shown to be the function of grain size d, oscillatory period T and specific sediment density s. For a given sediment, the inception velocity is found to increase sharply initially with T and then approach a constant at T>6.0 s. The present model is quite simple and gives good agreement with the available experimental data.     

The inception of sheet flow in oscillatory flow

A simple model is developed to study the inception of sheet flow in oscillatory flow based on the available experimental data. The inception of sheet flow in oscillatory flow is well defined by the simple model: A/d=KA²ω/ν+B, where A is the semi-excursion of wave orbital motion near the bed, d is the grain size, ω is the angular frequency, ν is the kinematic viscosity of water, and K and B are the coefficients and dependent on sediment properties only. The inception velocity of sheet flow derived from the model is shown to be the function of grain size d, oscillatory period T and specific sediment density s. For a given sediment, the inception velocity is found to increase sharply initially with T and then approach a constant at T>6.0 s. The present model is quite simple and gives good agreement with the available experimental data.     

In-line force on a cylinder translating in oscillatory flow

Experiments were conducted with smooth and sand-roughened cylinders moving with constant velocity in a sinusoidally oscillating flow to determine the drag and inertia coefficients and to examine the effect of wake biasing on the modified Morison equation. The various flow parameters such as the relative cylinder velocity. Reynolds number, and the Keulegan-Carpenter number were varied systematically and the in-line force measured simultaneously. The principal results, equally valid for both smooth and rough cylinders, are as follows: the drag coefficient decreases with increasing relative current for a given Reynolds number and Keulegan-Carpenter number; the effect of wake biasing on the drag and inertia coefficients is most pronounced in the drag-inertia dominated regime; and the two-term Morison equation with force coefficients obtained under no-current conditions is not applicable to the prediction of wave and current induced loads on circular cylinders.     

Blockage effect of oscillatory flow past a fixed cylinder

A numerical study of the effect of the width of the computational domain on viscous oscillatory flow past a circular cylinder has been conducted, for Keulegan–Carpenter numbers ranging between 0.1 and 6 at a fixed frequency parameter equal to 50. The finite element method was used for the solution of the Navier–Stokes equations, in the formulation where the stream function and the vorticity are the field variables. Simulations for blockage ratios in the range between 0.10 and 0.50 were performed assuming frictionless flow at the outer boundaries, the blockage ratio being defined as the cylinder diameter divided by the width of the solution domain. The first set of simulations was carried out for a constant stream function along the horizontal boundaries. Then the procedure was repeated, for stream function values at the outer boundaries derived from the irrotational solution around a circular cylinder. This boundary condition relieves considerably the blockage effect on the flow pattern and on the drag coefficient of the in-line force.     

Steady streaming around a circular cylinder in an oscillatory flow

Steady streaming induced by an oscillatory flow around a circular cylinder is investigated using a numerical method. Two-dimensional Reynolds-averaged Navier-Stokes equations are solved using a finite element method with a k-ω turbulent model closure. The range of the Keulegan-Carpenter (KC) number investigated is between 2 and 40, which is substantially higher than those reported in literature related to steady streaming to date. A constant value of Stokes number (β) of 196 is chosen in this study. The steady streaming structures and velocity distribution are analysed in detail. It is found that the characteristics of steady streaming are strongly related to the vortex shedding flow regimes.     

Measurement of fluid flow in pipe and porous media by high-resolution magnetic resonance imaging

The objective of this study is to understand the process of fluid flow in pipe and porous media with different pore structures.High-resolution Magnetic Resonance Imaging(MRI)technique was used to visualize the pore structure and measure fluid flow.The porous media was formed by packed bed of glass beads.Flow measurement was carried out by a modified spin echo sequence.The results show that the velocity distribution in pipe is annular and the linear relation between MRI velocity and actual velocity is found in pipe flow measurement.The flow distribution in porous media is rather heterogeneous,and it is consistent with heterogeneous pore structure.The flow through pores with the high volume flow rate is determined largely by geometrical effects such as pore size and cross-sectional area.     

Two-phase flow modelling of sediment motions in oscillatory sheet flow

In this paper, a two-phase flow model is presented which simulates the fluid and sediment motions in the sheet flow regime on a flat bed under oscillatory flow conditions. The model is developed based on the continuity equations and linearised momentum equations for the fluid and sediment phases, respectively. All major forcing terms such as the intergranular stresses and the turbulent stress are included in the model. From the detailed computations and comparison with the available laboratory data it has been demonstrated that the model is capable of predicting fairly accurately both flow kinematics and sediment concentrations. In particular, the model predicts that the well known phenomenon of fluid velocity over-shoot that exists in clear water also appears in the case of lighter sediments but vanishes when the materials are heavier, which is in perfect accord with the experimental observations considered.     

Wave energy losses in intermediate depths

Recent work on wave power devices has encouraged interest in the processes whereby waves lose energy and change direction in shoaling water, and especially in detailed calculations of their effects.^1,2 Here one of the most comprehensive sets of measurements available is examined, for four sites in depths of 15 to 100 m off South Uist in the Hebrides. The mean directional spectrum is recalculated for each site, and a proper allowance found for refraction which raises the estimates of net energy flux in intermediate depths by up to 10%. Indeed, the pattern of losses between 100 m and 23 m depths fits well with that expected from bottom friction. The estimated friction coefficient is quite high, as might be expected in view of the very rough sea bottom in the area.³     

Experimental study of forces on a cylinder in oscillatory flow with a cross current

Forces on a circular cylinder have been measured with nominally two-dimensional current and oscillatory flow at right angles. Previous results for purely oscillatory flow defined by a Keulegan-Carpenter number, Kc, have been extended for reduced velocities, Vr, in the range 3–10. For Kc<7 modification of the Karman street by oscillation is complex and locking-on has a dominant influence. For Kc > 7 simply adding forces due to the current and oscillation as though in isolation generally gives conservative results. The ‘current’ drag shows considerable variation and can even be negative. The Morison fit to the in-line force is generally less satisfactory when there is a current and can be wholly inadequate.     

Energy dissipation in oscillatory flow over rippled beds

Measurements of energy dissipation have been made with an oscillating tray apparatus similar to that of Bagnold (1946). Two different bed profiles were examined: one was sinusoidal and the other consisted of fins projecting perpendicularly fromthe plate in a regular two-dimensional pattern. The tests with the sinusoidal profile showed that significant variation in energy dissipation coefficient with Reynolds number occurs near the point at which vortex formation first starts to take place. It is suggested that Bagnold did not observe this effect because of the particular profile used in his tests. The tests with the finned beds showed that even when vortex formation is fully developed there is still some variation in energy dissipation coefficient with Reynolds number, at constant a/k_s, at high Reynolds numbers.     

Sheet flow and suspension of sand in oscillatory boundary layers

after revisionTime-dependent measurements of flow velocities and sediment concentrations were conducted in a large oscillating water tunnel. The measurements were aimed at the flow and sediment dynamics in and above an oscillatory boundary layer in plane bed and sheet-flow conditions. Two asymmetric waves and one sinusoidal wave were imposed using quartz sand with D₅₀ = 0.21 mm. A new electro-resistance probe with a large resolving power was developed for the measurement of the large sediment concentrations in the sheet-flow layer. The measurements revealed a three layer transport system consisting of a pick-up/deposition layer, an upper sheet flow layer and a suspension layer.In the asymmetric wave cases the total net transport was directed “onshore” and was mainly concentrated in the thin sheet flow layer (< 0.5 cm) at the bed. A small net sediment flux was directed “offhore” in the upper suspension layer. The measured flow velocities, sediment concentrations and sedimenl fluxes showed a good qualitative agreement with the results of a (numerical) 1DV boundary-layer flow and transport model. Although the model did not describe all the observed processes in the sheet-flow and suspension layer, the computational results showed a reasonable agreement with measured net transport rates in a wide range of asymmetric wave conditions.     

Fluid forces on a small cylinder in the presence of a large cylinder in relative oscillatory flow

The present brief paper is intended to show that the fluid forces on a small cylinder can be considerably magnified when it is in the flow field of a larger cylinder. Two cylinders of unequal diameter are oscillated in a tank of fluid, and the lift and in-line forces on the smaller cylinder are measured when the pair of cylinders is placed at various orientations and spacings.     

Measurements of sheet flow transport in acceleration-skewed oscillatory flow and comparison with practical formulations

Near-bed oscillatory flows with acceleration skewness are characteristic of steep and breaking waves in shallow water. In order to isolate the effects of acceleration skewness on sheet flow sand transport, new experiments are carried out in the Aberdeen Oscillatory Flow Tunnel. The experiments have produced a dataset of net transport rates for full-scale oscillatory flows with varying degrees of acceleration skewness and three sand sizes. The new data confirm previous research that net transport in acceleration-skewed flow is non-zero, is always in the direction of the largest acceleration and increases with increasing acceleration skewness. Large transport rates for the fine sand conditions suggest that phase lag effects play an important role in augmenting positive net transport. A comparison of the new experimental data with a number of practical sand transport formulations that incorporate acceleration skewness shows that none of the formulations performs well in predicting the measured net transport rates for both the fine and the coarser sands. The new experimental data can be used to further develop practical sand transport formulations to better account for acceleration skewness.     

A model of oscillatory rough turbulent boundary layer flow

Approximate analytical solutions of the boundary layer equation are obtained in closed form for oscillatory rough turbulent flow. The solutions are based on a time-varying eddy viscosity, and the aim of the study is to assess the effects of these time variations on the properties of the wave boundary layer. The flow and the eddy viscosity are made interdependent by a closure assumption which relates the peak value of viscosity in the wave cycle to the peak value of shear velocity. Instantaneous vertical profiles of horizontal velocity and shear stress, and time series of the bed shear stress, are presented for a typical case study. In addition, the wave drag coefficient, the boundary layer thickness and the phase lead of peak bed shear stress over peak free-stream velocity, are determined as functions of both the relative roughness and the parameter governing the magnitude of the time variations in viscosity. Reasonable agreement is demonstrated with previous experimental and theoretical results.     

Characteristic friction coefficient and scale effects in oscillatory porous flow

This work presents a simple method to evaluate the performance of a porous breakwater when it is impinged with normal incidence by a non-breaking monochromatic wave train. It is based on: 1) a potential flow model for wave interaction with permeable structures and 2) a set of experimental tests on a rectangular porous structure with uniform granular distribution. A characteristic friction diagram is obtained considering wave energy balance in a control volume, minimising the error between the numerical model and the experimental results for the wave transmission coefficient. Results show that, for large breakwater widths, the reflection process reaches a saturation regime before the waves exit the structure at a distance from the seaside between the interval 0.2 < x/L < 0.45. For larger breakwater widths, the reflection coefficient is almost constant (except for “resonant” conditions) and wave transmission decreases exponentially. Under such conditions, the wave propagation through the porous medium depends on the relative diameter D/L and the porosity of the material; the dependence on the relative breakwater width B/L and the ratio diameter wave height D/H is weak. This diagram intends to be useful for preliminary engineering studies of breakwater's efficiency and performance and as an adequate selection criteria of the experimental stone diameter to minimize scale effects in laboratory studies.     

Transport processes of uniform and mixed sands in oscillatory sheet flow

New experiments were carried out in the Large Oscillating Water Tunnel of WL|Delft Hydraulics (scale 1:1) using asymmetric 2nd-order Stokes waves. The main aim was to gain a better understanding of size-selective sediment transport processes under oscillatory plane-bed/sheet-flow conditions. The new data show that for uniform sand sizes between 0.2 < D < 1.0 mm, measured net transport rates are hardly affected by the grain size and are proportional to the third-order velocity moment. However for finer grains (D = 0.13 mm) net sand transport rates change from the ‘onshore’ direction into the ‘offshore’ direction in the high velocity range. A new measuring technique for sediment concentrations, based on the measurement of electro-resistance (see [McLean, S.R., Ribberink, J.S., Dohmen-Janssen, C.M. and Hassan, W.N.M., 2001. Sediment transport measurements within the sheet flow layer under waves and currents. J. Waterw., Port, Coast., Ocean Eng., ISSN 0733-950X]), was developed further for the improved measurement of sediment dynamics inside the sheet-flow layer. This technique enabled the measurements of particle velocities during the complete wave cycle. It is observed that for long period waves (T = 12.0 s), time-dependent concentrations inside the sheet-flow layer are nearly in phase with the time-dependent flow velocities. As the wave period decreases, the sediment entrainment from the bed as well as the deposition process back to the bed lags behind the wave motion more and more. The new data show that size-gradation has almost no effect on the net total transport rates, provided the grain sizes of the sand mixture are in the range of 0.2 < D < 1.0 mm. However, if very fine grains (D = 0.13 mm) are present in the mixture, net total transport rates of graded sand are generally reduced in comparison with uniform sand with the same D₅₀. The transport rates of individual size fractions of a mixture are strongly influenced by the presence of other fractions in a mixture. Fine particles in sand mixtures are relatively less transported than in that uniform sand case, while the opposite occurs for coarse fractions in a mixture. The relative contribution of the coarse grains to the net total transport is therefore larger than would be expected based on their volume proportion in the original sand mixture. This partial transport behaviour is opposite to what is generally observed in uni-directional (e.g. river) flows. This is caused by vertical sorting of grain sizes in the upper bed layer and in the sheet flow and suspension layers. Kinematic sorting is believed to be responsible for the development of a coarse surface layer on top of a relatively fine sub-layer, providing in this way a relatively large flow exposure for the coarser sizes. Furthermore fine grains are suspended more easily than coarse grains to higher elevations in the flow where they are subject to increasing phase-lag effects (settling lags). The latter also leads to reduced net transport rates of these finer sizes.