Steady Unidirectional Flow Research Articles

Impulse Turbine with Self-Pitch-Controlled Guide Vanes for Wave Power Generator. Control of Guide Vanes Connected by Link Motion.

Experimental investigations on improving the performance of the impulse turbine with self-pitch-controlled guide vanes are reported. A new type of guide vanes which are connected by link motion is presented and tested. The behavior of guide vanes in reciprocating flow is also shown relation to the axial flow velocity. The results show that a high-efficiency impulse turbine can developed by the use of guide vanes connected by link motion. Furthermore, it is found that the running and starting characteristics of this turbine in the reciprocating flow can be evaluated from the performance of the turbine with fixed nozzle and diffuser vanes in a unidirectional steady flow.

Quantitative studies of endothelial cell adhesion. Directional remodeling of focal adhesion sites in response to flow forces.

Focal adhesion sites were observed in cultured endothelial cells by tandem scanning confocal microscopy and digitized image analysis, techniques that provide real-time images of adhesion site area and topography in living cells. Image subtraction demonstrated that in the presence of unidirectional steady laminar flow (shear stress [tau] = 10 dyn/cm2) a substantial fraction of focal adhesion sites remodeled in the direction of flow. In contrast, focal adhesions of control (no flow) cells remodeled without preferred direction. In confluent monolayers subjected to shear stresses of 10 dyn/cm2, cells began to realign in the direction of flow after 7-9 h. This was accompanied by redistribution of intracellular stress fibers, alignment of individual focal adhesion sites, and the coalescence of smaller sites resulting in fewer, but larger, focal adhesions per cell. Cell adhesion, repeatedly calculated in the same cells as a function of the areas of focal contact and the separation distances between membrane and substratum, varied by < 10% during both short (30 min), or prolonged (< or = 24 h), periods of exposure to flow. Consistent with these measurements, the gains and losses of focal adhesion area as each site remodeled were approximately equivalent. When the glass substratum was coated with gelatin, rates of remodeling were inhibited by 47% during flow (tau = 10 dyn/cm2). These studies: (a) reveal the dynamic nature of focal adhesion; (b) demonstrate that these sites at the ablumenal endothelial membrane are both acutely and chronically responsive to frictional shear stress forces applied to the opposite (lumenal) cell surface; and (c) suggest that components of the focal adhesion complex may be mechanically responsive elements coupled to the cytoskeleton.

Analytical solutions for non-equilibrium solute transport in three-dimensional porous media

The movement of water and chemicals in soils is generally better described with multidimensional non-equilibrium models than with more commonly used one-dimensional and/or equilibrium models. This paper presents analytical solutions for non-equilibrium solute transport in semi-infinite porous media during steady unidirectional flow. The solutions can be used to model transport in porous media where the liquid phase consists of a mobile and an immobile region (physical non-equilibrium) or where solute sorption is governed by either an equilibrium or a first-order rate process (chemical non-equilibrium). The transport equation incorporates terms accounting for advection, dispersion, zero-order production, and first-order decay. General solutions were derived for the boundary, initial, and production value problems with the help of Laplace and Fourier transforms. A comprehensive set of specific solutions is presented using Dirac functions for the input and initial distribution, and/or Heaviside or exponential functions for the input, initial, and production profiles. A rectangular or circular inflow area was specified for the boundary value problem while for the initial and production value problems the respective initial and production profiles were located in parallelepipedal, cylindrical, or spherical regions of the soil. Solutions are given for both the volume-averaged or resident concentration as well as the flux-averaged or flowing concentration. Examples of concentration profiles versus time and position are presented for selected problems. Results show that the effects of non-equilibrium on three-dimensional transport are very similar to those for one-dimensional transport.

Impulse Turbine with Self-Pitch-Controlled Guide Vanes for Wave Power Generator. Improvement of Performance by the Use of Tandem Guide Vanes.

Experimental investigations directed towards improving the performance of the impulse turbine with self-pitch-controlled guide vanes are reported. Two types of tandem guide vanes are presented and tested : those with variable-pitch flat-plate and those with variable-pitch splitter. The results show that a high-efficiency impulse turbine can be developed through the use of the splitter. It is found that, in this case, the upstream guide vanes act as a slotted nozzle blade row and the downstream vanes as a tandem diffuser blade row by changing the pitch angle of the splitter automatically in a reciprocating flow. It is also found that the running and starting characteristics of this turbine in the reciprocating flow can be evaluated from the performance of the turbine with fixed nozzle and diffuser vanes in a unidirectional steady flow.

Impulse Turbine with Self-Pitch-Controlled Guide Vanes for Wave Power Generator. Turbine Characteristics in Periodically Oscillating Flow.

In order to clarify the unsteady characteristics of an impulse turbine with self-pitch-controlled guide vanes in a reciprocating flow, an experimental investigation has been made by a turbine equipment in which the sinusoidal flow conditions are simulated. The results have been compared with those of a Wells turbine and the analytical results that are calculated on the basis of the experimental data obtained by the model testing of a turbine rotor with fixed guide vanes under steady unidirectional flow conditions. As a result, it has been clarified that the impulse turbine presented here is superior to the Wells turbine both in starting characteristics and speed reduction of rotor. The quasi-steady analysis is available for this turbine.

Bed configuration in steady unidirectional water flows; Part 2, Synthesis of flume data

Data from 39 flume studies that report equilibrium bed configuration as well as water temperature, flow depth, flow velocity, and sediment size are used to develop the best approximation to the relationships among bed phases (ripples, dunes, lower-regime plane bed, upper-regime plane bed, and antidunes) produced by flows of water over loose sediments. We use a three-axis graph with dimensionless measures of mean flow depth, mean flow velocity, and sediment size along the axes. The relationships are presented as a series of depth-velocity sections and velocity-size sections through the dimensionless diagram. Boundaries between stability fields of the bed phases were drawn as smooth surfaces that minimize misplacement of data points. A large subset of the data, for which reliable values of bed shear stress are reported, was used to represent the stability relationships of the bed phases in a graph of dimensionless boundary shear stress against dimensionless sediment size. The graph shows substantial overlapping of the fields for dunes, upper plane bed, and antidunes owing to the decrease in bed shear stress in the transition from dunes to plane bed with increasing flow velocity. The topology of bed-phase boundaries was guided by the relationships shown in the dimensionless depth-velocity-size diagram.

Bed configurations in steady unidirectional water flows; Part 3, Effects of temperature and gravity

ABSTRACT A change in bed configuration caused by a change in water temperature without any change in flow and sediment variables in a unidirectional flow is analyzed in the context of the dimensionless depth-velocity-size diagram discussed in Part 2. Bed states that differ only in water temperature are termed temperature-related states. These are attainable from any given state solely by a change in water temperature. Such a set of bed states forms a curve in the dimensionless depth-velocity-size diagram. This curve, a straight line in a log-log-log plot, is termed a temperature-change line. To predict the change in bed state consequent upon a change in water temperature alone, one finds the temperature-related state lying along the temperature-change line passing through the ori inal bed state in the dimensionless depth-velocity-size diagram. Three examples from the literature are analyzed in this way to show how such changes in bed configuration can be put into the context of existing stability relationships among the various bed phases, without however addressing the general dynamical problem of why those relationships are as they are. The effect of the acceleration of gravity on the bed configuration is also examined from the standpoint of the dimensionless depth-velocity-size diagram. The results show that in a hypothetical open-channel water flow on Mars a given transition between two adjacent bed phases with increasing flow velocity (e.g., ripples to dunes) would take place at a lower velocity on Mars than on earth, by a factor of 0.74.

Bed Configurations in Steady Unidirectional Water Flows. Part 1. Scale Model Study Using Fine Sands

ABSTRACT Reynolds-Froude scale modeling using hot-water flows to model cold-water flows was applied to the study of unidirectional-flow bed configurations in a large, thermally insulated laboratory flume. Three different water temperatures, ranging from 14 to 75°C, provided three different scale ratios, from 1.1 to 2.3. Effective sand sizes, scaled to 10°C water, were about 0.12 mm, 0.18 mm, and 0.28 mm. Relative to 10°C water, use of hot water multiplied the effective flow depth and all flume dimensions by factors of up to 2.3, the flow velocity by factors of up to 1.5, and the water discharge by factors of up to 8. The effective dimensions of the flume, scaled to 10°C water temperature, ranged up to over 26 m long and 2 m wide, with a flow depth of up to 0.5 m. In the coarser sand sizes (0.17-0.26 mm), three bed phases were observed: ripples, dunes, and upper-regime plane bed. Dunes tended to be two-dimensional (crests straight and continuous) at low flow velocities and three-dimensional (crests sinuous and discontinuous) at relatively high flow velocities, except that at flow velocities transitional between ripples and dunes the bed showed a complex intermingling of irregular larger dunelike bed forms and smaller irregular ripples. In the dune range, ripples were prominently superimposed at relatively low flow velocities but nearly absent at relatively high flow velocities.

Bed load transport of sand mixtures in estuaries: A review

Real estuaries are fundamentally inhomogeneous. This is evident in their irregular boundaries, waters of varying density, fluid motions that arise from multiple unsteady forcings, and sediments that are mixtures of various grain sizes. In the paper, a review is given of the influence of one of these heterogeneities, namely, mixed particle size, on the transport of sand as bed load. Essential early studies and recent complete theories are discussed. Present‐day investigators commonly assume a reference transport function (RTF) which is any established formulation for the flux of bed load under steady unidirectional flow over a substrate of monosized particles. The aim of the modern work is to develop a procedure which yields tailored values of sheltering‐exposure coefficients for the different size fractions. These coefficients are correction factors which when applied to the acting bed shear permit the use of the RTF to compute fraction transports over a mixed bed. There are strong interactions among the various size fractions; for instance, minor admixture of a coarse‐end ingredient disproportionately reduces the overall mobility of a finer‐grained bed. However, coarse fractions are more mobile in a bed of mixed sizes than they are in a bed of the same uniform size. Recommendations are made for an estuarine field study utilizing a modified Helley‐Smith bed load yield sampler.

IDENTIFICATION OF AQUIFER DISPERSIVITIES: METHODS OF ANALYSIS AND PARAMETER UNCERTAINTY1

ABSTRACT: This paper presents a method for estimating aquifer dispersivities in solute transport models. Sensitivity equations are derived for the calculation of sensitivity coefficients. A modified Gauss‐Newton algorithm is used to perform the least‐squares minimization. A statistical procedure is outlined to assess reliability of the estimated parameters. The solute transport model is solved by the upstream weighted, multiple cell balance method which combines the concepts of local mass balance and finite element approximations. A one‐dimensional solute transport problem in a vertical column system is first used to illustrate the inverse technique. A second example considers the parameter identification problem for three‐dimensional solute transport with a unidirectional steady and uniform flow field. The third example solves the parameter identification problem in a three‐dimensional, stream‐aquifer, solute transport system with steady state flow. Numerical experiments are conducted to study data requirements for parameter identification.

The variational inequality formulation of a unidirectional gravity-driven free-boundary flow

Abstract We study a free-boundary problem arising from a unidirectional gravity-driven steady flow. Under certain geometrical assumptions, the free-boundary problem is equivalent to a complementarity problem, which, in turn, is shown to be equivalent to a variational inequality. Numerical results using a point successive overrelaxation method with projection are presented for specific geometries.

Studies on Wells Turbine for Wave Power Generator : 4th Report, Starting and Running Characteristics in Periodically Oscillating Flow

In order to clarify the starting and running characteristics of a Wells turbine in an oscillating flow, an experimental investigation has been performed. The results have been compared with the analytical results. In the analysis, both starting and running characteristics were calculated on the basis of the experimental results obtained under steady unidirectional flow conditions. Comparison between experiment and analysis has shown that the effect of hysteresis and Reynolds number on torque coefficient should be considered in the analysis. Furthermore, running characteristics have been investigated from a view point of the method of load control.

Finite-amplitude steady waves in plane viscous shear flows

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Studies on Wells turbine for wave power generator. (4th report, Starting and running characteristics in periodically oscillating flow)

In order to clarify the starting and runnning characteristics of Wells turbine in oscillating flow, an experimental investigation has been made by a newly deviced turbine equipment in which the oscillating flow condition is simulated. The results have been compared with the analytical results. In the analysis, both starting and running characteristics were calculated on the basis of the experimental results obtained from steady unidirectional flow conditions. The comparison between the experiment and analysis has shown that the effects of hysteresis and Reynolds number on torque coefficient should be considered in the analysis. Furthermore, running characteristics have been investigated from a viewpoint of the method of load control.

Multiple solutions and hysteresis in steady parallel viscous flows

A study is made of flows of viscous fluids when viscosity varies with temperature according to an Arrhenius law, and when viscous dissipation is taken into account. It is shown that for fluids with highly temperature-sensitive viscosity the graph of shear rate against shear stress is an S-shaped curve, with either one or three values of shear rate for given shear stress. In this situation hysteresis can occur if steady unidirectional flow is maintained. The velocity and temperature profiles are calculated, and the manner in which the temperature-sensitivity parameter affects the conclusions is discussed. The calculations serve as criteria for evaluating the importance of viscous-heating effects in applications.

Some elementary exact channel flows

AbstractNew polynomial solutions of the Navier-Stokes equations for steady uni-directional flow of viscous incompressible fluid, with a free surface, down inclined channels of specialized cross-section are considered. An inverse method is uded to obtain the geometrical shape of the channel by equating the polynomials solution to zero (i.e. the no-slip condition) and thence determining the boundary shape.

RELATIONSHIP BETWEEN ALONGSHORE WAVE ENERGY AND LITTORAL DRIFT IN THE MID-WEST COAST AT TAIWAN

Based on the wave pattern, the geographical location and the disposition of rivers, the littoral drift moves predominantly from NE to SW direction in section II as shown in Fig. 1. Seven rivers of rapid stream bring tremendous amount of sediments from the high mountain to the nearshore of this section in typhoon season (i.e. from June to September). But for the winter monsoon season, i.e. from October to the next April, the waves induced by NE monsoons migrate littoral drift from North toward South. Applying the energy approach for unidirectional steady flow derived by Bagnold(1963), the theoretical relationship between the littoral immersed weight transport rate and the alongshore breaking wave energy is found out. It reveals that the relationship is not strictly linear, i.e. the larger part of the alongshore breaking wave energy is supplied for transporting the sediment as the former increases. But for a coast having a steady oceanographical condition, the relationship could be considered as linear relation since the alongshore breaking wave energy is not varying very much. In this paper, the study of littoral drift vs wave energy at the Taichung Coast from the Ta-Chia River to the Ta-Tu River will be carried out. Using the wave records gained by the ultrasonic wave gauge at 19m depth and the littoral drift quantity obtained from long-term observation, the relationship between alongshore breaking wave energy and littoral immersed weight transport rate is found out. First, the waves which have the same direction are summed up. Then from "THE WAVE CHARACTER COMPUTING PROGRAM", the incident directions of these wave groups at 19m depth are determined. Then the alongshore breaking wave energy per unit time per unit length of beach could be calculated by the same PROGRAM.

Test of scale modelling of sediment transport in steady unidirectional flow

AbstractIn two steady uniform flows at different physical scales in a small open channel, with variables characterizing flow, sediment, and fluid adjusted for dynamic similitude by means of four dimensionless modelling parameters (a Reynolds number, a Froude number, a density ratio, and a length ratio), measured frequency distributions of height, spacing, and migration rate of current ripples were almost identical when scaled, thus verifying that exact Reynolds‐Froude modelling of loose‐sediment transport is valid and workable. Modelling should be valid as well for a wide range of other transport conditions in the same kind of flow, because no additional kinds of forces or effects would be present in transport of loose grains in modes other than as ripples. In scaled‐down modelling, a scale ratio of 2.5 is attainable without recourse to exotic fluids by use of water at 85°C to model natural flows at 10°C.

Conductimetric investigation of erythrocyte behaviour during shear flow of concentrated suspensions through a large tube.

The behaviour of canine erythrocytes in isotonic saline suspensions undergoing steady unidirectional shear flow in the vertical direction, at cell volume concentrations (ρ) ranging between 0.017 and 0.840, is studied by measuring suspension resistivities in three mutually orthogonal directions. Results are compared with the predicted behaviour of rigid spheroids and liquid drops. Analyses of suspension resistivities show that there are significant changes in erythrocyte shape with increasing shear rate ( k ) at all k covered (2.6 x 10 – 10 3 s -1 ) and at all ρ, very large changes occurring at ρ &gt; 0.65. However, the changes in the equivalent principal axis-ratios of erythrocytes with k deviate substantially from the flow behaviour expected of liquid drops, the average ‘shape factor’ for the cells decreasing rather than increasing with k . Neither the simple liquid drop nor the rigid spheroid model can adequately explain some aspects of the results obtained. Results show that cell concentration is a major determinant of erythrocyte behaviour and point to the existence of three concentration regimes in the range of flow rates investigated, with different mechanisms of particle orientation during shear flow predominating in each. At ρ &lt; 0.08 no significant change in orientation distribution with k is observed; but results show that erythrocytes tend to assume the orientation corresponding to the maximum dissipation of energy in a shear field or corresponding to the maximum energy dissipation of settling disks (the effect increasing as ρ is reduced) indicating a predominance of inertial effects. Between ρ ≃ 0.08 and ρ ≃ 0.65 the orientation distribution changes towards alignment of erythrocytes parallel to the plane of flow, the degree of alignment increasing with k and with ρ. Here, particle-particle interactions facilitate the orientation of erythrocytes by shear stresses. Above ρ ≃ 0.65 the change in cell shape with k increases sharply, suggesting that erythrocyte deformation becomes the principal mechanism of suspension flow.

FORCES ON A SPHERE UNDER LINEAR PROGRESSIVE WAVES

The rms horizontal forces which result from the action of a linear, deep and intermediate water, laboratory scale waves were measured on submerged spheres removed several diameters from the free surface. The study focuses on unseparated flows encountered at small values of (d0/D), where d0 is the orbital diameter and D is the sphere diameter. Under these conditions, a steady streaming around the vertical equator of the sphere was observed, giving rise to a circulation in the sense of rotation of the orbital motion. This phenomena was found to diminish the resultant of the wave pressure on the sphere predicted by potential theory. In approaching the onset of separation, the drag coefficients were found to compare in size with those reported for similar motions in steady unidirectional flow.