Showing papers on "Open-channel flow published in 1995"
01 Jul 1995
TL;DR: The Hydrologic Engineering Center's River Analysis System (HEC-RAS) as mentioned in this paper allows one-dimensional steady flow, unsteady flow, and sediment transport calculations.
Abstract: : Welcome to the Hydrologic Engineering Center's River Analysis System (HEC-RAS). This software allows you to perform one-dimensional steady flow, unsteady flow, and sediment transport calculations. The current version of HEC-RAS only supports one-dimensional, steady flow, water surface profile calculations. This manual specifically documents the hydraulic capabilities of the Steady flow portion of HEC-RAS. Documentation for unsteady flow and sediment transport calculations will be made available as these features are added to the HEC-RAS. This chapter discusses the general philosophy of HEC-RAS and gives you a brief overview of the hydraulic capabilities of the modeling system. Documentation for HEC-RAS is discussed, as well as an overview of this manual.
597 citations
TL;DR: In this article, direct numerical simulation (DNS) of two supersonic fully developed channel flows between very cold isothermal walls is used to provide insights into differences between conventional Reynolds and Favre averaging of the mean flow and turbulent quantities.
Abstract: The present paper addresses some topical issues in modelling compressible turbulent shear flows. The work is based on direct numerical simulation (DNS) of two supersonic fully developed channel flows between very cold isothermal walls. Detailed decomposition and analysis of terms appearing in the mean momentum and energy equations are presented. The simulation results are used to provide insights into differences between conventional Reynolds and Favre averaging of the mean-flow and turbulent quantities. Study of the turbulence energy budget for the two cases shows that compressibility effects due to turbulent density and pressure fluctuations are insignificant. In particular, the dilatational dissipation and the mean product of the pressure and dilatation fluctuations are very small, contrary to the results of simulations for sheared homogeneous compressible turbulence and to recent proposals for models for general compressible turbulent flows. This provides a possible explanation of why the Van Driest density-weighted transformation (which ignores any true turbulent compressibility effects) is so successful in correlating compressible boundary-layer data. Finally, it is found that the DNS data do not support the strong Reynolds analogy. A more general representation of the analogy is analysed and shown to match the DNS data very well.
484 citations
TL;DR: In this article, a localization procedure is proposed to remove the mathematical inconsistency to any desired order of accuracy in time, and the model coefficient vanishes in regions of quiescent flow, reproducing accurately the intermittent character of the flow on the stable side of the channel.
Abstract: Most applications of the dynamic subgrid‐scale stress model use volume‐ or planar‐averaging to avoid ill‐conditioning of the model coefficient, which may result in numerical instabilities. Furthermore, a spatially‐varying coefficient is mathematically inconsistent with the original derivation of the model. A localization procedure is proposed here that removes the mathematical inconsistency to any desired order of accuracy in time. This model is applied to the simulation of rotating channel flow, and results in improved prediction of the turbulence statistics. The model coefficient vanishes in regions of quiescent flow, reproducing accurately the intermittent character of the flow on the stable side of the channel. Large‐scale longitudinal vortices can be identified, consistent with the observation from experiments and direct simulations. The effect of the unresolved scales on higher‐order statistics is also discussed.
455 citations
TL;DR: In this article, a study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation Mach numbers, based on the bulk velocity and sound speed at the walls, of 15 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel halfwidth, are of the order of 3000.
Abstract: A study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation Mach numbers, based on the bulk velocity and sound speed at the walls, of 15 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel half-width, are of the order of 3000 Because of the relatively low Reynolds number, all of the relevant scales of motion can be captured, and no subgrid-scale or turbulence model is needed The isothermal boundary conditions give rise to a flow that is strongly influenced by wall-normal gradients of mean density and temperature These gradients are found to cause an enhanced streamwise coherence of the near-wall streaks, but not to seriously invalidate Morkovin's hypothesis : the magnitude of fluctuations of total temperature and especially pressure are much less than their mean values, and consequently the dominant compressibility effect is that due to mean property variations The Van Driest transformation is found to be very successful at both Mach numbers, and when properly scaled, statistics are found to agree well with data from incompressible channel flow results
402 citations
TL;DR: In this article, the authors demonstrate finite structures formed as a consequence of the reactive infiltration instability in a series of laboratory and numerical experiments with growth of solution channels parallel to the fluid flow direction, as predicted by linear stability analysis for growth of infinitesimal perturbations in porosity.
Abstract: We demonstrate finite structures formed as a consequence of the “reactive infiltration instability” (Chadam et al., 1986) in a series of laboratory and numerical experiments with growth of solution channels parallel to the fluid flow direction. Regions with initially high porosity have high ratios of fluid volume to soluble solid surface area and exhibit more rapid fluid flow at constant pressure, so that dissolution reactions in these regions produce a relatively rapid increase in porosity. As channels grow, large ones entrain flow laterally inward and extend rapidly. As a result, small channels are starved and disappear. The growth of large channels is an exponential function of time, as predicted by linear stability analysis for growth of infinitesimal perturbations in porosity. Our experiments demonstrate channel growth in the presence of an initial solution front and without an initial solution front where there is a gradient in the solubility of the solid matrix. In the gradient case, diffuse flow is unstable everywhere, channels can form and grow at any point, and channels may extend over the length scale of the gradient. As a consequence of the gradient results, we suggest that the reactive infiltration instability is important in the Earth's mantle, where partial melts in the mantle ascend adiabatically. Mantle peridotite becomes increasingly soluble as the melts decompress. Dissolution reactions between melts and peridotite will produce an increase in liquid mass and lead to formation of porous channels composed of dunite (>95% olivine). Replacive dunite is commonly observed in the mantle section of ophiolites. Focused flow of poly baric partial melts of ascending peridotite within dunite channels may explain the observed chemical disequilibrium between shallow, oceanic mantle peridotites and mid-oceanic ridge basalts (MORB). This hypothesis represents an important alternative to MORB extraction in fractures, since fractures may not form in weak, viscously deforming asthenospheric mantle. We also briefly consider the effects of crystallization, rather than dissolution reactions, on the morphology of porous flow via a second set of experiments where fluid becomes supersaturated in a solid phase. Formation of short-lived conduits parallel to the flow direction occurs rapidly, and then each conduit is eventually choked by interior crystallization; fluid flow then passes through the most permeable portion of the walls to form a new conduit. On long time scales and length scales, transient formation and destruction of conduits will result in random and diffuse flow. Where liquid cools as it rises through mantle tectosphere on a conductive geotherm, it will become saturated in pyroxene as well as olivine and decrease in mass. This process may produce a series of walled conduits, as in our experiments. Development of a low-porosity cap overlying high porosity conduits may create hydrostatic overpressure sufficient to cause fracture and magma transport to the surface in dikes.
293 citations
TL;DR: In this article, the upwellings and downdrafts are turned off by changing the boundary condition to free slip, and the dominant structures at the free surface become the attached vortices which pair, merge, and slowly dissipate.
Abstract: Direct numerical simulations of open‐channel flow indicate that turbulence at the free surface contains large‐scale persistent structures. They are ‘‘upwellings’’ caused by impingement of bursts emanating from the bottom boundary; ‘‘downdrafts’’ in regions where adjacent upwellings interact, and whirlpool‐like ‘‘attached vortices’’ which form at the edge of upwellings. The attached vortices are particularly long‐lived in the sense that once formed, unless destroyed by other upwellings, they tend to interact with each other and dissipate only slowly. If turbulence generation at the bottom wall is turned off by changing the boundary condition to free slip, then the upwellings (related to bursts) and downdrafts no longer form. The dominant structures at the free surface become the attached vortices which pair, merge, and slowly dissipate. In the central regions, as expected, the structure remains three dimensional throughout the decay process. Near the free surface, the structure appears to be quasi‐ two dimensional, as indicated by quantitative measures such as energy spectra, interwave number energy transfer, invariants of the anisotropy tensor, and length scales. In the decaying case, the quasi‐two‐dimensional region increases in thickness, with decay time, though the structure in the central regions of the flow remains three dimensional.
178 citations
TL;DR: In this article, a general mathematical model is developed to solve unsteady, depth-averaged equations using boundary-fitted coordinates, including effective stresses, and may be used to analyze sub- and super critical flows.
Abstract: A general mathematical model is developed to solve unsteady, depth-averaged equations. The model uses boundary-fitted coordinates, includes effective stresses, and may be used to analyze sub- and super critical flows. The time differencing is accomplished using a second-order accurate Beam and Warming approximation, while the spatial derivatives are approximated by second-order accurate central differencing. The equations are solved on a nonstaggered grid using an alternative-direction-implicit scheme. To enhance applicability, the equations are solved in transformed computational coordinates. The effective stresses are modeled by incorporating a constant eddy-viscosity turbulence model to approximate the turbulent Reynolds stresses. As is customary, the stresses due to depth-averaging are neglected. Excluding recirculating flows, it is observed that in most cases the effective stresses do not significantly affect the converged solution. The model is used to analyze a wide variety of hydraulics problems including flow in a channel with a hydraulic jump, flow in a channel contraction, flow near a spur-dike, flow in a 180° channel bend, and a dam-break simulation. For each of these cases, the computed results are compared with experimental data. The agreement between the computed and experimental results is satisfactory.
177 citations
TL;DR: In this paper, the maximum velocity in a channel cross section is highlighted with respect to its information content and relation to the mean velocity and entropy parameter, which can be used to continuously update the flow resistance during an unsteady flow.
Abstract: The maximum velocity in a channel cross section is highlighted with respect to its information content and relation to the mean velocity and entropy parameter. Under a wide range of discharge and water depth, a channel section seems to have propensity to establish and maintain an equilibrium state that corresponds to a value of entropy parameter. The entropy parameter of a channel section can be determined from the relation between the mean and maximum velocities. A technique has been developed to determine the discharge from a velocity profile on a single vertical passing through the point of maximum velocity in a channel cross section. The technique is an efficient way to estimate the discharge in streams and rivers, that can be used to continuously update the flow resistance during an unsteady flow, to enhance a filtering scheme designed to reduce uncertainties in flow forecasting. The use of the constant value of entropy parameter predetermined for a channel section can simplify the discharge estimation.
170 citations
TL;DR: In this paper, the authors studied the flow of an incompressible, thermodynamically compatible fluid of grade three in a pipe, where the temperature of the pipe is assumed to be higher than that of the fluid, and the shear viscosity of the liquid was modeled as a function of the temperature.
Abstract: The flow of a fluid-solid mixture is very complicated and may depend on many variables, such as the physical properties of each phase and the size and shape of the solid particles. One approach to the study of these flows is to model the mixture as a non-Newtonian fluid. Much effort has been put into analyzing various transport processes in non-Newtonian fluids, such as coal slurries. Heat transfer plays an important role in the handling and processing of these fluids. In this paper, the fully developed flow of an incompressible, thermodynamically compatible fluid of grade three in a pipe is studied. The temperature of the pipe is assumed to be higher than the temperature of the fluid and the shear viscosity of the fluid is assumed to be a function of the temperature.
157 citations
Book•
01 Jan 1995
TL;DR: The Navier-Stokes equations as discussed by the authors describe the flow of incompressible Newtonian fluids in pipes and channels, as well as non-Newtonian fluid flow in the presence of solid particles.
Abstract: Fluids in motion * Flow of incompressible Newtonian fluids in pipes and channels * Flow of incompressible non-Newtonian fluids in pipes * Pumping of liquids * Mixing of liquids in tanks * Flow of compressible fluids in conduits * Gas-liquid two-phase flow * Flow measurement * Fluid motion in the presence of solid particles * Introduction to unsteady flow * Appendix I: The Navier-Stokes equations * Appendix II: Further problems * Answers to problems * Conversion factors * Index.
151 citations
TL;DR: In this article, the main flow patterns of undular jumps are described and the disappearance of the undular jump occurs for Froude numbers ranging from 1.5 to 2.9.
Abstract: In open channels, the transition from supercritical to subcritical flows is called a hydraulic jump. For low upstream Froude numbers, free-surface undulations develop downstream of the jump and the hydraulic jump is called an undular jump. New experiments on undular hydraulic jumps were performed in a rectangular channel in which the upstream flows were fully developed turbulent shear flows. In this paper, the main flow patterns are described. Visual and photographic observations indicate five types of undular jumps. One of the main flow characteristics is the presence of lateral shock waves for Froude numbers larger than 1.2. The results show that the disappearance of undular jump occurs for Froude numbers ranging from 1.5 to 2.9 and that the wave length and amplitude of the free-surface undulations are functions of the upstream Froude number and the aspect ratio yc/W.
TL;DR: In this paper, a modified low-Reynolds-number k-e turbulence model is developed to predict the near-wall limiting flow behavior while avoiding occurrence of the singular difficulty near the reattachment point as applying to recirculating flow in sudden-expansion pipe.
Abstract: A modified low-Reynolds-number k-e turbulence model is developed in this work. The performance of the proposed model is assessed through testing with fully developed pipe flows and recirculating flow in pipe expansion. Attention is specifically focused on the flow region around the reattachment point. It is shown that the proposed model is capable of correctly predicting the near-wall limiting flow behavior while avoiding occurrence of the singular difficulty near the reattachment point as applying to the recirculating flow in sudden-expansion pipe.
TL;DR: In this article, the authors model a subduction shear zone as a long narrow channel, with the flow of subducted metasedimentary rocks in the channel driven by two sets of forces: the downward shearing force exerted by the subducting slab and the gradient in the hydraulic potential, which combines the effect of both pressure and buoyancy.
Abstract: A subduction shear zone can be modeled as a long narrow channel, with the flow of subducted metasedimentary rocks in the channel driven by two sets of forces: the downward shearing force exerted by the subducting slab and the gradient in the hydraulic potential, which combines the effect of both pressure and buoyancy. If the channel walls are effectively rigid, very slight narrowing or broadening of the channel (convergence angles 2 GPa in the channel at only 40 km depth. The model is consistent with a horizontal balance of forces across the plates and with a reasonable value for the thickness of subducted sediment (∼650 m). The practical limit for overpressures attainable in subduction zones is determined by the strength and permeability of the channel walls. At 40 km depth the channel is effectively confined on both sides by cold lithospheric mantle, which should be strong enough to support a significant tectonic overpressure. Episodic failure of the upper plate to produce great earthquakes at 30–40 km focal depth could vent overpressured fluid from the channel, allowing a cyclical buildup and release of both rock and fluid pressure. Topography on the subducting plate (e.g., seamounts and thinned continental crust) may lead to an anvil-like jamming of the channel and local high overpressures. Tectonic erosion by topography on the lower plate of slivers from overlying continental crust and the compression of these slivers between the topography and the narrowing channel walls could produce high overpressures in continental rocks. A decrease in the convergence rate or cessation of subduction, with a consequent general warming within the channel and associated viscosity decrease, promotes exhumation by buoyant reverse flow. The most rapid reverse flow occurs in the region of previously greatest overpressure. Since the exhumation distance is shorter than for a simple lithostatic pressure distribution and any increase in temperature is coupled with a strong increase in the rate of exhumation, preservation of high-pressure assemblages at the surface in fossil subduction zones is promoted for such a model.
TL;DR: An approximation model is presented to derive an approximation model for an open channel with backwater effects; the approximation model consists of functions that allow the application of effective control synthesis methods.
TL;DR: In this article, the influence of oscillatory flow conditions on the porous flow friction coefficients have been implemented in new expressions for porous flow coefficients, which can be used both to study scale effects in small-scale physical models and for the implementation in numerical models simulating porous flow.
Abstract: Permeability measurements were carried out in a U-tube tunnel to study flow through coarse granular material. The results are of importance for studying the flow in permeable structures such as rubble-mound structures and gravel beaches. The contributions of laminar and turbulence friction terms have been determined as well as the importance of inertial resistance. Differences between stationary flow and oscillatory flow conditions have been studied. The influence of oscillatory flow conditions on the porous flow friction coefficients have been implemented in new expressions for porous flow friction coefficients. These can be used both to study scale effects in small-scale physical models and for the implementation in numerical models simulating porous flow.
TL;DR: In this article, the initiation of bed-load transport of uniform spherical sediment particles on a horizontal bed in an open-channel flow is studied on the basis of micromechanical and fluid dynamical considerations.
Abstract: Initiation of bed-load transport of uniform spherical sediment particles on a horizontal bed in an open-channel flow is studied On the basis of micromechanical and fluid dynamical considerations,
TL;DR: A variational principle for lower bounds on the time-averaged mass flux for Newtonian fluids driven by a pressure gradient in a channel is derived from the incompressible Navier-Stokes equations and compared with the predictions of conventional turbulence theory.
Abstract: A variational principle for lower bounds on the time-averaged mass flux for Newtonian fluids driven by a pressure gradient in a channel is derived from the incompressible Navier-Stokes equations. When supplied with appropriate test background flow fields, the variational formulation produces explicit estimates for the friction coefficient. These rigorous bounds are compared with the predictions of conventional turbulence theory.
Book•
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01 Jan 1995
TL;DR: In this article, the authors consider the problem of quantifying the flow properties of a mixture of fluids in terms of the velocity and the energy of the mixture. But they do not consider the physical properties of the fluid.
Abstract: 1 Properties of Fluids.- 1.1. Physical Properties of Fluids.- 1.1.1. Liquids.- 1.1.2. Gases.- 1.1.3. Thermodynamic Notions.- 1.2. Transfer Properties.- 1.2.1. Viscosity.- 1.2.2. Thermal Conductivity.- 1.2.3. Fluid Mixtures. Mass Transfer.- 1.2.4. Non-Newtonian Media.- 2 Fundamental Equations of Viscous Flow.- 2.1. Kinematics of Fluid Flow.- 2.1.1. Lagrangian and Eulerian Descriptions.- 2.1.2. Strain Rates.- 2.1.3. Circulation. Stokes' Theorem.- 2.2. Equations of Motion.- 2.2.1. Continuity Equation.- 2.2.2. The Equations of Motion in Stresses.- 2.2.3. The Constitutive Relation for a Newtonian Fluid.- 2.2.4. Remarks on the Second Coefficient of Viscosity.- 2.2.5. Navier-Stokes Equations.- 2.2.6. Noninertial Coordinate System.- 2.3. The Energy Equation.- 2.3.1. Energy Balance for a Fluid Particle.- 2.3.2. Energy Equation for Incompressible Fluids.- 2.3.3. Energy Equation for Compressible Fluids.- 2.4 Orthogonal Curvilinear Coordinate Systems.- 2.4.1. Cylindrical Coordinates.- 2.4.2. Spherical Coordinates.- 3 Basic Equations and Flow Pattern.- 3.1. Posing the Problem of Fluid Flow.- 3.1.1. Assumptions Involved and Mathematical Character of the Basic Equations.- 3.1.2. Initial and Boundary Conditions.- 3.2. Dimensionless Parameters in Viscous Fluid Flow.- 3.2.1. Dimensionless Parameters in Navier-Stokes Equations.- 3.2.2. Dimensionless Parameters in the Energy Equation.- 3.3. Viscous Flow Pattern.- 3.3.1. Pure Viscous Flow.- 3.3.2. Visco-inertial Flow.- 3.3.3. The Boundary'1 Properties of Fluids.- 1.1. Physical Properties of Fluids.- 1.1.1. Liquids.- 1.1.2. Gases.- 1.1.3. Thermodynamic Notions.- 1.2. Transfer Properties.- 1.2.1. Viscosity.- 1.2.2. Thermal Conductivity.- 1.2.3. Fluid Mixtures. Mass Transfer.- 1.2.4. Non-Newtonian Media.- 2 Fundamental Equations of Viscous Flow.- 2.1. Kinematics of Fluid Flow.- 2.1.1. Lagrangian and Eulerian Descriptions.- 2.1.2. Strain Rates.- 2.1.3. Circulation. Stokes' Theorem.- 2.2. Equations of Motion.- 2.2.1. Continuity Equation.- 2.2.2. The Equations of Motion in Stresses.- 2.2.3. The Constitutive Relation for a Newtonian Fluid.- 2.2.4. Remarks on the Second Coefficient of Viscosity.- 2.2.5. Navier-Stokes Equations.- 2.2.6. Noninertial Coordinate System.- 2.3. The Energy Equation.- 2.3.1. Energy Balance for a Fluid Particle.- 2.3.2. Energy Equation for Incompressible Fluids.- 2.3.3. Energy Equation for Compressible Fluids.- 2.4 Orthogonal Curvilinear Coordinate Systems.- 2.4.1. Cylindrical Coordinates.- 2.4.2. Spherical Coordinates.- 3 Basic Equations and Flow Pattern.- 3.1. Posing the Problem of Fluid Flow.- 3.1.1. Assumptions Involved and Mathematical Character of the Basic Equations.- 3.1.2. Initial and Boundary Conditions.- 3.2. Dimensionless Parameters in Viscous Fluid Flow.- 3.2.1. Dimensionless Parameters in Navier-Stokes Equations.- 3.2.2. Dimensionless Parameters in the Energy Equation.- 3.3. Viscous Flow Pattern.- 3.3.1. Pure Viscous Flow.- 3.3.2. Visco-inertial Flow.- 3.3.3. The Boundary'Layer Concept.- 3.4. Other Forms of the Basic Equations.- 3.4.1. The Conservative (Eulerian) Form of the Basic Equations.- 3.4.2. The Equation for Vorticity.- 3.4.3. Two-Dimensional Row.- 3.4.4. Integral Relations (Control Volume Formulation).- 4 Steady Parallel Flow of Incompressible Fluids.- 4.1. Plane Parallel Flow.- 4.1.1. Couette Flow.- 4.1.2. Channel (Poiseuille) Flow.- 4.1.3. Open Channel Flow.- 4.1.4. Combined Couette-Poiseuille Flow.- 4.2. General Couette Flow.- 4.2.1 Two Circular Cylinders.- 4.2.2. Translation of a Semiplane in a Channel.- 4.3. Duct Flow.- 4.3.1. Circular Pipe.- 4.3.2. Ducts of Various Cross Sections.- 4.3.3. Hydraulic Radius.- 4.3.4. Analysis of a System of Ducts.- 4.4. Steady Parallel Flow of Viscoplastic Media.- 4.4.1. Plane Parallel Flow.- 4.4.2. Circular Duct.- 4.5. Influence of Porous Surfaces.- 4.5.1. Quasi-Parallel Flow.- 4.5.2. Channel and Duct Flow.- 5 Other Solutions of Navier-Stokes Equations (Steady Incompressible Flow).- 5.1. Flow upon Concentric Circles.- 5.1.1. Coaxial Rotating Cylinders.- 5.1.2. Particular Cases (Vortex).- 5.2. Motions upon Concurrent Lines.- 5.2.1. Motion between Two Nonparallel Walls.- 5.2.2. Approximate Solutions.- 5.3. Self-Similar Solutions.- 5.3.1. Flow Near a Stagnation Point.- 5.3.2. Flow Near a Rotating Disk.- 5.3.3. Fluid Rotation Near a Plane.- 5.4. Other Solutions.- 5.4.1. Solutions for the Stream Function.- 5.4.2. Pseudo-Plane Motions (Noninertial Coordinates).- 6 Unsteady Viscous Incompressible Flow.- 6.1. Parallel Unsteady Flow.- 6.1.1. General Remarks.- 6.1.2. Plane Unsteady Parallel Flow.- 6.1.3. Examples of Unsteady Parallel Flows.- 6.1.4. Parallel Axisymmetric Row in Ducts.- 6.2. Other Unsteady Motions.- 6.2.1. Unsteady Flow upon Concentric Circles.- 6.2.2. Plane Unsteady Flow.- 6.2.3. Three-Dimensional Unsteady Row.- 7 Thermal Effects in Incompressible Flow.- 7.1. Thermal Effects in Plane Couette Flow.- 7.1.1. Constant Wall Temperature.- 7.1.2. Adiabatic Wall.- 7.1.3. Variable Viscosity.- 7.1.4. Forced Heat Transfer in Slow Motion.- 7.2. Temperature Field in Flow Near Walls.- 7.2.1. Poiseuille Flow with Constant Viscosity.- 7.2.2. Couette-Poiseuille Flow.- 7.2.3. Free Convection between Parallel Walls.- 7.2.4. Temperature Field in Flow between Nonparallel Walls.- 7.2.5. Temperature Field in Flow between Coaxial Rotating Cylinders.- 7.2.6. Temperature Field Near a Stagnation Point.- 7.3. Temperature Field in Duct Flow.- 7.3.1. Influence of Dissipation.- 7.3.2. Circular Pipes.- 7.3.3. Thermal Entrance.- 7.3.4. Extensions.- 8. Compressible Viscous Fluid Flow.- 8.1. Flow between Parallel Plates.- 8.1.1. Couette Flow.- 8.1.2. Isothermal Flow between Parallel Walls.- 8.1.3. Effect of a Transversal Heat Transfer.- 8.2. Shock Wave Structure.- 8.2.1. Shock Structure without Consideration of the Second Coefficient of Viscosity.- 8.2.2. Influence of the Second Coefficient of Viscosity.- 8.2.3. Weak Shock Wave.- 8.3. Viscosity Effccts in Unsteady Flow.- 8.3.1. Impulsive Motion of a Wall.- 8.3.2. Sound Attenuation.- 9 Slow Viscous Flow in Thin Layers (Hydrodynamic Lubrication).- 9.1. Equations of Motion.- 9.1.1. Simplifications of the Equations of Motion.- 9.1.2. The Pressure Equation.- 9.1.3. Mechanisms of Lubrication.- 9.1.4. Boundary Conditions.- 9.2. Liquid Film Lubrication.- 9.2.1. Self-Acting Films.- 9.2.2. Hydrostatic Films.- 9.2.3. Grease Films.- 9.3. Gas Film Lubrication.- 9.3.1. Self-Acting Gas Films.- 9.3.2. Externally Pressurized Gas Films.- 9.4. Elasto-hydrodynamic Lubrication.- 9.4.1. Hydrodynamic Lubrication of Concentrated Contacts.- 9.4.2. Influence of Surface Deformation.- 10 Slow Viscous Flow.- 10.1. General Remarks.- 10.1.1. The Use of Biharmonic Functions.- 10.1.2. Plane Motions.- 10.1.3. Axisymmetric Flow.- 10.1.4. Hele Shaw Flow.- 10.1.5. Extensions of the Hele Shaw Analogy.- 10.2. Slow Rotation of a Viscous Fluid.- 10.2.1. Coordinate Systems.- 10.2.2. Steady Rotation of a Body.- 10.2.3. Unsteady Rotation of a Body.- 10.3. Flow Around Bodies of Revolution.- 10.3.1. Flow Around a Sphere.- 10.3.2. Extensions.- 10.4. Slow Plane Flow.- 10.4.1. General Considerations.- 10.4.2. Direct Methods.- 10.4.3. The Circle Theorem for Slow Viscous Flow.- 11 Visco-inertial Flow in Thin Layers.- 11.1. Incompressible Flow in Thin Layers.- 11.1.1. Approximate Methods.- 11.1.2. Motions between Surfaces at Rest.- 11.1.3. Two-Dimensional Flow between Moving Surfaces.- 11.1.4. Three-Dimensional Flow in Thin Layers.- 11.2. Compressible Flow in Thin Layers.- 11.2.1. General Equations.- 11.2.2. Motions between Surfaces at Rest.- 11.2.3. High-Speed Sliding Motions.- 12 Visco-inertial Flow Around Bodies.- 12.1. Small Perturbation Slow Flow (Oseen Flow).- 12.1.1. General Equations.- 12.1.2. Flow Around a Sphere.- 12.1.3. Plane Flow Past a Circle.- 12.2. Other Approximations for Visco-inertial Flow.- 12.2.1. Small Perturbations from Irrotational Flow.- 12.2.2. Second Direct Approximation for a Slow Flow Around a Sphere. Whitehead's Paradox.- 12.2.3. The Use of the Singular Perturbation Method.- References.
TL;DR: In this paper, the case of no net flow and a return flow in the (finite depth) upper layer is investigated, where the reflected jump is in the opposite direction to the incoming current.
Abstract: When a gravity current meets an obstacle a proportion of the flow may continue over the obstacle while the rest is reflected back as a hydraulic jump. There are many examples of this type of flow, both in the natural and man-made environment (e.g. sea breezes meeting hills, dense gas and liquid releases meeting containment walls). Two-dimensional currents and obstacles, where the reflected jump is in the opposite direction to the incoming current, are examined by laboratory experiment and theoretical analysis. The investigation concentrates on the case of no net flow, so that there is a return flow in the (finite depth) upper layer. The theoretical analysis is based on shallow-water theory. Both a rigid lid and a free surface condition for the top of the upper layer are considered. The flow may be divided into several regions: the inflow conditions, the region around the hydraulic jump, the flow at the obstacle and the flow downstream of the obstacle. Both theoretical and empirical inflow conditions are examined; the jump conditions are based on assuming that the energy dissipation is confined to the lower layer; and the flow over the obstacle is described by hydraulic control theory. The predictions for the proportion of the flow that continues over the obstacle, the speed of the reflected jump and the depth of the reflected flow are compared with the laboratory experiments, and give reasonable agreement. A shallower upper layer (which must result in a faster return velocity in the upper layer) is found to have a significant effect, both on the initial incoming gravity current and on the proportion of the flow that continues over the obstacle.
TL;DR: In this article, a large eddy simulation of turbulent flow in a compound open channel with one floodplain is reported for a Reynolds number of approximately 42000, which is in good agreement with experimental measurements and previous numerical calculations.
Abstract: A Large Eddy Simulation of turbulent flow in a compound open channel with one floodplain is reported for a Reynolds number of approximately 42000. The results are in good agreement with experimental measurements and previous numerical calculations. The mean velocity field, secondary circulation field, bed stress distribution, and lateral stress distribution are presented in detail.
TL;DR: In this paper, a new approach for predicting alluvial-channel resistance in the framework of the familiar Manning equation is proposed, where a relation for the Manning coefficient that incorporates directly the role of bed configuration is developed, which is then used as an independent variable to account for the resistance due to bed-form drag.
Abstract: A new approach for predicting alluvial-channel resistance in the framework of the familiar Manning equation is proposed. The new method proposes a relation for the Manning coefficient that incorporates directly the role of bed configuration in determining alluvial-bed resistance. A relation for bed-form height is developed, which is then used as an independent variable to account for the resistance due to bed-form drag. The method was applied to a large body (969 flows) of river and flume data with satisfactory agreement with the observed values. Mean normalized errors for predicted flow depths and velocities were about 10% for all 969 flows. The procedure can be applied to natural streams with compound channels, since variable roughness for the main channel and overbank sections can be computed separately in this approach. Prediction accuracy was generally better for flows that were clearly in the lower regime (ripple or dune) or in the upper regime (flat bed or antidune), but larger errors were associat...
TL;DR: In this paper, a complete second-order closure model of turbulence is used to predict the behavior of fully developed turbulent flows in open channels of both simple and compound cross sections, and data from simple rectangular channels are used to check the model's sensitivity to the effects of a free surface, while compound channels, both symmetric and asymmetric, serve to validate the model for a range of parameters typical of those encountered in practice.
Abstract: A complete second-order closure model of turbulence is used to predict the behavior of fully developed turbulent flows in open channels of both simple and compound cross sections. This level of closure entails the solution of seven differential transport equations for turbulence quantities and is found to reproduce fairly accurately the details of the turbulence-driven secondary motions that occur in the cross-stream planes. In particular, the number, location, and strength of the secondary-flow cells are well predicted, as is their effect on the bulk properties of the mean flow. Data from simple rectangular channels are used to check the model's sensitivity to the effects of a free surface, and data from compound channels, both symmetric and asymmetric, serve to validate the model for a range of parameters typical of those encountered in practice.
TL;DR: In this paper, the authors examined the efficiency and relevancy of the inclined plane test for determining fluid yield stress in a straight way by measuring the deepest fluid layer able to stay on the inclined planes.
Abstract: The aim of this paper is to determine precisely under which conditions an inclined plane can be used as a rheometer, which could represent a practical and rapid technique for various types of industrial or natural viscoplastic coarse suspensions. We first examine its efficiency and relevancy for determining fluid yield stress in a straight way by measuring the deepest fluid layer able to stay on the inclined plane. We have made experiments with different materials (clay-water suspensions) whose yield stress ranged from 35 to 90 Pa, using 1 m long open rectangular channels with a slope ranging from 10 to 30° and a width ranging from 5 to 25 cm. Our procedure involved measuring the final fluid depth far from edges a long time after the end of the slow gravity-induced emptying of a dam placed upstream. The fluid yield stress was also estimated independently by fitting a Herschel-Bulkley model to simple shear rheometry data obtained within a relatively wide shear rate range. A good agreement between inclined rectangular channel tests and independent usual rheometrical tests is obtained even for aspect ratios (flow depth to channel width ratio) as large as 1 when one assumes that, when the fluid has stopped, the side and bottom wall shear stresses are equal to the fluid yield stress. These results prove the efficiency of the inclined plane test for determining yield stress when appropriate experimental precautions are taken for both tests. In addition we examine the possibility of determining the simple shear flow curve of a mud suspension from fluid depth, velocity and discharge measurements of different steady flows in a wide open channel (8 m long; 60 cm wide) equipped with a recirculating system. The results obtained from inclined plane tests are in good agreement with independent rheometrical data (with torsional geometries). However it is technically difficult to cover a wide shear rate range from the inclined plane technique since this requires a rather wide channel flow rate range.
TL;DR: In this paper, an improved version of nonlinear low-Reynolds-number κ-e model is developed, where the limiting near-wall behavior and nonlinear Reynolds stress representations are incorporated.
TL;DR: In this paper, two free shear layer flows, a vertical supported jet and a horizontal hydraulic jump, were studied and the distributions of air concentration exhibit a Gaussian distribution profile with an exponential longitudinal decay of the maximum air content.
TL;DR: In this article, the role of vortical structures in production and destruction of Reynolds stresses in turbulent channel flow was investigated by using a 3D computer graphics software tool, and the spatial distribution of each term in the Reynolds stress transport equations was also examined in the instantaneous field.
TL;DR: In this article, the authors investigated the critical submergence for an air-entraining vortex at intakes in a uniform canal flow and found that the critical depth of the upper boundary of Rankine's ovoids reaches the water surface directly above the intake center.
Abstract: In this study, critical submergence for an air-entraining vortex at intakes in a uniform canal flow was investigated. The potential flow solution for the combination of a point sink and a uniform canal flow is available, and is known as Rankine's ovoids or half-bodies. This study was based on Rankine's ovoids. Experiments have shown that the critical submergence occurs when the upper boundary of Rankine's ovoids reaches the water surface directly above the intake center. Theoretical and experimental results have indicated that the critical submergence for an intake in a uniform canal flow is equal to the radius of an imaginary spherical sink surface (assuming no canal flow) where the radial velocity is equal to half of the velocity of the uniform canal flow. The imaginary spherical sink has the same center and discharge as the intake. The agreement between the theoretical critical submergence and experimental results is found to be good.
TL;DR: In this paper, the effects of mutual interaction of small-amplitude gravity waves with in-depth turbulence and statistical properties of the near free-surface region were investigated. But the authors focused on the effects upon the mutual interaction between small amplitude gravity waves and in depth turbulence.
Abstract: We report direct numerical simulations of incompressible unsteady open-channel flow. Two mechanisms of turbulence production are considered: shear at the bottom and externally imposed stress at the free surface. We concentrate upon the effects of mutual interaction of small-amplitude gravity waves with in-depth turbulence and statistical properties of the near-free-surface region. Extensions of our approach can be used to study turbulent mixing in the upper ocean and wind–sea interaction, and to provide diagnostics of bulk turbulence.
TL;DR: In this article, an approach is pursued by using a constitutive equation which relates the elongation viscosity to the local properties of the flow, and the results reproduce the qualitative outputs of the experiments.
Abstract: An efficient technique for drag reduction uses dilute solutions of a few p.p.m. of polymers. A possible reduction in drag of up to 80% is achieved. Several experimental observations have been made which tend to indicate that the polymers modify the turbulence structures within the buffer layer. Flow visualisations have shown that the changes consist of a weakening of the strength of the streamwise vortices. Existing literature reveals no attempts of numerical simulation of this phenomenon. In this paper an approach is pursued by using a constitutive equation which relates the elongation viscosity to the local properties of the flow. According to this model this viscosity is large in zones where the amount of strain rate is greater than the amount of vorticity, and is zero when the vorticity exceeds the strain rate. Simulations have been performed in a “minimal channel” to give good resolution with a limited number of grid points. The accuracy of the method is tested by comparison with the results of other techniques. For simulations with polymers, quantitative comparisons cannot be made, but the results reproduce the qualitative outputs of the experiments. The mean streamwise velocity is modified in the buffer layer; the peak of the streamwise turbulent intensity, in wall units, increases and its maximum moves far from the wall; and the vertical turbulent intensity is largely reduced in the wall region. An interesting outcome from both the simulation and the experiments is that the strength of the longitudinal vortices is reduced when the polymers are present.