Showing papers on "Open-channel flow published in 1991"

A dynamic subgrid‐scale eddy viscosity model

Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

The minimal flow unit in near-wall turbulence

Abstract: Direct numerical simulations of unsteady channel flow were performed at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic (in x and z) array of identical structures. The goal is to isolate the basic flow unit, to study its morphology and dynamics, and to evaluate its contribution to turbulence in fully developed channels. For boxes wider than approximately 100 wall units in the spanwise direction, the flow is turbulent and the low-order turbulence statistics are in good agreement with experiments in the near-wall region. For a narrow range of widths below that threshold, the flow near only one wall remains turbulent, but its statistics are still in fairly good agreement with experimental data when scaled with the local wall stress. For narrower boxes only laminar solutions are found. In all cases, the elementary box contains a single low-velocity streak, consisting of a longitudinal strip on which a thin layer of spanwise vorticity is lifted away from the wall. A fundamental period of intermittency for the regeneration of turbulence is identified, and that process is observed to consist of the wrapping of the wall-layer vorticity around a single inclined longitudinal vortex.

Near-wall turbulence closure modeling without ``damping functions''

Abstract: An elliptic relaxation model is proposed for the strongly inhomogeneous region near the wall in wall-bounded turbulent shear flow. This model enables the correct kinematic boundary condition to be imposed on the normal component of turbulent intensity. Hence, wall blocking is represented. Means for enforcing the correct boundary conditions on the other components of intensity and on the k — ɛ equations are discussed. The present model agrees quite well with direct numerical simulation (DNS) data. The virtue of the present approach is that arbitrary “damping functions” are not required.

Turbulent open-channel flows with variable depth across the channel

Abstract: The flow of water in straight open channels with prismatic complex cross-sections is considered. Lateral distributions of depth-mean velocity and boundary shear stress are derived theoretically for channels of any shape, provided that the boundary geometry can be discretized into linear elements. The analytical model includes the effects of bed-generated turbulence, lateral shear turbulence and secondary flows. Experimental data from the Science and Engineering Research Council (SERC) Flood Channel Facility are used to illustrate the relative importance of these three effects on internal shear stresses. New experimental evidence concerning the spatial distribution of Reynolds stresses τyx and τzx is presented for the particular case of compound or two-stage channels. In such channels the vertical distributions of τzx are shown to be highly nonlinear in the regions of strongest lateral shear and the depth-averaged values of τyx are shown to be significantly different from the depth mean apparent shear stresses. The importance of secondary flows in the lateral shear layer region is therefore established. The influence of both Reynolds stresses and secondary flows on eddy viscosity values is quantified. A numerical study is undertaken of the lateral distributions of local friction factor and dimensionless eddy viscosity. The results of this study are then used in the analytical model to reproduce lateral distributions of depth-mean velocity and boundary shear stress in a two stage channel. The work will be of interest to engineers engaged in flood channel hydraulics and overbank flow in particular.

Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylinders

Abstract: Two‐dimensional unsteady flows in complex geometries that are characterized by simple (low‐dimensional) dynamical behavior are considered. Detailed spectral element simulations are performed, and the proper orthogonal decomposition or POD (also called method of empirical eigenfunctions) is applied to the resulting data for two examples: the flow in a periodically grooved channel and the wake of an isolated circular cylinder. Low‐dimensional dynamical models for these systems are obtained using the empirically derived global eigenfunctions in the spectrally discretized Navier–Stokes equations. The short‐ and long‐term accuracy of the models is studied through simulation, continuation, and bifurcation analysis. Their ability to mimic the full simulations for Reynolds numbers (Re) beyond the values used for eigenfunction extraction is evaluated. In the case of the grooved channel, where the primary horizontal wave number of the flow is imposed from the channel periodicity and so remains unchanged with Re, the models extrapolate reasonably well over a range of Re values. In the case of the cylinder wake, however, due to the significant spatial wave number changes of the flow with the Re, the models are only valid in a small neighborhood of the decompositional Reynolds number.

Flow and Reactions in Permeable Rocks

Abstract: Preface 1. Introduction 2. The governing principles 3. General flow characteristics: patterns of flow 4. General flow characteristics: patterns of reactions 5. Instabilities 6. Pressure-driven flows 7. Thermal convection References Index.

Subgrid-scale backscatter in turbulent and transitional flows

Abstract: Most subgrid‐scale (SGS) models for large‐eddy simulations (LES) are absolutely dissipative (that is, they remove energy from the large scales at each point in the physical space). The actual SGS stresses, however, may transfer energy to the large scales (backscatter) at a given location. Recent work on the LES of transitional flows [Piomelli et al., Phys. Fluids A 2, 257 (1990)] has shown that failure to account for this phenomenon can cause inaccurate prediction of the growth of the perturbations. Direct numerical simulations of transitional and turbulent channel flow and compressible isotropic turbulence are used to study the backscatter phenomenon. In all flows considered roughly 50% of the grid points were experiencing backscatter when a Fourier cutoff filter was used. The backscatter fraction was less with a Gaussian filter, and intermediate with a box filter in physical space. Moreover, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much...

Turbulent Structure in Compound Open‐Channel Flows

Abstract: An investigation of three‐dimensional (3‐D) turbulent structure, including turbulence‐driven secondary currents in compound open‐channel flows, is a very important topic in hydraulic and river engineering, as well as in fluid mechanics. In this study, accurate measurements in fully developed compound open‐channel flows are conducted by means of a fiber‐optic laser Doppler anemometer (FLDA). Secondary velocities can be measured very accurately with the present 3‐D measurement system. The characteristics of compound open‐channel flows are recognized in the junction region between the main channel and flood plain, whereas the characteristics of rectangular open‐channel flows are observed in a region near the sidewall of the main channel. Strong, inclined secondary currents, which are associated with a pair of longitudinal vortices, are generated in the junction region between the main channel and the flood plain. The primary mean velocity field is directly influenced by these secondary currents. Turbulence i...

Lithospheric Extension Near Lake Mead, Nevada: A Model for Ductile Flow in the Lower Crust

Abstract: Small variations in gravity anomalies and topographic elevation observed in areas that have undergone highly variable amounts of upper crustal thinning can be satisfactorily explained by ductile flow of lower crustal material under the proper conditions. In this study we examine the boundary between the unextended Colorado Plateau and a strongly extended domain in the Basin and Range Province in the Lake Mead (Nevada) region. Bouguer gravity and topography data suggest that both present and preextensional variations in crustal thickness between the unextended and extended regions are small. Analytic channel flow models show that viscosities required for ductile flow in a lower crustal channel to reduce discontinuities in crustal thickness associated with variable amounts of extension are highly dependent on the channel thickness and on the length scale of flow required. Finite element modeling of Newtonian flow and power law creep shows that flow over the length scale of the eastern Basin and Range (500 km or more) corresponding to upper crustal extension by a factor of 1.4–3 over 10 m.y. requires effective viscosities less than 10^(18)–10^(20) Pa s for ductile channels 10–25 km thick. Flow over shorter length scales (150 km) may be accommodated with effective viscosities as high as 10^(21) Pa s. Modeling suggests that these effective viscosities may be sustained by lower crustal material deforming at laboratory-derived power law creep rates. The longer-scale flow may require elevated crustal temperatures (more than 700°C), depending on the composition and material properties assumed. Under the boundary conditions assumed in this study the linear viscous flow models yield a satisfactory approximation to deformation by power law creep. This work suggests that flow in the lower crust may be a viable mechanism for producing small variations in total crustal thickness between strongly extended and less extended regions, and thereby explaining the relative uniformity in gravity and topography between such regions.

Evolution and dynamics of shear-layer structures in near-wall turbulence

Abstract: Near-wall flow structures in turbulent shear flows are analyzed, with particular emphasis on the study of their space-time evolution and connection to turbulence production. The results are obtained from investigation of a database generated from direct numerical simulation of turbulent channel flow at a Reynolds number of 180 based on half-channel width and friction velocity. New light is shed on problems associated with conditional sampling techniques, together with methods to improve these techniques, for use both in physical and numerical experiments. The results clearly indicate that earlier conceptual models of the processes associated with near-wall turbulence production, based on flow visualization and probe measurements need to be modified. For instance, the development of asymmetry in the spanwise direction seems to be an important element in the evolution of near-wall structures in general, and for shear layers in particular. The inhibition of spanwise motion of the near-wall streaky pattern may be the primary reason for the ability of small longitudinal riblets to reduce turbulent skin friction below the value for a flat surface.

Zone broadening and dilution in rectangular and trapezoidal asymmetrical flow field-flow fractionation channels

Abstract: A new trapezoidal geometry of the asymmetrical flow field-flow fractionation (FFF) channel introduces an additional means to regulate the longitudinal flow velocity. The trapezoidal geometry, where the breadth decreases on going toward the channel outlet, makes it possible to level out the steep linear velocity gradients that can appear in the rectangular channels. Equations for the channel flow velocity gradient and the void time are derived

An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 2. Numerical simulations

Abstract: The stability of oscillatory channel flow to different classes of infinitesimal and finite-amplitude two- and three-dimensional disturbances has been investigated by direct numerical simulations of the Navier–Stokes equations using spectral techniques. All infinitesimal disturbances were found to decay monotonically to a periodic steady state, in agreement with earlier Floquet theory calculations. However, before reaching this periodic steady state an infinitesimal disturbance introduced in the boundary layer was seen to experience transient growth in accordance with the predictions of quasi-steady theories for the least stable eigenmodes of the Orr–Sommerfeld equation for instantaneous ‘frozen’ profiles. The reason why this growth is not sustained in the periodic steady state is explained. Two-dimensional infinitesimal disturbances reaching finite amplitudes were found to saturate in an ordered state of two-dimensional quasi-equilibrium waves that decayed on viscous timescales. No finite-amplitude equilibrium waves were found in our cursory study. The secondary instability of these two-dimensional finite-amplitude quasi-equilibrium states to infinitesimal three-dimensional perturbations predicts transitional Reynolds numbers and turbulent flow structures in agreement with experiments.

Sediment Management with Submerged Vanes. I: Theory

Abstract: Recent research results with the submerged‐vane technique for sediment control in rivers are described. Submerged vanes are small flow‐training structures (foils), designed to modify the near‐bed flow pattern and redistribute flow and sediment transport within the channel cross section. The structures are installed at an angle of attack of 15–25° with the flow, and their initial height is 0.2–0.4 times local water depth at design stage. The vanes function by generating secondary circulation in the flow. The circulation alters magnitude and direction of the bed shear stresses and causes a change in the distributions of velocity, depth, and sediment transport in the area affected by the vanes. As a result, the river bed aggrades in one portion of the channel cross section and degrades in another. The vanes can be laid out to develop and maintain any desired bed topography. Vanes have been used successfully for protection of stream banks against erosion and for amelioration of shoaling problems at water inta...

Large‐scale computer simulation of fully developed turbulent channel flow with heat transfer

Abstract: Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.

Stability of Transverse Shear Flows in Shallow Open Channels

Abstract: The bed-friction effect on the stability of transverse shear flows in shallow open channels is examined using a linear and “inviscid” theory. Numerical calculations are conducted for four groups of parallel flows with inflection-point velocity profiles. The necessary conditions for the transverse shear flows to become unstable, so that the large-scale transverse motion may coexist with the small-scale bed-generated turbulence, are determined from the calculations. The results are correlated with two dimensionless parameters: a bed-friction number and an ambient-velocity parameter. The bed-friction number quantifies the stabilizing effect of the bed-friction. The ambient-velocity parameter characterizes the changes in depth and roughness across the open-channel flows. In the limiting case of a weak transverse shear flow, when the change in velocity across the flow is small, the bed-friction number becomes the only dimensionless parameter governing the stability of the transverse shear flows. The critical values of this bed-friction number for the weak transverse shear flows with hyperbolic-tangent and hyperbolic-secant velocity profiles, are 0.120 and 0.145, respectively.

Dynamical eigenfunction decomposition of turbulent channel flow

Abstract: The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loeve(K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re,= 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90% of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, posses viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher-order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.

Two-layer hydraulics: a functional approach

Abstract: A new approach for investigating two-layer hydraulic exchange flows in channels is introduced. The approach is based on the functional formalism of Gill (1977) and applied to the flow through a contraction in width and to flow over a simple sill. The sill geometry is an extension of that looked at by earlier workers, in particular Farmer & Armi (1986) who used a Froude-number-plane approach. In the present paper a simple relationship between the composite Froude number and the hydraulic functional is derived, though the functional approach may also be applied to channels where a Froude number is not readily defined. The ability to trace roots of this functional from one reservoir to the other is a prerequisite for the flow to be realizable. Two hydraulic transitions are required for the flow to be fully controlled and the exchange flow rate to be maximal. If only one hydraulic transition is present, the flow is governed by the conditions in one of the reservoirs and the exchange flow rate is found to be submaximal. The flow along a channel is found to be very sensitive to small departures from symmetry about a horizontal plane. The response of the interface to the introduction of a net (barotropic) flow is found to be a discontinuous function of the strength of the forcing for some range of sill heights.

Convective accelerations and boundary shear stress over a Channel Bar

Abstract: Alternate bars are important features in alluvial channels as they determine flow and transport patterns. They appear fundamental to selection of meander wavelengths and the geometry of bends. Bend flow has been studied extensively: far less study has been made of flow over alternate bars. Field results from Solfatara Creek, a 5.2-m-wide, 0.2–0.7-m-deep gravel bed channel where flow exits an upstream bend and shoals over a bar in a straight reach, are used to examine patterns of flow and the fluid forces determining the flow field. Large cross-sectional area changes, tied primarily to variation in depth, force large stream-wise accelerations and substantial cross-stream flow off the central bar. The topographically driven downstream and cross-stream accelerations are sufficiently large that their influence upon the balance of forces is of the same order as the pressure gradient and the boundary shear stress. The importance of convective accelerations in the downstream flow equation in this straight reach concurs with bend flow results, but the similar importance of convective accelerations in the cross-stream equation contrasts with results from bend flow. While part of the difference may be attributed to the lower stage conditions herein, in the absence of significant curvature change the cross-stream force balance depends upon the flow going over and around the bar. Local boundary shear stress estimated from the law-of-the-wall and a roughness algorithm decreases out of the upstream bend, increases over the bar top to values approaching the threshold for motion, and then decreases in deeper flow. Strong bed surface coarsening maintains the topography in a stress field that would otherwise lead to planation of the bar top and filling of the deeper regions.

Suspended Sediment-Transport Capacity for Open Channel Flow

Abstract: A fairly simple correlation is formulated for calculating the suspended sediment-transport capacity of open channel flow. The correlation is based on the assumption that the work performed by buoyancy force on the sediment particles is proportional to the production of turbulent kinetic energy. The proportionality constant is determined by calibration using a wide range of experimental data. The new formula does not involve bed-load correlations, and, hence, avoids the considerable uncertainty generic to those correlations. By assuming a suitable concentration profile, the formula can be used for calculating the maximum, full-capacity concentration at a reference level, but the formula itself does not involve a priori profile assumptions. An approximate relation is provided between the depth-averaged concentration and the transport concentration itself. This makes it possible to calculate easily the reference bed concentration using a graphical chart provided for the cases where the Rouse profile for concentration is a good approximation.

Microchannel heat sink with alternating flow directions

Abstract: A microchannel heat sink with coolant flowing in alternate directions in adjacent channels. The microchannel heat sink is used for cooling the electronic device making thermal contact with the surface of the heat sink. The alternate directions of the coolant flow eliminate temperature variation along the channel length caused by the heating of the coolant. This new "alternating channel flow" heat sink design achieves a nearly uniform temperature and thermal resistance on the surface of the heat sink and effectively cools the electronic device in contact.

Large eddy simulation of magnetohydrodynamic turbulent channel flows under a uniform magnetic field

Abstract: Magnetohydrodynamic turbulent channel flows under a uniform magnetic field are studied by using a large eddy simulation technique. The effect of a uniform magnetic field is incorporated into the subgrid‐scale model in the form of a local damping factor. Compared with the experiment, this model is shown to work better than the usual Smagorinsky model in both turbulent and laminar states. This model predicts the detailed structures of the present flows, for which, one‐point global turbulence models of ensemble mean type are helpless.

Interaction of a viscous vortex pair with a free surface

Abstract: A vortex pair in a viscous, incompressible fluid rises vertically toward a deformable free surface. The mathematical, description of this flow situation is a time-dependent nonlinear free-surface problem that has been solved numerically for a two-dimensional laminar flow with the aid of the Navier-Stokes equations by using boundary-fitted coordinates. For a number of selected flow parameters, results are presented on the decay of the primary vortices and their paths, the generation of surface vorticity and secondary vortices, the development and final stage of the disturbed free surface, and the influence of surface tension. High and low Froude numbers represent the two extremes of free-surface yielding and stiffness, respectively. For an intermediate Froude number, a special rebounding due to the presence of secondary vortices has been observed: the path of the primary vortex centre portrays a complete loop.

Transition from supercritical to subcritical flow at an abrupt drop

Abstract: This paper presents a systematic investigation on the transition from supercritical to subcritical flow at an abrupt drop. Over a wide range of experimental conditions various types of flow have been classified and the concept of low and high drops defined. When the flow on the step is supercritical, the direction of the main flow passing over the step can be decided from the momentum equation. The reason why various flow conditions are formed has been explained. The hydraulic conditions required to form various types of flow and their length characteristics have been clarified.

Propagating structures in wall-bounded turbulent flows

Abstract: The Karhunen-Loeve (K-L) procedure for generating the empirical eigenfunctions is used to analyze two turbulent channel flow simulations of different geometry and origins. In one instance the Reynolds number ReT based on wall shear velocity, u r, and channel halfwidth, δ, is 80 and in the second instance ReT = 125. The latter case showed a well defined log-layer, while this was absent in the former case. According to accepted convention, the turbulence is said to be continuous when Rer = 80, and fully developed when Rer = 125. In both instances the empirical eigenfunctions reveal the presence of propagating plane wave structures. Thus the contrasts in the two cases is of some importance since they virtually eliminate the possibility that the waves are artifacts.

Cooling hole arrangements in jet engine components exposed to hot gas flow

Abstract: A jet engine component includes a body having a wall portion with an external surface exposed to hot gas flow and an internal surface exposed to a cooling air flow. The engine component incorporates an arrangement of cooling holes defined through the wall portion between the external and internal surfaces thereof to permit flow of cooling air from the hollow interior through the wall portion to the exterior of the component. Each cooling hole includes at least one flow inlet at the internal surface of the wall for receiving the cooling air flow, at least a pair of flow outlets at the external surface of the wall for discharging the cooling air flow, and at least a pair of flow branches extending through the wall portion and between the flow inlet and the flow outlets for permitting passage of the cooling air flow from the flow inlet to the flow outlets. In one V-shaped configuration, the flow branches merge and intersect with one another at the flow inlet. In another X-shaped configuration, there are a pair of flow inlets and the flow branches merge and intersect with one another at a location intermediate between and spaced from the flow inlets and outlets. The flow outlets are displaced preferably downstream of the flow inlet relative to the direction of gas flow past the external surface of the wall of the engine component.