Showing papers on "Open-channel flow published in 2008"

Variations of von Kármán coefficient in canonical flows

Abstract: The overlap parameters for the logarithmic law are obtained for available turbulent pipe and channel flow data using composite profiles fitted to the mean velocity. The composite profile incorporates κ, B, and Π as the varying parameters and their resulting behavior with Reynolds number is examined for these flows and compared to results from boundary layers. The von Karman coefficient in channel flow is smaller than the well-established value for zero pressure gradient turbulent boundary layers of 0.384, while in pipe flows it is consistently higher. In contrast, the estimates of the wake parameter Π are the smallest for channel flows and largest for boundary layers. Further, the Superpipe data are reanalyzed to reveal that κ=0.41 is a better value for the von Karman constant in pipe flow. The collective behavior of κ in boundary layers, pipes, and channels reveals that the von Karman coefficient is not universal and exhibits dependence not only on the pressure gradient but also on the flow geometry.

Efficient Generation of Inflow Conditions for Large Eddy Simulation of Street-Scale Flows

Abstract: Using a numerical weather forecasting code to provide the dynamic large-scale inlet boundary conditions for the computation of small-scale urban canopy flows requires a continuous specification of appropriate inlet turbulence. For such computations to be practical, a very efficient method of generating such turbulence is needed. Correlation functions of typical turbulent shear flows have forms not too dissimilar to decaying exponentials. A digital-filter-based generation of turbulent inflow conditions exploiting this fact is presented as a suitable technique for large eddy simulations computation of spatially developing flows. The artificially generated turbulent inflows satisfy the prescribed integral length scales and Reynolds-stress-tensor. The method is much more efficient than, for example, Klein’s (J Comp Phys 186:652–665, 2003) or Kempf et al.’s (Flow Turbulence Combust, 74:67–84, 2005) methods because at every time step only one set of two-dimensional (rather than three-dimensional) random data is filtered to generate a set of two-dimensional data with the appropriate spatial correlations. These data are correlated with the data from the previous time step by using an exponential function based on two weight factors. The method is validated by simulating plane channel flows with smooth walls and flows over arrays of staggered cubes (a generic urban-type flow). Mean velocities, the Reynolds-stress-tensor and spectra are all shown to be comparable with those obtained using classical inlet-outlet periodic boundary conditions. Confidence has been gained in using this method to couple weather scale flows and street scale computations.

Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime

Abstract: We have conducted a direct numerical simulation study of dilute turbulent particulate flow in a vertical plane channel by considering thousands of finite-size rigid particles with resolved phase interfaces. The particle diameter corresponds to approximately 11 wall units and their terminal Reynolds number is set to 136. The fluid flow with a bulk Reynolds number of 2700 is directed upward, which maintains the particles suspended on average. Two density ratios were simulated, differing by a factor of 4.5. The corresponding Stokes numbers of the two flow cases were O(10) in the near-wall region and O(1) in the outer flow. We have observed the formation of large-scale elongated streaklike structures with streamwise dimensions of the order of eight channel half-widths and cross-stream dimensions of the order of one half-width. At the same time, we have found no evidence of significant formation of particle clusters, which suggests that the large structures are due to an intrinsic instability of the flow, which is triggered by the presence of the particles. It was found that the mean fluid velocity profile tends toward a concave shape, and the turbulence intensity and the normal stress anisotropy are strongly increased. The effect of varying the Stokes number while maintaining the buoyancy, particle size, and volume fraction constant was relatively weak.

Coherent Structures in the Flow Field around a Circular Cylinder with Scour Hole

Abstract: Large-eddy simulation (LES) and laboratory-flume visualizations were used to investigate coherent structures present in the flow field around a circular cylinder located in a scour hole. The bathymetry corresponds to equilibrium scour conditions and is fixed in LES. The flow parameters in the simulation correspond to the experimental conditions in which the approach flow is fully turbulent. Detailed consideration is given to the interaction of the horseshoe vortex (HV) system within the scour hole with the detached shear layers formed from the cylinder, and the near bed turbulence. It is found that the overall structure of the HV system varies considerably in space and time, though a large, relatively stable, primary necklace vortex is present at practically all times inside the scour hole. The simulation captures the presence of bimodal chaotic oscillations inside the HV system, as well as the sharp increase in the resolved turbulent kinetic energy levels and pressure fluctuations reported in prior experimental investigations. High levels of the mean bed shear stress are observed beneath the primary necklace vortex, especially over the region where the bimodal oscillations are strong, as well as beneath the small junction vortex at the base of the cylinder. It is also found that the detachment and advection of patches of vorticity from the downstream part of the legs of the necklace vortices can induce large instantaneous bed shear stress values. When the critical bed shear stress value for sediment entrainment on a flat surface is adjusted for bed slope effects, the LES simulation correctly predicts that the distribution of the mean bed shear stress is consistent with equilibrium scour conditions.

Dynamics of prolate ellipsoidal particles in a turbulent channel flow

Abstract: The dynamical behavior of tiny elongated particles in a directly simulated turbulent flow field is investigated. The ellipsoidal particles are affected both by inertia and hydrodynamic forces and torques. The time evolution of the particle orientation and translational and rotational motions in a statistically steady channel flow is obtained for six different particle classes. The focus is on the influence of particle aspect ratio λ and the particle response time on the particle dynamics, i.e., distribution, orientation, translation, and rotation. Both ellipsoidal and spherical particles tend to accumulate in the viscous sublayer and preferentially concentrate in regions of low-speed fluid velocity. The translational motion is practically unaffected by the aspect ratio, whereas both mean and fluctuating spin components depend crucially on λ. The ellipsoids tend to align themselves with the mean flow direction and this tendency becomes more pronounced in the wall proximity when the lateral tilting of the elongated particles is suppressed.

Effect of bubble deformability in turbulent bubbly upflow in a vertical channel

Abstract: As bubbles rising in a vertical channel with upflow become bigger, it is well known that the void fraction distribution changes in a fundamental way, from a wall peak for small bubbles to a maximum void fraction at the channel center for larger bubbles. Here, we use direct numerical simulations of buoyant bubbles in a turbulent flow to show that it is not the size of the bubbles that matters, but their deformability.

Noninertial lateral migration of vesicles in bounded Poiseuille flow

Abstract: Cross-streamline noninertial migration of a vesicle in a bounded Poiseuille flow is investigated experimentally and numerically. The combined effects of the walls and of the curvature of the velocity profile induce a movement toward the center of the channel. A migration law (as a function of relevant structural and flow parameters) is proposed that is consistent with experimental and numerical results. This similarity law markedly differs from its analog in unbounded geometry. The dependency on the reduced volume ν and viscosity ratio λ is also discussed. In particular, the migration velocity becomes nonmonotonous as a function of ν beyond a certain λ.

Application of linear momentum actuator disc theory to open channel flow

Abstract: This report presents a step by step extension of the simple one-dimensional linear momentum actuator disc theory (LMADT), which results in the well known Betz-Lanchester limit for wind turbines, to a general cross sectional array of tidal turbines in an open channel tidal flow. Unlike previous models no restriction is placed on the geometry of the turbine array or the Froude number of the flow. One of the key findings from applying LMADT to open channel flow is that the efficiency of an arbitrary array of turbines can be determined relative to the total power extracted from the channel flow, including the effects of downstream mixing. A general form of this dimensionless efficiency may be more important for open channel flow, given the possibility of downstream constraints, than the typical dimensionless power co-efficient used for wind turbines.

Numerical Investigation of Flow Hydrodynamics in a Channel with a Series of Groynes

Abstract: The flow hydrodynamics in a straight open channel containing a multiple-embayment groyne field on one of its sides is investigated numerically using large eddy simulation. The vertical groynes are fully emerged. The mean flow depth in the groyne region is about half that of the main channel and the length and width of the embayments are much larger than the mean depth in the embayment region. The model is validated using mean velocity and turbulent fluctuations data collected at the free surface in a previous experimental study. It is found that despite the fact that the flow inside the main recirculation eddy in the embayments can be characterized as being quasi-two dimensional, the flow inside the mixing layer region between the embayments and the channel is strongly nonuniform over the depth. As this region controls the mass exchange processes between the groyne field and the main channel, a three-dimensional description of the flow in this area is essential. The large-scale eddies that populate the mixing layer can penetrate the embayment region over lateral distances of the order of the channel depth. These eddies advect with them channel fluid inside the embayment. Eventually, the channel fluid is mixed with the embayment fluid by the small scales. The other main mixing mechanism is due to the injection of patches of high-vorticity mixing-layer fluid near the tip of the downstream groyne and their subsequent convection in the form of a wall-attached jet-like flow into the embayment, first parallel to the downstream groyne face and then to the sidewall. It is shown that on average, most of the fluid leaves the embayment region via the top layer of the embayment-channel interface (upstream half) and enters the embayment region at levels situated around the middepth (practically over the whole length of the embayment) of the interface surface. This explains why the mass exchange coefficients are overestimated when predicted using methods that employ floating particles as a tracer. The instantaneous bed shear stress inside the cavity is found to peak close to the downstream groyne face of each embayment and to show a high variability around the mean values due to the interaction of the mixing layer eddies with the tip of the groynes and the formation of the jet-like flow parallel to the droyne face.

An investigation of the flow and scour mechanisms around isolated spur dikes in a shallow open channel: 1. Conditions corresponding to the initiation of the erosion and deposition process

Abstract: [1] The present study investigates the flow physics and the role played by the main coherent structures in the scouring processes around a vertical spur dike in a straight channel at conditions corresponding to the start (flat bed) of the scouring process. Large eddy simulation (LES) is performed at a relatively low channel Reynolds number (Re = 18,000), in the range where most flume studies with clear water scour conditions are conducted. Similar to these studies, the incoming flow is fully turbulent and contains realistic turbulence fluctuations. Visualization experiments are conducted to better understand the nature of the interactions between the dominant coherent structures playing a role in the erosion process. It is found that the structure of the horseshoe vortex (HV) system at the base of the spur dike changes considerably in time and in vertical sections perpendicular to the trajectory defined by the axis of the main necklace vortex. However, its intensity is the largest at vertical sections situated around the tip of the spur dike. It is in this region that the core of the main necklace vortex oscillates aperiodically between two preferred modes. In one of them (zero-flow mode), the necklace vortex is closer to the spur dike and more compact, and the near-bed jet flow beneath it is weak. In the other one (back-flow mode), a strong near-bed jet flow convects the primary necklace vortex away from the spur dike, and its core is more elongated and less compact. This explains the large amplification (by about 1 order of magnitude compared to the surrounding turbulent flow) of the turbulent kinetic energy and pressure fluctuations inside the HV system in the region situated around the tip of the spur dike and the double-peak distribution of the turbulent kinetic energy. Past the spur dike, in the legs of the necklace vortex, the intensity of the bimodal oscillations decreases such that they are not observed in spanwise sections situated at more than one channel depth behind the spur dike. It is found that the legs of the horseshoe vortices can interact, at times, with the vortex tubes shed in the detached shear layer (DSL) and with the tip of the spur dike. These events typically result in a significant change in the coherence of the HV system. The largest bed shear stress values in the mean flow are present in the strong acceleration region near the tip of the spur dike, but high bed shear stress values are also observed beneath the upstream part of the DSL. The bed shear stress fluctuations around the local mean values can be very high, especially in the region situated beneath the upstream part of the DSL. At random times, some of the vortices shed in the DSL merge or interact with eddies from the recirculation region. This leads to an increase in their strength and to a large increase of the bed shear stress along their path.

Turbulence Structures in Flow over Two-Dimensional Dunes

Abstract: This paper presents a large eddy simulation (LES) of turbulent open channel flow over two-dimensional periodic dunes. The Reynolds number R based on the bulk velocity U (bulk) and the maximum flow depth h , is approximately 25,000. The instantaneous flow field is investigated with special emphasis on the occurrence of coherent structures. Instantaneous vortices were visualized and it is shown that separated vortices are formed downstream of the dune crest due to Kelvin–Helmholtz instabilities. Near the point of reattachment the so-called kolk-boil vortex evolves in form of a hairpin vortex. Also present are previously separated vortices, which are convected along the stoss side of the downstream dune and elevated toward the water surface. The existence of near wall streaks which reform shortly after reattachment is also shown. The spacing between two low-speed streaks is very similar to that observed previously over smooth and rough walls. For validation, profiles of the time-averaged velocities, streamwise, and wall-normal turbulent intensities and the Reynolds shear stress calculated by the LES are presented and compared with available laser Doppler velocimetry measurements and overall good agreement is found.

Robust boundary control of systems of conservation laws

Abstract: The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a small C-1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stabilization condition by means of a boundary control, for systems of conservation laws subject to external disturbances. This stability result is then applied to the problem of the regulation of the water level and the flow rate in an open channel. The flow in the channel is described by the Saint-Venant equations perturbed by small non-homogeneous terms that account for the friction effects as well as external water supplies or withdrawals.

Direct numerical simulation of a separated channel flow with a smooth profile

Abstract: A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re τ = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated not only near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel.

Flow and bathymetry in sharp open‐channel bends: Experiments and predictions

Abstract: This paper focuses on experiments and simulations conducted in very sharp open-channel bends with flat and equilibrium bathymetry, corresponding to the initial and final phases of the erosion and deposition processes, respectively. The study of flow in curved open bends is relevant for flow in natural river configurations, as most river reaches are not straight. The configuration considered in the present work was designed as a test case in which the role of the cross-sectional flow is more severe than in meandering natural river reaches (radius of curvature of the channel is close to the channel width) and, thus, can serve for validation of numerical models used to predict flow and sediment transport in river engineering applications. This paper presents detailed new experimental data on the equilibrium bathymetry as well as depth-averaged distributions, vertical profiles, and cross-sectional patterns of the streamwise velocity, the cross-stream circulation, streamwise vorticity, and the turbulent kinetic energy at the initial and final stages of the erosion and deposition processes. The numerical simulations are performed using a three-dimensional nonhydrostatic RANS model for flow, sediment transport, and bathymetry, which employs fine meshes, accounts for the effect of small bed forms, and avoids the use of the law of the wall. The model predicts, rather accurately, the distribution of the streamwise velocity, the cross-stream circulation, and the turbulent kinetic energy in the simulations conducted with a fixed (flat and deformed bed corresponding to equilibrium conditions) prescribed bathymetry. In the case of a simulation conducted with loose bed, the model predicts satisfactorily the main features of the bathymetry at equilibrium conditions, despite the fact that including the interaction between the flow and the bathymetry increases the overall uncertainty in the model predictions. Results indicate that both improvements in the level of turbulence modeling and in the modeling of the sediment transport would allow further improvement in the predictive capabilities of morphodynamic models.

Boundary Control of Open Channels With Numerical and Experimental Validations

Abstract: The problem of the stabilization of the flow in a reach is investigated. To study this problem, we consider the nonlinear Saint-Venant equations, written as a system of two conservation laws perturbed by non-homogeneous terms. The non-homogeneous terms are due to the effects of the bottom slope, the slope's friction, and also the lateral supply. The boundary actions are defined as the position of both spillways located at the extremities of the reach. It is assumed that the height of the flow is measured at both extremities. Assuming that the non-homogeneous terms are sufficiently small in C 1-norm, we design stabilizing boundary output feedback controllers, i.e., we derive a new strategy which depends only on the output and which ensures that the water level and water flow converge to the equilibrium. Moreover, the speed of the convergence is shown to be exponential. The proof of this result is based on the estimation of the effects on the non-homogeneous terms on the evolution of the Riemann coordinates. This stability result is validated both by simulating on a real river data and by experimenting on a micro-channel setup.

A random-jet-stirred turbulence tank

Abstract: We report measurements of the flow above a planar array of synthetic jets, firing upwards in a spatiotemporally random pattern to create turbulence at an air–water interface. The flow generated by this randomly actuated synthetic jet array (RASJA) is turbulent, with a large Reynolds number and a weak secondary (mean) flow. The turbulence is homogeneous over a large region and has similar isotropy characteristics to those of grid turbulence. These properties make the RASJA an ideal facility for studying the behaviour of turbulence at boundaries, which we do by measuring one-point statistics approaching the air–water interface (via particle image velocimetry). We explore the effects of different spatiotemporally random driving patterns, highlighting design conditions relevant to all randomly forced facilities. We find that the number of jets firing at a given instant, and the distribution of the duration for which each jet fires, greatly affect the resulting flow. We identify and study the driving pattern that is optimal given our tank geometry. In this optimal configuration, the flow is statistically highly repeatable and rapidly reaches steady state. With increasing distance from the jets, there is a jet merging region followed by a planar homogeneous region with a power-law decay of turbulent kinetic energy. In this homogeneous region, we find a Reynolds number of 314 based on the Taylor microscale. We measure all components of mean flow velocity to be less than 10% of the turbulent velocity fluctuation magnitude. The tank width includes roughly 10 integral length scales, and because wall effects persist for one to two integral length scales, there is sizable core region in which turbulent flow is unaffected by the walls. We determine the dissipation rate of turbulent kinetic energy via three methods, the most robust using the velocity structure function. Having a precise value of dissipation and low mean flow allows us to measure the empirical constant in an existing model of the Eulerian velocity power spectrum. This model provides a method for determining the dissipation rate from velocity time series recorded at a single point, even when Taylor's frozen turbulence hypothesis does not hold. Because the jet array offers a high degree of flow control, we can quantify the effects of the mean flow in stirred tanks by intentionally forcing a mean flow and varying its strength. We demonstrate this technique with measurements of gas transfer across the free surface, and find a threshold below which mean flow no longer contributes significantly to the gas transfer velocity.

Laboratory measurements of 3-D flow patterns and turbulence in straight open channel with rough bed

Abstract: Laboratory experiments have been carried out in order to study secondary circulation and flow variability in straight open channel flows over a rough bed. 3D flow velocities and turbulence characteristics were measured using a micro Acoustic DopplerVelocimeter. Two flow conditions were analyzed, with aspect ratios b/h (width over depth) of 8.5 and 6.3, respectively. These two cases cannot be classified in principle as narrow (b/h 10) channel flows, but exhibited well defined secondary flows in the whole cross section. Bed shear stresses and turbulence patterns were consistent with the secondary flow cellular circulation. These results contradict the general perception that secondary circulation cells die out at a distance of b > 2.5 h from the walls. The behavior was attributed to the bed roughness (ks/h ∼ 0.1) and to the difference in roughness between bed and walls, the latter being much smoother. The results allowed for quantification of hydrodynamic variability in terms of secondar...

Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates

Abstract: The present paper studies the heat transfer flow of a third grade fluid between two heated parallel plates for the constant viscosity model. Three flow problems, namely plane Couette flow, plane Poiseuille flow and plane Couette–Poiseuille flow have been considered. In each case the non-linear momentum equation and the energy equation have been solved using the homotopy perturbation method. Explicit analytical expressions for the velocity field and the temperature distribution have been derived.