Showing papers on "Streamlines, streaklines, and pathlines published in 2011"

Hydraulic tortuosity in arbitrary porous media flow.

Abstract: Tortuosity (T) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate T directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or three-dimensional computer models. Based on numerical results obtained with this method, (a) a relation between the hydraulic tortuosity of an isotropic fibrous medium and the porosity is proposed, (b) a relation between the divergence rate of T with the system size at percolation porosity and the scaling of the most probable traveling length at bond percolation is found, and (c) a range of porosities for which the shape factor is constant is identified.

Endoscopic effects on peristaltic flow of a nanofluid

Abstract: In the present investigation we have studied the peristaltic flow of a nanofluid in an endoscope. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Analytical solutions have been calculated using Homotopy perturbation method (HPM) for temperature and nanoparticle equation while exact solutions have been calculated for velocity and pressure gradient. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves. Streamlines have been plotted at the end of the article.

MHD stagnation‐point flow towards a shrinking sheet

Abstract: Purpose – The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied.Design/methodology/approach – A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.Findings – The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non‐aligned and a reverse flow is formed near the surface due to shrinking effect.Practical implications – The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and fi...

Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear

Abstract: . A major impediment to the intensity forecast of tropical cyclones (TCs) is believed to be associated with the interaction of TCs with dry environmental air. However, the conditions under which pronounced TC-environment interaction takes place are not well understood. As a step towards improving our understanding of this problem, we analyze here the flow topology of a TC immersed in an environment of vertical wind shear in an idealized, three-dimensional, convection-permitting numerical experiment. A set of distinct streamlines, the so-called manifolds, can be identified under the assumptions of steady and layer-wise horizontal flow. The manifolds are shown to divide the flow around the TC into distinct regions. The manifold structure in our numerical experiment is more complex than the well-known manifold structure of a non-divergent point vortex in uniform background flow. In particular, one manifold spirals inwards and ends in a limit cycle, a meso-scale dividing streamline encompassing the eyewall above the layer of strong inflow associated with surface friction and below the outflow layer in the upper troposphere. From the perspective of a steady and layer-wise horizontal flow model, the eyewall is well protected from the intrusion of environmental air. In order for the environmental air to intrude into the inner-core convection, time-dependent and/or vertical motions, which are prevalent in the TC inner-core, are necessary. Air with the highest values of moist-entropy resides within the limit cycle. This "moist envelope" is distorted considerably by the imposed vertical wind shear, and the shape of the moist envelope is closely related to the shape of the limit cycle. In a first approximation, the distribution of high- and low-θe air around the TC at low to mid-levels is governed by the stirring of convectively modified air by the steady, horizontal flow. Motivated by the results from the idealized numerical experiment, an analogue model based on a weakly divergent point vortex in background flow is formulated. The simple kinematic model captures the essence of many salient features of the manifold structure in the numerical experiment. A regime diagram representing realistic values of TC intensity and vertical wind shear can be constructed for the point-vortex model. The results indicate distinct scenarios of environmental interaction depending on the ratio of storm intensity and vertical-shear magnitude. Further implications of the new results derived from the manifold analysis for TCs in the real atmosphere are discussed.

On the birth of stall cells on airfoils

Abstract: Critical point theory asserts that two-dimensional topologies are defined as degeneracies and any three-dimensional disturbance of a two-dimensional flow will lead to a new three-dimensional flowfield topology, regardless of the disturbance amplitude. Here, the topology of the composite flowfields reconstructed by linear superposition of the two-dimensional flow around a stalled airfoil and the leading stationary three-dimensional global eigenmode has been studied. In the conditions monitored the two-dimensional flow is steady and laminar and is separated over a fraction of the suction side, while the amplitudes considered in the linear superposition are small enough for the linearization assumption to be valid. The multiple topological bifurcations resulting have been analysed in detail; the surface streamlines generated by the leading stationary global mode of the separated flow have been found to be strongly reminiscent of the characteristic stall cells, observed experimentally on airfoils just beyond stall in both laminar and turbulent flow.

Stochastic flux-related analysis of transverse mixing in two-dimensional heterogeneous porous media

Abstract: [1] Transverse mixing of solutes in steady state transport is of utmost importance for assessing mixing-controlled reactions of compounds that are continuously introduced into the subsurface. Classical spatial moments analysis fails to describe mixing because the tortuous streamlines in heterogeneous formations cause plume meandering, squeezing, and stretching, which affect transverse spatial moments even if there is no mass transfer perpendicular to the direction of flow. For transverse solute mixing, however, the decisive process is the exchange of solute mass between adjacent stream tubes. We therefore reformulate the advection-dispersion equation in streamline coordinates (i.e., in terms of the potential and the stream function values) and analyze how flux-related second central moments of plumes increase with dropping hydraulic potential. We compare the ensemble behavior of these second central moments in random two-dimensional heterogeneous flow fields with the moments in an equivalent homogeneous system, thus defining an equivalent effective transverse dispersion coefficient. Unlike transverse macrodispersion coefficients derived by traditional moment analysis, our mixing-relevant, flux-related coefficient does not increase with travel distance. We present closed-form solutions for the mean enhancement of transverse mixing by heterogeneity in two-dimensional isotropic media for linear laws of local-scale transverse dispersion. The mixing enhancement factor increases with the log conductivity variance but remains fairly low. We also evaluate the variance of our cumulative measure of transverse mixing, showing that heterogeneity causes substantial uncertainty of mixing. The analytical expressions are compared to numerical Monte Carlo simulations for various values of log conductivity variance, indicating good agreement with the analytical results at low variability. In the numerical simulations, we also consider nonlinear models of local-scale transverse dispersion.

Flow phenomena and mechanisms in a field-scale experimental meandering channel with a pool-riffle sequence: Insights gained via numerical simulation

Abstract: [1] Large-eddy simulation of turbulent flow through a natural-like meandering channel with pool-riffle sequences installed in the St. Anthony Falls Laboratory Outdoor StreamLab is carried out to elucidate the hydrodynamics at bankfull flow condition. It is shown that the shallow flow in the riffle is dominated by the presence of large-scale roughness elements that enhance turbulent mixing; increase turbulence anisotropy; and induce multiple, streamwise secondary cells driven by turbulence anisotropy. The flow in the pool, on the other hand, is dominated by the formation and interaction of the center region and outer bank secondary flow cells and the large horizontal recirculation regions along the inner bank. The collision of the counterrotating center region and outer bank cells at the water surface gives rise to a line of three-dimensional separation (flow convergence) in the time-averaged streamlines at the surface and the associated strong downward flow toward the bed that redistributes streamwise momentum and increases the bed shear stress along the channel thalweg. Intense turbulence is produced along the line of separation due to highly anisotropic velocity fluctuations. Our results make a strong case that the center region cell is driven by the curvature effects while the outer bank cell is driven by the combined effects of turbulence anisotropy and the curvature-induced centrifugal force. The inner bank horizontal recirculation zone consists of multiple eddies, which collectively span the entire point bar. A striking finding is that the center of the primary eddy is located directly above the crest of the point bar.

Dispersion of a Point-Source Release of a Passive Scalar Through an Urban-Like Array for Different Wind Directions

Abstract: The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0°, 30°, 45°). The results agree well with available experimental data measured in a water channel for a flow angle of 0°. Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays.

An analytical study on stagnation points in nested flow systems in basins with depth‐decaying hydraulic conductivity

Abstract: [1] The existence of stagnation points in nested flow systems is relevant to a range of geologic processes. There has been no analytical study on the characteristics and locations of stagnation points in nested flow systems. We derived analytical solutions for hydraulic head and stream function in basins with isotropic and depth-decaying hydraulic conductivity. The solutions of hydraulic head and stream function are used to identify the positions of stagnation points and discuss the dynamics of groundwater around the stagnation points. Three types of stagnation points are identified by analytical and graphical means. For stagnation points on the basin bottom below the valley, only two regional flow systems converge from opposite directions. For stagnation points on the basin bottom below the regional high, only two regional flow systems part toward opposite directions. In contrast, for stagnation points under counterdirectional local flow systems, flow systems converging from and parting toward opposite directions coexist, and these stagnation points move deeper as the water table configuration becomes more rugged and the decay exponent of hydraulic conductivity increases. Moreover, the dividing streamlines around stagnation points under counterdirectional local flow systems are used to divide the local, intermediate, and regional flow systems accurately, from which the penetration depths of local and intermediate flow systems are precisely determined. A clear understanding of the location of stagnation points is critical for characterizing the pattern of hierarchically nested flow systems and has potential implication in studying solute and mineral concentration distributions in drainage basins.

A field study of mean and turbulent flow characteristics upwind, over and downwind of barchan dunes

Abstract: Field-measured patterns of mean velocity and turbulent airflow are reported for isolated barchan dunes. Turbulence was sampled using a high frequency sonic anemometer, deriving near-surface Reynolds shear and normal stresses. Measurements upwind of and over a crest-brink separated barchan indicated that shear stress was sustained despite a velocity reduction at the dune toe. The mapped streamline angles and enhanced turbulent intensities suggest the effects of positive streamline curvature are responsible for this maintenance of shear stress. This field evidence supports an existing model for dune morphodynamics based on wind tunnel turbulence measurements. Downwind, the effect of different dune profiles on flow re-attachment and recovery was apparent. With transverse incident flow, a re-attachment length between 2·3 and 5·0h (h is dune brink height) existed for a crest-brink separated dune and 6·5 to 8·6h for a crest-brink coincident dune. The lee side shear layer produced elevated turbulent stresses immediately downwind of both dunes, and a decrease in turbulence with distance characterized flow recovery. Recovery of mean velocity for the crest-brink separated dune occurred over a distance 6·5h shorter than the crest-brink coincident form. As the application of sonic anemometers in aeolian geomorphology is relatively new, there is debate concerning the suitability of processing their data in relation to dune surface and streamline angle. This paper demonstrates the effect on Reynolds stresses of mathematically correcting data to the local streamline over varying dune slope. Where the streamline angle was closely related to the surface (windward slope), time-averaged shear stress agreed best with previous wind tunnel findings when data were rotated along streamlines. In the close lee, however, the angle of downwardly projected (separated) flow was not aligned with the flat ground surface. Here, shear stress appeared to be underestimated by streamline correction, and corrected shear stress values were less than half of those uncorrected

Particle accumulation on periodic orbits by repeated free surface collisions

Abstract: The motion of small particles suspended in cylindrical thermocapillary liquid bridges is investigated numerically in order to explain the experimentally observed particle accumulation structures (PAS) in steady two- and time-dependent three-dimensional flows. Particles moving in this flow are modeled as perfect tracers in the bulk, which can undergo collisions with the free surface. By way of free-surface collisions the particles are transferred among different streamlines which represents the particle trajectories in the bulk. The inter-streamline transfer-process near the free surface together with the passive transport through the bulk is used to construct an iterative map that can describe the accumulation process as an attraction to a stable fixed point which represents PAS. The flow topology of the underlying azimuthally traveling hydrothermal wave turns out to be of key importance for the existence of PAS. In a frame of reference exactly rotating with the hydrothermal wave the three-dimensional flo...

View point evaluation and streamline filtering for flow visualization

Abstract: Visualization of flow fields with geometric primitives is often challenging due to occlusion that is inevitably introduced by 3D streamlines. In this paper, we present a novel view-dependent algorithm that can minimize occlusion and reveal important flow features for three dimensional flow fields. To analyze regions of higher importance, we utilize Shannon's entropy as a measure of vector complexity. An entropy field in the form of a three dimensional volume is extracted from the input vector field. To utilize this view-independent complexity measure for view-dependent calculations, we introduce the notion of a maximal entropy projection (MEP) framebuffer, which stores maximal entropy values as well as the corresponding depth values for a given viewpoint. With this information, we develop a view-dependent streamline selection algorithm that can evaluate and choose streamlines that will cause minimum occlusion to regions of higher importance. Based on a similar concept, we also propose a viewpoint selection algorithm that works hand-in-hand with our streamline selection algorithm to maximize the visibility of high complexity regions in the flow field.

Effects of Multiscale Anisotropy on Basin and Hyporheic Groundwater Flow

Abstract: Various subsurface flow systems exhibit a combination of small-scale to large-scale anisotropy in hydraulic conductivity (K). The large-scale anisotropy results from systematic trends (e.g., exponential decrease or increase) of K with depth. We present a general two-dimensional solution for calculation of topography-driven groundwater flow considering both small- and large-scale anisotropy in K. This solution can be applied to diverse systems with arbitrary head distribution and geometry of the water table boundary, such as basin or hyporheic flow. In a special case, this solution reduces to the well-known Toth model of uniform isotropic basin. We introduce an integral measure of flushing intensity that quantifies flushing at different depths. Using this solution, we simulate heads and streamlines and provide analyses of flow structure in the flow domain, relevant to basin analyses or hyporheic flow. It is shown that interactions between small-scale anisotropy and large-scale anisotropy strongly control the flow structure. In the classic Toth flow model, the flushing intensity curves exhibit quasi-exponential decrease with depth. The new measure is capable of capturing subtle changes in the flow structure. Our study shows that both small- and large-scale anisotropy characteristics have substantial effects that need to be integrated into analysis of topography-driven flow.

Numerical Study on Double Diffusive Mixed Convection with a Soret Effect in a Two-Sided Lid-Driven Cavity

Abstract: In the present study, a numerical analysis is performed to understand the mixed convection flow, and heat and mass transfer with Soret effect in a two-sided lid-driven square cavity. The horizontal walls of the cavity are adiabatic and impermeable, while vertical walls are kept at constant but different temperatures and concentrations. The vertical walls move in a constant velocity. According to the direction of the movement of walls, three cases have been studied for different combinations of parameters involved in the study. The governing unsteady equations are solved numerically by the finite volume method with the SIMPLE algorithm. The results are presented graphically in the form of streamlines, isotherms, and velocity profiles. Heat and mass transfer rates are reduced if both walls are moving the in same direction, while heat and mass transfer rates are enhanced if the walls are moving in the opposite direction.

Natural convection in a rotating anisotropic porous layer with internal heat generation

Abstract: In this article, linear and nonlinear thermal instability in a rotating anisotropic porous layer with heat source has been investigated. The extended Darcy model, which includes the time derivative and Coriolis term has been employed in the momentum equation. The linear theory has been performed by using normal mode technique, while nonlinear analysis is based on minimal representation of the truncated Fourier series having only two terms. The criteria for both stationary and oscillatory convection is derived analytically. The rotation inhibits the onset of convection in both stationary and oscillatory modes. Effects of parameters on critical Rayleigh number has also been investigated. A weak nonlinear analysis based on the truncated representation of Fourier series method has been used to find the Nusselt number. The transient behavior of the Nusselt number has also been investigated by solving the finite amplitude equations using a numerical method. Steady and unsteady streamlines, and isotherms have been drawn to determine the nature of flow pattern. The results obtained during the analysis have been presented graphically.

Numerical Simulation of Flow Over Two Side-By-Side Circular Cylinders

Abstract: In the present paper, the unsteady, viscous, incompressible and 2-D flow around two side-by-side circular cylinders was simulated using a Cartesian-staggered grid finite volume based method. A great-source term technique was employed to identify the solid bodies (cylinders) located in the flow field and boundary conditions were enforced by applying the ghost-cell technique. Finally, the characteristics of the flow around two side-by-side cylinders were comprehensively obtained through several computational simulations. The computational simulations were performed for different transverse gap ratios (1.5 =≤T /D =≤4) in laminar (Re =100, 200 and turbulent (Re =104) regimes, where T and D are the distance between the centers of cylinders and the diameter of cylinders, respectively. The Reynolds number is based on the diameter of cylinders, D. The pressure field and vorticity distributions along with the associated streamlines and the time histories of hydrodynamic forces were also calculated and analyzed for different gap ratios. Generally, different flow patterns were observed as the gap ratio and Reynolds number varied. Accordingly, the hydrodynamic forces showed irregular variations for small gaps while they took a regular pattern at higher spacing ratios.

The shape of an elastic filament in a two-dimensional corner flow

Abstract: The deformation of a flexible filament held fixed at one end in a nonuniform viscous flow with curved streamlines is considered, with a focus on the filament dynamics and steady-state shape. Our motivation arises from recent microfluidic experiments on biofilm formation in a channel with bends, where thread-like structures, or streamers, were observed, attached to the side walls downstream of each corner and connecting consecutive corners while floating in the middle plane of the channel [Rusconi et al., J. R. Soc. Interface 7, 1293 (2010)]. We discuss the time evolution and final shape of the filament in different corner geometries as a function of a non-dimensional elasticity parameter that compares viscous and elastic effects. Since the filament develops tension, when the flow has curved streamlines the filament does not align with the flow, as occurs in a rectilinear flow, but rather it crosses the streamlines.

Stability analysis and control of the flow in a symmetric channel with a sudden expansion

Abstract: The laminar flow in two-dimensional diffusers may produce either symmetric or nonsymmetric steady solutions, depending on the value of the Reynolds number as compared with some critical value. The stability properties of the flow are studied in the context of linear theory. In this context, a sensitivity analysis of the flow instability is carried out with respect to perturbations that may be produced by a realistic passive control, thus providing qualitative hints and quantitative information for the control design. Following the so-obtained information, a passive control is built by introducing a small cylinder in the flow with the aim of stabilizing the unstable symmetric flow configuration in the diffuser. The effectiveness of this control is finally assessed by direct numerical simulation. It is shown that the introduction of the cylinder, placed following the indications of the linear sensitivity analysis in the stable asymmetric flow configuration, allows a steady completely symmetric or less asymmetric flow to be recovered. The flow transient between the uncontrolled asymmetric solution and the symmetric controlled one is analyzed in terms of streamlines and vorticity evolution; the effects of the cylinder introduction on flow dissipation are also assessed.

Effect of Diffusion on Dispersion

Abstract: This paper (SPE 115961) was accepted for presentation at the SPE Annual Technical Conference and Exhibition, Denver, 21–24 September 2008, and revised for publication. Original manuscript received for review 7 July 2008. Revised manuscript received for review 11 February 2010. Paper peer approved 3 May 2010. Summary It is known that dispersion in porous media results from an interaction between convective spreading and diffusion. However, the nature and implications of these interactions are not well understood. Dispersion coefficients obtained from averaged cup-mixing concentration histories have contributions of convective spreading and diffusion lumped together. We decouple the contributions of convective spreading and diffusion in core-scale dispersion and systematically investigate interaction between the two in detail. We explain phenomena giving rise to important experimental observations such as Fickian behavior of core-scale dispersion and powerlaw dependence of dispersion coefficient on Peclet number. We track movement of a swarm of solute particles through a physically representative network model. A physically representative network model preserves the geometry and topology of the pore space and spatial correlation in flow properties. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes’ equation. Paths of all solute particles are deterministically known in the absence of diffusion. Thus, we can explicitly investigate purely convective spreading by tracking the movement of solute particles on these streamlines. Then, we superimpose diffusion and study dispersion in terms of interaction between convective spreading and diffusion for a wide range of Peclet numbers. This approach invokes no arbitrary parameters, enabling a rigorous validation of the physical origin of core-scale dispersion. In this way, we obtain an unequivocal, quantitative assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion in flow through porous media. Convective spreading has two components: stream splitting and velocity gradient in pore throats in the direction transverse to flow. We show that, if plug flow occurs in the pore throats (accounting only for stream splitting), all solute particles can encounter a wide range of independent velocities because of velocity differences between pore throats and randomness of pore structure. Consequently, plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading (in this case, only stream splitting), and, consequently, dispersion is simply the sum of convective spreading and diffusion. In plug flow, hydrodynamic dispersion varies linearly with the pore-scale Peclet number when diffusion is small in magnitude compared to convective spreading. For a more realistic parabolic velocity profile in pore throats, particles near the solid surface of the medium do not have independent velocities. Now, purely convective spreading (caused by a combination of stream splitting and variation in flow velocity in the transverse direction) is non-Fickian. When diffusion is nonzero, solute particles in the low-velocity region near the solid surface can move into the main flow stream. They subsequently undergo a wide range of independent velocities because of stream splitting, and, consequently, dispersion becomes asymptotically Fickian. In this case, dispersion is a result of an interaction between convection and diffusion. This interaction results in a weak nonlinear dependence of dispersion on Peclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data for a broad range of Peclet numbers. Thus, the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (1) stream splitting of the solute front at every pore, causing independence of particle velocities purely by convection; (2) velocity gradient in pore throats in the direction transverse to flow; and (3) diffusion. Taylor’s dispersion in a capillary tube accounts only for the second and third of these phenomena, yielding a quadratic dependence of dispersion on Peclet number. Plug flow in the bonds of a physically representative network accounts only for the first and third phenomena, resulting in a linear dependence of dispersion on Peclet number. When all the three phenomena are accounted for, we can explain effectively the weak nonlinear dependence of dispersion on Peclet number.

Momentum and Heat Transfer in MHD Stagnation-Point Flow Over a Shrinking Sheet

Abstract: The steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an electrically conducting incompressible viscous fluid toward a shrinking sheet is investigated. The sheet is shrunk in its own plane with a velocity proportional to the distance from the stagnation-point and a uniform magnetic field is applied normal to the sheet. Velocity component parallel to the sheet is found to increase with an increase in the magnetic field parameter M. A region of reverse flow occurs near the surface of the shrinking sheet. It is shown that as M increases, the tendency of this flow reversal decreases. It is also observed that the nonalignment of the stagnation-point flow and the shrinking sheet considerably complicates the flow structure. The effect of the magnetic parameter M on the streamlines is shown for both aligned and nonaligned cases. The temperature distribution in the boundary layer is found when the surface is held at constant temperature. The analysis reveals that the temperature at a point increases with increasing M in a certain neighborhood of the surface but beyond this, the temperature decreases with increasing M. For fixed M, the surface heat flux decreases with increase in the shrinking rate.

Periodic mixed convection of a nanofluid in a cavity with top lid sinusoidal motion

Abstract: The periodic mixed convection of a water–copper nanofluid inside a rectangular cavity with aspect ratio of 3 is investigated numerically. The temperature of the bottom wall of the cavity is assumed greater than the temperature of the top lid which oscillates horizontally with the velocity defined as u = u0 sin (ωt). The effects of Richardson number, Ri, and volume fraction of nanoparticles on the flow and thermal behaviour of the nanofluid are investigated. Velocity, temperature profiles, and streamlines are presented. It is observed that when Ri 1. The higher value of Ri corresponds to a lower value of the amplitude of the oscillation of Num in the steady periodic state. Moreover, increasing the volume fraction of the nanoparticles increases the heat transfer rate.

Experimental study of velocity fields in rectangular shallow reservoirs

Abstract: Velocity fields in rectangular shallow reservoirs with different length-to-width and expansion ratios were investigated in an experimental study, to evaluate the effect of geometry on the flow field. A wide range of combinations of these two non-dimensional geometric parameters were tested at constant hydraulic conditions. Ultrasound velocity profilers were used to measure the horizontal velocity components across the entire reservoir surface, allowing for the visualization of streamlines and of the instantaneous and average velocities. Five different types of flow patterns were identified, depending on the values of the length-to-width ratio and expansion ratio of the reservoir. Asymmetrical flow patterns were found to develop for certain combinations of these geometric parameters despite the perfect reservoir symmetry. A critical comparison of these new experimental results with those of other works is provided.