Showing papers on "Streamlines, streaklines, and pathlines published in 2012"

Flow structure on finite-span wings due to pitch-up motion

Abstract: The flow structure on low-aspect-ratio wings arising from pitch-up motion is addressed via a technique of particle image velocimetry. The objectives are to: determine the onset and evolution of the three-dimensional leading-edge vortex; provide complementary interpretations of the vortex structure in terms of streamlines, projections of spanwise and surface-normal vorticity, and surfaces of constant values of the second invariant of the velocity gradient tensor (iso- surfaces); and to characterize the effect of wing planform (rectangular versus elliptical) on this vortex structure. The pitch-up motion of the wing (plate) is from 0 to over a time span corresponding to four convective time scales, and the Reynolds number based on chord is 10 000. Volumes of constant magnitude of the second invariant of the velocity gradient tensor are interpreted in conjunction with three-dimensional streamline patterns and vorticity projections in orthogonal directions. The wing motion gives rise to ordered vortical structures along its wing surface. In contrast to development of the classical two-dimensional leading-edge vortex, the flow pattern evolves to a strongly three-dimensional form at high angle of attack. The state of the vortex system, after attainment of maximum angle of attack, has a similar form for extreme configurations of wing planform. Near the plane of symmetry, a large-scale region of predominantly spanwise vorticity dominates. Away from the plane of symmetry, the flow is dominated by two extensive regions of surface-normal vorticity, i.e. swirl patterns parallel to the wing surface. This similar state of the vortex structure is, however, preceded by different sequences of events that depend on the magnitude of the spanwise velocity within the developing vortex from the leading edge of the wing. Spanwise velocity of the order of one-half the free stream velocity, which is oriented towards the plane of symmetry of the wing, results in regions of surface-normal vorticity. In contrast, if negligible spanwise velocity occurs within the developing leading-edge vortex, onset of the regions of surface-normal vorticity occurs near the tips of the wing. These extremes of large and insignificant spanwise velocity within the leading-edge vortex are induced respectively on rectangular and elliptical planforms.

Peristaltic flow of a nanofluid in a non-uniform tube

Abstract: The present analysis discusses the peristaltic flow of a nanofluid in a diverging tube. This is the first article on the peristaltic flow in nanofluids. The governing equations for nanofluid are modelled in cylindrical coordinates system. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Temperature and nanoparticle equations are coupled so Homotopy perturbation method is used to calculate the solutions of temperature and nanoparticle equations, while exact solutions have been calculated for velocity profile and pressure gradient. The solution depends on Brownian motion number N b , thermophoresis number N t , local temperature Grashof number B r and local nanoparticle Grashof number G r . The effects of various emerging parameters are investigated for five different peristaltic waves. It is observed that the pressure rise decreases with the increase in thermophoresis number N t . Increase in the Brownian motion parameter N b and the thermophoresis parameter N t temperature profile increases. Streamlines have been plotted at the end of the article.

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

Abstract: SUMMARY This paper describes a numerical study of the two-dimensional and three-dimensional unsteady flow over two square cylinders arranged in an in-line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross-sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time-averaged and spanwise-averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender-body regime (G < 0.5), the reattach regime (G < 4) and co-shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.

Geometric scaling of a purely elastic flow instability in serpentine channels

Abstract: A combined experimental, numerical and theoretical investigation of the geometric scaling of the onset of a purely elastic flow instability in serpentine channels is presented. Good qualitative agreement is obtained between experiments, using dilute solutions of flexible polymers in microfluidic devices, and three-dimensional numerical simulations using the upper-convected Maxwell model. The results are confirmed by a simple theoretical analysis, based on the dimensionless criterion proposed by Pakdel & McKinley (Phys. Rev. Lett., vol. 77, 1996, pp. 2459–2462) for onset of a purely elastic flow instability. Three-dimensional simulations show that the instability is primarily driven by the curvature of the streamlines induced by the flow geometry and not due to the weak secondary flow in the azimuthal direction. In addition, the simulations also reveal that the instability is time-dependent and that the flow oscillates with a well-defined period and amplitude close to the onset of the supercritical instability.

Hierarchical Streamline Bundles

Abstract: Effective 3D streamline placement and visualization play an essential role in many science and engineering disciplines The main challenge for effective streamline visualization lies in seed placement, ie, where to drop seeds and how many seeds should be placed Seeding too many or too few streamlines may not reveal flow features and patterns either because it easily leads to visual clutter in rendering or it conveys little information about the flow field Not only does the number of streamlines placed matter, their spatial relationships also play a key role in understanding the flow field Therefore, effective flow visualization requires the streamlines to be placed in the right place and in the right amount This paper introduces hierarchical streamline bundles, a novel approach to simplifying and visualizing 3D flow fields defined on regular grids By placing seeds and generating streamlines according to flow saliency, we produce a set of streamlines that captures important flow features near critical points without enforcing the dense seeding condition We group spatially neighboring and geometrically similar streamlines to construct a hierarchy from which we extract streamline bundles at different levels of detail Streamline bundles highlight multiscale flow features and patterns through clustered yet not cluttered display This selective visualization strategy effectively reduces visual clutter while accentuating visual foci, and therefore is able to convey the desired insight into the flow data

Shear-induced alignment and dynamics of elongated granular particles.

Abstract: The alignment, ordering, and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical imaging and x-ray computed tomography. The experiments were complemented by discrete element simulations. The particles develop an orientational order. In the steady state the time- and ensemble-averaged direction of the main axis of the particles encloses a small angle with the streamlines. This shear alignment angle is independent of the applied shear rate, and it decreases with increasing grain aspect ratio. At the grain level the steady state is characterized by a net rotation of the particles, as dictated by the shear flow. The distribution of particle rotational velocities was measured both in the steady state and also during the initial transients. The average rotation speed of particles with their long axis perpendicular to the shear alignment angle is larger, while shear aligned particles rotate slower. The ratio of this fast/slow rotation increases with particle aspect ratio. During the initial transient starting from an unaligned initial condition, particles having an orientation just beyond the shear alignment angle rotate opposite to the direction dictated by the shear flow.

Pathline tracing on fully unstructured control-volume grids

Abstract: The trend toward unstructured grids in subsurface flow modeling has prompted interest in the issue of streamline or pathline tracing on unstructured grids. Streamline tracing on unstructured grids is problematic because a continuous velocity field is required for the calculation, while numerical solutions to the groundwater flow equations provide velocity in discretized form only. A method for calculating flow streamlines or pathlines from a finite-volume flow solution is presented. The method uses an unconstrained least squares method on interior cells and a constrained least squares method on boundary cells to approximate cell-centered velocities, which can then be continuously interpolated to any point in the domain of interest. Two-dimensional tests demonstrate that the method correctly reproduces uniform and corner-to-corner flow on fully unstructured grids. In three dimensions using regular hexahedral grids, the method agrees well with established semianalytical methods. Tests also demonstrate that the method produces physically realistic results on fully unstructured three-dimensional grids.

Peristaltic flow of a Phan-Thien-Tanner nanofluid in a diverging tube

Abstract: The present study examines the peristaltic flow of a PTT nanofluid in a diverging tube. This is the first article on the PTT peristaltic flow in nanofluid. The governing equations for PTT nanofluid are modelled in a cylindrical coordinates system. The flow is investigated in a wave frame of reference moving with velocity of the wave c1. Temperature and nanoparticle equations are coupled so the homotopy perturbation method is used to calculate the solutions of temperature and nanoparticle equations, while exact solutions have been evaluated for the velocity profile and pressure gradient. The solutions analyze the Brownian motion number Nb, thermophoresis number Nt, local temperature Grashof number Br, and local nanoparticle Grashof number Gr. The effects of various physical parameters of the model are investigated and discussed. It is observed that the pressure rise decreases with the increase in thermophoresis number Nt. Increases are noted in the Brownian motion parameter Nb and the thermophoresis parameter Nt as the temperature profile increases. Streamlines have been plotted at the end of the article. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20386

An advection-based model to increase the temporal resolution of PIV time series

Abstract: A numerical implementation of the advection equation is proposed to increase the temporal resolution of PIV time series. The method is based on the principle that velocity fluctuations are transported passively, similar to Taylor’s hypothesis of frozen turbulence. In the present work, the advection model is extended to unsteady three-dimensional flows. The main objective of the method is that of lowering the requirement on the PIV repetition rate from the Eulerian frequency toward the Lagrangian one. The local trajectory of the fluid parcel is obtained by forward projection of the instantaneous velocity at the preceding time instant and backward projection from the subsequent time step. The trajectories are approximated by the instantaneous streamlines, which yields accurate results when the amplitude of velocity fluctuations is small with respect to the convective motion. The verification is performed with two experiments conducted at temporal resolutions significantly higher than that dictated by Nyquist criterion. The flow past the trailing edge of a NACA0012 airfoil closely approximates frozen turbulence, where the largest ratio between the Lagrangian and Eulerian temporal scales is expected. An order of magnitude reduction of the needed acquisition frequency is demonstrated by the velocity spectra of super-sampled series. The application to three-dimensional data is made with time-resolved tomographic PIV measurements of a transitional jet. Here, the 3D advection equation is implemented to estimate the fluid trajectories. The reduction in the minimum sampling rate by the use of super-sampling in this case is less, due to the fact that vortices occurring in the jet shear layer are not well approximated by sole advection at large time separation. Both cases reveal that the current requirements for time-resolved PIV experiments can be revised when information is poured from space to time. An additional favorable effect is observed by the analysis in the frequency domain whereby the spectrum becomes significantly less prone to aliasing error for the super-sampled data series.

Flow field around side-by-side piers with and without a scour hole

Abstract: The present study provides the experimental results of the flow pattern around two-circular piers positioned in side-by-side arrangement. The experiments were performed for two bed configurations (with and without a scour hole). Velocities were measured by an Acoustic Doppler Velocimeter (ADV). Flat bed and scour hole were frozen by synthetic glue to facilitate the performance of the experiments. The contours and distributions of the time-averaged velocity components, turbulence intensities, turbulence kinetic energy, and Reynolds stresses at different horizontal and vertical planes are presented. Streamlines and velocity vectors obtained from time-averaged velocity fields are used to show further flow features. Bed shear stresses at specific points around the piers are given. The results of power-spectra analysis are presented inside and outside the scour hole. It is shown that the horseshoe vortex is elongated further to the downstream of the gap between the two piers. The flow between the two piers is accelerated into the scour hole so that it influences the vertical and transverse deflections of the flow around and especially between the two piers. The maximum downflow was inside the scour hole near the base of the pier. Between the two piers, the magnitude of downflow and vertical turbulence intensity as well as turbulence kinetic energy are greater than that at the outer sides of the two piers. Bed shear stress has substantially large values between the two piers, as much as two times in comparison to the other sides of the piers. The flow pattern including the contracted flow and interference between the horseshoe vortices play an important role in the creation and formation of the greater scour depth between the two piers. The presence of scour hole changes the behavior of vortex shedding considerably. The present detailed measurements can also be used for the verification of numerical models.

Peristaltic Hemodynamic Flow of Couple-Stress Fluids Through a Porous Medium with Slip Effect

Abstract: The present investigation deals with a theoretical study of the peristaltic hemodynamic flow of couple-stress fluids through a porous medium under the influence of wall slip condition. This study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for axial velocity, pressure gradient, frictional force, stream function and mechanical efficiency are obtained. Effects of different physical parameters reflecting couple-stress parameter, permeability parameter, slip parameter, as well as amplitude ratio on pumping characteristics and frictional force, streamlines pattern and trapping of peristaltic flow pattern are studied with particular emphasis. The computational results are presented in graphical form. This study puts forward an important observation that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the amplitude ratio.

Entropy Generation Due to Natural Convection in a Partially Open Cavity with a Thin Heat Source Subjected to a Nanofluid

Abstract: This article presents a numerical study of natural convection cooling of a heat source mounted inside the cavity, with special attention being paid to entropy generation. The right vertical wall is partially open and is subjected to copper–water nanofluid at a constant low temperature and pressure, while the other boundaries are assumed to be adiabatic. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for a Rayleigh number in the range 103 < Ra < 106, and for solid volume fraction 0 <ϕ <0.05. In order to investigate the effect of the heat source and open boundary location, six different configurations are considered. The effects of Rayleigh numbers, heat source and open boundary locations on the streamlines, isotherms, local entropy generation, Nusselt number, and total entropy generation are investigated. The results indicate that when open boundary is located up, the fluid flow augments and hen...

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.

Biased swimming cells do not disperse in pipes as tracers: A population model based on microscale behaviour

Abstract: There is much current interest in modelling suspensions of algae and other micro-organisms for biotechnological exploitation, and many bioreactors are of tubular design. Using generalized Taylor dispersion theory, we develop a population-level swimming-advection-diffusion model for suspensions of micro-organisms in a vertical pipe flow. In particular, a combination of gravitational and viscous torques acting on individual cells can affect their swimming behaviour, which is termed gyrotaxis. This typically leads to local cell drift and diffusion in a suspension of cells. In a flow in a pipe, small amounts of radial drift across streamlines can have a major impact on the effective axial drift and diffusion of the cells. We present a Galerkin method to calculate the local mean swimming velocity and diffusion tensor based on local shear for arbitrary flow rates. This method is validated with asymptotic results obtained in the limits of weak and strong shear. We solve the resultant swimming-advection-diffusion...

Biased swimming cells do not disperse in pipes as tracers: a population model based on microscale behaviour

Abstract: There is much current interest in modelling suspensions of algae and other micro-organisms for biotechnological exploitation, and many bioreactors are of tubular design. Using generalized Taylor dispersion theory, we develop a population-level swimming-advection-diffusion model for suspensions of micro-organisms in a vertical pipe flow. In particular, a combination of gravitational and viscous torques acting on individual cells can affect their swimming behaviour, which is termed gyrotaxis. This typically leads to local cell drift and diffusion in a suspension of cells. In a flow in a pipe, small amounts of radial drift across streamlines can have a major impact on the effective axial drift and diffusion of the cells. We present a Galerkin method to calculate the local mean swimming velocity and diffusion tensor based on local shear for arbitrary flow rates. This method is validated with asymptotic results obtained in the limits of weak and strong shear. We solve the resultant swimming-advection-diffusion equation using numerical methods for the case of imposed Poiseuille flow and investigate how the flow modifies the dispersion of active swimmers from that of passive scalars. We establish that generalized Taylor dispersion theory predicts an enhancement of gyrotactic focussing in pipe flow with increasing shear strength, in contrast to earlier models. We also show that biased swimming cells may behave very differently to passive tracers, drifting axially at up to twice the rate and diffusing much less.

Effect of Thermal Buoyancy on the Two-Dimensional Upward Flow and Heat Transfer Around a Square Cylinder

Abstract: The effect of aiding/opposing buoyancy on the two-dimensional upward flow and heat transfer around a heated/cooled cylinder of square cross section is studied in this work. The finite-volume-based commercial computational fluid dynamics (CFD) software FLUENT is used for the numerical simulation. The influence of aiding/opposing buoyancy is studied for Reynolds and Richardson numbers ranges of 50 to 150 and –1 to 1, respectively, and the blockage parameters of 2% and 25%. The flow exhibits unsteady periodic characteristics in the chosen range of Reynolds numbers (except for Reynolds number of 50 and blockage parameter of 25%) for the forced convective cases (Richardson number of 0). However, the vortex shedding is observed to stop completely at some critical value of Richardson number for a particular Reynolds number, below which the shedding of vortices into the stream is quite prominent. Representative streamlines and isotherm patterns for different blockage parameters are systematically presented and di...

Assessment of Two-Equation Turbulence Models and Validation of the Performance Characteristics of an Experimental Wind Turbine by CFD

Abstract: The very first step in the simulation of ice accretion on a wind turbine blade is the accurate prediction of the flow field around it and the performance of the turbine rotor. The paper addresses this prediction using RANS equations with a proper turbulence model. The numerical computation is performed using a commercial CFD code, and the results are validated using experimental data for the 3D flow field around the NREL Phase VI HAWT rotor. For the flow simulation, a rotating reference frame method, which calculates the flow properties as time-averaged quantities, has been used to reduce the time spent on the analysis. A basic grid convergence study is carried out to select the adequate mesh size. The two-equation turbulence models available in ANSYS FLUENT are compared for a 7 m/s wind speed, and the one that best represents the flow features is then used to determine moments on the turbine rotor at five wind speeds (7 m/s, 10 m/s, 15 m/s, 20 m/s, and 25 m/s). The results are validated against experimental data, in terms of shaft torque, bending moment, and pressure coefficients at certain spanwise locations. Streamlines over the cross-sectional airfoils have also been provided for the stall speed to illustrate the separation locations. In general, results have shown good agreement with the experimental data for prestall speeds.