Showing papers on "Streamlines, streaklines, and pathlines published in 2016"

Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno's mathematical model

Abstract: A numerical investigation is performed on the unsteady natural convection of water based nanofluid within a wavy-walled cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The left vertical wavy and right vertical flat walls of the cavity are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Hartmann number, undulation number, wavy contraction ratio, inclination angle of the magnetic field relative to the gravity vector and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wavy wall, as well as on the streamlines, isotherms and isoconcentrations are analyzed.

Streamline Variability Plots for Characterizing the Uncertainty in Vector Field Ensembles

Abstract: We present a new method to visualize from an ensemble of flow fields the statistical properties of streamlines passing through a selected location. We use principal component analysis to transform the set of streamlines into a low-dimensional Euclidean space. In this space the streamlines are clustered into major trends, and each cluster is in turn approximated by a multivariate Gaussian distribution. This yields a probabilistic mixture model for the streamline distribution, from which confidence regions can be derived in which the streamlines are most likely to reside. This is achieved by transforming the Gaussian random distributions from the low-dimensional Euclidean space into a streamline distribution that follows the statistical model, and by visualizing confidence regions in this distribution via iso-contours. We further make use of the principal component representation to introduce a new concept of streamline-median, based on existing median concepts in multidimensional Euclidean spaces. We demonstrate the potential of our method in a number of real-world examples, and we compare our results to alternative clustering approaches for particle trajectories as well as curve boxplots.

Elastic instabilities in planar elongational flow of monodisperse polymer solutions

Abstract: We investigate purely elastic flow instabilities in the almost ideal planar stagnation point elongational flow field generated by a microfluidic optimized-shape cross-slot extensional rheometer (OSCER). We use time-resolved flow velocimetry and full-field birefringence microscopy to study the behavior of a series of well-characterized viscoelastic polymer solutions under conditions of low fluid inertia and over a wide range of imposed deformation rates. At low deformation rates the flow is steady and symmetric and appears Newtonian-like, while at high deformation rates we observe the onset of a flow asymmetry resembling the purely elastic instabilities reported in standard-shaped cross-slot devices. However, for intermediate rates, we observe a new type of elastic instability characterized by a lateral displacement and time-dependent motion of the stagnation point. At the onset of this new instability, we evaluate a well-known dimensionless criterion M that predicts the onset of elastic instabilities based on geometric and rheological scaling parameters. The criterion yields maximum values of M which compare well with critical values of M for the onset of elastic instabilities in viscometric torsional flows. We conclude that the same mechanism of tension acting along curved streamlines governs the onset of elastic instabilities in both extensional (irrotational) and torsional (rotational) viscoelastic flows.

Heatline visualization of natural convection heat transfer in an inclined wavy cavities filled with nanofluids and subjected to a discrete isoflux heating from its left sidewall

Abstract: Natural convection visualization by heatlines in three types of inclined wavy cavities filled with Al 2 O 3 –water and Ag–water nanofluids and subjected to a discrete isoflux heating from its left sidewall is investigated numerically in this work. The right sidewall together with remaining regions in the left sidewall is insulated. The solution is based on the finite volume method. The upper and lower cavity walls are maintained at a constant cold temperature and follow a profile of sine wave. Numerical computations are carried out for various values of the solid volume fraction [ φ = 0, 0.05, 0.1, 0.15 and 0.2], number of undulations [ N = 1, 2 and 3], Rayleigh number [Ra = 10 3 –10 7 ], the ratio of heating element length to the cavity height [ e = 0.2, 0.4, 0.6, 0.8 and 1.0], the cavity inclination angle [ Φ = 0°, 30°, 60° and 90°] and the wave amplitude [ γ = 0.1, 0.15 and 0.2]. The results are presented in terms of heatlines, isotherms, streamlines together with local and average Nusselt numbers. It is found that the geometry of the wavy cavity has a cursive role on the flow and thermal fields pattern. The results also explained that streamlines and isotherms were affected significantly for high Rayleigh number and vertical cavity position [ Φ = 90°]. Also, when the solid volume fractions and wave amplitudes increase, the local Nusselt number along the heat source increases. Furthermore, velocity profiles increase as [ e ] increases near the left sidewall of the cavity while they decrease as [ e ] increases near the right sidewall of the cavity. For all three types of horizontal wavy cavities the heat functions increase for both nano and base fluids when the wave amplitude increases. Finally, results of the present work indicated that both heatlines and heat functions techniques are applied efficiently to describe the natural convection heat transfer inside wavy cavities filled with nanofluid.

Effect of variable heating on double diffusive flow in a square porous cavity

Abstract: Investigation of heat and mass transfer due to variable heating at the left vertical surface of a square cavity filled with porous medium is carried out The left surface of cavity is maintained at higher temperature and concentration as compared to right surface which has low temperature and concentration Finite element method is used to convert the partial differential equations into simpler algebraic form of equations The governing equations are solved in iterative manner to obtain the solution parametersResults are presented in terms of isothermal lines, iso-concentration lines and streamlines for variable wall temperature at left surface

Three-dimensional unsteady natural convection and entropy generation in an inclined cubical trapezoidal cavity with an isothermal bottom wall

Abstract: Numerical computation of unsteady laminar three-dimensional natural convection and entropy generation in an inclined cubical trapezoidal air-filled cavity is performed for the first time in this work. The vertical right and left sidewalls of the cavity are maintained at constant cold temperatures. The lower wall is subjected to a constant hot temperature, while the upper one is considered insulated. Computations are performed for Rayleigh numbers varied as 103 ⩽ Ra ⩽ 105, while the trapezoidal cavity inclination angle is varied as 0° ⩽ Φ ⩽ 180°. Prandtl number is considered constant at Pr = 0.71. Second law of thermodynamics is applied to obtain thermodynamic losses inside the cavity due to both heat transfer and fluid friction irreversibilities. The variation of local and average Nusselt numbers is presented and discussed, while, streamlines, isotherms and entropy contours are presented in both two and three-dimensional pattern. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. Also, the inclination angle effect on the total entropy generation becomes insignificant when the Rayleigh number is low. Moreover, when the Rayleigh number increases the average Nusselt number increases.

Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls

Abstract: The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls. Mathematical modeling is based upon the laws of mass and linear momentum. Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations. The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest. Trapping bolus scheme is also presented through streamlines.

Packing, alignment and flow of shape-anisotropic grains in a 3D silo experiment

Abstract: Granular material flowing through bottlenecks like the openings of silos tend to clog and to inhibit further flow. We study this phenomenon in a three-dimensional hopper for spherical and shape-anisotropic particles by means of X-ray tomography. The X-ray tomograms provide information on the bulk of the granular filling, and allows to determine the particle positions and orientations inside the silo. In addition, it allows to calculate local packing densities in different parts of the container. We find that in the flowing zone of the silo particles show a preferred orientation and thereby a higher order. Similarly to simple shear flows, the average orientation of the particles is not parallel to the streamlines but encloses a certain angle with it. In most parts of the hopper, the angular distribution of the particles did not reach the one corresponding to stationary shear flow, thus the average orientation angle in the hopper deviates more from the streamlines than in stationary shear flows. In the flowing parts of the silo shear induced dilation is observed, which is more pronounced for elongated grains than for nearly spherical particles. The clogged state is characterized by a dome, i. e. the geometry of the layer of grains blocking the outflow. The shape of the dome depends on the particle shape.

Mixed convection in thermally anisotropic non-Darcy porous medium in double lid-driven cavity using Bejan’s heatlines

Abstract: This paper discusses the problem of mixed convection in two-sided lid-driven enclosures saturated non-Darcy porous medium. The vertical walls of the cavity were kept thermally insulated. The bottom wall is cooled while the top wall is uniformly heated. The bottom and the top walls are moving in opposite direction. The governing equations were solved using finite volume method with SIMPLE algorithm. A new form for the heat function was derived. The obtained results were presented in contours maps for the streamlines, the isotherms and the heat function. The profiles of the horizontal velocity component and the maximum values of vertical velocity components as well as the mean Nusselt number were presented graphically. It is found that, for the low values of the Richardson number, the forced convection plays a dominant role in the flow region. The increase in inverse Darcy number leads to decrease the mean Nusselt number.

Scour Hole Influence on Turbulent Flow Field around Complex Bridge Piers

Abstract: Experimental results of detailed flow measurements using an Acoustic-Doppler Velocimeter (ADV) around a complex bridge pier (CBP) are presented. The pier consists of a column, a pile cap (PC) and a 2×4 pile group. The time-averaged velocities, turbulence intensities, and Reynolds stresses are studied and presented at different horizontal and vertical planes. Streamlines obtained from the velocity fields are used to show the complexity of the flow around the pier. It is shown that the main feature of the flow responsible for the entrainment of the bed sediments is a contracted (pressurized) flow below the PC toward the piles. A deflected flow around the PC and a strong down-flow along its sides are observed and have been measured. It is shown that these flow patterns also cause sediment entrainment. Vortex flow behind the PC and amplification of turbulence intensity along its sides near the downstream region can be other reasons for the scour hole (SH) development. Turbulence intensities and Reynolds shear stresses are presented and discussed. A comparison is made between the flow field measured with the equilibrium SH and that measured on the fixed flat-bed. The results show that the flow field around the PC is considerably influenced by the development of the SH. The extent of the wake region at the rear of the PC is about 1.4 times larger for the fixed bed (FB) than for the scoured bed (SB). Moreover, the size of the core of high turbulent kinetic energy K, as well as the maximum values of K behind the column for the FB case is larger than that of the SB case. When a scour hole develops, the flow below the PC around the piles is considered to be the main cause of the scour. This is the first time that these observations about the flow and turbulence field around a complex bridge pier are reported and analyzed. In addition to improving the understanding of the flow structure, the present detailed measurements can also be used for benchmarking and verification of numerical models.

Packing, alignment and flow of shape-anisotropic grains in a 3D silo experiment

Abstract: Granular material flowing through bottlenecks, like the openings of silos, tend to clog and thus inhibit further flow. We study this phenomenon in a three-dimensional hopper for spherical and shape-anisotropic particles by means of x-ray tomography. The x-ray tomograms provide information on the bulk of the granular filling, and allows us to determine the particle positions and orientations inside the silo. In addition, it allows us to calculate local packing densities in different parts of the container. We find that in the flowing zone of the silo particles show a preferred orientation and thereby a higher order. Similarly to simple shear flows, the average orientation of the particles is not parallel to the streamlines but encloses a certain angle with it. In most parts of the hopper, the angular distribution of the particles did not reach the one corresponding to stationary shear flow, thus the average orientation angle in the hopper deviates more from the streamlines than in stationary shear flows. In the flowing parts of the silo, shear induced dilation is observed, which is more pronounced for elongated grains than for nearly spherical particles. The clogged state is characterized by a dome, i.e. the geometry of the layer of grains blocking the outflow. The shape of the dome depends on the particle shape.

Velocity, thermal and concentration slip effects on a magneto-hydrodynamic nanofluid flow

Abstract: This article examines the magneto-hydrodynamic (MHD) flow of nanofluid bounded by a stretching surface. The slip conditions are utilized in the present analysis. The involved differential systems are solved for the velocity, temperature and mass fraction. Graphical and numerical results are reported for the analysis of various parameters of interest entering into the modeled problems. Combined effects of thermal and concentration jump are analyzed. Various tables are constructed to show the rheological effects of different physical parameters. Streamlines are plotted showing the rheology for the slip and no slip flow regime. Plots of skin friction are also prepared for the slip and magnetic field effects.