This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.
The hydraulic jump is the sudden transition from a high-velocity open channel flow regime to a subcritical flow motion. The flow properties may be solved using continuity and momentum considerations. In this review paper, recent advances in turbulent hydraulic jumps are developed: the non-breaking undular hydraulic jump, the positive surge and tidal bore, and the air bubble entrainment in hydraulic jumps with roller. The review paper demonstrates that the hydraulic jump is a fascinating turbulent flow motion and the present knowledge is insufficient, especially at the scales of environmental and geophysical flows.
Correlated experimental and numerical studies were carried out to analyze cavitating flows and to describe the two-phase flow structures of attached sheet cavitation in Venturi geometries. New double optical probe measurements were performed and special data processing methods were developed to estimate void ratio and velocity fields for cold water flows. By applying a computational method previously developed in LEGI ( ) based on the code Fine /Turbo and on a barotropic approach, several steady calculations were performed in cold water cavitating flows. Local and global analyzes based on comparisons between experimental and numerical results were proposed.
This article aims to numerically investigate mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. A discrete heat source is considered to be located on one of the walls of the cavity. Three different heating modes are considered which relate to the location of the heat source on three different walls (left, right and bottom) of the cavity. The analysis is carried out for a range of Richardson numbers and cavity aspect ratios. The results show that there are noticeable differences among the three heating modes. When the heat source is located on the right wall, the cavity with an aspect ratio of two has the highest heat transfer rate compared to other cavity heating modes. Moreover, when the heat source is located on the bottom wall, the flow field in the cavity with an aspect ratio of two experiences a fluctuating behaviour for Richardson number of 10. The results also show that at a fixed value of Richardson number, all three different heating modes show noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increases.
The present study is developed within the framework of marine structure design operating in transient regimes. It deals with an experimental and numerical investigation of the time–space distribution of the wall-pressure field on a NACA66 hydrofoil undergoing a transient up-and-down pitching motion from 0° to 15° at four pitching velocities and a Reynolds number = 0.75 × 10 . The experimental investigation is performed using an array of wall-pressure transducers located on the suction side and by means of time–frequency analysis and Empirical Modal Decomposition method. The numerical study is conducted for the same flow conditions. It is based on a 2D RANS code including mesh reconstruction and an ALE formulation in order to take into account the foil rotation and the tunnel walls. Due to the moderate Reynolds number, a laminar to turbulent transition model was also activated. For the operating flow conditions of the study, experimental and numerical flow analysis revealed that the flow experiences complex boundary layer events as leading-edge laminar separation bubble, laminar to turbulent transition, trailing-edge separation and flow detachment at stall. Although the flow is relatively complex, the calculated wall pressure shows a quite good agreement with the experiment provided that the mesh resolution and the temporal discretization are carefully selected depending on the pitching velocity. It is particularly shown that the general trend of the wall pressure (low frequency) is rather well predicted for the four pitching velocities with for instance a net inflection of the wall pressure when transition occurs. The inflection zone is reduced as the pitching velocity increases and tends to disappear for the highest pitching velocity. Conversely, high frequency wall-pressure fluctuations observed experimentally are not captured by the RANS model. Based on the good agreement with experiment, the model is then used to investigate the effects of the pitching velocity on boundary layer events and on hydrodynamic loadings. It is shown that increasing the pitching velocity tends to delay the laminar-to-turbulence transition and even to suppress it for the highest pitching velocity during the pitch-up motion. It induces also an increase of the stall angle (compared to quasi-static one) and an increase of the hysteresis effect during pitch-down motion resulting to a significant increase of the hydrodynamic loading.
We investigate the viscous instability of a miscible displacement process in a rectilinear geometry, when the viscosity contrast is controlled by two quantities which diffuse at different rates. The analysis is applicable to displacement in a porous medium with two dissolved species, or to displacement in a Hele-Shaw cell with two dissolved species or with one dissolved species and a thermal contrast. We carry out asymptotic analyses of the linear stability behaviour in two regimes: that of small wavenumbers at intermediate times, and that of large times. An interesting feature of the large-time results is the existence of regimes in which the favoured wavenumber scales with , as opposed to the scaling found in other regimes including that of single-species fingering. We also show that the region of parameter space in which the displacement is unstable grows with time, and that although overdamped growing perturbations are possible, these are never the fastest-growing perturbations so are unlikely to be observed. We also interpret our results physically in terms of the stabilising and destabilising mechanisms acting on an incipient finger.
The paper considers heat transfer characteristics of thin film flow over a hot horizontal cylinder resulting from a cold vertical sheet of liquid falling onto the surface. The underlying physical features of the developing film thickness, velocity and temperature distributions have been illustrated by numerical solutions of high accuracy for large Reynolds numbers using the modified Keller box method. The solutions for film thickness distribution are good agreement with those obtained using the Pohlhausen integral momentum technique thus providing a basic confirmation of the validity of the results presented.
An experimental study of pulsating turbulent flow in a pipe is reported in which measurements of instantaneous velocity were made using a two-component Laser Doppler Anemometer system. Local values of ensemble-averaged axial velocity, and radial and axial components of root-mean-square turbulent velocity fluctuation were obtained from the measurements. The frequency of the imposed pulsation of flow rate was varied systematically over a wide range covering inner scale dimensionless frequency from 0.004 to 0.04. In terms of outer scale frequency the corresponding values varied from 1.8 to 18. In addition, effects of changing the mean flow rate and the amplitude of flow rate pulsation were studied. Radial distributions of the amplitude of the modulation of ensemble-averaged axial velocity and the axial and radial components of RMS turbulent fluctuation, and their phase shifts relative to the imposed flow pulsation, are presented for conditions which include the , and ranges. These add to and reinforce the body of information available from earlier experimental work and have enabled useful progress to be made in evaluating and validating approaches used for correlating such data. By relating observed behaviour to the fundamental processes of turbulence production, redistribution of turbulence energy between its components and radial propagation of turbulence, a good understanding of the results has been obtained.
This study looks at MHD natural convection flow and heat transfer in a laterally heated enclosure with an off-centred partition. Governing equations in the form of vorticity–stream function formulation are solved using the polynomial differential quadrature (PDQ) method. Numerical results are obtained for various values of the partition location, Rayleigh, Prandtl and Hartmann numbers. The results indicate that magnetic field significantly suppresses flow, and thus heat transfer, especially for high Rayleigh number values. The results also show that the -directional magnetic field is more effective in damping convection than the -directional magnetic field, and the average heat transfer rate decreases with an increase in the distance of the partition from the hot wall. The average heat transfer rate decreases up to 80% if the partition is placed at the midpoint and an -directional magnetic field is applied. The results also show that flow and heat transfer have little dependence on the Prandtl number.
Pulsatile turbulent flow characteristics in an axisymmetric aortic aneurysm (AA) model were analyzed numerically using a simulated physiological waveform. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid–structure interaction (FSI) analysis was utilized in this work. We investigated the effects of turbulent flow characteristics on the distribution of wall stress and flow patterns in AA models. Wall stress distributions were calculated by computational solid stress (CSS) model, which ignores the effect of the blood flow, and the FSI model that takes into account flow and solid mechanics. Our results showed that peak wall stress and peak deformation were found to occur shortly after peak systolic flow in the FSI model and at the peak luminal pressure condition in the CSS model. Further, CSS model underestimated wall stress calculations when compared to the FSI model. There were also significant differences in the structure of flow fields between the flexible and rigid wall aneurysm models. Contour plots of kinetic energy dissipation and the application of the Kolmogorov microscale suggest that the conditions that result in red blood cell damage and platelet activation most likely occur in the near-wall region of AA during turbulent flow.
An analytical model for a time dependent two dimensional flow around a moving profile is developed. The model is suitable for fast aerodynamic and aeroelastic coupling calculations. It determines the inviscid pressure distribution in the vicinity of one blade and the force on the blade in arbitrary two dimensional motion. The method is more flexible than previous analysis: it can represent any profile, pitching motion and blade attachment position. The method is based on conformal mapping techniques and Laurent's series decomposition and is faster and more accurate than standard panel methods. A main idea is to directly treat the singularities of the flow in a mapped plane where any geometrical plane is simplified to a circle. The vorticity is assumed to be shed in the form of a continuous vortex sheet near the trailing edge.
We consider laminar high-Reynolds-number flow through a long finite-length planar channel, where a segment of one wall is replaced by a massless membrane held under longitudinal tension. The flow is driven by a fixed pressure difference across the channel and is described using an integral form of the unsteady boundary-layer equations. The basic flow state, for which the channel has uniform width, exhibits static and oscillatory global instabilities, having distinct modal forms. In contrast, the corresponding local problem (neglecting boundary conditions associated with the rigid parts of the system) is found to be convectively, but not absolutely, unstable to small-amplitude disturbances in the absence of wall damping. We show how amplification of the primary global oscillatory instability can arise entirely from wave reflections with the rigid parts of the system, involving interacting travelling-wave flutter and static-divergence modes that are convectively stable; alteration of the mean flow by oscillations makes the onset of this primary instability subcritical. We also show how distinct mechanisms of energy transfer differentiate the primary global mode from other modes of oscillatory instability.
Galloping is a well-known type of aeroelastic instability, but still difficult to predict as the relevant experimental data must first be obtained. Available information on non-rectangular cross-sections is scarce and non-systematic. The purpose of the present paper is to add new information gathered through static wind tunnel experiments. The effects of cross-sectional shape on the transverse galloping stability (according to the Glauert–Den Hartog criterion for galloping instability) of biconvex and rhomboidal cross-section bodies have been systematically analyzed. Measuring the aerodynamic coefficients and the pressure distributions along the body surfaces permits a better understanding of the galloping phenomenon and how the aerodynamic characteristics of the bodies evolve when changing parametrically the cross-section geometry from the known-case of the flat plate to the also known square or circular prisms. As a result of these investigations the potential unstable zones in the angle of attack – cross-section aspect ratio plane ( ) are identified.
The purpose of this work is to present a new numerical scheme for multi-material fluid flows in dimension . It is a totally Eulerian conservative scheme that allows to compute sharp interfaces between non-miscible fluids. The underlying flux scheme in single material cells is the so-called FVCF scheme, whereas interface reconstruction and directional splitting is used in multi-material cells. One of the novelty of our approach is the introduction of the concept of “condensate” which allows to handle mixed cells containing two or more materials. Moreover, it has been designed to allow free sliding of materials on each others, thanks to a material volume centered computation of variables in mixed cells.
The motion of saline gravity currents propagating horizontally in a tank of rectangular upper cross section and lower V-shaped valley is investigated both by lock-exchange experiments and a box model. The experiments were performed for equal depths of heavy and light fluid on both sides of the lock gate. The density ratio of the heavy fluid to the light fluid was in the range 1.04–1.13 and the lock height to length aspect ratios ranged from 0.5 to 1.6. We show that a box model with the Froude number of the head defined using the distance from the top of the current to the bottom of the valley predicts the position of the head in close agreement with the experiments. The presence of the valley results in three major differences in the gravity current compared to that flowing along a flat bottom. These are (a) the front of the current is approximately parabolic with radius of curvature proportional to the initial depth of the current, (b) for sufficiently large time , the velocity of the current in the V-shaped valley varies as compared to in the flat bottom case, and (c) the width of the current in the V-shaped valley decreases with time according to . Based on the box model, we predict that the steeper the flanks of the valley the faster the flow.
In this paper we study the motion of three linked ellipses moving through a viscous fluid in two dimensions. The angles between the ellipses change with time in a specified manner (the gait) and the resulting time varying configuration is similar to the appearance of a swimming leech. We simulate the motion using the particle method Smoothed Particle Hydrodynamics (SPH) which we test by convergence studies and by comparison with the inviscid results of Kanso et al. (2005) and the viscous results of Eldredge (2006, 2007, 2008) . We determine how the average speed and power output depends on the amplitude and oscillation frequency of the gait. We find that the results fit simple scaling rules which can be related to the analytical results of G.I. Taylor for the swimming of long narrow animals (1952). We apply our results to estimate the speed of a swimming leech with reasonable accuracy, and we determine the minimum power required to propel the bodies at a specified average speed.
The flow field, generated by an oscillating pressure gradient close to a rough wall, is investigated by means of direct numerical simulations of Navier–Stokes and continuity equations. The wall roughness consists of semi-spheres regularly placed on a plane wall. A comparison of the obtained results with the experimental measurements of Keiller and Sleath [D.C. Keiller, J.F.A. Sleath, Velocity measurements close to a rough plate oscillating in its own plane, J. Fluid Mech. 73 (1976) 673–691] supports the numerical findings. As in Keiller and Sleath [D.C. Keiller, J.F.A. Sleath, Velocity measurements close to a rough plate oscillating in its own plane, J. Fluid Mech. 73 (1976) 673–691], a secondary peak in the streamwise velocity component is observed close to flow reversal and the peak is shown to be generated by the coherent vortex structures which are shed by the roughness elements. The flow is found to be dominated by the shear layers which form at the top of the roughness elements during the accelerating phases of the cycle and by the horse-shoe vortices which form close to the base of the semi-spheres. The dynamics of the shear layers and of the horse-shoe vortices is found to have a relevant influence on the pressure distribution and on the force exerted by the fluid on the roughness elements. The obtained results shed light to the mechanism by which the sediment is picked-up from the bottom by the action of sea waves.
The strongly-modified turbulence statistics of Rayleigh–Bénard convection subject to various rotation rates is addressed by numerical investigations. The flow is simulated in a domain with periodic boundary conditions in the horizontal directions, and confined vertically by parallel no-slip isothermal walls at the bottom and top. Steady rotation is applied about the vertical. The rotation rate, or equivalently the Rossby number , is varied such that ranges from ∞ (no rotation) to (strong rotation). Two different Rayleigh numbers are used, viz. and , characterising buoyancy due to temperature differences. The Prandtl number , close to the value for air. Horizontally averaged statistics show that rotation reduces the turbulence intensity, although probability density functions clearly show that considerable (preferably cyclonic) vorticity is added to the flow by the Ekman boundary layers on the solid walls. Rotation changes the balance of the turbulent kinetic energy budget. It is found that for a range of rotation rates the buoyant production is higher than without rotation. Therefore, at appropriate rotation rates the heat flux through the fluid layer is increased relative to the non-rotating case. At sufficiently rapid rotation, however, the heat flux through the fluid layer is strongly attenuated.
In a previous study [D. Dutykh, F. Dias, Viscous potential free-surface flows in a fluid layer of finite depth, C. R. Acad. Sci. Paris, Ser. I 345 (2007) 113–118] we presented a novel visco-potential free-surface flows formulation. The governing equations contain local and nonlocal dissipative terms. From physical point of view, local dissipation terms come from molecular viscosity but in practical computations, rather eddy viscosity should be used. On the other hand, nonlocal dissipative term represents a correction due to the presence of a bottom boundary layer. Using the standard procedure of Boussinesq equations derivation, we come to nonlocal long wave equations. In this article we analyze dispersion relation properties of proposed models. The effect of nonlocal term on solitary and linear progressive waves attenuation is investigated. Finally, we present some computations with viscous Boussinesq equations solved by a Fourier type spectral method.
High-Reynolds number lid-driven flow in arc-shape cavities with different cross sections is considered up to . The unsteady streamfunction–vorticity transport formulation is adopted and a second order finite difference numerical method is applied to computational grids generated by body-fitted coordinate transformation. The effects of aspect or arc angle ratio , on the formation and growth of vortical structures, as well as on the existence and development of periodic solutions are discussed. It is found that for the case where , only a secondary vortex appears in addition to a primary core vortex, for stationary solutions, whereas tertiary and quaternary vortices appear for the cases where , near the curved wall. Periodic solutions at high Reynolds numbers are observed when ; while transient oscillations decay in time for .