Analysis of turbulent heat transfer from sinusoidal profile finned dissipators

 In the present work the effectiveness of thermal dissipators cooled by a fluid in turbulent flow is studied by varying the fins spacing and shape. The profile of the fin is described by a sinusoidal function depending on two parameters that define its amplitude and number of oscillations. The velocity distribution in the fluid, and the temperature distribution in the dissipator and in the fluid are determined with the help of a finite element method. The model allows to study the variations of the heat transfer coefficient due to the fluid dynamic conditions imposed by the fin profile. Lastly, a combination of geometrical parameters is proposed, which yields the best dissipator performance under particular conditions. Received on 29 June 2000     

Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel

The peristaltic flow of a Jeffrey fluid in an asymmetric channel is studied under long wavelength and low Reynolds number assumptions. The fluid is electrically conducting by a transverse magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Optimum performances of longitudinal convective fins with symmetrical and asymmetrical profiles

In the present work, the heat transfer performance of optimized dissipators with longitudinal fins of asymmetrical cross section is investigated and compared with that of optimized dissipators with symmetrical fins. In particular, the problem of optimizing the shape and the spacing of the fins of a thermal dissipator cooled by a fluid in laminar flow is studied by assigning two different polynomial lateral profiles to the fins. A finite element model is proposed to determine velocity and temperature distributions and is employed in a genetic algorithm to find the dissipator geometries which make the heat transfer coefficient as high as possible under different conditions. Some examples of optimized geometries are finally shown and discussed.     

Effect of viscous dissipation on the heat transfer in sinusoidal profile finned dissipators

In the present work, the efficiency of finned heat dissipators cooled by laminar flow is studied. The analysis is carried out by varying certain sizing parameters in correspondence with different viscous dissipation conditions. The velocity distribution in the fluid and the temperature distribution in the dissipator and in the fluid are determined by means of a finite element method. The model allows to study the variation of the heat transfer coefficient due to the fluid dynamic conditions imposed by the fin profile. Lastly, a comparison between the optimum fin shapes obtained under different viscous dissipation effects is carried out.     

Incompressible low-speed-ratio flow in non-uniform distensible tubes

The fluid flow in distensible tubes is analysed by a finite element method based on an uncoupled solution of the equations of wall motion and fluid flow. Special attention is paid to the choice of proper boundary conditions. Computations were made for sinusoidal flow in a distensible uniform tube with the Womersley parameter α = 5, and a ratio between tube radius and wavelenth from 0·0001 to 0·5. The agreement between the numerical results and Womersley's analytic solution depends on the speed ratio between fluid and wave velocity, and is fair for speed ratios up to 0·05. The analysis of the flow field in a distensible tube with a local inhomogeneity revealed a marked influence of wave phenomena and wall motion on the velocity profiles.     

Optimization of heat transfer through finned dissipators cooled by laminar flow

In the present work, the problem of optimizing the shape and the spacing of the fins of a thermal dissipator cooled by a fluid in laminar flow is studied. For a particular finned conduit, the velocity and temperature distributions on the transversal section are determined with the help of a finite element model and a global heat transfer coefficient is calculated. A polynomial lateral profile is proposed for the fins and the geometry is optimized in order to make the heat transfer coefficient as high as possible with the smallest dimensions or the lowest hydraulic resistance to the flow. The optimum fin profile and spacing, obtained by means of a genetic algorithm, are finally shown for different situations. Increases of 45% are obtained in the heat transfer coefficient referring to the maximum values which can be obtained with rectangular fin profiles.     

Large eddy simulation of separation control over a backward-facing step flow by suction

Separation control over a backward-facing step (BFS) flow by continuous suction was numerically investigated using the turbulence model of large eddy simulation (LES). The effect of suction control on the flow fields was scrutinised by altering the suction flow coefficient, and the results indicate that suction is not only very effective in shortening the reattachment length but also very influential in reducing the tangential velocity gradient and turbulence fluctuations of the reattached flows. With increasing increments of the absolute suction flow coefficient, the effect of suction control is more significant. Furthermore, the detailed flow fields (including the time-averaged stream and velocity fields) and turbulence characteristics (including the time-averaged resolved kinetic energy and RMS velocity) for the BFS models with or without suction are presented to discuss the mechanism of suction control. Comparisons of the time-averaged statistics between the numerical simulations and corresponding experiments are conducted, and it shows that the LES based on the dynamic kinetic energy subgrid-scale model (DKEM) can acquire exact results. Therefore, feasibility of the numerical methods to simulate suction-controlled models is validated.     

Wave interaction with a new type perforated breakwater

In this study examined is the wave interaction with a new modified perforated breakwater, consisting of a perforated front wall, a solid back wall and a wave absorbing chamber between them with a two-layer rock-filled core. The fluid domain is divided into three sub-domains according to the components of the breakwater. Then by means of the matched eigenfunction expansion method, an analytical solution is obtained to assess the hydrodynamic performance of the new structure. An approach based on a step approach method is introduced to solve the complex dispersion equations for water wave motions within two-layer porous media. Numerical results of the present model are compared with previous limiting cases. The effects of rock fill on the reflection coefficient and the horizontal wave force are discussed. The project supported by the Program for Changjiang Scholars and Innovative Research Teams in Universities (IRT0420). The English text was polished by Keren Wang.     

Numerical study of breaking waves by a two‐phase flow model

A two‐phase flow model, which solves the flow in the air and water simultaneously, is presented for modelling breaking waves in deep and shallow water, including wave pre‐breaking, overturning and post‐breaking processes. The model is based on the Reynolds‐averaged Navier–Stokes equations with the k ?ε turbulence model. The governing equations are solved by the finite volume method in a Cartesian staggered grid and the partial cell treatment is implemented to deal with complex geometries. The SIMPLE algorithm is utilised for the pressure‐velocity coupling and the air‐water interface is modelled by the interface capturing method via a high resolution volume of fluid scheme. The numerical model is validated by simulating overturning waves on a sloping beach and over a reef, and deep‐water breaking waves in a periodic domain, in which good agreement between numerical results and available experimental measurements for the water surface profiles during wave overturning is obtained. The overturning jet, air entrainment and splash‐up during wave breaking have been captured by the two‐phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems.Copyright © 2011 John Wiley & Sons, Ltd.     

Propogation of waves in a linear elastic fluid

The non-classical symmetry method is used to determine particular forms of the arbitrary velocity and forcing terms in a linear wave equation used to model the propogation of waves in a linear elastic fluid. The behaviour of solutions derived using the non-classical symmetry method are discussed. Solutions satisfy a given initial profile and wave velocity. For some solutions the arbitrary forcing terms and wave velocity can be written in terms of the initial wave profile. Relationships between the arbitrary forcing, arbitrary velocity and the solution are derived.     

Low-frequency model of a granular medium saturated with a viscous fluid

A mathematical model of a granular medium saturated with a viscous homogeneous fluid is constructed. The steady-state one-dimensional oscillations of cylindrical granules and an incompressible fluid under the action of a plane sonic wave whose length is significantly greater than the cell dimensions are investigated. The steady-state flow of the medium across the cell cross-section and the mean fluid velocity (Darcy’s law) are determined by means of passages to the limits with respect to the frequency and granule mass. The expressions obtained for the soil permeability coefficient under the action of a gravitational hydraulic head are compared with the representations of other authors.     

Nonlinear and viscous effects on wave propagation in an elastic axisymmetric vessel

In this paper, a power series and Fourier series approach is used to solve the governing equations of motion in an elastic axisymmetric vessel with the assumption that the fluid is incompressible and Newtonian in a laminar flow. We obtain solutions for the wave speed and attenuation coefficient, analytically where possible, and show how these differ under a number of different conditions. Viscosity is found to reduce the wave speed from that predicted by linear wave theory and the nonlinear terms to increase the wave speed in comparison to the linear solution. For vessels with a wall stiffness in the arterial range, the reduction in the wave speed due to the viscous terms is approximately 10% and the increase due to the nonlinear terms is approximately 5%. This difference between the linear and nonlinear wave speeds was found to be largely constant irrespective of the number of terms considered in the power series for the velocity profile. The linear wave speed was found to vary weakly with stiffness, whilst the nonlinear wave speed was found to vary significantly with the stiffness, especially at low values of stiffness. The 10% variation in the wave speed due to the viscous terms was found to be constant with wall stiffness whilst the 5% variation due to the nonlinear terms was found to vary with wall stiffness. The importance of the number of terms considered in the power series is discussed showing that only a relatively small number is required in the viscous case to obtain accurate results.     

Simulation and measurement of turbulent heat transfer in a channel with a surface-mounted rectangular heated block

Present study numerically and experimentally investigates the turbulent forced convective flow over a heated block mounted on one principal wall of an adiabatic channel. In the computation, thek-?, low-Reynolds-number, two-equation model was adopted for the turbulence closure. In the experiment, the flow measurement was performed by the laser Doppler velocimetry and the mass transfer measurement was carried out via the naphthalene sublimation technique. By virtue of the analogy between heat and mass transfer, the results could then be converted to predict the heat transfer coefficient. The effects of the Reynolds number and the aspect ratio of the block on heat transfer and fluid flow are thoroughly investigated. Distributions of the velocity and the turbulent kinetic energy are presented to gain an insight into the influence of the fluid flow on the heat transfer from the block. The Nusselt number hump is found on every face of the block, which is attributed to the separating bubble there. It is worth noting that the Nusselt number hump is located near the reattachment point of the separating bubble. In the absence of the separating bubble, the Nusselt number decreases or increases monotonously. Comparisons between numerical and experimental results of the local velocity and the heat transfer coefficient show reasonable agreement.     

Experimental and numerical investigation on the damping effect of net cages in waves

A series of laboratory experiments were conducted to investigate the damping effect of net cages in waves. The wave transmission coefficient of the net cage was investigated with different wave periods, wave heights, numbers of net cages, net solidities, measurement positions, geometrical shapes of the net cage and Reynolds numbers. The experimental results show that the net cage has noticeable influence on wave propagation and the damping effect of net cages has a close relationship with many parameters. For multiple net cages, the transmission coefficient tends to increase as the wave period increases. The transmission coefficient of net cages decreases with increasing wave height. As the number of net cages increases, the wave transmission coefficient will decrease gradually. The damping effect of net cages on wave propagation tends to increase with increasing net solidity. The measurement position has an effect on the value of wave transmission coefficient. For net cages with different geometrical shapes, the circular net cage has more noticeable damping effect than the square net cage. A numerical model is introduced to simulate the interaction between waves and net cages with the fishing net treated as the porous media fluid model. The wave transmission coefficient downstream from net cages shows good agreement between experimental and numerical results. The study will contribute to understanding of the damping effect of a large fish farm on wave propagation.     

Analytical and numerical studies for Seiches in a closed basin with bottom friction

A standing wave oscillation in a closed basin, known as a seiche, could cause destruction when its period matches the period of another wave generated by external forces such as wind, quakes, or abrupt changes in atmospheric pressure. It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy, resulting in damages around the area. One condition that might restrict the resonance from occurring is when the bottom friction is present. Therefore, a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena. The study will be conducted for several closed basin shapes. The model will be solved analytically and numerically in order to determine the natural resonant period of the basin, which is the period that can generate a resonance. The computational scheme proposed to solve the model is developed using the staggered grid finite volume method. The numerical scheme will be validated by comparing its results with the analytical solutions. As a result of the comparison, a rather excellent compatibility between the two results is achieved. Furthermore, the impacts that the friction coefficient has on the resonance phenomena are evaluated. It is observed that in the prevention of resonances, the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin. In addition, non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.     

Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure

The shedding and evolution of the vortical structures generated by a solitary wave propagating over a submerged cylindrical structure are investigated experimentally and numerically. The cylindrical structure consists of two concentric cylinders and represents a simplified model for an offshore submerged intake structure typically used in coastal power plants. Flow visualization by dye injection is used to identify the dominant vortical structures near the structure. The flow visualization results show an unexpected flow reversal that causes shedding of secondary vortical structures. The experimental results are used to check a three-dimensional volume of fluid-large eddy simulation (VOF-LES) numerical model. The VOF-LES model is then used to further study the flow structure. A total of six dominant vortical structures generated by the wave motion are identified, followed by two more generated by the flow reversal. In summary, this paper provides the vorticity evolution for a complex fluid–structure interaction problem and a three-dimensional numerical simulation tool has also been validated, which can be extended to study more complex geometries and wave conditions.     

Attenuated Wave Field in Fluid-Saturated Porous Medium with Excitations of Multiple Sources

This research addresses the investigation of an elastic wave field in a homogeneous and isotropic porous medium which is fully saturated by a Newtonian viscous fluid. A new methodology is developed for describing the wave field in the medium excited by multiple energy sources. To quantify the relative displacements between the fluid and solid of the medium, the governing equations of the elastic wave propagation are derived in the form of displacements specially. The velocities and attenuation of the waves are considered as functions of viscosity and frequency. Making use of the Hankel function and the moving-coordinate method, a model of the wave motion with multiple cylindrical wave sources is built. Making use of the model established in this research, the relative displacement between the fluid and the solid can be quantified, and the wave field in the porous media can then be determined with the given energy sources. Numerical simulations of cylindrical waves from multiple energy sources propagating in the porous medium saturated by viscous fluid are performed for demonstrating the practicability of the model developed.     

Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented.     

A unified view of energetic efficiency in active drag reduction,thrust generation and self-propulsion through a loss coefficient with some applications

An analysis of the energy budget for the general case of a body translating in a stationary fluid under the action of an external force is used to define a power loss coefficient. This universal definition of power loss coefficient gives a measure of the energy lost in the wake of the translating body and, in general, is applicable to a variety of flow configurations including active drag reduction, self-propulsion and thrust generation. The utility of the power loss coefficient is demonstrated on a model bluff body flow problem concerning a two-dimensional elliptical cylinder in a uniform cross-flow. The upper and lower boundaries of the elliptic cylinder undergo continuous motion due to a prescribed reflectionally symmetric constant tangential surface velocity. It is shown that a decrease in drag resulting from an increase in the strength of tangential surface velocity leads to an initial reduction and eventual rise in the power loss coefficient. A maximum in energetic efficiency is attained for a drag reducing tangential surface velocity which minimizes the power loss coefficient. The effect of the tangential surface velocity on drag reduction and self-propulsion of both bluff and streamlined bodies is explored through a variation in the thickness ratio (ratio of the minor and major axes) of the elliptical cylinders.