Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel

The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.     

Experimental study of heat flux in mixed convective flow over solid waves

In this experimental study, we address transport processes in a mixed convective flow over a heated wavy surface. Therefore, we combine digital particle image velocimetry (DPIV) and two-color planar laser induced fluorescence (PLIF) to simultaneously measure the velocity and temperature field. For this, we propose to use the dye combination Rhodamine B and Rhodamine 110, both excited with the Nd:YAG laser also used for the PIV measurements. We investigate the influence of mixed convection over a wavy surface on the velocity field, turbulence statistics, the temperature field and the heat flux. By computing these quantities we find a correlation between the maximum in the Reynolds stress profiles and the components of the heat flux vector, thus regions of maximum momentum and scalar transport coincide. In addition, we apply a proper orthogonal decomposition (POD) to extract the most dominant flow structures in a measurement plane above the wavy surface. This first POD mode is identified as streamwise-oriented, counter-rotating vortices whose spanwise scaling is also correlated with the maximum of heat flux.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

A mathematical study is developed for the electro-osmotic flow of a nonNewtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer(EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelen...     

Particle image velocimetry measurements of a backward-facing step flow

Particle image velocimetry (PIV) measurements were carried out on a backward-facing step flow at a Reynolds number of Re_h=U_Xh/9=4,660 (based on step height and freestream velocity). In-plane velocity, out-of-plane vorticity, Reynolds stress and turbulent kinetic energy production measurements in the x-y and x-z planes of the flow are presented. Proper orthogonal decomposition was performed on both the fluctuating velocity and vorticity fields of the x-y plane PIV data using the method of snapshots. Low-order representations of the instantaneous velocity fields were reconstructed using the velocity modes. These reconstructions provided insight into the contribution that the various length scales make to the spatial distribution of mean and turbulent flow quantities such as Reynolds stress and turbulent kinetic energy production. Large scales are found to contribute to the Reynolds stresses and turbulent kinetic energy production downstream of reattachment, while small scales contribute to the intense Reynolds stresses in the vicinity of reattachment.     

Propagation of shear-layer structures in the near-wall region of a turbulent boundary layer

Two non-intrusive techniques, namely laser Doppler anemometry (LDA) and the electrochemical method, have been used for simultaneous measurements of the instantaneous streamwise velocity (U) and longitudinal wall shear stress (S), evaluated in a zero pressure gradient turbulent boundary layer. The space-time correlation between the fluctuating velocity and shear stress suggests that the coherent flow structures are propagated (i) under a slight angle of 5° in the near-wall region and (ii) at an average angle of 15.5° for y⁺>30. It is shown that the time shift obtained from the correlation between the LDA and the electrochemical signals is due to the dynamic behaviour of the electrodiffusion probe, but also to the leaning character of the coherent structures.     

Exact solutions for the incompressible viscous fluid of a porous rotating disk flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions with suction and injection through the surface included. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the exact velocity equations obtained. Making use of this solution, analytical formulas corresponding to the permeable wall shear stresses are extracted.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. As a result, exact formulas are obtained for the temperature field which take different forms depending on whether suction or injection is imposed on the wall. The impacts of several quantities are investigated on the resulting temperature field. In accordance with the Fourier‘s heat law, a constant heat transfer from the porous disk to the fluid takes place. Although the influence of dissipation varies, suction enhances the heat transfer rate as opposed to the injection.     

槽道内涡波流场的POD分析

对槽道内涡波流场的瞬态速度矢量场进行了2DPIV测量实验,将2DPIV测量的矢量场数据进行POD分析,根据POD分解的各阶模态的能量比确定了表征涡波流场主导结构的前15阶模态。结果表明,POD分解的前15阶模态发现槽道内涡波流场是由槽道壁面剪切层诱导的涡列以及伴随的波状主流组成;流场中大尺度的涡旋发展为涡对,对波状主流的脉动频率产生影响;根据涡波流场中的驻点和鞍点,获取了流场的大尺度涡对、平均流场以及Helmholtz涡环等明显特征;最后根据POD分解的前15阶模态对槽道内涡波流场进行重组,重组流场表征了槽道内层流状态下波状主流的形态和涡旋共存的涡波结构以及驻点和鞍点的位置处涡旋的变化等主要特征,有效地剔除了PIV测量流场中的随机信息,保留了PIV测量流场的主导特征。     

Local Nusselt number and temperature field in turbulent flow through a heated square-sectioned U-bend

Local heat transfer coefficients and temperature distributions within the fluid for air flow around a 180° square-sectioned bend have been measured. The ratio of bend radius to hydraulic diameter of the duct is 3.35:1 and the flow entering the bend is sensibly fully developed. Measurements of air and wall temperatures span a range of Reynolds numbers from 9.9 × 10³ to 9.2 × 10⁴ with the principal emphasis given to the case of Re ? 5.6 × 10⁴. This Reynolds number and geometric configuration coincide with that of a companion LDA study carried out by Chang et al¹ which provides detailed maps of the mean and turbulent velocity fields. The data show that by 45° into the bend the heat transfer coefficients on the inner convex wall of the bend drop markedly while those on the other walls increase. By 90° the ratio of the heat transfer coefficients at the mid positions of the concave and convex walls is more than 2:1. Nevertheless this ratio is less than would be anticipated from considering two-dimensional flow on weakly curved surfaces. There is a general consistency between the velocity and the temperatyre field data in the heated fluid     

Filtered density function modelling of near-wall scalar transport with POD velocity modes

This paper addresses the problem of heat transfer in the near-wall region of a turbulent channel flow. We investigate the role of coherent eddy structures on the thermal exchange between the solid and fluid materials. In the present approach, the instantaneous velocity field is modelled by means of a low-order dynamical system based on proper orthogonal decomposition (POD) modes while the temperature field is accounted for by using a stochastic filtered density function (FDF) method. A good comparison of results with reference DNS data on mean temperature and on temperature r.m.s. at various Prandtl numbers and for different wall boundary conditions (isotemperature, isoflux, and conjugate heat transfer) is achieved.     

A domain decomposition approach to compute wave breaking (wave‐breaking flows)

A heterogeneous domain decomposition approach is followed to simulate the unsteady wavy flow generated by a body moving beneath a free surface. Attention being focused on complex free surface configurations, including wave‐breaking phenomena, a two‐fluid viscous flow model is used in the free surface region to capture the air–water interface (via a level‐set technique), while a potential flow approximation is adopted to describe the flow far from the interface. Two coupling strategies are investigated, differing in the transmission conditions. Both the adopted approaches make use of the inviscid velocity field as boundary condition in the Navier–Stokes solution. For validation purposes, two different two‐dimensional non‐breaking flows are simulated. Domain decomposition results are compared with both fully viscous and fully inviscid results, obtained by solving the corresponding equations in the whole fluid domain, and with available experimental data. Finally, the unsteady evolution of a steep breaking wave is followed and some of the physical phenomena, experimentally observed, are reproduced. Copyright © 2003 John Wiley & Sons, Ltd.     

Freon R141b flow boiling in silicon microchannel heat sinks: experimental investigation

This paper presents experimental investigations on Freon R141b flow boiling in rectangular microchannel heat sinks. The main aim is to provide an appropriate working fluid for microchannel flow boiling to meet the cooling demand of high power electronic devices. The microchannel heat sink used in this work contains 50 parallel channels, with a 60 × 200 (W × H) μm cross-section. The flow boiling heat transfer experiments are performed with R141b over mass velocities ranging from 400 to 980 kg/(m² s) and heat flux from 40 to 700 kW/m², and the outlet pressure satisfying the atmospheric condition. The fluid flow-rate, fluid inlet/outlet temperature, wall temperature, and pressure drop are measured. The results indicate that the mean heat transfer coefficient of R141b flow boiling in present microchannel heat sinks depends heavily on mass velocity and heat flux and can be predicted by Kandlikar’s correlation (Heat Transf Eng 25(3):86–93, 2004). The two-phase pressure drop keeps increasing as mass velocity and exit vapor quality rise.     

Fluid flow due to combined convection in lid-driven enclosure having a circular body

The present work is aimed to study mixed convection heat transfer characteristics for a lid-driven air flow within a square enclosure having a circular body. Flows are driven by the left lid, which slides in its own plane constant velocity. This wall is isothermal and it moves up or down in y direction while the other walls remain stationary. The horizontal walls are adiabatic. The cavity is differentially heated and the left wall is maintained at a higher temperature than the right wall. Three different temperature boundary conditions were applied for the inner cylinder as adiabatic, isothermal or conductive. The computation is carried out for wide ranges of Richardson numbers, diameter of inner cylinder and center and location of the inner cylinder. It was found that the most effective parameter on flow field and temperature distribution is the orientation of the moving lid. The circular body can be a control parameter for heat and fluid flow. An interesting obtained result that the thermal conductivity becomes insignificant for small values of diameter of the circular body.     

Comparison of molecular tagging velocimetry data and direct simulation Monte Carlo simulations in supersonic micro jet flows

We present results of a combined experimental computational study of free jet flow produced by a 1 mm (height)ǹ mm (span) nominally Mach 2 supersonic jet. Two-dimensional maps of u_x, the component of velocity parallel to the principal flow axis, are obtained experimentally, by acetone molecular tagging velocimetry (MTV), and computationally, by the direct simulation Monte Carlo (DSMC) method, at a stagnation pressure and temperature of 10 torr and 300 K, respectively. In all cases, direct comparison of the experimental data and the predictions from DSMC showed excellent agreement, with only minor deviations which, in most cases, can be ascribed to either the inherent uncertainty in the MTV or small uncertainties in the measured wall pressures.     

Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects

The problem of steady, laminar, thermosolutal Marangoni convection flow of an electrically-conducting fluid along a vertical permeable surface in the presence of a magnetic field, heat generation or absorption and a first-order chemical reaction effects is studied numerically. The general governing partial differential equations are converted into a set of self-similar equations using unique similarity transformations. Numerical solution of the similarity equations is performed using an implicit, iterative, tri-diagonal finite-difference method. Comparisons with previously published work is performed and the results are found to be in excellent agreement. Approximate analytical results for the temperature and concentration profiles as well as the local Nusselt and sherwood numbers are obtained for the conditions of small and large Prandtl and Schmidt numbers are obtained and favorably compared with the numerical solutions. The effects of Hartmann number, heat generation or absorption coefficient, the suction or injection parameter, the thermo-solutal surface tension ratio and the chemical reaction coefficient on the velocity, temperature and concentration profiles as well as quantitites related to the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are presented in graphical and tabular form and discussed. It is found that a first-order chemical reaction increases all of the wall velocity, Nusselt and Sherwood numbers while it decreases the mass flow rate in the boundary layer. Also, as the thermo-solutal surface tension ratio is increased, all of the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are predicted to increase. However, the exact opposite behavior is predicted as the magnetic field strength is increased.     

Influence of lateral mass flux on mixed convection heat and mass transfer over inclined surfaces in porous media

 The effect of lateral mass flux on mixed convection heat and mass transfer in a saturated porous medium adjacent to an inclined permeable surface is analyzed. A similarity solution is obtained when surface temperature and concentration, free stream velocity and injection/suction velocity of fluid are prescribed as power functions of distance from the leading edge. The cases when the flow and buoyancy forces are in the same and opposite directions are discussed both for aiding and opposing buoyancy effects. The governing parameters are the mixed convection parameter Gr, the Lewis number Le, the buoyancy ratio N, the lateral mass flux parameter f _w, representing the effects of injection or withdrawal of fluid at the wall, and λ which specifies three cases of the inclined plate. The interactive effect of these parameters on heat and mass transfer rates are presented. It is observed that the diffusion ratio (Le) has a more pronounced effect on concentration field than on flow and temperature fields. It is found that the rates of heat and mass transfer increase with suction and decrease with injection of the fluid. Received on 31 August 2000 / Published online: 29 November 2001     

Quantitative temperature imaging in gas-phase turbulent thermal convection by laser-induced fluorescence of acetone

In this paper, an acetone planar laser-induced fluorescence (PLIF) technique for nonintrusive temperature imaging is demonstrated in gas-phase (Pr = 0.72) turbulent Rayleigh-Bénard convection at Rayleigh number Ra = 1.3᎒⁵. The PLIF technique provides quantitative spatially correlated temperature data without the flow intrusion or time lag associated with physical probes, and without the significant path averaging that plagues most optical heat-transfer diagnostic tools, such as the Mach-Zehnder interferometer, thus making PLIF an attractive choice for quantitative thermal imaging in easily perturbed, complex three-dimensional flow fields. The "instantaneous" (20-ns integration time) thermal images presented have a spatial resolution of 176쐀아 µm and a single-pulse temperature measurement precision of - 2.5 K, or 2.5% of the total temperature difference. These images represent a two-dimensional slice through a complex three-dimensional flow, allowing for thermal structure of the turbulence to be quantified. Statistics such as the horizontally averaged temperature profile, root-mean square (rms) temperature fluctuation, two-point spatial correlations, and conditionally averaged plume structures are computed from an ensemble of 100 temperature images. The profiles of the mean temperature and rms temperature fluctuation are in good agreement with previously published data, and the results obtained from the two-point spatial correlations and conditionally averaged temperature fields show the importance of large-scale coherent structures in this turbulent flow.     

Transient natural convection between concentric and vertically eccentric spheres with mixed boundary conditions

Transient analysis has been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with constant heat flux on the inner wall and a specified isothermal temperature on the outer wall. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. The alternating direction implicit method and the successive over-relaxation techniques are applied to solve the finite difference form of governing equations. A physical model is introduced which accounts for the effects of fluid buoyancy as well as eccentricity of the outer sphere. Transient solutions of the entire flow field are obtained for a range of modified Rayleigh number (10³<Ra?<5×10⁵), for a Prandtl number of 0.7 and a radius ratio of 2.0, with the outer sphere near the top and bottom of the inner sphere (ε=±0.625). Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the modified Rayleigh number and the eccentricity of the spherical annulus. The results of average Nusselt numbers are also compared with the results obtained for flow between two isothermal spheres.     

POD analysis of flow structures in a scale model of a ventilated room

Measurements with particle image velocimetry have been carried out in a scale model of the Annex 20 room. Data were taken in a plane near the inlet. The flow consisted of a wall jet (Re=5,000) and a low-velocity region below the jet. POD was used to analyze dominant flow structures. The analysis showed that the flow some of the time has flow structures very different from the mean velocity field. A time-resolved data series was projected onto the orthonormal basis derived from the POD for analysis of the time variation of the POD amplitudes.     

Entropy generation and natural convection in square cavities with wavy walls

The aim of the present work is to study the entropy generation in the natural convection process in square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the hot wall geometry affects notably the heat transfer rate in the cavity. It has been found in the present numerical study that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh numbers. The study is performed for Rayleigh numbers 10³ < Ra < 10⁵, irreversibility coefficients 10^?4 < φ < 10^?2, and Prandtl numbers Pr = 0.71. The total entropy generation is found to increase with increasing undulation number.