Showing papers in "International Journal of Heat and Fluid Flow in 2000"

Heat transfer enhancement of nanofluids

Abstract: This paper presents a procedure for preparing a nanofluid which is a suspension consisting of nanophase powders and a base liquid. By means of the procedure, some sample nanofluids are prepared. Their TEM photographs are given to illustrate the stability and evenness of suspension. The theoretical study of the thermal conductivity of nanofluids is introduced. The hot-wire apparatus is used to measure the thermal conductivity of nanofluids with suspended copper nanophase powders. Some factors such as the volume fraction, dimensions, shapes and properties of the nanoparticles are discussed. A theoretical model is proposed to describe heat transfer performance of the nanofluid flowing in a tube, with accounting for dispersion of solid particles.

Strategies for turbulence modelling and simulations

Abstract: This is an attempt to clarify and size up the many levels possible for the numerical prediction of a turbulent flow, the target being a complete airplane, turbine, or car. Not all the author’s opinions will be accepted, but his hope is to stimulate reflection, discussion, and planning. These levels still range from a solution of the steady Reynolds-Averaged Navier‐Stokes (RANS) equations to a Direct Numerical Simulation, with Large-Eddy Simulation in between. However recent years have added intermediate strategies, dubbed ‘‘VLES’’, ‘‘URANS’’ and ‘‘DES’’. They are in experimental use and, although more expensive, threaten complex RANS models especially for bluA-body and similar flows. Turbulence predictions in aerodynamics face two principal challenges: (I) growth and separation of the boundary layer, and (II) momentum transfer after separation. (I) is simpler, but makes very high accuracy demands, and appears to give models of higher complexity little advantage. (II) is now the arena for complex RANS models and the newer strategies, by which time-dependent three-dimensional simulations are the norm even over two-dimensional geometries. In some strategies, grid refinement is aimed at numerical accuracy; in others it is aimed at richer turbulence physics. In some approaches, the empirical constants play a strong role even when the grid is very fine; in others, their role vanishes. For several decades, practical methods will necessarily be RANS, possibly unsteady, or RANS/LES hybrids, pure LES being unaAordable. Their empirical content will remain substantial, and the law of the wall will be particularly resistant. Estimates are oAered of the grid resolution needed for the application of each strategy to full-blown aerodynamic calculations, feeding into rough estimates of its feasibility date, based on computing-power growth. ” 2000 Elsevier Science Inc. All rights reserved.

Accurate computations of the laminar flow past a square cylinder based on two different methods : lattice-Boltzmann and finite-volume

Abstract: The confined flow around a cylinder with square cross-section mounted inside a plane channel (blockage ratio B=1/8) was investigated in detail by two entirely different numerical techniques, namely a lattice-Boltzmann automata (LBA) and a finite-volume method (FVM). In order to restrict the approach to 2D computations, the largest Reynolds number chosen was Re=300 based on the maximum inflow velocity and the chord length of the square cylinder. The LBA was built up on the D2Q9 model and the single relaxation time method called the lattice-BGK method. The finite-volume code was based on an incompressible Navier–Stokes solver for arbitrary non-orthogonal, body-fitted grids. Both numerical methods are of second-order accuracy in space and time. Accurate computations were carried out on grids with different resolutions. The results of both methods were evaluated and compared in detail. Both velocity profiles and integral parameters such as drag coefficient, recirculation length and Strouhal number were investigated. Excellent agreement between the LBA and FVM computations was found.

A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow

Abstract: A thorough numerical investigation of high Reynolds number ( Re =140,000) circular cylinder flow was performed based on large eddy simulation (LES). The objective was to evaluate the applicability of LES for practically relevant high- Re flows and to investigate the influence of subgrid scale modeling and grid resolution on the quality of the predicted results. Because the turbulent von Karman vortex street past circular cylinders involves most of the characteristic features of technical applications, it is an ideal test case for this purpose. Based on a parallelized finite-volume Navier–Stokes solver, computations were carried out on a series of grids applying both the Smagorinsky and the dynamic subgrid scale model. The simulations yielded information on the time-averaged flow field, the resolved Reynolds stresses and integral parameters such as drag coefficient, recirculation length and Strouhal number. The results were analyzed in detail and compared with experimental data. In general, the LES results agreed fairly well with the experimental data, especially in the near wake. Owing to the coarse resolution in the far wake, larger deviations were observed here. As expected, the importance of the subgrid scale model significantly increased for the high- Re case in comparison with a low- Re case predicted earlier. A critical issue for LES is grid refinement which did not automatically lead to an improved agreement between the predicted results and the experimental measurements. Possible explanations are offered in the paper.

Pressure velocity coupling in a subsonic round jet

Abstract: An experimental investigation involving simultaneous measurements of the radial distribution of velocity within the shear layer of a jet and the longitudinal distribution of pressure surrounding a jet is performed. The use of two statistical approaches (proper orthogonal decomposition, POD and linear stochastic estimation, LSE) permits the analysis, in terms of vortical structures, of the pressure fluctuations surrounding the jet. These structures are found to be responsible for the far-field noise emission. This method thus seems promising for providing a “structural model” of the turbulent flow field.

Experiments on turbulent natural convection in an enclosed tall cavity

Abstract: Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth). They were performed with temperature differentials between the vertical plates of 19.6°C and 39.9°C, giving Rayleigh numbers based on the width of 0.86×106 and 1.43×106. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small. A previously used experimental rig has been modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent temperature and velocity variations within the cavity have been measured, together with heat fluxes and turbulent shear stresses. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates. The results provide a greatly improved benchmark for the testing of turbulence models in this low turbulence Reynolds number flow.

Experimental study on microbubbles and their applicability to ships for skin friction reduction

Abstract: Microbubble experiments were carried out using a circulating water tunnel specially designed for microbubble experiments. The tunnel has a long test section, which enables measurements on the persistence of the skin friction reduction effect by microbubbles in the streamwise direction. It also has a damp tank, which enables continuous testing of microbubbles. Skin friction was measured using a skin friction sensor, which is a force gauge type of 250 N/m2 full scale, and skin friction reduction by microbubbles up to 40% was obtained. The local void ratio in the bubble condition was measured by putting a suction tube in the test section, and it was obtained that the local void ratio close to the wall has strong correlation with skin friction reduction. The scale effect and the applicability of microbubbles to full scale ships was discussed, based on experimental results using a long flat plate.

The effect of inclination on the heat transfer between a flat surface and an impinging two-dimensional air jet

Abstract: An experimental study was performed to determine the effect of the inclination of an impinging two-dimensional air jet on the heat transfer from a uniformly heated flat plate. The impingement surface was a stainless steel plate of the same width as the jet nozzle. Local Nusselt numbers were determined as a function of three parameters: (a) inclination angle of the air jet relative to the plate in the range of 90–40°, (b) nozzle exit-to-plate spacing ( z / D ) in the range of 4–12 and (c) Reynolds number based on the hydraulic diameter of the slot nozzle in the range of 4000–12 000 (corresponding to an exit jet velocity from 6.3 to 18.7 m/s). The results are presented in the form of graphs showing the variation of the local Nusselt number as a function of these parameters. The region of maximum heat transfer shifts towards the uphill side of the plate and the maximum Nusselt number decreases as the inclination angle decreases. The location of the maximum heat transfer region appears to fall between 0 and 3 D uphill from the geometrical impingement point, and was found to be insensitive to the Reynolds number in the range used in this study. For low values of inclination angle, the local Nusselt number on the uphill side from the maximum heat transfer point was insensitive to jet exit-to-plate spacing. Correlations are proposed to predict the local Nusselt number as a function of x / D , z / D , θ and Re .

Statistical simulation of particle deposition on the wall from turbulent dispersed pipe flow

Abstract: Deposition of particles towards the wall from a turbulent dispersed flow in a vertical pipe has been studied numerically. A fully developed turbulent pipe flow of air is chosen as the primary flow, and it is represented by the law-of-the-wall relations and the average turbulence statistics obtained from a direct numerical simulation reported in the literature. Trajectories and velocities of the particles are calculated, using a one-way coupling Lagrangian eddy–particle interaction model. Thousands of individual particles (typically 920 kg/m3 in density) of various diameters (2.0–68.5 μm) are released in the represented flow, and deposition velocities are evaluated. It is shown that the deposition velocities predicted are in good agreement with experimental data available in the literature. The influence of some forces in the particle equation of motion (i.e., the Saffman lift force, the centrifugal force, the conservation of angular momentum and the buoyancy force) on the prediction of the deposition velocities is examined. Also examined is the influence of the inlet particle concentration profile, on which little attention has been paid so far. The unique phenomenon of ‘near-wall build-up’ of small particles, which has been reported in some previous simulations and experiments, was also observed in the present simulation while the result for very small particles (τp+<3) should be accepted with reservation due to their possible spurious build-up associated with the random-walk approach.

A note on the solution of conjugate heat transfer problems using SIMPLE-like algorithms

Abstract: Conjugate conduction and convection heat transfer problems are often solved numerically in a unitary computational domain containing both the solid and fluid regions. When SIMPLE-like algorithms are employed in the computation, one has to pay close attention to the peculiarity of the energy equation or to the problem how to ensure the continuity of heat flux at the fluid–solid interface. For this reason, two approaches, i.e., the ‘pseudo-density’ method and the ‘pseudo-solid-specific-heat’ method, are suggested, respectively, for the solution of the energy equation, and typical computed results are presented.

Unsteady laminar hydromagnetic fluid–particle flow and heat transfer in channels and circular pipes

Abstract: The problem of unsteady laminar flow and heat transfer of a particulate suspension in an electrically conducting fluid through channels and circular pipes in the presence of a uniform transverse magnetic field is formulated using a two-phase continuum model. Two different applied pressure gradient (oscillating and ramp) cases are considered. The general governing equations of motions (which include such effects as particulate phase stresses, magnetic force, and finite particle-phase volume fraction) are non-dimensionalized and solved in closed form in terms of Fourier cosine and Bessel functions and the energy equations for both phases are solved numerically since they are non-linear and are difficult to solve analytically. Numerical solutions based on the finite-difference methodology are obtained and graphical results for the fluid-phase volumetric flow rate, the particle-phase volumetric flow rate, the fluid-phase skin-friction coefficient and the particle-phase skin-friction coefficient as well as the wall heat transfer for plane and axisymmetric flows are presented and discussed. In addition, these numerical results are validated by favorable comparisons with the closed-form solutions. A comprehensive parametric study is performed to show the effects of the Hartmann magnetic number, the particle loading, the viscosity ratio, and the temperature inverse Stokes number on the solutions.

Influence of curvature and torsion on turbulent flow in helically coiled pipes

Abstract: Fully-developed, statistically steady turbulent flow in straight, curved and helically coiled pipes is studied by means of direct numerical simulation for a Reynolds number of Reτ=230. The incompressible Navier–Stokes equations, written in orthogonal helical coordinates, are integrated numerically by means of a second order accurate finite volume method. It is shown that pipe curvature which induces a secondary flow has a strong effect on the flow quantities. Turbulence is significantly inhibited by streamline curvature and the flow almost relaminarizes for high values of the curvature parameter (κ=0.1). The torsion effect is weaker than the curvature effect. Nevertheless, it cannot be neglected. It influences the secondary flow induced by pure curvature and leads to an increase in fluctuating kinetic energy and dissipation rate.

Numerical prediction of air core diameter, coefficient of discharge and spray cone angle of a swirl spray pressure nozzle

Abstract: Theoretical predictions of air core diameter, coefficient of discharge and spray cone angle of a swirl spray pressure nozzle have been made from numerical computations of flow within the nozzle. The diameter of central air core that stabilizes inside the nozzle has been predicted from a hydrodynamic situation that yields the minimum resistance to the liquid flow in the nozzle at given operating conditions. The coefficient of discharge and spray cone angle have been evaluated from the distributions of the different velocity components of liquid flow at the nozzle orifice. It has been observed that the coefficient of discharge Cd decreases, while the air core diameter da and spray cone angle ψ increase with the increase in nozzle flow in its lower range. However, all these parameters Cd, da and ψ finally become independent of nozzle flow. Predicted values of da, Cd and ψ for different geometrical dimensions of the nozzle have been compared with the empirical data available in the literature.

Feedback control of wall turbulence with wall deformation

Abstract: Direct numerical simulation of turbulent channel flow was made in order to evaluate feedback control with deformable walls. When the local wall velocity is determined by an active cancellation control scheme similar to that of Choi et al. (Choi, H., Moin, P., Kim, J., 1994. J. Fluid Mech. 262, 75–110), the drag is decreased by about 12% with the wall deformation of the magnitude on the order of one viscous length. On the basis of the typical dimensions of the wall deformation thus obtained, a novel array of deformable actuators elongated in the streamwise direction is proposed. A new realizable control scheme by using wall information is developed based on physical arguments of the near-wall coherent structures. The location of quasi-streamwise vortices accompanied with streak meandering is successfully detected about 50 viscous lengths downstream from the sensing location, at which the spanwise gradients of wall shear stresses are measured. The wall velocity of each actuator is determined to counteract the wall-normal velocity induced by the streamwise vortices. By the present control scheme with the arrayed sensors and actuators, 10% drag reduction is achieved through selective manipulation of the streamwise vortices and streak meandering. It is also found that the energy input of the present control is one order of magnitude smaller than the pumping power saved.

Numerical simulation of transonic buffet flows using various turbulence closures

Abstract: The paper presents a numerical investigation of buffet flows using various turbulence models, including linear and non-linear low-Re eddy-viscosity models (EVM). The accuracy of the models is assessed against experimental data for transonic flows around the NACA-0012 aerofoil. The study shows that non-linear two-equation models in conjunction with functional cμ coefficient for the calculation of the eddy-viscosity (henceforth labelled NL-cμ), provide satisfactory results for transonic buffet flows. The computations also reveal that the Spalart–Allmaras one-equation model provides comparable results to the NL-cμ models, while larger inaccuracies are introduced by linear and non-linear models based on constant cμ coefficient. Moreover, the buffet onset boundaries are similarly predicted by the one-equation and NL-cμ models. The study has been performed using a second-order time accurate implicit-unfactored method which solves in a coupled fashion the Navier–Stokes and turbulence transport equations. The spatial discretisation of the equations is obtained by a Riemann solver in combination with a third-order upwind scheme.

On vortex generating jets

Abstract: Vortex generating jets (VGJs) are jets that pass through a wall and into a crossflow to create a dominant streamwise vortex that remains embedded in the boundary layer over the wall. The VGJ is characterized by its pitch and skew angles (Φ and Θ) and the velocity ratio (VR) between the jet and the crossflow. For VR=1.0, the VGJ configuration of Φ=30°, Θ=60° has been identified as that which produces the vortex with the highest peak mean vorticity. Three-component laser Doppler velocimetry (LDV) data for this particular configuration demonstrate many interesting features of the flow. Mean velocity data show a deficit of streamwise momentum in the core of the vortex, thinning of the boundary layer on the downwash side of the vortex, and thickening of the boundary layer on the upwash side. Plots of the turbulent kinetic energy and the turbulent shear stress 〈uv〉 show that the turbulent structure of the boundary layer is grossly disturbed by the presence of the vortex. The turbulent transport of the turbulent kinetic energy shows the possibility for a gradient diffusion model in most regions, but not the vortex core.

Film-cooling holes with expanded exits: near-hole heat transfer coefficients

Abstract: This paper presents detailed measurements of local heat transfer coefficients in the vicinity of three film-cooling holes with different hole geometries including a standard cylindrical hole and two holes with a diffuser shaped exit portion (i.e. a fanshaped and a laidback fanshaped hole). Tests were conducted over a range of blowing ratios M =0.25…1.75 at an external crossflow Mach number of 0.6 and a coolant-to-mainflow density ratio of 1.85. Additionally, the effect of the internal coolant supply Mach number was addressed. Surface temperatures downstream of the injection location were measured by means of an infrared camera system and used as boundary conditions for a finite element analysis to determine surface heat fluxes and heat transfer coefficients downstream of the injection location. Furthermore, the superposition method was applied to evaluate the overall film-cooling performance of the hole geometries investigated by combining heat transfer and adiabatic cooling effectiveness data. As compared to the cylindrical hole, both expanded holes show significantly lower heat transfer coefficients downstream of the injection location, particularly at high blowing ratios. The laidback fanshaped hole provides a better lateral spreading of the injected coolant than the fanshaped hole which leads to lower laterally averaged heat transfer coefficients. Coolant passage crossflow Mach numbers affect the flowfield of the jet being ejected from the hole and, therefore, have an important impact on film-cooling performance.

On the implementation of effects of Lorentz force in turbulence closure models

Abstract: The effects of Lorentz force on turbulent flow of conductive fluid are analysed within the framework of second-moment and eddy-viscosity closure models. Additional terms representing the magnetohydrodynamic interactions in the transport equations for the turbulent stress tensor and energy dissipation rate are derived in the exact form and the parts of the terms that cannot be treated exactly are then modelled. The modelling is based on the term-by-term analysis of the direct numerical simulations (DNS) of turbulent flow in an infinite plane channel subjected to transverse uniform magnetic field (Noguchi, H., Ohtsubo, Y., Kasagi, N., 1998. DNS database of turbulence and heat transfer). A priori validation of the new model is presented and compared with the DNS results for the Reynolds number based on the friction velocity Re τ =150 and for the Hartmann number Ha =6. The same approach is then followed to modify the the low- Re number k – e model. The new k – e model has been applied to solve the developing three-dimensional flow of mercury in a rectangular-sectioned duct at inlet Reynolds number Re =2×10 5 , subjected over a part of its length to a magnetic field with Ha =700 (corresponding to a Stuart number N =2.45). The predicted development of `M' shaped velocity profiles shows acceptable agreement with the experiments of Tananaev (1978) and visible improvement in comparison with the eddy-viscosity model of Ji and Gardner (Ji, H.C., Gardner, R.A., 1997. International Journal of Heat Mass Transfer 40, 1839–1851).

Effects of inner cylinder rotation on laminar flow of a Newtonian fluid through an eccentric annulus

Abstract: The paper concerns a computational and experimental study of fully developed laminar flow of a Newtonian liquid through an eccentric annulus with combined bulk axial flow and inner cylinder rotation. The results are reported for calculations of the flowfield, wall shear stress distribution and friction factor for a range of values of eccentricity e, radius ratio κ and Taylor number Ta. For fully developed flow the radial/tangential motion is decoupled from the axial component of velocity. However, the axial component of velocity is directly affected by the radial/tangential velocity field and rotation of the inner cylinder is found to have a strong influence on the axial velocity distribution, ultimately leading to two maxima in the case of a highly eccentred inner cylinder at high rotation speeds, a feature not reported hitherto. This influence of rotation on the axial velocity is mirrored in the behaviour of the shear stresses on the inner and outer cylinder walls and hence on the friction factor. An unexpected result is that (at fixed Reynolds number) as the Taylor number is increased the friction factor for high values of e(>0.9) increases rather than decreases.

Experimental study of a separating, reattaching, and redeveloping flow over a smoothly contoured ramp

Abstract: A turbulent boundary layer that separates, reattaches, and redevelops over a smoothly contoured ramp and a downstream flat plate has been examined. In order to resolve the flow in the viscous sublayer, a custom-built, two-dimensional LDA with a very high resolution was used. A small separation bubble occurred over the trailing edge of the ramp. The v ′ v ′ and − u ′ v ′ Reynolds stress components increased rapidly in the adverse pressure gradient boundary layer, and developed large outer layer peaks aligned with the inflection point in the mean velocity profile. The high stress levels were nearly unchanged by the reattachment process, decaying only after the mean velocity profile recovered and outer-layer production dropped. A key feature is that the inner layer recovered relatively quickly to a typical turbulent boundary layer in the redeveloping region, while the outer layer recovery was retarded by the large eddies generated in the separation region.

Complex turbulent wakes generated by two and three side-by-side cylinders

Abstract: Turbulent complex wakes generated by two and three cylinders in a side-by-side arrangement were investigated experimentally. In the present context, the complex wake refers to the flow formed by two or more simple wakes behind side-by-side cylinders. One cylinder was slightly heated; the temperature difference is about 1°C so that the temperature could be treated as a passive scalar. A combination of an X-wire and a cold wire was used to measure the velocity and temperature fluctuations. The present objective is to document the turbulence field of the complex wakes and examine the interactions between turbulent simple wakes and their effects on the momentum and heat transport phenomena. It is observed that the cross-stream distributions of the Reynolds normal stresses can be asymmetrical at a small spacing-to-diameter ratio. The Reynolds shear stress and its lateral transport distributions however remain symmetrical. This is explained in terms of the gap flow deflection behind side-by-side cylinders and the transport characteristics of vortical structures. The interactions between simple wakes do not seem to have any effect on the fine-scale turbulence, at least up to the scales in the inertial sub-range. On the other hand, the temperature spectra in the inertial sub-range have been affected; their slopes have been appreciably increased compared with the single-cylinder data. The gradient transport assumption is found to be valid for the turbulence field, but not for the temperature field. The heat flux and temperature gradient do not approach zero simultaneously near the centerlines of simple wakes, thus giving rise to a substantial variation in the heat transport. This leads to a significant drop in the turbulent Prandtl number. The superposition hypothesis, as proposed by Bradshaw and his co-workers, is also examined for the present complex wakes.

Effects of viscosity of fluids on centrifugal pump performance and flow pattern in the impeller

Abstract: Centrifugal pump performances are tested using water and viscous oil as working fluids whose kinematic viscosities are 1 and 48 mm2/s, respectively, the flows in the centrifugal pump impeller are also measured accurately by using a two-dimensional laser Doppler velocimeter (LDV) in best efficiency and part-loading points, while the pump is handling two kinds of working fluids. The effects of the viscosity on the performance and flow pattern within the impeller are established based on the experimental results. The high viscosity results in rapid increases in the disc friction losses over outsides of the impeller shroud and hub as well as the hydraulic losses in flow channels of the pump. The flow patterns near the impeller outlet are little affected by the viscosity of the fluids, but those near the impeller inlet are greatly affected by the viscosity. There is a wide wake near the blade suction side of the centrifugal pump impeller. The flow pattern is essentially different from the well-known jet/wake model.

Steady and pulsatile flow studies in Abdominal Aortic Aneurysm models using Particle Image Velocimetry

Abstract: Flow characteristics in Abdominal Aortic Aneruysm models have been investigated using Particle Image Velocimetry over a range of Reynolds numbers (from 400 to 1400) and Womersley numbers (from 17 to 22). Both steady and pulsatile flow experiments have been conducted. For the pulsatile flow, a sinusodial inlet flow waveform 1 + sin ωt was used. It was found that under the steady flow conditions, a recirculating vortex occupied the entire circular bulge with its core located closer to the distal end of the bulge. The strength of the vortex would increase as the Reynolds number increased but would not exceed more than 10% of the bulk flow in the parent tube. Under the pulsatile flow conditions, the vortex appeared initially near the proximal end of the bulge at the early stage of a flow cycle, occupying approximately 1/4 of the bulge. The subsequent deceleration of the bulk flow caused the vortex to reduce its extent in the direction of the flow but was enlarged in the transverse direction with higher strength. The vortex was convected slowly towards the distal end of the bulge by the bulk flow and an abrupt drop in its strength appeared when it reached there. Attempts have been made to explain the flow development using vortex dynamics.

Nonlinear eddy viscosity modelling for turbulence and heat transfer near wall and shear-free boundaries

Abstract: New turbulence and turbulent heat flux models are proposed for capturing flow and thermal fields bounded by walls or free surfaces. The models are constructed using locally definable quantities only, without any recourse to topographical parameters. For the flow field, the proposed model is a cubic nonlinear k–e–A three equation eddy viscosity model. It employs dependence on Lumley's stress flatness parameter A, by solving its modelled transport equation as the third variable. Since A vanishes at two-component turbulence boundaries, introducing its dependency enables a turbulence model to capture the structure of turbulence near shear-free surfaces as well as wall boundaries. To close the modelled A equation, an up-to-date second-moment closure is applied. For the thermal field, an explicit algebraic second-moment closure for turbulent heat flux is proposed. The new aspect of this heat flux model is the use of nonlinear Reynolds stress terms in the eddy diffusivity tensor. This model complies with the linearity and independence principles for passive scalar. The proposed models are tested in fully developed plane channel, open channel and plane Couette–Poiseuille flows at several fluid Prandtl numbers. The results show the very encouraging performance of the present proposals in capturing anisotropic turbulence and thermal fields near both wall and shear-free boundaries in the range of 0.025⩽Pr⩽95.

Turbulent heat transfer predictions using the –f model on unstructured meshes

Abstract: Durbin's three transport equation model, the so-called v 2 –f model, has been implemented in an industrial finite element code, N3S, developed at the research and development department of Electricite de France, enabling the use of unstructured meshes. Validations by comparison with other codes have been performed in the cases of the channel flow at Reτ=395, and the backward-facing step at Re=5100. The test case of the 2D periodic ribbed-channel flow has then been computed, without heat transfer at ReH=37,200, and with a constant heat flux imposed at the ribbed-wall at ReH=12,600. The results obtained show the ability of the model to predict accurately the enhancement of heat transfer due to the ribs, which is of primary interest for industrial applications.

Thermodynamic analysis of convective heat transfer in an annular packed bed

Abstract: A combination of the first and second law of thermodynamics has been utilized in analyzing the convective heat transfer in an annular packed bed. The bed was heated asymmetrically by constant heat fluxes. Introduction of the packing enhances wall to fluid heat transfer considerably, hence reduces the entropy generation due to heat transfer across a finite temperature diAerence. However, the entropy generation due to fluid-flow friction increases. The net entropy generations resulting from the above eAects provide a new criterion in analysing the system. Using the modified Ergun equation for pressure drop estimation and a heat transfer coeAcient correlation for an annular packed bed, an expression for the volumetric entropy generation rate has been derived and displayed graphically. In the packed annulus, the fully developed temperature profile and the plug flow conditions have been assumed and verified with experimental data. The volumetric entropy generation map shows the regions with excessive entropy generation due to operating conditions or design parameters for a required task, and leads to a better understanding of the behavior of the system. ” 2000 Elsevier Science Inc. All rights reserved.

Simultaneous measurements of temperature and velocity fluctuations in a slightly heated jet combining a cold wire and laser doppler anemometry

Abstract: Simultaneous measurements of two velocity components and temperature are performed combining Laser Doppler Anemometry (LDA) and cold wire thermometry. LDA is a common technique suitable for velocity measurements in turbulent jets where strong turbulence intensities and reverse flows may exist, but temperature measurements in association with LDA are difficult because the fine wire response is altered by the seeding deposit, so that the wire must be regularly cleaned. Results reported herein concern velocity–temperature correlations, as well as velocity and temperature marginal probability density functions and temperature (or velocity) probability density functions conditioned by the sign of the velocity (or temperature) fluctuation. The evolution of these various quantities is analysed in order to better understand the mixing properties in the near-field of a turbulent jet where the initial conditions still have a strong influence. It is shown that, while the velocity field tends to relax rather quickly (within a few nozzle diameters from the exit) to almost gaussian statistics, the temperature properties are still significantly skewed towards the hot jet exit temperature until x/Dj about 7–8. On the contrary, the signature of the cold ambient temperature vanishes rather quickly.

Finite element analysis of incompressible viscous flow with moving free surface by selective volume of fluid method

Abstract: A numerical technique for simulating incompressible viscous flow with free surface is presented. The flow field was calculated by the penalty finite element formulation. In this work, a modified volume of fluid (VOF) method based on four node elements in 2D geometry was proposed for its compatibility with the irregular meshes generally used with the finite element method (FEM). Numerical analyses were done for two benchmark examples, namely the broken dam problem and the solitary wave propagation problem. The numerical results showed close agreement with the existing data. In order to demonstrate the effectiveness of the proposed numerical scheme, mold filling process was studied.

Chaotic fluid mixing in non-quasi-static time-periodic cavity flows

Abstract: Fluid mixing in a two-dimensional square cavity with a time-periodic pulsating lid velocity is studied. A spectral element technique for spatial discretization is combined with a continuous projection scheme for temporal discretization to obtain a numerical representation of the non-quasi-static velocity field in the cavity. It is well known that mixing in a cavity with a steady lid velocity results in linear mixing of fluid inside the cavity. Here, it is shown that superposition of a pulsating component on the steady lid velocity can lead to chaotic mixing in the core of the cavity. An extra steady motion of the opposite cavity wall, resulting in a small perturbation to the original flow, causes the chaotically mixed region to be spread over almost the whole cavity. Poincare and periodic point analysis reveal the main characteristics for these transient time-periodic flows, and elucidate the details and properties of the chaotic mixing in these flows.

Direct numerical simulation for laminarization of turbulent forced gas flows in circular tubes with strong heating

Abstract: The direct numerical simulation (DNS) of turbulent transport for a gas with variable properties has been conducted to grasp and understand the laminarization phenomena caused by strong heating. In this study, the inlet Reynolds number based on a bulk velocity and pipe diameter was taken as Re=4300 as in the experiments by Shehata and McEligot (1998). The measured wall temperature distribution was applied as a thermal boundary condition. The number of computational nodes used in the heated region was 768×64×128 in the z-, r- and φ-directions, respectively. Turbulent quantities, such as the mean flow, temperature fluctuations, turbulent stresses and the turbulent statistics, were obtained via DNS. Predicted mean velocity and temperature distributions and integral parameters agreed well with the experiments. The Reynolds shear stress, indicating turbulent transport of momentum, decreases along the streamwise direction. The cause of this reduction can be considered to be that the fluid behavior changes drastically in the near wall region due to strong heating which induces significant variations of the gas properties and, in turn, acceleration and buoyancy effects. In a visualization of the results, one sees that the vortical structures are primarily suppressed within the first section of the heated region (z/D=0–5) and are not regenerated further downstream.