Influence of buoyancy in a mixed convection liquid metal flow for a horizontal channel configuration

This article presents the direct numerical simulation (DNS) of mixed convection turbulent heat transfer in a horizontal channel case for liquid lead. Cartesian mesh is used and the incompressible Navier-Stokes equations are discretized with highly accurate finite difference sixth-order compact schemes to perform the DNS. The influence of mixed convection in liquid metal with Prandtl number equal to 0.025 and Reynolds number equal to 4667 has been studied by varying the Richardson number (Ri = 0, 0.25, 0.50, 1.00). The obtained results are extensively analyzed and discussed in this article. In particular, large-scale circulation is observed under the influence of buoyancy. Compared to the forced convection case (Ri = 0), stronger velocity fluctuations are noticed that highlight the fact that turbulence is strongly enhanced with the increasing buoyancy. It also proves that the thermal plumes rising up from the hot wall of the channel activate the cross-stream eddies. Moreover, temperature fluctuations are found to be more homogeneously distributed with increasing buoyancy effects and mixing is more effective in the center of the channel. In addition, compared with forced convection, mixed convection has shown enlargement of the large-scale structures that only appear in the temperature field for low Prandtl number fluids. Extensive results of flow and temperature fields are analyzed and presented.     

Evaporation of Falling and Shear-Driven Thin Films on Smooth and Grooved Surfaces

One of the most important tasks in development of modern gas turbine combustors is the reduction of NO_x emissions. An effective way to reduce the NO_x emission is using the lean premixed prevaporization (LPP) concept. An important phenomenon taking place in LPP chambers is the evaporation of thin fuel films. To increase the fuel evaporation rate, the use of microstructured walls has been suggested. The wall microstructures make use of the capillary forces to evenly distribute the liquid fuel over the wall, so that the appearance of uncontrolled dry patches can be avoided. Moreover, the wall structures promote the thin film evaporation characterized by ultra-high evaporation rates. An experimental setup was built for the investigation of thin liquid films falling down on the outer surface of vertical tubes with either a smooth or structured surface. In the first testing phase water is used, fuel like liquids will be used later on. The thin film can be heated from both sides, by hot oil flowing inside the tube, and by hot compressed air flowing in co-current direction to the thin film. The film is partly evaporated along the flow. Results for the wavy film structure at different Reynolds numbers are reported. For theoretical investigations a model describing the hydrodynamics and heat transfer due to evaporation of the gravity- and shear-driven undisturbed liquid film on structured surfaces was developed. For low Reynolds numbers or low liquid mass fluxes the wall surface is only partly covered with liquid and the heat transfer is shown to be governed by the evaporation of the ultra-thin film in the vicinity of the three-phase contact line. A numerical model for the solution of a two-dimensional free-surface flow of a liquid film over a structured wall was also developed. The Navier–Stokes equations are solved using the Volume of Fluid (VOF) technique. The energy equation is included in the model. The model is verified by comparison with data from the literature showing favorable agreement. In particular, the proposed model predicts the formation of capillary waves observed in the experiments. The model is used to investigate the flow of liquid on a structured wall. This calculation is the first step towards the modeling of a three-dimensional wavy flow of a gravity- and shear-driven film along a wall with longitudinal grooves. It is found that due to the Marangoni effect, a circulating flow arises within the cavity, thereby leading to an enhancement in the evaporation rate.     

Turbulent mixed convection heat transfer to liquid sodium

The influences of buoyancy on turbulent heat transfer to a liquid metal flowing in a vertical pipe are considered. A theoretical model is presented which provides a criterion for the conditions under which such influences become significant and which predicts the impairment of heat transfer for upward flow and enhancement for downward flow. The variation with Peclet number of the maximum impairment of heat transfer and conditions under which it occurs are established. A generalization of the model leading to an equation for the entire mixed convection region is proposed. From this an equation for turbulent free convection to liquid metals is obtained.     

Experimental study on turbulent natural convection heat transfer in water with sub-millimeter-bubble injection

Using thermocouples and a particle tracking velocimetry technique, temperature and velocity measurements are conducted to investigate flow and heat transfer characteristics of turbulent natural convection from a vertical heated plate in water with sub-millimeter-bubble injection. Hydrogen-bubbles generated by the electrolysis of water are used as the sub-millimeter-bubbles. In the turbulent region, the heat transfer deterioration occurs for a bubble flow rate Q = 33 mm³/s, while the heat transfer enhancement occurs for Q = 56 mm³/s. Temperature and velocity measurements suggest that the former is caused by a delay of the transition due to the bubble-induced upward flow. On the other hand, the latter is mainly due to two factors: one is the enhancement of the rotation of eddies in the outer layer, and the other is the increase in the gradient of the streamwise liquid velocity at the heated wall. These are caused by bubbles, which are located in the inner layer, rising at high speed.     

下降液膜在逆向流动空气作用下的换热

以下一代核电站反应堆安全壳非能动冷却为背景，对竖直管内过冷下降液膜在逆向空气．水蒸汽流动作用下的换热提出了一个分析模型，对液膜采用边界层近似理论，对空气．水蒸汽混合气采用由热质传递比拟理论引出的关联式进行分析，考察了各种条件下液膜的厚度、温度、吸收热量与蒸发热量沿流向的变化，与相关研究进行了对比，表明了模型的合理性。     

Heat transfer and two-phase flow characteristics of refrigerants flowing under varied heat flux in a double-pipe evaporator

A mathematical model based on the annular flow pattern is developed to simulate the evaporation of refrigerants flowing under varied heat flux in a double tube evaporator. The finite difference form of governing equations of this present model is derived from the conservation of mass, energy and momentum. The experimental set-up is designed and constructed to provide the experimental data for verifying the simulation results. The test section is a 2.5 m long counterflow double tube heat exchanger with a refrigerant flowing in the inner tube and heating water flowing in the annulus. The inner tube is made from smooth horizontal copper tubing of 9.53 mm outer diameter and 7.1 mm inner diameter. The agreement of the model with the experimental data is satisfactory. The present model can be used to investigate the axial distributions of the temperature, heat transfer coefficient and pressure drop of various refrigerants. Moreover, the evaporation rate or the other relevant parameters that is difficult to measure in the experiment are predicted and presented here. The results from the present mathematical model show that the saturation pressure and temperature of refrigerant decrease along the tube due to the tube wall friction and the flow acceleration of refrigerant. The liquid heat transfer coefficient increases with the axial length due to reducing the thickness of the liquid refrigerant film. Due to increase of the liquid heat transfer coefficient, increasing wall heat flux is obtained.Finally, the evaporation rate of refrigerant increases with increasing wall heat flux.     

The variation of heat transfer in a two‐sided lid‐driven differentially heated square cavity with nanofluids containing carbon nanotubes for physical properties of fluid dependent on temperature

The behavior of nanofluids containing cylindrical nanoparticles are investigated numerically inside a two‐sided lid‐driven differentially heated square cavity to gain insight into the convective recirculation and flow processes induced by a nanofluid. The physical properties of the base fluid such as viscosity, thermal conductivity and thermal expansion coefficient are, respectively, assumed to be temperature independent (taking the mean temperature of the left and right walls) and temperature dependent. A model is developed to analyze the behavior of nanofluids taking into account the nanoparticle volume fraction whereas the transport equations are solved numerically with finite volume approach using SIMPLEC algorithm. The left and right moving walls are maintained at different constant temperatures while the upper and bottom walls are thermally insulated. The directions of the moving walls were considered in a way that the force and natural convections aid each other. The governing parameter Richardson number was 0.1<Ri<50.0 but due to space constraints only the results for 0.1<Ri<10.0 from fluid flow are presented. It was found that the temperature dependency of physical properties at different Richardson numbers and nanoparticle volume fractions affects the fluid flow and heat transfer in the cavities. Finally, comparisons between the behaviors of the average Nusselt number at the left wall for two cases are presented. Copyright © 2011 John Wiley & Sons, Ltd.     

下降液膜层流换热发展段中的积分分析

对等温竖直壁面上层流液膜发展段的流动换热进行了理论分析 ,用积分法得到并求解了速度和温度边界层的积分方程式 ,求得了发展段的流动和换热特性的变化规律 ,讨论了进口流态和普朗特数对换热的影响。     

Calculating liquid droplets settling on a cylinder in gas-liquid spray flow

Adding atomized liquid to air flowing around a cylinder gives an appreciable increase in heat transfer by forming a liquid film on the cylinder surface. The heat transfer coefficient depends upon the amount of liquid forming the film, which is limited by two phenomena: droplet deflection from the liquid film on the surface and droplets not striking the cylinder. This paper presents a method of calculating the quantity of liquid droplets settling on a cylinder surface in a gas-liquid spray flow. A coefficient $\text{k}$, the volume ratio of the liquid entering the film to the amount of liquid directed at the cylinder, is introduced. $\text{k}$ values were calculated by means of numerical computation and the theory verified experimentally. The calculation method permits estimation of the dependence of the amount of liquid settling on a cylinder on the droplet diameter distribution parameters and on the linear gas velocity     

Heat transfer to non-newtonian laminar falling liquid films with smooth wave free gas—liquid interface

The present paper investigates analytically the problem of heat transfer to a non-Newtonian laminar falling liquid film flowing along an inclined wall for the thermally developing and thermally developed regions. In the developing region of the temperature profile, the Nusselt number decreases monotonically until the thermal boundary layer touches the interface. But immediately after this point, the liquid film thickness decreases as well as the temperature difference in the film. The influence of parameters such as α (i.e. Fr/Re_mod ratio), γ (i.e. modified form of ?μ), modified Prandtl number and the flow behaviour index “n’ on heat transfer results is also presented.     

Conjugate forced convection and heat conduction in circular microchannels

The effects of axial heat conduction in the solid walls of microchannels of circular cross-sections are analyzed here. A systematic approach is adopted, with the aim of pointing out the influence of geometrical parameters and of solid wall thermal conductivity on microchannel heat transfer. The reliability of a commonly adopted criterium, based on the so-called axial conduction number, to assess the relevance of axial heat conduction is also discussed. Numerical simulations concern the simultaneously developing laminar flow of a constant property fluid in microchannels of different length, wall thickness and wall material, heated with a uniform heat flux at the outer surface, for different values of the Reynolds number. Moreover, since often in experimental tests the two end sections of the microchannel wall are not perfectly insulated, the effects of heat losses through these sections are also considered. A hybrid finite element procedure, which implies the step-by-step solution of the parabolized momentum equations in the fluid domain, followed by the solution of the energy equation in the entire domain, corresponding to both the solid and the fluid parts, is used for the numerical simulations.     

“Magnetic-ribs” in fully developed laminar liquid–metal channel flow

This paper documents the numerical investigation of the effects of non-uniform magnetic fields, i.e. magnetic-ribs, on a liquid–metal flowing through a two-dimensional channel. The magnetic ribs are physically represented by electric currents flowing underneath the channel walls. The Lorentz forces generated by the magnetic ribs alter the flow field and, as consequence, the convective heat transfer and wall shear stress. The dimensionless numbers characterizing a liquid–metal flow through a magnetic field are the Reynolds (Re) and the Stuart (N) numbers. The latter provides the ratio of the Lorentz forces and the inertial forces. A liquid–metal flow in a laminar regime has been simulated in the absence of a magnetic field (Re_H = 1000, N = 0), and in two different magnetic ribs configurations for increasing values of the Stuart number (Re_H = 1000, N equal to 0.5, 2 and 5). The analysis of the resulting velocity, temperature and force fields has revealed the heat transport phenomena governing these magneto-hydro-dynamic flows. Moreover, it has been noticed that, by increasing the strength of the magnetic field, the convective heat transfer increases with local Nusselt numbers that are as much 27.0% larger if compared to those evaluated in the absence of the magnetic field. Such a convective heat transfer enhancement has been obtained at expenses of the pressure drop, which increases more than twice with respect to the non-magnetic case.     

Turbulent forced convective heat transfer in two-phase evaporating droplet flow through a vertical pipe

A physical model was developed to study heat transfer in turbulent dispersed flow at very high vapor quality in a vertical pipe by numerically solving the coupling governing differential equations for both phases. Major heat transfer mechanisms included in the model were the thermal nonequilibrium effects, droplet vaporization, droplet deposition on the duct wall and thermal radiative transfer. The predicted results indicated that vapor superheating is dominant for the cases with high wall superheat, otherwise droplet vaporization dominates the energy transport processes. Heat transfer during the droplet-wall interaction only exists at low wall superheat but in small amounts.     

Experimental research on transient critical heat flux in vertical tube under oscillatory flow condition

The transient critical heat flux (CHF) experiments with forced sinusoidal inlet flow oscillation (oscillation period in 1–11 s, normalized amplitude of inlet flow oscillation in 0–3.0) were conducted in a vertical tube under low pressure condition. To analyze the triggering mechanism and aftermath of periodic dryout, the wall temperature fluctuation characteristics at the onset of periodic dryout and during post-periodic dryout were investigated. Under inlet flow oscillation condition, periodic dryout would be triggered at the wave trough of liquid film oscillation as wall heat flux far below the stable-flow CHF. The transient periodic dryout would give rise to temperature fluctuations on the tube wall, the amplitude of which increased with oscillation period and heat flux. The large wall temperature fluctuation during long-playing periodic dryout could significantly pre-trigger continuous dryout. The changing trends of the periodic dryout heat flux show a reasonable agreement with Okawa’s theoretical model, in which the liquid film oscillation was supposed be weakened by the axial mixing of liquid film. Moreover, the droplet entrainment at the oscillatory interface also has noticeable influence on the oscillation characteristics of liquid film. Based on the analysis of parameter effects on periodic dryout, a semi-empirical correlation was proposed to predict the periodic dryout heat flux under inlet flow oscillation condition.     

Wave regimes on a nonisothermal film of a viscous liquid flowing down a vertical plane

A thin film flow of a viscous liquid flowing down a vertical wall in the field of the gravity force is studied. The values of temperatures on the solid wall and on the free surface are constant. The viscosity and thermal diffusivity are functions of temperature. An equation that describes the evolution of surface disturbances is derived for small flow rates in the long-wave approximation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 89–97, March–April, 2008.     

Heat transfer in a thin layer of a viscous heavy noncompressible liquid under wavy flow conditions

The article describes a method for calculating the flow of heat through a wavy boundary separating a layer of liquid from a layer of gas, under the assumption that the viscosity and heat-transfer coefficients are constant, and that a constant temperature of the fixed wall and a constant temperature of the gas flow are given. A study is made of the equations of motion and thermal conductivity (without taking the dissipation energy into account) in the approximations of the theory of the boundary layer; the left-hand sides of these equations are replaced by their averaged values over the layer. These equations, after linearization, are used to determine the velocity and temperature distributions. The qualitative aspect of heat transfer in a thin layer of viscous liquid, under regular-wavy flow conditions, is examined. Particular attention is paid to the effect of the surface tension coefficient on the flow of heat through the interface.Notation x, y coordinates of a liquid particle - t time - v and u coordinates of the velocity vector of the liquid - p pressure in the liquid - c_v, , T,, andv heat capacity, thermal conductivity coefficient, temperature, density, and viscosity of the liquid, respectively - g acceleration due to gravity - surface-tension coefficient - c phase velocity of the waves at the interface - T_w wall temperature - h₀ thickness of the liquid layer - u₀ velocity of the liquid over the layer Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 147–151, July–August, 1970.     

TRPIV investigation of space-time correlation in turbulent flows over flat and wavy walls

The present experimental work is devoted to in- vestigate a new space-time correlation model for the turbulent boundary layer over a flat and a wavy walls. A turbulent boundary layer flow at Reo = 2460 is measured by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated at 3 different wall-normal locations in logarithmic layer. It is found that the scales of coherent structure increase with moving far away from the wall. The growth of scales is a manifestation of the growth of prevalent coherent structures in the turbulent boundary layer like hairpin vortex or hairpin packets when they lift up. The resulting contours of the space-time correlation exhibit elliptic-like shapes rather than straight lines. It is suggested that, instead of Taylor hypothesis, the elliptic model of the space-time correlation is valid for the wallbounded turbulent flow over either a flat wall or a wavy wall. The elliptic iso-correlation curves have a uniform preferred orientation whose slope is determined by the convection velocity. The convection velocity derived from the space-time correlation represents the velocity at which the large-scale eddies carry small-scale eddies. The sweep velocity rep- resents the distortions of the small-scale eddies and is intimately associated with the fluctuation velocity in the logarithmic layer of turbulent boundary layers. The nondimensionalized correlation curves confirm that the elliptic model is more proper for approximating the space-time correlation than Taylor hypothesis, because the latter can not embody the small-scale motions which have non-negligible distortions. A second flow over a wavy wall is also recorded using TRPIV. Due to the combined effect of shear layers and the adverse pressure gradient, the space-time correlation does not show an elliptic-like shape at some specific heights over the wavy wall, but in the outer region of the wavy wallbounded flow, the elliptic model remai     

Experimental study of wall pressure fluctuations in rigid and elastic pipes behind an axisymmetric narrowing

Wall pressure fluctuations, p_t, in rigid and elastic pipes behind a local axisymmetric narrowing are studied. A sharp increase in their rms level in a finite region immediately downstream of the narrowing, leading up to a pronounced maximum upstream of the point of jet reattachment, is found. Approximate estimates both for the distance from the narrowing to the point of maximum rms pressure and for the rms magnitude at this point are obtained. Inspection of the wall pressure power spectrum, P, reveals the presence of low-frequency maxima. The maxima are found to be associated with the large-scale eddies in the regions of separated and reattached flow, and their frequencies are close to the characteristic frequencies of the eddies’ formation. These maxima are the main distinguishing features of the spectrum under investigation compared to the power spectrum of the wall pressure fluctuations in a fully-developed turbulent flow in a pipe without narrowing. A comparative analysis of the data for rigid and elastic pipes shows that changes in the pipe wall bending stiffness cause alterations in the flow structure near the wall and the corresponding redistribution of flow energy among the vortices. This results in an increase in the wall pressure amplitude and the low-frequency level of the wall pressure power spectrum, as well as the appearance of new frequency components in this domain.     

Direct Numerical Simulation of Flow in a Ribbed Channel

The issue of turbine lifetime is an important one, particularly for modern turbines operating at high temperature regimes. A cooling design such as ribs may achieve an improved lifetime and complex mechanisms of heat transfer need to be well studied. In this paper, a Direct Numerical Simulation (DNS) is presented for a 3-D channel flow with two square ribs on the lower wall. The full unsteady compressible Navier-Stokes equations are solved with an original hybrid finite difference/finite element scheme. The Reynolds number of the simulation is 7 000 based on the bulk velocity at the inlet and the channel height. The present study is mainly devoted to understand the mechanism of heat transfer at the wall through the topological analysis of the flow and the temperature flux. Results show that the large-scale structures generated by obstacles splash onto the lower surface and induce longitudinal vortices which enhance heat transfer at the wall. A comprehensive data base including 56 correlations was set up for testing and improving turbulence models for this complex, separated flow.