Large eddy simulation of turbulent open channel flow with heat transfer at high Prandtl numbers

Summary. Large eddy simulation of a fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. The objective of this study is to analyze the behavior of turbulent flow and heat transfer in turbulent open channel flow, in particular for high Prandtl number, and to examine the reliability of the LES technique for predicting turbulent heat transfer near the free surface. The turbulent open channel flow with constant difference of temperature imposed on the free surface and bottom wall is calculated for the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re) 180 based on the wall friction velocity and the channel depth. To illustrate the turbulent flow and heat transfer behaviors, some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures of velocity and temperature fluctuations, are exhibited and analyzed.     

An investigation of the Prandtl number effect on turbulent heat transfer in channel flows by large eddy simulation

Summary Fully developed turbulent channel flow with passive heat transfer has been calculated to investigate the turbulent heat transfer by use of the large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objectives of this study are to examine the effectiveness of the LES technique for predicting the turbulent heat transfer at high Prandtl numbers and the effects of the Prandtl number on the turbulent heat transfer in a fully developed turbulent channel flow. In the present study, the Prandtl number is chosen as 0.1 to 200, and the Reynolds number, based on the central mean velocity and the half-width of the channel, is 10⁴. Some typical cases are computed and compared with available data obtained by direct numerical simulation (DNS), theoretical analysis and experimental measurement, respectively, which confirm that the present approach can be used to predict the heat transfer satisfactorily, even at high Prandtl numbers. To depict the effect of the Prandtl number on turbulent heat transfer, the distributions of mean value and fluctuation of resolved flow temperatures, the heat transfer coefficient, turbulent heat fluxes, and some instantaneous iso-thermal sketches are analyzed.     

The Difference in Turbulent Diffusion between the Active and Passive Scalars in a Thermally Stably Stratified Medium

The difference in the turbulent diffusion between the active (heat) and passive (mass) scalars in a thermally stably stratified medium is investigated. The axisymmetric problem is treated on the formation of a turbulent circulation flow above a heated disk and on the turbulent diffusion of a passive scalar (impurity) from a continuous surface source in a stably stratified medium. The results indicate that the thermal stratification causes appreciable differences in the coefficients of turbulent transfer between the active (heat) and passive (mass) scalars. This means that the assumption of the identity of the coefficient of turbulent diffusion of heat and mass, employed in conventional models of turbulence, produces significant errors in estimating the heat and mass transfer in a thermally stably stratified medium.     

Symmetry-Preserving Discretization of Heat Transfer in a Complex Turbulent Flow

Convective and diffusive operators are discretized such that their symmetries are preserved. The resulting discretization inherits all symmetry-related properties of the continuous formulation. It is shown that a symmetry-preserving discretization is unconditionally stable and conservative. A fourth-order, symmetry-preserving discretization method is developed and tested for the numerical simulation of turbulent (flow and) heat transfer in a channel with surface-mounted cubes, where the temperature is treated as a passive scalar. The Reynolds number (based on the channel width and the mean bulk velocity) is Re=13,000. The results of the numerical simulation agree well with available experimental data.     

Flow and heat transfer of finely dispersed turbulent flows in channels

Equations for the second moments of the velocity and temperature fluctuations are used to study the effect of particles on the rate of turbulent momentum and heat transfer in the flow of a gas suspension in circular pipes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 5, pp. 740–751, November, 1987.     

Finite element simulation of internal flows with heat transfer using a velocity correction approach

This paper enumerates finite-element based prediction of internal flow problems, with heat transfer. The present numerical simulations employ a velocity correction algorithm, with a Galerkin weighted residual formulation. Two problems each in laminar and turbulent flow regimes are investigated, by solving full Navier-Stokes equations. Flow over a backward-facing step is studied with extensive validations. The robustness of the algorithm is demonstrated by solving a very complex problem viz. a disk and doughnut baffled heat exchanger, which has several obstructions in its flow path. The effect of wall conductivity in turbulent heat transfer is also studied by performing a conjugate analysis. Temporal evolution of flow in a channel due to circular, square and elliptic obstructions is investigated, to simulate the vortex dynamics. Flow past an in-line tube bank of a heat exchanger shell is numerically studied. Resulting heat and fluid flow patterns are analysed. Important design parameters of interest such as the Nusselt number, Strouhal number, skin friction coefficient, pressure drop etc. are obtained. It is successfully demonstrated that the velocity correction approach with a Galerkin weighted residual formulation is able to effectively simulate a wide range of fluid flow features.     

The Hydrodynamics and Heat and Mass Transfer of Particles under Conditions of Turbulent Flow of Gas Suspension in a Pipe and in an Axisymmetric Jet

A mathematical model for the calculation of the hydrodynamic and thermal parameters of dispersed impurity in a round pipe and in a jet is given in Eulerian variables. The model is based on a unified set of equations describing the turbulent characteristics of particles in nonisothermal flow and of boundary conditions representing the interaction of the particles with the rough channel surface and the boundary of submerged jet. The effect of the anisotropy of turbulent fluctuations of the particle velocity and of the correlation between the thermal properties of the particle material and carrier gas on the intensity of momentum, heat, and mass transfer in the dispersed phase is investigated. The calculation results are compared with the experimental data.     

Effect of pulsations on two-layer channel flow

The effect of vertical wall vibrations on two-phase channel flow is examined. The basic flow consists of two superposed fluid layers in a channel whose walls oscillate perpendicular to themselves in a prescribed, time-periodic manner. The solution for the basic flow is presented in closed form for Stokes flow, and its stability to small periodic perturbations is assessed by means of a Floquet analysis. It is found that the pulsations have a generally destabilizing influence on the flow. They tend to worsen the Rayleigh–Taylor instability present for unstably stratified fluids; the larger the amplitude of the pulsations, the greater the range of unstable wave numbers. For stably stratified fluids, the pulsations raise the growth rate of small perturbations, but are not sufficient to destabilize the flow. In the latter part of the paper, the basic flow for arbitrary Reynolds number is computed numerically assuming a flat interface, and the motion of the interface in time is predicted. The existence of a time-periodic flow is demonstrated in which the ratio of the layer thicknesses remains constant throughout the motion.     

Hydrodynamics and heat transfer in pulsating turbulent flow of gas in a heated pipe

The paper deals with the investigation of the effect produced by the dependence of the physical properties on temperature and flow rate fluctuations on heat transfer and drag under conditions of turbulent pipe flow of gas. The method of finite differences is used to solve numerically a set of equations of motion, continuity, and energy written in a narrow channel approximation. A model of turbulence is used which takes into account the effect of the variability of the properties and of the nonstationarity of flow on turbulent transfer. In the particular case of steady-state flow of gas being heated, the calculation results fit well the available experimental data. It is found that the heat transfer depends on the heating rate more significantly than the friction drag. In the case of pulsating flow, the part of hydraulic drag is estimated which is spent for the variation of longitudinal velocity along the pipe and is due to the thermal acceleration of gas. It is demonstrated that the main features of pulsating flow, which were previously investigated for a liquid of constant properties and for a dropping liquid of variable viscosity, are retained for the gas being heated as well. Comparison is made for the gas and dropping liquid of the effect made by various process parameters such as the Reynolds, Stokes, and Prandtl numbers, the heating rate, and the form of thermal condition on the wall on the period average Nusselt number and coefficient of friction drag.     

Heat transfer under conditions of turbulent pipe flow of electrically conducting liquid in longitudinal magnetic field in the region of hydrodynamic stabilization

Numerical simulation is performed of heat transfer under conditions of turbulent pipe flow in the vicinity of entry to longitudinal magnetic field. Use is made of the model of turbulence which was previously employed for performing calculations in the region of stabilized flow and heat transfer. The model describes the suppression of turbulence by the magnetic field and the laminarization of turbulent (at the pipe inlet) flow. The calculation results agree well with the experimental data on heat transfer and temperature profiles in the initial thermal region. The effect made on heat transfer by Joule heat release from electric currents caused by turbulent fluctuations is investigated.     

Isotropie der turbulenten Wirbelströmung in Seitenkanalverdichtern

The impeller with a high number of blades causes a turbulent vorticity flow in the side channel, which is the reason for the specific impuls flow and the energy transfer in the side channel. High frequency pressure oscillations were caused according to the changes of the vorticity structure in the side channel. The dissipation loses are the reason for the heat up of the gas during the compression. According to the transported gas mass flow the turbulent vorticity flow is superposed from the average flow velocity of the gas. They depend from the peripheral speed of the impeller and the size of the compressor. The superposition of the turbulent vorticity flow and the average flow velocity cause the question of the isotrope of the turbulent vorticity flow in the side channel for the working area of the compressor. Experimental results from side channel compressors will give an answer to this.     

凹陷阵列印刷电路板式换热器里超临界甲烷换热和流动特性模拟研究

为了强化液化甲烷在印刷电路板式微通道换热器中的换热能力,提出了一种凹陷阵列的微小通道换热器整体性能提高的被动式强化技术并进行了数值模拟验证。研究了流体温度范围125—265 K范围内的超临界甲烷在凹陷阵列结构微通道内的换热和流动特性,考察了凹陷阵列微通道和光滑微通道下,流体温度、质量流量、雷诺数和进口压力对传热系数、努塞尔数、摩擦因子和综合效益系数(PEC)的影响。此外,通过凹陷结构的局部流动特性分析强化换热机理,数值模拟结果表明相较于光滑微通道,凹陷阵列微通道的换热特性得到大大强化,且随雷诺数(由质量流量或者流体温度改变)的增大而增强,而摩擦因子只是有较弱的劣化。     

High-Rayleigh-number turbulent natural convection on an inclined surface

High-Rayleigh-number natural-convection heat transfer on inclined surfaces is treated. The analysis of the effect of thermogravitational forces on turbulent transfer of momentum and heat in the wall region is based on the balance equations for the second moments of pulsations of velocity and temperature. Analytical dependences are derived for the coefficient of turbulent thermal conductivity and for the Nusselt number in a wide range of values of the Prandtl number.     

Turbulent flow through a circular pipe: Resistance and heat exchange at the constant boundary temperature

In this work, problems of the velocity profile, hydraulic resistance and heat exchange at constant equal temperature on the walls, steady-state turbulent flow, and established heat exchange in a straight channel limited by coaxial circular cylinders (a circular pipe) are solved. A moving incompressible fluid is considered as the medium, its viscous and heat-conducting properties being defined not only by its physical properties, but also by stable vortex structures that are formed upon the turbulent flow and generate local anisotropy of the medium. A vector called the director is a characteristic parameter of anisotropy. Director dynamics within the flow is assigned by a separate equation. The flow region consists of two near-wall subregions, which are adjacent to solid flow boundaries. The boundary between the subregions is determined during solving the problem. A closed set of equations is formulated for the desired values (velocity, temperature), and boundary conditions are laid. The velocity profile and temperature field in the flow were obtained in form of solutions to the corresponding boundary problems. The results of solution are compared with the experimental data and empirical formulas.     

Experiments on dry-out during flow boiling in a round minichannel

Temperature measurements during flow boiling of R134a in a 0.96 mm single circular channel are reported in order to provide a criterion for the determination of the critical conditions in the channel. The flow boiling heat transfer is obtained by using a secondary fluid; the wall temperature displays larger fluctuations in the zone where dryout occurs. These temperature fluctuations in the wall denote the presence of a liquid film drying up at the wall with some kind of an oscillating process. These temperature fluctuations never appear during condensation tests, neither are present during flow boiling at low vapour qualities. The fluctuations also disappear in the post-critical condition zone. Experimental values of dryout quality measured with the above method are reported in this paper at mass velocity ranging between 300 and 600 kg m^?2s^?1. In the practical applications of flow boiling, the dryout quality is a key parameter in the two-phase systems for cooling of devices, both for ground and microgravity applications. The test conditions reported here refer to relatively high mass velocities, and are obtained at earth gravity. Nevertheless, since the critical heat flux differences between the two gravity environments decrease with increasing velocity, the present data may also be used for inertia dominated systems at low g.     

Forced convection of low temperature nitrogen gas in rectangular channels with small aspect ratio

Forced convection of low temperature (80-150 K) nitrogen gas flowing through rectangular channels with hydraulic diameters of 0.513-1.814 mm and aspect ratios of 0.013-0.048 has been investigated experimentally. Close attention was focused on the effects of channel depth and heat addition on the heat transfer and flow characteristics, the transition from laminar to turbulent flow and the existence of an optimum channel depth. A dimensionless heating number was adopted to characterize the heating effect. The experimental correlation developed for the Nusselt number shows that the heat addition is the most important effect, followed by the channel aspect ratio, Reynolds number and Prandtl number.     

蜂窝板换热器内部流动传热特性研究

建立了蜂窝板换热器湍流流动的物理数学模型,并应用数值分析方法模拟了蜂窝板换热器的三维流动传热过程;分析了不同雷诺数下通道内流动阻力和换热性能及其随雷诺数的变化规律,并与相同当量直径的平行平板通道的流动换热性能进行了对比。结果表明,蜂窝板换热器在换热系数提高的同时流动阻力也增大了,在雷诺数Re=3000~15000的范围内,其传热努塞尔数比平行平板增大了0.93~2.12倍,阻力系数增大了2.24~2.35倍。最后从场协同理论的角度分析了蜂窝板强化传热的机理。     

Direct numerical simulation of turbulent heat transfer modulation in micro-dispersed channel flow

Summary The objective of this paper is to study the influence of dispersed micrometer size particles on turbulent heat transfer mechanisms in wall-bounded flows. The strategic target of the current research is to set up a methodology to size and design new-concept heat transfer fluids with properties given by those of the base fluid modulated by the presence of dynamically-interacting, suitably-chosen, discrete micro- and nano-particles. We ran direct numerical simulations for hydrodynamically fully developed, thermally developing turbulent channel flow at shear Reynolds number Re _τ = 150 and Prandtl number Pr = 3, and we tracked two large swarms of particles, characterized by different inertia and thermal inertia. Preliminary results on velocity and temperature statistics for both phases show that, with respect to single-phase flow, heat transfer fluxes at the walls increase by roughly 2% when the flow is laden with the smaller particles, which exhibit a rather persistent stability against non-homogeneous distribution and near-wall concentration. An opposite trend (slight heat transfer flux decrease) is observed when the larger particles are dispersed into the flow. These results are consistent with previous experimental findings and are discussed in the frame of the current research activities in the field. Future developments are also outlined. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday It is our great pleasure to take part in this Festschrift Issue dedicated to the celebration of the 70th birthday of Professor Franz Ziegler. To honour his activity and his scientific achievements, we prepared this paper, crafted with friendship and respect. We wish Franz many more productive, enjoyable and happy years and a solid and long collaboration as Editors of Acta Mechanica.     

Experimental Study of the Relation Between Heat Transfer and Flow Behavior in a Single Microtube

The flow boiling heat transfer in microchannels have become important issue because it is extremely high-performance heat exchanger for electronic devices. For a detailed study on flow boiling heat transfer in a microtube, we have used a transparent heated microtube, which is coated with a thin gold film on its inner wall. The gold film is used as a resistance thermometer to directly evaluate the inner wall temperature averaged over the entire temperature measurement length. At the same time, the transparency of the film enables the observation of fluid behavior. Flow boiling experiments have been carried out using the microtube under the following conditions; mass velocity of 105 kg/m² s, tube diameter of 1 mm, heat flux in the range of 10 ~ 380 kW/m² s, and the test fluid used is ionized water. Under low heat flux conditions, the fluctuations in the inner wall temperature and mass velocity are closely related; the frequency of these fluctuations is the same. However, the fluctuations in the inner wall temperature and heat transfer coefficient are found to be independent of the fluctuation in the mass velocity under high heat flux conditions.     

Suppression of turbulence in magnetically stabilized ferroliquids

Under conditions of saturated magnetization ferroliquids obey Boussinesq equations in which the body force term is a combination of the ordinary gravitational force and a magnetic force that is proportional to the gradient of the magnetic field and the local temperature fluctuation. Hence non-isothermal flows of ferroliquids can be stabilized or destabilized by the application of a magnetic field. In this paper we examine the effects of magnetic stabilization which can be used to delay the transition from laminar to turbulent flow, or to suppress the level of turbulent transport in fully turbulent flows. The analogy between ferroliquid flows and stratified flows is developed to permit the application of results from studies of stratified flows. Using this analogy the magnitude of turbulence suppression is examined for a limiting case of fully developed turbulent channel flow with constant transverse heat flux. It is found that the channel friction factor can be reduced perceptably with attainable magnetic field strengths and moderate heat fluxes, and that reductions exceeding one order of magnitude can be achieved in extreme conditions. The friction factor reduction is largest for small Reynolds number and decreases with increasing flow rate when the heat flux is held constant.