Large eddy simulation of turbulent heat transfer in pipe flows with respect to Reynolds and Prandtl number effects

Heat transfer in a fully developed turbulent pipe flow is investigated by the use of the large eddy simulation technique. Isoflux condition is imposed at the wall. Four Prandtl numbers are considered (0.71, 3, 5, and 7) and three Reynolds numbers (5,500, 10,000, and 20,000). The effects of Reynolds and Prandtl numbers on turbulent heat transfer in pipe flow are investigated in order to obtain a more detailed knowledge of the thermal field in circular pipe flow. The objective of this study is also to examine the effectiveness of the large eddy simulation approach for predicting the turbulent heat transfer at different Prandtl numbers larger than 0.71, for various Reynolds numbers up to 20,000. Validation is achieved by comparing the present predictions to the available results of the literature. The effects of Prandtl and Reynolds numbers on many statistical quantities, such as mean temperature profiles, RMS of fluctuating temperature, turbulent heat fluxes, higher-order statistics, and heat transfer coefficient, are examined. Visualizations of instantaneous filtered temperature fields are analyzed.     

Large- and very-large-scale motions in channel and boundary-layer flows

Large-scale motions (LSMs; having wavelengths up to 2-3 pipe radii) and very-LSMs (having wavelengths more than 3 pipe radii) have been shown to carry more than half of the kinetic energy and Reynolds shear stress in a fully developed pipe flow. Studies using essentially the same methods of measurement and analysis have been extended to channel and zero-pressure-gradient boundary-layer flows to determine whether large structures appear in these canonical wall flows and how their properties compare with that of the pipe flow. The very large scales, especially those of the boundary layer, are shorter than the corresponding scales in the pipe flow, but otherwise share a common behaviour, suggesting that they arise from similar mechanism(s) aside from the modifying influences of the outer geometries. Spectra of the net force due to the Reynolds shear stress in the channel and boundary layer flows are similar to those in the pipe flow. They show that the very-large-scale and main turbulent motions act to decelerate the flow in the region above the maximum of the Reynolds shear stress.     

Direct numerical simulation of stably and unstably stratified turbulent open channel flows

Summary Direct numerical simulation of stably and unstably stratified turbulent open channel flow is performed. The three-dimensional Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method based on high-order accurate spatial schemes. The objective of this study is to reveal the effects of thermally stable and unstable stratification on the characteristics of turbulent flow and heat transfer and on turbulence structures near the free surface of open channel flow. Here, fully developed weakly stratified turbulent open channel flows are calculated for the Richardson number ranging from 20 (stably stratified flow) to 0 (unstratified flow) and to −10 (unstably stratified flow), the Reynolds number 180 based on the wall friction velocity and the channel depth, and the Prandtl number 1. To elucidate the turbulent flow and heat transfer behaviors, typical quantities including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of velocity and temperature fluctuations are analyzed.     

Calculation of unsteady flow past a cube on the wall of a narrow channel using URANS and the Spalart–Allmaras turbulence model

The results of numerical simulation of fully developed turbulent flow in a channel with the cube on the lower wall (for the characteristic Reynolds number Re = 40,000) within the framework of the traditional approach to the solution of unsteady Reynolds-averaged Navier–Stokes equations (URANS) in combination with the semiempirical Spalart–Allmaras turbulence model (with a correction for rotation) have been presented. A detailed comparative analysis of the results of numerical simulation of local and integral flow characteristics and the Martinuzzi experimental data has shown that the self-oscillating regime of flow past the cube is a superposition of oscillations of the arms of a horseshoe vortex and the rear arched and detached vortex structures. Using fast Fourier transformation, it has been found that the oscillations are of a bimodal character in the longitudinal and vertical directions, whereas in the transverse direction, they are of a unimodal character.     

风洞校验均速管的速度分布修正系数研究

在口径为300 mm的风洞段后接上25D～30D的相同口径的长直管流场中进行数值模拟和实验.建立了风洞管段和具有充分发展的湍流的长直管段两个仿真模型,通过对比两个模型管段中不同雷诺数下均速管流量计的差压值以及流量系数,得到一个与雷诺数有关的速度分布修正公式.从而实现直接以风洞作为大管道气体流量校验装置,节省校验装置直管段长度.     

微管道内湍流转捩的实验研究

研究旨在确定微管道内流动从层流到湍流转捩的临界雷诺数。利用微观粒子图像测速技术(Micro-PIV)研究了去离子水在内径为230μm的圆形截面玻璃微管道内的流场结构,得到了从层流到充分发展湍流各流动状态下的轴向平均速度分布和湍流度分布,实验雷诺数为1020~3145,同时研究了微管道内的流动阻力特性。平均速度场和脉动速度场的实验结果表明微管道内从层流到湍流的转捩发生在Re=1800~1900左右,与流动阻力的测量结果一致,与宏观流动比较,并未发现微管道内的流动转捩有明显提前。实验结果还显示,当Re>2700时,微管道内的平均流速分布和相对湍流度分布呈现典型的充分发展湍流状态特征。     

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.     

Edge states intermediate between laminar and turbulent dynamics in pipe flow

We studied the dynamics near the boundary between laminar and turbulent dynamics in pipe flow. This boundary contains invariant dynamical states that are attracting when the dynamics is confined to the boundary. These states can be found by controlling a single quantity, in our case the energy content. The edge state is dominated by two downstream vortices and shows intrinsic chaotic dynamics. With increasing Reynolds number the separation between the edge state and turbulence increases. We can track it down to Re=1900, where the turbulent lifetimes are short enough that spontaneous decay can also be seen in experiments.     

不同雷诺数条件下静止管道车环状缝隙流场数值模拟

为了探究雷诺数对于静边界环状缝隙流场的影响,采用Fluent软件对雷诺数为115513、154018、192522三种工况下静止管道车环状缝隙流场进行了数值模拟,并通过物理试验进行验证,结果表明:同一雷诺数条件下,在环状缝隙入口处流速最大,之后沿管道车车身方向,环状缝隙流流速呈现先减小后增大的变化趋势,且环状缝隙流流速大于管道内水流的平均流速;各横断面环状缝隙流场均以管道中心呈同心圆分布,即半径相同的各点环状缝隙流流速值大致相同,且从管道车壁面到管壁面方向环状缝隙流流速呈现二次抛物线的变化形式;不同雷诺数条件下,管道内压强值沿程变化趋势大致相同,管道车上游位置处压强沿程呈现逐渐降低的变化趋势,环状缝隙内部和管道车下游位置处的压强值沿程呈现先升高后降低的变化趋势;随着雷诺数的增加,环状缝隙流流速值与压强值和涡量值均呈现出逐渐增大的变化趋势;数值模拟结果同试验结果基本吻合,两者所得环状缝隙流流速最大相对误差不超过7%,表明通过数值模拟来研究管道车环状缝隙流场的方法是可行的。     

Dynamical systems and the transition to turbulence in linearly stable shear flows

Plane Couette flow and pressure-driven pipe flow are two examples of flows where turbulence sets in while the laminar profile is still linearly stable. Experiments and numerical studies have shown that the transition has features compatible with the formation of a strange saddle rather than an attractor. In particular, the transition depends sensitively on initial conditions and the turbulent state is not persistent but has an exponential distribution of lifetimes. Embedded within the turbulent dynamics are coherent structures, which transiently show up in the temporal evolution of the turbulent flow. Here we summarize the evidence for this transition scenario in these two flows, with an emphasis on lifetime studies in the case of plane Couette flow and on the coherent structures in pipe flow.     

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.     

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。     

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.     

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.     

A study of a flexible fiber model and its behavior in DNS of turbulent channel flow

The dynamics of individual flexible fibers in a turbulent flow field have been analyzed, varying their initial position, density and length. A particle-level fiber model has been integrated into a general-purpose, open source computational fluid dynamics code. The fibers are modeled as chains of cylindrical segments connected by ball and socket joints. The equations of motion of the fibers contain the inertia of the segments, the contributions from hydrodynamic forces and torques, and the connectivity forces at the joints. Direct numerical simulation of the incompressible Navier–Stokes equations is used to describe the fluid flow in a plane channel, and a one-way coupling is considered between the fibers and the fluid phase. We investigate the translational motion of fibers by considering the mean square displacement of their trajectories. We find that the fiber motion is primarily governed by velocity correlations of the flow fluctuations. In addition, we show that there is a clear tendency of the thread-like fibers to evolve into complex geometrical configurations in a turbulent flow field, in fashion similar to random conformations of polymer strands subjected to thermal fluctuations in a suspension. Finally, we show that fiber inertia has a significant impact on reorientation timescales of fibers suspended in a turbulent flow field.     

煤化工专用控制阀多相流流场特性研究

针对煤化工专用控制阀易磨损失效的问题,提出基于数值模拟的阀内流场分析方法.今基于可实现k-ε(Realizable k-ε)双方程湍流模型,通过有限元分析法(finite element analysis,FEA),对控制阀的多相流流场中的湍流特征进行数值模拟研究,得到湍流流场内的压力、速度的分布,并结合Preston磨削经验公式,得到控制阀内最易磨损的区域,从而为后续控制阀的结构优化设计及表面强化打下了基础.     

Numerical study on transient local entropy generation in pulsating turbulent flow through an externally heated pipe

This study presents an investigation of transient local entropy generation rate in pulsating turbulent flow through an externally heated pipe. The flow inlet to the pipe pulsates at a constant period and amplitude, only the velocity oscillates. The simulations are extended to include different pulsating flow cases (sinusoidal flow, step flow, and saw-down flow) and for varying periods. The flow and temperature fields are computed numerically with the help of the Fluent computational fluid dynamics (CFD) code, and a computer program developed by us by using the results of the calculations performed for the flow and temperature fields. In all investigated cases, the irreversibility due to the heat transfer dominates. With the increase of flow period, the highest levels of the total entropy generation rates increase logarithmically in the case of sinusoidal and saw-down flow cases whereas they are almost constant and the highest total local entropy is also generated in the step case flow. The Merit number oscillates periodically in the pulsating flow cases along the flow time. The results of this study indicate that flow pulsation has an adverse effect on the ratio of the useful energy transfer rate to the irreversibility rate.     

Hydrodynamics and Heat Transfer in Pulsating Turbulent Pipe Flow of a Liquid of Variable Properties

The effect of the variability of properties on the characteristic features of heat transfer and of pulsating turbulent pipe flow of incompressible liquid is investigated. The results are obtained by using the method of finite differences to solve numerically a set of equations of motion, continuity, and energy written in a narrow channel approximation. The set is closed by relaxation equations for turbulent stress and turbulent heat flux. A stable difference scheme is used, which is valid for high relative amplitudes of oscillation. The calculations are performed for a dropping liquid in view of the temperature dependence of viscosity. The results of calculation of heat transfer and friction resistance for two limiting cases of steady-state flow of a liquid of variable properties and of pulsating weakly nonisothermal flow fit well the available experimental data.     

The Damping Coefficient of a Pressure Wave under Conditions of Pulsating Turbulent Flow of Gas in a Channel

The available results of experimental and prediction studies of the damping coefficient and phase propagation velocity of waves under conditions of pulsating turbulent flow in a narrow channel are reviewed and analyzed. It is demonstrated that the concept of complex damping coefficient may be introduced strictly on condition of certain restrictions imposed on an oscillating and time average flow. The dependences of the complex damping coefficient on the oscillation frequency and on the Reynolds and Mach numbers of time average flow are analyzed. The calculations are performed using the data on the relative amplitude and phase of oscillation of the tangential wall stress, obtained with the aid of the turbulence model including the relaxation equations for turbulent viscosity and tangential stress. It is demonstrated that quasi-stationary models of turbulence are invalid in the region of relatively high frequencies. Numerical simulation based on the difference solution of a set of channel cross section-averaged equations of motion, continuity, and energy is performed with due regard for the experimental conditions and measuring techniques. The calculation results agree well with the experimental data.     

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.