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.     

Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Steady-state and quasi-steady-state flows in a round pipe with constant density of heat flux to the wall

Integral relations are derived for the calculation of the Nusselt number and coefficients of hydraulic drag and friction drag under conditions of pipe flow of dropping liquid and gas of temperature-dependent physical properties. In the limiting case of steady-state flow of liquid of constant properties, the expression for the Nusselt number transforms to the well-known Lyon integral. The results of calculation of heat transfer and drag by an integral method are compared with more exact results obtained using the numerical solution of the set of differential equations of convective heat transfer. An inference is made about the conditions under which integral methods may be employed. An algorithm is developed for the calculation by an integral method of heat transfer and drag under conditions of quasi-steady-state pulsating flow. It is demonstrated that the flow rate oscillations superposed on the flow in the pipe enhance the effect of the variability of the properties on heat transfer, and for gas on friction drag. For a dropping liquid under conditions of pulsating flow, the friction drag depends less significantly on the variability of the properties (viscosity) than in the case of steady-state flow. The degree of manifestation of the effects identified above is the higher, the higher the oscillation amplitude and the lower the value of the Reynolds number of averaged flow.     

Pulsating Turbulent Flow of Gas in a Round Pipe

An analysis is performed of the presently available results of experimental and prediction studies into pulsating turbulent flow of liquid in a narrow pipe under conditions when the compressibility is apparent. It is demonstrated that the simulation of such flows in the general case may be performed only numerically, using a model of turbulence that adequately includes the effect of oscillation on turbulent transfer. Use is made of a model of turbulence whose validity is proved by comparing the calculation and experimental results for a wide range of flows. Calculations are performed for a pulsating flow of gas in pipes with isothermal and adiabatic walls, acoustically closed at the outlet, in the frequency range corresponding to the first resonance harmonic. The predicted variations of the heat flux to the wall and of the hydraulic drag, averaged over the oscillation period, as functions of the process parameters such as the Reynolds number of the mean flow and the dimensionless oscillation frequency are discussed.     

脉动冲击射流的传热特性研究

为了深入理解脉动冲击射流的传热传质特性,研究脉动流的温度相关热物理性质对于靶面局部努塞尔数分布的影响,分别对正弦和方波非稳态脉动冲击射流进行了数值模拟.结果显示单个正弦脉冲的强化传热并不明显,而方波脉冲的强化传热效果却十分明显.对于脉动冲击射流中的流场分析表明,靶面上的瞬态换热效率与非线性热力学和水力学边界层随时间的发展密切相关.     

Effect of the size of air bubbles on enhancement of heat transfer in an impinging liquid jet

The numerical modeling of heat transfer in a bubbly impinging jet is carried out. The axisymmetric system of RANS equations that take into account the two-phase nature of the flow is resolved based on the Euler approach. The turbulence of the liquid phase is described by the Reynolds stress transport model with taking into account the effect of bubbles on modification of the turbulence. The effect of the gas volumetric flow rate ratio and the bubble size on the flow structure and the heat transfer in a gas–liquid impact stream is studied. It is shown that the addition of the gas phase in a turbulent fluid causes an increase up to 1.5-fold in heat transfer. The comparison of the simulation results with experimental data showed that the developed model enables the simulation of turbulent bubbly impinging jet with heat transfer with the pipe wall in a wide range of gas fraction.     

Heat Transfer in a Turbulent Flow of Gas in a Tube under Conditions of Resonance Oscillation of the Flow Rate

A prediction study is made into the heat transfer in a turbulent flow of gas (air) in a narrow tube with superimposed resonance oscillation. The model of turbulent transfer includes the effect of nonstationarity on the turbulent stress and heat flux. The finite difference method is used to solve the equations of motion and energy. The distribution of the flow rate and pressure along the tube is found by way of numerical solution of a set of cross section-averaged nonstationary equations of motion, continuity, and energy. The effect of the process parameters (Reynolds number, dimensionless oscillation frequency, thermal boundary conditions on the wall) on the period-average heat transfer and heat flux to the wall is analyzed.     

Hydrodynamics and heat transfer in turbulent pipe flow of liquid under conditions of monotonic time variation of the flow rate

The available experimental and theoretical studies of hydrodynamics and heat transfer in turbulent pipe flow of liquid under conditions of monotonic increase or decrease of the flow rate are reviewed and analyzed. The reason is found why the effect of hydrodynamic nonstationarity on heat transfer and skin friction coefficient turns out to be different from that in the case of laminar flow. The differences in this effect on heat transfer and drag are treated. The experimentally observed effects are reproduced most accurately when simulated on the basis of equations for turbulent stresses and heat fluxes.__________Translated from Teplofizika Vysokikh Temperatur, Vol. 43, No. 2, 2005, pp. 212–222.Original Russian Text Copyright © 2005 by E. P. Valueva.     

乙烷脉动热管的CFD数值模拟研究及实验对比

为了更好地了解脉动热管内部的内在运行机制,本文在实验的基础上采用VOF模型对乙烷脉动热管的传热特性进行了数值模拟研究.结果表明:充注工质后,脉动热管内部形成了随机的气液分布;在启动过程和稳定运行过程中,温度波动的频率随着加热功率的增大而增大;在稳定运行过程中,脉动热管内的流型也在不停地变化.将模拟结果与前期的实验结果进...     

Dynamic characteristics of pulsating turbulent flow of compressible gas in a channel

A model of turbulent transfer that allows for the effect of flow-rate oscillations on the turbulent stress is used to investigate pulsating turbulent flow of a compressible gas in a narrow channel. An algorithm for solving numerically the system of equations that describes this process by the finite-difference method with the use of an implicit iteration scheme is proposed. The effect of operating parameters on the amplitude-frequency characteristic is considered.     

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.     

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.     

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.     

Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Pulsating high-frequency flow

An integral method is suggested for approximate calculation of oscillation-period average heat transfer and drag under conditions of pulsating high-frequency flow of gas in a pipe with constant density of heat flux to the wall. It is found that the flow rate oscillation superimposed on the flow has little effect on the period average Nusselt number and coefficient of friction drag; these quantities may be calculated by the method developed for a steady-state flow of liquid of variable properties. The oscillation affects significantly the period average coefficient of hydraulic drag whose values increase with the amplitude of superimposed oscillation.     

Numerical modeling of heat exchange and turbulent flow of fluid within tubes at supercritical pressure

Modes of normal and degraded (with peaks of wall temperature) heat transfer are computed for the turbulent flow of carbon dioxide within a circular tube at supercritical pressure. Computation is based on a set of motion, continuity, and energy equations written under the approximation of a narrow channel. The turbulence model uses the Prandtl formula for the turbulent viscosity. The relationship for the travel length takes into account the effect of variation in the fluid properties and thermal acceleration through the tube section. Computation results for variation in the wall temperature along the tube fit the experimental data. An explanation is given for causes of the appearance of the peak on the wall temperature distribution along the tube in the area, where the fluid temperature is close to the pseudocritical temperature.     

Convective heat transfer coefficients for near-horizontal two-phase flow of nitrogen and hydrogen at low mass and heat flux

Correlations for convective heat transfer coefficients are reported for two-phase flow of nitrogen and hydrogen under low mass and heat flux conditions. The range of flowrates, heat flux and tube diameter are representative of thermodynamic vent systems (TVSs) planned for propellant tank pressure control in spacecraft operating over long durations in microgravity environments. Experiments were conducted in normal gravity with a 1.5° upflow configuration. The Nusselt number exhibits peak values near transition from laminar to turbulent flow based on the vapor Reynolds number. This transition closely coincides with a flow pattern transition from plug to slug flow. The Nusselt number was correlated using components of the Martinelli parameter and a liquid-only Froude number. Separate correlating equations were fitted to the laminar liquid/laminar vapor and laminar liquid/turbulent vapor flow data. The correlations give root-mean-squared (rms) prediction errors within 15%.     

Temperature distribution in cylindrical packed beds

The heat transfer problem in a cylindrical packed bed with continuous flow of gases has been studied by treating the solid phase as a pseudo-homogeneous substance. A set of finite difference equations governing the temperature distributions in the solid and gaseous phases have been obtained using a mixing-cells model, to account for the turbulent mixing phenomenon. Numerical solutions are obtained by solving this set of equations of temperature distributions using relaxation method.     

单面波浪平板脉动热管的传热性能

对一种单面波浪平板脉动热管的传热性能进行了实验研究,分析在空气强制对流冷却条件下充液率、加热功率、倾角等因素对其传热性能的影响。研究结果表明,除0°倾角外,脉动热管的最佳充液率为20%～30%,倾斜角度对脉动热管传热性能的影响很小,但90°时相对最好。脉动热管在0°放置时其传热性能较差,在低充液率的情况下甚至丧失脉动效果,主要是工质回流不畅的原因,与平板脉动热管的槽道设计有很大关系。此外低加热功率时热管传热性能存在波动,有时甚至不能启动。     

An integrated,finite element‐based process model for the analysis of flow,heat transfer,and solidification in a continuous slab caster

An integrated, finite element‐based process model is presented for the prediction of full three‐dimensional flow, heat transfer, and solidification occurring in a continuous caster. Described in detail are the basic models for the analysis of turbulent flow and heat transfer in the liquid steel zone, in the zone of mixture of the liquid steel and solidified steel, and in the solidified zone. Then, the models are integrated to form a process model which can take into account the strong interdependence between the heat transfer behaviour and the flow behaviour. The capability of the process model to reveal the detailed aspects of turbulent flow, heat transfer, and solidification occurring in a continuous caster is demonstrated through a series of process simulations. Copyright © 2003 John Wiley & Sons, Ltd.     

用于测量脉动气流平均流量的稳压箱的研究

以稳压箱为控制体建立基本方程对其无量纲化后进行数值求解，并用准则方程式予以拟合。计算结果表明，按本准则方程得到的曲与ＩＳＯ／ＴＲ３３１３中提供的实验数据的吻合程序优于该技术报告中的理论分析结果与实验数据的吻合程度。     

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.