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.     

Comparative analysis of turbulence models

A comparative analysis is performed for a complete locally anisotropic turbulence model of the second order and existing turbulence models. The comparison draws on experimental data, data of a direct numerical simulation of the nonstationary Navier-Stokes equations for a developed channel flow and a uniform channel flow with a constant velocity shift, and results for turbulence damping behind a grid. The K-ɛ model and the quasi-isotropic turbulence model are shown to have marked disadvantages, especially in describing turbulent flows with a high degree of anisotropy of pulsatory motion. Use of a locally anisotropic turbulence model improves the accuracy of determining Reynolds stresses. Consideration is given to the advantages and disadvantages of the turbulence models discussed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 328–339, March—April, 2000.     

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 Dynamic Characteristics of a Pulsating Turbulent Flow of Compressible Gas in a Pipe under the Effect of Time-Average Flow

The effect of time-average flow with the values of Mach number M = 0.03–0.3 on the transfer functions of a gas pipeline is investigated. A set of cross section-averaged equations of motion, continuity, and energy, written in a narrow-channel approximation, are solved by the finite difference method. The variability of the gas density and sound velocity is taken into account. The heat flux to the wall is assumed to be constant. The wall friction is calculated using the data previously obtained by solving a nonstationary equation of motion simultaneously with relaxation equations for turbulent stress and turbulent viscosity. The calculations are performed in three characteristic frequency regions, namely, regions of quasi-stationary and frozen turbulence and an intermediate region. It is demonstrated that the effect of time-average flow leads to a decrease in the amplitudes of oscillation of velocity and pressure in the resonance mode.     

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.     

Calculation of a turbulent monodisperse flow in an axisymmetric channel

A stationary isothermal model of the aerodynamics of a two-phase flow in an axisymmetric channel has been constructed with allowance for the turbulent and pseudoturbulent mechanisms underlying the transfer of the solid phase momentum. The equations of dispersed phase motion are closed at the level of the equations for the second moments of the pulsation velocities of particles, whereas the equation of momentum transfer of the carrier is closed on the basis of a one-parameter model of turbulence extended to the case of two-phase turbulent flows. The results of calculations are compared with experimental data. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 844–855, September–October, 2008.     

On a rational theory of turbulence

Based on the Theory of Micromorphic Fluid Dynamics, a thermodynamically admissible and frame-independent theory of turbulence is introduced. Field equations, boundary and initial conditions are given. The theory is applied to obtain the solution of turbulent channel flow. Turbulent mean velocities predicted by the theory are in good agreement with experimentally measured turbulent mean velocities.     

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.     

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.     

Surface Oscillations of an Electromagnetically Levitated Droplet

The natural oscillation frequency of freely suspended liquid droplets can be related to the surface tension of the material, and the decay of oscillations to the liquid viscosity. However, the fluid flow inside the droplet must be laminar to measure viscosity with existing correlations; otherwise the damping of the oscillations is dominated by turbulent dissipation. Because no experimental method has yet been developed to visualize flow in electromagnetically levitated oscillating metal droplets, mathematical modeling can assist in predicting whether or not turbulence occurs, and under what processing conditions. In this paper, three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k−ɛ turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem when the interior flow is turbulent. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to available experimental results.     

Formation and development of turbulence during movement of a disperse system in a round tube

The experimental results are presented for a study of the turbulence intensity, coefficient of intermittence, and average velocity profile during the transition of the laminar flow of an aqueous dispersion of bentonite clay to turbulent flow. A calculation of the critical value of the Reynolds number is offered.     

ISOTHERMAL PREDICTION OF PARTICLE AND GAS FLOW IN A COAL-FIRED REACTOR

The steady, turbulent gas flow with entrained coal particles in a laboratory-scale axisymmetric coal gasification reactor is numerically analyzed. The reactor is designed to provide rapid mixing and heatup of the coal in a configuration which results in a nearly isothermal and uniform flow in the main reaction chamber so as to allow controlled study of coal gasification. A detailed knowledge of the reactor dynamics is required in order to interpret experimental results. The nonreacting, isothermal flow pattern is first presented as a base case. Calculations are performed with an iterative, implicit scheme suitable to the elliptic nature of the gas flow equations in an Eulerian frame-work. The turbulent motion is resolved using the eddy-viscosity concept with the standard k-ε turbulence model. Coal particle trajectories are then calculated using the Lagrangian form of the momentum equations. The influence of solid particles on the gas phase is neglected. Particle trajectories and residence time distributions are presented for a variety of particle sizes and particle inlet locations. The influence of the inlet conditions, turbulent diffusion, and gravity on the particle motion, are investigated. Implications of the predictions, with respect to the design of the reactor, are discussed.     

Incompressible micromorphic fluid model for turbulence

A theory of incompressible micromorphic fluids is introduced as a rational model for turbulence studies. Balance laws and constitutive equations are given. The theory is then applied to obtain the solution of the turbulent channel flow problem. Turbulent velocity, gyrations, Reynolds stresses, root-mean squares of longitudinal and transverse turbulent velocities, and turbulent shear stress are given.     

Approximate method for calculating turbulent two-phase flow in a channel with permeable walls

Based on a model of a double-velocity and two-temperature medium the authors constructed a system of equations that describes plane or axisymmetric turbulent flow of a gas suspension in a channel with permeable walls. The system of equations of motion and heat transfer reduces to a system of ordinary differential equations, whose integration is much less difficult than solution of the initial system. The authors obtained the distribution of the velocity and local characteristics of turbulence in the channel with injection with allowance for the inverse effect of a condensed phase.     

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.     

Mathematical analysis of whirled turbulent flow through a pipe

The effect of rotation of the stream on the development of turbulent flow in a pipe is analyzed by a numerical method. Calculated distributions of average turbulence velocity and energy are compared with experimental data.     

Gas-particle turbulent flow of foursquare tangential jets in a simplified pulverized-coal firing boiler

An experimental cold-model of a simplified tangential firing boiler was established to investigate the mesoscale turbulent flow behaviors, including gas vortex structures, particle motions and interactions between two phases. A modified PIV technology, employing two pairs of lasers and cameras, was applied to measure the velocity and velocity gradient of turbulent flow in foursquare tangential jets alternatively. At a given initial gas velocity and particle mass loading, the interaction between gas and particles was studied at three different particle sizes. It was found that two main coherent vortex structures, circular eddy and hairpin eddy, distributed mainly in low speed area and heavy impingement area, respectively. The characteristics of particle motion in foursquare tangential jets correlated with gas turbulence dissipation, particle size, particle concentration and particle density. Small particles were easily entrained by gas vortex, so that they consumed more turbulence energy and attenuated the gas turbulence intensity. On the contrary, large particles had more inertia and led to heavier impingement in the chamber center, resulting in particle random distribution and complex momentum transfer between gas and particles. Moreover, large particles stretched the coherent vortex to be narrow and long, while small particles pulled down the vortices rotation intensity.     

Numerical Simulation of Self-Excited Oscillation of a Turbulent Jet Flowing into a Rectangular Cavity

The example of a plane jet flow into a rectangular cavity (“dead end”) is used in comparing the capabilities of different approaches to numerical simulation of self-oscillatory turbulent flows characterized by global quasi-periodic oscillation of all flow parameters. The calculations are performed for two flow modes, of which the first one is statistically steady according to the available experimental data, and the second one is self-oscillatory. In both cases, three approaches are used to describe the turbulence, namely, the method of large eddy simulation (LES) in combination with the subgrid model of Smagorinsky, and steady and unsteady Reynolds averaged Navier-Stokes equations (SRANS and URANS) with two well-known differential models of turbulence. In the case of the first flow mode, all three approaches produce qualitatively similar and quantitatively close results. In the case of the second (self-oscillatory) mode, a steady-state solution of Reynolds equations may only be obtained in half the domain using the symmetry boundary conditions; within the framework of the other two approaches, the solutions turn out to be unsteady-state. In so doing, their characteristics calculated using the LES and URANS methods differ significantly from each other; in the case of URANS, they further depend on the model of turbulence employed. The best results as regards the accuracy of prediction of the amplitude-frequency characteristics of self-oscillation are produced by the use of the LES and three-dimensional URANS methods. A similar inference may be made with respect to the mean flow parameters. From this standpoint, the worst results are those obtained from calculations involving the use of the symmetry boundary conditions on the geometric symmetry plane of the flow.__________Translated from Teplofizika Vysokikh Temperatur, Vol. 43, No. 4, 2005, pp. 568–579.Original Russian Text Copyright © 2005 by D. M. Denisikhina, I. A. Bassina, D. A. Nikulin, and M. Kh. Strelets.     

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.     

Analysis of high temperature gasdynamics in a rectangular channel using a coupled core-boundary layer model

In this paper two-dimensional steady state compressible, turbulent boundary layer equations along with the core are solved for a channel of rectangular cross-section. The behaviour of core velocity, core temperature, pressure profile, friction coefficient and heat flow for different mass flow rates and inlet pressures are analysed for combustion gases. The results are compared with experimental results obtained onzinc (zero induction channel) during the commissioning of themhd plant at Tiruchirapalli. The results match the theoretical predictions quite well.