A numerical study of turbulent flow and conjugate heat transfer in concentric annuli with moving inner rod

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Abstract

A numerical study is conducted to investigate turbulent flow and conjugate heat transfer in a concentric annulus with a heated inner cylinder moving in the streamwise direction. A modified two-equation kε model with low Reynolds number treatment near wall is employed to model the Reynolds stress and turbulent thermal field which are based on Boussinesq’s approximation. The governing equations are numerically resolved by means of a hybrid finite analysis method. A uniform inlet flow and thermal conditions are specified to consider the effects of entrance of both solid and fluid regions. For a constant Prandtl number of 6.99 of water flow, calculating results of the time-averaged streamwise velocity, turbulent viscosity and temperature field are obtained for the Reynolds numbers from 1.0 × 104 to 5.0 × 105, rod velocity ratio between 0 and 1.0, and the radius ratio ranging from 0.286 to 0.750. The parametric studies show that the bigger rod speed ratio or the radius ratio is, the temperature is higher within solid rod. For a certain absolute rod speed, temperature profile diminishes at both sides of solid rod and fluid as Reynolds number grows. Numerical results also show that compared with the case of β=0 where solid rod is stationary, for large rod speed ratio the averaged axial velocity and turbulent viscosity profiles have substantial deformations, that is, the gradient of averaged axial velocity and turbulent viscosity near rod surface greatly reduced by the axial movement of solid rod.

Introduction

The problems of heat transfer and turbulent flow in concentric annuli with moving inner solid cores are encountered in various industrial applications, such as in manufacturing processes of extrusion and drawing, in cooling system of hot rolling for steel rod, in transportation of trains traveling in a long tunnel, and in nuclear reactors during emergency core cooling of nuclear fuel channels. In these cases, the moving core exchanges heat energy with the surrounding environment continuously, and the fluid flow can be either laminar or turbulent. In this paper we just study the turbulent flow and heat transfer phenomena.

Barrow and Pope [1] made a simple analysis of turbulent flow and heat transfer in the proposed railway tunnel between England and France. Shigechi et al. [2] and Lee and Shigechi [3] obtained analytical solutions for friction factors and Nusselt number for turbulent flow and heat transfer in concentric annuli with moving cores, using a modified turbulence model which is originally presented by Van Driest [4] and Reichardt [5]. Their study shows that the friction factor decreases while the Nusselt number increases with an increase in relative velocity of inner core to the averaged flow velocity. Lee and Kim [6] studied an inverted annular film boiling during an emergency core cooling of nuclear fuel channels which involved similar fluid flow and heat transfer phenomenon. Torii and Yang [7], [8] numerically investigated the effects of various parameters such as Prandtl number, relative velocity of inner core, radius ratio, on turbulent Couette flow and heat transfer in the same geometry as that in Shigechi’s study [2], by using a version of low Reynolds number turbulence model by Launder and Shima [9]. It is found in their investigation that in the region near inner core, a reduction of velocity gradient due to its axial movement results in a decrease in heat transfer performance. Azouz and Shirazi [10] made an evaluation of several turbulence models for turbulent flow in concentric and eccentric annuli and their numerical results showed that a kind of mixing length model performs as well as low Reynolds two-equation model [11] except in the case where the annular gap is narrow.

It is worthwhile to notice that almost all of above researches are only involved in flow and heat transfer problems in annular fluid region for a given thermal boundary conditions, and no considerations are given to the heat conduction within the inner moving solid cores. In fact, it is often a basic requirement to know temperature distribution within moving solid rod in some applications such as hot rolling process where it is very hard to set a thermal boundary condition on the rod surface. Therefore, in both solid and fluid regions the heat transport phenomenon should be discussed together. When the interaction of heat conduction in solid rod with convection heat transfer in flow field must be considered simultaneously, such situations are referred to as conjugate flow and heat transfer problems. To authors’ knowledge, there is seldom research done before on the conjugate heat transport phenomena in concentric annuli with moving inner cores [12].

The main objectives of this paper are to investigate the turbulent flow and conjugate heat transfer characteristics in concentric annuli with inner moving rod in the flow direction. A recently developed numerical scheme called hybrid finite analysis method (HFAM) [13] is used to discretize the governing equation sets for both flow and temperature fields in concentric annulus and the inner solid rod. A modified two-equation kε model with low Reynolds number treatment near walls [14] is employed to model the Reynolds stress and turbulent thermal field which are based on Boussinesq’s approximation and Reynolds analogy respectively. Uniform flow and isothermal boundary conditions at both flow and solid rod inlets are specified to consider the effects of entrance region. Emphases of our researches are placed on the effects of movement of inner solid rod, various radius ratio and Reynolds number on thermal fields in whole domain and heat transfer rate on the surface of moving rod. Particularly, further attentions are paid on turbulent flow and temperature properties at outlet of both flow field and solid rod.

Section snippets

Governing equations and solution procedure

As shown in Fig. 1, we consider two dimensional axisymmetric turbulent convection flow and heat transfer coupled with a hot inner solid rod moving in a pipe concentrically. Assuming that effects of gravity are neglected as well as the effect of buoyancy due to temperature difference, the flow and heat transfer within both flow and solid areas can be regarded as a steady axisymmetric problem at stable operation condition. In two dimensional cylindrical coordinates, the averaged dimensionless

Results and discussion

The numerical results and consequent discussions are divided into three parts to introduce. In part one is the verification of numerical procedure. Part two shows temperature fields in the total domain of physical model, along with thermal properties on the rod surface, say, Nusselt numbers. The definition of local Nusselt number isNu=q(R2−R1)(Ts−TwfR=R1=θrr=R1/(R2−R1).

Part three concerns temperature and averaged turbulent flow velocity profiles at outlet of the computation domain.

Conclusions

Numerical predictions have been performed for two dimensional axisymmetrical turbulent flow and conjugate heat transfer in a concentric annulus with a heated inner cylinder moving in the streamwise direction. A modified two-equation kε model with low Reynolds number treatment near wall is employed to model the Reynolds stress and turbulent thermal field. The governing equations are numerically resolved by means of a HFAM. The following conclusions are derived from the present study.

For a

Acknowledgements

The authors acknowledge the financial support that was received from Korea Science and Engineering Foundation (KOSEF).

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