Laminar Mixed Convection in Two Concentric Vertical Cylinders

Laminar Mixed Convection in Two Concentric Vertical Cylinders

Ahmed Hadjadj (Faculty of Hydrocarbons and Chemistry, Boumerdes University, Boumerdes, Algeria) and Seghir Maamir (Engineering Faculty, Boumerdes University, Boumerdes, Algeria)
DOI: 10.4018/IJCCE.2016010103
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Abstract

The flow patterns and heat transfer have been studied numerically for contained air in the space formed by two vertical concentric cylinders. The inner cylinder rotates about its vertical axis and the outer cylinder is kept stationary. This geometry simulates, for example, the gaps at the ends of the rotor of vertical electric motors. The results facilitate the thermal design of such devices. The governing equations for velocity and temperature are solved by finite volume techniques in which the SIMPLE algorithm is incorporated. Results are presented for a range of Reynolds numbers (Re) and for various values of aspect ratio. It has been found that for high values of Re, the flow is dominated by centrifugal forces whereas for low values of Re the flow is dominated by gravitational buoyancy. To facilitate the use of results for design, some correlations were developed which represent the heat transfer coefficient as a continuous function of the investigated independents parameters.
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Introduction

Heat and mass transfer from rotating cylindrical bodies occur in many practical applications, the most common being the cooling of conventional rotating machinery, such as electrical motors. The development of new rotating devices has further enhanced interest in this area. Among these are “barrel reactors” used in the chemical vapor deposition (CVD) process and rotating heat exchangers operating in a variety of different ways are being introduced in the chemical, automotive and nuclear industries. Buoyant rotating flows also occur in nature (e.g. oceanic and atmospheric circulation) which could provide useful models for study. Moreover, the authors are interested by the application of simulation results to the rotating drill motion in oil and gas wells.

Some works have been reported concerning mixed convection heat transfer within rotating vertical annulus. A theoretical investigation was conducted by (Badr & Denis, 1985) to evaluate the effect of rotation on the convective heat transfer process from a rotating cylinder (Hessami, De Vahl Davis, Leonardi & Reizes, 1987) and (Ho & Tu, 1993) have studied numerically the laminar mixed convection for air and water respectively contained in vertical annulus with the inner cylinder and one of the horizontal end walls rotating about the vertical axis, in order to simulate the heat transfer behavior of a small fluid-cooled electric motor. Also, a hydrodynamically and thermally developing laminar flow in a heated vertical channel was studied by (Yao, 1983, 1987). In the same way, (Guo & Zhang, 1992) have conducted a numerical study of heat transfer in a vertical rotating cylinder with a temperature difference imposed on the top and bottom ends. They suggested a dimensionless parameter group Gr/() to replace the ratio which is commonly used in mixed convection (Mokheimer & El-Shaarawi, 2004) obtained critical values of Gr/Re that make the free convection effects offset the friction inside a vertical eccentric annulus. Furthermore, (Ball & Farouk, 1987) and (Ball, Farouk & Dixit, 1989) presented a series of studies concerning the buoyancy effects on the fluid flow patterns and heat transfer characteristics developed in a taller annulus with a heated rotating inner cylinder. In particular, the buoyancy effects on the bifurcation and stability of the Taylor-Couette flow were addressed numerically (Mokheimer & El-Shaarawi, 2004) and experimentally (Ball & Farouk, 1987) by the authors. The structure of the Taylor vortices was found to be greatly distorted by buoyant flows. It is widely known that a critical speed of rotation exists above which appears a stable secondary mean flow consisting of regularly spaced toroidal vortices. This flow is commonly referred to as Taylor-Couette or Taylor-vortex flow and results from an inherent hydrodynamic instab1lity. In a flow regime controlled by gravitational buoyancy and Coriolis forces, (Hasan & Sanghi, 2004) show that the Coriolis forces play a dual role of enhancing the convection as well as suppressing it. Comprehensive reviews of this flow problem are available in (DiPrima & Swinney, 1985), (Chen & Hsieh, 1991), (Jackson, Cotton, & Axcell, 1989), (Sathyamurthy, Karki, & Patankar 1992), (Sparrow & Preston, 1982) and the references therein should be consulted for further details.

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