HMOUDA Imen1*, RODRIGUEZ Ivette2 and BOUDEN Chiheb1

1Energy in Buildings and Solar Energy, National School of Engineers of Tunis
ENIT B. P. 37 1002 Tunis — Belvedere Tunisia

2Centre Tecnologic de Transferencia de Calor (CTTC), Universitat Politecnica de Catalunya (UPC), C.

Colom 11, 08222, Terrassa, Barcelona, Spain
Corresponding Author e-mail : ih tn@yahoo. fr

Abstract

Thermal energy storage tank is an essential component of solar heating systems. In this process, the buoyancy convection plays an important role where it is essential to ensure the availability of energy at the following days. Long-thermal behaviour of cooling an initially isothermal Newtonian fluid in a vertical cylinder by unsteady natural convection has been investigated in this study by scaling analysis and direct numerical simulation. The studied case assumes that the fluid cooling is due the imposed fixed temperature on the vertical side wall where as the top and bottom boundaries are adiabatic. Transient, axi-symmetric and natural convection in storage tank is studied. The unsteady natural convection has been investigated numerically by mean of an appropriate CFD code developed and validated using different benchmarking cases. The long-term behaviour of the fluid cooling in the cylinder is well represented by the average fluid temperature function of time, and the average Nusselt number on the cooling boundary. The scaling analysis shows that the dimensionless temperature is related to the dimensionless time, the Rayleigh number and the aspect ratio of the vertical cylinder. The dimensionless temperature ejj) is scaled

cylinder, Ra the Rayleigh number, and C a proportionality constant. A series of direct numerical simulations with the selected values of A, Ra, and Pr (Pr is the Prandtl number) in the ranges of 1/3< A <3, 6.106< Ra < 6.1010 and 1< Pr <1000 have been carried out to validate the developed scaling relations, and it is found that these numerical results agree well with the scaling relations. The numerical simulations reveal that the flow has considerably different transient features and vigorous flow activities mainly occur in the vertical thermal boundary layer on the side wall.

Key words: CFD, natural convection, cooling-term.

1. Introduction

The phenomenon of laminar convection in fluids in a cylindrical enclosure, driven by density difference, often occurs in technical applications and industrial processes. The fluid motion caused by this phenomenon has a great impact on the working characteristic of devices and processes where it occurs. This problem arises in applications such as: tanks for energy storage. Indeed, buoyancy convection plays an important role in process of thermal energy storage where it is essential to ensure the availability of energy at the following days. Thus, the system response to changing boundary conditions and the understanding of its behavior is of fundamental interest and practical importance.

Several works concerning this subject are available in the literature, involving experimental and numerical analysis. Cotter and Charles [1-2], in two papers, investigated, during the cooling
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process, the transient natural convection of a warm crude oil contained in a vertical cylindrical tank. The numerical results have been compared with experimental data and a time dependence of Nusselt number for several oil viscosity has been defined. Natural convection was also analyzed by Ivancic et al. [3]. They investigated the case of the cylindrical tank using an adiabatic sidewall while maintaining low temperature at the top and high temperature at the bottom. Different tank aspect ratios (1 — 5) and Prandlt number (10-2 — 105) have been examined.

Oliveski et al. [4] made a numerical and an experimental analysis of velocity and an temperature fields inside a storage tank submitted to natural convection. They studied the effect of aspect ratio, volumes and insulation thicknesses on the thermal performance of the storage tank. Correlations for the Nusselt number were obtained. A good agreement between the numerical and experimental results have been obtained. Adopting the same methodology, these authors [5], compared the one­dimensional results with detailed model and experimental results. They shown that simplified model can agree with experimental only when several computational artifices were included.

In [6], [7], the authors carried out a scaling analysis and direct numerical simulation of the transient processes of cooling-down an initially homogeneous fluid by natural convection in a vertical cylinder. Many direct numerical simulations under different flow situations in terms of Ra, Pr and A were studied. The results show that vigorous flow activities concentrate mainly in the thermal boundary layer along the sidewall.

More recently, Rodriguez et al. [8] carried out a scaling analysis and numerical simulation of transient process of cooling-down an initially homogeneous fluid in a vertical cylinder submitted to natural convection. The obtained correlations can be extrapolated to other situations as they are expressed in term of non-dimensional parameters governing the phenomenon that occurs inside the tank.

In this work, a long-term cooling process of a storage tank submitted to unsteady natural convection is numerically investigated. The the top and upper walls of the stoarge tank are supposed adiabatic while the sidewall is submitted to ambient temperature. A series of numerical simulations with the selected values of A, Ra, and Pr (Pr is the Prandtl number) in the ranges of 1/3< A <3, 6.106< Ra < 6.1010 and 1< Pr <1000 have been carried out to validate the developed scaling relations.