Modeling and CFD study of heat transfer within the circulation pipes of solar water heating systems

The main objective of this work is to study numerically the thermal behavior of solar collectors. In particularly, we performed a detailed design and parametric study of the circulation pipe of an evacuated tube collector. Indeed, we altered the geometry of the anodes by adopting three configurations: circular, rectangular and triangular. In each configuration, we changed the inlet position of cold water and the outlet of hot water: either at the top, middle or bottom. The obtained results show that rectangular shape is most optimal due to the large exchange area. On the other hand, the water inlet must be positioned at the bottom and the outlet at the top in order to take profit of the stratification of the hot water and subsequently obtain high efficiency.


INTRODUCTION
Actually, intensive efforts have been made in attempt to either integrate or replace conventional energy sources with renewable energy sources (RES) in order to meet power demands [1]. This is due to the fact that RES are non-polluting and non-depletable whilst they also have low operation and maintenance costs thus making them potential sources of alternative energy [1][2]. Solar water heating systems (SWHS) are among the most common and favorable renewable energy systems as the use of these systems can result in significant energy savings. However, there are limiting factors to be considered when utilizing SWHS. These include: unpredictable behavior (energy produced from renewable energy sources may not always meet the demand), economic viability and thermal performance.
It is important to investigate ways to overcome these limitations so as to increase the viability of SWHS. A common solution to these problems is the use of an effective thermal energy storage system (one that is able to store thermal energy at the highest possible temperature whilst exhibiting minimal thermal losses). The main thermal energy storage techniques include: thermally stratified storage and reversible chemical heat storage [3]. A second method, conducted in the present study, involves to an optimization study on the design of equipment sentatives significant energy loss as the storage tank, the pipes of circuits circulation in order to increase the This paper focuses on thermal behaviour of solar collectors and aims to provide some information on thermal performance of the circulation pipe of an evacuated tube collector. So, the layout of this paper is as follows: The problem formulation and schematic configuration are presented in Section 2. The formulation of the physical model is presented in Section 3. In Section 5, a parametric study is presented together with a discussion and analysis of the corresponding results.

DEFINITlONS OF SCHEMATIC CONFIGURATIONS
In curr ent paper, we are interested in an alternative of evacuated solar collectors where the storage tank is separated from the vacuum tube as represented in Figure 1. The geometry adopted is a straight pipe. The physical model considered is shown schematically in Figure 2. We imposed a temperature of 90°C at the anodes, the rest is maintained adiabatic except the inlet and outlet pipe in which we have imposed an inlet speed water of 1 m.s-1. The initial temperature of the inlet water is equal to 15°C.

PHYSICAL MODEL AND BASIC EQUATIONS
The following assumptions are made in the analysis: • The Boussinesq approximation is valid, i.e., liquid density variations arise only in the buoyancy source term, but are otherwise neglected.

•
The water is Newtonian.
• Fluid motion is laminar and two-dimensional.
With the foregoing assumptions, the conservation equations for mass, momentum and energy may be stated as: Where u is the velocity vector, p the pressure and T the temperature and r is the viscous stress tensor for a Newtonian fluid: The integration occurs over a control V surrounded by a surface S , which is oriented outward unit normal vector ii . The source term in contains two parts: Au =pf3(T-T,,, )g Where /3 is the coefficient of volumetric thermal expansion and g the acceleration of gravity vector. The first part of the term source represents the buoyancy forces due to the thermal dilatation. In Eq.(5), T,11 is the reference temperature.
The conservation Eqs. 1-3 are solved by implementing them in a house code. This code has been successfully validated in several situations involving flow and heat transfer as in [4][5].

RESULTS AND DISCUSSION
In the current paper, we developed a parametric study on three types of anodes by changing their geometry: rectangular, circular and triangular anodes. The factors that we varied in the current study is the location of the pipe inlet and outlet.
We will presented for each form the temperature field and the outlet temperature, the streamlines and the Nusselt number on the heated source. For all simulations performed in this study, we adopted approximately a Prandtl number equal to 7 (Which corresponds to water).  The water inlet and are both chosen in middle. From the graph it can be observed that the evolution of the output temperature is slow. Initially, the water comes out at 15°C and then its outlet temperature grow slowly until reaching 55 °C for 10 min.
Contrariwise, the water average temperature inside interior pipe increases rapidly due to anodes which are used to heat water to an average temperature of 45°C.   For the case of a triangular anodes geometry, Figure 11 shows the evolution of the water temperature at the outlet and the average temperature within the pipe. The inlet/outlet are positioned in the middle of the pipe. After about 5min, the average temperature does not exceed 45°C while the outlet temperature reaches 55°C.  To compare between different geometries of anodes and to assess the optimal location of the water input/output, we based on the water outlet temperature as a criterion. Indeed, the aim is to heat the water inside the pipe therefore the most appropriate form which delivers the highest output temperature in a minimum time.
The graphs referring to figures 18, 19 and 20 depict the output temperature evolution for all anode's geometry and various inlet/outlet positions. All obtained results show that the rectangular shape is most optimal given the large surface area. The results presented previously showed that the rectangular shape is the most optimal thanks to the large exchange surface.
The objective is to select the optimal location of the water inlet/outlet based on the outlet temperature. Figure