NUMERICAL INVESTIGATION OF A MANTLE HEAT EXCHANGER

: The following work deals with numerical investigation of a storage tank equipped with a mantle annular cavity surrounding it. Heat is transferred via the working fluid flowing in the mantle side to the inner storage tank. Water at constant temperature of 60 oC enters the mantle to heat the tank and exits at a lower temperature. The study is carried out using the commercial software Ansys−Fluent to track the change of water temperature in the tank and mantle side during the simulated period of 60 minutes. Temperature contours of tank water and mantle water are drawn at several time intervals during the simulated period. The effects of changing working fluid mass flow rate were taken into account through three values, namely; 0.0077, 0.015 and 0.02 kg/s. Three values of mantle gap thickness; 10, 15 and 20 mm, and three values of mantle length; 250, 300 and 350 mm were applied in the simulation program and their effects were monitored and displayed. Results show that increasing the value of mass flow rate causes more heat transfer rate to the storage tank. The gap thickness of 10 mm which is the smallest value among the three applied values gave the best heat transfer rate and the mantle length of 300 mm was the optimum among the applied values. The heat transfer rate to the tank was studied in terms of tank mean temperature. The maximum mean tank temperature achieved at the end of the simulated period was 42 o C.


Introduction
Mantle heat exchangers or mantled storage tanks are usually employed in the field of solar energy engineering as a means of heat transfer between the solar collector working fluid and the storage medium. The importance of using mantle heat exchangers are the efficient heat transfer between the working fluid and the storage tank, freeze protection inside the solar collector that is connected to the mantle and the simplification in design and mounting because the heat exchanger and tank becomes a single unit Furbo [1]. A typical mantle heat exchanger consists of a conventional water storage tank wrapped from outside by an annular cavity or (mantle) through which the working fluid flows. The area of heat transfer is greatly increased by this configuration and the frictional losses are decreased. Thermal stratification inside the tank may also be enhanced especially in vertical orientation of the storage tank. The research work in mantle Heat exchangers started at the early nineties by the works of Furbo [1], Furbo and Berg [2] and Furbo [3]. The researches focused on transient modeling using finite differences. Another approach was adopted by Baur et al. [4], by dividing the storage tank into several horizontal layers. The water at each layer was assumed fully mixed with radial temperature ignored. Detailed CFD modeling on a vertical mantled tank was conducted by Shah and Furbo [5]. The water flow rate employed was comparable in value to that applicable in solar water heaters. Three dimensional body fitted technique was applied to the tank domain with 42, 25 and 10 nodes in axial, radial and circumferential directions respectively. Buoyancy effects were modeled using Boussinesq approximation. The theoretical results were also experimentally validated. Visualization techniques were also used to monitor and understand the flow patterns of working fluid in the tank and mantle sides. Shah et al. in 1999 [6] applied Particle Image Velocimetry PIV technique on a rectangular mantle storage tank. The results obtained from the rectangular device approaches the results of circular device for small mantle gap/tank diameters ratios. The effects of using mantle heat exchanger on the yearly performance of a solar water heater was investigated by (L. J. Shah, 2001) [7]. CFD results were combined with empirical correlations describing the long term performance of the system. Various values mantle gap thickness, tank height to diameter ratio and mass flow rate were used in the correlations. The results were compared with actual measurements of temperature and heat flux and good agreement was achieved. The effect of using mantle heat exchanger on thermal stratification was further studied experimentally and numerically by Knudsen and Furbo [8]. A Ph.D. thesis (S. Knudsen, 2004) [9] was entirely devoted to study and analyze a low flow rate solar domestic water heater containing mantle heat exchanger. Knudsen and Morrison, 2005 [10] performed a visualization study on the mantle and tank sides via PID method. The initial condition of the tank was assumed fully mixed once and thermally stratified once again. The effect of a variable inlet port temperature was also considered.
Previous research work on mantle heat exchangers included most of the relevant design and performance parameters. However, detailed studies regarding the temperature distributions in both mantle and tank sides are still required. The aim of the present work is to numerically analyze the thermal performance of a vertical mantle heat exchanger. The study will employ the commercial software Ansys Fluent to estimate the temperature and velocity distributions on both mantle and tank sides. The theoretical results will be compared with experimental measurements for the sake of validation. The effect of some design and performance parameters will also be studied.

Numerical Computation
The problem at hand is a three-dimensional transient heat transfer between the working fluid flowing at a constant inlet velocity in the mantle and the stagnant water in the tank via the metal interface between the mantle and tank. To solve the problem and estimate the transient velocity and temperature distributions in both the mantle and tank sides, the commercial CFD software Ansys Fluent is used. The simulation procedure is divided into the following steps: a-The geometrical model is created by the (Design Modeler) b-Discretizing the mantle and tank domains through the (Mesh Platform) c-Resolving the issue by (Fluent 16.2 CFD solver)

Geometric Modeling
The current system's geometries are drawn using Ansys Design Modeler. The first step in numerical simulation is to define the geometry. It entails drawing a cylindrical tank surrounded by a mantle, with inlet and outlet ports on both the mantle and tank sides, as shown in (Fig. 1). The system's dimensions are given in (table 1). Water, stainless steel, and glass wool properties are given in (table 2).

Mesh Generation
The temperature distributions in the tank and mantle sides are evaluated by discretizing the two domains into tiny elements. The entire computational domain is transformed into a mesh like grid with a massive number of elements. The tank and mantle domains were analyzed and discretized as computational domains. The mesh generation process is carried out by the CFD software Ansys 16.2 to generate 255,609 elements in both domains. (Fig. 2) depicts the discretized mantle heat exchanger.

Boundary Conditions
In the computational model, three types of boundary conditions were used: 1. Inlet boundary condition: the mantle inlet temperature is 60 °C. In both modes, the mantle inlet velocity is 0.1 m/s and the velocity in the tank is zero. 2. Initial condition: The tank is initially assumed to be at 20 °C. 3. Wall boundary condition: The velocity at any solid surface is assumed to be zero (no slip condition).

Boundary Conditions
The thermal problem in the mantle heat exchanger is analyzed using continuity, momentum, and energy equations in three dimensions. The transient case will be examined to determine how temperature profiles change over time. Depending on the definitions of , Γ ϕ and S ϕ in (table 3) [11], the following general equation (1) can be used to form the three conservation laws.
Where denotes a general variable that can represent the physical quantity under consideration per unit mass. The symbols Vr, V, and Vz represent the r, v, and z velocity components, respectively. The remaining symbols ρ, Γϕ and Sϕ, represent the density, diffusion coefficient, and source term corresponding to ϕ, respectively.

Results and Discussion
The simulations are designed to investigate the system's transient thermal performance as a result of various operating conditions and geometrical parameters. The simulations were run at different time intervals ranging from 300 to 3600 seconds. The simulations used three different mass flow rate values. The effects of changing the mantle gap thickness and length were also taken into account. The sequence of variation of mantle and tank temperature contours for selected time intervals between 0 and 3600 s for a mass flow rate of 0.0077 kg/s, mantle gap of 10 mm, and mantle length of 300 s is shown in Fig. 3. Fig. 4 show the effects of increasing the mass flow rate to 0.0077, 0.015 and 0.02 kg/s, respectively. Increasing the mass flow rate has a clear effect on increasing the tank's heating rate and accelerating heat penetration. Fig .5 show temperature contours for mantle gaps of 10, 15 and 20 mm, respectively. Increasing the value of the mantle gap results in a slower heating rate and less thermal energy penetration in the tank water. The increased length of the mantle provides more heat transfer area and better heat penetration in the tank water.

Comparison With other Works
The numerical results of the present work were compared with the results of Arslan and Igci

Conclusions
The present work is a numerical and experimental study of a mantle heat exchanger. Thermal performance in the transient phase is estimated by a simulation procedure using the commercial CFD software Ansys−Fluent. The following conclusions can be drawn from the present study:  11. M. Arslan and A. A. Igci, "Thermal performance of a vertical solar hot water storage tank with a mantle heat exchanger depending on the discharging operation parameters," Sol. Energy