The energy efficiency ratio of heat storage in one shell-and-one tube phase change thermal energy storage unit
Introduction
With the increasing power consumption of industrial, commercial, and residential activities, the problems of energy shortage and air pollution have become serious. To help relieve this situation, the use of renewable energy, such as wind energy and solar energy [1], [2], [3], [4], [5], on a global scale is highly recommended. However, these types of energy have some shortcomings: they are unstable and can be unreliable due to their dependence on the weather, time, and season. Thus, thermal energy storage (TES) units have become a necessary component in applying renewable energy. The main task of the energy storage, then, is to eliminate the mismatch between energy supply and energy demand.
TES includes sensible, latent, and thermal–chemical heat storage units. The latent TES system with solid–liquid phase change has gained greater attention due to its advantages. It has high energy storage density and heat charging/discharging at a nearly constant phase change temperature. These characteristics result in a greater flexibility and more compactness of the phase change material (PCM) heat storage system [6]. Therefore, phase change thermal energy storage (PCTES) has been a main topic in research for the last 20 years. The state of the art developments are summarized in many review papers [7], [8], [9], [10]. Zalba et al. [7] carried out a review of the history of solid–liquid PCTES with phase change materials and applications. Sharma et al. [8] summarized the analysis of the available thermal energy storage systems for different applications. Agyenim et al. [9] performed a review of the materials, heat transfer, and phase change problem formulation for latent heat thermal energy storage systems. Al-Abidi et al. [10] completed a review of thermal energy storage for air conditioning systems.
In most PCTES systems, as shown in Fig. 1, a shell-and-tube is the core unit of PCTES. There are many reported studies on this unit [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. Refs. [11], [12], [13], [14], [15] use experimental methods to investigate the performance characteristics of this unit. Trp [11] experimentally analyzed the transient heat transfer performance during phase change material melting and solidification. Akgun et al. [12], [13] studied on melting/solidification characteristics of three kinds of paraffin as PCM. A novel tube-in-shell storage geometry was introduced and the effects of the Reynolds number and Stefan number on the melting and solidification behaviors were examined. Wang et al. [14] used β-aluminum nitride as additive to enhance the thermal conductivity and thermal performance of form-stable composite phase change materials. Mddrano et al. [15] experimentally evaluated the performance of commercial heat exchanger used as PCM thermal storage systems. Numerous experimentally validated mathematical models of the unit have been developed over the years. These models have been used to determine the performance of the unit for design [16], [17], [18], [19], [20], [21]. Trp et al. [16] presented a mathematical model regarding the conjugated problem of transient forced convection and solid–liquid phase change heat transfer based on the enthalpy formulation. The transient heat transfer phenomenon of the unit was analyzed. Fang et al. [17] investigated the effects of different multiple PCMs on the melted fraction, heat storage capacity and heat transfer fluid (HTF) outlet temperature of the unit. Adine and Qarnia [18] numerically analyzed the thermal behavior of the unit. Tao et al. [19], [20] performed the numerical study on thermal energy storage performance of PCM in the unit with enhanced tubes. Wang et al. [21] numerically studied the heat charging and discharging characteristics of such kind unit. A CFD model of the PCM system within a tube-in-tank assembly has been developed and validated [22], [23].
In order to optimize the design of the PCTES unit, it is necessary to pay attention to the efficiency of the unit. Tay et al. [24], [25] numerically investigated the heat transfer effectiveness of the tube-in-tank PCTES system using the effectiveness-number of transfer unit (NTU) method. Amin et al. [26] demonstrated that a suitable relationship for the effective thermal conductivity was developed as a function of the Rayleigh number. It has been proven experimentally that the effectiveness-NTU method is applicable for PCM encapsulated in spheres in a tank. The heat transfer effectiveness of PCM encapsulated in a sphere system has been experimentally investigated using the effectiveness-NTU method [27]. Gil et al. [28] directly measured the change in effectiveness through the application of square radial fins and showed a 20% increase. The investigation demonstrated that a correlation existed between the effectiveness of heat transfer and the mass flow rate.
Above studies pay more attention to the heat transfer processes, but ignore another important aspect that pumping HTF will consume energy. Few studies have addressed the energy consumed to pump HTF. It is believed that optimization design of the PCTES unit should consider the energy consumed in pumping HTF. Motivated by this, in this paper, from aspect of the energy consuming to pump HTF, we focus on developing a dimensionless parameter to indicate the how much energy is consumed in charging or discharging process. Then, we demonstrate the characteristics and possible indications of this parameter in designing and operating of the PCTES unit.
Section snippets
Physical model and mathematical model
To account for the mechanical energy consumed in pumping HTF to complete a charging or discharging process, the charging or discharging time is needed. There are two methods of obtaining it: the experimental and numerical methods. Available results [16], [17], [18], [19], [20], [21], [22], [23], [24], [25] show that the validated numerical method can also predicate the performances of charging or discharging processes reasonable. Thus, in the present study, the numerical method is used. The
The energy efficiency ratio of the PCTES unit
To define a parameter that can indicate the energy efficiency ratio of the PCTES unit, the mechanical energy consumed by fluid flow of HTF inside the tube should be considered. For the present case, in the time period of tmax, the energy consumed is as follows:where tmax is the time needed to complete phase change process, andIn this period, the heat energy stored in the unit is,The energy efficiency ratio of the unit can be
Discretization of the model
The finite volume method is used to discretize the governing equations. For easy capturing of the discretization process, the schematic diagram of grid system is shown in Fig. 3.
For HTF,
For the tube wall,
For PCM,
Solving of the discretization equations
Eqs. (42), (43), (44) are solved using the
The energy efficiency ratio of the PCTES unit
Based on the energy efficiency ratio of the PCTES unit defined in Eq. (41), we numerically investigated the characteristics of the energy efficiency ratio in many cases. The results and discussions will be presented in the following sections.
The heat storage rate of the PCTES unit
The above results indicate that using the energy efficiency ratio of a PCTES unit as the only parameter to evaluate the heat storage performance of the PCTES unit is not sufficient. It is important that the heat is stored by PCM per unit time in the phase change process. Based on heat energy stored in the unit defined in Eq. (35), we defined the heat storage rate of the PCTES unit in the time period of tmax. It follows that,The physical meaning is
Conclusion
In the present paper, we have focused on developing a parameter that can be used to indicate the energy efficiency ratio of the single shell-and-tube phase change heat storage unit. Based on the energy efficiency ratio defined, the sensitivity of the energy efficiency ratio on HTF initial inlet temperature, HTF working conditions, the unit structure size, and the material properties of HTF and PCM are numerically investigated, respectively. The following conclusions can be derived:
- (1)
Although two
Acknowledgments
This work was supported by the China National Hi-Tech R&D (863 Plan) Project (2013AA050502), the National Key Basic Research Program of China (973 Program) (2013CB228304), and the National Natural Science Foundation of China (No. 51176155).
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