Enhancement of nanoparticle-phase change material melting performance using a sinusoidal heat pipe
Introduction
As the amount of fossil fuel in the world becomes less and its price keeps increasing during the past decades, the development of renewable energy is more significant due to the increased energy demand for industry and daily life. Unfortunately, the clean energy such as solar energy or wind energy has a characteristic of time-dependent, territorial, and intermittent supply. To solve this issue, the effective energy storage technologies are indispensable for making the wide application of renewable energy possible [1]. Thermal energy storage (TES) which stores heat in the materials and applies it to generate electricity with heat engine cycles is one of the most commonly used energy storage techniques. It could be classified as three different types including latent heat TES, sensible heat TES, and concrete thermal storage. Latent heat thermal energy storage (LHTES) makes use of the latent heat of phase change materials (PCMs) during solid-liquid phase change process to store high density energy at a nearly constant temperature so that it becomes attractive for many applications. However, the drawback of LHTES is the low thermal conductivities of PCMs which impedes its energy storage efficiency. Under this situation, several heat transfer enhancement approaches for PCMs have been investigated which include the uses of heat pipes, high thermal conductivity nanoparticles or metal foams, extended internal fins, and microencapsulated PCMs.
As a commonly used heat exchanger device, heat pipes could efficiently transfer heat between the heat transfer fluid (HTF) and PCMs so that the charging and discharging processes of LHTES could be accelerated [2]. Different analytical [3], numerical [4], and experimental [5] approaches have been used to optimize the configuration and arrangement of heat pipes in LHTES system such as using heat pipe network [5] or oscillating heat pipes [6] in purpose of improving the energy storage efficiency. Unfortunately, the heat transfer area of smooth circular heat pipes is highly limited which affects their effectiveness of accelerating energy storage rate to some extent. Due to this reason, the simple circular heat pipe should be redesigned in order to ameliorate its thermal performance in LHTES systems. The heat transfer area of heat pipes could be highly improved with microgrooved, corrugated, or wavy surface configurations. Furthermore, the unsmooth heat pipe surfaces could stir the local fluid flow under which circumstance the thermal boundary layer is interrupted and the corresponding heat transfer rate is enhanced. Yong et al. experimentally investigated the thermal performance of heat pipe with micro grooves fabricated using the Extrusion-ploughing process [7], and it was found that this kind of heat pipe could have a larger final heat transfer limit. Wang et al. numerically and experimentally studied the pulsating heat pipes with corrugated configuration [8], and the results showed that the overall performance of pulsating heat pipes is remarkably improved with the application of corrugated configuration. Ma et al. experimentally and numerically studied the heat transfer and pressure drop of cross-wavy primary surface heat exchanger [9], and the results showed that the cross-wavy channels with similar structures but different equivalent diameters have the similar thermal-hydraulic performance. However, the heat transfer depths of the aforementioned heat pipes are not sufficient for fast charging and discharging processes in the entire LHTES system. To handle this issue, the high thermal conductivity external fins are coupled with heat pipes to prolong heat transfer depths in the LHTES unit and accelerate the solid-liquid phase change rate of PCMs. Tiari et al. numerically investigated the LHTES unit with finned heat pipes [10], and the obtained results demonstrate that increasing the number of heat pipes and the length of fins could obviously reduce the PCM charging time. Pan et al. optimized the structure of a longitudinal finned heat pipe in a LHTES system [11], and the results indicated that thinner fins result in a lower system cost and there is a thickness limit for the fins to be economically welded on a heat pipe. Mahdi et al. studied the PCM melting via novel fin configurations in the triplex-tube heat exchanger [12], and it was found that using longer fins at the conduction dominated lower half of the storage unit results in a higher energy storage rate. Besides, the thermal performance of finned heat pipes could be further consolidated by using wavy fins as investigated by the previous experiment [13], numerical simulation [14], and optimization work [15]. Although inserting different configurations of fins on the heat pipe could improve its thermal performance, the energy storage capacity of LHTES system is reduced because of the existence of fin areas. Based on this, developing a novel heat pipe with higher heat transfer rate which has no influence on the energy storage density of LHTES system is highly important for renewable energy applications.
Specifically, the sinusoidal shape has similar functions as corrugated or wavy configurations which could be used to enhance the heat transfer area on the heat pipes. In addition, when the amplitude of the sinusoidal function becomes large, each peak of sinusoidal heat pipe could serve like fins to increase the heat transfer depth in the system. Researches have been carried out to investigate the fluid wake [16], natural convective heat transfer [17], and magnetohydrodynamic convection [18] with sinusoidal cylinders. The most attractive characteristic of sinusoidal heat pipe is that the cross-section area is independent from its undulation number and magnitude. As a consequence, the volume fraction of heat pipes and the corresponding PCM energy storage density in the LHTES system could be kept as a constant when different configurations of sinusoidal heat pipes with same radius are applied. However, according to the author’s knowledge, the LHTES system using sinusoidal heat pipes is not investigated by any researches until now. Besides, although the effective thermal conductivity of PCMs could be enhanced by adding nanoparticles [19], the increment of PCM viscosity with nanoparticles could impede the development of convective heat transfer. Based on these trade off effects, the effectiveness of enhancing LHTES charging and discharging rates by using nanoparticles requires further investigation and should be seriously compared with other heat transfer enhancement techniques such as applying heat pipes. According to the previous discussions, the current paper focuses on the improvement of nanoparticle enhanced-phase change material (NEPCM) melting performance in LHTES unit using a sinusoidal heat pipe which will have potential impacts for achieving high energy storage efficiency in renewable energy applications.
During the past decades, lattice Boltzmann method (LBM) has been developed as a powerful numerical approach for simulating complex fluid dynamics [20] and phase change heat transfer problems [21]. For solid-liquid phase change phenomenon, the enthalpy-based single-relaxation-time (SRT) [22] and multiple-relaxation-time (MRT) [23] LBM developed by Huang et al. are robust and efficient. The MRT collision scheme could highly improve the computational stability and reduce the numerical diffusion so that it is widely used for modelling engineering problems with solid-liquid phase change processes. Li et al. further developed enthalpy based-MRT LBM for axisymmetric [24] and three dimensional [25] solid-liquid phase change problems respectively. Due to the highly parallel characteristics of LBM, it has been successfully fitted onto graphics processor units (GPU) to achieve high performance computing for different heat transfer problems including double diffusive convection [26], PCM melting in metal foams [27], electrothermal flow in microfluidics [28] and so on. In addition, immersed boundary method with direct forcing scheme is widely used for tackling the complex or moving geometries by adding ‘momentum force’ and ‘energy force’ into the fluid flow [29] and heat transfer [30] governing equations. Recently, Ren et al. coupled the enthalpy based-MRT-LBM with IBM to study the solid-liquid phase change process of PCM with a circular heat pipe [31]. In the current work, immersed boundary-lattice Boltzmann method (IB-LBM) is used to optimize the melting performance of NEPCM with a cross-section sinusoidal heat pipe at different parametric conditions. The remainder of the paper is organized as follows. In Section 2, the mathematical model and immersed boundary-lattice Boltzmann method for modelling the NEPCM melting process with a sinusoidal heat pipe in the LHTES system is presented. Then, the detailed discussions and optimization about enhancement of NEPCM melting performance using a sinusoidal heat pipe are carried out in Section 3. Finally, a conclusion is drawn in Section 4.
Section snippets
Mathematical model and numerical method
The schematic of LHTES system of using a heat pipe (HP) with sinusoidal cross-section is shown in Fig. 1 in terms of different heat pipe undulation number and magnitude . The profile of the sinusoidal heat pipe surface follows the pattern as:where is the radius of the sinusoidal heat pipe; is the radius of the circular heat pipe when ; is the undulation number of the sinusoidal heat pipe; is the sinusoidal amplitude of heat pipe which is for the specific
Results and discussions
In this paper, the NEPCM melting performance in the LHTES unit with a sinusoidal heat pipe is studied with respect to sinusoidal heat pipe undulation number and sinusoidal amplitude, heat pipe temperature and radius, nanoparticle volume fraction, and eccentricity of heat pipe location. To describe the transient NEPCM melting process, the Fourier number is defined as:
Conclusions
In this paper, the enthalpy-based immersed boundary-lattice Boltzmann method is developed to investigate the enhancement of NEPCM melting performance in a LHTES enclosure with a sinusoidal heat pipe. By replacing the circular heat pipe with the sinusoidal heat pipe, the heat transfer area between HTF and NEPCM is enlarged to accelerate the NEPCM melting rate while the energy storage capacity of LHTES unit is kept unchanged. According to the investigations at different parametric conditions, the
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 51806168) and the China Postdoctoral Science Foundation (No. 2017M623169).
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