Performance of a bi-layer solar steam generation system working at a high-temperature of top surface

Abstract

Many efforts have been focused on enhancing the vapor generation in bi-layer solar steam generation systems for obtaining as much pure water as possible. However, the methods to enhance the vapor temperature is seldom studied although the high-temperature vapor has a wide use in medical sterilization and electricity generation. In this work, to probe the high-temperature vapor system, an improved macroscopic heat and mass transfer model was proposed. Then, using the finite element method to solve the model, the influences of some main factors on the evaporation efficiency and vapor temperature were discussed, including effects of the vapor transport conditions and the heat dissipation conditions. The results show that the high-temperature vapor could not be obtained by enhancing the heat-insulating property of the bi-layer systems but by applying the optimal porosity and proper absorbers. This paper is expected to provide some information for designing a bi-layered system to produce high-temperature vapor.

Graphical abstract

Keywords

solar steam generation / solar energy / numerical method / porous material

1 Introduction

Solar-enabled evaporation, as a solar energy harvesting technology [1–12], has potential applications not only in seawater desalination [13–18], but also in wastewater treatment [19], medical sterilization [20], and even for electricity generation [21–24]. Recently, a bi-layered seawater desalination system [25] has attracted widespread attentions due to its efficient utilization of solar energy. Many efforts have focused on improving and optimizing the used materials [18,26–29], structures [17,22,30], and overall devices [13,14,31] for obtaining a high efficiency of vapor generation in bi-layer systems. Besides focusing on improving vapor generation efficiency to produce more pure water, some solar steam generation systems were also developed to supply high-temperature vapor which can be used in medical sterilization etc [14,32,33]. Until now, most studies concentrate on developing solar steam generation systems to produce more pure water or produce high-temperature vapor (two different targets). Previous works [14,32,33] pointed out that to obtain high-temperature vapor, the transport of vapor in the system should be impeded, at the same time heat dissipation through boundaries should be hindered. To produce more pure water, the transport of vapor should be improved for obtaining a high evaporation efficiency.

Although many experiments have been conducted, there are scarce theoretical works to reveal the influencing factors of the evaporation process in a bi-layer system [32,34]. In Refs. [32,34], a model to describe the macroscopic heat and mass transfer in bi-layer systems working at a low temperature was theoretically established and experimentally verified. With the model solved by the finite element method, some influencing factors [32,34] on evaporation efficiency of bi-layer structure systems were analyzed, as listed in Fig. 1. Although the previous theoretical model could be used to predict the evaporation efficiency of a system working at a low temperature, it still could not be used directly to consider a system which can produce high-temperature vapor.

In this paper, to consider a high temperature condition, the macroscopic heat and mass transfer model was first improved based on Refs. [32,34] by further taking into account the temperature dependences of material properties, and the thermal radiation losses from the surface of the system to the environment when these energy losses could not be ignored because of the high temperature. Then, this improved model was verified by experiments and the initial model under a low temperature condition. Finally, the model improved was used to probe the influence of the vapor transport conditions and the conditions of heat dissipation from boundaries on the evaporation efficiency and the vapor temperature. This paper is expected to provide some information for designing a bi-layered system to produce high-temperature vapor.

2 Mathematical and physical model

Assumptions, governing equations, and numerical technical details about the macroscopic heat and mass transfer model can be found in Refs. [32,34]. The model improvement was made by carefully considering the temperature dependence of material properties, and the thermal radiation losses from the surface of the system to the environment.

The ignorance of the energy loss through the thermal radiation of the system to the environment is reasonable when the system works at a low temperature, while it should be considered when the system working at a high temperature. In this paper, an improved formula, as expressed in Eq. (1) was applied.

(1)-\mathit{n}\cdot \mathit{q}={{\displaystyle \epsilon }}_{\mathrm{a}}{G}^{*}-{{\displaystyle \epsilon }}_{\mathrm{e}}{{\displaystyle e}}_{\mathrm{b}}\left(T\right),

where n is the normal vector and q is the net heat flux through the surface, the irradiation G* is calculated by G* = G_sun + G_amb, G_sun = q_e∙FEP(T_sun), and G_amb = e_b∙ (T_amb)∙FEP(T_amb); ε_a and ε_e are absorptivity and emissivity of top surface, respectively; e_b(T) is the total blackbody hemispherical emissive power at a specific temperature, q_e is the solar radiation heat flux, FEP(T) is the fractional blackbody emissive power at a specific temperature; T_amb and T_sun are temperature of ambient and sun, respectively.

Temperature-dependence material properties were applied to include the influence of temperatures on vapor evaporation. The temperature-dependence properties are given in Appendix A.

The predictions given by the improved model were compared with the results of the experiment and the model in Ref. [34], as shown in Fig. 2. It is observed that the improved model could match the original model and experiments well when the system works at a low temperature of around 300 K, which may validate the improved model. The relative error between the improved model and the experiment is no more than 6%, suggesting a good rationality and effectiveness of the improved macroscopic heat and mass transfer model. The definition of evaporation efficiency is added in Appendix B. The details of the experiments could be referred to in Ref. [34].

A structure model of bi-layer system as demonstrated in Fig. 3 was applied for obtaining high-temperature vapor. The bi-layer system is placed in an insulated container and the contact area of the system to the bulk water is limited to reduce the heat transfer and convective heat transfer losses. In this system, nanoparticles, carbon nanotubes, or graphene can be applied as the first layer while woods, cellulose nanofibers, or sponges can be used as the second layer. The polyurethane foam or air can be used as a thermal insulator. The lengths of AB, BC, GH, HK, KL, LM, MT, TS, TU, NO, and JD is respectively 120, 90, 5, 20, 30, 10, 12.5, 5, 5, 10, and 50 mm. Boundary conditions are similar to those in Refs. [32,34]. It should be noted that FA and BC are air inlet boundary, and AB is the air outflow boundary. Applying customized mesh in boundary layers, different number of mesh grids were applied to get the temperature distributions in the first layer (which can be also considered as the temperature of vapor). When the number of grids becomes larger than 43436, the increase in the number of grids has a negligible effect on results. Thus, the mesh with 43436 grids is applied in this work. Other material properties and parameters used in the simulation are summarized in Table A3.

3 Results and discussion

The evaporation efficiency and the temperature of the vapor generated mainly depend on the conditions of vapor transport and the heat dissipation through boundaries, which determine the temperature field in the system. In this work, simulation experiments were performed to figure out how the influencing factors can affect evaporation efficiency and vapor temperature by influencing the vapor transport and heat dissipation through boundaries. The vapor transport can be affected both by the extension height of insulating materials and the porosity of the second layer, while the heat dissipation can be influenced by many factors, such as the ratio of surface emissivity to absorptivity, the water absorption locations in the system (d in Fig. 3), the thermal conductivity, and the heat capacity of the insulation material. It is noteworthy that the insulation material is regarded as completely adiabatic except when considering the effect of heat conduction. The results of evaporation efficiency, maximum surface temperature, and average temperature in the system at different influence factors were exhibited in Fig. 4.

As depicted in Fig. 4(a), with the extension height increasing from 0 to 30 mm, the temperature of vapor increases rapidly from about 335 to 365 K, and then gradually converges to a constant value of about 365 K after the extension height reaching 25 mm. The rapid increase in vapor temperature results from the deterioration of vapor dissipation from the system surface and the weakening of surface convective heat transfer. When the extension height reaches 25 mm, the influence of the extension height of insulating materials on the vapor transport conditions and convective heat transfer of bi-layer system becomes extremely limited, thus the vapor temperature finally converges to a stable one.

Figure 4(b) illustrates the influence of the second-layer porosity on evaporation efficiency and vapor temperature. Before evaporation efficiency rising to its maximum, the temperature field in the bi-layer system is mainly determined by the improved vapor transport conditions, while further increasing the porosity, the temperature field of the bi-layer system is mainly dominated by the large heat dissipation caused by the enlarged effective thermal conductivity of the second layer. Therefore, the temperature curve is similar to a broken line, and the turning point is near the optimal evaporation efficiency. When the porosity of the second-layer is lower than 40%, with the decrease in the porosity, the surface temperature rises rapidly while the evaporation efficiency is reduced greatly. High-temperature vapor or high evaporation efficiency cannot be simultaneously obtained by improving vapor transport conditions. To obtain a high-temperature vapor, a quite low porosity should be applied. Except in Fig. 4(b), a porosity of about 10% was applied, thus there is a quite low evaporation efficiency in Figs. 4(a) and 4(c)–4(f).

According to Wien’s displacement law, the thermal radiation density of a 370 K object peaks at a wavelength of 7700 nm, while this wavelength of sunlight is about 500 nm. Although the absorptivity of an object at a wavelength equals to its emissivity at the same wavelength according to Kirchhoff’s law, an absorber can still be designed which possess a high absorptivity at the wavelength related to the solar peak radiation density (500 nm) but a low emissivity at the wavelength related to the absorber temperature (7700 nm), e.g. commercially available cermet-coated copper substrate [17]. For easy description, the absorptivity of the first layer at the wavelength ranging from about 280 to 2500 nm was defined to be ε_a, and the emissivity at the wavelength from 2500 nm to infinity to be ε_e. In Fig. 4(c), the influence of ε_e/ε_a on the vapor temperature was depicted. The vapor temperature decreases rapidly and linearly with the increase in ε_e/ε_a. A higher vapor temperature and higher evaporation efficiency can be obtained simultaneously by applying selective absorbers.

The effect of the water absorption locations of the bi-layer structure on vapor temperature is depicted in Fig. 4(d). The system with the water absorbed from the middle of the system gives the lowest vapor temperature, while the vapor temperature can be raised by moving the water absorption locations far away from the middle part. The location-caused rise of vapor temperature arrives from the deterioration of the heat dissipation. In Fig. 4(e), with the thermal conductivity of insulating materials increasing from 0.05 to 3.0 W/(m·K), the vapor temperature first increases rapidly and then gradually converges to a constant value after the thermal conductivity reaching about 0.7 W/(m·K). The increase in vapor temperature with the decrease in thermal conductivity is due to the reduced heat conduction losses. The saturated vapor temperature is determined by the limitation of the convective heat transfer and the difficulty of heat dissipating from the insulating materials to the environment. The effect of heat capacity of insulation material on vapor temperature can be neglected as presented in Fig. 4(f). Figures 4(d)–4(f) indicate that it is difficult to obtain high-temperature vapor by deteriorating heat conduction.

4 Conclusions

A macroscopic heat and mass transfer calculation model was further improved to analyze the evaporation efficiency and temperature of produced vapor in a high-temperature-vapor generation bi-layered system. Then, the calculation model was used to further probe the effects of the vapor transport conditions controlled by the extension height of insulating materials and the porosity of second layer, and the heat dissipation conditions depended on the ratio of surface emissivity to absorptivity and the water absorption locations in the bi-layer system. The results demonstrate that there is an optimal extension height for producing high-temperature vapor, which is about 25 mm in this work. Besides, high-temperature vapor can be obtained by reducing the porosity because of the weakened vapor transport, especially when the porosity is lower than that related to the optimal evaporation efficiency. In addition, high-temperature vapor and high evaporation efficiency cannot be simultaneously obtained by improving vapor transport conditions. Moreover, the vapor temperature decreases rapidly and linearly with the increase of ε_e/ε_a. High vapor temperature and high evaporation efficiency can be obtained simultaneously by applying selective absorbers. Furthermore, water absorption locations, and thermal conductivity and heat capacity of the insulation material have a limited effect on enhancing vapor temperature. Therefore, it is difficult to obtain high-temperature vapor by only enhancing the heat-insulating property of the bi-layer systems.

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