Exergy analysis of a passive solar still

Abstract

This paper presents a steady-state and transient theoretical exergy analysis of a solar still, focused on the exergy destruction in the components of the still: collector plate, brine and glass cover. The analytical approach states an energy balance for each component resulting in three coupled equations where three parameters—solar irradiance, ambient temperature and insulation thickness—are studied. The energy balances are solved to find temperatures of each component; these temperatures are used to compute energy and exergy flows. Results in the steady-state regime show that the irreversibilities produced in the collector account for the largest exergy destruction, up to 615 W/m² for a 935 W/m² solar exergy input, whereas irreversibility rates in the brine and in the glass cover can be neglected. For the same exergy input a collector, brine and solar still exergy efficiency of 12.9%, 6% and 5% are obtained, respectively. The most influential parameter is solar irradiance. During the transient regime, irreversibility rates and still temperatures find a maximum 6 h after dawn when solar irradiance has a maximum value. However, maximum exergy brine efficiency, close to 93%, is found once T_col<T_w (dusk) and the heat capacity of the brine plays an important role in the modeling of collector–brine interaction. Nocturnal distillation is characterized by very low irreversibility rates due to reduced temperature difference between collector and an increase in exergy efficiency towards dawn due to ambient temperature decrease.

Introduction

Shallow solar stills are commonly used in arid coastal zones to provide low-cost fresh water from the sea. The simplest design of a solar still consists of a rectangular box with a transparent upper cover, Fig. 1. The solar distillation process is as follows: (a) the still is partially filled with brine in the bottom deposit which is a black surface (collector) used to absorb incoming radiation after it passes through the glass cover and the brine, (b) the collector increases its temperature and transfers heat to the brine, (c) water evaporates at the free surface, (d) a natural convection flow of humid air circulating inside the enclosure takes place due to the temperature difference between the free surface of the heated brine and the upper cool cover, and (e) this inclined transparent sheet serves as a condensing plate where the distillate water runs by gravity along its internal face to a small collector channel in the shortest sidewall of the arrangement. Distillate rates close to 5 l/m²day in La Paz, México (24°N latitude) on a sunny summer day can be currently achieved, making the process economically attractive for those water-scarce areas. Looking into the basic phenomena within the still, a highly unstable process, consisting of evaporation, moisture convective transport and condensation is produced. A detailed description of the apparatus and its operation can be found in [1].

Although the basis of solar still modeling are well understood, there are recent studies in this area [2], [3], [4], [5], [6] trying to improve heat transfer equations by taking into account all the parameters, conditions and geometric configurations. Most of the models used to study solar distillation are based on a lumped parameter analysis that considers three main subsystems [7], [8], [9]:

• The collector plate, which acts both as the water recipient and the absorbing surface of radiation.

• The brine to be evaporated.

• The glass cover where water vapor condensates.

The result is a system of three coupled equations describing the thermal behavior of the three components:

$${\epsilon }_{\mathrm{col}}G=h_3(T_{\mathrm{col}}-T_{\mathrm{w}})+\frac{K_{\mathrm{ins}}}{x_{\mathrm{ins}}}(T_{\mathrm{col}}-T_{\mathrm{a}})+C_{\mathrm{col}}\frac{\mathrm{d}{T}_{\mathrm{col}}}{\mathrm{d}t},\mathrm{collector},$$

$$h_3(T_{\mathrm{col}}-T_{\mathrm{w}})=h_1(T_{\mathrm{w}}-T_{\mathrm{g}})+C_{\mathrm{w}}\frac{\mathrm{d}{T}_{\mathrm{w}}}{\mathrm{d}t},\mathrm{brine},$$

$$h_1(T_{\mathrm{w}}-T_{\mathrm{g}})=C_{\mathrm{g}}\frac{\mathrm{d}{T}_{\mathrm{g}}}{\mathrm{d}t}+h_2(T_{\mathrm{g}}-T_{\mathrm{a}}),\mathrm{glass}\mathrm{cover}.$$

In Eqs. (1), (2), (3), h₁, h₂ and h₃ are the heat transfer coefficients due to convection, evaporation and radiation between the brine surface and the glass cover, radiation and forced convection between the glass cover and the surrounding air, and free convection between the collector and the brine, respectively. These heat transfer coefficients are constants, independent of temperature. T_col, T_w, T_g and T_a are the temperatures of collector, brine, glass cover and ambient, respectively. G is the solar irradiance arriving at the collector surface, ε_col is the emissivity of the collector, K_ins and x_ins are, respectively, the thermal conductivity and thickness of the insulation. C_col, C_w and C_g are the heat capacity per unit of area of the collector, brine and glass cover, respectively, and t is the time along the day. These equations, along with the usual assumption of constant heat transfer coefficients, constitute the widely known energy model for a passive solar still [7].

The unknown variables of these equations are the temperatures of the collector plate, the brine and the glass cover. Once these temperatures are known, it is possible to calculate the theoretical exergy flows and exergy destruction. Most of the analytical studies in solar stills aim to solve an energy balance equation in order to obtain theoretical temperatures and therefore, the distillation yield that is found according to

$$m_{\mathrm{ev}}=\frac{h_{\mathrm{eff}}(T_{\mathrm{w}}-T_{\mathrm{g}})}{{\lambda }_{\mathrm{ev}}}\text{,}$$

where h_eff is the convective heat transfer coefficient due to evaporation and λ_ev is the latent heat of water. Table 1 provides typical values for some of the parameters and properties of a passive solar still.

Based on empirical relations [1], the expressions for solar irradiance and ambient temperature functions for a 24 h period, respectively, are

$$G=\left(\frac{G_{\max }}{2}\right)\left[\sin \left(\frac{\pi t}{12}\right)\right]+\left|\left(\frac{G_{\max }}{2}\right)\left[\sin \left(\frac{\pi t}{12}\right)\right]\right|\text{,}$$

$$T_{\mathrm{a}}=A\times \sin \left(\frac{\pi t}{24}\right)+T_{\mathrm{a},\mathrm{i}}\text{,}$$

where t is the time and T_a,i is the ambient temperature at the beginning of the day. The highest solar irradiance value that accounts for global radiation (direct and diluted) G_max is taken, arbitrarily, equal to 1000 W/m². Solving these energy balances, still temperatures and distillate output can be found for a 24 h day (Fig. 2).

Assumed in the model is the following:

• vapor–air mixture and insulation are not regarded as systems or participating media,

• brine and glass cover do not interact with incoming solar radiation,

• the shape factor in the exchange of radiation between collector and glass cover is taken as 1,

• the solar still is a closed system,

• all physical properties of materials are not affected by temperature differences,

• there are no temperature gradients across brine depth, collector plate or glass cover

• the amount of brine in the still is constant.

The investigation of solar systems according to the laws of thermodynamics has attracted the attention of many researchers widely discussed by several authors and reviewed by Bejan [10], [11] and Petela [12]. Thermodynamic analysis is an effective means to obtain precise and valuable information about energy efficiency and losses due to irreversibility in a real situation. It is clear then that the current tendency in the design of real processes is the minimization of entropy production, looking forward to designing systems that are economical and technically optimal. Although the methods employing the second law and the exergy concept are well established [13], [14], [15], [16], [17], [18] the tools used in solar engineering are still based on the first law of thermodynamics. The first law is only concerned with the conservation of energy and gives no information on how, where, and how much the system performance is degraded. Exergy analysis is a powerful tool for the design, optimization, and performance evaluation of energy systems. To the best knowledge of the authors of the present paper, there are no previously published results of second law analysis in solar stills except for the general overview written by Kwatra [19]. In this paper, an analysis of the exergy flows and its destruction in a solar still operating in steady and unsteady state is presented.