Solar Refrigeration

This post, exceptionally, is not about popular science. It is addressed to thermal engineering experts, especially those interested in solar energy applications for refrigeration and air conditioning.

http://www.green-the-world.net/solar_air_heater.html

Solar Refrigeration*

Antonio Pralon F. Leite

Solar Energy Laboratory, Federal University of Paraíba

Brazil
*PDF available for download at the end

1. Introduction

Refrigeration and cooling using solar energy have always been attractive technologies since the world energy crisis in the 1970's, especially for developing countries, which often have warm or hot climates.

In spite of the great effort that has been focused worldwide on systems integrating solar energy to produce cold for both refrigeration and air conditioning applications, information on this subject is dispersed and little concise.

So, this publication was elaborated in order to offer the theoretical basic fundamentals about solar refrigeration, as the equations governing the cold production process and the regeneration one, based on sorption thermodynamic cycles.

In addition, we will give concentrated information about the main experiments worldwide using solar thermal energy for running refrigeration and air conditioning systems, particularly those based on solid sorption processes.

Cold production is a very interesting application of solar energy, because we have the availability of energy in phase with the demand, as shown in the graphic (Fig. 1), in contrast to the case of heating in which the storage of solar energy is often required.

Fig. 1 Time variations of the solar radiation and demands of refrigeration and heating.

There is a great demand for refrigeration in warm-weather regions and remote areas for storage of food, beverage and medicine, as well as, for thermal comfort. In such areas, life-sustaining products like vaccines, sera, drugs and blood plasma, and other essential products like fish, meat and milk must be stored under low temperatures.

We will provide some fundamentals on solid sorption, in order to obtain the basic equations for modeling and dimensioning solar adsorption refrigeration or cooling systems. Then, we will present the main experimental data around the world in the fields of refrigeration and air conditioning based on adsorption, which means a solid sorption cycle without any chemical reaction.

2. Fundamentals of refrigeration

Among the different methods to obtain cooling effect we have the vaporization one, which is applied in the most common equipments of refrigeration and air conditioning.

These technologies are based on the evaporation of a refrigerant or working fluid following a compression refrigeration cycle, where heat (Q_E) is removed from a low-temperature space or source and rejected (Q_C) to a high-temperature sink with the help of external work (Fig. 2a). The diagram temperature-entropy (Fig. 2b) shows the different phases and states of the working fluid for a compression Rankine cycle.

Fig. 2 Refrigeration principle schematic (a), and the Rankine thermodynamic cycle (b).

The process represented by AB line is the evaporation (at low temperature and pressure), BC represents the gaseous fluid compression, CD is the condensation process, and DA is the expansion process of the fluid through the valve.

Besides this conventional cycle we have others, in which most of the external work can be replaced by a thermal energy, among them: the Stirling cycle, the ejector-compression hybrid cycle and the sorption cycle.

2.1 Refrigeration and environment

Some considerations about the relationship between refrigeration and environment should be highlighted, as those concerning the conventional working fluids and the primary energy consumption.

These fluids have the power of “radiative forcing”, which is a potential greenhouse gas effect and, consequently, they contribute for warming the atmosphere when liberated from the equipments.

According to a scenario of the Intergovernmental Panel on Climate Change (IPCC) for 2020, the halogen fluids (CFC, HCFC and HFC, still widely used in developing countries) represent 7.2% of the total radiative forcing given by all greenhouse gases (IPCC Report, 2007).

In regard to this aspect, adsorption refrigeration systems are particularly advantageous because they always use natural fluids, such as the water, ammonia and methanol.

Concerning the primary energy consumption, we consider as global average values 3 for the coefficient of performance (COP) and 1/3 for the thermoelectric conversion efficiency (n), which gives a cold production global efficiency equal to 1 (Fig. 3). So, in order to be energetically competitive the sorption systems must provide a COP at least of 1 (Meunier, 1992).

Fig. 3 Scheme of the global energetic criterion taken into account.

Otherwise, they will consume more fossil fuels, and produce more carbon emissions. However, if renewable energy is used, we could have sorption systems with a COP lower than one and they would still reduce carbon emissions. By the way, as we will show soon, the most sorption systems based on thermal solar energy and adsorption has a COP lower than one.

On the other hand, solid sorption can be used in air conditioning systems driven by solar energy to mitigate the “heat island” effect, which is when the urban climate is modified  (due to human activity) with respect to that of surrounding rural areas [3].

This effect results in an increase of the ambient temperature. The heat island is due to many factors, amongst the them, we can identify the anthropogenic heat released from energy consumption, albedo modification by use of materials which absorb solar energy, reduction of evaporating surfaces and the urban greenhouse effect that contributes to warm the atmosphere.

So, the use of solar energy for air conditioning systems can contribute to counterbalance heat island so as to prevent solar irradiation from heating the ambient air. With this approach, it can be possible to increase the apparent albedo related to the global average albedo and much higher than the local one, which is suitable to create an “oasis effect” that means to have urban areas cooler than rural surrounding areas (Meunier, 2007).

2.2 Refrigeration sorption cycles

In refrigeration sorption cycles, the evaporation, condensation and expansion processes are analogous to those occurring in compression. The main difference concerns the fluid movement that in a sorption cycle is due to physical-chemical interactions between different phases.

Figure 4 shows the two principal fields of technologies involving the refrigeration sorption cycle, and the subfields concerning each one. In absorption, vapor is absorbed by a solution which has a great affinity with it (liquid-gas) or a solid which reacts chemically with it to form another product (solid-gas).

Fig. 4 Organogram of the sorption technologies.

In adsorption, a fluid in gaseous phase is absorbed by a porous material without resulting in a new product; if the fluid is the hydrogen we have a thermodynamic cycle with two steps in which two metals are hydrogenated.

All of these systems need essentially a thermal energy input for working, which could be provided by different sources such as heat of combustion, vapor process, thermal waste or solar energy.

The field of solid-gas adsorption encompasses closed cycles and open cycles; this last one is used in air conditioning applications and technically called dessicant cooling, where the ambient interacts directly with the adsorbent.

We will focus on cooling systems based on the solid sorption area that is where we find the most of the studies and experimental achievements using thermal solar energy. In other words, solar refrigeration or cooling by adsorption is currently worldwide the most mature technology, especially those applied to the autonomous solar-powered machines.

3. Adsorption refrigeration

Generically, the adsorption can be defined as the capacity the certain bodies have to selectively fix the molecules of a fluid. It is a solid sorption process where the binding forces between fluid molecules and the solid medium are from electrostatic origin or dispersion-repulsion forces (Van der Waals forces). 

The gas adsorption on a solid adsorbent is an exothermic process due to the gas-liquid phase change. The quantity of the energy released during the adsorption is called isosteric heat; its intensity depends on the nature of the adsorbent-fluid (adsorbate) pair.

The adsorbent can be usually characterized as a porous medium that is a body composed of a solid structure, which contains cavities (or pores) that are often interconnected and susceptible to containing one or more fluid phase (Yang, 1987).

3.1 Thermodynamics of adsorption

The thermodynamic equilibrium of an adsorbent-adsorbate pair can be described by an equation of state, called isotherm of adsorption, correlating temperature (T), pressure (P) and concentration of the adsorbed phase (a) in the form f (T, P, a) = 0. Several models are found in the scientific literature, among them (Leite, 1998): Theory of Gibbs, Henry’s Law, Langmuir’s Approach and Theory of the Adsorption Potential. 

This last one is a purely thermodynamic approach, and it is derived from a theory originally proposed by Polany towards the end of the 1920’s (Polany, 1932). It is based on the surface forces distribution at the microporous surface of the adsorbent.

As example, we will present next the Dubinin-Astakhov isotherm, which is based on the adsorption surface forces field, and, then, give the equations for modeling a microporous adsorbent bed that is valid for activated carbons. So, the Dubinin-Astakhov isotherm is given as (Dubinin & Astakhov, 1971):

where W_o is the maximum capacity of adsorption (volume of adsorbate/mass of adsorbent), sm_l is the specific mass of the adsorbate in liquid state, P_s is the saturating pressure, D is the coefficient of affinity and n is the characteristic parameter of the adsorbent-adsorbate pair.

This equation is particularly suitable for the activated carbon-methanol pair under low-grade thermal energy conditions which allows its usage in several engineering applications, such as those in the solar refrigeration and air conditioning.

An experimental study demonstrated the validity of the Dubinin-Astakhov isotherm for the activated carbon-methanol pair, for a large range of adsorbed mass concentration and for a wide range of moderate temperature (Kariogas & Meunier, 1986).

3.1.1 Isosteric heat of adsorption

It can be demonstrated that the Gibbs isotherm in the integral form, related to the temperature, leads to a function denoted as isoster (a constant adsorbed mass function) given as:

where q_st is the isosteric heat of adsorption. This equation is known as the Clausius-Clapeyron formula.

Applying Eq. (2) to the saturation condition (P = P_s), the latent heat of phase change (L) is obtained to be:

The partial derivation of Eq. (1) gives:

with

where alfa is the coefficient of thermal expansion of the liquid adsorbate.

Multiplying each term of the differential equation by (RT²), the final expression for the heat of adsorption as function of the pressure and temperature is obtained:

3.1.2 Kinetics of adsorption

In most refrigeration applications using low-grade energy sources like the solar one the diffusion through the adsorbent porous media can be neglected, i.e., it can be considered an instantaneous equilibrium between the adsorbed and gaseous phases that could be represented by just an isotherm.

However, when the adsorption in microporous materials is not mainly controlled by the diffusion inside the porous structure, we need to consider the diffusion through the mesoporous and macroporous. In this case, the relative importance of these mechanisms on the global effect of the diffusion is essentially dependent on pressure.

One of the existent approaches for interparticle diffusion, based on two hypotheses (a uniform temperature of the grain, and an equilibrium concentration at the solid interface), gives the mass transfer resistance as the following linear equation (Sakoda & Suzuki, 1984):

where D_i is the diffusion coefficient, a_eq the equilibrium concentration (adsorbed mass/adsorbent mass) at the interface, and r_g is the average radius of the grain.

In mesopores and macropores it can be identified at least four simultaneous mechanisms of diffusion: superficial diffusion (D_s), molecular diffusion (D_m), Knudsen’s diffusion (D_K) and Poiseuille’s diffusion (D_P). For a global analysis, it is usually considered an effective diffusion coefficient (D_e) as a function of D_s, D_m, D_K, D_P and the tortuosity of the medium (ttt), given by (Sakoda & Suzuki, 1984):

with

3.1.3 Ideal thermodynamic cycle

The ideal adsorption refrigeration cycle can be represented by a hypothetical four-temperature machine, as shown in Figure 5.

Fig. 5 Scheme of an ideal four-temperature adsorption refrigeration machine.

During the regeneration of the adsorbent (or desorption process), mass at the temperature T_DE is transferred from the “adsorbed phase” to the liquid phase at the condensation temperature (T_C). This mass transfer leads to a generation of internal energy, resulting from the difference binding energy between the adsorbed phase and the liquid phase.

During the cooling effect production, the mass transport from the liquid phase takes place at a low temperature (T_E) to the adsorbed phase at an adsorption temperature (T_AD) that is the maximum temperature above the ambient temperature in which adsorption can occur.

The adsorption temperature can be determined with the aid of the Clapeyron diagram where is represented an ideal adsorption refrigeration cycle (Fig. 6). The curbs on the diagram show the isosters (functions with a constant adsorbed phase concentration) for a given adsorbent-adsorbate pair, and they are determined by Eq. (2).

As shown in Figure 6, and similarly to the compression cycle (Fig. 2b), AB represents the evaporation (adsorption) process, BC is the isosteric heating, CD is the condensation (desorption) and DA is the isosteric cooling.

Fig. 6 Ideal adsorption refrigeration cycle and the isosters in a Clapeyron diagram.

By applying the fundamental laws of thermodynamics to the desorption and adsorption processes, we obtain the efficiency parameter of the cycle that is the coefficient of performance (COP).

It can be demonstrated that the COP of an adsorption machine based on the ideal cycle (or Carnot cycle) is given approximately by the ratio between the condensation temperature (T_C) and the desorption temperature (T_DE) (Leite, 1998):

In terms of energy, the COP can be defined as:

where Q_E is the cooling effect (or the heat transferred from the evaporator) and E_INP is the input energy. For a compression vapor cycle, E_INP is the compression mechanical work (W_C), and for an adsorption cycle E_INP is equal to the regeneration energy necessary to the desorption process (Q_DE).

So, for a refrigeration adsorption cycle we have:

For sorption systems in general, COP is usually expressed in function of a parameter (r) that represents the efficiency of the heat exchange in the regenerator, as:

where COP_i is the ratio of the cooling effect (Q_E) to the sum of the enthalpy of sorption and the inertia effects of the regenerator.

For liquid sorption systems, the experience shows the r ranging between 0.75 and 0.85, and, for solid sorption systems, 0.4 < r < 0.75; the COP_i varies from 0.2 to 0.5 (Meunier, 1992).

Figure 7 shows, for temperatures of evaporation and condensation typical of cooling applications, the COP in function of the regenerating temperature, for the ideal cycle (Carnot cycle) and absorption and adsorption cycles (Henning, 2007).

Fig. 7 COP in function of the regenerating temperature, for different cycles (Henning, 2007).

As shown in the figure, for temperatures provided by flat plate solar collectors (between 75ºC and 90ºC), we have for both on stage absorption and adsorption systems an expected COP around 0.6.

For solar adsorption cooling systems, it is usual to take into account the solar coefficient of performance (COP_s), defined as:

where ste is the solar thermal efficiency, which is the ratio of the useful heat (Q_DE) to the solar energy received.

3.2 Principle of functioning

Figure 8 shows a functioning scheme of an adsorption refrigeration system. We have a high pressure zone and a low pressure zone, and an expansion valve connecting one to the other.

Fig. 8 Schematic of the adsorption system functioning.

During the cooling step, when heat (Q_E) is transferred to the evaporator at pressure P_AD and temperature T_AD, the working fluid in gaseous phase is evaporated and adsorbed by an adsorbent material, where an adsorbed phase takes place with a dissipation of heat (Q_AD) is released.

During the regeneration step, when an input of heat (Q_DE) occurs, the gas is desorbed and condensed (at P_DE and T_DE) releasing heat (Q_C), completing then the thermodynamic cycle.

3.3 Main adsorption pairs

The main adsorbents used in refrigeration and air conditioning are the silica gel, activated alumina, zeolite and activated carbon. The most commonly used adsorbent-adsorbate pairs and their respective heat of adsorption are given in Table 1 (Srivastava & Eames, 1998).

Table 1 Heat of adsorption for the most commonly used adsorbent-adsorbate pair (Srivastava & Eames, 1998).

The heat of adsorption is a very important thermophysical property, because it represents the energy that needs to be provided by an external source.

So, for dimensioning solar adsorption systems, we need to know the value of this property in order to choose the suitable solar technology for supplying the regeneration energy input.

3.4 Specific cooling power

For analyzing an adsorption refrigeration system, besides the COP we need to take into account the specific cooling power (SCP) that is the energy required to be removed from the evaporator to provide the design low temperature.

Figure 9 shows, for given evaporation and condensation temperature (typical of an air conditioning application) and different adsorbent-adsorbate pairs, the variation of the SCP in function of the COP (Riffel, 2008). These curbs are resulting from numerical simulation based on a statistic model.

Fig. 9 Specific cooling power (SCP) in function of the COP for different adsorbent-adsorbate pairs (Riffel, 2008).

As shown in the figure, for all range of expected COP the best pair is the activated carbon-methanol. For COP values around 0.6, which can be obtained with middle temperature solar collectors, we can have a SCP of 124 W/kg using activated carbon-methanol, against 56 W/kg and 32 W/kg with silica gel-water and zeolite-water, respectively.

3.5 Technological options

In the field of the adsorption refrigeration we have basically two kinds of technologies, which are based on: an intermittent cycle (or basic cycle) that operates with one adsorbent bed, and a continuous cycle (or advanced cycle) that operates with two or more adsorbent beds.

In the basic cycle, the cooling effect and the regeneration process occur alternatively; it is technologically simple, but produces a low COP.

In advanced cycles the cooling and regeneration processes occur simultaneously, they can produce higher COP and encompass different technologies such as heat and mass recovery cycles, thermal wave cycle, convective thermal wave cycle and cascading cycle (Wang, 2001).

4. Solar technology

Figure 10 shows schematically, for different sorption systems and their possible applications, the appropriated solar technology for obtaining the design low temperature.

Fig. 10 Thermal refrigeration systems for the corresponding required solar technologies and evaporation temperatures (Pridasawas & Nemariam, 2003).

As shown, for adsorption systems, with middle temperature solar technologies, as evacuated tube collector (or high efficiency transparent insulation material), it is possible to have both refrigeration and air conditioning applications, which require evaporation temperatures ranging from few negative degrees to around 8ºC.

5. Mathematical model

For dimensioning a solar adsorption system and modeling it to obtain its dynamic behavior, we need to know basically the heat and mass transfer equations for: the adsorbeur (the device containing the adsorbent), the condenser and the evaporator.

In this way, we will give next the equations concerning an autonomous solar-powered cooling machine that utilizes a multi-tubular adsorber, whose surface is the solar collection front surface (or the solar radiation absorber plate). The adsorbent occupies an annular space between the solar collection plate and the axial tube formed by a metallic net where the adsorbate diffuses. The condenser could be an air one (normally integrated to the adsorber) or a water one (an open recipient).

The system behavior depends on the variation of the meteorological parameters, such as the solar irradiation (that can be obtained from hourly data), the ambient temperature, as well as the wind velocity.

The main hypotheses considered in the model are (Leite & Daguenet, 2000): a) thermodynamic equilibrium of the adsorbent-adsorbate il all points of the adsorber and at any moment (diffusion can occurs only in the gaseous phase); b) resistance to the mass diffusion through the interparticle voids and pores is neglected (the pressure inside the adsorber is assumed to be uniform at any moment); c) the temperature distribution of the adsorbent is a function only of the radial direction (one-dimensional heat conduction); d) the adsorbent-adsorbate system is treated as a continuous medium for the thermal conduction effect; e) convection effects within the adsorbent are negligible; and, f) pressure drops in the components and tubes, as well as inside the adsorber, are neglected.

5.1 Heat and mass equations for the adsorber

We consider separately one equation for the adsorber envelope (the top surface – the solar irradiation plate – and the bottom surface) and another for the adsorbent (the porous medium).

5.1.1 Solar radiation absorbing plate

As the solar-power machine works intermittently, we need to consider an equation for the sunlight stage and another for the nocturnal stage. So, we have [15]:

where L_t is the equivalent tube length, h is the convective heat transfer coefficient, U_t is the global heat loss coefficient at the collector top, U_b is the loss coefficient at the bottom of the adsorber, h is the thermal conductance at the tube/adsorbent interface, T is the adsorbent temperature, I_p(t) is the incident solar radiation on the absorber plate, T_p is the solar absorbing plate temperature,  and T_amb is the ambient temperature that can be expressed as:

where D_j is the daylight hours, and ti is the time interval between the maximal solar irradiation and the maximal ambient temperature.

U_t is calculated by (Klein, 1979):

where sigma is the Stefan-Boltzmann constant, h_V is the convective coefficient due to the wind; e_p and e_g are respectively the solar absorber plate and the glass emittances; C, f and g are empirical characteristic parameters.

For the nocturnal stage, the U_t term in Eq. (15) is replaced by an equivalent heat loss coefficient, including convection and radiation losses between the solar plate and the glass sheet.

The total daily solar radiation (I(t)) can be calculated with a help of model given by a classical references in solar energy fundaments and applications from hourly data of the incident solar radiation (Duffie & Beckman, 1991).

5.1.2 Adsorbent

The heat balance equation for the adsorbent porous medium can be expressed by [15]:

with

where C₁ and C₂ are respectively the heat capacity of the adsorbent and the adsorbate, sm and k are respectively the specific mass and the conductivity of the adsorbent.

The dlnP/dt term depends on the process that occurs in the adsorber; for an isosteric process (with constant adsorbed phase concentration), when the the adsorber is isolated we have:

When the condensation or evaporation takes place, the system pressure becomes equal to the saturation pressure, and, thus P = P_s(t).

5.2 Equation for the condenser

For the whole cycle, the energy equation can be written as:

where m_con is the metallic mass of the condenser, h_c,con is the convective heat transfer coefficient, A_con is the condenser surface, L is the latent heat of condensation, T_con is the condensation temperature and T_∞ is the (air or water) temperature.

5.3 Equation for the evaporator

The corresponding energy equation is:

where m_ev is the metallic mass of the condenser, h_c,ev is the convective heat transfer coefficient, A_ev is the condenser surface, L is the latent heat of condensation, T_ev is the evaporation temperature and T_cool is the cooling temperature around the evaporator.

For solving the equations system formed by the heat and transfer equations applied for the adsorber, condenser and evaporator, we need to know the boundary and initial conditions, which require the values of some thermal properties of the adsorbent-adsorbate pair, such as k and h.

6. Overview of solar adsorption refrigeration experiments

A reliable comparison between several systems’ COP_s would require tests under the same conditions, and this is difficult to be achieved. Therefore, we will give just the most representative experimental results worldwide about adsorption cooling systems.

We will present next some representative test data about autonomous solar powered cooling machines based on adsorption in the 1980’s, 1990’s and 2000’s.

To learn more about the adsorption field and we invite the reader to look for the updated references (Zhai & Wang, 2010; Wang et al., 2009; L. W. Wang et al., 2009; Clausse & Meunier, 2008; Alghoul et al., 2007; Yong & Wang, 2007; Wang & Oliveira, 2006), where possible refrigeration and air conditioning applications, including technologies based on advanced adsorption cycles, are presented.

We also recommend a comparative study of five solar cooling systems for subtropical cities, which includes the electric compression, mechanical compression, absorption, solid dessicant and adsorption (Fong et al., 2010).

Tests of a zeolite-water adsorption refrigerator in Abidjan, Ivory Coast, reported a COP_s of 0.08 to 0.09, with the corresponding incident solar radiations varying from 5.7 to 4.6 kWh/m² (Adell, 1985). 

A prototype of a solar adsorptive icemaker, with an air condenser, was tested in Orsay, France, and the obtained COPs varied from 0.085 to 0.093, for a solar radiation ranging from 5.3 to 6.1 kWh (Pons & Grenier, 1987).

The performances of three commercial solar adsorptive ice machines using activated carbon-methanol, using an integrated collector-condenser, were tested during over two years in Agadir, Morocco. The daily ice production of these machines was about 4 kg/m² for over 60% of the year, corresponding to an average solar coefficient of performance of about 0.07, under a daily average solar irradiation of 5.4 kWh (Boubakri et al., 2000).

A prototype of an adsorption refrigerator, using silica gel-water, a multi-tubular adsorber and an air condenser, was tested in Yverdon-les-Bains, Switzerland, and it was obtained a monthly average COP_s of 0.13, with an incident solar radiation of 4.3 kWh (Hildebrand et al., 2004).

An activated carbon-methanol ice machine, also using a multi-tubular adsorber, but bifacially irradiated and covered by a high efficient transparent insulation material, was tested in João Pessoa, Brazil, and produced 6,0 kg of ice/m² and a corresponding COPs of 0.085, under a predominantly clear sky day and a solar incidence of 6.6 kWh (Leite et al., 2007).

7. Final remarks

Solar refrigeration is mainly advantageous in sunny regions where electricity is not available or is unreliable. In most of these areas, absorption refrigerators working with gas or kerosene is often used, but they imply problems of safety, technological reliability and fuel supply. So, in this case, adsorption cooling systems driven by solar thermal energy can be an alternative for providing cold for storage essential products like food and medicine.

The concepts, properties and equations presented in this chapter allow dimensioning an autonomous intermittent solar cooling machine, in which the solar collector is integrated to the adsorber. In addition, these elements can predict the dynamic behavior and the solar coefficient of performance of an adsorptive refrigerator, under the given meteorological conditions.

Finally, we have gathered most reliable tests results with some adsorptive solar-powered refrigerators obtained in different climates, and the range of COP_s varying roughly from 0.07 to 0.13, with an incident solar radiation ranging from 4.5 to 7 kWh.

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