TRNSYS software is a highly flexible graphical software environment used to simulate the behavior of transient systems. While the vast majority of simulations focus on evaluating the performance of thermal and electrical power systems, TRNSYS can also be used to model other dynamical systems such as circulation or biological processes.

TRNSYS is made up of two parts. The first part is an engine (called a kernel) that reads and processes the input file, resolves the system iteratively, determines convergence, and plots system variables. The kernel also provides utilities that (among other things) determine thermophysical properties, invert matrices, perform linear regressions, and interpolate external data files. The second part of TRNSYS is an extensive library of components, each of which models the performance of a part of the system. In this study, we therefore propose a refrigeration production system capable of meeting conservation needs.

In our work, we used meteorological data contained in the TRNSYS software database from SOLARGIS. These data are corroborated by those provided by those provided by the meteorological stations of Burkina Faso. Satellite data have the advantage of being continuous over time with a fine mesh of space. This allows us to easily obtain the data for our study site.

Ouagadougou is located in the center of the country at an altitude of 300 meters, in the middle of the intertropical zone, with strong sunshine as shown in Figure 1 [10] . The city has, on average, 3135 hours of sunshine per year. Ouagadougou’s climate is tropical, warm all year round, with a dry season from November to March and a rainy season that runs approximately from late April to early October. During the day, it can be very hot all year round, but especially from March to May, before the rainy season. The city has a tropical savannah climate, with two seasons: the harmattan and the monsoon. Cut off from the influence of the

desert and any ventilation, the city then suffered from scorching weather, with scorching days (from 38˚C at the end of February to 40˚C to 42˚C and even 43˚C in April) and hot nights (on average 24˚C to 26˚C at least, with even a few nights when the temperature did not drop below 30˚C in April).

The city has a tropical savannah climate, with two seasons: the harmattan and the monsoon. Cut off from the influence of the desert and any ventilation, the city then suffered from scorching weather, with scorching days (from 38˚C at the end of February to 40˚C to 42˚C and even 43˚C in April) and hot nights (on average 24˚C to 26˚C at least, with even a few nights when the temperature did not drop below 30˚C in April) according to Figure 2 [11] .

The working principle of the adsorption refrigeration system is based on an adsorption-desorption thermal cycle. This cycle can be represented on a Clapeyron diagram on Figure 3 [13] . It is divided into four phases, namely isosteric heating in phase 1, desorption in phase 2, isosteric cooling in phase 3 and adsorption in phase 4.

1) Initially, the adsorption bed is saturated with water vapour and is isolated from the condenser and evaporator using valves. It is heated adsorber until the vapour pressure in the adsorption bed reaches the condensation pressure (Pcd) of the water.

2) At this time, the adsorption bed is connected to the condenser and the desorbed liquid is cooled to a temperature (Tcd) until it condenses in the condenser.

3) Meanwhile, the adsorbent bed is closed, and the adsorbent releases the heat using a cold fluid source. During this cooling phase, the temperature and pressure inside the adsorbent bed decrease.

4) The bed is connected to the evaporator as soon as the bed pressure becomes slightly lower than the evaporation pressure (Pev). As the adsorbent continues to cool, the liquid water vaporized in the evaporator is adsorbed by the adsorbent. This vapor is produced by evaporation of the liquid in the evaporator, thus producing cold. The amount of cold produced is proportional to the latent heat of vaporisation of the adsorbat.

To ensure the continuity of operation of the cold production by adsorption, we have a second adsorption bed. According to Figure 3 the operating principle is as follows:

1) During phase 1, the adsorbent of the first compartment (reactor 2) is “regenerated” by heating (hot water from the solar collector).

2) During phase 2, the water vapour produced flows under the influence of a vacuum pushed to the condenser where it is condensed. Thus, the condensed water flows through the expansion valve to the low-pressure evaporator where it is evaporated (low-temperature production step).

3) Then in phase 3, the adsorbent in the second chamber (reactor 1) maintains low pressure by adsorbing water vapor from the evaporator.

4) Finally, wind phase 4, or the compartment, needs to be cooled to maintain the adsorption process.

When the production of cold decreases (the adsorbent becomes saturated with water vapour), the functions of the two compartments are reversed (by opening and closing the valves). For systems with mass recovery, connect the generator (reactor 2) through the valve to the adsorber (reactor 1) in phase 3. The adsorbate is evaporated from the generator and transferred directly to the adsorber until pressure equilibrium is reached [14] . The mass of adsorption and desorption increases, leading to an increase in the cycled mass, which translates into an increase in cold production.

To simplify the equations we have formalized the following information: adsorption/desorption takes place at equilibrium, temperature and pressure are uniform in all chambers, the empty volume of the chambers is neglected, the adsorbent is inert, the thermal mass of the heat transfer fluid is neglected during the adsorption/desorption process, the adsorbed phase is assumed to be a saturated liquid, and the average isosteric adsorption heat is constant [16] . The energy and mass balances for each component of the system are carried out in a non-steady state.

The mass balance of the adsorbate during the cycle is expressed in the following equations which describe the principle.

${\stackrel{\dot{}}{m}}_{v,des}=-m_{sg}\frac{\text{d}{q}_{des}}{\text{d}t}$ (1)

$\frac{\text{d}{m}_{w,cond}}{\text{d}t}={\stackrel{\dot{}}{m}}_{v,des}-{\stackrel{\dot{}}{m}}_w$ (2)

$\frac{\text{d}{m}_{w,eva}}{\text{d}t}={\stackrel{\dot{}}{m}}_w-{\stackrel{\dot{}}{m}}_{v,ads}$ (3)

$m_{sg}\frac{\text{d}{q}_{ads}}{\text{d}t}={\stackrel{\dot{}}{m}}_{v,ads}$ (4)

Define the different terms of Equations (1) to (4).

During the adsorption/desorption cycle, neglecting changes in kinetic and potential energy, the first law of thermodynamics allows us to obtain the following equation at the level of:

$\begin{array}{l}\left(m{c}_{p,ads}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{des}\right)\right)\frac{\text{d}{T}_{des}}{\text{d}t}\\ ={\stackrel{\dot{}}{m}}_{heat}{c}_{p,w}\left(T_{heat,in}-T_{heat,out}\right)+\delta {\stackrel{\dot{}}{m}}_{v,des}\left(h_v{T}_{des}-h_v{T}_{cond}\right)+m_{sg}\frac{\text{d}{q}_{des}}{\text{d}t}{q}_{st}\end{array}$ (5)

$\begin{array}{l}\left(m{c}_{p,ads}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{ads}\right)\right)\frac{\text{d}{T}_{ads}}{\text{d}t}\\ =\stackrel{\dot{}}{m}{h}_{ads}{c}_{p,w}\left(T_{cool,in}-T_{coola,out}\right)+\left(1-\varphi \right){\stackrel{\dot{}}{m}}_{v,ads}\left(h_v{T}_{eva}-h_v{T}_{ads}\right)+m_{sg}\frac{\text{d}{q}_{ads}}{\text{d}t}{q}_{st}\end{array}$ (6)

$\begin{array}{l}\left(m{c}_{cond}+m_{w,cond}{c}_{p,w}\right)\frac{\text{d}{T}_{cond}}{\text{d}t}\\ ={\stackrel{\dot{}}{m}}_{cond}{c}_{p,w}\left(T_{cool,in}-T_{cool,out}\right)+\left(1-\delta \right){\stackrel{\dot{}}{m}}_{v,des}\left(h_v{T}_{des}-h_v{T}_{cond}\right)+{\stackrel{\dot{}}{m}}_{v,des}{h}_{fg}{T}_{cond}\end{array}$ (7)

$\begin{array}{l}\left(m{c}_{p,eva}+m_{w,eva}{c}_{p,w}\right)\frac{\text{d}{T}_{eva}}{\text{d}t}\\ ={\stackrel{\dot{}}{m}}_{chill}{c}_{p,w}\left(T_{chill,in}-T_{chill,out}\right)-{\stackrel{\dot{}}{m}}_{v,ads}{h}_{fg}{T}_{eva}\\ +{\stackrel{\dot{}}{m}}_w{c}_{p,w}\left(T_{cond}-T_{eva}\right)+\varphi {\stackrel{\dot{}}{m}}_{v,ads}\left(h_v{T}_{eva}-h_v{T}_{ads}\right)\end{array}$ (8)

For the heat transfer of the heat transfer fluid at the level of the first adsorber/desorber, we have:

$T_{heat,out}=T_{des}+\left(T_{heat,in}-T_{des}\right){\text{e}}^{\frac{-U{A}_{des}}{{\stackrel{\dot{}}{m}}_{heat}{c}_{p,w}}}$ (9)

For the heat transfer of the heat transfer fluid at the level of the second adsorber/desorber, we have:

$T_{coola,out}=T_{ads}+\left(T_{cool,in}-T_{ads}\right){\text{e}}^{\frac{-U{A}_{ads}}{{\stackrel{\dot{}}{m}}_{ads}{c}_{p,w}}}$ (10)

For the heat transfer of the heat transfer fluid within the condenser, we have:

$T_{cool,out}=T_{cond}+\left(T_{cool,in}-T_{cond}\right){\text{e}}^{\frac{-U{A}_{cond}}{{\stackrel{\dot{}}{m}}_{cond}{c}_{p,w}}}$ (11)

For the heat transfer of the heat transfer fluid within the evaporator we have:

$T_{chill,out}=T_{eva}+\left(T_{chill,in}-T_{eva}\right){\text{e}}^{\frac{-U{A}_{eva}}{{\stackrel{\dot{}}{m}}_{chill}{c}_{p,w}}}$ (12)

For the heat recovery equation at the level of the first adsorber/desorber, we have:

$\left(m{c}_{ads}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{des}\right)\right)\frac{\text{d}{T}_{des}}{\text{d}t}={\stackrel{\dot{}}{m}}_{heat}{c}_{p,w}\left(T_{heat,in}-T_{heat,out}\right)$ (13)

$m_w{c}_{p,heat}\frac{\text{d}{\bar{T}}_m}{\text{d}t}=\stackrel{\dot{}}{m}{c}_{p,heat}\left(T_{heat,in}-T_{heat,out}\right)+U{A}_{des}\left(T_{des}-{\bar{T}}_m\right)$ (14)

For the heat recovery equation at the level of the second adsorber/desorber, we have:

$\left(m{c}_{ads}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{ads}\right)\right)\frac{\text{d}{T}_{ads}}{\text{d}t}={\stackrel{\dot{}}{m}}_{ads}{c}_{p,w}\left(T_{cool,in}-T_{coola,out}\right)$ (15)

$m_w{c}_{p,cool}\frac{\text{d}{\bar{T}}_m}{\text{d}t}=\stackrel{\dot{}}{m}{c}_{p,cool}\left(T_{cool,in}-T_{cool,out}\right)+U{A}_{ads}\left(T_{ads}-{\bar{T}}_m\right)$ (16)

For the heat recovery equation at the condenser, we have:

$\left(m{c}_{cond}+m_{w,cond}{c}_{p,w}\right)\frac{\text{d}{T}_{cond}}{\text{d}t}={\stackrel{\dot{}}{m}}_{cond}{c}_{p,w}\left(T_{cool,in}-T_{cool,out}\right)$ (17)

For the heat recovery equation at the evaporator, we have:

$\left(m{c}_{eva}+m_{w,eva}{c}_{p,w}\right)\frac{\text{d}{T}_{eva}}{\text{d}t}={\stackrel{\dot{}}{m}}_{chill}{c}_{p,w}\left(T_{chill,in}-T_{chill,out}\right)$ (18)

At rest, the heat losses due to the first adsorber/desorber are determined by:

$\left(m{c}_{ads}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{des}\right)\right)\frac{\text{d}{T}_{des}}{\text{d}t}=U{A}_{des,amb}\left(T_{room}-T_{des}\right)$ (19)

At rest, the heat losses due to the second adsorber/desorber are determined by:

$\left(m{c}_{ads}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{ads}\right)\right)\frac{\text{d}{T}_{ads}}{\text{d}t}=U{A}_{ads,amb}\left(T_{room}-T_{ads}\right)$ (20)

At rest, heat losses from the condenser are determined by:

$\left(m{c}_{cond}+c_{w,cond}\right)\frac{\text{d}{T}_{cond}}{\text{d}t}=U{A}_{cond,amb}\left(T_{room}-T_{cond}\right)$ (21)

At rest, heat losses in the evaporator are determined by:

$\left(m{c}_{eva}+c_{w,eva}\right)\frac{\text{d}{T}_{eva}}{\text{d}t}=U{A}_{eva,amb}\left(T_{room}-T_{eva}\right)$ (22)

The adsorption equilibrium equation is given by:

$q^{*}=k_s\left(q^{*}-q\right)$ (23)

At equilibrium, we have:

$\frac{\text{d}q}{\text{d}t}=k_s\left(q^{*}-q\right),k_s=\frac{15D_s}{R_p^2}$ (24)

For the recovery of the mass, we have:

$\begin{array}{l}\left(m{c}_{ads}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{ads}\right)\right)\frac{\text{d}{T}_{ads}}{\text{d}t}\\ =m_{sg}\frac{\text{d}{q}_{ads}}{\text{d}t}{q}_{st}+m_{sg}\frac{\text{d}{q}_{ads}}{\text{d}t}\left(h_v{T}_{des}-h_v{T}_{ads}\right)\end{array}$ (25)

$\left(m{c}_{des}+m_{sg}\left(c_{p,sg}+c_{p,w}{q}_{des}\right)\right)\frac{\text{d}{T}_{des}}{\text{d}t}=m_{sg}\frac{\text{d}{q}_{des}}{\text{d}t}{q}_{st}$ (26)

$m_{sg}\frac{\text{d}{q}_{ads}}{\text{d}t}=-m_{sg}\frac{\text{d}{q}_{des}}{\text{d}t}$ (27)

Starting from the assumption in which we neglect the energy consumed by the circulators and other accessories, the Coefficient of Performance (COP) is determined by the following formula:

$COP=\frac{Q_{ev}}{Q_{gn}}$ (28)

$Q_{ev}$ and $Q_{gn}$ are respectively the amount of cold produced at the evaporator and the amount of heat at the hot source.

And the specific cooling power is given by:

$SCP=\frac{Q_{ev}}{m_{ads}}$ (29)

To solve the equations of the model, we used the TRNSY software to analyze the influence of the different parameters on the functioning of the studied system.

We also used the test bench for experimental measurements that validated the results obtained from the simulation.

We have developed a model of the system on TRSYS for simulation purposes. The diagram in Figure 5 explains the steps involved in simulating the operating parameters of the system.

Table 1 and Table 2 , together with Figure 6 , provide a clear and complete overview of both the experimental setup and the simulation conditions. The test bench shown in Figure 6 consists of an adsorption machine, whose characteristics are detailed in Table 1 . The input parameters used for the numerical simulation are listed in Table 2 .

We carried out the numerical and experimental simulation of the system focusing on its operating parameters. Figures 7-9 show the variation of the water inlet/outlet temperatures of the adsorbent beds as a function of time. The temperatures show a regular variation according to the succession of the adsorption and desorption phases for an average cycle time of about 14 minutes in the simulation and 10 min for the experiment, so there appears to be a convergence between the simulation and the experiment. The water outlet temperature of the adsorbent beds varies between the hot water inlet temperature (90˚C) which favors the driving power for desorption and the cooling water inlet temperature (25˚C) when cooling the adsorbent bed during the adsorption phase. This behaviour is

due to the succession of adsorption/desorption phases and the role swap between the two compartments. During the desorption phase, the thermal power borrowed from the heating water decreases during the evolution of the desorption process, which is illustrated by the increase in the water outlet temperature of the desorbeur. Indeed, a large part of the heat input is accumulated by the reactor structure and by the adsorbent (silica gel) while a small part is reserved for the desorption process. When this temperature reaches its maximum value, the compartment is perfectly heated, thus allowing the water to desorption. During the adsorption phase, the thermal power dissipated in the cooling water decreases during the evolution of the adsorption process, which is illustrated by the decrease in the water outlet temperature of the desorber. Similarly, a large part of the heat rejection corresponds to the cooling of the reactor structure and the adsorbent (silica gel) while a small part is reserved for the adsorption process. Whereas when the temperature reaches its minimum value, the compartment is cooled, and the silica gel begins to adsorb water vapor.

The numerical and experimental values of the condenser’s water outlet temperature vary according to the cycle and fluctuate between 25˚C and 40˚C. Figure 5 shows the numerical and experimental values of the inlet/outlet temperatures from the cold-water circuit to the evaporator. It is noticeable that the outlet temperature fluctuates between 11˚C and 13˚C with continuous cold production for a 14-minute cycle.

The following figures are obtained by numerical and experimental simulation of the variation of temperatures and pressures in the system studied. These results allow the model to be validated in order to study the performance of the system and vary the operating temperatures.

The comparison of the model with the experimental results allowed its validation in order to allow its use in simulation. Figure 10 shows the effect of the heating temperature on the performance of the machine. The machine’s coefficient of performance (COP) as well as the amount of cold produced increase with the generation temperature. The performance is even better in the case of mass recovery.

The temperature of the condenser corresponds to the cooling temperature of the adsorption bed. Thus, we studied the effect of the variation of the condenser temperature on the system’s COP during the day. By varying the temperature of the condenser, we also determined the variation in the amount of cold produced. Figure 11 shows the results obtained.

These figures show that the increase in the temperature of the condenser leads to a decrease in the performance of the machine.

The COP reaches its maximum value for a temperature Tc = 25˚C and after 600 s which corresponds to one cycle. However, it takes 1200 s, or two cycles, to reach the maximum value of the COP when Tc increases. However, the COP decreases when Tc increases.

Similarly, the SCP reaches its maximum value for a temperature Tc = 25˚C and 30˚C after 600 s, which corresponds to one cycle. However, it takes 1200 s, or two cycles, to reach the maximum value of the SCP when Tc increases. However, the SCP decreases as Tc increases.

We varied the heating temperature Tg and measured the variation in the performance of the machine and the variation in the amount of cold produced. The results are presented in Figure 10 and Figure 11 and highlight the variation of COP and SCP as a function of Tg temperature.

Indeed, the COP reaches its maximum value for a temperature Tg = 90˚C and after 600 s which corresponds to one cycle. However, it takes 1200 s, or two cycles, to reach the maximum value of COP when Tg decreases. We can also see that the COP decreases when Tg decreases.

We observed the variation in machine performance and the variation in the amount of cold produced as a function of the evaporator temperature. The results are presented in Figure 12 and highlight the variation in COP and SCP as a function of temperature Te. In fact, the COP reaches its maximum value at a temperature of Te = 16˚C and after 600 seconds, which corresponds to one cycle. However, it takes 1200 seconds, or two cycles, to reach the maximum COP value when Te decreases. We also see that the COP decreases when Te decreases. Similarly, the SCP reaches its maximum value for a temperature Te = 16˚C after 1200 s, which corresponds to two cycles. However, it takes 600 s, or one cycle, to reach the maximum SCP value when Te decreases. The results show that we have one of the best system performances and the amount of cold produced when the temperature in the evaporator approaches that of the condenser.

Similarly, the SCP reaches its maximum value for a temperature Tg = 90˚C after 1200 s, which corresponds to two cycles. However, it takes 600 s, or one cycle, to reach the maximum value of the SCP when Tg decreases. However, the SCP decreases as Tc increases. The results show that increasing the heating temperature increases the performance of the system and the amount of cold produced.