Integration of Evacuated Tube Collectors and Stratified Phase Change Material Storage in Solar Absorption Refrigeration: Annual Performance Assessment for Food Conservation

2.1 System description

The studied solar-assisted refrigeration system (Figure 1) comprises four interconnected subsystems: an evacuated-tube collector field incorporating PCM, a vertically stratified water–PCM storage tank, a single-effect LiBr–H₂O absorption machine, and a 50 m³ cold room. An electric resistance heater is installed in the generator loop as a backup source. Solar heat is prioritized, and the auxiliary heater supplies only the residual thermal demand when the storage temperature or available tank power is insufficient. The configuration is therefore treated as a solar-assisted hybrid absorption refrigeration system [17].

Figure 1. The schematic illustration of the solar absorption refrigeration system

2.1.1 Evacuated tube solar collectors

Retained collection surface: A_coll = 10 m²

Inclination and orientation: β = 35°, south-facing

Collector PCM: 15.9 kg of RT82 paraffin

PCM phase-change peak: T_melt = 82 ℃

PCM storage capacity: 170 kJ.kg⁻¹ over the 70–85 ℃ interval

PCM specific heat: 2.0 kJ·kg⁻¹·K⁻¹

Solar-loop mass flow rate: 0.015 kg·m⁻²·s⁻¹ (0.150 kg·s⁻¹)

Heat-transfer fluid: equivalent water–glycol mixture; c_p = 3.9 kJ·kg⁻¹·K⁻¹

Role: solar heat collection and short-term latent buffering; collector outlet temperature limited to 100 ℃. The selection of evacuated-tube collectors is supported by their ability to maintain comparatively high thermal performance at elevated operating temperatures, mainly because the vacuum envelope limits conductive and convective heat losses, while selective coatings improve solar-energy absorption [7].

The evacuated-tube collector model uses a nominal optical efficiency η₀ = 0.718 and thermal-loss coefficients a₁ = 1.36 W·m⁻²·K⁻¹, and a₂ = 0.0025 W·m⁻²·K⁻². These coefficients define the useful thermal output as a function of incident irradiance and the collector-to-ambient temperature difference, with the calculated efficiency bounded between 0 and 0.75. PCM integration absorbs part of the high-irradiance heat and delays its transfer when solar input decreases, thereby reducing short-term fluctuations in the temperature delivered to the tank [12, 18].

The RT82 phase change is represented by a continuous enthalpy formulation over a 3 K transition interval. The selected PCM mass provides approximately one hour of buffering equivalent to 15% of the nominal generator thermal power. Charging is enabled when the collector outlet reaches at least 85 ℃, whereas discharge toward the tank requires a minimum positive temperature difference of 3 K [19].

2.1.2 Stratified storage tank

Total volume: V_sto = 700 L

Storage-to-collector ratio: 70 L/m²

Configuration: 20 fixed vertically stratified water nodes

Water mass: approximately 663 kg

Tank PCM: approximately 26.9 kg of RT82 (5% of tank volume)

PCM distribution: 70% in the upper 7 nodes, 30% in the middle 6 nodes, 0% in the lower 7 nodes

Overall heat-loss coefficient: U_sto = 0.35 W·m⁻²·K⁻¹

Maximum storage temperature: 95 ℃

Role: store solar heat and supply the absorption generator

The tank is represented by twenty equal fixed vertical nodes. Heat losses are evaluated for each node, and adjacent nodes exchange heat through an equivalent axial conductance accounting for water conduction, wall conduction, and residual mixing. The twenty-layer architecture and fourth-order Runge–Kutta basis are consistent with the model of Karlina et al. [20] and with validated one-dimensional multi-node storage models [21]. Solar heat is introduced at the thermally compatible level, with 90% supplied to that node and 10% to the immediately lower node. Hot water is withdrawn from the upper node for the generator, and the cooler return is reintroduced at a temperature-compatible level. A 60 s internal time step, a maximum Courant number of 0.35, and a conservative correction of adjacent inversions exceeding 0.10 K are used to limit artificial mixing.

The PCM is concentrated near the upper part of the tank to retain latent storage close to the generator operating temperature. The lower seven nodes contain no PCM so that a comparatively cool return can be maintained for the solar collectors. The adopted 70/30/0 distribution is a design assumption evaluated within the comparative cases: without PCM, collector PCM only, tank PCM only, and combined collector and tank PCM. The temperatures reported as upper, middle, and lower storage temperatures are representative outputs from the twenty-node field, not three computational zones [17].

2.1.3 LiBr–H₂O absorption machine

Type: single effect

Calculated peak cooling load for the reference Typical Meteorological Year (TMY): Q̇_peak = 2.65 kW

Design load (safety factor 1.15): Q̇_design = 3.05 kW

Selected nominal cooling capacity: Q̇_{cool, nom} = 3.50 kW

Nominal generator thermal power: Q̇_{gen, nom} = 5.00 kW

Evaporator temperature: T_evap = 0 ℃; nominal condenser temperature: 35 ℃

Generator temperature range: 75–95 ℃; nominal value 90 ℃; modeled condenser range: 28–45 ℃

Nominal COP: 0.70

Minimum part-load ratio: 40%

Control: ON/OFF at 5.5 ℃ and 4.5 ℃

The nominal machine capacity is derived automatically from the calculated cold-room load. For the reference Meteonorm TMY, a peak load of 2.65 kW becomes 3.05 kW after applying a 15% safety factor; the selected capacity is therefore 3.50 kW. Single-effect LiBr–H₂O machines are compatible with the medium-temperature heat supplied by evacuated-tube collectors [9, 10]. The working-pair properties are evaluated using established LiBr–H₂O formulations [22].

The instantaneous COP is adjusted according to generator, condenser, and evaporator temperatures and is limited to the range 0.62–0.75. The effective condenser temperature is estimated from the outdoor wet-bulb temperature with a 7 K cooling-tower approach and is bounded between 28 and 45 ℃. The machine starts when the refrigerated-air temperature reaches 5.5 ℃ and stops at 4.5 ℃, producing a 1 K hysteresis band around the 5 ℃ setpoint. During operation, the cooling output is not allowed to fall below 40% of nominal capacity; lower average loads are represented by cycling and the resulting duty cycle.

A 5.00 kW electric resistance heater, with an efficiency of 0.98, supplies only the generator heat not covered by the stratified tank. It is therefore a thermal backup for the absorption cycle and not a separate vapour-compression refrigeration unit. Solar generator input, auxiliary thermal input, auxiliary electricity, system auxiliaries, and unmet cooling demand are accounted for separately in the energy balance.

2.1.4 Cold room

Reference product: fresh oranges

Internal dimensions: 5.0 m × 4.0 m × 2.5 m

Volume: 50 m³

Target temperature: T_target = 5 ℃

Selected product-specific evaluation interval: 3–8 ℃

Air mass and specific heat: 60 kg; c_p,air = 1005 J·kg⁻¹·K⁻¹

Stored product mass: 1500 kg; c_p,p = 3400 J·kg⁻¹·K⁻¹

Daily product intake: 300 kg/day at 15 ℃; c_p,in = 3800 J·kg⁻¹·K⁻¹

Envelope surface and transmittance: A_wall = 85 m²; U_wall = 0.18 W·m⁻²·K⁻¹

Air–product conductance: UA_ap = 45 W·K⁻¹; added fast thermal capacitance: C_fast = 350 kJ·K⁻¹

Fresh oranges are selected as the reference food product. The room setpoint is 5 ℃, and 3–8 ℃ is used as a product-specific thermal-performance interval, consistent with postharvest guidance for oranges [23]. This interval must not be presented as a universal HACCP temperature band because Codex guidance requires product-specific hazards, critical limits, monitoring, and records rather than one temperature range for all fresh produce [24].

The cold room is represented by two coupled thermal nodes. The air-side node includes the heat capacity of 60 kg of air and an additional effective capacitance of 350 kJ·K⁻¹representing internal surfaces, shelving, the evaporator, and rapidly responding parts of the stored load. The product node contains 1500 kg of oranges and exchanges heat with the air through an overall conductance of 45 W·K⁻¹. Both nodes are initialized at 5 ℃.

The refrigeration load includes envelope transmission, permanent leakage, door-opening infiltration, sensible and latent infiltration loads, incoming-product cooling, lighting, occupants, evaporator-fan heat, and a 40 W product respiration gain. For the reference Meteonorm TMY, the resulting peak load of 2.65 kW provides the basis for selecting the 3.50 kW absorption unit. Because the peak is calculated from the meteorological input, these two values must be updated if the TMY file or operating assumptions are changed. The adopted effective capacitance, conductance, and biological-load parameters are retained as model assumptions and should be examined through sensitivity analysis and future experimental calibration [25, 26].

2.2 Mathematical modeling

The mathematical model was developed to describe the main thermal and energy interactions within the proposed solar-assisted refrigeration system. It includes a two-node representation of the refrigerated room, an evacuated-tube solar collector field, PCM, a vertically stratified water–PCM storage tank, and a single-effect LiBr–H₂O absorption chiller. The governing equations are formulated from mass and energy conservation principles and are coupled through the heat-transfer rates exchanged between the different subsystems.

2.2.1 Two-node cold-room model

The refrigerated air and the stored products are represented by two interacting thermal nodes. Their energy balances are written as:

$C_{\mathrm{air}} \frac{\mathrm{d} T_{\mathrm{air}}}{\mathrm{d} t}=\dot{Q}_{\mathrm{ext}}+U A_{\mathrm{ap}}\left(T_{\mathrm{p}}-T_{\mathrm{air}}\right)-\dot{Q}_{\text {cool }}$              (1)

$C_{\mathrm{p}} \frac{\mathrm{d} T_{\mathrm{p}}}{\mathrm{d} t}=U A_{\mathrm{ap}}\left(T_{\mathrm{air}}-T_{\mathrm{p}}\right)$              (2)

The effective thermal capacitances of the air-side node and the product node are

$C_{\text {air }}=m_{\text {air }} c_{p, \text { air }}+C_{\text {fast }}, C_{\mathrm{p}}=m_{\mathrm{p}} c_{p, \mathrm{p}}$              (3)

The total thermal load applied to the air node is decomposed into transmission, permanent air leakage, door-opening infiltration, incoming-product, and internal contributions:

$\dot{Q}_{\mathrm{ext}}=\dot{Q}_{\mathrm{tr}}+\dot{Q}_{\mathrm{leak}}+\dot{Q}_{\mathrm{door}}+\dot{Q}_{\mathrm{prod}}+\dot{Q}_{\mathrm{int}}$              (4)

where, $U A_{\mathrm{ap}}$ is the overall air-product conductance, $C_{\text {fast}}$represents the rapidly responding internal thermal mass, and $\dot{Q}_{\text {cool }}$ is the cooling power supplied by the absorption machine. The leakage and door-opening terms each include their sensible and latent components

2.2.2 Solar collector modelling

The useful thermal power delivered by the solar collector field is calculated as:

$\dot{Q}_{\text {solar }}=\eta_{\text {coll }} A_{\text {coll }} G_\beta$                           (5)

where, η_coll is the instantaneous collector efficiency, A_coll is the total collector area, and G_β is the total solar irradiance incident on the tilted collector surface.

The instantaneous collector efficiency varies with the operating conditions and is determined from the quadratic performance correlation:

$\eta_{\mathrm{coll}}=\eta_0-a_1 \frac{\left(T_{\mathrm{m}}-T_{\mathrm{ext}}\right)}{G_\beta}-a_2 \frac{\left(T_{\mathrm{m}}-T_{\mathrm{ext}}\right)^2}{G_\beta}$                     (6)

where, η₀ is the optical efficiency, a₁ and a₂ are the first- and second-order heat-loss coefficients, respectively, T_ext is the ambient temperature, and T_m is the mean fluid temperature inside the collector.

The mean fluid temperature is defined as:

$T_{\mathrm{m}}=\frac{T_{\mathrm{in}}+T_{\mathrm{out}}}{2}$                           (7)

where, T_in and T_out denote the collector inlet and outlet fluid temperatures, respectively.

2.2.3 Phase Change Material enthalpy formulation

For each storage node i, the total sensible and latent energy of water and PCM is represented by the nodal enthalpy:

$\begin{gathered}H_i=\left(m_{\mathrm{w}, i} c_{p, \mathrm{w}}+m_{\mathrm{pcm}, i} c_{p, \mathrm{pcm}, i}\right)\left(T_i-T_{\mathrm{ref}}\right)+m_{\mathrm{pcm}, i} L_{\mathrm{pcm}, i} f_i\end{gathered}$                           (8)

The liquid fraction varies continuously within the phase-change interval:

$f_i= \begin{cases}0, & T_i \leq T_{\text {fus }, i}-\Delta T_{\text {fus }} \\ \frac{T_i-\left(T_{\text {fus }, i}-\Delta T_{\text {fus }}\right)}{\Delta T_{\text {fus }}}, & T_{\text {fus }, i}-\Delta T_{\text {fus }}<T_i<T_{\text {fus }, i}, \\ 1, & T_i \geq T_{\text {fus }, i} .\end{cases}$                           (9)

where, Hᵢ is a nodal energy expressed in joules, while fᵢ = 0 and fᵢ = 1 correspond to the fully solid and fully liquid states, respectively.

2.2.4 Stratified water-Phase Change Material storage tank

The tank is discretized into 20 fixed vertical nodes. The enthalpy balance of node i is:

$\frac{\mathrm{d} H_i}{\mathrm{~d} t}=\dot{Q}_{\mathrm{hyd}, i}+\dot{Q}_{i-1, i}-\dot{Q}_{i, i+1}-\dot{Q}_{\mathrm{loss}, i}$                           (10)

The axial heat transfer between adjacent nodes and the thermal loss to the surroundings are expressed as:

$\dot{Q}_{i, i+1}=U A_{\text {inter }}\left(T_i-T_{i+1}\right)$                            (11)

$\dot{Q}_{\text {loss }, i}=U_{\text {tank }} \frac{A_{\text {tank }}}{N_{\text {nodes }}} \max \left(0, T_i-T_{\text {ext }}\right)$                            (12)

where, $\dot{Q}_{\mathrm{hyd}, i}$ is the signed hydraulic power associated with charging, thermal-energy withdrawal by the absorption-machine generator, and return-flow reinjection, whereas $U A_{\text {inter}}$ governs heat transfer between adjacent layers.

2.2.5 Absorption machine and auxiliary heater

The single-effect absorption machine is described by a thermal COP. Before applying the capacity and control constraints, the cooling potential associated with the thermal power supplied to the generator is

$\dot{Q}_{\text {cool}, \text {th}}=C O P \times \dot{Q}_{\text {gen,total}}$                            (13)

The cooling capacity under the prevailing generator and condenser temperatures is corrected by the dimensionless factor f_cap:

$\dot{Q}_{\text {cap}, \text { avail }}=f_{\text {cap}} \times \dot{Q}_{\text {cool }, \text { nom }}$                            (14)

The cooling demand is limited to the capacity available at the current operating conditions:

$\dot{Q}_{\text {cool }, \text { cmd }}=\min \left(\dot{Q}_{\text {cool }, \text { req }}, \dot{Q}_{\text {cap }, \text { avail }}\right)$                            (15)

The machine is operated only when Q̇_cool,cmd ≥ PLR_min Q̇_cool,nom; otherwise, it is switched off and the commanded cooling power is set to zero.

During operation, the part-load ratio, the bounded COP, and the corresponding generator demand are evaluated as

$P L R=\frac{\dot{Q}_{\text {cool,cmd }}}{\dot{Q}_{\text {cool,nom }}}$                            (16)

$\begin{gathered}C O P=\min \left[C O P_{\max }, \max \left(C O P_{\min }, C O P_{\text {base }}(0.94\right.\right. +0.06 P L R))]\end{gathered}$                            (17)

$\dot{Q}_{\text {gen,req }}=\frac{\dot{Q}_{\text {cool,cmd }}}{C O P}$                            (18)

Eq. (17) restricts the calculated COP to the interval from COP_min to COP_max and replaces the programming-specific clip operator with standard minimum and maximum functions.

Solar heat is used first, while the auxiliary heater supplies only the remaining generator demand:

$\dot{Q}_{\text {gen }, \text { total }}=\dot{Q}_{\text {gen,solar }}+\dot{Q}_{\text {aux }}$                            (19)

$\begin{gathered}\dot{Q}_{\text {aux }}=\min \left[\dot{Q}_{\text {aux,nom }}, \max \left(0, \dot{Q}_{\text {gen,req }}\right.\right. \left.\left.-\dot{Q}_{\text {gen,solar}}\right)\right]\end{gathered}$                             (20)

The cooling power actually delivered is limited by both the command and the thermal power effectively available at the generator:

$\dot{Q}_{\text {cool }}=\min \left[\dot{Q}_{\text {cool,cmd }}, \operatorname{COP}\left(\dot{Q}_{\text {gen,solar }}+\dot{Q}_{\text {aux }}\right)\right]$                             (21)

This formulation gives priority to solar energy, prevents operation below the admissible part-load range, and accounts explicitly for the nominal limit of the auxiliary heater.

2.2.6 Performance indicators

The thermal annual COP, based exclusively on the thermal energy supplied to the absorption generator, is:

$C O P_{\text {th,annual }}=\frac{E_{\text {cool }}}{E_{\text {gen,total }}}$                            (22)

The conventional thermal solar fraction at the generator is:

$S F_{\text {th }}=100 \frac{E_{\text {gen,solar }}}{E_{\text {gen,total }}}$                            (23)

The fraction of the useful solar energy collected by the field that is effectively transferred to the generator is:

$\eta_{\text {solar,use }}=100 \frac{E_{\text {gen,solar }}}{E_{\text {solar }}}$                            (24)

Cold-room temperature compliance is evaluated over the product-specific admissible interval of 3–8 ℃:

$R_{3-8}=\frac{100}{N} \sum_{k=1}^N I\left(3 \leq T_{\text {air }, \mathrm{k}} \leq 8\right)$                            (25)

where, $T_{\text {air}, k}$ is the cold-room air temperature at time step k, and N is the total number of evaluated hourly time steps. For a non-leap-year annual simulation, N = 8760.

2.3 Simulation algorithm

The annual simulation was performed in MATLAB using hourly Meteonorm data, with each hour divided into 60 internal steps of 60 s. At each time step, the model calculates the collector thermal output, updates the collector PCM and the 20-node stratified storage tank, evaluates the cold-room thermal loads, controls the absorption machine, and determines the solar and auxiliary heat supplied to the generator. The cold-room air and product temperatures, as well as the continuous storage states, are integrated using the fourth-order Runge–Kutta method. Hydraulic flows, PCM charging and discharging, and ON/OFF switching are handled through conservative operator splitting. The main temperatures, energy flows, COP, operating time, solar fraction, and unmet cooling demand are then stored for annual performance analysis.

This study assessed the annual performance of a solar-assisted absorption refrigeration system combining evacuated-tube collectors, PCM, a stratified thermal storage tank, and a single-effect LiBr–H₂O absorption chiller for a 50 m³ food-storage cold room in Constantine, Algeria. The developed transient model enabled the evaluation of the annual energy balance, the thermal behavior of the main components, and the individual and combined effects of PCM integration under identical climatic, operating, and control conditions.

The combined PCM configuration achieved an annual thermal COP of 0.727 and a thermal solar fraction of 95.263% at the absorption-chiller generator level. This value indicates that solar heat covered most of the annual thermal demand of the generator, while auxiliary heating supplied the remaining fraction. The generator-level solar fraction excludes the electricity consumed by the backup heater and auxiliary components and should therefore not be interpreted as complete energy autonomy of the overall system.

The proposed system maintained the cold room air temperature between approximately 4.10 and 5.60 ℃ throughout the simulated year, resulting in 100% compliance with the selected product-specific temperature interval of 3–8 ℃ and no unmet cooling demand. These results indicate that the complete hybrid system maintained the selected product-specific temperature interval throughout the simulated year. However, this temperature-compliance indicator represents conformity with the selected storage interval and should not be considered equivalent to complete HACCP certification.

The four-case comparison showed that PCM integration mainly improves the management and temporal utilization of solar thermal energy rather than the intrinsic COP or cooling capacity of the absorption machine. The reference configuration without PCM already achieved a thermal solar fraction of 94.637% at the generator level. Integrating PCM into both the collectors and the storage tank increased this value by 0.626 percentage points, reduced unused solar heat by 1.65%, and decreased electrical backup consumption by 11.68%. The collector-only configuration provided a slightly greater improvement than the tank-only configuration, whereas the combined arrangement achieved the most favourable overall energy-management performance.

The increase in solar fraction remained moderate because the reference configuration already supplied most of the generator demand from solar energy, leaving limited potential for further improvement. The results indicate that collector-level and tank-level PCM provide largely complementary thermal-buffering effects, although their combined contribution is not strictly additive. Their main benefit lies in improving the temporal matching between solar availability and generator demand, reducing curtailed solar heat, and limiting dependence on auxiliary heating.

Overall, the proposed configuration appears thermodynamically feasible for solar-assisted food refrigeration under the simulated climatic and operating conditions. Future investigations should include experimental validation, the use of measured or independently validated weather data, and sensitivity analyses of PCM mass, phase-change temperature, collector area, storage volume, and control parameters. Economic and environmental assessments are also required to determine whether the achieved reduction in auxiliary-energy consumption justifies the additional cost and complexity associated with PCM integration.