# Comprehensive analysis of waste heat recovery and thermal energy storage integration in air conditioning systems

Bilal Lamrani, Safae El Marbet, Tauseef-Ur Rehman, Tarik Kousksou

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Bilal Lamrani, Safae El Marbet, Tauseef-Ur Rehman, Tarik Kousksou. Comprehensive analysis of waste heat recovery and thermal energy storage integration in air conditioning systems. Energy Conversion and Management: X, 2024, 24, pp.100708. 10.1016/j.ecmx.2024.100708. hal-04845990

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# Comprehensive analysis of waste heat recovery and thermal energy storage integration in air conditioning systems

Bilal Lamrani<sup>a,*</sup>, Safae El Marbet<sup>a,b</sup>, Tauseef-ur Rehman<sup>c</sup>, Tarik Kousksou<sup>b,*</sup>

## ARTICLE INFO

### Keywords:

Waste heat recovery

Hot water production

Air conditioning

PCM

Thermal energy storage

Dynamic modeling

## ABSTRACT

The proposed work aims to address the challenge of effectively recovering and storing wasted heat in air conditioning (AC) systems, which is crucial for improving energy efficiency and system stability. This study focuses on the comprehensive analysis of a Waste Heat Recovery (WHR) system integrated with Thermal Energy Storage (TES) tanks. A lumped-dynamic thermal model was developed and validated against literature data to accurately simulate the system's performance. Through a detailed parametric study, the research explores how factors like WHR effectiveness, TES type, PCM type, and TES volume influence the system. The results demonstrate that recovering and storing wasted heat from AC systems significantly enhances operational stability and performance. Notably, increasing WHR effectiveness from 0.55 to 0.85 extends the duration of constant thermal power recovery and also results in higher recovered water temperatures with reduced water pump energy consumption. Furthermore, latent heat storage (PCM tank) extends the duration of stable thermal power recovery by over 61 % compared to sensible storage. Using PCM RT 44HC is more effective for WHR in AC units compared to RT 50 and RT 54HC. Finally, it was shown that increasing PCM tank volume from 2 to 4 m3 improves the duration of constant thermal power recovery by up to 52 % while stabilizing the recovered water temperature.

## 1. Introduction

Without refrigeration, most industries could not function, including those in agri-food, chemicals, plastics, biotechnology, electronics, data centers [1], and construction, among others [2–4]. 20 % of all power used worldwide is used in the refrigeration industry, which includes air conditioning (AC) [5]. This 20 % is very important, especially considering how much more energy-efficient refrigeration technology is becoming. It draws attention to the critical relevance of the refrigeration industry, which is predicted to increase significantly in the upcoming years as a result of both global warming and the growing need for refrigeration in a variety of fields [6]. As a result, it is projected that by 2030, the rise in worldwide electricity consumption brought on by refrigeration may equal three times the UK’s present electricity production capacity [7]. In order to facilitate the shift to low-carbon energy systems, heat recovery integration in this industry is vital [8–10]. This strategy seeks to mitigate the reduction of carbon dioxide emissions related to energy production in addition to lowering total energy consumption and operating expenses [11].

Lund et al. [12] highlight the significance of overcoming difficulties that prevent the integration of waste heat recovery systems into district heating systems (DHS) in order to move forward toward the next generations of such systems [13]. Miro et al. [12] conducted an examination of the potential for industrial waste heat recovery in Europe in 2018, and they estimated that it might be anywhere from 1106 to 2708 petajoules per year. Using a process-specific examination, Fleiter et al. [14] studied 1608 industrial sites across Europe, evaluating the surplus heat capacities of each facility and comparing these capabilities to the DHS demands in the surrounding area. According to the authors’ projections, DHS will be able to utilize 151 PJ of surplus heat by the year 2020, which will account for nearly 8 % of EU DHS’s total energy consumption.

The thermal heat that can be recuperated in the cold industry has the potential to be effectively utilized for the purpose of producing hot water [15,16]. The water in question possesses the capacity to be effectively repurposed within the nearby industrial sector, thereby making a substantial contribution to various operations that require thermal energy. Furthermore, it is capable of being stored before its transfer to a district

<footnote><sup>a</sup> Laboratoire MANAPSE, Faculté des Sciences, Université Mohammed V de Rabat, B.P. 1014 RP Rabat, Morocco</footnote>

<footnote><sup>b</sup> E2S, SIAME, Université de Pau et des Pays de l'Adour, Pau, France</footnote>

<footnote><sup>c</sup> School of Mechanical Engineering, Kyungpook National University, Daegu 41566, South Korea</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: b.lamrani@um5r.ac.ma (B. Lamrani), tarik.kousksou@univ-pau.fr (T. Kousksou).</footnote>
heating system, expanding its benefits beyond the confines of the spe-
cific industry under consideration. Phase change materials (PCM) can be
employed to store the recovered heat from the refrigeration system prior
to its transmission to the DHS [17,18]. The utilization of this thermal
resource inside a DHS makes it easily accessible to supplementary con-
sumers, including nearby businesses, community facilities, and even
residential areas.

At the moment, the effective use of heat recovery in refrigeration
systems stands out as an exceedingly attractive method to improve the
energy efficiency of such systems and to reduce the impact that they
have on the environment [19]. Heat rejection in refrigeration systems
takes place at three primary places. The first location is the compressor
discharge line and the oil cooler, where heat is rejected in the form of
sensible heat. The second location is the condenser, where heat is lost as
latent heat due to the condensation of the refrigerant [19]. The latent
heat produced during the process of refrigerant condensation demon-
strates a notable increase compared to its sensible heat. As a result, the
efficiency of recovering the heat wasted at the condenser surpasses that
of the heat rejected in the discharge line or at the oil cooler. It is relevant
to note that the specific heat of air is four times lower than that of water,
justifying the preference for water as a heat transfer fluid to recover the
heat rejected at the condenser [20]. Furthermore, the latent heat of the
refrigerant is considerably higher than its sensible heat. Consequently,
recovering the heat dissipated at the condenser will be more efficient
than that rejected in the discharge line or at the oil cooler [21]. How-
ever, the successful implementation of this method necessitates strict
respect for the following rules and precautions [22,23]:

* A heat recovery system is a viable option for a refrigeration unit only if it produces a substantial amount of heat during its operation.

* The refrigeration system should include two control strategies: one for gradually adjusting the condensation pressure to ensure optimal heat recovery while maintaining a nearly constant pressure difference at the expansion valves and another for regulating the amount of recoverable heat.

* Refrigeration production should constantly be prioritized.

One of the most common methods of waste heat recovery (WHR) in AC systems involves integrating Thermal Energy Storage (TES) systems, which store the recovered heat for later use. TES systems can be classified into three main types: sensible heat storage, latent heat storage, and thermochemical storage. Among these, latent heat storage, using PCMs, has been widely studied due to its high energy storage density and ability to provide a nearly constant temperature during the phase transition process. In the literature several work have been presented on the application of PCMs in AC systems [24]. For instance L.Jian-you [25] studied the feasibility of recovering wasted heat from an AC using triplex concentric tube with PCM. In another work, Gu et al. [26] have presented a detailed study on the use of TES for heat recovery in AC systems. They concluded that the AC performances are significantly improved when a TES heat recovery system is integrated. Recently, Wiriyasart and Kaewluan [27] have investigated a WHR system in an AC unit. They have shown the advantage of recovering heat and its effect on the AC system. They used a double tube heat exchanger to recover heat from the compressor and to produce hot water. They have founded that by recovering heat from AC water temperature could be increased from 25 °C to up 40 °C. In another work, Ramadan et al.[28] studied the feasibility of using an air-to-water heat recovery system from AC unit. They have found this WHR system could increase the water temperature from 25 °C to 70 °C.

During heat recovery process, the careful consideration of conden-
sation pressure is of utmost importance. Conformity to the constraints
given by the refrigeration system is crucial when considering the po-
tential benefits of a higher condensation temperature, such as improved
heat recovery. The implementation of this measure serves to mitigate
any adverse effects on the system's electrical consumption, so preserving

the benefits derived from the heat recovery system from being removed.
A condensation temperature of approximately 60 °C seems to be an
acceptable compromise that is suitable for a wide range of refrigerants
and installations [11,29].

In this study, we aim to assess the feasibility of harnessing excess
heat from a refrigeration system by incorporating a heat exchanger
between the compressor unit's output and the condenser outlet. It is
interesting to note that this heat exchanger is investigated using the
effectiveness method as adopted by several researchers [30–32].

Our primary objective is to recover both sensible heat from the
compressor discharge line and latent heat at the condenser stage in AC
systems. This recovered heat is then stored in TES systems. We evaluate
two distinct approaches for thermal energy storage:

*   **Sensible Heat Storage:** This system uses water as the storage medium, representing a traditional and efficient method for heat storage.

* Latent Heat Storage: This approach employs PCM, which offer supe-
rior thermal storage capabilities by capturing and releasing sub-
stantial amounts of latent heat during phase transitions.

Additionally, we have developed a water flow rate regulating unit
designed to recover constant thermal power and ensure stable operation
of the AC system.

Through this study, we aim to provide valuable insights into the
effectiveness of different thermal storage systems and their impact on
energy efficiency and system stability in refrigeration applications. Our
work contributes to enhancing sustainability and operational perfor-
mance by exploring innovative solutions for heat recovery and storage
in AC systems.

## 2. Materials and methods

The investigated system is composed of an air conditioning (AC)
setup integrated with a waste heat recovery (WHR) unit, a TES tank, and
a regulated pump system (Fig. 1). Within the TES tank, two storage
mediums are considered: sensible TES utilizing water and latent TES
employing PCMs.

The process of refrigeration in the studied AC system, with R134a as refrigerant, involves several stages, depicted on the Pressure-Enthalpy (P-h) diagram (Fig. 2). Initially, the refrigerant enters the compressor as a low-pressure, low-temperature vapor (state A), where it undergoes compression. As the compressor compresses the vapor, its pressure and temperature rise significantly (state B), increasing its enthalpy. Following compression, the high-pressure, high-temperature vapor enters the condenser, where it releases a significant amount of heat to the surroundings (wasted heat) and condenses into a high-pressure liquid (state C). Indeed, this high amount of wasted heat in the surroundings can be captured and used for several applications, such as heating and hot water production purposes. Subsequently, the high-pressure liquid refrigerant passes through an expansion valve or throttle valve, undergoing a rapid decrease in pressure and temperature (state D). The low-pressure liquid-vapor mixture then enters the evaporator, typically located indoors, where it absorbs heat from the indoor air, evaporating into a low-pressure vapor (state A) and thus producing a cooling effect.

In order to recover the wasted heat from state B to state C, a WHR
unit in the form of a heat exchanger is used. The latter captures this
wasted heat and employs it to produce hot water. This hot water can be
either directly used or stored in a TES tank. In this work, a thermal
battery is used to store the produced hot water and accumulate sub-
stantial heat. Two different types of TES tanks are considered, i.e., latent
TES PCMs-based and sensible TES tanks using water as the storage
medium. More details about these TES tanks are given in section 3.2.
The entire process of waste heat recovery, hot water production, and
heat storage process operates in a continuous loop, providing an effi-
cient and sustainable method for utilizing waste heat and managing
thermal energy within the AC system.
<figure><img src="image_4.png" /><figcaption>Fig.1. Coupled Air conditioning system-heat recovery system-TES tank.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig.2. P-h diagram for air conditioning system with R134a as refrigerant [33].</figcaption></figure>

### 3. Mathematical modeling and validation

In this section, a mathematical model of each component of the studied system, i.e., the WHR system, the TES tank, and the circulation pump, is developed and presented. These models are based on energy balances in both steady and unsteady conditions.

#### 3.1. Waste heat recovery system

The WHR system plays a crucial role in recovering waste heat generated by various industrial processes or equipment such as AC systems. Its primary function is to capture the excess heat that would otherwise be lost to the surroundings and utilize it for beneficial purposes, such as heating water, preheating air, or generating steam. The WHR typically consists of heat exchangers, pumps, valves, and controls designed to facilitate the transfer of heat from the hot process stream to a secondary fluid, such as water. This secondary fluid can then be used for heating purposes within the same system or transferred to other processes where heat is required. In the present work, a WHR system is implemented to recover heat from the AC system, with the primary aim of producing hot water. The heat is exchanged between produced hot

gas from the AC-compressor and cold water coming from the TES tank (See Fig. 3).

The effectiveness method is adopted [30–32], and the following assumptions are considered to simulate this process:

- The AC system is operating in steady-state conditions.

- Pressure drops across the heat exchanger and piping are assumed to be negligible.

- There is no mixing of the hot and cold streams within the WHR unit, ensuring that the heat transfer process remains efficient.

- The heat exchanger operates in steady-state conditions, and its effectiveness varies between 0.55 and 0.85.

- Potential energy and kinetic energy variation are negligible.

By using the previous assumptions, the effectiveness of the used WHR unit, which is defined as the ratio between the actual energy transfer and the maximum possible energy transfer, can be expressed as the following [34]:

$$ \epsilon = \frac{\Delta h_{WHR,act}}{\Delta h_{WHR,max}} = \frac{h_{out,water} - h_{inlet,water}}{h_{inlet,R134a} - h_{inlet,water}} \quad (1) $$

Where $\Delta h_{WHR,act}$ is the actual energy transferred to the water in the WHR unit, and $\Delta h_{WHR,max}$ is the maximum possible energy to be transferred from the hot gas to the cold water. $h_{out,water}$ and $h_{inlet,water}$ are water enthalpies at the outlet and the inlet of the WHR system. $h_{inlet,R134a}$ is the gas enthalpy coming from the AC compressor. It should be noted that during the functioning of the AC system, the gas pressure and temperature at the outlet of the compressor are assumed to be equal to 1100

<figure><img src="image_6.png" /><figcaption>Fig.3. Schema of the waste heat recovery (WHR) system.</figcaption></figure>
kPa and 65 °C (See Fig. 2). By using these two thermodynamic properties, the gaze enthalpy coming from the compressor ($h_{inlet,R134a}$) is determined by using the EES library [33] and its value is equal to 296.9 kJ/kg. Based on the effectiveness of the WHR, which varies in this work between 0.55 and 0.85, the water enthalpy at the outlet of the WHR is calculated, and thus the recovered water temperature is deduced as the following:

$$T_{out,water} = \frac{h_{inlet,water} + \varepsilon(h_{inlet,R134a} - h_{inlet,water})}{C_{p,water}} \quad (2)$$

Where $C_{p,water}$ is the water heat capacity.

## 3.2. Thermal energy storage unit

The second key component of the studied system is the TES tank, whose main objective is to store the recovered waste heat from the AC unit. The TES is designed as a shell-and-tube exchanger, where the shell side accommodates the storage medium—either PCM for latent storage or water for sensible storage (Fig. 4). Meanwhile, recovered hot water from the WHR unit circulates in the tube side. The studied storage mediums with their thermophysical properties are summarized in Table 1. This TES system operates in tandem with the WHR unit and a controlled circulating pump. The pump’s primary function is to regulate the flow rate of hot water based on inlet/outlet temperatures and the desired thermal power to be recovered and stored in the TES system. During the charging process, hot water circulates from the top to the bottom of the storage unit, while the discharging process involves circulating cold water from the bottom to the top. The properties of the used TES system are given in Table 2.

The design parameters of the considered TES are given in the following table 2.

Energy balances are employed under transient conditions to simulate the operation of this integrated system and are given in the following section.

### Controlled circulating pump model

In the described system, a controlled circulating pump plays a crucial role in regulating the flow rate to maintain a desired function constant. Specifically, in this study, the aim is to keep the recovered thermal power from the AC unit constant, which will subsequently be stored in the TES tank. By ensuring a steady thermal power recovery from the cooling unit, the operation of the AC system remains stable. This controlled approach not only enhances system reliability but also optimizes overall efficiency and performance, contributing to an enhanced system operation. The mass flow rate is regulated as the following to reach this objective [36]:

<figure><img src="image_7.png" /><figcaption>Fig. 4. Studied TES tanks in the coupled AC-WHR system.</figcaption></figure>

<table><caption>**Table 1**
Considered storage mediums in the TES tank [35].</caption><thead><tr><th>Properties</th><th>Water</th><th>PCM RT<br>44HC</th><th>PCM RT<br>50</th><th>PCM RT<br>54HC</th></tr></thead><tbody><tr><td>Density (kg/m³)</td><td>998</td><td>880/770</td><td>880/760</td><td>850/800</td></tr><tr><td>Thermal conductivity (W/mK)</td><td>0.6</td><td>0.2</td><td>0.2</td><td>0.2</td></tr><tr><td>Heat capacity (kJ/kgK)</td><td>4.18</td><td>2</td><td>2</td><td>2</td></tr><tr><td>Heat of fusion (kJ/kg)</td><td>334</td><td>250</td><td>160</td><td>200</td></tr><tr><td>Melting temperature (°C)</td><td>0</td><td>41–44</td><td>48–51</td><td>53–54</td></tr></tbody></table>

<table><caption>**Table 2**
TES design parameters.</caption><thead><tr><th>Properties</th><th>Value</th></tr></thead><tbody><tr><td>PCM tank volume (m³)</td><td>6</td></tr><tr><td>PCM tank length (m)</td><td>5</td></tr><tr><td>Number of tubes in the PCM tank (–)</td><td>400</td></tr><tr><td>Tube diameter in the PCM tank (m)</td><td>0.036</td></tr></tbody></table>

$$\dot{m}_{flow} = \frac{Q_{suitable}}{C_{p,f}(T_{f,out} - T_{f,in})} \quad (3)$$

In equation (3), $Q_{suitable}$ represents the desired thermal power to be recovered from the AC system and stored in the TES tank. $C_{p,f}$ denotes the heat capacity of water while $T_{f,out}$ and $T_{f,in}$ represent the outlet and inlet water temperatures at the TES tank, respectively.

The chosen constant thermal power ($Q_{suitable}$) to be consistently recovered from the AC system is set at 100 kW. Additionally, the capacity of the controlled circulation pump ranges from 0.2 to 1.58 kg/s [17,37]. Considering the limitations imposed by the maximum and minimum flow rates of commercial water pumps, the variation of the water mass flow rate can be estimated using the subsequent formula:

$$\dot{m}_{flow} = \begin{cases} \dot{m}_{flow,min} & \text{if } \frac{Q_{suitable}}{C_{p,f}(T_{f,out} - T_{f,in})} < \dot{m}_{flow,min} \\ \dot{m}_{flow,max} & \text{if } \frac{Q_{suitable}}{C_{p,f}(T_{f,out} - T_{f,in})} > \dot{m}_{flow,max} \\ \frac{Q_{suitable}}{C_{p,f}(T_{f,out} - T_{f,in})} & \text{if } \dot{m}_{flow,min} \le \frac{Q_{suitable}}{C_{p,f}(T_{f,out} - T_{f,in})} \le \dot{m}_{flow,max} \end{cases} \quad (4)$$

### TES unit model

The TES tank model employed in this study relies on energy balances for each component under transient conditions. The main components of the TES tank include the heat transfer fluid domain (water) and the storage medium domain (PCM or water) (See Fig. 4). To model the TES tank, a lumped-capacitance approach is utilized, leveraging the analogy between thermal and electrical transfer. The TES tank is divided into multiple control volumes, with uniform temperature assumed within each volume. This modeling method has been previously validated and utilized by various authors, with detailed explanations available in our previous works [36,37]. The general expression of energy balance for a given storage medium control volume that exchanges heat by convection with the heat transfer fluid (water) is given as:

$$(mC_p)_{st,i} \frac{\partial T_{st,i}}{\partial t} = h_f A (T_{f,i} - T_{st,i}) \quad (5)$$

Where $T_{st,i}$ is the storage medium temperature at a given control volume. $m$ and $C_p$ are the mass and the heat capacity of the considered control volume. $T_{f,i}$ is the heat transfer fluid temperature at the same control volume, $A$ is the heat transfer area and $h_f$ is the convective heat transfer coefficient calculated using the Gnielinski's correlation [38,39]:
$$h_f = \frac{k_f}{D_h} \left\{ \begin{array}{ll} 4.36R_e \le 2300 & \\ \frac{\left(\frac{f}{8}\right)(R_e - 1000)P_r}{1 + 12.7\left(\frac{f}{8}\right)^{0.5}\left((P_r)^{\frac{2}{3}} - 1\right)} & R_e > 2300 \end{array} \right. \quad (6)$$

$k_f$ and $D_h$ are the transfer fluid thermal conductivity and the hydraulic diameter, respectively. $R_e$ and $P_r$ are the dimensional Reynold and Prandtl numbers.

As in equation (5), there are two unknown temperatures, i.e., storage medium temperature ($T_{st,i}$) and the heat transfer fluid temperature (water) ($T_{f,i}$), a second energy balance equation on the water domain is necessary for completing and solving the problem. Thus, the energy balance of the water domain is given as:

$$(mC_p)_{f,i} \frac{\partial T_{f,i}}{\partial t} = h_f A (T_{st,i} - T_{f,i}) + \dot{m}_{flow} C_{p,f} (T_{f,inlet,i} - T_{f,out,i}) \quad (7)$$

In this equation, A is the heat transfer area between the storage and the fluid domain. m and Cp are the mass and the heat capacity of the used fluid. $T_{f,inlet,i}$ and $T_{f,out,i}$ are the inlet and the outlet temperature at each control volume. These temperatures are relied on the average control volume fluid temperature by the following equation:

$$T_{f,i} = \frac{T_{f,inlet,i} + T_{f,out,i}}{2} \quad (8)$$

It is interesting to note that in each control volume, there are two unknown temperatures, which are storage medium temperature ($T_{st}$) and transfer fluid temperature ($T_f$). As in this work, two types of storage medium are investigated, i.e., PCM for latent storage and water for sensible storage. The phase change process must also be modeled and simulated to consider the melting/solidification process of PCM. Therefore, the effective heat capacity method is employed. This method is based on the use of the dependent-temperature expression of the PCM heat capacity as the following [40]:

$$C_{p,pcm}(T) = C_{base}(T) + C_{excess}(T) \quad (9)$$

Where:

$$C_{base}(T) = (1 - f(T))C_{0,s} + f(T)C_{0,l} \quad (10)$$

$$C_{excess}(T) = L_s \frac{\partial f(T)}{\partial T} \quad (11)$$

$f(T)$ is the PCM liquid fraction in each control volume and $L_s$ is the heat of fusion. $C_{0,s}$ and $C_{0,l}$ are the PCM heat capacity at the solid and liquid state, respectively. The expression of the $f(T)$ can be given as [40]:

$$f(T) = \frac{1}{\pi} \left[ \arctan \left[ \frac{2\gamma(T - T_m)}{\Delta T} \right] + \frac{\pi}{2} \right] \quad (12)$$

$T_m$ is the average melting point temperature and $\gamma$ is the dimensionless tilt.

By using this expression, Equation (9) can be formulated as:

$$C_{p,pcm}(T) = (1 - f(T))C_{0,s} + f(T)C_{0,l} + L_s \frac{\frac{2\gamma}{\Delta T}}{\pi \left[ \left( (T - T_m) \left( \frac{2\gamma}{\Delta T} \right) \right)^2 + 1 \right]} \quad (13)$$

This temperature-dependent PCM heat capacity is integrated into the energy balance equation of PCM (Eq.5) to consider its phase change process. The previously described energy equations are solved using Engineering Equation Solver (EES) software. This numerical tool is able to solve coupled ordinary and partial equations, enabling comprehensive modeling and simulation of complex systems [33].

### 3.3. Model validation

Simulated results are compared with experimental data from the literature to validate the developed dynamic models. Medved et al. [40] conducted experimental analysis to observe the variation of the PCM heat capacity versus temperature. The developed EES code was employed to simulate these conditions using identical design and operational conditions as input parameters, and the results were subsequently compared with the measured data. Fig. 5 illustrates the variation of the PCM heat capacity with temperature, showing data obtained from both the developed model and the measurements from Ref. [41]. The findings demonstrate that the proposed approach accurately estimates the variation in PCM heat capacity. Notably, the model effectively captures the transition between the sensible heat transfer domain, characterized by constant low values of heat capacity, and the latent heat transfer domain, marked by a significant jump in heat capacity with temperature.

A practical case study of a 180-kWh TES in shell and tube configuration is utilized to verify the reliability of the dynamic model described earlier [42]. The dynamic computational model is configured employing identical design and operational parameters from this referenced study [42]. The resulting numerical outcomes are then juxtaposed against experimental data for comparison. It's worth noting that the 180-kWh TES is designed to maintain a constant thermal power output with an optimal water temperature during peak load periods. Fig. 6 depicts the fluctuations in the produced water temperature from the TES. An evident correlation emerges between the measured and simulated water temperatures from the TES tank, showcasing a close dynamic resemblance. Upon analysis, the measured and predicted water temperatures demonstrate a maximum absolute error of 2.5 °C and a mean absolute error of 0.8 °C. Furthermore, the maximum relative error for water temperature is capped at 3.7 %, while the mean relative error remains at 1.1 %. Based on obtained results in this validation section, it can be concluded that the proposed simulation model is able to simulate the dynamic behavior of the studied system with acceptable accuracy.

### 4. Results and discussion

This section aims to comprehensively analyze the WHR system integrated with TES tanks in air conditioning systems. Fig. 7 depicts the time-wise variation of the enthalpy of the refrigerant (R134a) during the heat recovery process. It can be seen that the inlet enthalpy at the WHR unit, coming from the AC compressor, remains approximately constant at about 297 kJ/kg, while the outlet enthalpy varies between 197 kJ/kg

<figure><img src="image_8.png" /><figcaption>Fig.5. Measured and simulated PCM heat capacity Vs. temperature from Ref [41].</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. Simulated results Vs. experimental results from [42].</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Variation of R134a enthalpy at the inlet and the outlet of the WHR unit.</figcaption></figure>

(at the start of recovery) and 297 kJ/kg (at the end of recovery). It is interesting to note that this recovered thermal energy from the R134a is directly stored in a TES tank. In fact, at the beginning of the heat recovery process, the refrigerant enthalpy at the outlet of the WHR unit remains minimal and constant. This stability is ensured by the controlled water pump, which works to recover and store constant thermal power throughout the entire process (See Fig. 1). By maintaining a constant outlet R134-a enthalpy, the operation of the AC system is stabilized, ensuring optimal performance. As the heat recovery operation progresses, the enthalpy at the outlet of the WHR unit gradually increases until it matches the inlet enthalpy, indicating that no further heat is being recovered from the AC system. The recovered thermal energy is then directly stored in a TES tank. Once the maximum storage capacity of this system is reached, the WHR process is stopped. This observation underscores the efficiency of the integrated WHR and TES system in maximizing heat recovery while stabilizing the operation of the AC system and optimizing its performance.

The instantaneous stored thermal power recovered from the WHR system is given in Fig. 8 to visualize the real amount of recovered and stored thermal energy. It can be observed that the recovered 100 kW-thermal power coming from the AC system is maintained constant for about 4.1 h. During this period, the water pump regulates the flow rate in the WHR system from about 0.6 kg/s to 1.58 kg/s and provides a

<figure><img src="image_11.png" /><figcaption>Fig. 8. Recovered thermal power and water mass flow rate variation in the PCM tank.</figcaption></figure>

stable operation of the AC. After reaching the maximal capacity of the water pump, the recovered thermal power from the AC system starts decreasing until the end of the TES tank charging process. This result confirms the ability of the water flow regulation system to recover and store stable thermal power during the entire thermal storage process.

Fig. 9 presents the temperature of the storage medium (latent PCM tank) at various locations, i.e., top, middle, and bottom. This data is used to analyze the thermal behavior of the TES storage system during the WHR process. It is interesting to note that PCM RT 44HC is used as a storage medium. It can be seen that at the beginning of the charging process, the storage medium temperatures increase until reaching the melting PCM point (41 °C to 44 °C), where it becomes stable. During this period, the PCM phases its physical state from solid to liquid, and the recovered thermal energy is stored in the form of latent heat. When the PCM temperature becomes entirely liquid (end of the melting process), the PCM temperature increases until reaching the steady state temperature (about 65 °C). A notable observation from the temperature profiles is the disparity in temperature increase among different positions within the tank. Specifically, PCM located at the top of the tank undergoes a rapid temperature rise compared to those at the middle and bottom. This discrepancy can be attributed to the charging mode of the system, where hot water recovered from the process enters the tank from the top and gradually moves downward. Consequently, PCM near the tank's top is heated more rapidly compared to those at other locations due to direct

<figure><img src="image_12.png" /><figcaption>Fig. 9. Variation of the TES temperature at different positions during the WHR process.</figcaption></figure>
contact with the incoming hot water.

## 4.1. Effect of R134a temperature and WHR effectiveness

In this section, the influence of the compressed gas (R134a) temperature and the WHR effectiveness on the recovered/stored thermal power and the water pump energy consumption is investigated. The considered refrigerant gas temperature at the compressor outlet varies between 50 °C and 65 °C [29]. The effect of this temperature on the produced constant thermal power and recovered water temperature is given in Fig. 10. It is interesting to note that RT44HC is used as the storage medium in the PCM tank. From these results, it can be seen clearly that the duration of the constant thermal power recovery process is significantly influenced by the produced temperature at the compressor outlet. This duration of constant thermal power recovery increases from about 1.1 h to 4.1 h when the gas (R134a) temperature is increased from 50 °C to 65 °C (Fig. 10-a). This behavior is mainly due to the increase in the amount of available gas enthalpy to be recovered with its temperature. In other words, a higher gas temperature allows for recovering more thermal energy from the AC system.

The same behavior is observed when analyzing recovered water temperature (Fig. 10-b). In fact, increasing the produced gas temperature from the compressor leads to increase the recovered water temperature. For example, when the used gas temperature is equal to 60 °C, recovered water temperature varies between 54 °C and 58 °C.

To analyze the WHR effectiveness effect on the recovered thermal power is given, the WHR effectiveness is considered to vary between

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 10. Effect of the used compressed gas temperature on the WHR process.</figcaption></figure>

0.55 and 0.85. It can be seen in Fig. 11 that increasing the WHR effectiveness extends the duration of constant recovering/storing thermal power of 100 kW. This observation implies that a higher WHR effectiveness allows for a longer period during which the system maintains a steady state of recovering and storing thermal power at 100 kW. As an example, this duration is increased from 85 min to 250 min when the WHR is increased from 0.55 to 0.85. Such an increase in the duration of constant recovering/storing thermal power is highly beneficial, particularly for sustaining long periods of stable AC operation.

Fig. 12 shows the time-variation of the recovered water temperature from the WHR unit using different values of heat recovery effectiveness. It can be seen that improving the WHR effectiveness is suitable for recovering water with higher temperatures. In fact, this behavior is due to the increase in the amount of transferred heat from the AC condenser to the water with the recovery unit effectiveness. As this WHR unit is coupled to the PCM tank, the recovered hot water enters the PCM tank, and the heat is transferred by conduction and convection to the storage medium. When the PCM temperature reaches the melting interval, the water temperature becomes nearly constant which justifies the observed plateau in this figure. Based on this result, it can be concluded that the choice of an appropriate WHR design will depend mainly on the required temperature levels. For example, if the needed water temperature at the load must between 55 °C and 65 °C during the entire recovering period, the WHR effectiveness must be higher than 0.75.

The water mass flow rate used during the waste heat recovery process for each case study is illustrated in Fig. 13. The objective is to evaluate the impact of the chosen WHR unit design on water pump consumption. The results demonstrate that high WHR effectiveness is advantageous not only for improving energy performance but also for enhancing the hydraulic system's energy efficiency. Specifically, increasing WHR effectiveness leads to a reduction in the water flow rate required, which consequently decreases the water pump's energy consumption. In Fact, the needed duration to reach the maximal water pump capacity is increased from 85 min to 250 min when the WHR effectiveness is increased from 0.55 to 0.85. such an increase allows using the water pump with lower capacity for a long duration of the heat recovery process.

## 4.2. Effect of TES type

During the heat recovery process, thermal energy could be stored and then used whenever necessary. This thermal storage can be done by using sensible storage or a latent storage system. In order to identify the suitable storage approach, two different tanks are considered, i.e., the water tank (sensible storage) and the PCM tank (latent storage). It is

<figure><img src="image_15.png" /><figcaption>Fig. 11. Influence of the used WHR effectiveness on the recovered/stored thermal power.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. 12. Effect of the WHR effectiveness on the recovered water temperature.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 13. Effect of the WHR effectiveness of the used water flow rate.</figcaption></figure>

interesting to note that both tanks have the same volume. Fig. 14 shows the time-variation of recovered and stored thermal power from the AC system using two different storage tanks. Using a latent heat storage tank is more suitable than the sensible one as it leads to recovering and

<figure><img src="image_18.png" /><figcaption>Fig. 14. Effect of TES type on the recovered thermal power.</figcaption></figure>

storing the wasted heat for a long duration with a high constant value. This duration is increased from 155 min to 250 min which represents a substantial increase of 61 %. This result is justified by the high amount of energy density of the PCM tank compared to the sensible water tank.

Fig. 15 illustrates the temperature at various locations within each tank to demonstrate the thermal behavior of latent and sensible storage systems. This data confirms the distinct processes involved in latent and sensible heat storage. In the PCM tank, where recovered heat is stored in both sensible and latent forms, the temperature initially increases linearly (sensible storage) until reaching the melting temperature range (41–44 °C). Within this range, the tank’s temperature stabilizes as the heat is stored in latent form. Once the PCM is completely melted, the temperature resumes its linear increase (sensible storage) until reaching a steady state. In contrast to the PCM tank, the water tank’s temperature increases linearly (sensible storage only) without stabilization until it reaches the steady state temperature. Notably, both systems exhibit temperature stratification, with higher temperatures at the top compared to the middle and bottom of the tank. This stratification is due to the water circulation mode in the system, where hot water from the AC unit enters the tank from the top and gradually moves downward. As a result, the storage medium near the top of the tank heats more rapidly than in other locations due to direct contact with the incoming hot water.

Fig. 16 illustrates the influence of the type of storage medium on the water mass flow rate variation during the heat recovery process. It can be seen that using PCM as a storage medium offers advantages in terms of water pump capacity utilization. In fact, when water is used as the storage medium, the maximum water pump capacity is reached rapidly within just 150 min from the start of the heat recovery process. However, with PCM as the storage medium, this maximum capacity is reached only after more than 250 min from the beginning of the heat recovery process. This delay in reaching maximum pump capacity with PCM results in reduced water pump energy consumption.

### 4.3. Effect of PCM type

From our previous results, we demonstrated that using PCM as a storage medium in the waste heat recovery process is beneficial, enhancing both energy recovery capacity and hydraulic energy efficiency. To evaluate the impact of the PCM type on the recovery and storage process, we considered three types of PCM: RT 44HC, RT 50, and RT 54HC. These PCMs were selected primarily for their suitable melting

<figure><img src="image_19.png" /><figcaption>Fig. 15. Storage medium temperature variation during the WHR process.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Fig. 16. Mass flow rate variation with different TES types in the WHR system.</figcaption></figure>

temperature ranges for domestic hot water utilization, and their properties are provided in Table 1.

Fig. 17 shows the influence of the PCM type on the recovered/stored waste thermal power. PCM RT 44HC enables a constant thermal power recovery of 100 kW for a longer duration compared to both RT 50 and RT 54HC. Specifically, the duration of constant thermal power recovery is increased from 125 min and from 130 min to 250 min when using PCM RT 44HC instead of RT 54HC and RT 50, respectively. This behavior can be attributed to two main factors. Firstly, PCM RT 44HC has a higher heat of fusion compared to both RT 50 and RT 54HC. Secondly, the melting temperature range plays a crucial role in heat recovery and storage capacity. A lower melting temperature interval allows for a faster and more complete phase change process, thereby enabling the recovery and storage of a larger amount of both sensible and latent heat.

Fig. 18 illustrates the time-wise evolution of the water temperature at the inlet and outlet of the WHR system. It's important to note that the WHR unit is coupled in a closed loop with the PCM tank (see Fig. 1), meaning the inlet WHR temperature is equal to the outlet tank temperature. The results indicate that the variation in recovered water temperature is influenced by the type of PCM used. Specifically, the melting temperature range of the PCM affects the recovered water temperature, particularly during the phase change process. For instance, when RT 44HC is used as the storage medium, the recovered water temperature stabilizes around 61 °C during the phase change process. In

<figure><img src="image_21.png" /><figcaption>Fig. 18. Effect of PCM type on the recovered water temperature from the WHR unit.</figcaption></figure>

contrast, with PCM RT 54HC, the recovered water temperature stabilizes around 63 °C. RT 54HC has a higher melting point compared to other PCMs used in the study. As a result, it takes longer to absorb enough heat to fully melt. During this extended melting process, the water temperature in the case of RT 54HC remains relatively constant around the RT 54HC melting point. This prolonged phase change period leads to a different slope in the water temperature profile compared to other PCMs, as seen in Fig. 18. Fig. 19 shows the instantaneous variations in water flow rate within the WHR system to assess the effect of PCM type on water pump capacity utilization. The results confirm that PCM RT 44HC is also the most suitable in terms of water pump capacity utilization. Specifically, the maximum water flow rate is reached after more than 250 min from the beginning of the heat recovery process when RT 44HC is used. In contrast, when RT 54HC is used as the storage medium, the maximum water pump capacity is reached much more quickly, within just 122 min from the start of the waste heat recovery process.

In conclusion, the choice of PCM type plays a critical role in the performance of the waste heat recovery system, impacting the duration of constant power recovery, temperature evolution, and water pump capacity utilization. PCM RT 44HC demonstrated superior performance, enabling a longer duration of constant thermal power recovery and more efficient water pump capacity utilization. Therefore, selecting the

<figure><img src="image_22.png" /><figcaption>Fig. 17. Effect of PCM type on the recovered thermal power.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 19. Effect of PCM type on the used mass flow rate in the coupled WHR/storage system.</figcaption></figure>
appropriate PCM is crucial for optimizing the efficiency and effectiveness of the WHR system based on specific temperature and operational requirements.

### 4.4. Effect TES volume

During the design phase of a PCM tank for the heat recovery process, the volume of the storage system plays a crucial role. Its effect on both the recovery process performance and water pump capacity utilization is presented in this section. Fig. 20 shows the recovered/stored thermal power from the AC system using three different tank volumes: 2, 4, and 6 m³. It is interesting to note that PCM RT 44HC is used as the storage medium, and the WHR unit effectiveness is fixed at 0.85.

The results illustrate that increasing the PCM tank volume extends the duration of constant thermal power recovery. For instance, this duration increases by about 52 % when the PCM tank volume is increased from 2 to 4 m³. In fact, the system's storage capacity increases with the tank volume, improving heat recovery performance. Therefore, the choice of PCM tank volume will depend on the required duration of constant thermal power recovery.

Fig. 21 shows the impact of the PCM tank volume on the water temperature variation at the outlet and inlet of the WHR unit. It can be seen that increasing the tank volume delays the water temperature rise and stabilizes the recovered water temperature during the phase change process. This behavior is due to the fact that the amount of thermal energy required for the melting process is proportional to the tank volume. For example, the duration of latent heat storage, indicated by the first plateau of the recovered water temperature, is about 50 min for a tank volume of 2 m³. However, this period increases to 150 min when the tank volume is increased to 6 m³.

The tank volume also impacts the hydraulic system utilization. In Fig. 22, it is shown that the water flow rate during the waste heat recovery process is proportional to the amount of PCM in the tank. Increasing the PCM tank volume requires a minimal water flow rate to maintain constant recovered thermal power. This result is due to the ability of a large storage tank to recover a high amount of thermal energy with minimal water flow rate. When a 6 m³ PCM tank is used, the maximum water flow rate is reached after more than 250 min from the beginning of the waste heat recovery process. In contrast, with a smaller PCM tank volume, the maximum water pump capacity is reached rapidly, leading to higher pumping energy consumption.

In conclusion, the choice of PCM tank volume plays a significant role in the performance of the WHR system. Larger PCM tank volumes extend the duration of constant thermal power recovery, delay the increase in water temperature, and stabilize the recovered water temperature

<figure><img src="image_24.png" /><figcaption>Fig. 21. Inlet and recovered water temperature from the WHR unit using different TES volume.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 22. Variation in water mass flow rate for different TES volumes during the WHR process.</figcaption></figure>

during the phase change process. Additionally, larger tanks require minimal water flow rates to maintain constant thermal power, thereby delaying the maximum water pump capacity usage and reducing pumping energy consumption. Therefore, selecting an appropriate PCM tank volume is crucial for optimizing the efficiency and effectiveness of the WHR system based on specific operational requirements.

## Conclusions

The main objective of this work is to comprehensively analyze the Waste Heat Recovery (WHR) system integrated with Thermal Energy Storage (TES) tanks in air conditioning (AC) systems. A lumped-dynamic thermal model is developed for each system component and obtained simulation results are validated with measured data from the literature. By using this validated dynamic model, a detailed parametric study is presented to understand how various factors, including WHR effectiveness, TES type, PCM type, and TES volume, influence the performance of the WHR system in terms of thermal power recovery, water pump energy consumption, and overall system stability. The main findings of this study can be summarized as the following:

<figure><img src="image_26.png" /><figcaption>Fig. 20. Effect of PCM tank volume on the recovered thermal power.</figcaption></figure>
* Recovering and storing wasted heat from AC systems ensures stable operation and improves the system performance.

* Increasing WHR effectiveness from 0.55 to 0.85 extends the duration of constant thermal power recovery from 85 min to 250 min.

* Higher refrigerant temperature leads to produce a high-water temperature (up to 65 °C) with long duration of constant thermal power recovery.

* The use of latent heat storage (PCM tank) provides a longer and more constant thermal power recovery, increasing the constant recovery duration by over 61 % compared to sensible storage (water tank).

* PCM RT 44HC allows for a longer duration of constant thermal power recovery compared to RT 50 and RT 54HC.

* Increasing PCM tank volume from 2 to 4 m³ extends the duration of constant thermal power recovery up to 52 % and stabilizes the recovered water temperature.

The aforementioned proposed modeling tool is suitable for WHR system design and decision-making, demonstrating significant potential for recovering wasted heat from AC systems. Potential perspectives for further optimizing WHR and TES systems include implementing advanced control algorithms to enhance performance, investigating the scalability of these systems for various AC sizes, and conducting comprehensive cost-benefit analyses to assess the economic feasibility of different configurations.

## CRediT authorship contribution statement

**Bilal Lamrani:** Writing – original draft, Investigation, Conceptualization. **Safae El Marbet:** Software, Data curation. **Tauseef-ur Rehman:** Visualization, Validation, Conceptualization. **Tarik Kousksou:** Writing – original draft, Supervision, Funding acquisition, Formal analysis.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

No data was used for the research described in the article.

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