Review on parameters influencing the efficiency of the dual-medium thermocline storage system

ABSTRACT

Thermal storage systems are needed to overcome solar intermittency and make this energy source more flexible and competitive for concentrated solar power plants. Single-tank sensible heat storage using both fluids and materials is a promising option for reducing storage costs and promoting the development of concentrated solar power. This work is a thorough review on the parameters influencing the performance of a dual-medium thermocline storage system for concentrated solar power plants. Thus, indicators such as efficiency, utilisation rate, thermocline thickness and energy efficiency of the storage system are presented in order to quantify the performance of the system. In addition, the impact of geometric and operating parameters on the performance of the thermocline storage system has been discussed.

KEYWORDS:

• Heat storage
• dual medium thermocline
• parameters effect
• concentration solar power

Nomenclature

Table

Acronyms		Index
eq	Equation	ch	on charge
$\mathrm{dt}$	Time differential	d	on discharge
dT	Temperature differential	e	relating to entry
CSP	Concentrated Solar Power	en	energetic
DMT	Dual Media Thermocline	ex	exergetic
SMT	Single Media Thermocline	f	relating to fluid phase
TES	Thermal Energy Storage	H	hot temperature
Latin letters		L	low temperature
$a_p$	Superficial particle area per unit bed volume [m^2]	max	maximum
$a_w$	Superficial area of the storage unit per unit volume of the bed [m^2]	s	relating to solid phase
$c_p$	Specific heat capacity [J.kg^−1.K^−1]	tank	relating to tank
D	Diameter [m]	tres_c	threshold charge temperature
E	Energy [J]	tres_d	threshold discharge temperature
$\dot{m}$	Mass flow [kg.s^−1]	w	relating to wall
R	Rayon [m]	Exhibitor
$T$	Temperature [K]	in_out	relating to the input during charging
$\mathrm{TU}$	Utilisation rate [−]	in_d	relating to the input during discharging
$U$	Overall heat loss coefficient [W·m^−2·K^−1 ]	out_ch	relating to the output during charging
$u$	Interstitial fluid velocity [m·s^−1]	out_d	relating to the output during discharging
Greek letters
$ϵ$	Porosity [−]
$\rho$	Density [Kg.m^−3]
$\lambda$	Thermal conductivity [W m^−1.K^−1]
µ	Dynamic viscosity [Pa s]
η	Efficiency [−]

1. Introduction

As a result of technological progress, energy demand is increasing exponentially. Up still now, the energy demand is based on fossil resources. Fossil resources exploration and utilisation can increase environmental pollution. Solar energy is considered one of the sustainable energy sources to reduce greenhouse gas emissions from the use of fossil fuels (Gil et al. 2010). Solar thermal technology, such as concentrated solar power (CSP), is a promising solution for producing clean energy (Tiskatine et al. 2017). This is a technology based on converting direct solar radiation into heat to produce electricity. According to the operating principle of the CSP, mirrors concentrate the direct sunlight on a small area called the receiver where a heat transfer fluid is heated to a high temperature. The heated heat transfer fluid transfers the heat to the steam generator which, thanks to an alternator, produces electricity. The intermittency of solar radiation has a direct impact on the process and hinders the large-scale industrial commercialisation of this technology (Reddy and Pradeep 2021). Therefore, the use of a Thermal Energy Storage (TES) system in this technology compensates for the unpredictability of solar energy and ensures the continuity of steam generation for electricity production. The TES system not only minimises the unpredictable effect of solar insolation by distributing the power plant’s output but also reduces the cost of electricity (Bradshaw and Siegel 2016; Jemmal, Zari, and Maaroufi 2016). TES is composed of three main elements (Hoffmann 2015): a storage principle, an energy transfer mechanism and a containment system. The storage principle is based on the storage of thermal energy in the form of latent, sensible and thermochemical heat. Transfer mechanism plays the role of charging and discharging the heat from the storage system in an appropriate manner. Containment system holds the two components together and allows them to be isolated from the outside. Sensible heat storage is the most mastered and mature in terms of complexity and feasibility (Rodrigues and De Lemos 2020; Erregueragui, Boutammachte, and Bouatem 2016). The technology for storing thermal energy in the form of sensible heat has two types of configurations: two-tank configuration and single-tank configuration. The two-tank system performs better than the single-tank system, but has huge costs that can make CSP less accessible to developing countries (Cocco and Serra 2015). One-tank configuration is 35% less expensive than the two-tank configuration (Nandi, Bandyopadhyay, and Banerjee 2018). The key operating characteristic of single-tank storage is the principle of stratified buoyancy, which provides thermal separation (Calderón-Vásquez et al. 2021). However, the stratification feature added to the non-uniform flows and the imperfect heat exchange between fluid and solid in the single tank system decrease the performance and lower the efficiency of the storage system. Thus, numerical and experimental simulation studies were carried out on the single-tank storage system to find parameters that could improve the efficiency of thermocline storage.

This work aims to review the main characteristics and design parameters of the packed thermal storage system that generate major effects on the efficiency of the thermocline through previous numerical and experimental work. The aim is to provide, through the literature, the optimum conditions for increasing the efficiency of the single-tank sensible heat storage system that will make CSP a reliable technology.

2. Single-tank sensible heat storage system

The enormous costs associated with the huge quantities of thermal fluids involved in two-tank systems led researchers to develop the one-tank system. This promising approach, tested in the 1980s on a pilot scale, allows the cost of the system to be reduced by combining the hot tank and the cold tank into a single tank (Angelini, Lucchini, and Manzolini 2014; Medrano et al. 2010). The principle of this system is such that during charging a hot fluid such as molten salt or thermal oil is pumped into the top of the tank in order to expel the cold fluid which is sucked downwards, and during the discharge the cold fluid passes through the bottom of the system and drives out the hot fluid (Yang et al. 2016). The cohabitation of hot and cold fluid creates a thermal gradient within the system and is ideally stabilised and preserved by buoyancy effects (Qin et al. 2012; Bayón and Rojas 2014). This system is called thermocline storage because of the thermal gradient that develops within the system (Yang et al. 2016). During charging or discharging, the thermocline created rises or falls until it exits the vessel as shown in Figure 1 (Xu et al. 2012b).

Figure 1. Charging and discharging process in a thermocline tank.

When only fluid is used as a storage medium in the system then it is called Single Medium Thermocline (SMT) (Boubou et al. 2021). However, thermal convection within the single-tank system prevents ideal temperature stratification from being achieved. A solid packing material can therefore be inserted to maintain the gradient and reduce natural convection in the fluid. The use of solid material and fluid in a single-tank storage system is called Dual Media Thermocline (DMT) (Boubou et al. 2021). Figure 2 shows the difference between the DMT system and the SMT system. The DMT system is economically viable compared to the SMT system because part of the fluid is substituted by solid materials. In addition, the addition of solid materials increases the theoretical storage energy density by about 50% compared to a two-tank storage system (Cocco and Serra 2015; Calderón-Vásquez et al. 2021; Galione et al. 2015). With low-cost solid materials, it would be possible to reduce the overall capital cost of the thermal storage system (Calderón-Vásquez et al. 2021). Fasquelle et al. (2018a) showed that the Thermocline single-tank system reduced annual electricity production at maximum storage capacity by only 3.4%, but expenses are reduced by an average of 30% mainly due to the reduced amount used in the single-tank system. These findings are similar to those of Brosseau et al. (2005) who reported a 10-35% reduction in costs, depending on the method and storage capacity considered.

Figure 2. Difference between SMT and DMT (Fasquelle 2017).

Despite economic gain obtained with the single-tank system, several technical problems continue to limit the large-scale use of the compact thermocline bed system. For instance, the thermocline transition zone tends to gradually widen or deteriorate after multiple charge–discharge cycles. In order to resolve these difficulties, it is essential to develop a comprehensive understanding of the system’s functioning and the intrinsically interconnected heat and matter transfer mechanisms.

3. Storage materials used in sensible single-tank storage

The efficiency of sensible heat storage is closely linked to the choice of materials. It is important not only that the heat transfer fluid and the solid material both have a high operating temperature to increase the efficiency of the cycle, but also that they are chemically stable enough to ensure the reversibility of the storage process over a large number of cycles (Gil et al. 2010; Medrano et al. 2010). In addition, solid materials must be available in large quantities so that the storage system is less costly. The heat transfer fluid and storage materials selected must also be long-lasting, have a negligible impact on the environment and be non-toxic and non-flammable (Fasquelle 2017). Other criteria mentioned in (Hoffmann et al. 2018) are also necessary for the choice of materials.

3.1. Heat transfer fluids

There are two types of heat transfer fluid: liquids and gases. The liquid heat transfer fluids generally used in CSPs are molten salts, thermal oils and water. Air and other gases are considered to be gaseous heat transfer fluids. Table 1 presents some of the physical properties of heat transfer fluids. Fluids are selected according to the type of collectors used in the installation. In fact, molten salts and air with a high temperature range under atmospheric pressure are usually used in tower systems, whereas thermal oils used in parabolic trough or Fresnel collector system (Vannerem 2022).

Table 1. Thermophysical properties of fluid for sensible heat storage.

Heat transfer fluids	TC /TH [°C]	$\mathit{\rho }$ [kg.m^−3]	$\mathit{Cp}$ J/(kg.K)	$\mathit{\lambda }$ [J.kg^−1.K^−1]	$\mathit{\rho Cp}$ [kWh.m^−3.K^−1]	µ Pa·s	ref
Water	0/100	990–1000	4180	0.64	1.15	0.00055	Esence et al. (2017)
Minerals oils	200/300	770	2600	0.12	0.55	–	Gil et al. (2010), Kuravi et al. (2013)
Silicone oils	300/400	900	2100	0.1	0.52	–	Gil et al. (2010), Kuravi et al. (2013)
Synthetic oil	250 /350	900	2300	0.11	0.57	–	Gil et al. (2010), Kuravi et al. (2013)
Nitrate salt	265/565	1870	1600	0.52	0.25	–	Gil et al. (2010), Medrano et al. (2010), Kuravi et al. (2013)
Hitec	142 / 535	1790	1560	$\sim$0.2	0.775	0.0018	Vignarooban et al. (2015), Esence et al. (2017)
Solar salt	220 / 600	1835	1510	0.52	0.77	0.0018	Vignarooban et al. (2015)
Air	–/–	0.5	1075	0.05	1.5*10^−4	3.4*10^−5	Esence et al. (2017)

Water is the most abundant liquid heat transfer fluid and has a low cost (Mawire and McPherson 2009). It has a large storage capacity compared with other heat transfer fluids. Its use as a thermal fluid increases the efficiency and reduces the cost of electricity production (Modi and Haglind 2014). However, it cannot exceed 100°C at atmospheric pressure, beyond which it is transformed into steam. To use it in applications with temperatures above 100°C, the water has to be pressurised, a process that increases costs.

The thermal oils used in CSPs are mineral oils, silicone oils and synthetic oils. These oils are thermally stable up to 400°C and have a low viscosity (Modi and Haglind 2014; Tian and Zhao 2013). Their disadvantage is that they are relatively expensive and flammable, and their thermal properties deteriorate with heat, which reduces their lifetime.

Because of their storage capacity and high temperature range, molten salts are widely used as heat transfer fluids. Compared to synthetic oils, they are less expensive, non-toxic and non-flammable, which makes them the preferred choice (Vignarooban et al. 2015). In addition, the properties of molten salts are thermodynamically stable and can be accurately estimated using correlations confirmed by experiments (Wang, Yang, and Duan 2015). However, they are corrosive and the risk of pipe damage is high due freezing.

Air is the most abundant gaseous heat transfer fluid (Zunft et al. 2011). It is free, safe, non-flammable and can be used at atmospheric pressure, which reduces installation costs and safety risks (Liu et al. 2014). However, the thermal properties of air are very low compared with those of other fluids, which means that large surface areas and high flow rates are required to facilitate heat exchange.

3.2. Filling materials

Table 2 presents the thermo physical properties of some solid materials. Natural rocks (quartzite, basalt, etc.) are commonly used in dual media thermocline storage systems because of their availability in large quantities and their low cost. They also have better thermal properties and are thermally stable. However, the irregular shape and size of these natural rocks is a disadvantage that reduces the performance of TES (Boubou et al. 2021).

Table 2. Thermophysical properties of packing materials for dual media thermocline sensible heat storage.

Filling materials	Tmax [°C]	$\mathit{\rho }$ [kg.m^−3]	$\mathit{Cp}$ [J.kg^−1.K^−1]	$\mathit{\lambda }$ [W.m^−1.K^−1]	$\mathit{\rho Cp}$ [kWh.m^−3.K^−1]	ref
Firebrick	700	1 820	1000	1.5	0.505^a	Py and Olives (2016)
Concrete	400	2 200	850	1.5	0.519^a	Py and Olives (2016)
Quartzite	600	2600	850	5.5	0.61	Esence et al. (2017), Clauser, Huenges, and Bodenforschung (1995)
Basalt	600	2900	900	2.0	0.73	Esence et al. (2017), Clauser, Huenges, and Bodenforschung (1995)
cofalit	1000	3120	800–1034	2.1–1.4	0.693–0.896^a	Py et al. (2011)
Steel industry dairy worker	1000	2980	996	3.5–2		Calvet et al. (2013), Py and Olives (2016)
Ceramics from sand, bottom ash and clay	610	1730–2050	1391–1671^a	0.331–1.014	0.668–0.951^a	Bagre et al. (2022)

^a Values calculated.

A number of studies have shown the potential of industrial waste for the production of ceramics as thermal storage materials whose shape can be controlled (Hoffmann 2015; Py et al. 2011; Calvet et al. 2015; Gutierrez et al. 2016; Calvet et al. 2013; Py and Olives 2016). Solid materials from industrial waste have better storage capacity by volume, but their price is prohibitive and their availability is not guaranteed. Recently, Bagré et al. have shown that ceramic balls made from sand, bottom ash and clay can be used as fillers in TES (Bagre 2021). These materials are locally available, less expensive and have interesting properties that can improve the performance of storage systems.

4. Parameters affecting the performance of the thermocline dual media storage system

4.1. Basic mathematical equations in the dual media storage system

There are several mathematical models for predicting the performance of thermocline dual media storage systems (Nandi, Bandyopadhyay, and Banerjee 2018; Esence et al. 2017; Sassine, Donzé, and Bruch 2017; Capocelli et al. 2019; Arpino et al. 2014; Fernández-torrijos, Sobrino, and Almendros-ibáñez 2017; Bagre et al. 2023; Mira-Hernández, Flueckiger, and Garimella 2014). Ismail and Stuginsky, presented and summarised many models of regenerative thermal storage (Ismail and Stuginsky 1999). Similarly, Esence et al. (2017) and Calderón-Vásquez et al. (2021) have reviewed the different numerical models used because of the assumptions made and the degree of simplification involved. Among many others, we have the Schumann model (eq 1 and eq2), which is the oldest and most common heat transfer model for lined beds (Ismail and Stuginsky 1999). (1) $ϵ{\rho }_f{c}_{\mathrm{pf}}.\left({\displaystyle \frac{\mathrm{\partial }{T}_f}{\mathrm{\partial }t}+\mathrm{\nabla u}{T}_f}\right)=h_p{a}_p\left(T_s-T_f\right)-U_w{a}_w\left(T_f-T_s\right)$(1) (2) $\left(1-ϵ\right).{\rho }_s{c}_{\mathrm{ps}}.{\displaystyle \frac{\mathrm{\partial }{T}_s}{\mathrm{\partial }t}=h_p{a}_p\left(T_f-T_s\right)}$(2) Most of the mathematical models developed to predict the performances of DMT are based on Schumann model (Calderón-Vásquez et al. 2021; Esence et al. 2017).

4.2. Performance indicators for the thermocline dual media storage system

To evaluate the performance of a storage system, performance indicators are required. They vary according to some studies (Haller et al. 2009; Ibrahim and Marc 2011). Haller et al. (2009) reviewed the various approaches (performance indicators) for evaluating the performance of a thermocline storage system. Commonly used indicators are energy and exergy efficiency, utilisation rate and thermocline thickness. In addition, the times at which charging and discharging are interrupted are also criteria to be taken into account when assessing storage performance.

The energy efficiency${\eta }_{\mathrm{en}}$, is defined as the ratio between the energy restored during discharge $E_d$ and the energy stored during charge$E_{\mathrm{ch}}$. This indicator is widely used in the literature to assess storage system performance. (3) ${\eta }_{\mathrm{en}}={\displaystyle \frac{E_d}{E_{\mathrm{ch}}}={\displaystyle \frac{\int \dot{m}{\int }_{T_e}^{T_s}c\left(T\right)\mathrm{dTd}{t}_d}{\int \dot{m}{\int }_{T_s}^{T_e}c\left(T\right)\mathrm{dTd}{t}_{\mathrm{ch}}}}}$(3) Exergy efficiency, also known as the efficiency rate of the second law, is a measure used to determine the efficiency of a process, taking into account the second law of thermodynamics.

According to Ibrahim and Marc (2011), exergy analysis based on the second principle of thermodynamic makes it possible to detect the origins and extent of deficiencies in cycle processes and to specify that energy can undergo a change in quality that leads it to a state of total equilibrium with the environment, where it loses all usefulness for carrying out tasks. For TES, the exergy evaluation identifies the maximum capacity linked to the incoming thermal energy. Many studies have used exergy efficiency to assess the performance of storage systems (Haller et al. 2009; Rosen, Tang, and Dincer 2004; Rosen 2001; Rosen and Dincer 1997; Rosen 2012; Bejan 1978; Rosen 1999). In general, exergy efficiency is defined by comparing the exergy of the fluid leaving during discharge with that of the fluid entering during charging, as shown in equation 4 (Vannerem 2022): (4) ${\eta }_{\mathrm{ex}}={\displaystyle \frac{{\xi }_d^{\mathrm{flux}}}{{\xi }_{\mathrm{ch}}^{\mathrm{flux}}}}$(4) (5) $\mathrm{Avec}{\xi }^{\mathrm{flux}}=\int \dot{m}.\left[\underset{T_{\mathrm{\infty }}}{\overset{T_f}{\int }}{C}_f\mathrm{dT}-T_{\mathrm{\infty }}\underset{T_{\mathrm{\infty }}}{\overset{T_f}{\int }}{\displaystyle \frac{C_f}{T}\mathrm{dT}}\right].\mathrm{dt}$(5) The utilisation rate is a criterion that is independent of the charging or discharging process. It is used to assess charging and discharging in isolation. For the charge, it is defined as the ratio (equations 6 and 7) (Vannerem 2022) between the quantity of energy actually stored in the reservoir $E_{\mathrm{ch}}$ at the end of the process and the maximum quantity of energy $E_{\mathrm{ch}\mathrm{\_max}}$ which could be stored if all the components (fluids, solids, wall) of the storage system were brought to the high temperature considered from the initial low temperature (equation 6 and 7). (6) $T{U}_{\mathrm{ch}}={\displaystyle \frac{E_{\mathrm{ch}}}{E_{\mathrm{ch}\mathrm{\_max}}}}$(6) (7) $={\displaystyle \frac{\underset{0}{\overset{H_{\mathrm{bed}}}{\int }}\left[\pi R_{\mathrm{tank}}^2.\left[ϵ.\underset{T_f^{\mathrm{in}\mathrm{\_ch}}}{\overset{T_f^{\mathrm{out}\mathrm{\_ch}}}{\int }}{\rho }_f{C}_f\mathrm{dT}+\left(1+ϵ\right).\underset{T_s^{\mathrm{in}\mathrm{\_ch}}}{\overset{T_s^{\mathrm{out}\mathrm{\_ch}}}{\int }}{\rho }_s{C}_s\mathrm{dT}\right]+\pi \left({\left(R_{\mathrm{tank}}+e_w\right)}^2-R_{\mathrm{tank}}^2\right).\underset{T_w^{\mathrm{in}\mathrm{\_ch}}}{\overset{T_w^{\mathrm{out}\mathrm{\_ch}}}{\int }}{\rho }_w{C}_w\mathrm{dT}\right]\mathrm{dz}}{\underset{0}{\overset{H_{\mathrm{bed}}}{\int }}\left[\pi R_{\mathrm{tank}}^2.\left[ϵ.\underset{T_f^{\mathrm{in}\mathrm{\_ch}}}{\overset{T_H}{\int }}{\rho }_f{C}_f\mathrm{dT}+\left(1+ϵ\right).\underset{T_s^{\mathrm{in}\mathrm{\_ch}}}{\overset{T_H}{\int }}{\rho }_s{C}_s\mathrm{dT}\right]+\pi \left({\left(R_{\mathrm{tank}}+e_w\right)}^2-R_{\mathrm{tank}}^2\right).\underset{T_w^{\mathrm{in}\mathrm{\_ch}}}{\overset{T_H}{\int }}{\rho }_w{C}_w\mathrm{dT}\right]\mathrm{dz}}}$(7) This expression in equation 7 can be written simply as equation 8 (Vannerem 2022). (8) $T{U}_{\mathrm{ch}}={\displaystyle \frac{{\sum }_{\mathrm{sfw}}\left(E_{\mathrm{sfw}}\left(T^{\mathrm{out}\mathrm{\_ch}}\right)-E_{\mathrm{sfw}}\left(T^{\mathrm{in}\mathrm{\_ch}}\right)\right)}{{\sum }_{\mathrm{sfw}}\left(E_{\mathrm{sfw}}\left(T_H\right)-E_{\mathrm{sfw}}\left(T^{\mathrm{in}\mathrm{\_ch}}\right)\right)}}$(8) The discharge utilisation rate $T{U}_d$ (equation 9) is evaluated by comparing the energy extracted from the storage during the discharge process with the maximum energy that could be fully extracted if the storage were perfectly cooled to the lowest temperature. Its expression is similar to that of the charge utilisation rate. (9) $T{U}_d={\displaystyle \frac{{\sum }_{\mathrm{fsw}}\left(E_{\mathrm{fsw}}\left(T^{\mathrm{in}\mathrm{\_d}}\right)-E_{\mathrm{fsw}}\left(T^{\mathrm{out}\mathrm{\_d}}\right)\right)}{{\sum }_{\mathrm{fsw}}\left(E_{\mathrm{fsw}}\left(T^{\mathrm{in}\mathrm{\_d}}\right)-E_{\mathrm{fsw}}\left(T_L\right)\right)}}$(9) Two necessary conditions must be met in order to assess the cycle utilisation rate. Firstly, the temperature $T^{\mathrm{in}\mathrm{\_ch}}$ at the start of the charge must be identical to the low temperature$T_L$. Secondly, the final charge temperature $T^{\mathrm{out}\mathrm{\_ch}}$ must match the initial discharge profile$T^{\mathrm{in}\mathrm{\_d}}$. These two conditions are only met for numerical studies. The cycle utilisation rate is then obtained by multiplying the charge and discharge utilisation rates according to equation 10 and 11 (Vannerem 2022). (10) $T{U}_{\mathrm{cycle}}=T{U}_{\mathrm{ch}}\ast T{U}_d$(10) (11) $T{U}_{\mathrm{cycle}}={\displaystyle \frac{{\sum }_{\mathrm{fsw}}\left(E_{\mathrm{fsw}}\left(T^{\mathrm{out}\mathrm{\_ch}}\right)-E_{\mathrm{fsw}}\left(T^{\mathrm{in}\mathrm{\_ch}}\right)\right)}{{\sum }_{\mathrm{fsw}}\left(E_{\mathrm{fsw}}\left(T_H\right)-E_{\mathrm{fsw}}\left(T^{\mathrm{in}\mathrm{\_ch}}\right)\right)}}$(11)

By definition, the cycle utilisation rate is the comparison between the amount of energy recovered during discharge and the maximum amount of energy available between the initial charge temperature and the maximum discharge temperature.

The thickness of the thermocline zone is also a criterion used to assess performance, in particular the stratification zone in the reservoir, in accordance with the constraint of conditions in a specific temperature range before reaching the top or bottom of the reservoir (Xie and Xie 2022). This criterion is mainly defined as the temperature range between the charging temperature threshold and the discharging temperature threshold illustrated in equations 12 and 13 respectively (Fasquelle et al. 2018b). (12) $T_{\mathrm{tres}\mathrm{\_c}}=T_H-n\text{\%}(T_H-T_L)$(12) (13) $T_{\mathrm{tres}\mathrm{\_d}}=T_L+n\text{\%}(T_H-T_L)$(13) The choice of value is based on experimental data and the choice of temperatures upstream (solar panel) and downstream (power block) of the storage system (Fasquelle 2017; Vannerem 2022). This criterion has a significant impact on system performance. The dimensionless thickness of the thermocline zone is defined by equation 14. (14) $L_{\mathrm{thermocline}}={\displaystyle \frac{z\left\{T=T_L+n\text{\%}(T_H-T_L)\right\}-z\left\{T=T_H-n\text{\%}(T_H-T_L)\right\}}{H}}$(14) according to several studies, the percentage of the temperature threshold n% can be taken as 20% (Fasquelle et al. 2018a, 2018b; Hoffmann et al. 2017; Hoffmann et al. 2016; Xu et al. 2012a, 2012b). So equations 12 and 13 can be written as equations 15 and 16. (15) $T_{\mathrm{tres}\mathrm{\_c}}=T_H-20\text{\%}(T_H-T_L)$(15) (16) $T_{\mathrm{tres}\mathrm{\_d}}=T_L+20\text{\%}(T_H-T_L)$(16) Influence on performance indicators by geometric parameters, operating parameters and thermo-physical properties through numerical and experimental work according to the literature will be the subject of the next section.

4.3. Effect of geometric and operating parameters on the performance of dual media thermocline storage

Dual media thermocline sensitive heat storage is more economical, and many numerical and experimental studies have been carried out to improve its performance. Table 3 below presents some numerical and experimental studies on the influence of geometric and operating parameters on the performance of storage systems and some of the results obtained.

Table 3. Studies of the impact of geometrical and operating factors on the sensitive heat dual media thermocline system.

Reference and year	Materials (solid/fluid)	Experimental /Numerical	performance indicators	Parameters studied	Results
Aly and El-Sharkaw (1990)	Air/ Aluminium Air/Steel Air/ Rock	Num	-rate and capacity of energy storage -rate of temperature	-density, -thermal conductivity -specific heat	The increase in storage capacity and the decrease in the rate of temperature rise are linked to the increase in density
Adebiyi et al. (1993)	Zirconium oxide/air	Num-exp	-First and Second-law Efficiencies	-Flow rate -Inlet temperature -Energy Input -Thermal Conductivity of Storage Medium	-for maximum efficiency, a longer bed is needed to increase the amount of energy supplied -intraparticle conductivity had no effect on system performance -Reducing the mass flow rate causes a slight drop in maximum efficiency
Yang and Garimella (2010)	molten salt hitec/ quartzite	Num	-discharge efficiency	-particle size -Reynolds’s numbers -tank height	-improved discharge efficiency for low Reynolds’s numbers and high reservoir heights -the use of smaller particles greatly increases the efficiency of the discharge.
Hänchen, Brückner, and Steinfeld (2011)	Air/Aluminium Air/ Rock Air/Steatite Air/Steel	Num	-charge and discharge efficiencies -overall efficiency -Capacity ratio	-height tank -mass flow rate, -particle diameter -volumetric heat capacity -thermal conductivity	-a low height of the storage system, a low volumetric thermal capacity of the solid material with a high air mass flow rate leads to a higher capacity factor but a reduction in overall efficiency -the thermal conductivity of the solid has a negligible effect
Xu et al. (2012a)	Molten salt/ Quartzite	Num	-thermocline thickness -discharge efficiencies	-flow rate -temperature inlet -porosity -height -thermal losses	-fluid inlet velocity, inlet temperature have little impact on the thermocline and efficiency of the effective discharge -a large tank size reduces the thermocline zone and improves performance -Good insulation avoids heat loss and improve system stability.
Xu et al. (2013)	Molten salt/ Quartzite	Num	-thermocline thickness -out temperature	-height tank -particle diameter -different solids	-System performance is affected by the particle size of the solid material -thermal conductivity is therefore desirable for solid particles to ensure effective discharge
Yang and Garimella (2013)	Molten salt/ Quartzite	Num	-Cycle efficiency	-tank diameter -particle diameter -number Reynolds -length ratio -thermal capacity	-Cycle performance improves as Re decreases and thermal capacity increases. -Larger tanks also improve cycle efficiency
Bayón and Rojas (2013)	(Solar salt, caloria HT43, water)/ (rock + sand)	Num	-Discharge efficiency -thermocline thickness	-dimensionless velocity -porosities -temperature difference	-A wide temperature range means a high thermocline tank height for high theoretical efficiency -there is a decrease in the thickness of the thermocline and an increase in the efficiency of the reservoir as the dimensionless velocity increases
Zanganeh et al. (2015)	Air/ rock	Num	-thermal losses -pumping work, -discharge outflow temperature -overall storage efficiency	-diameter/height ratio -particle diameter -inclination of the cone -insulation	The temperature drop during the discharge phase is minimised and efficiency is improved by reducing the diameter/height ratio of the reservoir and the diameter of the rock, even if this leads to a drop in pressure and an increase in pumping work. -Increasing the inclination of the cone reduces storage capacity, but amplifies the reduction in temperature during discharge. Thin layers of insulation are adequate to ensure low heat loss.
Bruch, Fourmigue, Couturier, and Molina (2014), Bruch et al. (2017)	Thermal oil/ silica gravel	Num-exp	dimensionless out temperature discharge	-Reynolds number -charge and discharge temperature difference	The effects of mass flux, charge and discharge temperature variation and partial load were examined with no significant impact on the dimensionless axial temperature profile demonstrating the resilient and controllable nature of dual media thermocline energy storage.
Motte et al. (2014)	Cofalit/solar salt	Num	dimensionless out temperature discharge	-inlet velocity -aspect ratio -Thermal conductivities, densities and heat capacities	-reducing the fluid velocity gives good thermocline behaviour -low thermal conductivity values lead to a non-uniform temperature distribution, while high thermal conductivity values are responsible for an increase in the thickness of the thermocline: this generates a trade-off -Similar results were obtained for the fluctuation of densities and heat capacities, for both fluid and solid states
Hoffmann et al. (2017)	Vegetable oils/Quartzite	Exp-Num	-thermocline thickness -efficiency during charging and discharging	-mass flow -particle size	-the smaller the particles, the more efficient the storage due to better heat transfer between the fluid and the solid -An optimum speed is obtained for which below this value, heat losses are too high, and above this value, the heat flux transported by the forced convection of the heat transfer fluid is too high in relation to the heat flux exchanged between the liquid and the solid
Ortega-fernández et al. (2017)	Air/ Steel Slag	Num	the storage capacity and overall thermal efficiency	-aspect ratio, -fluid velocity -particle size -tank geometry	Particles with a diameter of around 1 cm are the most effective for all the mass flow rates considered.
Abdulla and Reddy (2017)	Molten salt /(Quartzite rock and silica sand)	Num	-thermocline thickness -out temperature discharge -discharging efficiency	-operating temperature difference -inlet velocity -particle diameter -power output	Small particle size, low fluid velocity and a small operating temperature range improve system performance. Of all the parameters, the operating temperature range appears to have the greatest influence on the thermal performance of the TES system.
Yin et al. (2017)	Molten salt/Zirconium ball Molten sal/Silicon carbide (SiC) foam	Num-exp	-thermocline thickness -out temperature discharge -storage efficiency -discharging efficiency	-inlet velocity -inlet temperature -temperature difference	a respective increase in the fluid flow rate, inlet temperature and temperature difference induces an expansion of the thermocline thickness and a lower outlet temperature during discharge.
Cárdenas et al. (2018)	Air/basalt rock	Num	-pressure drop -exergy efficiency	-aspect ratio -particle size -mass overrating factor	It has been established that the most profitable configuration from a technical and economic point of view is the one with a 50% increase in storage mass, an aspect ratio of 0.6 and a grain size of 3.7 mm, with a round-trip exergy efficiency of 98.24%
Nandi, Bandyopadhyay, and Banerjee (2018)	Molten salt/ Quartzite	Num	-charge and discharge efficiencies -Stratification numbers	-inlet fluid Reynolds number -aspect ratio -porosity -filler size -inlet and outlet temperature	-No significant effect of the variation in temperature difference on the performance of the storage system. -They found optimum values for the four parameters for better performance of the TES thermocline: aspect ratio of 0.25, inlet Reynolds number of 10, porosity of 0.8 and filler size of 0.01 m,
Esence, Brunch, et al. (2019)	Air /Alumina beads	Num	Utilszation rate Efficiency -out temperature discharge	-inlet velocity	existence of a fluid velocity that maximises the storage utilisation rate
Hernandez et al. (2018)	Magnetite ore/ Delcoterm Solar E15 oil	Num	-pressure drop -energy stored	-aspect ratio H/D -particle size -outlet temperature	-maximum aspect ratio of 2 is a suitable design value. -Particles with a smaller diameter significantly increase storage capacity
Kocak and Paksoy (2020)	Therminol 66 /demolition wastes	Exp-Num	-energetic and energy efficiency	-fluid velocity -charging temperature	-The energy efficiency of the TES system decreases as the charge temperature increases. -The lowest energy performance is obtained at low fluid superficial velocities
Rodrigues and De Lemos (2020)	Air/ rock	Num	-Charging efficiency -thermocline Thickness	-Reynolds number, -thermal conductivity ratios,(ks/kf) -thermal capacity ratio (Cps/Cpf)	-Lower ks/kf ratios improve load efficiency by reducing heat loss, which in turn allows higher temperatures to be achieved.
Wang et al. (2020)	Molten salt/ (firebrick, steel and ceramic)	Num	Thermocline thickness	-inlet temperature -inlet velocity -porosity -filler particle diameter -effective thermal conductivity -thermal capacity	-high inlet velocity, high inlet temperature and high specific heat capacity of solid materials reduce the thickness of the thermocline -The low porosity, small diameter and medium thermal conductivity of the particles also improve the efficiency of the system.
Vannerem, Neveu, and Falcoz (2021)	Jarysol/ Alumina Sphere	Exp-Num	-utilisation rate	-mass flow rate -inlet temperature	-The showed that, there is existence of a fluid velocity value that maximises the storage utilisation rate. -the impact of fluid velocity is experimentally too moderate to observe an optimum velocity
Bagre et al. (2023)	Jatropha curcas/ ceramic ball	num	-thermocline thickness -storage efficiencies -discharge efficiency	-Particle size -porosity -fluid velocity	The results show that high fluid velocity, high porosity (> 45%) and a large diameter of the packing materials degrade the thermocline and therefore reduce the performance of the storage system

4.3.1. Effect of geometrical parameters

4.3.1.1. Effect of tank configuration

The thermocline storage system can be designed in cylindrical, rectangular and truncated cone shapes according to the literature (Figure 3).

Figure 3. Tank configuration, (a): cylindrical tank (Xie 2022), (b): conical tank (Zanganeh et al. 2015), (c): rectangular tank (Touzo et al. 2020).

Firstly, the cylindrical shape is the preferred configuration for storage tanks, as it effectively withstands the pressure exerted on the walls while eliminating edge effects and allowing the flow to be distributed evenly (Melanson and Dixon 1985). Moreover, the vertical layout of this type of configuration has the advantage of reducing the impact of natural convection by minimising the exchange of material between the cold lower region and the hot upper region. In addition, this configuration not only reduces heat loss but also saves some of the mechanical difficulties involved in the installation (Melanson and Dixon 1985).

Secondly, a conical tank can be used to reduce the effects of thermal ratcheting (Geissbühler et al. 2018). Thus, Zanganeh et al. (2012) proposed a conical tank which reduces the ratio between the surface area and the volume of the upper part of the tank, the aim of which is to limit the mechanical stresses and heat losses of the hot thermocline storage part. Sassine et al. (2018) have also shown that the use of this type of tank would lead to a 20% reduction in the mechanical stress exerted on surfaces compared to a cylindrical tank. However, the cost of this type of tank could be higher, and its construction more complex.

Finally, the rectangular shape of the storage tank in a vertical position is also mentioned in several studies (Odenthal et al. 2020a, 2020b; Nicolas et al. 2019; Touzo et al. 2020). The experimental and numerical study on a horizontal rectangular reservoir by Touzo et al. showed that no channelling effect and a moderate radial thermal gradient were detected, despite the reservoir having a horizontal geometry (Touzo et al. 2020). With a prototype horizontal air/bauxite thermocline tank, Lopez et al. also observed no thermal gradient or thermal stratification in the direction of fluid flow (Nicolas et al. 2019). They proved that the temperatures were virtually equal for a given axial coordinate. The horizontal position has a benefit associated with thermo mechanical consequences (Touzo 2021). According to the literature, the packing bed compresses during temperature variations, causing an increase in stress on the walls of the tank and this can cause damage to the tank and the materials that make up the bed (Esence, Desrues, et al. 2019). Reducing the vertical dimension of the tank in relation to its horizontal dimension naturally reduces the pressure on the wall caused by the settling of particles, which reduces the risk of being exposed to mechanical stress. the horizontal layout of the rectangular tank offers many advantages for its design and installation on a site, although it can provide poor thermal performance (Touzo 2021).

On a laboratory and industrial scale, the effect of the shape and dimensions of the tank on the performance of the storage system is quite remarkable. The cylindrical shape with the vertical position performs best in terms of discharge efficiency and energy storage capacity. This shape is therefore the most effective, although the truncated cone shape has advantages in terms of reducing mechanical stress.

4.3.1.2. Effect of tank height and size

The choice of reservoir height and diameter influences the performance of the storage system, according to these studies (Xu et al. 2012a; Yang and Garimella 2013; Cárdenas et al. 2018; Odenthal et al. 2020b; Nicolas et al. 2019). Chao et al. in 2012, numerically studied the effect of the height and diameter of a cylindrical storage system using molten salt and quartzite. The results showed that the energy storage capacity increased proportionally by 2.33 times as the height of the reservoir increased from 6 to 14 m. The system can therefore take longer to discharge, as shown in Figure 4(a). The effective discharge time increases from 1.88 to 4.57 hours, or 2.43 times (Xu et al. 2012a). Figure 4(b) confirms the improvement in discharge time with the increase in reservoir height, favoured by the thinness of the thermocline thickness obtained with the increase in this parameter. In the literature $\frac{H}{D_{\mathrm{tank}}}$ tank or $\frac{D_{\mathrm{tank}}}{H}$ratios are generally calculated for the cylindrical configuration in order to assess the storage performance (thickness of the thermocline). Some studies have shown that the thickness of the thermocline becomes thinner as the $\frac{H}{D_{\mathrm{tank}}}$ aspect ratio increases (Xu et al. 2012a; Flueckiger and Garimella 2012; Chang et al. 2015). The numerical study by Yang et al. also confirmed the positive influence of increasing this aspect ratio (Yang and Garimella 2013). Zanganeh et al. (2015) have shown that the lower $\frac{D_{\mathrm{tank}}}{H}$ aspect ratio gives not only higher output temperatures but also the best overall efficiency for a cone-shaped storage system. For the different aspect ratios $\frac{H}{D_{\mathrm{tank}}}$ and $\frac{D_{\mathrm{tank}}}{H}$, an increase in one translates into a decrease in the other, so the results of these previous studies corroborate each other. It is assumed that a high reservoir height improves the efficiency of the thermal storage system on a laboratory or pilot scale. However, high-rise tanks present structural challenges that make them impractical as well as compact, leaving them vulnerable to heat loss. This is why the height limit for industrial-scale foundations is twelve metres (Vannerem 2022). To achieve this, it is essential to find a compromise that minimises the proportional dimension of the thermocline in the high-bay tank, while taking into account the practical aspects. On an industrial scale, limiting the maximum height of a reservoir means increasing the diameter of the reservoir to increase storage capacity, to the detriment of the aspect ratio (Vannerem 2022).

Figure 4. Variations in the molten salt temperature at the outlet and the thermocline thickness with the discharging time using different tank heights (a). Variations in normalised thermocline thickness with the discharging time using different tank heights (b) (Xu et al. 2012a).

In addition, Cárdenas et al. (2018) numerically studied the effect of geometrical parameters on the energy efficiency of an industrial-scale dual-media thermocline storage system and the results revealed that an $\frac{H}{D_{\mathrm{tank}}}$aspect ratio between 0.5 and 0.8 improves the discharge efficiency.

The choice of minimum tank height and diameter will depend on the scale of applications. At laboratory or pilot scale, $\frac{H}{D_{\mathrm{tank}}}$ aspect ratios in excess of 1 up to 4 can be taken to obtain the best storage and destorage efficiencies. However, on an industrial scale, the aspect ratio would be less than unity to compensate for mechanical constraints.

4.3.1.3. Effect of particle size

The size and shape of the packing materials also influence the performance of the thermocline storage system. Most studies taking into account the spherical shape of solid materials have observed that smaller diameter spheres increase the efficiency of the storage system (Xu et al. 2013; Yang and Garimella 2013; Abdulla and Reddy 2017; Van Lew et al. 2011). In fact, a small size simultaneously increases the contact surface and the rate of interstitial heat transfer between the thermal fluid and the filler material. This is confirmed by the work of Van Lew et al. (2011) and Yang and Garimella (2010) who state that solids with very small diameters are effective in improving thermal stratification by increasing the total exchange surface between the fluid and the solid, while reducing the adimensional Biot number of the solids. D. Schlipf et al. studied a thermocline system using air as a heat transfer fluid and quartzite, sand and basalt as packing materials (Schlipf et al. 2015). Theoretical and experimental results (Figure 5) have shown that materials with particularly small grains offer very good heat storage potential thanks to the rapid diffusion of temperature in the material, which favours the generation of a thermocline with a very small thickness. Laube et al. (2020) have carried out a numerical study on a laboratory and industrial scale of a high-temperature storage concept using several fluids (Solar salts, liquid metals) as thermal fluids and quartzite as fillers materials They observed that, on an industrial scale, particle diameter did not significantly affect the efficiency of the discharge. On the other hand, a clearer sensitivity to particle size was observed at laboratory scale, showing that small-diameter particles are more preferred. In addition, on an industrial scale, Bruno Cárdenas et al. showed numerically that particles with a diameter of 3.7 mm help to reduce the size of the thermocline and increase energy efficiency by more than 98.24% (Cárdenas et al. 2018).

Figure 5. (a): Temperature behaviour trough the packed-bed for 530 °C inlet temperature (basalt gravel with 4 mm, air flow: 25 Nm³/h); (b): Comparison of the temperature behaviour through the packed-bed (quartz gravel with 2 mm, silica sand < 1 mm, air flow: 35 Nm³/h) (Schlipf et al. 2015).

It is agreed that small-grained solid materials improve the performance of the thermocline storage system. However, very small particle sizes such as sand can cause substantial pressure drop and lower system efficiency (Cárdenas et al. 2019). In addition, Bruch, Fourmigué, and Couturier (2014) analysed the flow of thermal oil through a 3 mm sand substrate and a 3 cm rock substrate in a pilot-scale storage system. The results showed that the smaller particles facilitate the diffusion of the fluid flow to increase the heat transfer surface area. However, the small size of the particles can cause a more significant increase in pressure losses (Bruch, Fourmigue, Couturier 2014). The size of the particle is a parameter to be taken into account when designing the thermocline storage system. It is accepted that, whatever the filling material, a small diameter particle (of the order of a millimetre for sands and a few centimetres for rocks) is always desirable to improve the performance of the storage system on a laboratory, pilot or industrial scale.

4.3.1.4. Effect of porosity

Filling materials can be arranged in bulk or not. Loose fill is characterised by a poorly organised arrangement of irregular solids, whereas structured fill is a well-organised arrangement of regular solids. The packing bed is mainly defined by porosity, which represents the percentage of the bed volume that is not filled by solid particles (Esence et al. 2017), i.e. the volume occupied by the fluid. Bulk packing beds composed of spherical solids of uniform size generally have a porosity of between 0.3 and 0.4 (Faas et al. 1986). According to some studies found in the literature, a porosity of 0.25 can be obtained by mixing solids of two different sizes (Bruch, Fourmigue, Couturier 2014; Raymon and Robert 1997; Pacheco, Showalter, and Kolb 2001; Bagre et al. 2023). Low porosity reduces costs in solid/liquid systems, where the liquid used is often more expensive than the solids, whereas in solid/gas systems, it increases storage density because the solids generally have a higher heat capacity by volume than the fluid. Jon T. Van Lew et al. (Touzo et al. 2020) studied numerically the behaviour of a storage system composed of Therminol VP-1 as a thermal oil and granites as packing materials with a storage capacity greater than that of the fluid (Van Lew et al. 2011). They observed that as porosity increases storage efficiency falls as shown in Figure 6. However, increasing the porosity above 0.7 leads to an increase in storage efficiency although a void fraction of 0.7 is almost unachievable from a theoretical point of view. This phenomenon could be due to the fact that above a certain porosity, the dual media system behaves like a single media system composed of a fluid with a high storage capacity.

Figure 6. Effect of the pack bed void fraction on the thermal storage efficiency (track down) (Van Lew et al. 2011).

In contrast, Xu et al. (2012a) have shown numerically that low porosity of a storage system composed of molten salt with a filler material with a lower heat capacity by volume than the salt results in a short discharge time and a large thickness of the thermocline, reflecting low storage efficiency (Figure 7).

Figure 7. Variations in the molten salt temperature at the outlet and the thermocline thickness with the discharging time using different porosities (Xu et al. 2012a).

Recently, Bagré et al in 2023 also numerically studied the impact of porosity on the performance of a thermocline storage system based on jatropha oil and ceramic balls (Cárdenas et al. 2019). They showed that low porosity increases the efficiency of the discharge, favoured by the generation of a thin thermocline (Zhao et al. 2018).

In the light of these studies, it is clear that low porosity considerably reduces the cost of storage, but its effect on the efficiency of the dual media thermocline storage system is directly linked to the heat capacity of the packing material used in relation to that of the fluid. This parameter is taken into account when designing storage systems on a laboratory, pilot or industrial scale, taking into account the heat capacities of the fluid or solid materials.

4.3.1.5. Effect of tank wall and insulation

The temperature ranges used and the size of the storage system selected determine the type of material selected for the tank wall (Xie and Xie 2022). Most of the materials used in the design of storage tanks are metals such as carbon steel, given their high strength and ability to withstand high pressures in high-temperature applications (Baoshan et al. 2022). These metals have a high thermal conductivity, often higher than that of the fluid. The use of such a material can lead to high heat loss due to its high thermal conductivity. Baoshan et al. (2022) and Motte, Bugler-Lamb, and Falcoz (2015) evaluated the impact of wall material on the performance of a lined thermocline storage tank using three numerical models with two experimental set-ups, one at laboratory scale and the other at pilot scale. The wall of the pilot-scale tank is steel and that of the laboratory-scale tank is polycarbonate. Analyses show that whatever the material, a thin wall has a reduced effect on energy and exergy performance. In addition, the same study showed that better insulation considerably reduces the thickness of the thermocline by around 20% and increases energy efficiency from 5% to 7% and the capacity ratio from 3% to 5% (Motte, Bugler-Lamb, and Falcoz 2015). This is why a judicious choice of tank construction materials and adequate tank insulation are necessary, especially for laboratory-scale storage systems. It is desirable to take into account the effect of the wall during numerical studies to better predict the performance of storage systems.

4.3.2. Effect of operating parameters

Numerous numerical and experimental studies have investigated the effects of operating parameters on the performance of the thermocline storage system.

4.3.2.1. Effect of inlet temperature and temperature difference

The temperature difference between the hot and cold storage sources is a parameter that seems to influence the performance of thermocline storage systems according to the literature. A number of numerical and experimental studies have investigated the effect of varying the temperature difference on the operation of the thermal storage system. Studies by Bruch et al. Yang and Garimella (2010), Flueckiger and Garimella (2012), Bayón and Rojas (2013), Xu et al. (2012a), have shown that varying the temperature difference between the hot and cold source does not significantly influence the thickness of the thermocline (Figure 8(a)), nor the temperature profiles at the end of the charging and discharging stages, nor the utilisation rate (Figure 8(b)).

Figure 8. Effect of inlet temperature on thermocline thickness and discharge time (a) (Xu et al. 2012a) and on temperature profiles during a thermal cycle (b) (Bayón and Rojas 2013).

Contrary to previous studies, Yin et al., through a numerical study, observed that a charging with the lowest temperature variation had the highest charging efficiency (Yin et al. 2017). In addition, Abdulla and Reddy have numerically investigated the effect of a few geometrical and operating parameters on the performance of the TES system by observing the evolution of the thermocline and discharge efficiency (Abdulla and Reddy 2017). They found that the operating temperature difference is a crucial factor impacting the thermal performance of the TES system, since the overall efficiency decreases by 12% when the temperature difference increases from 50 K to 150 K. This can be seen in Figure 9(b), which shows that the discharge efficiency is high at low operating temperatures and tends to decrease as the temperature difference increases. This naturally explains the increase in the thickness of the thermocline as the temperature difference increases (Figure 9(a)) (Abdulla and Reddy 2017).

Figure 9. (a): Variation in thermocline thickness with different temperature ranges, (b): Variation of discharge efficiency with evolution temperature ranges (Abdulla and Reddy 2017).

In general, from study to another, there is some controversy about the effect of inlet temperature or operating temperature deviation on the performance of the dual media thermocline storage system. In view of the lack of consensus on the influence of this parameter, Vannerem Ségolem in his thesis in 2022 suggests that these predecessors may have omitted some important assumptions from the calculations of certain performance indicators, which led to a contradiction in their results. By reformulating the hypotheses and concepts of a number of indicators and using experimental and numerical studies, Vanerem Ségolem showed that the temperature difference had no major impact on the overall performance of the TES.

Although some studies agree that temperature has a limited effect on storage system performance, there is still no consensus on the overall trend in the effect of temperature difference, nor on the physical explanation for this phenomenon. The incomprehension of the impact of this parameter is maybe due to the use of different fluids with thermo-physical properties varying with temperature during the tests. Experimental and numerical studies are therefore still needed to clarify the impact of this parameter on the storage system performance. The variation of HTF properties as function of temperature could be a reason of these differences in results.

4.3.2.2. Effect of fluid velocity

The velocity of the fluid in the reservoir during charging or discharging is a parameter that has an impact on the performance of the thermal energy storage system. Indeed, a few numerical and experimental studies have shown its influence on performance indicators. Rocío Bayón and Esther Rojas have shown through a simulation study based on a single-phase model that increasing the fluid inlet velocity leads to a decrease in thermocline thickness and an increase in discharge efficiency (Bayón and Rojas 2013). Bruch et al. experimentally studied the influence of fluid velocity by assessing its impact on the utilisation rate and energy efficiency (Bruch et al. 2017). The results showed that fluid velocity had a non-significant effect on the utilisation rate, but energy efficiency increased as velocity increased. In opposition, the study by Abdulla and Reddy based on a two-dimensional biphasic model shows that an increase in fluid velocity leads to a considerable drop in discharge efficiency (Abdulla and Reddy 2017). Similarly, F. Motte et al. (Karim 2011), Yang and Garimella (2010), Yin et al. (2017) also observed a decrease in discharge efficiency with increasing fluid velocity.

These previous studies show a contradiction in results, revealing a lack of understanding of the phenomenon induced by fluid velocity. The difference in results is due to differences in the underlying assumptions of the numerical models, differences in the definitions of the performance indicators, and differences in the simulated operating conditions used by the authors.

To resolve this contradiction, some numerical and experimental investigations predict the existence of an optimal speed that improves performance (Fernández-torrijos, Sobrino, and Almendros-ibáñez 2017). Indeed, Hoffmann et al. (2017) conducted an experimental study on a laboratory-scale storage system composed of quartzite and Rapeseed oil, with the aim of understanding the impact of fluid mass flow rate on system performance. The experimental and numerical results obtained show an optimum mass flow rate (Figure 10(a)) (Hoffmann et al. 2017). In addition, Esence, Brunch, et al. (2019) numerically evaluate the effect of fluid velocity on the utilisation rate for different heat loss coefficients (Figure 10(b)). They noted a reduction in the utilisation rate at low fluid velocity, even for the adiabatic case, and showed that the ideal velocity relates to an equilibrium not only with stratification but also with heat losses.

Figure 10. (a): influence of mass flow rate on discharge efficiency, (b): evolution of utilisation rate with fluid velocity for different heat loss coefficients.

Recently, the thesis work of Vannerem (2022), which was largely based on the study of the influence of operating parameters on the performance of a thermocline storage system, also highlighted the existence of an optimum speed depending on the chosen performance indicator (Vannerem, Neveu, and Falcoz 2021). Vannerem Ségolène observes that the cycle utilisation rate peaks at an interstitial velocity of 4.10⁻³, while the exergy efficiency is highest at a velocity of 6.7*10⁻³. According to the author, the difference in these values is due to heat loss, the thermal conductivity of the solid and the fluid and thermal convection between the fluid and the solid.

Studies on the effect of fluid velocity show that this parameter should be taken into account, despite the difficulty of reaching a clear consensus on its impact on system performance. Several experimental studies followed by meticulous numerical investigations with well-defined hypotheses will be needed to clarify the effect of fluid velocity on the performance of a storage system.

4.3.2.3. Effect of fluid distribution

The method of distributing the fluid can disrupt its flow within a thermocline storage system and affect its performance.

On one side, fluid distribution is extensively studied numerically or experimentally for single medium thermocline storage systems in the studies (Mawire and McPherson 2009; Li et al. 2013; Nellis and Klein 1977; Wildin 1996; García Mari et al. 2013; Li et al. 2014; Lou, Fan, and Luo 2020; Shah and Furbo 2003; Farmahini-Farahani 2012). The impact of this parameter is much more noticeable for single media thermocline storage systems using water as the storage medium (Li et al. 2013; Shah and Furbo 2003; Eames and Norton 1998; Hasan and Theeb 2021; Lou, Fan, and Luo 2020) for this type of configuration, the influence of fluid distribution is directly linked to the geometry or position of the diffuser used (García Mari et al. 2013; Farmahini-Farahani 2012). Using a single media thermocline storage system, Li et al. (2014) showed experimentally that a slot-type diffuser geometry improves performance over single pipe and shower-type diffusers. Precisely as shown in Figure 11, discharge efficiency drops from 71% to 25% for the shower-shaped diffuser, while it decreases from 90% to 64% for the slot configuration when the volume flow rate is multiplied by three, demonstrating the robustness of the slot diffuser compared with the others (Li et al. 2014). Wildin also investigated the effect of diffuser height and inlet Reynolds number on thermocline generation during loading for a water storage system (Wildin 1996). He found that thermocline generation is effective using a diffuser of reduced height.

Figure 11. Effective discharging effective of the tanks with different inlets(track down) (Li et al. 2014).

On the other hand, the effect of fluid distribution on the performance of a dual-media thermocline storage system has been less studied experimentally and much more numerically (Mira-Hernández, Flueckiger, and Garimella 2014; Wang, Yang, and Duan 2015; Bellenot et al. 2019; Vannerem 2022). Wang, Yang, and Duan (2015) numerically investigate the effect of fluid distribution on the performance of a DMT system using annular diffusers with variable injection area and constant fluid flow rate. they achieved that despite considerable obstruction (80% of the surface area) at the entrance, the flow distribution has only a moderate impact on exploitable energy production (<3% variation). They also concluded that an axial distribution offers better performance than a uniform distribution. Based on a constant flow rate assumption, it is difficult to make differentiate difference between the impact of fluid velocity and that of the diffusers on the TES performance. The thesis work of Bellenot (2021), based on the influence of fluid distribution on the thermo-hydraulic behaviour of a dual-media single-tank thermal storage reservoir, aimed to overcome this problem. An experimental series of tests on the STONE installation using different fluid injection and collection mechanisms (Figure 12) on a pre-industrial-sized thermal reservoir showed that there is no significant distinction between the various injection techniques during charging time. However, the amount of energy recovered during discharges differs from one distributor to another, as axial collection does not recover as much energy as radial collection. This difference in recovery energy during discharge is smaller, so the influence of the distributors is not so important. Gregoire Bellenot confirmed the conclusions from the experimental study by means of a multidimensional numerical study (Bellenot et al. 2019).

Figure 12. Schematic of the STONE system with the different injection modes (Bellenot et al. 2019).

To improve the understanding of the impact of fluid distribution, Ségolène Vannerem has undertaken numerical and experimental studies on the effect of this parameter (Vannerem 2022). By experimentally evaluating the influence of fluid velocity on storage behaviour with three types of diffusers (peripheral, central and uniform), he observed that no diffuser affected the behaviour of the storage system. According to the author, these results are due to the packing materials, which naturally act as a distributor and homogenise the velocity field, whatever the injection method used (Figure 13).

Figure 13. (a) Evolution of the discharge utilisation rate with flow rate for the three distributors tested (b) Charge, discharge and cycle utilisation rates for the three distributors tested (Vannerem 2022).

From all the above, single medium thermocline storage systems are greatly affected by the geometry of the diffuser. However, the effect of fluid distribution is found to be insignificant on the performance of dual media thermocline systems. The packing homogenises fluid circulation for fluid collection and injection. DMT is therefore ideal for use in industrial-scale power plants.

4.3.2.4. Cycling operation effect

The cycling process involves alternating charges and discharges. Instead, the tank is heated until it reaches a charge temperature threshold, then cooled until it reaches a discharge temperature threshold, and this is repeated several times (Touzo 2021). This process has an impact on the performance of the storage system. It is during the thermal cycling process that the bed of solid materials expands in volume due to thermal expansion. These dilations induce a compression of the bed of solids as a result of the stresses on the wall. Performance degradation is therefore proportional to the number of cycles. Numerical and experimental work has been carried out to understand the effect of cycling on the performance of dual-media thermocline systems (Touzo et al. 2020; Bruch, Fourmigue, Couturier 2014; Cascetta et al. 2014). Fasquelle (2017) has numerically demonstrated the effect of cycling on the performance of a storage system depending on the temperature thresholds for charging or discharging. It has been shown that the performance of the thermocline decreases rapidly if the temperature thresholds that determine charging and discharging shutdowns are very strict. This is shown in Figure 14(a), where the charge and discharge curves are very close after 20 cycles, revealing that a large part of the tank is occupied by the thermocline zone. However, he showed that a flexible choice of threshold temperatures enables stability to be achieved after around 3 cycles (Figure 14(b)). It should be noted that greater extraction from the thermocline zone during charging and discharging leads to good conservation of stratification, and better conservation of thermal stratification provides good storage system performance. Aubin Touzo et al. have numerically and experimentally evaluated the impact of cycling on system performance Touzo et al. 2020). His results seem to confirm the work of Thomas Fasquelle showing that a flexible choice of threshold temperature effectively promotes rapid stability of the storage system, thus reducing the degradation of system performance.

Figure 14. (a) Final temperature profiles for cycling with thresholds of 0.1 (b) Final temperature profiles for cycling with thresholds of 0.3 (Fasquelle 2017).

In the light of these studies, a judicious choice of threshold temperatures in a flexible mode would minimise the effect of cycling on the behaviour of the storage system.

4.3.3. Effect of the thermo-physical properties of the fluid and solid materials

The physical properties of the materials, such as thermal conductivity and thermal capacity, also influence the performance of the thermocline storage system, according to a few studies reported in the literature.

4.3.3.1. Effect of the thermal conductivity of fluids and solids

The thermal conductivity of the fluid or solid has an effect on the efficiency of the TES (Karim 2011). Aly and El-Sharkaw (1990) have shown numerically that an increase in the thermal conductivity of solids induces a significant increase in the loading rate and the amount of stored energy, causing a rise in temperature throughout the bed during a given loading period, but which is completely reversed beyond the given period.

Gang Wang et al. carried out an exhaustive analysis of the parameters influencing the thermal and mechanical performance of a dual media thermocline reservoir (Wang et al. 2020). In this study, they evaluated the impact of variation of the thermal conductivity of the filler material on the thickness of the thermocline and on the output temperature during charging and discharging (Wang et al. 2020). As shown in Figure 15, they observed that the increase in thermal conductivity did not significantly influence the output temperature during either charging or discharging. However, the thickness of the thermocline increases as the conductivity increases for a charging or discharging time of less than 4 hours, and this effect becomes virtually insignificant after 4 hours. In addition, Fernando A. Rodrigues and Marcelo J.S. De Lemos conducted a study on the effect of storage material properties on the thermal efficiencies of a thermocline storage system using air as the heat transfer fluid (Rodrigues and De Lemos 2020). With different Reynolds numbers, the authors numerically evaluated the effect of varying the ks/kf ratio on the thickness of the thermocline, on the charging efficiency and on the storage efficiency. The performance survey showed that a reduction of the ks/kf ratio, i.e. a lower thermal conductivity of the solid than that of the fluid, improved the efficiency of the system for small Reynolds numbers, whereas increasing the Reynolds number gradually reduced this effect (Rodrigues and De Lemos 2020).

Figure 15. Thermocline thickness and outlet molten salt temperature variations during discharging (a) and charging (b) processes under different thermal conductivities of filler particle.

Contrary to previous studies, Vannerem, Neveu, and Falcoz (2021), through a numerical study, have shown that increasing the effective thermal conductivity means reducing the utilisation rate, favouring destratification and thus considerably reducing storage performance.

The effect of the thermal conductivity of the materials is not well understood, given the conclusions of the above studies. A more in-depth study of the effect of the thermal conductivity of the solid or fluid on the performance of the storage system should therefore be carried out to refine the choice of the best pairings (solid material or thermal fluid) in order to improve the performance of Dual Media Thermocline storage systems.

4.3.3.2 . Effect of the heat capacity of the fluid and the solid

Just as the thermal conductivity of the materials has an impact on the performance of the storage system, so the thermal capacity or specific heat also has an effect. Aly and El-Sharkaw (1990) have examined how the properties of the storage substrate affect the thermal behaviour of packed systems during charging. The results showed that increasing the specific heat resulted in a significant improvement in the charging rate and an increase in the storage capacity of the packing bed, while reducing the rate at which the temperature of the solid rose. The influence of this parameter has also been demonstrated numerically by Wang et al. (2020). They observed that increasing the specific heat of the particle led to a total increase in discharge and charge time, with a simultaneous decrease in the thickness of the thermocline. However, they also noticed that the high value of this parameter causes high mechanical stress. Therefore, a higher specific heat of the particle can lead to an improvement in thermal performance, but at the same time an increase in the maximum mechanical stress of the wall. In addition, Rodrigues and De Lemos (2020), mentioned the influence of the ratio of the specific heat of the solid and that of the fluid on the performance when charging a TES. A high value of this ratio with a high Reynolds number increases the efficiency of the storage.

From the above, we can see that the influence of specific heat is closely linked to the mass flow rate or speed of the fluid, creating a trade-off between an increase in thermal storage capacity and an increase in mechanical stress. Therefore, to efficiently store and remove heat in a packed tank, a high specific heat of the solid materials compared to that of the fluid would be an advantage.

5. Conclusion

A review of the literature shows that there is a lack of experimental data on the effect of operating and geometric parameters on the performance of dual media storage systems. However, there are many numerical studies on the impact of these parameters. All these experimental and numerical studies have allowed some conclusions to be drawn:

• Cylindrical tanks (tall and narrow for laboratory or pilot scale applications, short and wide for industrial scale) are the most widely used and are more efficient than truncated cone and horizontal rectangular tanks.

• Better storage efficiency is achieved with very small spherical particles and better thermal insulation of the system, especially on a laboratory and pilot scale.

• A porosity of less than 0.2 improves the efficiency of solid/gas systems, while a high porosity has no significant effect on solid/liquid systems.

• There is still some incoherence about the effect of operating temperature or temperature difference on storage performance. Similarly, there is a contradictory prediction of the effect of fluid speed, despite some authors suggesting the existence of an optimum fluid velocity.

• The effect of fluid distribution is very significant in single medium thermocline storage systems and less noticeable in dual media thermocline systems due to the packing, which homogenises fluid circulation for fluid collection and injection, whatever the type of diffuser.

• Judicious selection of threshold temperatures in a flexible way minimises the effect of cycling on the behaviour of the storage system.

• There is some controversy about the impact of thermal conductivity and this shows that the effect of this phenomenon on performance is not well understood. A more in-depth study of the effect of this parameter on the performance of the storage system is therefore required.

• The effect of thermal capacity or specific heat on system performance is closely linked to the mass flow rate or fluid velocity and there is a trade-off between thermal storage capacity and the mechanical stresses generated.

The dual media thermocline storage system is undoubtedly a promising alternative for reducing the cost of storage systems and making CSP attractive and accessible to developing countries. A better understanding of this system is therefore necessary to increase its maturity in thermodynamic solar power plants. It is very important that, in the future, we focus on the compensatory effects of the various geometric and operational parameters through meticulous numerical studies validated by experimental studies in order to determine the optimum values of the parameters for improved efficiency of the dual media thermocline storage system. The compensatory effects of criteria such as porosity and fluid velocity; temperature difference and heat capacity of the fluid or solid; fluid velocity and variation in thermal conductivity or heat capacity; reservoir height and variation in thermal conductivity or heat capacity; particle diameter and thermal conductivity or heat capacity; porosity and temperature difference, etc. should be taken into account in future studies to better understand the phenomena that govern and act on the performance of the dual-media thermocline system.

Disclosure statement

No potential conflict of interest was reported by the author(s).