Experimental data analysis and dimensionless exergy levels in a commercial stratified thermal storage

The continuously rising demand for renewable energy sources within the energy system has highlighted the need for technologies capable of mitigating the impact of renewable energy intermittency and addressing the generation-demand mismatch in the system. Thermal energy storage (TES) emerges as a versatile storage medium with a wide range of applications, spanning from solar energy utilization and power peak shaving to the storage of industrial waste heat. In this study, data collected from an operating commercial stratified tank are used to validate a 2-D axisymmetric CFD model. Temperature profiles are collected throughout one month with a one-minute refresh rate. The model replicating the tank is generated in COMSOL Multiphysics® and validated by emulating the registered charging phases of the real storage. The model is then employed to optimize the stratification capability of the tank, by varying the logics applied to pinpoint optimal values of both inlet water temperature and velocity. The study aims to maximize the exergetic efficiency of the system using dimensionless exergy, a parameter often utilized in literature to identify the ability of the storage to generate and preserve optimal temperature stratification. Finally, the experimental dimensionless exergy has been evaluated for the aforementioned temperature profiles.


Introduction
The escalating energy requirements resulting from industrialization and population expansion have spurred a global drive towards clean, dependable, cost-effective, and sustainable energy alternatives.It is widely acknowledged that energy holds the key to addressing numerous contemporary challenges and unlocking new prospects.The United Nations underscores the significance of ensuring universal availability of these energy resources.Among the array of renewable energy sources, solar power emerges as the most promising, owing to its extensive potential and versatility.However, the intermittent nature of solar energy can give rise to a discrepancy between energy supply and demand, necessitating the integration of solar energy storage systems.These storage systems play a pivotal role in various sectors, including power generation fields such as solar thermal, geothermal, and nuclear power plants.
Thermal energy storage (TES) systems, which rely on renewable thermal energy sources, represent a cost-effective and robust solution for large-scale applications.Recent advancements in materials have sparked a revolution in TES technologies [1].TES typically involve the storage of thermal energy through the modification of a material's temperature (sensible heat) or the phase transition of a substance (latent heat), or a combination of both, resulting in hybrid TES technology that caters to a broader operating range [2].Sensible thermal energy systems (STES) have gained popularity and commercial viability as TES methods due to their relative affordability and ease of operation and maintenance.STES utilizes heat transfer fluids that exhibit stability at high temperatures, and its effectiveness relies on several factors [3].Stratified sensible TES (SSTES) has emerged as one of the most extensively studied sensible thermal energy storage methods over the past four decades, primarily due to its ability to reduce the overall setup cost and enable cost-effective power generation [4][5][6][7].Moreover, the simplicity of this technology allows for efficient scalability to meet a wide range of power requirements, making it a preferred choice over alternative approaches such as the two-tank method [8].Several numerical studies have been conducted on SSTES.Ievers and Lin [9] have investigated the flow dynamics using 3-D CFD models of storages with several geometrical aspect ratios.Kocijel et al. [10] numerically tested the influence of various geometrical and process parameters on the stratification capabilities of the storage.Nevertheless, several more or less accurate models have been developed using the finite differences method [11][12][13].A great number of numerical studies have been validated on experimental data, but the vast majority of said studies have resorted to modelling and simulating an in-house experimental setup, thus under finely controlled testing conditions.However, the literature is lacking when it comes to models related to storages implemented into industrial systems and working under real load conditions.
In this study, dimensionless exergy  * is evaluated for an experimental stratified thermal energy storage using pure water as a fluid working in a real industrial application.Subsequently, a 2-D axisymmetric CFD model has been generated in COMSOL Multiphysics® and validated by comparing numerical and experimental data of various charging phases of the system.The model has then been deployed to numerically test the tank under different realistic loading conditions to assess the capability to restrain its stratification under more severe boundary conditions.

Stratified thermal storage 2.1. Layout of the system
This study has been conducted using as a reference a Stratified Thermal Energy Storage (STES) utilized as a buffer tank in an industrial solar water-heating system located in Switzerland.The system is mainly formed of four parts: the production circuit, the thermal block, the storage circuit, and the consumption circuit.The production circuit consists of ten rows of High-Vacuum Flat Plate Collectors (HVFPC) connected in series, for a total of 96 solar units.The model of HVFPC is MT-Power v4 SK, manufactured by TVP Solar.In the production circuit flows a 30% mixture of water and glycol.
The storage circuit is a short loop, receiving thermal energy from the production circuit using a flat plate heat exchanger, as schematized in Figure 1.Thus, the fluid utilized in this loop differs from the one used in the production section of the system by being pure water.The pump that feeds the circuit (Calpeda TM-65E) works under inverter and has a maximal flow rate of 4.2  3 /ℎ.The flow rate is measured using an IFM SV8150 vortex flowmeter.Two thermocouples, model Endress+Hauser Easytemp® TMR31, are placed at the inlet and outlet section of the heat exchanger.Given the short length of the pipe leading to the tank, it is reasonable to assume the absence of heat losses in this trait, therefore assuming the latter as the inlet temperature of the storage.The STES utilized in the system is produced by Jenni Energietechnik AG and has a total capacity of 25030 .It is a cylindrical vertical storage with a radius of 2.60  and a height of 5.10  from the base.The storage is realized in stainless steel, while the isolation is provided by using a   The tank utilizes two identical diffusers for both the inlet and the outlet section, placed specularly.The diffuser is a large cylinder measuring 280  in diameter and 450  in height, and it is characterized by the presence of annular bulges on the sides, as displayed in Figure 3.The fluid enters the diffusers from a horizontal pipe with a diameter of 50  that splits into a T-shaped section with a diameter of 65 .
To not disclose information regarding the internal energy management of the company, the consumption circuit will not be displayed.Thus, the charging phases will be the only ones analysed in this study.

Dimensionless Exergy
To quantify the thermal stratification of the fluid in the thermal storage, a lot of approaches has been proposed in literature.Consul et al. [14] proposed a parameter called dimensionless exergy  * and defined as: where, for a given set of initial conditions, Ξ  , Ξ  , and Ξ  are the instantaneous exergies of the experimental storage, a fully stratified equivalent, and a fully mixed equivalent, respectively.The instantaneous exergy can be defined as follows: where the specific exergy  is obtained from Equation (3), when neglecting kinetic and potential contributions.
The reference temperature chosen for this analysis is 273.15  to have a realistic ambient temperature reference while also being always lower than the temperatures reached by the storage fluid at any point.In this study, dimensionless exergy has been deployed to evaluate the resilience of the tank in maintaining its internal stratification under various inlet conditions related to real charging phases.

Mathematical model
The two-dimensional axisymmetric fluid dynamics of the tank is described by the Navier-Stokes equations, coupled with the Boussinesq assumption, and written in cylindrical coordinates along the radius  and the height : (7)

CFD Model
Both the computational domain and the meshing were realized using the CAD Module of COMSOL MultiPhysics ® , and the simulations were carried out using the same software.The model has been built as a 3-D representation, then a 2-D reduction was obtained using cut-plane properties.While the external shell of the storage is transposed into a computational domain with no modification, the diffuser had to be slightly modified for the axisymmetric to be verified.Indeed, the T-shaped tube at the end of the inlet and outlet sections could not be maintained in the 2-D transposition, thus needing to be modified into an axisymmetric circular section, while maintaining the overall area for the fluid to flow through.The domain has been divided into five subdomains.Since the temperature values observable in the data are largely discretized and lack further details, each volume is initially ( = 0) set to the temperature  ,0 measured by the thermocouple at the start of the simulated charging phase.The turbulent flow is numerically approached using a RANS method, with a standard - model.In fact, given the absence of flow separation and adverse pressure gradients, said model was chosen for its robustness and lower computational burden.The velocity scale parameter is set to 1 / and the length scale factor is 0.035.The time-dependent solver deployed was based on AMG (Algebraic Multigrid) method.
Table 1.Summary of the boundary conditions and initial conditions applied to the model.The boundary and initial conditions applied are summarized in Table 1.Considering that the charging phases simulated occupied short periods, averaging at around one hour per phase, the conduction along the walls was neglected to not burden the computational time needed.Therefore, both the external walls and the diffuser walls are set to adiabatic.The inlet temperature of the water is set as a time-dependent boundary condition, to reflect the actual temperature of input of the fluid.Since the volume flow at the inlet section is nearly stationary, a single value of inlet velocity was imposed.For the validation phase, given the average volume flow rate of 3  3 /ℎ and an inlet section of 7.85 • 10 −3  2 , the inlet velocity of the fluid was set to 0.42 /.

Boundary
In the validation phase, the time simulated per charge phase has been set to one hour.The applied time step was 30 .Initially, the fluid in the storage is supposed to not have residual kinetical energy, thus being still.An initial temperature  ,0 is set for each node, without the presence of gradients.Nonetheless, it must be noted that COMSOL automatically generates small gradients between the various bodies of fluid at different temperatures within the first minutes of simulated time to stabilize the simulation.Said gradients could be slightly overestimated, but the discretized experimental data do not allow for a more thorough investigation.

Validation
The model was validated by simulating three real charging phases and comparing the results, as shown in Figure 4.The discriminating factor in the choice of the charging phases has been to select those which were followed by a steep decline of the  * , thus selecting three case studies related to portions of charging phases occurred on December 6 th , 2022, December 20 th , 2022, and January 7 th , 2023, which will be subsequently referred to as Charge Phase 1, Charge Phase 2, and Charge Phase 3, respectively.The model proves to be capable of predicting the actual evolution of the temperature layers in the tank in all the scenarios analysed.The maximum deviation registered between field data and numerical results equals to 2.05°C and can be attributed to slight inaccuracies in the definition of the initial conditions in the model, inherently dependent on the coarse distribution of the thermocouples and, therefore, of the acquired data.Nonetheless, the fit is precise in most of the cases and the model can be considered validated.

Case studies
Charge Phase 1 has been adopted as a case study baseline.The temperature distribution inside the tank (i.e., the initial conditions) has been kept unchanged.Four case studies have been analysed to assess the behaviour of the storage when charged at different inlet temperatures (Figure 5a).The temperature at which the water enters the STES has been varied with a step of 15  between 318  and 363 , the latter being the operating temperature limit of the physical storage.In all the case studies the length of the charging phase has been set to two hours and the volumetric flow entering the tank is   = 3  3 /ℎ.The case with an average inlet temperature of 318  emulates a scenario in which the storage circuit pump activates once the field temperatures are barely higher than the ones registered at the bottom of the tank.This case is the only one presenting a positive slope of the dimensionless exergy during the initial period of charge.It must be noted that, while the overall quantity of thermal energy stored in the tank is still barely increasing, the overall time length of the charging phase plays a major role.In fact, as the duration of the charging phase increases, the volume of cold fluid (at a lower temperature than the inlet temperature) in the tank will be exhausted and fully replaced by a volume of water at the inlet temperature conditions.Conversely, given the geometrical position of the inlet, this volume of colder fluid has to cross the other volumes of hotter water on its path to the bottom of the tank, inevitably triggering phenomena such as thermal diffusion and heat exchange (Figure 6a).Therefore, for longer charging phases, this process would inevitably prompt a decrease in the overall exergy related to the storage fluid.The cases with higher inlet temperatures (  = 348  and   = 363 , respectively) show similar trends (Figure 6b).The dimensionless exergy value lowers at first, and then increases to higher values than the ones registered in the reference case (  = 333 ).The time at the inflection point appears to be inversely proportional to the temperature, thus manifesting earlier when the inlet temperatures rise.When varying the inlet velocity, a more regular pattern can be observed (Figure 5b).The volumetric flow of the fluid has been varied between 2  3 /ℎ and 5  3 /ℎ.Again, he initial temperature distribution in the STES is the one taken from the "Charge Phase 1" case.The inlet temperature is set to   = 333 .In each of the simulations, a total volume of 5  3 of water has been introduced in the storage and, as a result, the four charging phases have a different duration, ranging from one hour (case with   = 5  3 /ℎ) to two and a half hours (case with   = 2  3 /ℎ).A dimensionless time , as in Equation ( 8), has been employed to visually compare the results more clearly.
The dimensionless exergy shows an inverse proportionality to the volumetric flow registered at the inlet.This is a direct effect of the laminarization of the flow at lower velocity regimes, which causes a lower amount of fluid mixing.Nonetheless, it must be noted that the inlet velocity and the inlet temperature are strictly related under the given temperatures of the fluid flowing into the production circuit.Also, considering the negligible differences among the values of  * registered, all the inlet velocities imposed in the different cases appear to be in the operating range of the diffuser.In fact, with a slight exception for the 2  3 /ℎ case, all the curves collapse on very similar values when the objective volume of charge is reached ( = 1).

Conclusions
In this study, information gathered from an industrial stratified tank has been used to validate a 2-D axisymmetric CFD model, generated in COMSOL Multiphysics® to mirror the design of the storage, by replicating the documented charging stages of the real storage.Once validated, the model is utilized to parametrically test various charging phase inlet conditions, varying both the inlet temperature and the inlet velocity of the fluid to trace behavioral characteristics and pinpoint optimal solutions.The parametrical analysis conducted on the inlet temperature of the fluid did not evidence a very specific pattern.The temporal length of the charging phases appears to be a discriminating factor when evaluating optimal charging temperatures.The parametrical analysis of the inlet velocity of the fluid exhibits a more linear pattern, whereas lower velocities inevitably tend to result in a more refined stratification.Nonetheless, given the results obtained in the latter, plant logics that focus on the temperature as a control parameter rather than the inlet velocity can have a larger impact on obtaining optimal performances out of the thermal storage.

Figure 1 .
Figure 1.Layout of the system.
40th UIT International Heat Transfer Conference (UIT 2023) Journal of Physics: Conference Series 2685 (2024) 012005 IOP Publishing doi:10.1088/1742-6596/2685/1/0120053 250  thick layer of rock wool.The temperature of the storing fluid is measured at five different heights using the thermocouples model RTD PT100 Endress+Hauser, as shown in Figure 2.

Figure 2 .
Figure 2. Thermocouples position in the analyzed STES.Figure 3. Inlet and outlet diffusers' geometry.Image courtesy of Jenni Energietechnik AG.

Figure 3 .
Figure 2. Thermocouples position in the analyzed STES.Figure 3. Inlet and outlet diffusers' geometry.Image courtesy of Jenni Energietechnik AG.

Figure 4 .
Figure 4. Comparison between field-acquired data and numerical results for the validation of the model in the three charging phases used as case studies.

Figure 6 .
Figure 6.Temperature profiles at different time steps for   = 318 (a) and   = 348 (b).Arrows indicate the direction of convective heat transfer phenomena.
SSTES overcomes existing technological limitations and holds substantial potential in revolutionizing the solar energy landscape. 2