Tank Temperature Research Articles

Thermo-economic analysis on trans-critical compressed CO2 energy storage system integrated with the waste heat of liquid-cooled data center

Compressed CO2 energy storage (CCES) technology has the advantages of high energy storage density, low economic cost, low carbon emission, which is suitable for the construction of large-scale and long-time energy storage system. Besides, as a scene with massive heat, the electricity consumption of servers in data center is mostly converted into heat. Thus, the purpose of this work is to integrate a trans-critical compressed CO2 energy storage system with the waste heat of data centers, so as to improve the system performance and reduce the operating cost of data center. Based on different operating principles of compressors, a single-stage compression system (System-CP) and a double-stage compression system (System-VP) are constructed. To analyze and compare the energy and exergy performance of these two systems under design conditions, a quasi-dynamic model is developed by considering the variations of pressure and temperature in the storage tank. On this basis, an economic model is developed to obtain the economy performance for the systems. The obtained results show that the round-trip efficiency (RTE) of System-CP and System-VP are 64.67 % and 67.41 %, respectively. For the energy storage capacity 15 MW × 5 h, volumes of high-pressure S-CO2 storage tank are 314,387.51 m3 and 287,982.91 m3 for System-CP and System-VP, respectively. Thereby, the energy storage density (ESD) of System-CP and System-VP are 0.24 kW·h/m3 and 0.26 kW·h/m3, respectively. Meanwhile, the total capital cost (TCC) is $477.84 × 106 for System-CP, and $437.41 × 106 for System-VP, and the corresponding payback period (PBP) are 14.76 years and 12.39 years respectively. Further, the effect of key parameters on systems performance is revealed. The results show that with the decrease of slip-pressure range decreases, RTE, TCC and the volume of storage tanks increase linearly.

Waterborne novolac epoxy‐based thermal resistant and fire‐retardant thermal insulation coatings

AbstractWaterborne novolac epoxy based thermal resistant and fire‐retardant thermal insulation coatings were developed in this work. Novolac (phenolic) epoxy emulsion (PEE) was prepared by the phase inversion method based on formulation optimization by orthogonal array testing. The prepared emulsions have similar particle size, viscosity, and stability to commercial bisphenol a glycidyl ether epoxy emulsion (PZ). DSC results showed that the varnish film based on PEE had a higher glass transition temperature and initial thermal decomposition temperature compared with PZ cured by the same curing agent. Waterborne thermal insulation coating with PEE and PZ as binders and hollow glass microspheres (HGMs) as thermal insulation fillers were studied. The results indicated that the thermal conductivity of the coating decreased with an increase in HGMs content. Specifically, the thermal conductivity of the PEE coating containing 20 wt% HGMs is as low as 0.093 W/(m·K). It reduces the exterior temperature of the hot tank from approximately 200 °C to approximately 106 °C. Furthermore, the HGMs/PEE waterborne thermal insulation coating exhibits good thermal stability and flame retardance.

Legionella in Primary School Hot Water Systems from Two Municipalities in the Danish Capital Region.

Legionella contamination in public water systems poses significant health risks, particularly in schools where vulnerable populations, including children, regularly use these facilities. This study investigates the presence of Legionella in the hot water systems from 49 primary schools across two municipalities in the Danish capital region. Water samples were collected from taps in each school, and both first-flush and stabile temperature samples were analysed for Legionella contents. The findings revealed that 97% of schools in Municipality 1 and 100% in Municipality 2 had Legionella in their hot water systems. The content of Legionella colonies was significantly higher in schools in Municipality 1, which was probably because of overall lower water temperatures. At stabile temperatures, 76% and 50% of the schools in the two municipalities exceeded the European Union's recommended limit of 1000 CFU/L. Stabile peripheral water temperatures were achieved after 3 min. Tap water temperatures above 54 °C and central tank temperatures above 59 °C were associated with Legionella contents below 1000 CFU/L. This study highlights the need for more stringent Legionella control procedures in schools, including higher water temperatures and refining Legionella reducing interventions with the addition of regular flow and draining procedures.

Application of PVT Coupled Solar Heat Pump System in the Renovation of Existing Campus Buildings

A photovoltaic thermal panel (PV/T) is an integrated module that harnesses both photovoltaic and solar thermal technologies to convert solar energy into electricity and heat, thereby enhancing overall energy efficiency. This paper aims to explore the suitability of PV/T solar heat pump systems across various climate zones and assess their potential for widespread application. By analyzing the operating principles of an indirect expansion PV/T solar heat pump system in conjunction with the climate characteristics of different regions, MATLAB R2019b/Simulink software was employed to evaluate the photoelectric performance of PV and PV/T systems in representative cities across five distinct climate zones in China during typical winter days. Key metrics, such as power generation, hot water storage tank temperature, indoor temperature, and system COP, were chosen to assess the heating performance of the PV/T solar heat pump system. The findings indicate that the winter ambient temperature significantly affects the photoelectric efficiency of both the PV and PV/T systems. While higher latitudes with lower ambient temperatures yield greater photoelectric efficiency, the southern regions exhibit higher power generation during winter. The winter heating effectiveness of the PV/T solar heat pump system is mainly influenced by indoor and water tank temperatures, with Harbin’s system performing the poorest and failing to meet heating demands, whereas Nanjing’s system shows the best results.

دراسة عملية لاداء سخان ماء شمسي ذو الدوران الطبيعي المتصل على التوالي

This research paper presents an experimental study on the performance of a natural circulation solar water heater system with two typical collectors connected in series. The paper provides a comprehensive analysis of the system's thermal performance under different load conditions, including no-load, intermittent, and continuous load. Mean storage tank, solar collector means plate (the left) temperature and thermosyphon flow rate in a vertical tank were measured. Results showed that there was variation in solar water tank and collector plate temperature under load and no-load conditions. Analysis of thermal performance of the system was conducted for each condition. The highest plate temperature (100 ˚C or even more) with no circulation of both collector and load conditions, indicate the high quality of the solar collectors even during the cold season. The collector’s arrangement in series connection is of highest gain in energy and higher storage tank mean water temperature. Several characteristic equations obtained to represent the performance of the present natural circulation system under collector connection arrangement in series. In fact, when large amount of hot water was required for a certain purpose (Industrial sector for example - MSF plant or central heating), multiple collectors are to be deployed in series and in parallel to produce the required amount (quantity) and desired temperature (quality) at the same time. Key words: Thermosyphon solar water heater, storage tank profile temperature, Solar Water Heaters (SWHs), instantaneous efficiency, collector flow factor, collector efficiency factor, collector heat removal factor

Enhanced temperature regulation in compound heating systems: Leveraging guided policy search and model predictive control

With the widespread application of solar-energy-air-source heat pump composite heating, optimizing the regulation of air temperature in heating zones, enhancing system thermal comfort, and reducing energy consumption have become crucial. To ensure residential comfort while minimizing HVAC system energy costs, a control method combining guided policy search (GPS) with model predictive control (MPC) is proposed for composite heating systems. This method replaces state estimation in MPC with policy search and substitutes the offline trajectory optimization used in guided policy search with MPC, thus integrating the strengths of both approaches. This strategy not only improves control precision but also reduces energy consumption and enhances system robustness. The GPS-MPC control algorithm was validated against reinforcement learning and MPC. A simulation model was developed and validated on a real physical platform. Simulations compared the control effects of on-off control and MPC on pump frequency, flow rate, stratified thermal storage tank temperature, component, and system energy consumption. The data results indicate that the GPS-MPC algorithm offers superior predictive accuracy, efficiency, and robustness in composite heating control systems compared to conventional methods. Under the GPS-MPC strategy, indoor temperature fluctuations, pump frequency response speed, and energy consumption were significantly improved, with temperature fluctuation limited to only 0.8 °C, and the system achieving energy savings of over 12 %.

Energy, economic and environmental analysis of a photovoltaic-thermal integrated dual-source heat pump system under a system coefficient of performance − based switching strategy

The photovoltaic-thermal integrated dual-source heat pump system can offer performance improvement by addressing the limitations of a single heat pump system, which not only improves energy efficiency and system performance but also reduces pollutant emissions. However, the operational performance of the system is significantly affected by different switching strategies between two heat sources, which has not been given adequate attention from researchers. Therefore, this study introduced a system coefficient of performance − based switching strategy, which can alternate between air-source heat pump and solar water heat pump modes to make full use of air and solar energy, to optimize the operation of the photovoltaic-thermal integrated dual-source heat pump system and compare with the conventional water temperature of the heat storage tank − based switching strategy. A TRNSYS model of the system was developed and validated, and the simulated results demonstrated the better performance of system coefficient of performance − based switching strategy in energy, economic and environmental perspectives. The average photoelectric and photothermal conversion efficiency under system coefficient of performance − based switching strategy were higher than those under water temperature of the heat storage tank − based switching strategy by 1.1 % and 4.0 %, respectively, with average modified coefficient of performance of 7.43 and 6.55. Furthermore, the system not only achieved savings of 5.63 % in annual electrical cost and 5.33 % in yearly operational cost but also reduced standard coal by 19.25 kg and total pollutant emissions by 242.55 kg per year under system coefficient of performance − based switching strategy, compared to water temperature of the heat storage tank − based switching strategy.

Transient modeling of stratified thermal storage tanks: Comparison of 1D models and the Advanced Flowrate Distribution method

Thermal energy storage (TES) is one of the key technologies for enabling a higher deployment of renewable energy. In this context, the present study analyzes the modeling strategies of one of the most common TES systems: stratified thermal storage tanks. These systems are essential to many solar thermal installations and heat pumps, among other clean energy technologies. Three different one-dimensional tank models are compared by their computing speed and resilience to long time steps. Two of the models analyzed are numerical, one being explicit and the other one implicit, and the other is analytical. The models are validated against data from experiments carried out considering small-scale stratified tanks, showing that their performance can be improved by using the Advanced Flowrate Distribution (AFD) method. The results show that the analytical model maintains its accuracy with longer time steps and is robust against divergence. Conversely, the numerical models show equivalent performance for short time steps, while the computation time is reduced. Although the AFD method shows promising results by achieving an improvement of 43% in terms of Dynamic Time Warping, its parameter optimization must be generalized for different tank designs, flow rates, and temperatures.

Off-design operation and performance of pumped thermal energy storage

In this article, we describe off-design models and control strategies for a Pumped Thermal Energy Storage (PTES) system that uses liquid thermal energy storage: specifically molten salt for hot storage and methanol for cold storage. Off-design conditions arise when load-following, or due to variations in storage tank temperatures or ambient temperatures. We propose a control strategy that uses inventory control to manage the mass flow rate in the thermodynamic cycles, which facilitates load following. We also propose a control strategy for the storage fluid mass flow rates, which are varied to ensure the molten salt is maintained at its design temperature. This maximizes efficiency and minimizes problems with salt freezing or degradation. The cold storage fluid mass flow rate is varied so that the cold tanks have the same state-of-charge as the hot tanks. This leads to variations in cold fluid temperature, but these variations are shown to be acceptably small (e.g. 7.5 % increase), and this control method is shown to be simpler and more efficient than an alternative strategy where tanks become unbalanced. The ambient temperature and storage tank temperatures are moved ±50 °C from the design values and the impact on power, duration, and tank temperatures is quantified. Results demonstrate that the proposed control strategy is stable and self-correcting – that is, storage temperatures converge on stable values after two-to-three charge-discharge cycles. When inputs return to design values, the system returns to its design point after two charge-discharge cycles. We also demonstrate that inventory control enables delivery of the target power output even when off-design conditions exist that would normally reduce the power output.

Dynamic modelling and optimal operation of the photovoltaic/thermal

This paper aims to introduce a dynamic model for a photovoltaic/thermal system, highlighting an approach and synthesis of existing dynamic models to depict the full photovoltaic/thermal system. The model was validated using data from an experimental setup at the Institute of Energy Technology, Faculty of Energy Technology, University of Maribor, under different weather conditions. The model's accuracy was assessed through normalized Root Mean Square Error, normalized Mean Bias Error, Correlation Coefficient, and the coefficient of determination error metrics, focusing on the temperature and electrical output power of the photovoltaic/thermal modules, as well as the temperature of the thermal energy storage tank. Furthermore, the paper also focuses on the optimal operation of the photovoltaic/thermal system under different mass flow rates of the working medium.

Experimental investigation on dynamic thermal storage and extraction performance of seasonal thermal storage

The initial investment for a buried pipe system using soil as a seasonal thermal storage medium is costly and not suitable for small rural buildings. To promote the cost-effective heating in rural areas, this study proposes a novel seasonal thermal storage system utilizing water and soil as thermal storage medium with copper rods to enhance thermal transfer between water tank and the surrounding soil. An experimental platform was established to discuss the temperature variation characteristics and investigate the thermal performance under different operating modes and experimental parameters. The results show that the temperature of the soil without copper rods is linearly related to the depth, while the highest temperature at the end of the copper rods occurs at the middle depth. The soil with short copper rods exhibits the most rapid thermal storage response and a relatively shorter thermal extraction response time. Intermittent operation can significantly enhance the thermal extraction rate and outlet temperature of the thermal storage unit, whereas the energy storage efficiency decreases with the extension of the downtime. The soil contribution rate of the thermal storage unit is influenced by the operational duration, initial temperature of the water tank and outdoor ambient temperature.

Definition of a PVT coupled water source heat pump system through optimization of individual components

Exploiting renewable resources considering their discontinuity compared to building needs, necessitates energy system designs that simultaneously maximize generation and storage performance in different seasons. This article presents the optimization of RESHeat European project, concerning a high-performance system which combines water-source heat pump, cooled photovoltaic panels and thermal storage. The research regards the Italian demo site, near Rome, to define a solution for Mediterranean regions which alongside the requirement for heating have notable need for summer cooling. The targets are system's efficiency, with a minimum sCOP of 5, and a minimum 70 % coverage from renewable sources focusing ambient temperature management.A dynamic model of plant and building was used for parametric analysis, which covered separately heating and cooling modes, involving significant parameters: operating temperatures of the heat pump, number of strings comprising the photovoltaic array, volume of the buffer tank connecting PVTs and WSHP and setpoint temperature of a cooler added for tank temperature control in cooling. 184 alternative configurations were evaluated by Multi-Criteria Decision Making (MCDM) method based on energy, economic and logistic criteria, and weighted by five indices. The optimal system includes 15 PVT panels strings for 25 kWp, a 3 m³ storage tank and cooling setpoint temperature of 25 °C.

Modelling and performance evaluation of a parabolic trough solar water heating system in various weather conditions in South Africa

In recent years, various energy sources and methods have been used to heat water in domestic and commercial buildings. Water heating methods for large households or commercial buildings include electrical heating elements, gas heaters, and solar energy (solar concentrators, flat plate collectors, evacuated tube collectors, etc.). In recent decades, the focus of water heating has shifted to solar energy, which is abundantly available in most African countries. The weather condition of a region has a huge impact on the system's performance. South Africa is characterised by four different weather seasons (winter, spring, summer, and autumn), unlike most African countries. Therefore, this study focuses on the impact of weather seasons on the system's performance for water heating through the combined use of solar energy and solar concentrator techniques. The system performance was modelled by using Matlab Simulink®, where historical weather data for Pretoria, South Africa, was fed into the model. Based on the weather data input, the system behaviour varied per season due to the change in solar intensity. The average outlet temperatures of the absorber, in the order of magnitude, were 333, 332, 328, and 325 K during the autumn, summer, spring, and winter seasons, respectively. Similarly, the average storage tank temperatures, in the order of magnitude, were 366, 364, 363, and 360 K in spring, summer, autumn, and winter, respectively. From this study, it is concluded that the different weather seasons in South Africa, have a direct impact on the performance of the system. Irrespective of the season, the system produced the required volume of hot water required throughout the year.

Thermo-economic analysis of a pumped thermal energy storage combining cooling, heating and power system coupled with photovoltaic thermal collector: Exploration of low-grade thermal energy storage

As renewable energy penetration grows, traditional power systems face significant challenges due to their intermittency and volatility. Pumped thermal energy storage (PTES) is a potential energy storage technology that has a low specific cost and geographical restriction. In this paper, a PTES system which is coupled with solar photovoltaic thermal (PVT) collectors is proposed to satisfy the demand for cooling, heating and electricity supply, and achieve energy cascade utilization. An ejector refrigeration cycle and the turbine extraction heating are accompanied with a PTES system. Thermodynamic analysis of the system is performed by evaluating the influence of key parameters on system performances for 1 MW power output. The economic analysis adopted levelized cost of energy storage (LCOS), which mainly includes investment costs, operation and maintenance costs and system depreciation. The results show that the maximum amplification of roundtrip efficiency with PVT is 12.04 % compared to the system without PVT. Moreover, the maximum average power generation benefit of PVT is 4.85 %. The increase in cold energy storage tank temperature can effectively improve the roundtrip efficiency of the system. The lower cold energy storage tank temperature and higher hot energy storage tank temperature have a negative impact on system thermal efficiency (ηthermal) but benefits for LCOS. Multi-objective optimization is carried out to obtain the optimal design performance that ηthermal and LCOS are 51.06 % and 0.533$/kWh respectively.

A hybrid solar-driven membrane distillation-assisted liquid desiccant air conditioning system: Mathematical modeling and feasibility analysis

Membrane distillation (MD) is a promising method for liquid desiccant (LD) regeneration as it can mitigate LD carryover and produce freshwater as a by-product. Previous research on MD regeneration was mainly focused on performance evaluation and optimization of the regenerator itself. This paper proposed a hybrid solar-driven direct contact MD (DCMD) regeneration-assisted liquid desiccant air conditioning (LDAC) system for air dehumidification, cooling, and freshwater production. A mathematical model for the DCMD regenerator was first developed by considering both temperature and concentration polarizations. This model was validated against the experimental data in terms of the outlet channel temperature and LD solution concentration in the feed tank with relative deviations of ± 9.8 % and ± 0.5 %, respectively. The DCMD model was further integrated into an LDAC system with a batch-wise operation. To investigate the technical feasibility of the proposed system, a one-week simulation was conducted in a residential house during summer in a tropical climate area of Australia. The results showed that the latent heat load was effectively removed from the process air and the regenerated liquid desiccant solution can meet the dehumidification requirement with a concentration over 30.0 wt%. The dehumidification rate and regeneration rate were at 0.49–1.25 kg/h and 0.95–4.25 kg/h, respectively. Solar energy contributed to 52 %-78 % of the total system thermal energy consumption. Furthermore, this system can produce 11.0–12.8 kg of water daily.

An innovative variable flow control strategy and system performance analysis of a solar collector field

The dynamic changes in the environmental variables and the fluctuation characteristics of the thermal storage temperature have notable influences on the efficiency of solar collector fields. In addition, the optimal flow rate of solar collector fields varies under different combinations of variables and depends primarily on the collector scale and connection form. On this basis, it is imperative to carefully and comprehensively determine and adjust the optimal operating flow rate, considering the specific characteristics of the employed solar collector field under diverse variable combinations. To address this, this study proposes and develops a variable flow control strategy for solar collector fields based on maximizing net income. The presented strategy adjusts the operation flow according to environmental variables and the thermal storage tank temperature. The control principle of the proposed strategy and the corresponding method of obtaining the optimal flow are described. Based on this principle, the optimal flow optimization model is established, and the polynomial function of the optimal flow value is obtained by regression. Using the developed model, several conventional control methods are defined and simulated, and an analysis is performed to compare the collector’s performance under different scenarios. The results indicated that the variable flow control strategy proposed in this study can significantly improve the economic feasibility of solar collector fields. A 100 m2 series–parallel flat-plate solar collector field is considered as an example, and the proposed variable flow control strategy is implemented. As a result, a notable increase in the net income is reported compared to other conventional operation strategies, ranging from 6.70 % to 14.04 % in three different regions, namely Lhasa, Yinchuan, and Xi’an.

Enhancing the performance of parabolic trough solar collectors: Cost-effective innovative designs for sustainable energy harvesting

This study aims to improve the performance and stability of parabolic trough solar collectors (PTSC), especially those with heat storage capacity. Three different receiver tube designs have been meticulously developed to achieve this goal. As a result of the research, the Black surface (BS) -PTSC and PTSC- Paraffin wax (PW) systems achieved 26.5% and 56.8% more thermal energy flow, respectively, compared to the conventional PTSC. In addition, while the average thermal efficiencies of the PTSC, BS-PTSC, and PTSC-PW systems were found to be 11.2%, 14.1%, and 16.9%, respectively, the average exergy efficiencies of the PTSC, BS-PTSC, and PTSC-PW were 1.4%, 1.9%, and 2.3%. Painting the black copper pipe and filling the receiver tube with paraffin wax PCM increased thermal and exergy efficiency. Besides, comparing the temperature differences based on the PTSC system, it was found that BS-PTSC and PTSC-PW systems have 12.3% and 16.4% higher tank temperatures, respectively. The findings of this research have demonstrated the potential of parabolic trough solar collectors equipped with heat storage. It has also increased the sustainability index in terms of sustainability and reduced CO2 emissions into the atmosphere. Furthermore, it has been shown that these simple and inexpensive designs, without significant modifications to the system, can achieve high thermal performance without unnecessary expensive components.

TdT: A tool for building thermal systems analysis and comparison

This work describes the tool “Towards Dynamic Thermoeconomics” (TdT), which has been designed to analyse the thermal systems of buildings from a dynamic point of view for further thermoeconomic analysis, since HVAC systems consume a significant part of the global energy and have a significant environmental impact. TdT is presented as a versatile, open-source application developed in Python, which provides dynamic energy and exergy performances of components, as well as the most vulnerable points in the system to be optimised. As a novelty TdT introduces a new methodology for analysing inertial systems that defines non-periodic time intervals in which the tank temperature is Ttank,rep, thus avoiding misleading cost results. Two case studies are presented as examples of typical applications: a domestic hot water system and a heating system, analysed with TdT in eight different climatic locations in Spain. The corresponding results are extracted and analysed, with a particular focus on the influence of the outdoor temperature (T0) on both the exergy and energy efficiency of the components, the identification of irreversibilities and the total exergy consumption. It becomes evident that as the T0 increases by 38 %, the exergy efficiency of the boiler decreases in both systems, with an average yearly exergy efficiency decrease of 1.4 % on the DHW system. Furthermore, the boiler is the component with the highest irreversibilities, followed by the inertial and distribution components, information that could not be obtained from energy analysis. Ultimately, the TdT provides valuable insights and a novel methodology for analysing inertial components, which will improve the efficiency and sustainability of building thermal systems.

Sensitivity analysis and calibration for a two-dimensional state-space model of metal hydride storage tanks based on experimental data

In this paper, a state-space model of a metal hydride tank is formulated and analyzed in detail. Firstly, a three-dimensional state-space model of the metal hydride tank is simplified by assuming that the tank temperature can be measured. Secondly, the model is completed with a pipe model, which allows to compute the input flow from the pipe pressure that can be easily measured. The proposed model solves the problem that the conventional metal hydride tank models usually take the mass flow rate as input and ignore the pressure as system input. Thirdly, the first-order trajectory sensitivity analysis method is adopted to determine the sensitivity of selected unknown parameters. Latter, the particle swarm optimization algorithm is used to estimate the unknown model parameters from experimental data. Finally, a comparison between experimental data and simulation results demonstrates that the proposed model can reflect the dynamic characteristics of the metal hydride tank.

Study of Condensation during Direct Contact between Steam and Water in Pressure-Relief Tank

Direct contact condensation (DCC) is a phenomenon observed when steam interacts with subcooled water, exhibiting higher heat and mass transfer rates compared to wall condensation. It has garnered significant interest across industries such as nuclear, chemical, and power due to its advantageous characteristics. In the context of pressure-relief tanks, understanding and optimizing the DCC process are critical for safety and efficiency. The efficiency of pressure-relief tanks depends on the amount of steam condensed per unit of time, which directly affects their operational parameters and design. This study focuses on investigating the direct gas–liquid contact condensation process in pressure-relief tanks using computational fluid dynamics (CFD). Through experimental validation and a sensitivity analysis, the study provides insights into the influence of inlet steam parameters and basin temperature on the steam plume characteristics. Furthermore, steady-state and transient calculation models are developed to simulate the behaviour of the pressure-relief tank, providing valuable data for safety analysis and design optimization. There is a relatively high-pressure area in the upper part of the bubble hole of the pressure-relief tube, and the value increases as it is closer to the holes. The steam velocity in the bubbling hole near the 90° elbow position is higher. This study contributes to the understanding of steam condensation dynamics in pressure-relief tanks. When the steam emission and pressure are fixed, the equilibrium temperature increases linearly as the initial temperature increases (where a = 1, b = 20 in y = a x+ b correlation), the equilibrium pressure increases nearly exponentially, and the equilibrium gas volume decreases. When the steam emission and initial temperature are fixed, the equilibrium temperature does not change as the steam discharge pressure increases. The correlations between the predicted equilibrium parameters and the inlet steam parameters and tank temperature provide valuable insights for optimizing a pressure-relief tank design and improving the operational safety in diverse industrial contexts.