Multi-node Model Research Articles

A multi-node thermodynamic model on temperature-vacuum swing adsorption (TVSA) for carbon capture: Process design and performance analysis

The adsorption technology plays a significant role in the carbon capture domain for mitigating the CO2 emissions, whereas the heterogeneous character is presented in practical adsorption process. In this study, a multi-node thermodynamic model is established for temperature-vacuum swing adsorption (TVSA) considering the end non-uniform adsorption. It shows superior performance for the assessment of practical TVSA cycle compared with lumped model. Through the influence analysis of different operation parameters based on multi-node model, specific exergy consumption increases from 41.6 to 62.4 kJ/mol caused by simultaneous drop of heat consumption and lift of work consumption as feed pressure raises from 1.0 to 3.0 bar. Exergy efficiency ranges between 13.8 % and 15.0 % as CO2 concentration increases from 10 % to 20 %. However, those under ppm-level are below 0.86 %, presenting the higher exergy consumption but lower desorption capacity represented for direct air capture. The heat consumption of front half part of adsorption bed is 39.7 % higher than the latter one, proving the potential cascaded desorption of subzone heating is superior for reducing the energy consumption. Furthermore, exergy consumption is lifted due to enhancement of work consumption of vacuum pump as vacuum pressure reduces from 1.0 to 0.02 bar, resulting exergy efficiency drops from 19.6 % to 13.4 %.

Spatialized carbon-energy-water footprint of emerging coal chemical industry in China

Concerns about energy security have driven the launch of the emerging coal chemical industry (ECCI) across China. However, the resulting spatially explicit carbon–energy–water footprint remains unclear. This study aims to comprehensively identify the spatial heterogeneity, distribution, and transfer characteristics of the carbon–energy–water footprint of the ECCI in China. An original spatialized accounting method based on a multi-flow multi-node model is developed to address the difficulty that spatially integrating large amounts of spatial data for ECCI projects and their upstream coal mines and power plants. The results indicate that the provincial intensities of the carbon footprint, energy footprint, and water footprint varied by −13.4–43.6 %, −7.2–1.8 %, and −22.6–59.5 % relative to the national averages, respectively. The three intensity types have quite different spatial heterogeneities, always showing an impossible trinity of carbon reduction, energy saving, and water conservation at the provincial level. The total national carbon footprint, energy footprint, and water footprint reached 280.20 Mt CO2-eq, 5.35 EJ, and 1155.18 Mt, respectively, of which more than 90 % were centrally distributed in North China, Northwest China, and East China. Interprovincial coal transport and electricity transmission driven by the spatial mismatch between the upstream and downstream processes together led to the transfer of 10.35 Mt CO2-eq of carbon footprint, 68.72 PJ of energy footprint, and 100.92 Mt of water footprint, whereas their respective contributions significantly varied by footprint type. These results provide spatial-specific knowledge and insights for layout optimization and sustainability enhancement for the ECCI across the country.

Numerical Modeling and Experimental Validation of Heat Transfer Characteristics in Small PTCs with Nonevacuated Receivers

The development of small-sized parabolic trough collectors (PTCs) for processing heat production at medium temperatures (100–250 °C) represents an interesting approach to increase the utilization of solar thermal technologies in industrial applications. Thus, the development of simplified models to analyze and predict their performance under different operative and climatic conditions is crucial for evaluating the application potential of this low-cost technology. In this paper, we present a numerical method that by combining three-dimensional finite element simulations (implemented with COMSOL Multiphysics software version 6.1) with a one-dimensional analysis (based on a MATLAB script) allows for the theoretical determination of the power output of a small-PTC with a nonevacuated tubular receiver operating at a medium temperature. The finite element model considers both the nonuniformity of the concentrated solar flux on the receiver tube (evaluated using Monte Carlo ray-tracing analysis) and the establishment of natural convection in the air gap between the glass envelope and absorber tube. The model calculates, for several values of direct normal irradiance (DNI) and inlet temperatures, the thermal power transferred to the heat transfer fluid (HTF) per unit length. The data are fitted using the multiple linear regression method, obtaining a function that is then used in a one-dimensional multi-nodal model to estimate the temperatures and the heat gains along the receiver tube. The outputs of the model are the outlet temperature and the total thermal power transferred to the HTF. In order to validate the developed methodology for the assessment of the heat transfer characteristics in the small-PTC with a nonevacuated receiver, an experiment at the ENEA Trisaia—Solar Thermal Collector Testing Laboratory was carried out. This work compares the theoretical data with those acquired through experimentation, obtaining a good agreement, with maximum differences of 0.2% and 3.6% for the outlet temperatures and the power outputs, respectively.

Community microgrid planning in Lombok Island: an Indonesian case study

Rural electrification, diesel generator replacement, and resilient electrification systems against natural disasters are among the main targets for Perusahaan Listrik Negara (PLN) in Indonesia to achieve a universally accessible, resilient, and environment-friendly electricity supply. Microgrids, therefore, become a popular and available way to achieve the aforementioned targets due to their flexibility and resiliency. This paper aims to provide a resilience-oriented planning strategy for community microgrids in Lombok Island, Indonesia. A mixed-integer linear program, implemented in the distributed energy resources customer adoption model (DER-CAM), is presented in this paper to find the optimal technology portfolio, placement, capacity, and optimal dispatch in a community microgrid. The multinode model is adopted for the planning, and hence, power flow constraints, N-1 contingency, and technology constraints are considered. The results show that the placement of photovoltaic (PV) arrays, battery energy storage systems (BESSs), and diesel generators (DGs) as backup sources in multi-node community microgrids lead to multiple benefits, including 100% rural electrification, over 25% cost savings, as well as over 22%, in particular CO2 emission reduction in multinode community microgrids.

Synergies of electrical and sectoral integration: Analysing geographical multi-node scenarios with sector coupling variations for a transition towards a fully renewables-based energy system

The cost-optimal pathway for moving from the current fossil-fuel based energy system to 100% renewables is still an open question. This work presents the first study that analyses the transition towards a 100% renewable energy system under different spatial resolutions (1-node, 6-nodes electrically isolated and interconnected) and various coupling configurations for the power, heat, transport and desalination sectors. With the LUT Energy System Transition Model for the case of Chile, 12 scenarios were investigated in an hourly resolution and considering more than one hundred energy-related technologies. The results show that: (1) 1-node systems deliver too simplistic results for key metrics; (2) power sector simulations can lead to a strongly distorted resources allocation compared to scenarios that include other sectors; (3) a multi-node model better reflects transmission bottlenecks and local resources, and; (4) the lowest-cost solution is reached when power transmission lines are considered. Thus, it is concluded that a cost-optimal, balanced, and realistic solution to reach a fully defossilised energy system is transitioning towards a multi-node, interconnected, and fully sector-coupled energy system. This can be called, in short, the ‘Power-to-X economy’, which in the case of Chile would more accurately be a ‘Solar-to-X economy’, given the high solar share found in the simulations.

Assessment of embodied carbon transfer in China’s interregional gas–electricity–heat trade based on multi-stream and multi-node model

With the implementation of the national ”dual carbon” goal, fully and effectively evaluating the spatial carbon transfer of regional natural gas–electricity–heat trade flows will help to better clarify the regional carbon emission reduction responsibilities and improve the efficiency of regional coordinated emission reduction. Therefore, this paper adopts an accounting system based on production and consumption, constructs a multi-stream and multi-node carbon transfer assessment model of regional natural gas–electricity–heat chain, calculates the embodied carbon transfer of natural gas–electricity–heat trade transmission, and analyzes the path of spatial transfer of implied carbon emissions between regions in China. The results show that the implicit spatial carbon transfer pattern of China’ s gas, electricity and heat cross-regional trade shows that Beijing, Tianjin and coastal developed areas have gradually become the main carbon inflows, and the NWC, NEC and other regions with rich resources but underdeveloped areas have become the main carbon outflows; the path of regional carbon transfer is roughly from upstream underdeveloped regions to downstream regions with better economic development, of which the secondary and tertiary transfers of embodied carbon from natural gas account for 6.1% and 0.8% of the total transfer.

A fast and accurate 1-dimensional model for dynamic simulation and optimization of a stratified thermal energy storage

As renewable energies are incorporated in larger shares in the electricity grid and district heating and cooling networks, the integration of storage solutions becomes more important. Thermal Energy Storage is an effective way to store heat and utilize the synergies between different energy carriers. Stratified storage tanks are a promising technology because of their low cost, simplicity and reliability. However, the modeling of the thermocline region in a stratified tank remains a challenge. There is a need to develop a fast and accurate 1D model for simulations and optimizations of TES. In this paper, a new discretization scheme is applied to the vertical axis of the storage tank. Orthogonal Collocation accurately represents the temperature profiles inside the storage tank with less points than the traditional multinode model, therefore running faster. Oscillations appear in the temperature profiles computed with orthogonal collocation if the thermocline represented is too steep and a low number of discretization points is used. But if a realistic thermocline is used as initial condition, the model performs well. Thus, it is appropriate to represent the real behavior of a storage tank, where uniform temperature conditions are avoided. Orthogonal Collocation on Finite Elements runs even faster and represents a good perspective for optimization studies. The model developed in this paper is validated with real data from a solar thermal plant with storage. A continuous and smooth model is also developed for natural convection inside the storage tank. The limitations of the model are discussed and perspectives on the modeling of natural convection for optimization models are given.

Experimental validation of a hybrid 1-D multi-node model of a hot water thermal energy storage tank

Hot water-based thermal energy storage (TES) tanks are extensively used in heating applications to provide operational flexibility. Simple yet effective one-dimensional (1-D) tank models are desirable to simulate and design efficient energy management systems. However, the standard multi-node modelling approach struggles to reproduce the dynamics of highly thermally stratified tanks due to their artificial numerical diffusion. In this paper, a novel 1-D multi-node modelling approach is introduced for accurately simulating water tanks with a high extent of thermal stratification. A non-linear, hybrid continuous–discrete time model able to capture the sudden temperature change within the tank is presented. The modelling approach was adopted to simulate a commercial TES tank, with the model being implemented in MATLAB/Simulink. Results from experimental tests were compared with simulation results, demonstrating that a hybrid continuous–discrete 12-node model accurately estimates the temperatures of the tank. It is also shown that the hybrid model avoids the numerical diffusion exhibited by standard multi-node models. This has been evidenced by the reduced root mean square and mean absolute errors exhibited by the hybrid model when compared with the experimental data.

A new thermal comfort model based on physiological parameters for the smart design and control of energy-efficient HVAC systems

Indoor thermal comfort represents a key aspect of building design. The reference standards do not consider the thermal adaptability of the human body, and HVAC system control strategies are based on a steady-state assumption that returns an incorrect estimate of occupants' thermal demand with a consequential misleading of the building energy consumption and of system sizing. To overcome these issues, a physiological thermal comfort model for the human body thermal behaviour evaluation is developed in MatLab environment for assessing the dynamic variation of the physiological parameters and for characterizing the occupants’ thermal sensation. Finally, the developed human body multi-node model is implemented in a building energy simulation tool (called DETECt 2.4) to perform three proposed strategies for the dynamic control of the building thermo-hygrometric parameters of the building and of the corresponding heating and cooling demands. These strategies provide an hourly regulation of relative humidity and air temperature by means of a two-step optimization that maximizes the thermal comfort of the occupants and minimizes energy consumption. To show the potentiality of the developed model, a suitable case study consisting of an office space is considered. Here, space heating and cooling demands obtained by applying the novel developed model are compared to those obtained through standard set-point values of air temperature and relative humidity (20 °C, 45% for heating needs, and 26 °C, 50% for cooling ones). By the comparison, between the proposed model – which considers the optimal hourly set point assessing the occupant in thermal evolution – and the reference ones, interesting results are obtained. Generally, a higher consumption is achieved by considering the proposed comfort strategies (from 2 to 16%), representing the price to be paid to maximize the comfort of the occupants and to annul the 3650 h of discomfort of the reference case.

Nexus Between Human Thermoregulation and Cardiovascular Functions—A Preliminary Simulation for a Moderate Variation of Temperature

AbstractThough the interaction between cardiovascular functions and thermoregulation is enormously complex yet immensely important, very little effort to date has been spent to simulate it from a system point of view. The present work aims at simulating the mutual interaction of human thermoregulation and cardiovascular functions by combining simple models of these two systems. While for thermoregulation, a lumped parameter multi-node model has been developed, a SIMULINK-based approach of electrical analogy has been taken for the cardiovascular system. These two models are coupled by different physiological and control actions, represented by well-established correlations. Three case studies have been conducted. In the first case, thermoregulation of a healthy human being is considered for a prescribed temperature cycle of moderate variation. Under heat stress, cardiac output increases by a joint effect of heart rate and stroke volume while under the cold condition, the variation of the cardiac output is less and is primarily governed by the heart rate. For the case of a reduced ejection fraction of the left ventricle, though there is a notable decrease in skin blood flow, negligible variation in skin and core temperature is observed. In the case of acute aortic stenosis, it is found that the blood pressure falls severely from its normal level causing hypotension and is further aggravated even under moderate heat stress. Such a situation might have further consequences like heat stroke. Finally, the limitations of the present study have been highlighted and suggestions have been made for further improvement.

Heat transfer of a large-scale water pit heat storage under transient operations

An accurate and less time demanding model is required when integrating pit thermal energy storage (PTES) into solar heating systems. Multi-node (1D) models are commonly used, but these models face challenges when calculating PTES thermal stratification and heat loss. Therefore, a full-scale computational fluid dynamics (CFD) model of PTES inclusive water and soil regions is developed using FLUENT to improve the accuracy of heat transfer calculation of a multi-node model. The CFD model is validated against the Dronninglund PTES measurements regarding PTES thermal stratification, inlet/outlet energy flow, and soil temperature distribution. The model corresponds well to the measurements in three aspects: (i) a maximum temperature difference of 1 K in the water region; (ii) a maximum temperature difference of 2 K in the soil region; (iii) a maximum outlet temperature difference of 3 K. An indicator RΔT/δ defined as the ratio between the thermocline temperature difference and the thermocline thickness is proposed to assess suitable grid size for PTES models, and the quantitative relationship between RΔT/δ and grid size is recommended. Investigations with a range of grid sizes show that by using the recommended grid size, the prediction accuracy of the multi-node model TRNSYS Type 343 is significantly improved. The root mean square deviations of the predicted MIX number are decreased by 11–43 % for different years, and the relative differences of the monthly charge/discharge energy from the measurement are within 5 %. The findings of this study provide guidance for selecting appropriate grid sizes to achieve better calculation accuracy for large-scale PTES.

Assessing spatially multistage carbon transfer in the life cycle of energy with a novel multi-flow and multi-node model: A case of China's coal-to-electricity chain

Fully assessing the spatial carbon transfer associated with energy production and consumption activities helps to better understand the drivers of related carbon emissions and clarify the corresponding carbon reduction responsibility. However, previous work based on the single network method and input-output analysis is not ideal for boundary integrity, data reliability, or scale generality. Here, an original multi-flow and multi-node model is proposed, taking the coal-to-electricity chain as an example to explain how to address these challenges. The model ingeniously integrates the trade network of coal used for electricity generation and the transmission network of coal power to compose a spatialised coal-to-electricity chain, to address how embodied carbon emissions are transferred successively in geography. This is applied to a Chinese case to demonstrate its scientificity and advancement. The results show that 118.3 Mt CO2eq and 598.8 Mt CO2eq of carbon are interprovincially transferred due to coal trade and electricity transmission, respectively. The two-stage carbon transfer leads to a significant difference of 504.7 Mt CO2eq in production- and consumption-based carbon accounting. If the embodied carbon emissions in the coal trade are not accounted, a total of 237.0 Mt CO2eq of embodied carbon emissions would be omitted. Only a small part of carbon transfer with coal trade undergoes a secondary transfer with electricity transmission, accompanied by a small amount of carbon reflux or exchange, which is suggested to optimise the spatial pattern of the coal-to-electricity chain in a targeted manner. The proposed multi-flow and multi-node model is flexible in sectoral and spatial scales and its design idea can also help other energy activities to fully assess carbon transfer.

Effect of beta angle and contact conductances on the temperature distribution of a 3U CubeSat

Contact conductances are a significant factor in the thermal analysis aimed at assuring safe on-orbit temperatures for a nanosatellite. In this work, the effect of the thermal contact conductances and the β angle on the temperature of the components of a realistic 3U CubeSat model is investigated theoretically. As part of the explanation of the methodology used, Python scripts are provided that compute the temperature of a simplified multinodal model. When β=0°, the subsystems of the realistic satellite model present temperatures within their operating ranges for contact conductance variations spanning an order of magnitude. Reduction of the contact conductances yields dissimilar effects on the internal and external components: the amplitudes and average values of the temperature oscillation of external components, like the solar cells, increase; in contrast, the oscillation amplitudes of internal components decrease and insignificant changes are observed in their average temperature. Increase of β from 0° to 75° produces a raise of the average temperature, but a decrement of the oscillation amplitude, for all subsystems. All components stay inside their operating ranges, for β from 0° to 15°. The results suggest that, if the payload (camera) is insulated, this domain could be extended up to β=45°. We expect that our results will guide the design of CubeSat missions.

The Potential of Simulating Energy Systems: The Multi Energy Systems Simulator Model

Energy system modelling is an essential practice to assist a set of heterogeneous stakeholders in the process of defining an effective and efficient energy transition. From the analysis of a set of open-source energy system models, it emerged that most models employ an approach directed at finding the optimal solution for a given set of constraints. On the contrary, a simulation model is a representation of a system used to reproduce and understand its behaviour under given conditions without seeking an optimal solution. In this paper, a new open-source energy system model is presented. Multi Energy Systems Simulator (MESS) is a modular, multi-energy carrier, multi-node model that allows the investigation of non optimal solutions by simulating an energy system. The model was built for urban level analyses. However, each node can represent larger regions allowing wider spatial scales to be represented as well. In this work, the tool’s features are presented through a comparison between MESS and Calliope, a state of the art optimization model, to analyse and highlight the differences between the two approaches, the potentialities of a simulation tool and possible areas for further development. The two models produced coherent results, showing differences that were tracked down to the different approaches. Based on the comparison conducted, general conclusions were drawn on the potential of simulating energy systems in terms of a more realistic description of smaller energy systems, lower computational times and increased opportunity for participatory processes in planning urban energy systems.

Development of a virtual biomechanical manikin used in vibrations studies in occupied spaces

In this paper is developed and applied a virtual biomechanical manikin used in occupied spaces. This multi-nodal numerical model is applied in the vibrations of the different sections of the human body, under transient conditions. The integration of second order equations systems, based in Newton equation, after being converted in a first order equation system, is solved through the Runge-Kutta-Fehlberg method with error control. This multi-nodal numerical model will be used, in this work, in the study of the vibrations that a standing person is subjected when stimuli are applied to the feet. The influence of various types of stimuli is analyzed, with periodic irregularities, in the dynamic response of the vibrations in different sections of the human body. The signals of the stimuli, the displacement of some sections of the body and the power spectrum of the same signals will be presented. In the study the influence of the floor vibration in the human body sections is analyzed and presented.

Numerical simulation of stratified thermal energy storage tanks

ABSTRACTStratified tanks are being widely used for thermal energy storage (TES), allowing a decoupling between the energy source (commonly a renewable energy source or heat rejected by some industrial process) and the demand. A high degree of stratification is required to make more efficient use of the stored energy, and several design configurations have been developed in order to create and maintain a good stratification. Numerical and experimental approaches are used to monitor and design the process, and also to predict the behavior of these tanks under different conditions. Detailed numerical simulation, however, is computationally expensive and not suitable for the long-time simulations (typically years) required to assess the performance and the economics of energy systems which include TES tanks.In this paper, a relatively simple, computationally inexpensive numerical approach, called Multi-node model, is used to simulate the energy transfer and the stratification inside the tank. The results obtained are compared to a software package for simulation of energy systems called TRNSYS and some experimental results to validate the model.

Development of benchmark scenarios for sector coupling in the Italian national energy system for 100% RES supply to power and mobility

The urgence of decarbonization has pushed many countries to set ambitious net-zero CO2 emission targets by 2050. This requires a substantial transformation of energy sources, conversion methods, and final uses. This work investigates the structure of the future Italian energy system – in terms of power generation capacity, energy storage, mobility fuel shares – and assesses benchmark scenarios able to reach a fully decarbonized supply in power and transport sectors, considering their long-term evolution. The analysis adopts a multi-node multi-vector model that simulates the year-long energy system behaviour with hourly time resolution and optimizes sizing (installed capacities) and operation (energy flows). The model considers power generation from different sources, electric consumption, and mobility demand for energy vectors, focusing on electricity and hydrogen. The required installed capacities of RES power plants and energy storage systems appear to be extremely high (at least 10x today’s solar PV or more), but in general positively influenced by sector integration strategies and energy vector multiplicity. Energy storage and flexibility solutions are essential, combining battery storage, Power-to-Hydrogen, Power-to-Power, smart charging, and vehicle-to-grid. If capacity installation is limited (e.g., due to land availability), the need to satisfy consumption yields significant import requirements, which also depend upon the mobility mix and the decarbonization targets.

The comparison of design airflow rates with dynamic and steady-state displacement models in varied dynamic conditions

A temperature-based method is usually applied in displacement ventilation (DV) design when overheating is the primary indoor climate concern. Different steady-state models have been developed and implemented to calculate airflow rate in rooms with DV. However, in practical applications, the performance of DV depends on potentially dynamic parameters, such as strength, type and location of heat gains and changing heat gain schedule. In addition, thermal mass affects dynamically changing room air temperature. The selected steady-state and dynamic models were validated with the experimental results of a lecture room and an orchestra rehearsal room. Among the presented models, dynamic DV model demonstrated a capability to take into account the combination of dynamic parameters in typical applications of DV. The design airflow rate is calculated for the case studies of dynamic DV design in the modelled lecture room in both dynamic and steady-state conditions. In dynamic conditions of heavy construction in 2–4 hours occupancy periods, the actual airflow rate required could be 50% lower than the airflow rate calculated with the steady-state models. The difference between steady-state and dynamic multi-nodal model is most significant with heavyweight construction and short occupancy period (17%–28%). In cases with light construction, the dynamic DV model provides roughly the same airflow rates for four-hour occupancy period than the Mund’s model calculates. The dynamic model can significantly decrease the design airflow rate of DV, which can result in a reduction of investment costs and electrical consumption of fans.

Evaluation of comfort levels in office space equipped with HVAC system based in personalized ventilation system using energy produced in DSF systems

In this study the numerical simulation of a Heating, Ventilating and Air Conditioning (HVAC) system, based in a personalized ventilation system, installed in an occupied office desk is made. The energy is produced in a Dual Skin Facades (DSF) system installed in the outdoor environment. The personalized ventilation system, placed above and below the writing area, installed in the desk central area. The office desk is occupied by eight virtual manikins. The numerical simulation is made in a winter typical day. This numerical study considers a coupling of a differential numerical model and an integral numerical model. The differential numerical model simulates the Computational Fluids Dynamics (CFD), evaluates the air velocity, air temperature, turbulence intensity and carbon dioxide concentration and calculates the indoor air quality. The integral numerical model simulates the Multi-Node Human Thermo-physiology Model, evaluates the tissue, blood and clothing temperatures distribution and calculates the thermal comfort level. The HVAC system, based on a DSF system, is built using three DSF unities, is equipped with internal venetian blinds. Each one, installed in a virtual chamber, is turned to south. The personalized ventilation system, made with eight upper and eight lower air terminal devices, is installed in the desk central area. On each table top two upper and two lower air terminal devices are considered in the left and right manikin area, while on each side of the table two upper and two lower air terminal devices are placed between the manikins. The office desk is occupied by eight virtual manikins, one sitting on each table top and three sitting on each side of the meeting table. In this numerical study, carried out in winter conditions, the occupants’ clothing level is 1 clo. In these situations a typical activity level of 1.2 met is considered. The evolution of indoor environmental conditions, in the DSF and in the office room, are calculated during a full winter typical day. The thermal comfort, the indoor air quality, the effectiveness for heat removal, the effectiveness for contaminant removal and the Air Distribution Index (ADI), are evaluated. In accordance with the obtained results the thermal comfort levels increase when the air renovation rate increases and the indoor air quality level increases when the air renovation rate increases. However, the ADI is quite constant when the inlet airflow rate increases, because the thermal comfort number decreases when the inlet airflow rate increases and the air quality number increases when the inlet airflow rate increases.

Energy modeling of solar water heating systems with on-off control and thermally stratified storage using a fast computation algorithm

This work presents a simplified model for the rapid computation of the yearly solar fraction of direct solar water heating systems using on-off control. Thermal stratification was included using a simple one-dimensional multi-node model. A time-step dependency analysis showed that a time step of 0.05h is a good compromise between accuracy and computation speed. The solar fraction increases with collector flow rate when the flow rate is low. In fully-mixed storage, the solar fraction keeps increasing with flow rate, although with a decreasing rate of increase. However, in stratified storage, the solar fraction reaches a maximum at an optimum flow rate, before it starts decreasing with flow rate. When the number of tank nodes increases from 1 to 4, the maximum solar fraction increases 5–28%; this increase is superior for less efficient collectors and lower collector areas. In low-stratified systems, the optimum flow rate is the maximum allowed by the system. However, in stratified systems, the optimum flow rate is reduced to values of 0.006–0.016m3h−1 per square meter of collector area. Unless the tank walls are covered by a rather thick layer of thermal insulation (about 0.2m), storage tank losses cannot be ignored.