Lumped Parameter Numerical Model Research Articles

Modelling thermal dynamics in intermittent operation of a PEMEL for green hydrogen production

Green hydrogen plays a pivotal role in the imminent energy transition, addressing energy storage and electricity generation decarbonization. The European Commission’s hydrogen strategy underscores the goal to install at least 40 GW of green hydrogen electrolysers by 2023. Despite various electrolyser technologies, efficiency improvement and durability enhancement remain challenges, especially considering voltage intermittencies from renewable energy sources. This study emphasizes the impact of thermal gradients within electrolysers due to voltage interruptions, affecting membrane operation and causing premature wear. The study explores methods to minimize thermal gradients, revealing trade-offs between efficiency and durability. A lumped-parameter numerical model is developed and experimentally adjusted to simulate electrochemical and energy transport phenomena. Experimental and numerical results are compared, highlighting the need for a comprehensive thermal management code for effective electrolyser performance. The study addresses the importance of accurately modelling transient thermal responses for both proton exchange membrane electrolysis (PEMEL) and solid oxide electrolysis (SOEL) designs, providing insights for future advancements in thermal management strategies.

An investigation of a supersonic fluidic oscillator generating pulsations in chambers during pressurization

A load-type supersonic fluidic oscillator has potential application for introducing small oscillations in the chamber of a superplastic forming process to improve performance. This paper presents a study of a special bi-stable load-type supersonic fluidic oscillator capable of simultaneously producing self-sustained oscillations in two gas pressure chambers during their filling at high-pressure. The experimental portion of the work verifies the robust nature of the device performance. Distinct differences, however, are observed compared to those previously shown for a similar prototype supplying pressure fluctuations to a single chamber at low pressure. It is also found that a three-dimensional computational fluid dynamics model is required to accurately simulate the transient filling process of the current oscillator facility, unlike the previous case. This leads to an unaffordable computational cost. To address this issue, a low-order fluid circuit model is developed. This simplified approach is based on a quasi-steady assumption and is of the same form as the one which accurately predicts the performance of the previous prototype. The model is “numerically empirical” in that the model parameters are determined using steady state 3D-CFD analysis rather than physical experiments. The circuit model combined with a lumped parameter numerical model of tank filling with realistic heat transfer to the surroundings provides an accurate and rapid prediction of the transient performance of the device. Also, the usefulness of the circuit model as an industrial design tool is demonstrated by predicting the effect of two design changes.

Viable Energy Recovery Strategies Through Advanced Directional Control Valve

The demand for more efficient machines is pushing hydraulic manufacturers to develop a new generation of systems capable of energy saving and recovering. An advanced flow sharing directional control valve with downstream compensation reduces meter-out pressure losses and recovers energy both in combined movements and with overrunning loads. Tests carried out on a prototype on a test bench confirm the proper functioning of the concept and allow tuning its lumped parameters numerical model. A control strategy based on keeping the optimal compensator position allows computing the maximum theoretical recovery. The simulation of a mini-excavator digging cycle shows the energy saving and recovery compared to a standard flow sharing system.

Experimental investigation and modelling of a laboratory-scale latent heat storage with cylindrical PCM capsules

Heat storage efficiency is required to maximize the potential of combined heat and power generation or renewable energy sources for heating. Using a phase change material (PCM) could be an attractive choice in several instances. Commercially available paraffin-based PCM was investigated using T-history method with sufficient agreement with the data from the manufacturer. The introduced LHTES with cylindrical capsules is simple and scalable in capacity, charging/discharging time, and temperature level. The overall stored energy density is 9% higher than the previously proposed design of similar design complexity. The discharging process of the designed latent heat thermal energy storage (LHTES) was evaluated for two different flow rates. The PCM inside the capsules and heat transfer fluid (HTF) temperature, as well as the HTF flow rate, were measured. The lumped parameter numerical model was developed and validated successfully. The advantage of the proposed model is its computational simplicity, and thus the possibility to use it in simulations of a whole heat distribution network. The so-called state of charge (SoC), which plays a crucial role in successful heat storage management, is a part of the evaluation of both experimental and computational data.

A Fast and Effective Method for the Optimization of the Valve Plate of Swashplate Axial Piston Pumps

Abstract This research presents a lumped parameter numerical model aimed at designing and optimizing an axial piston pump. For the first time, it has been shown that a lumped parameter model can accurately model axial piston pump dynamics based on a comparison with computational fluid dynamic (CFD) models and experimental results. Since the method is much more efficient than CFD, it can optimize the design. Both steady-state and dynamic behaviors have been analyzed. The model results have been compared with experimental data, showing a good capacity in predicting the pump performance, including pressure ripple. The swashplate dynamics have been investigated experimentally, measuring the dynamic pressure which controls the pump displacement; a comparison with the numerical model results confirmed the high accuracy. An optimization process has been conducted on the valve-plate geometry to control fluid-born noise by flow ripple reduction. The nonlinear programming by quadratic Lagrangian (NLPQL) algorithm is used since it is suitable for this study. The objective function to minimize is the well-known function, the nonuniformity grade (NUG), a parameter directly correlated with flow ripple. A prototype of the best design has been realized and tested, confirming a reduction in the pressure ripple. An endurance test was also conducted. As predicted from the numerical model, a significant reduction of cavitation erosion was observed.

Thermodynamic analysis for hydriding-dehydriding cycle of metal hydride system

Thermodynamic analyses for a hydriding-dehydriding cycle process of a hydrogen storage system are carried out. Assuming the mass flow rate and the mass source term are both constant, the analytical solutions for lumped temperature in the metal hydride hydrogen storage tank are obtained in the absorption, dormancy and desorption processes. The analytical solution is important to understand the hydriding-dehydriding process, which can be used as a benchmark to validate lumped/distributed parameter models for further study. A lumped parameter numerical model is developed on the Matlab/Simulink software platform. The numerical solutions of this model with constant source term coincide with the analytical solutions. Different analytical solutions are solved with various combinations of the hydrogen inflow/outflow temperature. The analytical solution in present work is compared with the reduced model in the reference, and shows more accurate than the reduced model. The variable source term is applied to the validated lumped parameter model. The results of parametric study show that the source term of metal hydride is roughly constant when the hydrogen storage capacity is not beyond about 90% of its limited capacity.

A revised capacitance resistance model for large diameter shallow bore ground heat exchanger

Ground heat exchangers (GHE) for residential heat pumps have the advantage of rejecting (extracting) heat to a lower (higher) temperature sink (source) as compared with air source heat pumps. The thermal performance of shallow GHEs with larger diameter and of helical shape is modelled in this study using both a lumped parameter numerical model and a commercially available computational fluid dynamics (CFD) software. Measurements in a real test site single-family residence are also used for soil property calibration. The lumped parameter numerical model (Capacitance Resistance Model, CaRM) is validated against the CFD simulation results and improved in order to capture detailed heat transfer processes within the core of the GHE. As result, the new CaRM model is able to better simulate the thermal behaviour of the helical GHE without high computational resources of the CFD model. Detailed local and global temperatures predicted by the numerical models are presented and discussed. Results indicate that the new CaRM tool better matches the trend of the CFD model. The average root-mean-square deviation between the revised CaRM and CFD models are 0.29 °C for the average core temperature and 0.75 °C for the borewall temperature which is an improvement of 27% and 35% respectively, in comparison to the previous version of CaRM.

An experimental and numerical analysis of the performances of a Wankel steam expander

In the last decades, the energy market increased its interest towards the smart grids and electrically isolated systems. These systems utilize small size power generators in which volumetric expanders may be employed for a wide range of operative conditions, because of their robustness and reliability.In this work a study on a volumetric expander based on the Wankel mechanism was carried out. The aim of this study was to develop a lumped parameters numerical model able to predict the brake effective torque and working fluid consumption of the expander. This model was validated by comparison with experimental results obtained using steam as working fluid. This model allowed to trace the trends of mechanical and thermal losses versus rotating speed and inlet pressure. The experimental results encouraged the need for a further development of this expander, and showed the capability of the numerical model to predict the effective performances of the device.

Modal Analysis of Fuel Injection Systems and the Determination of a Transfer Function Between Rail Pressure and Injection Rate

A detailed analysis of a common rail (CR) fuel injection system, equipped with solenoid injectors for Euro 6 diesel engine applications, has been performed in the frequency domain. A lumped parameter numerical model of the high-pressure hydraulic circuit, from the pump delivery to the injector nozzle, has been realized. The model outcomes have been validated through a comparison with frequency values that were obtained by applying the peak-picking technique to the experimental pressure time histories acquired from the pipe that connects the injector to the rail. The eigenvectors associated with the different eigenfrequencies have been calculated and physically interpreted, thus providing a methodology for the modal analysis of hydraulic systems. Three main modal motions have been identified in the considered fuel injection apparatus, and the possible resonances with the external forcing terms, i.e., pump delivered flow rate, injected flow rate, and injector dynamic fuel leakage through the pilot valve, have been discussed. The investigation has shown that the rail is mainly involved in the first two vibration modes. In the first mode, the rail performs a decoupling action between the high-pressure pump and the downstream hydraulic circuit. Consequently, the oscillations generated by the pump flow rates mainly remain confined to the pipe between the pump and the rail. The second mode is centered on the rail and involves a large part of the hydraulic circuit, both upstream and downstream of the rail. Finally, the third mode principally affects the injector and its internal hydraulic circuit. It has also been observed that some geometric features of the injection apparatus can have a significant effect on the system dynamics and can induce hydraulic resonance phenomena. Furthermore, the lumped parameter model has been used to determine a simplified transfer function between rail pressure and injected flow rate. The knowledge obtained from this study can help to guide designers draw up an improved design of this kind of apparatus, because the pressure waves, which are triggered by impulsive events and are typical of injector working, can affect the performance of modern injection systems, especially when digital rate shaping strategies or closely coupled multiple injections are implemented.

An experimental and numerical analysis of the performances of a Wankel steam expander

In the last decades, the energy market increased its interest towards the smart grids and electrically isolated systems. These systems utilize small size power generator, which often feature volumetric expanders that are very robust and reliable for a wide range of operative conditions. In this work a study that focuses on a Wankel volumetric expander was carried out. In order to predict the extractable specific work from the expander, a thermodynamic lumped parameters numerical model was developed. The model was validated by means of experimental data obtained using water steam as working fluid. The experimental results encouraged the need to improve the research of this expander, as well as the capability of the numerical model to predict the effective performances of the device.

The impact of ocular hemodynamics and intracranial pressure on intraocular pressure during acute gravitational changes.

Exposure to microgravity causes a bulk fluid shift toward the head, with concomitant changes in blood volume/pressure, and intraocular pressure (IOP). These and other factors, such as intracranial pressure (ICP) changes, are suspected to be involved in the degradation of visual function and ocular anatomical changes exhibited by some astronauts. This is a significant health concern. Here, we describe a lumped-parameter numerical model to simulate volume/pressure alterations in the eye during gravitational changes. The model includes the effects of blood and aqueous humor dynamics, ICP, and IOP-dependent ocular compliance. It is formulated as a series of coupled differential equations and was validated against four existing data sets on parabolic flight, body inversion, and head-down tilt (HDT). The model accurately predicted acute IOP changes in parabolic flight and HDT, and was satisfactory for the more extreme case of inversion. The short-term response to the changing gravitational field was dominated by ocular blood pressures and compliance, while longer-term responses were more dependent on aqueous humor dynamics. ICP had a negligible effect on acute IOP changes. This relatively simple numerical model shows promising predictive capability. To extend the model to more chronic conditions, additional data on longer-term autoregulation of blood and aqueous humor dynamics are needed.NEW & NOTEWORTHY A significant percentage of astronauts present anatomical changes in the posterior eye tissues after spaceflight. Hypothesized increases in ocular blood volume and intracranial pressure (ICP) in space have been considered to be likely factors. In this work, we provide a novel numerical model of the eye that incorporates ocular hemodynamics, gravitational forces, and ICP changes. We find that changes in ocular hemodynamics govern the response of intraocular pressure during acute gravitational change.

Influence of the Displacement Profile on the Performance and Mechanical Stresses of an Axial Piston Compressor for Refrigeration Applications

Abstract Axial piston compressors are commonly equipped with rotating disk plates that make the pistons following a sinusoidal displacement. The variation of the plate angle leads to stroke increments without changing the displacement profile. The axial piston architecture allows one to make piston displacement profiles that are different from a sinusoidal one by using rotating disk with a shaped circumferential profile. In this work, a detailed analysis on the thermodynamic cycle of compressors with different disk geometries was carried out.A lumped parameter numerical model of a compressor for refrigeration application was developed. The compressor performance (i.e. indicated power, compressed mass of gas and specific power) was estimated by imposing piston displacement profiles that are different from the sinusoidal one. The influence on the cycle COP in which the compressor runs was evaluated for each analysis. For each profile, the study of the forces acting on the rotating plate was also investigated. A sensitivity analysis allowed the definition of a profile design that guarantees the optimization of both the thermodynamic cycle and the mechanical stresses.

Simulation of Apical and Atrio-aortic VAD in Patients with Transposition or Congenitally Corrected Transposition of the Great Arteries

VADs could be used for transportation of the great arteries (TGA) and for congenitally corrected transposition (ccTGA) treatment. A cardiovascular numerical model (NM) may offer a useful clinical support in these complex physiopathologies. This work aims at developing and preliminarily verifying a NM of ccTGA and TGA interacting with VADs. Hemodynamic data were collected at the baseline (BL) and three months (FUP) after apical (atrio-aortic) VAD implantation in a TGA (ccTGA) patient and used in a lumped parameter NM to simulate the patient's physiopathology. Measured (MS) and simulated (SIM) data were compared. MS and SIM data are in accordance at the BL and at FUP. Cardiac output (l/min): BL_m = 2.9 ± 0.4, BL_s = 3.0 ± 0.3; FUP_m = 4.2 ± 0.2, FUP_s = 4.1 ± 0.1. Right atrial pressure (mmHg): BL_m = 21.4 ± 4.1, BL_s = 18.5 ± 4.5; FUP_m = 13 ± 4, FUP_s = 14.8 ± 3.6. Pulmonary arterial pressure (mmHg): BL_m = 56 ± 6.3,BL_s = 57 ± 2, FUP_m = 37.5 ± 7.5, FUP_s = 35.5 ± 5.9. Systemic arterial pressure (mmHg): BL_m = 71 ± 2, BL_s = 74.6 ± 2.1; FUP_m = 84 ± 9, FUP_s = 81.9 ± 9.8. NM can simulate the effect of a VAD in complex physiopathologies, with the inclusion of changes in circulatory parameters during the acute phase and at FUP. The simulation of differently assisted physiopathologies offers a useful support for clinicians.

CONSTRUCTION OF AN ELEMENTARY MODEL FOR THE DYNAMIC ANALYIS OF A PRESSURIZED WATER REACTOR

A lumped-parameter numerical model was constructed based on the conservation laws of mass and energy and the point neutron kinetics with 6 groups of delayed neutron to represent the dynamics of a pressurized water reactor core. On the viewpoint of control theory, the coupled phenomenon of neutron kinetics and thermal-hydraulics can be recognized as a dynamic system with feedback loops by the Doppler effect and the coolant temperature. Scilab was implemented to construct the equivalent transfer functions and associated feedback loops of a PWR core. The dynamic responses were performed by the perturbations of positive reactivity insertion, coolant flow rate, and coolant inlet temperature. This elementary PWR core model has been qualitatively assessed against independent numerical data to ensure the models and codes have a certain level of confidence or validation.

Construction of an Elementary Model for the Dynamic Analysis of a Pressurized Water Reactor

A lumped-parameter numerical model was constructed based on the conservation laws of mass and energy and the point neutron kinetics with 6 groups of delayed neutron to represent the dynamics of primary loop of a pressurized water reactor (PWR) core. On the viewpoint of control theory, the coupled phenomenon of neutron kinetics and thermohydraulics can be recognized as a dynamic system with feedback loops which is caused by the Doppler effect and the coolant temperature difference. Scilab was implemented to representing the equivalent transfer functions and associated feedback loops of a PWR core. The dynamic responses were performed by the perturbations of coolant inlet flow, coolant inlet temperature, and reactivity insertion.

Lumped parameter model of sintered heat pipe: Transient numerical analysis and validation

This paper describes a lumped parameter numerical model which is able to simulate the transient as well as the steady-state operation of a sintered heat pipe. The main objective of the work is to build a simple, engineering-approach simulation tool to define the HP characteristics of small HPs, which are now in the market with doubtful specifications. The code has been validated by comparisons with numerical and experimental results readily available from the open literature and an extensive numerical simulation campaign has been carried out in order to characterize the thermal–hydraulic behavior of mini heat pipes. This analysis focuses particularly on the effects of wick thickness, porosity, grain structure and void fraction level in the evaporator on thermal performance and working limits. Mini HPs with different dimensions (8, 5 and 3 mm outer diameter, 1 mm wall thickness, sintered copper wick, water as filling fluid) have been considered. It was found that there is an optimum wick thickness which minimizes the thermal resistance with no remarkable grain radius effect, while, as expected, the grain size affects the evaporator wick dryness.

Robust Sliding Mode Control for Tokamaks

Nuclear fusion has arisen as an alternative energy to avoid carbon dioxide emissions, being the tokamak a promising nuclear fusion reactor that uses a magnetic field to confine plasma in the shape of a torus. However, different kinds of magnetohydrodynamic instabilities may affect tokamak plasma equilibrium, causing severe reduction of particle confinement and leading to plasma disruptions. In this sense, numerous efforts and resources have been devoted to seeking solutions for the different plasma control problems so as to avoid energy confinement time decrements in these devices. In particular, since the growth rate of the vertical instability increases with the internal inductance, lowering the internal inductance is a fundamental issue to address for the elongated plasmas employed within the advanced tokamaks currently under development. In this sense, this paper introduces a lumped parameter numerical model of the tokamak in order to design a novel robust sliding mode controller for the internal inductance using the transformer primary coil as actuator.

Development of a Hybrid (numerical-hydraulic) Circulatory Model: Prototype Testing and Its Response to IABP Assistance

Merging numerical and physical models of the circulation makes it possible to develop a new class of circulatory models defined as hybrid. This solution reduces the costs, enhances the flexibility and opens the way to many applications ranging from research to education and heart assist devices testing. In the prototype described in this paper, a hydraulic model of systemic arterial tree is connected to a lumped parameters numerical model including pulmonary circulation and the remaining parts of systemic circulation. The hydraulic model consists of a characteristic resistance, of a silicon rubber tube to allow the insertion of an Intra-Aortic Balloon Pump (IABP) and of a lumped parameters compliance. Two electro-hydraulic interfaces, realized by means of gear pumps driven by DC motors, connect the numerical section with both terminals of the hydraulic section. The lumped parameters numerical model and the control system (including analog to digital and digital to analog converters)are developed in LabVIEW environment. The behavior of the model is analyzed by means of the ventricular pressure-volume loops and the time courses of arterial and ventricular pressures and flows in different circulatory conditions. A simulated pathological condition was set to test the IABP and verify the response of the system to this type of mechanical circulatory assistance. The results show that the model can represent hemodynamic relationships in different ventricular and circulatory conditions and is able to react to the IABP assistance.

Modelling of cardiovascular system: development of a hybrid (numerical-physical) model.

Physical models of the circulation are used for research, training and for testing of implantable active and passive circulatory prosthetic and assistance devices. However, in comparison with numerical models, they are rigid and expensive. To overcome these limitations, we have developed a model of the circulation based on the merging of a lumped parameter physical model into a numerical one (producing therefore a hybrid). The physical model is limited to the barest essentials and, in this application, developed to test the principle, it is a windkessel representing the systemic arterial tree. The lumped parameters numerical model was developed in LabVIEW environment and represents pulmonary and systemic circulation (except the systemic arterial tree). Based on the equivalence between hydraulic and electrical circuits, this prototype was developed connecting the numerical model to an electrical circuit--the physical model. This specific solution is valid mainly educationally but permits the development of software and the verification of preliminary results without using cumbersome hydraulic circuits. The interfaces between numerical and electrical circuits are set up by a voltage controlled current generator and a voltage controlled voltage generator. The behavior of the model is analyzed based on the ventricular pressure-volume loops and on the time course of arterial and ventricular pressures and flow in different circulatory conditions. The model can represent hemodynamic relationships in different ventricular and circulatory conditions.

Left ventricular outflow tract mean systolic acceleration as a surrogatefor the slope of the left ventricular end-systolic pressure-volume relationship

ObjectivesThe goal of this study was to analyze left ventricular outflow tract systolic acceleration (LVOTAcc) during alterations in left ventricular (LV) contractility and LV filling. BackgroundMost indexes described to quantify LV systolic function, such as LV ejection fraction and cardiac output, are dependent on loading conditions. MethodsIn 18 sheep (4 normal, 6 with aortic regurgitation, and 8 with old myocardial infarction), blood flow velocities through the LVOT were recorded using conventional pulsed Doppler. The LVOTAcc was calculated as the aortic peak velocity divided by the time to peak flow; LVOTAcc was compared with LV maximal elastance (Em) acquired by conductance catheter under different loading conditions, including volume and pressure overload during an acute coronary occlusion (n = 10). In addition, a clinically validated lumped-parameter numerical model of the cardiovascular system was used to support our findings. ResultsLeft ventricular Em and LVOTAcc decreased during ischemia (1.67 ± 0.67 mm Hg·ml−1 before vs. 0.93 ± 0.41 mm Hg·ml−1 during acute coronary occlusion [p < 0.05] and 7.9 ± 3.1 m·s−2 before vs. 4.4 ± 1.0 m·s−2 during coronary occlusion [p < 0.05], respectively). Left ventricular outflow tract systolic acceleration showed a strong linear correlation with LV Em (y = 3.84x + 1.87, r = 0.85, p < 0.001). Similar findings were obtained with the numerical modeling, which demonstrated a strong correlation between predicted and actual LV Em (predicted = 0.98 [actual] −0.01, r = 0.86). By analysis of variance, there was no statistically significant difference in LVOTAcc under different loading conditions. ConclusionsFor a variety of hemodynamic conditions, LVOTAcc was linearly related to the LV contractility index LV Em and was independent of loading conditions. These findings were consistent with numerical modeling. Thus, this Doppler index may serve as a good noninvasive index of LV contractility.