Lumped Parameter Model Research Articles

Mesas.py v1.0: a flexible Python package for modeling solute transport and transit times using StorAge Selection functions

Abstract. StorAge Selection (SAS) transport theory has recently emerged as a framework for representing material transport through a control volume. It can be seen as a generalization of transit time theories and lumped-parameter models to allow for arbitrary temporal variability in the rate of material flow in and out of the control volume, and in the transport dynamics. SAS is currently the state-of-the-art approach to interpreting tracer transport. Here, we present mesas.py, a Python package implementing the SAS framework. mesas.py allows SAS functions to be specified using several built-in common distributions, as a piecewise linear cumulative distribution function (CDF), or as a weighted sum of any number of such distributions. The distribution parameters and weights used to combine them can be allowed to vary in time, permitting SAS functions of arbitrary complexity to be specified. mesas.py simulates tracer transport using a novel mass-tracking scheme and can account for first-order reactions and fractionation. We present a number of analytical solutions to the governing equations and use these to validate the code. For a benchmark problem the time-step-averaging approach of the mesas.py implementation provides a reduction in mass balance errors of up to 15 times in some cases compared with a previous implementation of SAS.

Heat transfer characteristics of subsea long-distance pipeline subject to direct electrical heating

For deep-water pipelines with long tie-back distances, high external pressure, and low ambient temperature, it is a key issue to ensure flow safety by controlling the generation of hydrates and waxes through electric heating technology. In-detail analysis of the heat transfer performance of electric heating pipelines is of great engineering significance for developing the safety of pipeline flow in offshore oil-gas fields. This paper proposed an electrical heating analytical method applicable to long-distance submarine pipelines. Based on the thermal equilibrium theory and the differential equation of heat conduction, a mathematical model of heat-fluid coupling for electric heating pipes is established, involving the theoretical model of the steady-state distribution of the electric heating in the axial and radial directions. Then, the definition of the average temperature of the pipeline is introduced and combined with the two-point Hermite approximation interpolation method, and an improved lumped parameter model of the transient heat transfer of the electric heating pipeline is established. Meanwhile, the finite difference method is applied to solve the ordinary differential equation of the pipeline and the energy equation of the internal fluid. The steady-state calculation result is utilized as the initial value of the transient heat transfer process, and the model is applied to analyze the influence variation on the transient temperature response characteristics of the pipeline under different working conditions, finally determining the prediction formula of the average temperature of the fluid under normal transportation and shutdown conditions.

Experimental correlation of natural convection in low Rayleigh atmospheres for vertical plates and comparison between CFD and lumped parameter analysis

This paper offers a comprehensive exploration of thermal analysis for space systems operating in low Rayleigh atmospheres, with a primary focus on enhancing the accuracy and reliability of convective heat transfer modeling. The study centers around an analysis of a vertical heated plate experiment, where a lumped parameter model is employed to encompass conductive, radiative, and convective heat transfer mechanisms. To advance the accuracy of convective heat transfer coefficient calculations, this paper introduces a novel approach involving the utilization of Nusselt number correlations. These correlations are developed through an analytical solution derived from the Navier-Stokes equations, tailored specifically for the internal natural convection problem. This approach treats convection as a heat exchange process between the heated plate and the surrounding air, thereby improving the precision of modeling internal convection within a lumped parameter framework. A specific correlation (González-Bárcena et al.) is obtained for the proposed problem, derived from experimental tests conducted in a thermal vacuum chamber, under varying pressure conditions to control the Rayleigh number. Additionally, the findings are validated using Computational Fluid Dynamics (CFD) tools to calculate the velocity and temperature fields within the cavity. The González-Bárcena et al. correlation significantly enhances temperature predictions, demonstrating an improvement of up to 10∘C when compared to conventional literature correlations. The methodology presented in this paper holds promise for extension to more complex experiments in low Rayleigh atmospheres, including those conducted in the Earth's stratosphere or on the Martian surface, thereby contributing to the advancement of thermal analysis in challenging space environments.

Influence of Active-to-Passive Ratio on the Deformation in Circular Dielectric Elastomer Actuators.

To further improve the performance of dielectric elastomer actuaotrs (DEAs), the development of novel elastomers with enhanced electro-mechanical properties is focal for the advancement of the technology. Hence, reliable techniques to assess their electro-mechanical performance are necessary. Characterization of the actuator materials is often achieved by fabricating circular DEAs with the pre-stretch of the membrane fixed by a stiff frame. Because of this set-up, the electrode size relative to the carrier frame's dimension has an impact on actuator strain and displacement. To allow for comparable results across different studies, the influence of this effect needs to be quantified and taken into account. This paper presents an in-depth study of the active-to-passive ratio by proposing two simplified analytical models for circular DEA and comparing them. The first model is taking the hyperelastic material properties of the dielectric film into account while the second model is a linear elastic lumped parameter model based on the electro-mechanical analogy. Both models lie in good agreement and show a significant linear impact of the radial active-to-passive ratio on the electro-active strain and a resulting maximum of displacement around 50% radial coverage ratio. These findings are validated by experiments with actuators fabricated using silicone membranes. It is shown that the electrode size is not only an important parameter in the experimental design, but in some cases of higher significance for the accuracy of analytical models than the hyperelastic properties of the material. Furthermore, it could be shown that a radial coverage ratio of around 50% is desirable when measuring displacement as it maximizes the displacement and lowers the impact of deviations in electrode sizes due to fabrication errors.

Double closed-loop feedback control strategy for enhanced external counterpulsation to regulate hemodynamic response of human common carotid artery

Enhanced external counterpulsation (EECP) is a mechanical therapy for the clinical management of ischemic cardio-cerebrovascular diseases. Applying different EECP modes to different patients would be based on the experience of physicians. Existing hemodynamic models could describe the quantitative relationship between different EECP modes and hemodynamic parameters of specific parts of human blood circulatory system. However, currently there is no closed-loop control system available for precisely, personally, and intelligently performing the EECP. Therefore, to significantly improve the clinical benefits of rehabilitation treatment of ischemic cardio-cerebrovascular diseases with the EECP, this study developed a double closed-loop physiological control algorithm for the EECP device. Firstly, a detailed lumped parameter model describing the hemodynamics of human blood circulatory system was updated based on the available models; then the EECP device was coupled to it and the updated model was tested with the clinical data; finally, a double closed-loop feedback control strategy for precise regulation of the carotid hemodynamic response by the EECP was proposed. The control objectives were to maintain the mean arterial pressure and EECP pressure amplitude of patients with two gain-scheduled proportional-integral (PI) controllers. In-silico results showed that the clinical data can prove the accuracy of the updated model, and the appropriate EECP pressure amplitude could provide patients with the best benefits. The proposed control system could generate satisfied hemodynamic effects even with noise, demonstrating its feasibility and robustness. It is also easy to apply with high accuracy, and may be the effective solutions for developing intelligent and personalized EECP devices.

Investigation on the vibration localization of mistuned bladed disk with frictional contact

The mistuning phenomenon is commonly seen in the bladed assemblies of turbomachinery, leading to an unreasonably localized energy distribution that may increase the risk of high cycle fatigue and potentially cause blade failure. The friction coupling interaction is often introduced to attenuate the effect of excessive amplification on the structural vibration. To investigate the vibration localization of damped and mistuned bladed-disk system, a typical mistuning characterization is applied to an improved four-degree-of-freedom lumped parameter model to explicit the vibratory properties with coupled frictional contact. The statistical findings of natural frequency and modal localization factor are obtained by employing the Monte Carlo simulation to explore the influence of mistuned variance and coupled stiffness on the modal localization of free and damped bladed-disk system, respectively. The forced response sensitivity featured in the mistuned variance is quantitatively analyzed from the perspective of vibration localization and energy distribution by the nonlinear solution method. The influence of excitation order and normal load are further, respectively, discussed on the response localization level of the mistuned system. The results can provide fundamental knowledge of the impact of the mistuning pattern on vibration localization for the early design of the aeroengine.

A Study of Seating Suspension System Vibration Isolation Using a Hybrid Method of an Artificial Neural Network and Response Surface Modelling

A reliable prediction model can greatly contribute to the research of car seating system vibration control. The novelty of this paper lies in the development of a hybrid method of an artificial neural network (ANN) and response surface methodology (RSM) to predict the peak seat-to-head transmissibility ratio of a seating suspension system and to evaluate its ride comfort for different seat design parameters. Additionally, this method can remove the experimental design of the RSM model. In this paper, four seat design parameters are selected as input parameters and arranged using the central composite design method. The peak transmissibility ratio from seat to head at 4 Hz is chosen as the response target output value. To illustrate this hybrid method, the response target output value of the peak transmissibility ratio is calculated from the frequency response of a five-degrees-of-freedom (5-DOF) lumped-parameter biodynamic seating suspension model. The input design parameters and the response target output values are used to train an ANN to establish the relationship between the seat design parameters and the peak transmissibility ratio. At the same time, the input design parameters and the response target output values predicted by the ANN are used to develop the relationship between the seat design parameters and the peak transmissibility ratio using the response surface method and linear regression models. The hybrid of the ANN and response surface methods makes the planning or design of experiments not essential. The hybrid model of the ANN and response surface method is more accurate and convenient than a linear regression model for the study of seating system vibration isolation.

Comparative study of various adsorbents for adsorption-based thermal energy storage

Adsorption-based thermal energy storage (ATES) systems can potentially replace conventional heating technologies. This research explores the application of ATES systems for heating, focusing on the performance of various adsorbents using lumped parameter modeling. UiO-66, MOF-801, and their modified counterparts are evaluated alongside silica gel in terms of total and useful energy for end-users. Analysis of the ATES system encompasses Coefficient of Performance (COPh), Specific Heating Power (SHP), and Temperature Lift (ΔT) across different operating conditions. Isotherm characteristics reveal that (CH3)2-MOF-801 and NH-UiO-66 excel in water uptake at low relative pressures (Henry's region), resulting in high total and useful energy density. Notably, higher cooling water flow rates generally enhance Energy Storage Density (ESD) for materials like silica gel, UiO-66, and NH2-UiO-66, albeit at the cost of reduced SHP and COPh. Conversely, lower flow rates can lead to higher temperature lift (ΔT) for specific materials, although with a slight ESD decrease. Adjusting the chilled water inlet temperature typically favors ESD and COPh with higher temperatures while affecting SHP and ΔT differently. Heat source temperature impacts ESD and SHP variably due to isotherm characteristics and dynamic water uptake. The results highlight the superiority of (CH3)2-MOF-801 and N-UiO-66, achieving 91 % and 76 % of total energy density, with 94 kg of (CH3)2-MOF-801 covering 89 % of energy requirements for a single South Korean home annually.

Analysis and control strategy design for PEMFC purging process

In this study, a lumped-parameter model for shutdown purging has been developed using MATLAB/Simulink®. Data gleaned from actual operational scenarios on a fuel cell experimental platform serve as the basis for parameter identification within the model. The study encompasses a comparative analysis of purging processes under various operational parameters, including stack temperatures, purging currents, and purging flow rates. Moreover, an innovative purging strategy is proposed, employing an open-loop control mechanism to modulate the purging flow rate. The analysis reveals that an elevated stack temperature and a reduced purging current markedly enhance purging efficiency and diminish the water content at equilibrium. A negative correlation is observed between purging time and purging flow rate, with energy consumption demonstrating a U-shaped pattern across different flow rates. According to the proposed purging strategy, the optimal purging flow rate is ascertained through a Multi-dimensional Array Programming (MAP) lookup. This lookup is contingent upon stack temperature, purging current, and initial membrane water content. Validation confirms that this strategy not only truncates the purging duration but also curtails the system energy expenditure. These analytical insights and the newly-formulated purging strategy hold both theoretical and pragmatic implications for optimizing stack shutdown purging operations and advancing future purging methodologies.

Estimation of pulmonary vascular resistance for Glenn physiology.

Children with single ventricle heart disease typically require a series of three operations, (1) Norwood, (2) Glenn, and (3) Fontan, which ultimately results in complete separation of the pulmonary and systemic circuits to improve pulmonary/systemic circulation. In the last stage, the Fontan operation, the inferior vena cava (IVC) is connected to the pulmonary arteries (PAs), allowing the remainder of deoxygenated blood to passively flow to the pulmonary circuit. It is hypothesized that optimizing the Fontan anatomy would lead to decreased power loss and more balanced hepatic flow distribution. One approach to optimizing the geometry is to create a patient-specific digital twin to simulate various configurations of the Fontan conduit, which requires a computational model of the proximal PA anatomy and resistance, as well as the distal Pulmonary Vascular Resistance (PVR), at the Glenn stage. To that end, an optimization pipeline was developed using 3D computational fluid dynamics (CFD) and 0D lumped parameter (LP) simulations to iteratively refine the PVR of each lung by minimizing the simulated flow and pressure error relative to patients' cardiac magnetic resonance (CMR) and catheterization (CATH) data. While the PVR can also be estimated directly by computing the ratio of pressure gradients and flow from CATH and CMR data, the computational approach can separately identify the different components of PVR along the Glenn pathway, allowing for a more detailed depiction of the Glenn vasculature. Results indicate good correlation between the optimized PVR of the CFD and LP models (n = 16), with an intraclass correlation coefficient (ICC) of 0.998 (p = 0.976) and 0.991 (p = 0.943) for the left and right lung, respectively. Furthermore, compared to CMR flow and CATH pressure data, the optimized PVR estimates result in mean outlet flow and pressure errors of less than 5%. The optimized PVR estimates also agree well with the computed PVR estimates from CATH pressure and CMR flow for both lungs, yielding a mean difference of less than 4%.

A Lumped-Parameter Model of the Cardiovascular System Response for Evaluating Automated Fluid Resuscitation Systems.

Physiological closed-loop controlled (PCLC) medical devices, such as those designed for blood pressure regulation, can be tested for safety and efficacy in real-world clinical settings. However, relying solely on limited animal and clinical studies may not capture the diverse range of physiological conditions. Credible mathematical models can complement these studies by allowing the testing of the device against simulated patient scenarios. This research involves the development and validation of a low-order lumped-parameter mathematical model of the cardiovascular system's response to fluid perturbation. The model takes rates of hemorrhage and fluid infusion as inputs and provides hematocrit and blood volume, heart rate, stroke volume, cardiac output and mean arterial blood pressure as outputs. The model was calibrated using data from 27 sheep subjects, and its predictive capability was evaluated through a leave-one-out cross-validation procedure, followed by independent validation using 12 swine subjects. Our findings showed small model calibration error against the training dataset, with the normalized root-mean-square error (NRMSE) less than 10% across all variables. The mathematical model and virtual patient cohort generation tool demonstrated a high level of predictive capability and successfully generated a sufficient number of subjects that closely resembled the test dataset. The average NRMSE for the best virtual subject, across two distinct samples of virtual subjects, was below 12.7% and 11.9% for the leave-one-out cross-validation and independent validation dataset. These findings suggest that the model and virtual cohort generator are suitable for simulating patient populations under fluid perturbation, indicating their potential value in PCLC medical device evaluation.

Grey-box modelling and identification of the industrial oven of a shrink tunnel

This paper presents a lumped-parameter grey-box sampled-data state-space model for the industrial oven of a shrink tunnel. The model is derived following the thermal-electrical analogy. A novel discretization strategy is developed to take into account that the sampling time of the system is equal to the lowest period of the pulse-width-modulated voltage signals which drive the heat resistors of the industrial oven. The model parameters are estimated by means of an extensive experimental campaign. Experimental results show that the derived model outperforms state-of-the-art transfer-function models while depending on fewer parameters.

Development of a Lumped Parameter Model of Human Whole Body Circulatory Loop

Development of a Lumped Parameter Model of Human Whole Body Circulatory Loop

Ammonia blends for gas-turbines: Preliminary test and CFD-CRN modelling

Ammonia, with its high hydrogen density, cost effectiveness and ease of storage, is emerging as a potential fuel to meet decarbonisation targets in various sectors. However, the combustion of pure ammonia poses challenges due to its low calorific value and reactivity. Existing gas turbine combustion systems, refined over decades with conventional fuels, struggle to maintain comparable flue gas emission concentrations when burning ammonia.Overcoming this challenge requires a paradigm shift in gas turbine combustion, with implications for chemistry and combustor design methodology. Research into the chemical kinetic mechanism for ammonia combustion worldwide reveals differences in flame radical pools compared to methane combustion. The dominant NOx formation mechanism shifts to a "fuel-bound nitrogen" type, which differs from the "thermal" mechanism in hydrocarbon and hydrogen combustion.The integration of chemical reaction rates into Computational Fluid Dynamics (CFD) models with transport equations results in impractical computational times for industrial applications. Therefore, streamlined approaches such as chemical reaction reduction methods are being developed. This involves the construction of lumped parameter models (Chemical Reactor Network - CRN) to identify key parameters that affect species production. A reliable CRN implementation involves the identification of critical volumes using a preliminary CFD approach (CFD-CRN).This paper analyses preliminary experimental tests by Baker Hughes on an industrial burner using different ammonia, hydrogen, and methane fuel mixtures. The NOx results show a different behavior between methane and hydrogen. While the detailed mechanisms behind these results remain open questions, the CFD-CRN modelling approach is adopted. A proposed CRN is investigated for methane, hydrogen, and ammonia blends, providing insight into key parameters and a reasonable physical explanation for the different NOx results. A single calibration parameter (ϕpilot/ϕref) is used to predict accurately NOx emissions using experimental data available from experimental campaign.

A lumped parameter model for evaluating coronary artery blood supply capacity.

The coronary artery constitutes a vital vascular system that sustains cardiac function, with its primary role being the conveyance of indispensable nutrients to the myocardial tissue. When coronary artery disease occurs, it will affect the blood supply of the heart and induce myocardial ischemia. Therefore, it is of great significance to numerically simulate the coronary artery and evaluate its blood supply capacity. In this article, the coronary artery lumped parameter model was derived based on the relationship between circuit system parameters and cardiovascular system parameters, and the blood supply capacity of the coronary artery in healthy and stenosis states was studied. The aortic root pressure calculated by the aortic valve fluid-structure interaction (AV FSI) simulator was employed as the inlet boundary condition. To emulate the physiological phenomenon of sudden pressure drops resulting from an abrupt reduction in blood vessel radius, a head loss model was connected at the coronary artery's entrance. For each coronary artery outlet, the symmetric structured tree model was appended to simulate the terminal impedance of the missing downstream coronary arteries. The particle swarm optimization (PSO) algorithm was used to optimize the blood flow viscous resistance, blood flow inertia, and vascular compliance of the coronary artery model. In the stenosis states, the relative flow and fractional flow reserve (FFR) calculated by numerical simulation corresponded to the published literature data. It was anticipated that the proposed model can be readily adapted for clinical application, serving as a valuable reference for diagnosing and treating patients.

Dynamic Modeling and Combination Analysis of Plunger Valve Considering Both Flow and Actuator

The plunger valve has an important role in a large compressor system as its operating characteristics directly affect the aerodynamic boundary condition of the compressor equipment. In this study, dynamic modeling and analysis method of the plunger valve are proposed for an accurate control of the system. By considering the interaction between the dynamic flow in the valve and actuator action, a lumped parameter model for the fluid–structure interaction force and multibody dynamic model of the actuator are developed based on intrinsic correlation parameters. A combination analysis to simultaneously predict valve flow and actuator dynamic characteristics is proposed. The predicted results are in a good agreement with experimental data, which validates the proposed model and analysis method. The analysis results show that the coupling effect between the valve flow and actuator is significant and has an important role in valve control, particularly when the valve opening is smaller. Compared to the experimental data and computational fluid dynamics results, the presented methods are accurate for valve control and effective for prediction of flow rate.

A lumped-parameter model of the free-flooded ring transducer array.

The free-flooded ring (FFR) transducer is an extensively used ring-type acoustic transducer in underwater environments owing to its broad operating frequency bandwidth and small size. However, achieving high sound pressure levels with a single FFR transducer is often difficult, thus necessitating the construction of vertically arranged FFR transducer arrays. This study presents a comprehensive analysis of the electrical and acoustic characteristics of an FFR transducer array by considering the mutual radiation load and the effects of gaps between adjacent piezoelectric rings. The lumped-parameter models of the piezoelectric ring, cylindrical cavity, cylindrical gap, and radiation impedance constitute an entire impedance matrix. The radiation impedance matrix for the FFR transducer array is calculated using the Helmholtz-Kirchhoff integral formula by considering the interaction of the FFR surfaces with the surrounding fluid medium. The proposed model predicts the resonance peaks in the admittance and transmitted voltage response (TVR) with a relative error of 5%, and the TVR level within a 3 dB range. Detailed analyses of a four-FFR transducer array reveal that a wider gap between each FFR leads to a decreased chance of negative conductance and broader operating bandwidth. The proposed model offers valuable insights into the design of FFR transducer arrays.

Comprehensive modeling of ventilation systems for Nearly Zero Energy Buildings

In the present work, a lumped-parameter model of a multifunctional ventilation unit for residential applications was developed in the Simulink environment, also relying on the Simscape toolbox with Moist Air and Two-Phase fluid libraries. A simple, yet effective method to analyze and optimize the efficiency of the combined HVAC – air distribution system is proposed. To investigate the impact of boundary conditions on system performance, a parametric study of different installation conditions was also carried out, including outdoor air and indoor air temperature, humidity, static pressure, filter fouling, pressure drop in the intake and distribution ducts. The model highlights a strong decrease in the useful cooling/heating heat flow rate produced by the system as the installation and maintenance conditions become more challenging.

Development of lumped-parameters models for the thermal evaluation and air quality in aircrafts

Aircraft cabins are a challenging category when dealing with thermal comfort and air quality inside means of transport. Two simplified dynamic models are developed. The first one is a lumped resistance-capacitance model for assessing the cabin thermal behaviour during the cruise phase. The fuselage is discretised into several slices and each one is represented through an RC network consisting of eleven nodes, thirteen resistances and three capacities. A thermal balance equation is set for each node and the linear system is solved to calculate the air and surfaces’ temperatures. The model is validated by comparison with literature experimental data from ten flights, showing that the predicted temperatures agree well with the measured ones, presenting an RMSE of 1.5, 1.9 and 1.3 °C for cabin air, floor and cabin internal surface temperatures, respectively. A sensitivity analysis is conducted, for which the internal air temperature increases linearly with occupancy rate and decreases with cruising altitude. Secondly, an air quality model is proposed to evaluate the presence of pollutants inside the cabin, based on a simple concentration balance equation. Ventilation flow rates recommended from standards and a recirculation rate below 50-60% should be set to maintain acceptable CO2 levels.

Proposal of Application of a Simple Analysis Code DYMOS for Accident Analyses of Molten Salt Reactors

The Molten Salt Reactor (MSR) possesses unique characteristics, including the circulation of liquid fuel salt in-core and ex-core, and the absence of cladding tubes of fuel rods. To perform safety analyses for accidents and transients, the selection of appropriate models is crucial. Proposed models vary from the coupling of a three-dimensional (3-D) nuclear reactor model and a detailed thermal/hydraulic (T/H) model to a simple point reactor model coupled with a lumped parameter model of the T/H system. The authors have been investigating the development of a simple and accurate model that can be utilized during the design stage and licensing evaluation, while also providing transparency, which means that models can be easily understandable by experts and reproduced in licensing evaluation. Given the distinctive features of the MSR, the peak heat flux or fuel cladding peak temperature is not a requirement. Instead, the most decisive parameter for safety evaluations is the fuel salt temperature in the fuel salt boundary. As demonstrated in this paper, the outlet of the MSR core consistently displays the highest temperature.Based on the afore-mentioned prospects for both nuclear and T/H systems, the authors have developed a simple safety and transient analysis code for MSR (DYMOS). The DYMOS code has been verified for MSRE experiments, as described in this paper. However, the previous verification was limited to small experimental MSRs, and there is a lack of verification for large reactor systems. This paper shows that the DYMOS code is applicable to these larger reactors. In other words, the main objective of this article is not to claim the originality of the model of DYMOS code, but to propose applicability of such simple code to large reactor systems.