Lumped Parameter Analysis Research Articles

Dynamic performance by mathematical modeling and trajectory tracking control in an FPGA-based architecture for an XYZ Cartesian system

This paper presents a novel methodology for analyzing, modeling, and experimental validating a dynamical model for a three-degree-of-freedom (3DoF) cartesian robot. The mathematical model is developed from a lumped parameter analysis of this study’s XYZ Cartesian system design. The Lagrangian equation of motion is applied to represent the dynamic behavior of the variables of the complete system. The control law improves performance by improving the dynamical model and the position error. Control algorithms for the Cartesian system are studied, with the best-fit controller consisting of a hyperbolic tangent, which is analyzed and simulated using MATLAB to study the system response. The controller is also implemented in a FPGA architecture to control the mechanism, and the results are compared with the simulation of the dynamical model with the control to verify performance, giving an 88% similitude between both the experimental and the simulated data. The error between the desired position and the real position is also obtained, giving the error in a rank between 1 and -2 mm in the position of each axis. The comparison of the experimental and simulated results demonstrates a diminished position error and a higher precision performance, which validated the method used to obtain the equations.

Lumped Parameter Analysis of Autogenous Propellant Pressurization System for Nuclear Thermal Rocket

This work proposes a new propellant management configuration for an ammonia-fueled nuclear thermal propulsion system. The suggested configuration maximizes the advantage deriving from the autogenous pressurization of ammonia by exploiting the thermal power lost by the nuclear reactor toward the vacuum space due to leaking radiation. In this layout, a tank containing ammonia in saturated conditions is placed near the nuclear reactor and receives an input thermal power proportional to the dose of gamma rays and neutrons absorbed by the tank walls and the ammonia itself. Such a thermal power accelerates the vaporization process of the saturated ammonia, thus increasing the pressure in the tank. A pressure regulator valve exploits this overpressure to pressurize the ammonia propellant contained in a run tank to the level required by the mission by connecting the two ammonia volumes. The pressure achieved inside the run tank pushes the propellant with an adequate mass flow rate inside the nuclear reactor. The developed lumped parameter analysis shows how this propellant management system can provide a constant mass flow to the nuclear reactor without using a turbopump assembly. Moreover, it is shown how the proposed concept allows for a reduction in the radiation shield mass.

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.

Research on hydrogen risk prediction in probability safety analysis for severe accidents of nuclear power plants

The risk of hydrogen combustion after the Fukushima nuclear accident has always been a topic of concern for the nuclear power industry. In the hydrogen risk assessment of probability safety analysis (PSA) in nuclear power plants, the traditional methods by using lumped parameter program method is fast but may have large uncertainties, while the newly developed CFD analysis method is more accurate but has not yet been widely applied to the hydrogen risk analysis of PSA due to a variety of factors. The lumped parameter analysis program MAAP is used firstly to obtain the hydrogen parameters under the severe accident of small LOCA in this paper, based on China's third-generation large-scale pressurized water reactor (PWR) nuclear power plant HPR1000, and then the probability of deflagaration to detonation (DDT) for hydrogen risk is analyzed with uncertainty. Secondly, the CFD software GASFLOW program is used to analyze the same accident sequence to obtain more accurate hydrogen distribution and other parameters, and at the same time to obtain the DDT probability value of hydrogen risk. The hydrogen distribution obtained by CFD calculation can be used to guide the uncertainty value of the lumped parameter program to produce more accurate DDT value of hydrogen risk. The analysis results show that there is a certain uncertainty in hydrogen risk assessment when using lumped parameter program method, which can be corrected by combining the gas distribution analysis results given by CFD software, to obtain a more accurate and reliable probability value, so as to provide a more accurate reference for PSA analysis and to improve the overall safety of the nuclear power plant.

Experimental Investigation on Thermal Stability of Dual Particle Magnetorheological Fluid and Performance

Magnetorheological fluid and their properties are essential in Magnetorheological applications. The present study aims to obtain the thermally stable carrier fluid for Magnetorheological damper application through thermogravimetric analyses of three base fluids for higher stability fluid to synthesize Magnetorheological fluid. Scanning electron microscopic images of particles were also tested for their morphology. Magnetorheological fluid samples with 10%, 15%, and 20% by volume were prepared in-house with a 3% calcium base additive (base fluid). Sedimentation and thermal conductivity studies reveal that increasing particle concentration increases the settling time and thermal conductivity. The flow properties show an increase in yield stress with an increase in particle concentration and magnetic fields. The application part of the fluid consists of Magnetorheological damper fabrication and dynamic testing of 20% volume concentration particles at 10 mm amplitude, 2 Hertz frequency, and 0 Ampere and 0.5 Ampere currents, and the temperature of the system is captured with a K-type thermocouple. The results show an 8.2 °C rise at 0.5 Ampere with a 26.2% force decrease within 1000 cycles. The theoretical model based on the lumped parameter analysis predicts the temperature rise, similar to the experimental analysis with a 9.5% error.

Numerical investigation of buoyancy-induced thermo-fluid characteristics of different types of infrared suppression (IRS) devices

The present work reports numerical investigation of natural convection heat transfer characteristics for three different types of infrared suppression (IRS) devices (i.e., conical, cylindrical, and hybrid) by varying Rayleigh number and diameter ratio in the range of 1010-1012, and 1.025–1.5, respectively. The effect of relevant parameters on average Nusselt number and induced air-flow rate through the IRS device has been elucidated graphically. Numerically computed results indicate that the average Nusselt number from IRS device is higher for cylindrical IRS devices for all Rayleigh number when DR>1.05. The average Nu initially increases with diameter ratio, attains the maximum (1.1 ≤ DR ≤ 1.15), and decreases with a further increase in diameter ratio. The Nu is significantly influenced by the diameter ratio of cylindrical and hybrid IRS devices than the conical IRS devices. It has been found that the dimensionless induced mass-flow rate at a particular diameter ratio decrease with the Rayleigh number and is found to be more for conical IRS device. In addition, correlation for the average Nusselt number as function of relevant input parameters has been proposed. The cooling time estimation based on lumped parameter analysis shows a faster cooling rate for cylindrical IRS devices followed by hybrid and conical IRS devices.

First-principles-based microkinetic rate equation theory for oxygen carrier reduction in chemical looping

The reduction kinetics of oxygen carriers with reacting gases are typically modeled using shrinking-core-based models, in which, the elemental surface reaction mechanisms are simplified as only one global reaction, and the kinetic parameters are obtained by fitting with experimental data. In this study, a theoretical scheme is proposed to couple the elemental surface reaction mechanisms with the bulk diffusion of lattice oxygen, and a first-principle-based microkinetic rate equation theory is developed to model the reduction kinetics of oxygen carrier in chemical looping. The elemental surface reaction mechanisms are computed using quantum chemistry and are integrated into the mean-field microkinetic model, in which, oxygen bulk diffusion is also included. The elemental steps of gas adsorption, surface reaction, and surface species desorption are considered in the theory. The kinetic parameters used in the model are directly calculated by using transition state theory and density functional theory instead of fitting with experimental data. The developed theory is applied to predict the reduction kinetics of a CaMn0.775Ti0.125Mg0.1O2.9-δ perovskite oxygen carrier and validated to accurately predict the reduction kinetics by H2 and CO under a wide range of temperatures and gas concentrations. The effect of surface reaction and bulk diffusion on the overall reaction rate is analyzed and the rate-controlling step is discussed. When the bulk diffusion is considerably rapid, the interior oxygen concentration in the grain remains uniform throughout the reduction process and can be considered as a function of time only. Lumped parameter analysis is used to simplify the bulk diffusion of lattice oxygen without sacrificing accuracy. The developed microkinetic rate equation theory couples the surface reaction mechanism with the bulk diffusion, bridges the gap between atom-scale first-principles quantum chemistry calculations with particle-scale heterogeneous kinetics, and provides a theoretical framework for oxygen carrier reduction/oxidation kinetics, gas conversion mechanisms, and product selectivity in chemical looping.

Absorber Type Optimization for Night-Shift Operation of Solar Air Heater

In the current study, the effect of using heat storage materials aimed at the night shift operation was studied by simulation tools. The Finite Volume Method (FVM) is used as a method to discretize the governing equations in the 2-D domain, and the RNG K- turbulence model is applied for simulation. The effect of absorption type based on five different materials such as Aluminum, Water, Asphalt, Graphite, and Sand on the performance of solar air heaters (SAH) is carried out thermally. The results show that the optimum material to obtain the maximum difference in temperature (38.32 K) between the absorber and the surrounding occurs once the asphalt is used, while the sand is the worst case, which is (31.71 K). Following, the focus is on the best absorber for night time operation. The Lumped Parameter Analysis is applied to the time required to dissipate the heat energy from the storage layer to reduce it to the assumed final temperature of a 5-degree difference (higher) than the ambient. After solving the transient equation, it is found that water can operate the system for a longer period (4.31 hrs.) as well as Graphite can operate the system for a shorter period (0.46 hrs.). Then ten different velocities in the entry section are used to consider the influences on the system performance. The results show that the velocity has a significant effect on the outlet temperature and operation period for night time.

Modeling method of an active–passive ventilation wall with latent heat storage for evaluating its thermal properties in the solar greenhouse

Active-passive phase change heat storage technologies have been obtained extensive application to decrease greenhouse’s demands for fossil energy during off-seasons. To develop the utilization ratio of solar energy in solar greenhouses during winter, the active–passive ventilation wall with latent heat storage (APVW-L) was introduced and could be integrated into greenhouse’s back-wall. However, system design and operation parameters are subjected to numerous factors, including its structure, material performance and outdoor meteorological parameters. To achieve optimization in the energy performance of this system, this study used finite element analysis and lumped parameter analysis to establish coupled energy balance equations of the APVW-L and the air inside vertical air passages, and the cubic spline interpolation was used to calculate the continuous relationship between phase change material’s equivalent specific heat capacity and temperature. This modeling method of the APVW-L was accurately validated against the measured data, and then used in the optimization design and operation strategy of the APVW-L in the greenhouses. This study demonstrated that the optimized APVW-L could store 5.36 MJ/(m2·day) of solar energy in Beijing. Compared to the identical conventional greenhouses, aftermidnight, the experimental greenhouse having APVW-L increased the back-wall’s interior surface temperature by 2.2–3.4 °C, and the average indoor air temperature by 0.8–1.4 °C. This study provides methods for the APVW-L's optimization design and its operation strategy, even for the rationalizationof the near-zero energy consumption of the solar greenhouse during winter.

Lumped Parameter Analysis of Bridge Wire in an Electro Explosive Device of a Power Cartridge for Water-Jet Application: A Case Study

Lumped Parameter Analysis of Bridge Wire in an Electro Explosive Device of a Power Cartridge for Water-Jet Application: A Case Study

Experimental study of wet porous sand layer air-drying characteristics

An experimental study has been carried out to investigate the convective air-drying characteristics of a wet sand layer. The experimental setup allows dynamic measurements of both sand layer weight and temperature, with hot air flowing towards the sand layer surface to ensure a uniform drying of it. Experiments are conducted for a 4 mm thick sand layer for three air temperatures of 45, 60 and 75 °C. The lumped parameter method is used to analyze the sand layer heat transfer. The results show that the sand layer temperature continuously increases throughout the drying process, which can be divided into three stages, i.e. the initial rapid, intermediate slow, and final rapid increase stages. There is no constant temperature stage that is often observed in water film evaporation experiment. The drying process can also be divided into three stages according to the sand layer drying rate variation, they are the increasing, constant, and decreasing rate stages, which roughly correspond to the three temperature rise stages. The lumped parameter analysis result supports that the convective heat from the hot air is used mainly for the water evaporation.

A lumped parameter model to explain the cause of the hysteresis in OWC-Wells turbine systems for wave energy conversion

A Wells turbine is an axial-flow turbine consisting of a rotor usually with symmetric (uncambered) blades staggered at a 90 degree angle relative to the machine’s axis. This turbine is used within oscillating water column systems: during its normal operation, the blades experience a continuous change in incidence angle, that according to many authors is at the origin of a hysteresis in its force coefficients. Aerodynamic hysteresis in rapidly moving airfoils is a well-known phenomenon, but happens only at non-dimensional frequencies significantly larger than the ones encountered in Wells turbines. This work presents a re-examination of the two phenomena, that shows the unlikeliness of the presence of any aerodynamic hysteresis in Wells turbines. A simple yet effective lumped parameter analysis is used to prove how the real cause of the hysteresis is to be found in a different phenomenon. Results are compared to experiments and CFD analyses for the same problem, with an excellent agreement.

Lumped analysis criteria for heat transfer in a diluted co – current moving bed heat exchanger with isothermal walls

In this study, a mathematical method was applied to establish modelling selection criteria for lumped parameter analysis (LPA), in the solid phase, of a diluted co-current moving bed heat exchanger (MBHE), with isothermal walls. Simplified expressions for particle temperature errors are obtained, showing, for certain parametric ranges, excellent agreement with the exact solution results. Another remarkable result is that for a MBHE with isothermal walls and very low particle Biot numbers, the possibility of steep intraparticle temperature gradients is demonstrated. Through a scale analysis, this behavior is explained, along with the physical foundations guiding the LPA selection criteria. The differences between two basic forms of approximation in MBHE modelling, that is, the uniform particle temperature assumption (UPTA) and LPA, are characterized. Also, new contributions are provided by the determination of parametric condition for the equality between the temperatures of the fluid and the particle surface and by limiting solutions.

Experimental investigations and analysis of wet porous sand layer air-drying process

Experimental studies have been conducted to investigate the wet porous material convective air-drying characteristics. An experimental setup is designed and constructed to examine the air-drying process of a wet sand layer, and it allows dynamic measurements of both the sand layer weight and temperature. Hot air flows down towards the sand layer upper surface to realize a uniform drying of it and multiple thermocouples are embedded in the sand layer to evaluate its temperature distribution. Experiments are carried out for three sand layer thicknesses of 2, 4 and 8 mm and for three hot air temperatures of 45, 60 and 75 °C. Water film evaporation experiments are also performed to obtain the convective heat and mass transfer coefficients, which are then used for the lumped parameter analysis of the sand layer heat and mass transfer. The results show that in the water film evaporation experiment, the water temperature initially increases and then remains constant at the air wet-bulb temperature for a long period of time until the water all evaporates. In the sand layer drying experiment, however, the sand layer temperature continues to increase throughout the drying process, which can be divided into three stages, i.e. the initial rapid, intermediate slow, and final rapid increase stages. The lumped parameter method is employed to analyze the sand layer heat transfer because of the small sand layer thickness. Such analysis uses the heat transfer coefficient obtained in the water film evaporation experiment and the sand layer temperature increasing rate to calculate the sand layer moisture content and drying rate. The obtained results agree well with the experimental data. The evolution of water film cover fraction on the sand layer upper surface during drying is also discussed by assuming that the water evaporation occurs mainly at the sand layer upper surface at the drying stage at which the sand layer upper surface is fully wet or partly wet.

A robust two-stage active disturbance rejection control for the stabilization of a riderless bicycle

In this work we propose a two-stage observer-based feedback control approach to automatically stabilizing a riderless bicycle in its upright position when moving forward at a constant speed. Our strategy uses a modern control approach called Active Disturbance Rejection Control (ADRC), based on Generalized Proportional Integral (GPI) extended observers, to estimate a unified signal that groups all the discrepancies between an adopted linear model and the actual behavior of the plant. These estimations are used in the feedback controller as an additive, close cancellation and terms devising proper output feedback control laws that linearly regulate the lean angle with respect to its upright position. From a control-design perspective, the bicycle is a perturbed, uncertain system with an unstable and non-linear behavior that is strongly forward speed dependent. The ADRC scheme allows one to solve this problem easily by using a control strategy based on an acceptable mathematical model derived from lumped-parameter analysis, and its effectiveness has been validated by the successful results from real implementation experiments on an instrumented bicycle prototype. A detailed description of all the stages of the mechatronics process design is included for a proper reference.

Lumped parameter analysis criteria for heat transfer in a co-current moving bed with adiabatic walls

In this study, a mathematical method was developed and applied to an existing analytical solution of a model for heat transfer in a co-current diluted moving bed, making it possible to determine criteria for selecting the lumped parameter analysis. This procedure differs from those previously reported, which generally follow an empirical approach or are based on very simplified models of the physics associated with moving beds. In developing the criteria, conditions for the lumped parameter analysis are obtained and error expressions are determined. A comparison between criteria described in the literature and those proposed herein is presented and the results enable a rational understanding of the existing criteria. The mathematical method is very general and could be applied to other problems in the fields of engineering and physics.

Rapid prediction of exergy destruction in data centers due to airflow mixing

ABSTRACTA novel lumped parameter approach is introduced to predict data center exergy destruction due to airflow mixing, resulting in a speedup of several orders of magnitude compared to detailed computational fluid dynamics (CFD) simulations. Both lumped parameter and detailed CFD methods agree within 8.5% for 11 test cases on an example data center. A significant time-saving design strategy is also introduced using two detailed CFD simulations to predict bulk flow parameters, and then applying lumped parameter analysis on flow-independent design parameters. The strategy shows agreement within 0.39% when computer room air conditioner (CRAC) supply temperature is varied from 12–20°C.

Disk cavities in soft materials: Their bubble-like resonance and use in thin underwater sound blocking materials

The acoustics of gas-filled cavities in soft viscoelastic solids, such as rubber and gels, has been a renewed subject of research in recent years owing to usefulness in studies of multiple scattering and importance to sound insulating and anechoic materials. A brief review is followed by a presentation of recent research on disk cavity resonance done at the Naval Research Laboratory [J. Acoust. Soc. Am. 138, 2537–2547]. A lumped parameter analysis of the breathing mode of a disk cavity is presented which yields a natural frequency expression valid for a high-aspect ratio cavity embedded in an elastic medium. A verification approach using finite-element methods is also described which directly computes resonance in the framework of COMSOL Multiphysics. Calculation of scattering cross sections and visualization of the elastic displacement field indicates the importance of shear wave radiation. As an application example, a specially designed single layer array of disk cavities in a thin silicone rubber (PDMS) sheet was modeled that resonantly blocks underwater sound by nearly 20 dB for a favorable wavelength/thickness ratio of 240. Disk cavities are found to provide a wider bandwidth than near-spherical cavities. [Work sponsored by the Office of Naval Research.]

Infinite Cylinder Lumped Parameter Analysis Method of Unsteady-State Conduction

The paper extends the traditional lumped parameter analysis method of unsteady-state. Under the convection boundary 0<Bi<∞, a mean temperature lumped parameter analysis method is studied and the mean temperature response formula has been established. Taking an infinite cylinder as an example, the paper presents the regular pattern of the transient mean temperature value and discusses the numerical analysis. The method for solving the unsteady-state conduction in the paper is more convenient and practical than the M.P. Heisler charts that had been used in textbooks of native and foreign countries.

Parametric analysis of a solar still with inverted V-shaped glass condenser

A parametric analysis of a solar still with an inverted V-shaped glass condenser is presented. Results are based on a new mathematical model obtained from a lumped-parameter analysis of the still, with an approach that makes each glass plate of the condensing system sensitive to orientation and depicts its thermal differences. Numerical computations are made to evaluate productivity and temperature differences between the condensing plates as a function of condenser orientation, extinction coefficient and thickness. From this study it was found a significant influence of incident solar radiation on the thermal performance of each condensing plate. Large extinction coefficients and thick glass plates increase absorption losses that result in an appreciable temperature difference. An extinction coefficient of 40 m-1 produces a temperature difference of 2.5°C between both condensers. A glass thickness of 10 mm may increase this temperature difference up to 3.5°C. With respect to the production, due to the still orientation, a difference of 8.7% was found for the condensing plates facing an east-west direction. The proposed model is able to reproduce the temperature and distillate production differences that arise between both condensers in good agreement with experimental data. The overall performance of the still, studied with this new approach, was also in accordance with the widely used traditional models for solar distillation. In addition, the condensing plates parameters of the still can be used to force a differential heating such that for the whole day the temperature of one condensing plate is always higher.