Simple Lumped Parameter Model Research Articles

Modeling automotive gas-exchange solenoid valve actuators

We develop a finite-element analysis (FEA) model to describe transient and static operation of gas-exchange valves. Such valves, directly controlled by solenoids, are a promising method for enhancing automotive engine efficiency. The FEA model is validated by experimental testing on an actual automotive prototype valve. We show that a nonlinear lumped-parameter model that uses FEA results also closely matches experimental data. The lumped-parameter model is suitable for optimization of design and can be readily used for closed-loop simulation. We present a simplified lumped-parameter model to facilitate controller design. Finally, we compare a dynamic open-loop simulation with experimental results.

Modeling and simulation of a solar powered two bed adsorption air conditioning system

A simple lumped parameter model is established to investigate the performance of a solar powered adsorption air conditioning system driven by flat-type solar collectors with three different configurations of glazes: (i) single glazed cover; (ii) double glazed cover and (iii) transparent insulation material (TIM) cover. The dynamic performance of a continuous adsorption cycle using a double adsorber along with heat recovery is measured in terms of the temperature histories, gross solar coefficient of performance and specific cooling power. Also, the influences of some important design and operational parameters on the performance of the system are studied. It is found that the chosen three types of collector configurations make no big difference on the performance, but the adsorbent mass and lumped capacitance have significant effects on the system performance as well as on the system size. Simulation results indicate that the effect of overall heat transfer coefficient is not predominant if the cycle duration is longer. Also, there exists an optimum time to initiate the heating of the adsorbent bed in a day's operation.

Numerical modelling of the pressure wave propagation in the arterial flow

AbstractA differential model of blood flow through an arterial vessel is presented. It consists of a one‐dimensional model describing the non‐linear fluid–wall interaction coupled with a simple lumped parameter model which accounts for outlet boundary conditions. The model includes a local stiffening of the vessel and the wave propagation of disturbances due to prosthetic implantations is also studied. The non‐linear problem is solved by a finite‐difference method on a staggered grid and some numerical simulations are analysed and discussed. Copyright © 2003 John Wiley & Sons, Ltd.

Model of the filling of an automotive fuel tank

One of the problems associated with automotive fuel tanks is premature shut-off during the filling process. This occurs when the fuel dispensing nozzle shuts off before the fuel tank is completely filled. A comprehensive but simplified lumped parameter model has been developed to determine the pressure and flow rate associated with the automotive fuel tank for the purpose of predicting premature shut-off. Unlike previous work, this model includes the entire fuel system, including a closed rectangular tank with a filler tube, rollover valve, and vent tube that connects the filler tube to the tank. The system was divided into several control volumes and connecting valves. Continuity equations were written for each of the control volumes and energy equations were written for each of the connecting valves. The model includes the effects of the fuel tank system geometry, fuel nozzle dispensing rate, fuel volatility, multiphase, multicomponent flow through the filler tube, air/fuel vapour in the tank dome, vapour generation and choking in the vent tube, and the rollover valve due to the low speed of sound of the vapour droplet flow. This mathematical model consists of five nonlinear, integral equations and a number of algebraic equations. A commercial numerical solver (Simulink) was used to solve these equations subject to appropriate boundary conditions. The simplified model was used to generate results to compare with existing experimental results. In spite of its simplicity, it was capable of predicting the nature of the shut-off for all of the corresponding sets of experimental data. Prediction of the magnitudes of the tank dome pressure and the filler tube pressure were, however, only in fair agreement with the experimental values. The model was also used to perform a sensitivity analysis of model parameters. The results were found to be most sensitive to vent area around the filler nozzle, liquid dispensing flowrate, and fuel volatility.

Cycle-averaged models of cardiovascular dynamics

Time-varying ventricular elastance models have been used extensively in the past to simulate the pulsatile nature of cardiovascular waveforms. Frequently, however, one is interested in dynamics that occur over longer timescales in which case a detailed simulation of each cardiac contraction becomes computationally burdensome. In this paper, we apply circuit-averaging techniques to a simplified lumped-parameter model of the cardiovascular system. The resultant cycle-averaged model is linear and time invariant, and greatly reduces the computational burden. It is also amenable to systemic order reduction methods that lead to further efficiencies. Despite its simplicity, the averaged model captures the dynamics relevant to the representation of a range of cardiovascular reflex mechanisms.

Development and Demonstration of an Explicit Lumped-Parameter Biofilter Model and Design Equation Incorporating Monod Kinetics

Biofiltration is an economical air pollution control (APC) technology, particularly suitable for the treatment of air-streams having high flow rates and low concentrations of volatile organic compounds (VOCs). This technology utilizes enzymatic catalysis at ambient conditions to mineralize such pollutants to CO2, H2O, and salts. A pilot-scale study conducted for more than 4 years investigated the development of a new biofiltration technology employing trickle bed air biofilters (TBABs). Following the completion of this experimental study, additional data analysis was performed to develop a simple lumped-parameter biofilter model, assuming first-order kinetics. This model related the observed biofilter performance to the principle independent physical, thermodynamic, and biochemical parameters. The initial model has subsequently been expanded to incorporate Monod kinetics. In this paper, the development and use of the final explicit lumped-parameter biofilter model and design equation, incorporating Monod kinetics, are presented. To facilitate the application of this model, practical procedures are also presented for the determination of VOC solubility, VOC biokinetic Monod parameters, and the maximum practical biofilter inlet VOC concentration.

Effect of passive techniques on interior temperature in small houses in the dry, hot climate of northwestern Mexico

A simple lumped parameter model is used to represent the time variations of internal temperature of a simple house, under hot, extreme weather variation, characteristic of northwestern Mexico. Results are validated by experimental work in a physical model without ventilation, with materials and building techniques typical of low-income family housing in this region. Energy balance in the present work is achieved by means of a system of three simultaneous differential equations, each depicting energy equilibrium in one of the basic building elements: the window glazing, the building materials, and inside air. With the mathematical model properly calibrated, heat transfer coefficients between walls, ceiling and windows are calculated. Passive techniques, such as window shading, orientation and thermal inertia, are evaluated by a normalized temperature index. Results show that interior temperature in the house can be reduced resulting in comfort increase. Then economical pertinence of studied passive elements can be evaluated.

ADAPTIVE TORQUE PULSATION COMPENSATION FOR A HIGH-TORQUE DC BRUSHLESS PERMANENT MAGNET MOTOR

Brushless permanent magnet (PM) servomotors are appealing candidates for many high-performance applications. A persistent problem with PM motors is the non-uniformity in the developed torque which gives rise to a torque pulsation that varies as a function of operating conditions. In this paper an adaptive torque pulsation compensation scheme is developed. The adaptive scheme is based on a simple lumped parameter model for the motor and on the prescribed and actual angular position measurements. The compensating signal is directly added to the motor's position control signal, so that no new hardware is necessary. The adaptive scheme is implemented on a PC computer and the effectiveness of the adaptive torque pulsation compensation is demonstrated by experiments.

Discrete-time VSS temperature control for a plastic extrusion process with water cooling systems

The plastic extrusion process with water cooling is a variable structure system in nature. To implement discrete-time variable structure control, three important problems are considered. They are: choice of dynamic sliding surface for a system with relative degree greater than one, computation of the discrete-time dynamic sliding surface variable (s/sub k/), and self-tuning of the switching control magnitude to reduce chatterings. A simplified lumped parameter model is constructed to decouple the original multichannel system into multiple single-channel subsystems. Experimental results show the effectiveness of the proposed method.

CHF in Oscillatory Flow Boiling Channels

Recent advanced technologies in boiler manufacturing bring about highly efficient and compact water-tube boilers for gas firing or oil firing. These boilers have very simple water-circulation system, which often brings about flow instabilities followed by critical heat flux, CHF, problems. This paper describes such an oscillatory flow (CHF) at relatively low mass flux and at low pressure. CHF is a decreasing function of the amplitude and period of the flow oscillation, and reaches almost 40 % of the steady state value. When the tube wall is thin, CHF is mainly controlled by the two-phase flow dynamics and is well simulated using a simple lumped-parameter model of boiling channel. At very low mass flux, CHF depends significantly on the flow orientation, and is closely related to the flow pattern transition.

Estimation of 222Rn Flux from Ground Surface Based on the Variation Analysis of 222Rn Concentration in a Closed Chamber

A method for quantification of the 222 Rn flux from the ground surface into the atmosphere is described. A chamber made of polymethylmethacrylate (PMMA) was embedded in the soil and 222 Rn concentration and various affecting environmental factors were measured every hour. How environmental factors affect the 222 Rn concentration was considered and it was found that there were clear relationships between the variations of 222 Rn concentration and various environmental factors, especially air pressure. A simple lumped-parameter model approach was developed to obtain the undisturbed 222 Rn flux, which is the hypothetical situation without the chamber. The values of the parameter were found by fitting the model to the measured data for air pressure and 222 Rn concentration in the chamber. The effective diffusion coefficient obtained by the analysis agreed well with that obtained by the relation reported by Rogers and Nielson. The undisturbed 222 Rn flux from the ground surface into the atmosphere was estimated by using the parameter values obtained.

Modeling expiratory flow from excised tracheal tube laws.

Flow limitation during forced exhalation and gas trapping during high-frequency ventilation are affected by upstream viscous losses and by the relationship between transmural pressure (Ptm) and cross-sectional area (A(tr)) of the airways, i.e., tube law (TL). Our objective was to test the validity of a simple lumped-parameter model of expiratory flow limitation, including the measured TL, static pressure recovery, and upstream viscous losses. To accomplish this objective, we assessed the TLs of various excised animal tracheae in controlled conditions of quasi-static (no flow) and steady forced expiratory flow. A(tr) was measured from digitized images of inner tracheal walls delineated by transillumination at an axial location defining the minimal area during forced expiratory flow. Tracheal TLs followed closely the exponential form proposed by Shapiro (A. H. Shapiro. J. Biomech. Eng. 99: 126-147, 1977) for elastic tubes: Ptm = K(p) [(A(tr)/A(tr0))(-n) - 1], where A(tr0) is A(tr) at Ptm = 0 and K(p) is a parametric factor related to the stiffness of the tube wall. Using these TLs, we found that the simple model of expiratory flow limitation described well the experimental data. Independent of upstream resistance, all tracheae with an exponent n < 2 experienced flow limitation, whereas a trachea with n > 2 did not. Upstream viscous losses, as expected, reduced maximal expiratory flow. The TL measured under steady-flow conditions was stiffer than that measured under expiratory no-flow conditions, only if a significant static pressure recovery from the choke point to atmosphere was assumed in the measurement.

Friction Damper Optimization: Simulation of Rainbow Tests

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimization via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called “rainbow tests” where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disk assembly. A new method of analysis—a combination of the harmonic balance method and structural modification approaches—is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called “rainbow tests” in turbomachinery applications. A simple lumped-parameter model of a bladed-disk model was used and different damper weights were modeled using friction elements with different characteristics. Resonance response levels were obtained for bladed disks with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disk assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disk is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

A dynamic Model of the Vapor Compression Refrigeration Cycle with the Variable Speed Compressor and Expansion Valve.

A dynamic model of the vapor compression refrigeration cycle is presented and examined with experimental results. The model is simple lumped parameter model so that the simulator based on the model can compute the responses in 1/3 of real time. Then the simulator can be readily used to design refrigeration cycle and its controller. The comparisons of simulation results with experimental data prove that the model simulates the cycle in qualitative sense, but contain some inaccuracy due to the simplifications.

High-frequency respiratory impedance measured by forced-oscillation technique in infants.

Measurements of respiratory input impedance (Zin) in infants using forced oscillations at the airway opening up to 256 Hz have been shown to include a first antiresonance (ar,1). We wondered whether features derived from high-frequency Zin change during methacholine-induced airway obstruction in infants, whether those changes could be explained by a lumped parameter model as in dogs (providing a value for respiratory resistance [Rrs]), or whether they are similar to Zin data in human adults with airway obstruction. In 13 wheezy infants (age 58 +/- 19 wk) Zin(omega) was assessed at baseline, and in nine infants after methacholine challenge, using a provocation dose defined by fall of more than 30% in VmaxFRC (rapid chest-compression technique). Following methacholine challenge, VmaxFRC decreased significantly (p < 0.0005), the frequency at which ar,1 occurred ( far,1) increased significantly (p = 0.0007), and the relative maximum in the real part at far,1 [Zinre( far,1)] increased significantly (p = 0.02), whereas Rrs did not change. We conclude that in wheezy infants ar,1 is highly sensitive to changes in lung mechanics. Although ar,1 cannot be explained by a simple lumped-parameter model, it is likely due to wave propagation phenomena, as in human adults. In either case, far,1 potentially contains information about airway wall compliance, which is important for the understanding of flow limitation in infant wheezing disorders.

A Reduced Order Modeling Technique for Mistuned Bladed Disks

Abstract The analysis of the response statistics of mistuned turbomachinery rotors requires an expensive Monte Carlo simulation approach. Simple lumped parameter models capture basic localization effects but do not represent well actual engineering structures without a difficult parameter identification. Current component mode analysis techniques generally require a minimum number of degrees of freedom which is too large for running Monte Carlo simulations at a reasonable cost. In the present work, an order reduction method is introduced which is capable of generating reasonably accurate, very low order models of tuned or mistuned bladed disks. This technique is based on component modes of vibration found from a finite element analysis of a single disk-blade sector. It is shown that the phenomenon of mode localization is well captured by the reduced order modeling technique.

A new hybrid model for electrorheological fluid dampers and application to dynamic vibration absorption

Dampers incorporating electrorheological or magnetorheological fluid (whose damping parameters can be adjusted by altering an imposed electric or magnetic field, respectively) as part of their structure hold great promise as adaptive-passive vibration reduction devices. Extant models of electrorheological dampers are insufficient, because of excessive complexity or the lack of broad experimental validation, to allow the prediction of the response of the damper over a wide range of operating conditions. The subject work proposes a new, simple lumped parameter model for electrorheological dampers, validates the new model against empirical data, and explores the application of an electrorheological damper in a tuned dynamic vibration absorber. The vibration absorption capacity of an electro- or magnetorheological damper in a dynamic vibration absorber is found to depend on the displacement amplitude and frequency of the vibration, but a substantial reduction in vibration is achievable with only adaptive-passive control. [Work supported by U.S. Army Research Office.]

Dynamic simulation of an absorption heat transformer incorporated with an evaporation plant

This study presents a simple lumped parameter model of an absorption heat transformer (AHT). The model is compared with operating data from a pilot-scale AHT unit incorporated with one of the sulphite-liquor evaporation plants at a major pulp and paper mill. The expected performance of a full size AHT incorporated in different ways to the evaporation plant is also discussed.

ADAPTIVE-PASSIVE NOISE CONTROL WITH SELF-TUNING HELMHOLTZ RESONATORS

A tunable Helmholtz resonator and a novel feedback based control law that achieves optimal resonator tuning for time varying tonal noise control applications are presented in this paper. The proposed tuning strategy combines an open loop tuning algorithm based on a simple lumped parameter model of the resonator with a gradient descent approach based on a feedback control structure that ensures robust performance. Optimal tuning of the resonator is achieved despite system uncertainties such as variations in the excitation frequency and environmental changes. An experimental verification of the proposed control law is included. Sound pressure level reductions of up to 30 dB were achieved in an experimental duct system using a tunable Helmholtz resonator.

Analysis of harmonic distortion in electroacoustic transducers under indirect drive conditions

Nonlinear transducer equations for the six major types of electroacoustic transducers (electrostatic, variable reluctance, moving coil, piezoelectric, electrostrictive, and magnetostrictive) are formulated in a common way and solved approximately by perturbation analysis for indirect drive, i.e., current drive of electric field transducers and voltage drive of magnetic field transducers. The direct drive analysis, i.e., voltage drive of electric field transducers and current drive of magnetic field transducers, was given in J. Acoust. Soc. Am. 98, 1596–1611 (1995). Expressions and graphs are given for some of the indirect drive harmonics which apply to all six transducer types. The solutions for direct and indirect drive are compared, and some of the differences are discussed with emphasis on the question of which drive gives lower harmonic distortion. No answer to this question has been found that is applicable to all nonlinear mechanisms in all transducers at all frequencies. However, it is shown that for transducers of all types with low electrical loss operated near resonance direct drive usually gives lower second harmonics. The exceptions occur when mechanical springs are the dominant nonlinearity and the electromechanical coupling is very high; then indirect drive gives lower second harmonics. It is shown how the results, although based on simple lumped parameter models, can be applied in some cases to more complex transducer structures.