Lumped Capacitance Model Research Articles

Modulating Frequency and Responsivity of Pyroelectric Energy Converters by Finite Element Analysis

Pyroelectric energy conversion techniques can be used to convert radiated heat, especially in pulsed periodic waveforms, to electric output. Most existing modeling of the response is done through a lumped capacitance heat model which assumes a sufficiently thin sample with adiabatic substrate. A finite element model of a pulsed heat source and the resultant heat distribution is developed to study the optimization of the pyroelectric energy conversion process. The model uses simultaneous analysis of a temperature domain and the attached circuitry for the determination of the voltage responsivity. It is found that the low frequency cutoff of the responses is limited by the thermal time constant of the pyroelectric elements including the sample and the substrate; while the high frequency limit is due to combined effects of the electrical time constant of the material and the trans-impedance of the amplifier. For thin samples the results are consistent with the lumped capacitance model that is effective in predicting the response. For thicker samples however the behavior of the pyroelectric conversion deviates appreciably from that of the lumped model.

A hybrid lumped capacitance-CFD model for the simulation of data center transients

Transient thermal events in air-cooled data centers may lead to undesirable operating conditions such as the formation of hot spots and associated degradation of equipment reliability. These transients may be caused by cooling equipment failures, server load changes, or other time-dependent scenarios in data center operations. This paper introduces a fast-executing hybrid computational fluid dynamics (CFD)/Lumped-Capacitance model for predicting server inlet temperatures resulting from common transient events such as server shutdown, partial or total chilled water interruption, or partial or total failure of the computer room air handlers (CRAH). The model uses initial steady-state CFD or experimental data in combination with several lumped-capacitance models of the various thermal masses in the data center, including the servers, the room enclosure, the CRAHs and the underfloor plenum. The inclusion of these thermal capacitances and their associated thermal conductance was found to be an important contributor to the overall transient response of the data center air-space. The model predictions have been compared with experimental data obtained in a three-rack data-center test cell and found to agree well with the experimental measurements. Examples of the application of the model to more realistic data center configurations are also given.

A Comparison of LCM Results to Calorimetric Data in Predicting Heat Generation from Lithium-Ion Pouch Cells

Estimating the rate of heat generation in a Li-ion battery is very critical for designing a battery thermal management system. Much research has been done that establishes the relationship between the rate of heat generation of a cell to its temperature, state-of-charge (SOC), and rate of charge or discharge. However, experimental studies of the thermal behavior of these cells have focused mainly on the small coin and cylindrical cell formats and at low C-rates.1 Available literature on the heat generation of large format cells at high C-rates are scant and was the impetus for this study. The lumped capacitance method (LCM) is a useful technique that can greatly simplify an otherwise complicated problem in transient heat transfer. However, the validity of LCM results hinges on how well certain assumptions and conditions hold. The criterion in this case is to have spatial temperature uniformity throughout the cell. This condition becomes tenuous as the cell is inherently anisotropic and is subjected to increasingly higher C-rates. Often times, computer simulation models summarily assume pouch cells have negligible temperature difference across their thicknesses regardless of size or C-rate.2 They have also considered thermal properties to be isotropic and independent of temperature.3 The objective of this research is to determine how well the LCM predicts the rate of heat generation in a large format pouch cell at several different C-rates of full constant-current discharge. The rate of heat generation will be also measured by a battery calorimeter. The LCM data will be compared to the calorimetric data. Experimental Setup The initial step in this investigation was to determine the average convection coefficient of the cell geometry when oriented as a vertical plate in natural convection. This was accomplished by first having the 14Ah cell self-heat during a 5C discharge. An infrared video camera recorded the cell surface temperature as it naturally cooled to ambient room temperature. Using the lumped capacitance model (LCM), an average convection coefficient was found from curving the LCM model. The predicted cooling rate was found to have an extremely good correlation to the measured data. This was due in large part to the high area-to-volume ratio of the cell format. The derived value of the average convection coefficient was then used in an energy balance equation. It was then possible to model the rate of heat generation of the pouch cell under different rates of discharge by simply knowing the cell surface and ambient temperatures as well as some thermodynamic properties.This same cell then underwent various rates of discharge while having its surface temperature recorded by the infrared video camera at ambient room temperature. From this data, the rate of heat loss through convection and stored within the bulk mass was calculated and summed to equate to the internal rate of heat generation. Precautions were taken to minimize heat loss through conduction. Preliminary Results During a full discharge at a C/5 constant-current rate, the heat generation predicted by LCM did extremely well in matching the calorimetric data. However, during a 1C discharge, the rate of heat generation predicted by LCM tended to be in lower than that measured by the calorimeter for most of the time. The average rate of measured heat generation was 2.82W while LCM predicted 2.13W. This computes to LCM being 24% lower than the calorimetric data on average.The major contributor to the discrepancy between the LCM calculations and calorimetric data is the rate of temperature change as a function of time. This value is used to calculate the rate of heat storage within the cell. Heat storage (and heat generation for that matter) are volumetric phenomena. It is very difficult to accurately calculate this rate of temperature change based on surface measurements. In addition, as the C-rates become increasingly higher, temperature gradients become more pronounced throughout the cell core. This has a detrimental effect on being able to apply LCM.

Coupled Zero-Dimensional/One-Dimensional Model for Hybrid Heat Transfer Measurements

This paper covers the application of an improved model to address errors associated with transient heat transfer experiments, which also include the application of lumped capacitance. Using transient thermochromic liquid crystals techniques, and applying thermochromic liquid crystals underneath lumpable features, it is possible to calculate the heat transfer using a lumped heat capacitance approach. In previous studies using the classical lumped capacitance model, the heat loss into the surface underneath the lumped features was not accounted for. In this paper, an exact, closed-form analytical solution to the enhanced lumped capacitance model is derived for discrete bodies for the case of perfect thermal contact. To validate the model and its exact solution, the transient heat conduction in a representative two-dimensional ribbed surface is simulated numerically using the finite volume method. The modeled behavior of the coupled zero-dimensional/one-dimensional model has reasonable agreement with the numerical simulation. The solution for perfect contact can also be extended for imperfect contact.

Transient thermal response of an individual multiwall carbon nanotube

AbstractWe have proposed a method for measuring the transient thermal response of an individual carbon nanotube under Joule heating with pulse current. A transient temperature response with a time constant of about 50 ns was measured. A simplified lumped capacitance model revealed that this fast response corresponds to the small heat capacity of the nanotube. The measured transient response was fairly well reproduced by finite element method analysis using parameters of bulk graphite, which indicates that the bulk graphite parameters are compatible with those of well‐graphitized nanotubes. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Applying Lumped Capacitance Method to Calculate Heat Rates in the Charge/Discharge of Prismatic Lithium Cells in Natural Convection

To determine heat rates is very critical in designing thermal management of the lithium-ion battery under different rates of charge and discharge. The objective of this research is to determine heat rates in charge/discharge of a prismatic lithium ion battery under natural condition by applying the lumped capacitance method. A prismatic lithium cell is treated as a lumped capacitance model during natural convection cooling and is found to have extremely good correlation to measured data. This is due in large part to the high area-to-volume ratio. As a result, the average convection coefficient (that was found from a best-fitting curve exercise) was used in an energy balance equation. This made it possible to determine the rate of heat generated by the cell under different C-rates of discharge. It was found that the average rate of heat generation during an entire discharge cycle has a linear relationship with the C-rate.

Impacts of contaminant storage on indoor air quality: Model development

A first-order, lumped capacitance model is used to describe the buffering of airborne chemical species by building materials and furnishings in the indoor environment. The model is applied to describe the interaction between formaldehyde in building materials and the concentration of the species in the indoor air. Storage buffering can decrease the effect of ventilation on the indoor concentration, compared to the inverse dependence of indoor concentration on the air exchange rate that is consistent with a constant emission rate source. If the exposure time of an occupant is long relative to the timescale of depletion of the compound from the storage medium, however, the total exposure will depend inversely on the air exchange rate. This lumped capacitance model is also applied to moisture buffering in the indoor environment, which occurs over much shorter depletion timescales of the order of days. This model provides a framework to interpret the impact of storage buffering on time-varying concentrations of chemical species and resulting occupant exposure. Pseudo-steady-state behavior is validated using field measurements. Model behavior over longer times is consistent with formaldehyde and moisture concentration measurements in previous studies.

Transient Behavior of Glow Plugs in Direct-Injection Natural Gas Engines

Glow plugs are a possible ignition source for direct injected natural gas engines. This ignition assistance application is much different than the cold start assist function for which most glow plugs have been designed. In the cold start application, the glow plug is simply heating the air in the cylinder. In the cycle-by-cycle ignition assist application, the glow plug needs to achieve high surface temperatures at specific times in the engine cycle to provide a localized source of ignition. Whereas a simple lumped heat capacitance model is a satisfactory representation of the glow plug for the air heating situation, a much more complex situation exists for hot surface ignition. Simple measurements and theoretical analysis show that the thickness of the heat penetration layer is small within the time scale of the ignition preparation period (1–2 ms). The experiments and analysis were used to develop a discretized representation of the glow plug domain. A simplified heat transfer model, incorporating both convection and radiation losses, was developed for the discretized representation to compute heat transfer to and from the surrounding gas. A scheme for coupling the glow plug model to the surrounding gas computational domain in the KIVA-3V engine simulation code was also developed. The glow plug model successfully simulates the natural gas ignition process for a direct-injection natural gas engine. As well, it can provide detailed information on the local glow plug surface temperature distribution, which can aid in the design of more reliable glow plugs.

Spatial-resolution, lumped-capacitance thermal model for cylindrical Li-ion batteries under high Biot number conditions

The time-efficient yet accurate thermal modeling of the battery cells for electric and hybrid electric vehicles is essential improving the performance, safety, and lifetime of the battery system. This paper presents a spatial-resolution, lumped-capacitance (LC) thermal model for cylindrical battery cells under high Biot number (Bi⩾1) conditions where the classical LC thermal model is generally inapplicable because of a significant temperature variation in the cell volume. The spatial-resolution LC model was formulated using zero- and first-order Hermite integral approximations. For model validation, a one-dimensional, transient analytical (exact) solution using Green functions was obtained for a cylindrical Li-ion battery cell with uniform volumetric battery heat generation of Joule and entropic heating under convective cooling boundary conditions. It was found from the comparison of the results that the spatial-resolution LC thermal model can accurately and quickly predicts the cell temperatures (core, skin and area-averaged) under various dynamic battery duty cycles even for high Biot numbers due to highly convective conditions such as liquid cooling.

Improved lumped-capacitance model for heat and mass transfer in adsorbed gas discharge operations

An improved lumped-capacitance formulation for heat and mass transfer in adsorbed gas discharge operations has been developed. The formulation is obtained by employing the Coupled Integral Equations Approach (CIEA) for reducing one-dimensional transport equations for adsorbed gas storage in a cylindrical domain to a lumped-capacitance form. The CIEA is based on the traditional Hermite formulas for approximating integrals, which are used for producing relations between average potentials and values at boundaries. This approach is shown to reduce the original spatial-dependent PDEs to two time-dependent ODEs, as similar to the ones obtained using classical lumped-system analyses, the main differences being an additional equation that is required for calculating the reservoir wall temperature, and modified Biot numbers. Two different approximation schemes are tested, and one of them is demonstrated to extend the application range of the classical lumped formulation for Fourier values at least two orders of magnitude smaller than the usual limit seen for this problem.

A single-mask thermal displacement sensor in MEMS

This work presents a MEMS displacement sensor based on the conductive heat transfer of a resistively heated silicon structure towards an actuated stage parallel to the structure. This differential sensor can be easily incorporated into a silicon-on-insulator-based process, and fabricated within the same mask as electrostatic actuators and flexure-based stages. We discuss a lumped capacitance model to optimize the sensor sensitivity as a function of the doping concentration, the operating temperature, the heater length and width. We demonstrate various sensor designs. The typical sensor resolution is 2 nm within a bandwidth of 25 Hz at a full scale range of 110 µm.

Suitability analysis of lumped-capacitance formulations for adsorbed gas storage

Abstract Mathematical modeling and numerical solutions can be of great assistance for simulating heat transfer in adsorbed gas (AG) storage operations, leading to better thermal designs of AG reservoirs. Nevertheless, the complexities associated with modeling heat and mass transfer that occur within adsorbed gas processes can lead to formulations that require a great computational effort. In this paper, a complex multidimensional formulation is shown to be reducible to a simple lumped-capacitance model via an averaging procedure. Naturally, this simpler formulation cannot represent accurately a significant number of cases. Hence, a comparison between the simpler lumped formulation with one that considers spatial dependence is provided for estimating ranges of applicability for the simpler form. The results indicate that the Biot number alone cannot be used as a criteria for determining whether a lumped-capacitance model can be accurately employed.

Double-sided wet fabric evaporator utilizing wind and solar energy efficiently — One-dimensional transient simulations

The performance of the double-sided fabric seawater evaporator suggested by Nosoko et al. ( Desalination and Water Treatment16 (2010) 254) was simulated for a sunny day under subtropical and maritime climate conditions by a one-dimensional transient modeling. The concentration of seawater increases exponentially with the downstream distance along the fabric while the temperature and the evaporation rate increase gradually. In a polyester fabric, seawater flows fast and the concentration of the effluent brine is kept constant in a small range by adjusting the rate of influent seawater according with the solar radiation. In a cotton fabric, seawater flows slow, causes a large time lag between the influent and effluent, and thus varies the effluent concentration greatly. The temperature and evaporation rate of the polyester are approximately the same as those of the cotton. The daily evaporation is 9.41 kg/ day ⋅ m 2 − fabric under a solar radiation of 27.6 MJ/ m 2. Lumped capacitance model ( Desalination and Water Treatment16 (2010) 254) was found to predict quite accurately the averages of the evaporation rate and temperature of fabric, but to fail in prediction of the temporal variations of the effluent concentration.

A Wideband and Compact Partial Electromagnetic Bandgap Structure With a Narrow Via Pitch for a Signal Via Shield

A wideband and compact partial electromagnetic bandgap (PEBG) structure and a corresponding stopband-estimation model are proposed for the suppression of simultaneous switching noise (SSN) coupling in a multilayer printed circuit board. The proposed PEBG structure achieves a wide stopband with a compact size by adopting a geometric arrangement of patches that allows for a periodic narrow via pitch (NVP). In addition, the lumped capacitance model of the previously reported effective phase constant equation is replaced with the resonant cavity model to obtain the precise impedance of the patch in high frequency. Finally, it was successfully verified that, by applying the NVP-PEBG structure, wideband suppression of SSN coupling to the signal via is achieved with a bandwidth of 11.2 GHz below -40 dB. The proposed estimation model was validated through experimental measurements.

Simple Rig for Measuring Radiation Heat Fluxes from a Jet Fire

This paper presents an experimental rig for measuring the incident radiation heat flux distribution surrounding a jet fire. The methodology uses a line of surface thermocouples attached to a steel bar. The thermocouples measure the temperature time history of the steel bar in response to an imposed incident heat flux. The theoretical basis of the methodology is an energy balance for any point on the steel bar. The energy balance is formulated as a lumped capacitance model. All of the assumptions in the theory are shown to be valid and the accuracy of the experimental methodology is demonstrated. Finally the educational value of the rig is discussed with an indication of how it can be used to enhance the educational experience of an undergraduate engineer taking an advanced heat transfer module.

Measuring Radiation Heat Fluxes from a Jet Fire Using a Lumped Capacitance Model

This paper presents an experimental methodology for measuring the incident radiation heat flux distribution surrounding a jet fire. The methodology uses a line of surface thermocouples attached to a steel bar. The thermocouples measure the temperature time history of the steel bar in response to an imposed incident radiation heat flux. The theoretical basis of the methodology is an energy balance for any point on the steel bar. The energy balance is formulated as a lumped capacitance model. All of the assumptions in the theory are shown to be valid and the accuracy of the experimental methodology demonstrated.

Kinetics study of the copper/hydrochloric acid reaction for thermochemical hydrogen production

The exothermic reaction of hydrochloric acid with particulate copper occurs during the hydrogen production step in the thermochemical copper–chlorine water splitting cycle. In this paper, this chemical reaction is modeled kinetically, and a parametric study is performed to determine the influences of particle size, temperature and molar ratios on the hydrogen conversion aspects. It is obtained that the residence time of copper particles varies between 10 and 100 s, depending on the operating conditions. The hydrogen conversion at equilibrium varies between 55% and 85%, depending on the reaction temperature. The heat flux at the particle surface, caused by the exothermic enthalpy of reaction, reaches over 3000 W/m 2 when the particle shrinks to 0.1% from its initial size. The estimated Biot number varies from 0.001 to 0.1, depending on the operating conditions and the accuracy of thermophysical data of the substances. A numerical algorithm is developed to solve the moving boundary Stefan problem with a chemical reaction that models the shrinking of copper particles in the hypothesis that the chemical reaction and heat transfer are decoupled. The model allows for the estimation of the temperature of a copper particle, assumed spherical, in the radial direction on the hypothesis of large Biot numbers. For small Biot numbers, the transient heat transfer equation results in a lumped capacitance model. In all cases, the particle decomposes in about 10–20s.

Liquid DEP actuation and precision dispensing of variable volume droplets

Droplet based microfluidic systems, in recent years, have demonstrated numerous advantages and exciting potential for Lab-On-a Chip applications. In order to fully realize the potential benefits of this technology, one requires precision dispensing and manipulation of droplets of known volume and sample concentration, in a rapid and controlled manner. In this article, we demonstrate the rapid and controlled microactuation of aqueous samples and subsequent dispensing of variable volume droplets in nanolitre to picolitre regime by using a coplanar tapered electrode structure that leverages the phenomena of liquid dielectrophoresis (L-DEP). The transient behavior of the tapered liquid jet departs significantly from that of a uniform liquid jet case and is not adequately explained in terms of a simplified lumped capacitance model as in the case of the uniform jet, during the L-DEP actuation. A more generalized numerical model is developed for the tapered actuation scheme to account for the experimental observations. We furthermore demonstrate that the density of the dispensed droplets can be proactively controlled by the judicious placement of electrode bumps and pinches in the electrode structure thus overcoming the limitations imposed by Rayleigh's instability criterion. The proposed droplet dispensing schemes are superior to existing L-DEP based dispensing schemes which are restricted in size and spacing of the dispensed droplets by Rayleigh's instability criteria and furthermore mostly restricted to equi-volume droplets.

Prediction of Indoor Climate and Long-Term Air Quality Using the BTA-AQP Model: Part I. BTA Model Development and Evaluation

The objective of this research was to develop a building thermal analysis and air quality predictive (BTA-AQP) model to predict ventilation rate, indoor temperature, and long-term air quality (NH3, H2S, and CO2 concentrations and emissions) for swine deep-pit buildings. This article, part I of II, presents a lumped capacitance model (BTA model) to predict the transient behavior of ventilation rate and indoor air temperature according to the thermo-physical properties of a typical swine building, setpoint temperature scheme, fan staging scheme, transient outside temperature, and the heat fluxes from pigs and supplemental heaters. The obtained ventilation rate and resulting indoor air temperature, combined with animal growth cycle, in-house manure storage level, and typical meteorological year (TMY3) data, were used as inputs to the air quality predictive model (part II) based on the generalized regression neural network (GRNN-AQP model), which was presented in an earlier article. The statistical results indicated that the performance of the BTA model for predicting ventilation rate and indoor air temperature was very good in terms of low mean absolute error, a coefficient of mass residual values equal to 0, an index of agreement value close to 1, and Nash-Sutcliffe model efficiency values higher than 0.65. Graphical presentations of predicted vs. actual ventilation rate and indoor temperature are provided to demonstrate that the BTA model was able to accurately estimate indoor climate and therefore could be used as input for the GRNN-AQP model discussed in part II of this research.

Thermal Analysis and Heat Exchanger Design for Pulse Detonation Engine

The thermal environment of a pulse detonation engine was modeled using a space-time averaging procedure. The method allowed the one-dimensional, lumped-capacitance model to be used. The tube dimensions were a bore of 100 mm and a length of 1 m. For the calculations, the PDE pulse was split into a heating, exhaust and purging subprocess. Assumptions for the duration of each process were made based on previous experiments. The PDE was also assumed to operate at about 19 Hz. The calculations were performed for a stoichiometric air and octane mixture initially at STP. Wall materials consist of stainless steel, copper and Haynes alloy. Different water flow rates and jacket radii were used. The study showed that high water flow rates and large jackets were able to reduce the temperature at the water jacket. The temperatures of the inner and outer PDE walls were unaffected by the coolant flow or the jacket dimensions. These surfaces remain at high temperatures and indicate that a PDE requires advanced cooling te...