One-dimensional Transient Model Research Articles

Thermal behavior analysis of coated cutting tool using analytical solutions

Nowadays, almost all cutting tools are coated due to improvements in manufacturing processes. The two main reasons are: (1) coatings allow a cut with less friction and less wear resulting in longer tool life and (2) thermal barrier effect, since the contact between workpiece–tool–chip occurs in the coating and not in the tool material (substrate). This paper analyzes, the thermal effect of the coating without considering the tribological effect. The thermal behavior with three types of coating: cobalt (Co), titanium nitride (TiN), and aluminum oxide ( $$\hbox {Al}_2 \hbox {O}_3$$ ) on a ISO K10 carbide insert of 3 mm thickness was investigated. This paper investigates the behavior of inserts with coatings of thickness of 1, 2, 5, 10, and $$20\,\upmu$$ m in a one-dimensional transient thermal model proposed for a material composed of two layers. A constant heat flux simulates the heat generated in the tool–piece–chip interface for coated and non-coated inserts. The solution of the diffusion equation is obtained using the Green function method. The effect of the coating can then be calculated by analyzing the evolution of the temperature at the cutting interface in contact with the heat flux and the evolution of the temperature at the coating–substrate interface. It can be concluded that coatings have thermal barrier effect, although for coatings of $$2\,\upmu$$ m thickness, this influence is very small and produces temperature reduction of up to 14%. For thicknesses greater than $$5 \upmu$$ m, the effect becomes considerable depending on the coating–substrate pair. In the case of TiN carbide, the temperature reduction is 26, 34, and 41% for the thicknesses of 5, 10, and $$20\, \upmu$$ m, respectively.

Preparation and photo-thermal conversion performance of modified graphene/ionic liquid nanofluids with excellent dispersion stability

Dispersion stability has been long considered as a critical issue for applying nanofluids in various fields, especially for the applications at elevated temperatures. Herein a novel route is explored to improve the dispersion stability of graphene (GE)/ionic liquid (IL) nanofluids for use as working fluids in medium- and high-temperature direct absorption solar collectors (DASCs), which involves modifying GE according to the molecular structure of the IL. Specifically, GE was modified using the reagents and process for synthesizing [HMIM]BF4, followed by dispersing the modified GE (MGE) into [HMIM]BF4. It is verified that the molecular chains similar to [HMIM]BF4 have been grafted on the nanosheets of GE, and the MGE/[HMIM]BF4 nanofluids exhibit much better dispersion stability than the one containing the unmodified GE, even at elevated temperatures. Moreover, the temperature profiles of the nanofluids containing MGE and GE were obtained both from the experimental measurement and the theoretical prediction using a one-dimensional transient heat transfer model. It is shown that the experimental data are in good agreement with the numerical ones for the MGE nanofluids, while a large deviation between them is found for the one containing the unmodified GE. And the MGE nanofluid shows enhanced receiver efficiency as compared to the GE one due to its much improved dispersion stability. Further, the transient model was used to predict the performance of the MGE nanofluid based DASCs under high solar concentrations. And by integrating the MGE concentration and the receiver height into a parameter, namely optical thickness, the optimization of the MGE nanofluid based DASC was carried out varying solar concentration, MGE concentration, nanofluid height and exposure time. It is revealed that the photo-thermal conversion performance of nanofluids greatly depends on its dispersion stability at elevated temperatures, and the MGE/[HMIM]BF4 nanofluids possess excellent dispersion stability and show great potentials for use as the working fluids in DASCs. This work sheds light on effective routes for improving dispersion stability of nanofluids as well as numerical investigations on nanofluid based DASCs.

Transient modeling of electrochemically assisted CO2 capture and release

The present work aims to develop a model of a new electrochemical CO2 separation and release technology. We present a one-dimensional transient model of an electrochemical cell for point source CO2 capture and release, which mainly focuses on the simultaneous mass transport and complex chemical reactions associated with the separation process. For concreteness, we use an ionic liquid (IL) with 2M thiolate anion (RS−) in 1M disulfide (RSSR) as an electrolyte in the electrochemical cell to capture, transport and release CO2 under standard operating conditions. We computationally solved the model to analyze the time-dependent behavior of CO2 capture and electro-migration transport across the cell length. Given high nonlinearity of the system, we used a finite element method (FEM) to numerically solve the coupled mass transport equations. The model describes the concentration profiles by taking into account the individual transport of all participating species, charged as well as neutral. The model predicts performance characteristics of electrochemically assisted CO2 capture and release in terms of faradaic efficiency and cell current density as the cell dynamics evolves and approaches the steady state. The model provides an opportunity to better understand electrochemically assisted CO2 capture and release, and when coupled with experimental results will provide an early assessment of feasibility for large-scale application in realistic conditions.

Liquid Holdup Discretized Solution's Existence and Uniqueness Using a Simplified Averaged One-Dimensional Upward Two-Phase Flow Transient Model

This article presents a one-dimensional numerical model for vertical upward multiphase flow dynamics in a pipeline. A quasi-steady-state condition is used for the gas phase as well as liquid and gas momentum equations. A second-order polynomial for homogeneous flows and a sixth-order polynomial for separated flows are derived to determine the two-phase flow dynamics, assuming that the gas flow mass is conserved. The polynomials are formulated based on the homogenous and separate flows' momentum equation and the homogeneous flows' rise velocity equation and their zeros are the flow actual liquid holdup. The modeling polynomial approach enables the study of the polynomial liquid holdup zeros existence and uniqueness and as a result the design of a stable numerical model in terms of its outputs. The one-dimensional solution of the flow for the case of slug and bubble flow is proven to exist and to be unique when the ratio of the pipe node length to the time step is inferior to a specific limit. For the annular flow case, constraints on the inlet gas superficial velocity and liquid to gas density ratio show that the existence is ensured while the uniqueness may be violated. Simulations of inlet pressure under transient condition are provided to illustrate the numerical model predictions. The model steady-state results are validated against experimental measurements and previously developed and validated multiphase flow mechanistic model.

A transient model for temperature prediction in a salt-gradient solar pond and the ground beneath it

Salt-gradient solar ponds are cost-effective long-term solar collectors that can store low-grade heat and deliver it continuously. For design and operation purposes, it is important to develop computational tools that can represent energy fluxes at the interface between the bottom of the pond and the ground beneath it. In this study, a robust one-dimensional transient model is developed to represent the thermal evolution of a salt-gradient solar pond and the ground that surrounds it. The model was evaluated under different contrasting scenarios: buried or unburied ponds, artificially or naturally heated ponds and for deep or shallow groundwater tables. Experimental data from an indoor laboratory-scale solar pond were used for the development, calibration and validation of the model. A good agreement between experimental and modeled results was observed, with a root mean square error (RMSE) of 1.21 °C and 1.54 °C for the upper and lower convective zones respectively, during a 28-days validation period. Further, the model was validated using experimental data from three outdoor salt-gradient solar ponds obtaining RMSEs that ranged between 1.5 and 6.5 °C. Results show that dividing the ground into multiple layers contributes to the robustness of the model, as it allows the representation of the ground heat storage.

Dynamic modeling of temperature change in outdoor operated tubular photobioreactors.

In this study, a one-dimensional transient model was developed to analyze the temperature variation of tubular photobioreactors operated outdoors and the validity of the model was tested by comparing the predictions of the model with the experimental data. The model included the effects of convection and radiative heat exchange on the reactor temperature throughout the day. The temperatures in the reactors increased with increasing solar radiation and air temperatures, and the predicted reactor temperatures corresponded well to the measured experimental values. The heat transferred to the reactor was mainly through radiation: the radiative heat absorbed by the reactor medium, ground radiation, air radiation, and solar (direct and diffuse) radiation, while heat loss was mainly through the heat transfer to the cooling water and forced convection. The amount of heat transferred by reflected radiation and metabolic activities of the bacteria and pump work was negligible. Counter-current cooling was more effective in controlling reactor temperature than co-current cooling. The model developed identifies major heat transfer mechanisms in outdoor operated tubular photobioreactors, and accurately predicts temperature changes in these systems. This is useful in determining cooling duty under transient conditions and scaling up photobioreactors. The photobioreactor design and the thermal modeling were carried out and experimental results obtained for the case study of photofermentative hydrogen production by Rhodobacter capsulatus, but the approach is applicable to photobiological systems that are to be operated under outdoor conditions with significant cooling demands.

Analysis of self-propagating intermetallic reaction in nanoscale multilayers of binary metals

Nanoscale multilayers of two different metals could exhibit super-fast intermetallic reaction wave that accompanies high level of exothermic heat release, while additional advantage is a very small ignition delay. They could be a promising candidate for the core technology in realizing micron-sized initiation device for explosives detonation or propellants ignition in various defense and civilian applications. This numerical investigation focuses on the numerical modeling and computations of the ignition and self-propagating reaction behaviors in nanoscale intermetallic multilayer structures made of alternating binary metal layers of boron and titanium. Due to thin film nature of metallic multilayers, intermetallic reaction propagation across the repeating bimetallic multilayers is approximated to the one-dimensional transient model of thermal diffusion and atomic species diffusion, and the intermetallic reaction between two metal species is assumed to follow Arrhenius dependence on temperature. The computational results show the details of ignition and propagation characteristics of intermetallic reaction wave by evaluating and discussing the effects of key parameters, such as multilayer thickness, excess of one metal species, and presence of atomic premixing at interface of boron and titanium layers, on ignition delay and propagation speed of self-sustaining reaction wave.

Evolving one-dimensional transient jet modeling by integrating jet breakup physics

High-speed optical measurements of unsteady liquid fuel jets under engine-like conditions have shown that the initial penetration of the jets does not follow the behavior predicted by previously introduced one-dimensional jet models based on gas-jet principles. The experimental data indicate that the transient jet penetration velocity is initially controlled by the jet exit velocity, transitioning to gas-jet like mixing-dominated penetration further downstream. This behavior is consistent with the common description of high-pressure fuel jets as containing a liquid core surrounded by entrained gas and fuel droplets. In this paper, a new one-dimensional modeling methodology is introduced that couples the transport equations for the evolution of the liquid core of the jet and the surrounding sheath of droplets resulting from breakup. This allows for the penetration of the jet to be initially governed by the liquid core, which is relatively unaffected by the ambient gas, transitioning to spray penetration dominated by the entrained ambient gas. The model also provides a defined jet centerline velocity, which allows for the shape of the radial profiles of fuel velocity and fuel volume fraction to be solved for directly, without the need for a steady-jet assumption, as was used in previous one-dimensional models. This change removes the need for a constant momentum flux assumption, improving the transient nature of the model. The results of the model are validated against the aforementioned optical transient jet measurements. The model and all associated experimental data have been made available for use at rothamer.erc.wisc.edu/dlp .

Modeling the defrost process in complex geometries – Part 1: Development of a one-dimensional defrost model

Frost formation is a common, often undesired phenomenon in heat exchanges such as air coolers. Thus, air coolers have to be defrosted periodically, causing significant energy consumption. For the design and optimization, prediction of defrosting by a CFD tool is desired. This paper presents a one-dimensional transient model approach suitable to be used as a zero-dimensional wall-function in CFD for modeling the defrost process at the fin and tube interfaces. In accordance to previous work a multi stage defrost model is introduced (e.g. [1, 2]). In the first instance the multi stage model is implemented and validated using MATLAB. The defrost process of a one-dimensional frost segment is investigated. Fixed boundary conditions are provided at the frost interfaces. The simulation results verify the plausibility of the designed model. The evaluation of the simulated defrost process shows the expected convergent behavior of the three-stage sequence.

Numerical Simulation on the Ignition Characteristics of the Inner Hole Surface of Perforated Propellant Grains

The flow and heat transfer process of ignition flame in the inner hole of perforated propellant grains as well as the ignition characteristics of its inner surface are studied in this paper. An unsteady one-dimensional flow model of ignition flame in the micro-perforated inner hole was proposed according to the physical model of flow. Meanwhile, by the considering the convection and radiation between ignition flame and the inner surface of propellant, a transient one-dimensional model of heat transfer was derived. The flow process of ignition flame in the hole as well as heat transfer process between flame and inner surface is simulated by appropriate scheme. The variation and distribution of inner surface temperature as well as the temperature, pressure and velocity of ignition flame are illustrated and analyzed. The numerical results indicated that the ignition of the inner surface of propellant grains does not occur at the same time, the non-simultaneous ignition of the propellant surface will change the combustion properties of propellant.

Effects of Nozzle Geometry on the Characteristics of an Evaporating Diesel Spray

The effects of nozzle geometry on diesel spray characteristics were studied in a spray chamber under evaporating conditions using three single-hole nozzles, one cylindrical and two convergent, designated N1 (outlet diameter 140 μm, k-factor 0), N2 (outlet diameter 140 μm, k-factor 2) and N3 (outlet diameter 136 μm, k-factor 2). Spray experiments were performed with each nozzle at two constant gas densities (15 and 30 kg/m3) and an ambient temperature (673 K) at which evaporation occurs, with injection pressures ranging from 800 to 1600 bar. A light absorption and scattering method using visible and UV light was implemented, and shadow images of liquid and vapor phase fuel were recorded with high-speed video cameras. The cylindrical nozzle N1 yielded larger local vapor cone angles than the convergent nozzles N2 and N3 at both gas densities, and the difference became larger as the injection pressure increased. The vapor phase penetration values for nozzle N1 and N3 were quite similar and always lower than those for N2. This is consistent with the impingement measurements, which showed that the momentum flux of nozzle N1 was only slightly greater than that of nozzle N3, while that of nozzle N2 was substantially greater. The vapor volume fractions measured along the spray’s center line were well explained by the one-dimensional transient diesel jet model, indicating that diesel spray vaporization is controlled by turbulent fuel-air mixing.

A transient one-dimensional numerical model for kinetic Stirling engine

A third-order numerical model based on one-dimensional computational fluid dynamics is developed for kinetic Stirling engines. Various loss mechanisms in Stirling engines, including gas spring hysteresis loss, shuttle loss, appendix displacer gap loss, gas leakage loss, finite speed loss, piston friction loss, pressure drop loss, heat conduction loss, mechanical loss and imperfect heat transfer, are considered and embedded into the basic control equations. The non-equilibrium thermal model is adopted for the regenerator to capture the oscillating features of the gas and solid temperatures. To improve the numerical stability and accuracy, the implicit second-order time difference scheme and the second-order upwind scheme are adopted for discretizing the time differential terms and convective terms, respectively. Experimental validations are then conducted on a beta-type Stirling engine with the extensive experimental data for diverse working conditions. The results show that the developed model has better accuracies than the previous second-order models. Good agreements are achieved for predicting various critical system parameters, including pressure-volume diagram, indicated power, brake power, indicated efficiency, brake efficiency and mechanical efficiency. In particular, both the experiments and simulations show that the Stirling engine charged with helium tends to have much lower optimal working frequencies and poorer performances compared to the hydrogen system. Based on the analyses of the losses, it reveals that the pressure drop in the flow channels plays a critical role in shaping the different behaviors. The pressure drop in the helium system is much larger and more sensitive to the frequency increase due to the much larger viscosity of gaseous helium. Hydrogen is a superior working gas for a Stirling engine. The transient characteristics of the oscillating flow and the associated thermal interactions between gas and solid in the regenerator are finally analyzed in order to have an insight of the complex thermodynamic process. The study provides a promising numerical approach in simulating Stirling engines for further understandings of their operating characteristics and the underling mechanisms.

Experimental testing and mathematical modelling of diesel particle collection in flow-through monoliths

The honeycomb monolith is the most prevalent geometry in automotive exhaust aftertreatment, with applications including oxidation catalysts, partial-flow and wall-flow filters. Particle collection mechanisms at the leading edge of honeycomb monoliths and in open channels are usually neglected by engineers of these devices. Under specific conditions however, these phenomena can make an appreciable contribution to overall particle collection and deposits on channel walls may affect catalyst performance. In the current study, experimental measurements of deposit loading, capture efficiency and pressure drop at constant flow conditions are presented for three flow-through monoliths with different cell densities and lengths, while particle distribution is varied in an additional case. The processed results reveal the evolution of deposit distribution at the leading edge, the entry zone inside the channel and the remaining part of the monolith. Next a one-dimensional transient mathematical model is proposed, which takes into account interception at the edge and coupled diffusion–interception inside the channel. After fitting the model parameters, all experimental cases are predicted with sufficient accuracy with the exception of loadings extended beyond 12 hours. Finally, further application of the model reveals the negative effect of flow rate on collection efficiency and the potential to maximize or minimize collection efficiency using various cell designs.

Green Function Formulation and Finite Element Discretization for Solving the Heat Radiative Transfer in a Slab

ABSTRACTThe radiative transport problem involving the nonlinear coupling between temperature and radiative transfer poses several difficulties to be solved numerically. In this paper, we sought numerical solutions for the transient one-dimensional model by applying the Green Function Decomposition Method to the radiative transport equation and a finite element scheme to the energy balance equation. We apply this new numerical implementation to calculate the evolution of temperature in a slab of glass. The proposed scheme has been found computationally efficient and we have achieved better accuracy than the previous results from the literature.

Problem of transient turbulent convection and a semiempirical profile of turbulent heat exchange coefficient in freshwater bodies

A problem of convective cooling of both freshwater and saltwater lake is formulated. A transient one-dimensional turbulent model with variable layer depth is proposed to describe the process of freezing. The dependence of layer depth on time is determined by a universal equation describing the propagation of Deardorff convective layer. A combination of the main form of equations of Kolmogorov–Obukhov theory and available experimental data is shown to allow the construction of a universal profile of turbulent exchange coefficient, depending on the height.

Modeling the oscillative behavior and carbon monoxide removal by current pulsing technique in H2/CO mixtures for Pt catalyst layer

The main objectives of this study are to investigate the carbon monoxide (CO) poisoning and a mitigation method of high-level CO in a platinum (Pt) catalyst layer using hydrogen (H2)/CO mixture as the inlet fuel. Two separate levels of poisoning, 1000 and 10,000 ppm CO at the anode fuel, are considered and investigated in detail. For this purpose, a one-dimensional transient model is developed including the diffusion of hydrogen and carbon monoxide, the conservation of adsorbed species, and ionic and electronic charges. As a result of CO poisoning, oscillations in overpotential and coverage of adsorbed species are observed for 1000 ppm CO level, while the similar situation is not detected for 10,000 ppm CO. Hence, the behavior of oscillations throughout the catalyst layer thickness, and the reasons are explored for the lower concentration case. For 10,000 ppm CO, a mitigation technique, in which current density is pulsed from 0.1 to 2.5 A/cm2 for a period of time, is performed in order to remove the adsorbed CO from the Pt sites. It is concluded that up to 92% of CO coverage within the catalyst layer can be removed, and 70% of the catalyst layer length is determined to be completely CO-free following the application of current pulsing.

Effect of CO2 on oxy-fuel combustion of coal-char particles in a fluidized bed: Modeling and comparison with the conventional mode of combustion

A char combustion model is developed to study the effect of CO2 on the combustion of coarse char particles under oxy-fuel conditions in a fluidized bed (FB). It is a transient one-dimensional model, taking into account the heat and mass transfer from the bed to the particle and the heterogeneous combustion and gasification of char. The model shows good ability to predict the char temperature history measured in our previous work for different combinations of O2/CO2 and O2/N2 with various coal types. Simulations are carried out to establish the role of CO2 in oxy-fuel conversion at different O2 levels, particle sizes, and bed temperatures. The model is used to analyze the relative contribution of carbon in the char consumed by CO2 (gasification) and O2 (combustion), as well as the differences of the peak temperatures and the burnout times in O2/CO2 and O2/N2 for char particles in a commercial FB combustor. The results indicate that the conversion of coarse (mm size) char particles in an oxy-FB is controlled by the diffusion of O2 both in the O2/CO2 and O2/N2 case. The burn-out time decreases with the bed temperature also in both cases. The lower O2 diffusion rate in CO2 compared to N2, is the main reason for the longer burnout time and lower peak temperature found using O2/CO2 at bed temperatures of 1073–1173K. In that temperature window, the contribution of the CO2-char gasification is limited, being notable only at high bed temperature in O2/CO2, e.g. 1223K. In such high temperature conditions (rarely expected to be found in commercial coal FBC) the predicted burnout time of a lignite char-particle becomes shorter in O2/CO2 than in O2/N2.

Quantification of ionic transport within thermally-activated batteries using electron probe micro-analysis

The transient transport of electrolytes in thermally-activated batteries is studied using electron probe micro-analysis (EPMA), demonstrating the robust capability of EPMA as a useful tool for studying and quantifying mass transport within porous materials, particularly in difficult environments where classical flow measurements are challenging. By tracking the mobility of bromine and potassium ions from the electrolyte stored within the separator into the lithium silicon anode and iron disulfide cathode, we are able to quantify the transport mechanisms and physical properties of the electrodes including permeability and tortuosity. Due to the micron to submicron scale porous structure of the initially dry anode, a fast capillary pressure driven flow is observed into the anode from which we are able to set a lower bound on the permeability of 10−1 mDarcy. The transport into the cathode is diffusion-limited because the cathode originally contained some electrolyte before activation. Using a transient one-dimensional diffusion model, we estimate the tortuosity of the cathode electrode to be 2.8 ± 0.8.

Low-Calorific Gas Combustion in a Two-Layer Porous Burner

To promote the effective utilization of different varieties of low-calorific gas mixtures in a porous media burner, combustion behaviors of three typical low-calorific gas mixtures in a two-layer porous burner are simulated with a two-energy and one-dimensional transient model. The equivalence ratio and inlet velocity are kept constant. A baseline simulation for the three mixtures is presented, and partial results are compared against the experimental measurement of axial temperatures and emission levels. A parametric study is conducted on the conductivity and convective coefficient of up- and downstream sections. The study shows that the upstream convective coefficient has more influence on temperature behaviors than that in the downstream. The solid conductivity effect on temperature behaviors is closely associated with the reaction zone location relative to the interface. CO emission behavior is found to be fairly sensitive to the change in upstream material properties. The results suggest that, for cl...

Geothermal well behaviour prediction after air compress stimulation using one-dimensional transient numerical modelling

The non-discharges geothermal wells have been a main problem in geothermal development stages and well discharge stimulation is required to initiate a flow. Air compress stimulation is one of the methods to trigger a fluid flow from the geothermal reservoir. The result of this process can be predicted by using by the Af / Ac method, but sometimes this method shows uncertainty result in several geothermal wells and also this prediction method does not take into account the flowing time of geothermal fluid to discharge after opening the well head. This paper presents a simulation of non-discharges well under air compress stimulation to predict well behavior and time process required. The component of this model consists of geothermal well data during heating-up process such as pressure, temperature and mass flow in the water column and main feed zone level. The one-dimensional transient numerical model is run based on the Single Fluid Volume Element (SFVE) method. According to the simulation result, the geothermal well behavior prediction after air compress stimulation will be valid under two specific circumstances, such as single phase fluid density between 1 - 28 kg/m3 and above 28.5 kg/m3. The first condition shows that successful well discharge and the last condition represent failed well discharge after air compress stimulation (only for two wells data). The comparison of pf values between simulation and field observation shows the different result according to the success discharge well. Time required for flow to occur as observed in well head by using the SFVE method is different with the actual field condition. This model needs to improve by updating more geothermal well data and modified fluid phase condition inside the wellbore.