Balance Laws Of Mass Research Articles

Analysis of Pressure Pulsation Influence on Compressed Natural Gas (CNG) Compressor Performance for Ideal and Real Gas Models

This work investigates the effects of pressure pulsations on reciprocating natural gas compressor performance thermodynamically. A nonlinear hybrid numerical model is thus developed to consider the interaction between the compressor and the pipeline system. The suction chamber, compressor cylinder and discharge chamber are modelled integrally based on the first law of thermodynamics and mass balance, and the pipeline flow is described by using the gas dynamic model. Methane is considered as the working fluid and its properties are computed based on ideal and real gas assumptions. For the real gas model, the methane properties are obtained by means of calling the NIST REFPROP database. The validity of numerical results is confirmed by previous experimental values. Results from the examinations of pressure pulsation influence demonstrate that discharge resonance requires more specific work than suction resonance in the same harmonic; in the suction system, the first harmonic response reduces the mass flow rate but significantly increases specific work, and the second harmonic response has a strong supercharging effect but the specific work is increased slightly; in the discharge system, the mass flow rate is changed little by pressure pulsations, but the indicated power and specific work are increased significantly; for the real gas model, the in-cylinder temperature during the compression and discharge phases, mass flow rate and indicated power are higher than those for the ideal gas model, whereas the specific work is less for the real gas model than for the ideal gas model.

Modeling Immiscible Two‐Phase Flow in Rough Fractures From Capillary to Viscous Fingering

AbstractWe develop an efficient computational model for simulating fluid invasion patterns emerging in variable aperture fractures. This two‐dimensional model takes into account the effect of capillary force on the fluid‐fluid interfaces and viscous pressure drop in both fluid phases. The pressure distribution is solved at each time step based on mass balance and local cubic law, considering an imposed pressure jump condition at the fluid‐fluid interface. This pressure jump corresponds to the Laplace pressure which includes both terms related to the out‐of‐plane (aperture‐spanning) curvature and to the in‐plane curvature. Simulating a configuration that emulates viscous fingering in two‐dimensional random porous media confirms that the model accounts properly for the role of viscous forces. Furthermore, direct comparison with previously obtained experimental results shows that the model reproduces the observed drainage patterns in a rough fracture reasonably well. The evolutions of tip location, the inlet pressures, and the invading phase fractal dimensions are analyzed to characterize the transition from capillary fingering to viscous fingering regimes. A radial injection scenario of immiscible invasion is also studied with varying modified capillary number and viscosity ratio, showing displacement patterns ranging from capillary fingering to viscous fingering to stable displacement. Such simulations using two contact angles show that the invading phase becomes more compact when the wetting condition changes from strong to weak drainage, as already observed in 2‐D porous media. The model can be used to bridge the gap in spatial scales of two‐phase flow between pore‐scale modeling approaches and the continuum Darcy‐scale models.

Analysis of Maisotsenko humid air bottoming cycle employing mixed flow air saturator

Maisotsenko Humid Air Bottoming Cycle (MHABC) is a viable option for the waste heat recovery of gas turbine topping cycle to attain a higher efficiency point of the combined cycle power plant; thus, having a potential of lower CO2 emissions towards environment. In this work, instead of the typically proposed counter flow configuration of the air saturator, a novel mixed flow configuration is proposed. The proposed configuration uses a hybrid cross-flow and a regenerative counter-flow heat and mass exchanger (HMX). This hybrid HMX is numerically simulated to estimate optimal amount of saturated air which can lead to maximum efficiency and power output. The mathematical model of the mixed flow configuration HMX based air saturator is developed by applying mass and energy balance laws on a selected control volume. The results of the air saturator are initially validated using previously published experimental data for air cooling applications. Furthermore, simulations for high-pressure operations suitable for power generation are performed and a parametric analysis shows that optimal mass flow rate ratio between the working air in the dry channel and incoming air for cross-flow part is 0.65. Optimal mass flow ratio between the working air wet channel and working air dry channel for the counter-flow part is 0.5. The integration of hybrid air saturator in MHABC can yield a maximum of ~57 MW of output work and ~42% of thermal efficiency. The proposed system can achieve a 7% increment in total output work, and 9% increment in thermal efficiency as compared to the counter-flow configuration as an air saturator in the bottoming cycle. Furthermore, the proposed system has ~55% fewer carbon footprint as compared to counter-flow configuration alone as an air saturator.

A non-linear reciprocating compressor model representing the interaction between thermodynamic process and unsteady flow

Accurate comprehension of the thermodynamic demeanor and pressure pulsation propagation is of great attractive in a reciprocating compressor plant. A numerical model has been built to consider the reciprocal interaction between compressor and pipelines. Simulation of the thermodynamic process is performed based on mass balance and first law of thermodynamics in the suction chamber, cylinder volume and discharge chamber, together with thermodynamic relationships. Pressure pulsations in the pipelines are predicted by solving one dimensional unsteady flow equations. Comparison between numerical results and previous experimental results encounters good agreement and the mutual influence between thermodynamic process and pressure pulsation is then highlighted by extending a further analysis of the compressor and the pipelines.

Mechanics of adsorption–deformation coupling in porous media

This work extends Coussy's macroscale theory for porous materials interacting with adsorptive fluid mixtures. The solid-fluid interface is treated as an independent phase that obeys its own mass, momentum and energy balance laws. As a result, a surface strain energy term appears in the free energy balance equation of the solid phase, which further introduces the so-called adsorption stress in the constitutive equations of the porous skeleton. This establishes a fundamental link between the adsorption characteristics of the solid-fluid interface and the mechanical response of the porous media. The thermodynamic framework is quite general in that it recovers the coupled conduction laws, Gibbs isotherm and the Shuttleworth's equation for surface stress, and imposes no constraints on the magnitude of deformation and the functional form of the adsorption isotherms. A rich variety of coupling between adsorption and deformation is recovered as a result of combining different poroelastic models (isotropic vs. anisotropic, linear vs. nonlinear) and adsorption models (unary vs. mixture adsorption, uncoupled vs. stretch-dependent adsorption). These predictions are discussed against the backdrop of recent experimental data on coal swelling subjected to CO2 and CO2CH4 injections, showing the capability and versatility of the theory in capturing adsorption-induced deformation of porous materials.

A coupled model of transport-reaction-mechanics with trapping. Part I – Small strain analysis

A fully coupled model for mass and heat transport, mechanics, and chemical reactions with trapping is proposed. It is rooted in non-equilibrium rational thermodynamics and assumes that displacements and strains are small. Balance laws for mass, linear and angular momentum, energy, and entropy are stated. Thermodynamic restrictions are identified, based on an additive strain decomposition and on the definition of the Helmholtz free energy. Constitutive theory and chemical kinetics are studied in order to finally write the governing equations for the multi-physics problem. The field equations are solved numerically with the finite element method, stemming from a three-fields variational formulation. Three case-studies on vacancies redistribution in metals, hydrogen embrittlement, and the charge–discharge of active particles in Li-ion batteries demonstrate the features and the potential of the proposed model.

A dynamic model used for controller design for fast cut back of coal-fired boiler-turbine plant

Fast cut back (FCB) technology of thermal power plant can restore electricity supply quickly after electric grid fault is repaired. In order to optimize the control technology for FCB, it is necessary to establish an accurate and simple mathematical model for thermal power plant. In this work, a mathematical model of coal-fired boiler-turbine is built up, basing on the balance laws of mass and energy. The steam turbine bypass system, boiler feedwater system and feedwater heaters playing vital roles during FCB are emphatically considered. Model parameters are estimated by FCB field test under the condition of 100% economize continue rate (ECR) load and validated by FCB field test under the condition of 50% ECR load. The model can be used in the controller design for thermal power plant during FCB. Moreover, FCB simulation test for plant with turbine-driven feedwater pump is carried out, showing that it is likely to cause the drum water level out of safe range during FCB.

Contaminant transport in a small deformation aquitard affected by the delayed drainage phenomenon

AbstractThis paper presents a formulation accounting for the effect of delayed drainage phenomenon (DDP) on the breakthrough of contaminant flux in an aquitard, by considering the movement of soil particles, porosity variation, hydraulic head variation, and transient flow during the consolidation. The water flow equation in an aquitard was based on the Terzaghi's consolidation theory, and the contaminant transport equation was derived on the basis of the mass balance law. Two cases were used to illustrate the effect of DDP on the contaminant transport in an aquitard of small deformation. It is found that the breakthrough time of contaminant in an aquitard is very long, which is mainly ascribed to the low permeability of aquitard and sorption of soil particles. It is also found that the increase of depletion, which is in general induced by the increase of thickness and specific storativity and the decrease of hydraulic conductivity, enhances the impact of DDP on the contaminant transport in an aquitard. A larger delay index (τ0) of DDP gives a greater delay breakthrough time (DBT) of solute transport in an aquitard, which controls the difference of the breakthrough time of contaminant transport in aquitards with and without the occurrence of DDP. For the cases where advection plays a dominant role during the process of solute transport, τ0 is almost linearly correlated with DBT, and the ratio of DBT over the breakthrough time without consideration of DDP also approximately shows a linear relationship with the ratio of specific storativity to porosity, given a fixed drawdown in the adjacent aquifer with the sorption being ignored.

Modeling eutrophic lakes: From mass balance laws to ordinary differential equations

Starting from integral balance laws, a model based on nonlinear ordinary differential equations (ODEs) describing the evolution of Phosphorus cycle in a lake is proposed. After showing that the usual homogeneous model is not compatible with the mixture theory, we prove that an ODEs model still holds but for the mean values of the state variables provided that the nonhomogeneous involved fields satisfy suitable conditions. In this model the trophic state of a lake is described by the mean densities of Phosphorus in water and sediments, and phytoplankton biomass. All the quantities appearing in the model can be experimentally evaluated. To propose restoration programs, the evolution of these state variables toward stable steady state conditions is analyzed. Moreover, the local stability analysis is performed with respect to all the model parameters. Some numerical simulations and a real application to lake Varese conclude the paper.

РАСЧЕТ ЭНТРОПИИ РАБОЧЕГО ТЕЛА В ЦИЛИНДРЕ ДИЗЕЛЯ

When using the method of numerical modeling for working processes in diesel engines, parameters are described by three equations: the first law of thermodynamics, mass balance and Clapeyron equation. They are combined in a system of differential equations and solved together at each step of the modeling. If the angular velocity ω of crankshaft is the same, it’s convenient to take a crankshaft angle φ as the argument. If the system is solved with reference to pressure p , temperature T ц and mass G it’s also possible to determine entropy s of working medium. In order to achieve acceptable accuracy of modeling the isochoric heat capacity cv cannot be considered as constant value as it results big calculating error. In order to avoid this, it’s enough to determine cv by quadratic polynomial of absolute temperature of working medium. The offered procedure was checked by numerical modeling of working process of two-stroke engine MAN-B&W 6S26MC and four stroke engine 6 ChN 25/34-2. Results showed that working processes of two- and four-stroke engines in T - s coordinates are looking identically. Moreover, the working processes of engines in T - s coordinates have the likeness of kind with theoretical diagram of Sabathe cycle. This suggests that it’s possible to create quality indexes in order to assess the difference between theoretical and real processes and work out recommendations for process improving.

Numerical model of a shaft furnace operation

PurposeThe model of a shaft furnace operation is presented in this paper. Aim of this model is to predict concentrations of carbon monoxide and dioxide, the temperature of the lava and the heat losses.Design/methodology/approachThe mathematical model is based on 1D mass and heat balance laws for flue gas, coke and four materials used in a mineral wool production. Process parameters should be optimized for the minimal heat loss and the carbon monoxide concentration while keeping the prescribed lava temperature. The model consists of heterogeneous and homogeneous reactions for coke combustion, dolomite decomposition, rock and coke heating and a rock-melting model. The resulting system of partial differential equations is discretized by the finite volume method and solved with the explicit Euler scheme together with the point-implicit preconditioning of sources in species balance equations.FindingsNumerical results are compared with the measured data on the pilot-scale device and show good agreement. It is found that in the lower region of the furnace, the large amount of carbon monoxide is present despite high oxygen levels.Practical/implicationsBased on the numerical model, the parameters of the secondary air stream could be studied (position, volume flux, oxygen enrichment and temperature) to decrease levels of carbon monoxide emissions while keeping lava temperature at needed levels.Originality/valueThe paper includes mathematical and numerical model needed for simulation of shaft furnaces in mineral wool industry. It can be used as a valuable tool for design engineers and furnace operators during research or redesign of existing devices.

A sequential approach for numerical simulation of two-phase multicomponent flow with reactive transport in porous media

We develop a new scheme for numerical solution of immiscible compressible two-phase flow in porous media with geochemistry. The problem is modelled by the mass balance law for each phase, Darcy–Muskat’s law, and the capillary pressure law. Coupling with chemistry occurs through reactions rates. These rates can be either given nonlinear functions of concentrations in the case of kinetic chemical reactions or unknown for equilibrium chemical reactions. Each kinetic reaction produces an ordinary differential equation while each equilibrium reaction gives rise to a mass action law that is an algebraic relation that links the activities of concerned species. An implicit finite volume scheme is applied to solve the two-phase flow equations, which is then sequentially coupled to a method for solving the reactive transport problem. More precisely, we used firstly the module 2p2c implemented in the parallel open-source simulator DuMuX to solve a simplified two-phase two-component flow with two dominant species without chemistry. Secondly, we have developed and integrated a reactive transport module in the DuMuX framework to deal with the other species using a sequential iterative approach (SIA) where transport, equilibrium chemical reactions and kinetic chemical reactions are solved sequentially. A new module for transport and a code using the GSL library for the chemical problem have been coupled. Finally, our approach has been validated by solving several test cases. Here we will present two benchmark tests to demonstrate the ability of our method to approximate solutions of single and two-phase flows with reactive transport in heterogeneous porous media.

Numerical simulation of steady and unsteady flow for generalized Newtonian fluids

This work presents the numerical solution of laminar incompressible viscous flow in a three dimensional branching channel with circle cross section for generalized Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. Numerical solution is based on cetral finite volume method using explicit Runge- Kutta time integration. In the case of unsteady computation artificial compressibility method is considered.

Multi-Scale Modeling of Multi-Physics Processes in Lithium Ion Battery Cells

Lithium-ion (Li-ion henceforth) batteries application to high power and high capacity demanding systems still encounters limitations. This technology is based on the classical intercalation reaction, during which Li is inserted into or extracted from electrodes. During this process the hosting material experiences large volume changes, leading to mechanical degradation, loss of integrity and of electric contact with current collectors. Nano-structured and composite material electrodes may reduce such damaging phenomena.Computational modeling and simulations may be helpful in designing new combinations of materials and geometries. To simulate a whole battery cell at the scale at which Lithium ions intercalate would be computationally unfeasible. A multi-scale approach is desirable and the Computational Homogenization (CH) technique is here adopted. This allows to track micro structural events that initiate damage and lead to macroscopic failure from macroscopic boundary conditions, while limiting the computational cost.This contribution extends to large strains the framework of the CH developed in [1,2]. Temperature dependence is also included, towards modeling batteries under extreme conditions. The adopted approach originates from the fundamental balance laws (of mass, force, charge) and the weak formulation derived has a clear energy interpretation. Electroneutrality assumption has been taken into account. Maxwell's equations are considered in a quasi-static sense in a rigorous setting. All the materials forming the multi-component porous electrode are clearly identified. Migration, diffusion, and intercalation of Lithium in the active particles are modeled. Constitutive assumptions, that emanate from a rigorous thermodynamic setting, complete the formulation. After spatial discretization, a Backward Euler time-advancing algorithm has been implemented in FEM codes. Different finite elements have been designed to deal with the electrolyte, the electrodes and the reaction layer between them. Several case studies have been simulated to validate the implemented formulation.

The State of Charge of Electrodes and Its Effects on Lithium-Iron-Phosphate Battery Simulation

A lithium-iron-phosphate (LFP) battery is one of the ideal energy storage devices owing to its outstanding characteristics such as high power output, no memory effect, and slow degradation. While electrochemical models have been widely used to simulate the LFP battery behaviors, we found the accuracy of simulated LFP battery characteristics, including the cell voltage, lithium concentration distribution, and cell capacity, are highly related to the initial concentrations, namely, the state of charge (SOC) of each individual electrodes. The amount of active lithium in an LFP battery, which determines the cell capacity, is a result of the SOCs of the anode and the cathode at the beginning of charge or the end of discharge processes. The SOC also dictates the equilibrium potential of individual electrodes, which in turn contributes to the full cell potential. However, it is difficult to estimate the amount of lithium in each individual electrode after the activation cycles because a certain amount of lithium is consumed to form the solid electrolyte interface (SEI) layer. Incorporation of inaccurate SOCs in models could lead to erroneous cell potential and capacity estimation. In this study, the initial concentrations of the anode and the cathode are estimated from the experimentally measured equilibrium potentials. By evaluating the characteristic points of individual electrodes and the corresponding reference points of a full cell, on the basis of low-rate discharge potential curves, the SOC of each individual electrode can be accurately calculated. In order to evaluate the discharge performance of the LFP battery and gain insight into the effects of electrode SOCs, an electrochemical model based on coupled mass balance, charge balance, and reaction kinetics constitution laws is developed. To determine the initial SOCs of individual electrodes of the LFP battery, equilibrium potentials are experimentally measured by low-rate discharge while the characteristic points are calculated by identifying critical points of the discharge curves. The LFP battery model with such formally determined SOCs is validated by comparing the simulated discharge curves with experimental measurements under various loading demands, up to 2C. The simulated voltage plateau is closely matching the corresponding experimental results for a range of SOCs as shown in Figure 1. Overestimated cell voltage near the earlier stage of discharge and underestimated cell capacity at all C rates are observed in our simulation results, which could be improved by precise measurements of equilibrium potentials of the electrodes and the full cell. Further understanding of the effects of lithium loss during activation process with experiments and model simulation can assist the LFP battery design and optimize fabrication. Figure 1

Redistribution of iron during directional solidification of metallurgical-grade silicon at low growth rate

Redistribution of iron during directional solidification of metallurgical-grade silicon (MG-Si) was conducted at low growth rate. Concentrations of iron were examined by ICP-MS and figured in solid and liquid phases, at grain boundary and in growth direction. Concentrations are significantly different between solid and liquid phases. The thickness of the solute boundary layer is about 4 mm verified by mass balance law, and the effective distribution coefficient is 2.98×10−4. Iron element easily segregates at grain boundary at low growth rate. In growth direction, concentrations are almost constant until 86% ingot height, and they do not meet the Scheil equation completely, which is caused by the low growth rate. The effect of convection on the redistribution of iron was discussed in detail. Especially, the “dead zone” of convection plays an important role in the iron redistribution.

A multi-level analysis of China's phosphorus flows to identify options for improved management in agriculture

Phosphorus (P) is a finite natural resource and is essential for food production. The amount of P involved in food production in China relative to the increase of food production has increased dramatically over the past decades, which has led to serious environmental pollution. Because of China's enormous share in global P fertilizer production (30%) and consumption (37.5%), it evidently plays a crucial role in developing a more sustainable use of this essential resource for agriculture. We performed an integrated analysis of the P flows, P stocks, P utilization efficiencies (PUE) and environmental implications at the national level in China for the year 2010, complemented with an analysis at regional, county and farm levels. The static Material Flow Analysis approach based on the law of mass balance was used. We found that P accumulation in the arable land and P losses in the livestock raising industry are the major contributors to environmental pollution. Improving the PUE in arable land and the livestock raising industry, on the basis of the actual demands combined with efforts to promote the use of residual soil P on arable land and the recycling of organic manure and wastes, will significantly reduce the consumption and losses of P from the food chain, and will slow down the depletion of this finite natural resource.

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

A generalized continuum theory with internal corner and surface contact interactions

We consider a classical derivation of a continuum theory, based on the fundamental balance laws of mass and momenta, for a body with internal corner and surface contact interactions. The balances of mass and linear and angular momentum are applied to the arbitrary parts of a continuum which supports non-classical internal corner and surface contact interactions. The form of the specific corner contact interaction force measured per unit length of the corner is derived. A generalized form of Cauchy’s stress theorem is obtained, which shows that the surface traction on an oriented surface depends in a specific way on both the oriented unit normal as well as the curvature of the surface. An explicit form of the surface-couple traction which acts on every oriented surface is obtained. Two fields in the continuum, which are denoted as stress and hyperstress fields, are shown to exist, and their role in representing the surface traction and the surface-couple traction is identified. Finally, the field equations for this theory are determined, and a fundamental power theorem is derived. In the absence of internal corner and surface-couple traction interactions, the equations of classical continuum mechanics are recovered. There is no appeal to any ‘principle of virtual power’ in this work.

Governing equations for a two-scale analysis of Li-ion battery cells

This contribution describes a computational homogenization approach to model the multi-physics processes in Li-ion batteries in a multi-scale view. The adopted approach originates from the fundamental balance laws (of mass, momentum, charge) at both scales and the multi scale analysis roots itself on an energy-based weak formulation of the balance laws, which allows to extend the Hill–Mandel energy averaging theorem to the problem at hand. Electroneutrality assumption has been taken into account. Maxwell’s equations are considered in a quasi-static sense in a rigorous setting. Time dependent scale transitions are formulated, as required by the length/time scales involved in Li-ion batteries processes, while scale separation in time is argued. Constitutive assumptions, computational procedures and simulations will be collected in a companion paper.