Balance Laws Of Mass Research Articles

Efficient numerical approximations for a nonconservative nonlinear Schrödinger equation appearing in wind‐forced ocean waves

AbstractWe consider a nonconservative nonlinear Schrödinger equation (NCNLS) with time‐dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy conservation, but instead mass and energy change in time under explicit balance laws. In this paper, we extend to the particular NCNLS two numerical schemes which are known to conserve energy and mass in the discrete level for the cubic nonlinear Schrödinger equation. Both schemes are second‐order accurate in time, and we prove that their extensions satisfy discrete versions of the mass and energy balance laws for the NCNLS. The first scheme is a relaxation scheme that is linearly implicit. The other scheme is a modified Delfour–Fortin–Payre scheme, and it is fully implicit. Numerical results show that both schemes capture robustly the correct values of mass and energy, even in strongly nonconservative problems. We finally compare the two numerical schemes and discuss their performance.

Moving horizon estimation for pipeline leak detection, localization, and constrained size estimation

Advanced pipeline leak detection and localization techniques are needed to reduce greenhouse gas emissions from hydrocarbon transportation pipelines. Developing effective leak detection and localization methods is challenging due to the spatiotemporal dynamics of process variables, the presence of process/measurement disturbances and constraints, and the limited measurement data. To address this issue, this manuscript proposes a novel moving horizon estimation design for pipeline leak detection, constrained estimation of leak size and location by using an infinite-dimensional pipeline hydraulic model. Based on the mass and momentum balance laws and the Cayley–Tustin time-discretization method, an infinite-dimensional discrete-time pipeline hydraulic model is proposed considering (unknown but bounded) disturbance and leak. By introducing a coordinate transformation, we decouple the leak size and location estimation problems. The implementable discrete-time moving horizon estimator and observer are designed for constrained leak size and location estimation. The effectiveness of the proposed designs is validated via simulation examples.

Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective

This study investigates the growth of an avascular tumour described through the interchange of mass among its constituents and the production of inelastic distortions induced by growth itself. A key contribution of this research examines the role of non-local diffusion arising from the complex and heterogeneous tumour micro-environment. In our context, the non-local diffusion is enhanced by a variable-order fractional operator that incorporates crucial information about regions of limited nutrient availability within the tissue. Our research also focuses on the identification of an evolution law for the growth-induced inelastic distortions recast through the identification of non-conventional forces dual to suitable kinematic descriptors associated with the growth tensor. The establishment of such evolution law stems from examining the dissipation inequality and subsequently determining a posteriori connections between the inelastic distortions and the source/sink terms in the mass balance laws. To gain insights into the dynamics of tumour growth and its response to the proposed modelling framework, we first study how the variables governing the tissue evolution are affected by the introduction of the new growth law. Second, we investigate how regions of limited diffusion within the tumour, encoded into a fractional operator of variable-order, influence its growth.

A coupled model of transport-reaction-mechanics with trapping, Part II: Large strain analysis

A coupled finite strain chemo-transport-mechanical formulation with trapping is here proposed to extend a previous work set in the realm of small strain theory in continuum mechanics. The theory is rooted in non-equilibrium rational thermodynamics. The kinematics is based on a multiplicative decomposition of the deformation gradient to account for swelling and shrinking, thermal, elastic and inelastic contributions. Mass balance laws and balance of linear and angular momentum, as well as the laws of thermodynamics for a convecting body, are directly formulated in their material description, after specifications of some standard transformation rules between current and reference configuration. Thermodynamic restrictions are identified based on the functional dependence of the referential Helmholtz free energy density, which is chosen as the thermodynamic potential, and further subjected to a constitutive additive decomposition. Constitutive prescriptions for the chemical potentials, referential heat and mass fluxes, chemical kinetics and the generalized heat equation lead to the establishment of the governing equations. The theoretical framework is complemented by numerical simulations, highlighting the potential of the proposed formulation in multi-physics applications.

A linear mass and energy conserving numerical scheme for two-phase flows with thermocapillary effects

In this paper, a thermodynamically consistent phase-field model is employed to simulate the thermocapillary migration of a droplet. The model equations consist of a general Navier–Stokes equation for the two-phase flows, a Cahn–Hilliard equation for the diffuse interface, and a heat equation, and meanwhile satisfy the balance laws of mass, energy and entropy. In particular, the total energy of the system includes kinetic energy, potential energy and internal energy, which leads to a highly coupled and nonlinear equation system. We therefore develop a linear mass and energy conserving, semi-decoupled numerical method for the numerical simulations. As the model contains a heat (energy) equation, a simple error term introduced by the temporal discretization of the momentum equation can be absorbed into the heat equation, such that the numerical solutions satisfy the conservation laws of mass and energy exactly at the temporal discrete level. Several numerical tests are carried out to validate our numerical method.

Performance Investigation of Ejector Assisted Power Cooling Absorption Cycle

In this paper, new cycle is developed to generate simultaneously electrical and cooling power by placing a turbine between the generator and ejector in the conventional ejector-assisted absorption cooling cycle. The aim of developed cycle is to increase the exergy efficiency of cycle by adding an electrical power generation made it more environmentally friendly and reduce its dependents of fossil energy sources. The first, second laws of thermodynamic, mass and energy balance is applied for each cycle component and the constant mixing pressure ejector model is used to develop a numerical model of proposed cycle. The results depict that the augmentation of generation temperature is positively affected the work produced in the turbine contrary for cycle coefficient of performance, for every working conditions there are a certain value of generation temperature which its exergy performance of cycle achieves the maximum, the augmentation of output pressure of turbine is positively affected the cycle coefficient of performance contrary of the work produced in the turbine and the cycle exergy efficiency and the augmentation of condensation temperature is positively affected the cycle exergy efficiency and the work produced in the turbine contrary for cycle coefficient of performance and the augmentation of evaporation temperature is positively affected the cycle coefficient of performance and the cycle exergy efficiency contrary for the work produced in the turbine The results also show that the improvement of exergy efficiency of proposed cycle is 29.41% and 46% compared with the absorption cooling cycle with double and triple effect under the same operating conditions.

The Identifiability of Mathematical Models in Epidemiology: Tuberculosis, HIV, COVID-19

The paper is devoted to the short review and application of sensitivity-based identifiability approaches for analyzing mathematical models of epidemiology and related processes described by systems of differential equations and agent-based models. It is shown that for structural identifiability of basic SIR models (describe the dynamic of Susceptible, Infected and Removed groups based on nonlinear ordinary differential equations) of epidemic spread and linear compartmental models it is possible to use a priori information about the process. It is demonstrated that a model can be structurally identifiable but be practically non-identifiable due to incomplete data. The paper uses methods for analyzing the sensitivity of parameters to data variation, as well as analyzing the sensitivity of model states to parameter variation, based on linear and differential algebra, Bayesian, and Monte Carlo approaches. It was shown that in the SEIR-HCD model of COVID-19 propagation, described by a system of seven ordinary differential equations and based on the mass balance law, the parameter of humoral immunity acquisition is the least sensitive to changes in the number of diagnosed, critical and mortality cases of COVID-19. The spatial SEIR-HCD model of COVID-19 propagation demonstrated an increase the sensitivity of the partial immunity duration parameter over time, as well as a decrease in the limits of change in the infectivity and infection parameters. In the case of the SEIR-HCD mean-field model of COVID-19 propagation, the sensitivity of the system to the self-isolation index and the lack of sensitivity of the stochastic parameters of the system are shown. In the case of the agent-based COVID-19 propagation model, the change in the infectivity parameter was reduced by more than a factor of 2 compared to the statistics. A differential model of co-infection HIV and tuberculosis spread with multiple drug resistance was developed and its local identifiability was shown.

Implementation and verification of a user‐defined element (UEL) for coupled thermal‐hydraulic‐mechanical‐chemical (THMC) processes in saturated geological media

AbstractEfficient and accurate modeling of the coupled thermal‐hydraulic‐mechanical‐chemical (THMC) processes in various rock formations is indispensable for designing energy geo‐structures such as underground repositories for high‐level nuclear wastes. This work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user‐defined element (UEL) subroutine which is then combined with the general‐purpose FE software Abaqus Standard to solve initial‐boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic‐mechanical (HM) and thermal‐hydraulic‐mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed‐form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three‐dimensional case study is performed with reference to the in‐situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical‐concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

A formulation of volumetric growth as a mechanical problem subjected to non-holonomic and rheonomic constraint

Starting from a reformulation of the mass balance law based on the Bilby–Kröner–Lee (BKL) decomposition of the deformation gradient tensor, we study some peculiar mechanical aspects of growth in a monophasic continuum by regarding the reformulated mass balance equation as a non-holonomic and rheonomic constraint. Such constraint restricts the admissible rates of the growth tensor, i.e., one of the two factors of the BKL decomposition, to comply with a growth law provided phenomenologically. For our purposes, we put the constraint in Pfaffian form, and treat time as a fictitious, additional Lagrangian parameter, subjected to the condition that its rate must be unitary. Then, by taking some suggestions from the literature, we assume the existence of generalized forces conjugated with the virtual variations of the growth tensor, and we write a constrained version of the Principle of Virtual Work (PVW) that leads to a mixed boundary value problem whose unknowns are the motion, the growth tensor, and the Lagrange multipliers of the considered theory. This allows to extrapolate a physical interpretation of the role that the growth-conjugated forces play on the components of the growth tensor, especially on the distortional ones, i.e., those that are not directly related to the variation of mass of the body. The core message of our work is conceptual: we show that the growth laws usually encountered in the literature, which are prescribed phenomenologically, but may be difficult to justify theoretically, can be put in the framework of the PVW by regarding them as constraints. Moreover, we retrieve more particularized frameworks of growth available in the literature, while being able to switch to a theory of growth of grade one, such as a Cahn–Hilliard model of growth.

Thermodynamic and kinetic analysis of ternary intermetallics formation in Al–Cu–La alloy

The thermodynamic and kinetic analysis of rare earth (RE) intermetallics formation in Al–Cu–La alloy was carried out in this study. The formation enthalpy, excess entropy, excess Gibbs free-energy and activity of each component of Al–Cu–La ternary alloy were calculated combining Miedema model with Toop model. The calculated results show that the formation enthalpy, excess entropy and excess Gibbs free-energy of Al–Cu–La ternary alloy are all negative in the whole alloy composition range. The activities of Al, Cu and La are all tiny in the central zone of composition triangle of Al–Cu–La ternary alloy, indicating that Al, Cu and La components are easy to form ternary intermetallics. Moreover, the parabolic growth kinetics equation of RE intermetallics was derived integrating the Fick's second law with the mass balance law. According to the parabolic growth rate, the thickness of the RE intermetallics increases in proportion to the square root of the diffusion time.

Bulk oxygen conduction kinetics of iron oxides on the chemical looping combustion

Oxygen-ion conduction is generally considered the rate-determining step during the chemical looping combustion process, which is vital for the design of the oxygen carriers. However, the redox reaction is heavily influenced by gas diffusion, making it very difficult to derive convincing intrinsic kinetic data. This work aims to establish a methodology to evaluate the intrinsic kinetics of oxygen carriers for chemical looping combustion by using an ultra-thin oxygen conducting membrane to exclude the influence of gas diffusion. From mass balance and Fick's second law, a mathematical kinetics model describing the intrinsic oxygen conduction performance was established. The intrinsic activation energy took value of 77.84 kJ/mol for pure Fe2O3. The kinetics parameters can be used for the high throughput design and screening of oxygen carriers.

Evaluation of a helicoidal flux photoreactor applied in the dicloxacillin degradation by UV-C/H2O2 and UV-A/photo-Fenton including the effect of photon absorption

The efficiency of a helical flow photoreactor in the oxidation of the antibiotic Dicloxacillin as a function of the recirculation flow, the local volumetric rate of photon absorption (LVRPA) and photonic efficiency using oxidation processes based on UV-C/H2O2 and UV-A/photo-Fenton were evaluated in this work. Mathematical modeling of the degradation process and experiments in lab-scale helicoidal reactor were done. Mathematical evaluation was supported in function of photon flux, mass balance and reaction rate law. The LVRPA was calculated by modified Beer-Lambert Equation. The effect of the concentration of hydrogen peroxide and iron (II) on the efficiency of the oxidation of the antibiotic Dicloxacillin was evaluated by means of the photo-Fenton. In 45 min, 100% degradation of dicloxacillin was achieved using 1.5 mM H2O2 and 7.32 μM ferrous ion in the photo-Fenton experiments with the helical flow photoreactor. The optical thickness of the reaction and distribution of energy absorption confirmed the kinetic and photonic efficiency performance. The prediction of the model presented a global error less to 2.4% between experimental and simulated data.

THM-coupled numerical analysis of temperature and groundwater level in-situ measurements in artificial ground freezing

Belarusian Potash salt deposits are bedded under aquifers and unstable soil stratums. Therefore, to develop the deposits a vertical mine shaft sinking is performed using the artificial ground freezing technology. Nowadays, real time observations of ground temperature and groundwater level is applied to control the ground freezing process. Numerical simulation can be used for a comprehensive analysis of measurements results. In this paper a thermo-hydro-mechanical model of freezing of water saturated soil is proposed. The governing equations of the model are based on balance laws for mass, energy and momentum for a fully saturated porous media. Clausius-Clayperon equation and poroelastic constitutive relations are adopted for description of a coupled change in water and ice pore pressure, porosity and a stress-strain state of freezing soil. The proposed model enables us to describe evolution of equivalent water content measured in Mizoguchi’s test and predict frost heave strain in one-sided freezing test. Numerical simulation of ground freezing in the Petrikov mining complex located in Belarus has shown that the model is able to describe field measurements of pore pressure inside a forming frozen wall. Furthermore, the mismatch between hydro- and thermo-monitoring data obtained during the artificial freezing is analyzed.

Constitutive modeling of an electro-magneto-rheological fluid

The present article deals with a continuum mechanics-based method to model an electro-magneto-rheological (EMR) fluid deformation subjected to an electromagnetic field. The proposed method follows the fundamental laws of physics, including the principles of thermodynamics. We start with the general balance laws for mass, linear momentum, angular momentum, energy, and the second law of thermodynamics in the form of Clausius–Duhem inequality with Maxwell’s equations. Then, we formulated a generalized constitutive model for EMR fluids following the representation theorem. Later, we validate the model with the results of an EMR rheometer and ER fluid valve system-based configurations. At last, the possible simulation-based velocity profiles are also discussed for parallel plate configuration. As a result, we succeed in providing more physics-based analytical findings than the existing studies in the literature.

Comparative energy analysis of R1234yf, R1234ze, R717 and R600a in Vapour Compression Refrigeration system as replacement of R134a

In this study effect of utilization of refrigerants with low Global warming potential is studied theoretically based on first law of thermodynamics and mass balance. Refrigerants like R1234yf, R1234ze, R717, and R600a are used instead of R134a in the Vapour Compression Refrigeration system of 1 TR. The Global Warming Potential of all the refrigerants is negligible (below 4) as compared to that of R134a (1300). The results obtained show that R1234ze and R600a are better refrigerants in the context of COP and power consumed as compared to R134a. Other refrigerants are not very behind and obtain a COP value comparable to that of R134a. R1234yf and R717 may consume slightly more power but their low Global Warming Potential makes them a decent option. R717 requires the least mass flow rate as compared to all the chosen refrigerants.

Simulation of Thermal Decomposition of Calcium Oxide in Water with Different Activation Energy and the High Reynolds Number

In this article, we are going to suggest the parameters to control the thermal decomposition in a reactor that is continuously providing a cooling environment inside the tube. For this purpose, 5 governing partial differential equations gained through mass, momentum, and energy balance laws and one ordinary differential equation are used to simulate this chemical reaction with finite element package COMSOL Multiphysics 5.6. In the simulation, the thermal decomposition of calcium oxide in the water is controlled with the use of Reynolds numbers ranging from 100 to 1000, activation energy from 75,000 j/mol to 80,000 j/mol, and an initial concentration of 1% to 5%. The results are presented through the graphs and tables for conversion profile, temperature distribution, enthalpy change, diffusivity, the heat source of reaction, and Sherwood and Lewis number along the axial length of the reactor. Specifically, it was found a low‐speed profile at the inlet will give a 100% conversion at Re = 100 for 3% to 5% of the initial concentration. The maximum temperature and enthalpy change in the reactor are decreasing increase in the Reynolds number. Also, the decrement of the Sherwood number along the length showed that the mass diffusion is always dominant over convection‐diffusion for all cases of parameters. The validation is made by comparing the numerical results with the experimental correlations.

A moving-boundary dynamic model for in-situ alloyed and additive manufacturing TiAl-Nb alloys

Controlling the dissolution of the solid metal contact liquid metal or alloys is significantly important for some industrial processes, in particular for high temperature and long-time processes. A model for quantitatively evaluating the relationship between the dissolution thickness of Nb crucible and the increase of Nb concentration caused by dissolution is established based on the mass balance law, which supports in-situ alloyed and additive manufacturing process of TiAl-based alloys.

Growth kinetics analysis of Nb–Al intermetallic compounds interfacial layers based on Nb–Al phase diagram

A model for studying the growth kinetics of intermetallic compounds by means of binary phase diagrams was proposed with some assumptions. The parabolic growth relationship of intermetallic compound is deduced mathematically using analytical solution of diffusion equations and the mass balance law. By comparing the solubility of the adjacent phase in intermetallic compound phase, the predominant parameter controlling the growth kinetics is the solute diffusion coefficient. The diffusion coefficient of Al atoms in intermetallic layers is quantitatively described and the smallest diffusion coefficient is 0.373 × 10−21 m2/s in Nb3Al phase. It is demonstrated intermetallic layers formed at interface indeed inhibit the Nb container being corroded further by TiAl melt, and Nb3Al layer is a dominant factor.

A fully coupled numerical model of thermo-hydro-mechanical processes and fracture contact mechanics in porous media

Various phenomena in the subsurface are characterised by the interplay between deforming structures such as fractures and coupled thermal, hydraulic and mechanical processes. Simulation of subsurface dynamics can provide valuable phenomenological understanding, but requires models which faithfully represent the dynamics involved; these models therefore are themselves highly complex.This paper presents a mixed-dimensional thermo-hydro-mechanical model designed to capture the process–structure interplay using a discrete–fracture–matrix framework. It incorporates tightly coupled thermo-hydro-mechanical processes based on balance laws for momentum, mass and energy in subdomains representing the matrix and the lower-dimensional fractures and fracture intersections. The deformation of explicitly represented fractures is modelled by contact mechanics relations and a Coulomb friction law, with a novel formulation consistently integrating fracture dilation in the governing equations.The model is discretised using multi-point finite volume methods for the balance equations and a semismooth Newton scheme for the contact conditions and is implemented in the open-source fracture simulation toolbox PorePy. Finally, simulation studies demonstrate the model’s convergence, investigate process–structure coupling effects, explore different fracture dilation models and show an application of the model to stimulation and long-term cooling of a three-dimensional geothermal reservoir.

A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions

This work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the field equations and constitutive relations. In the process, the conjugated kinematic and kinetic variables for mechanical, thermal, and chemical contact are identified, and the analogies between mechanical, thermal, and chemical contact are highlighted. Particular focus is placed on the thermodynamics of chemical bonding distinguishing between exothermic and endothermic contact reactions. Distinction is also made between long-range, non-touching surface interactions and short-range, touching contact. For all constitutive relations, examples are proposed and discussed comprehensively with particular focus on their coupling. Finally, three analytical test cases are presented that illustrate the thermo-chemo-mechanical contact coupling and are useful for verifying computational models. Although the main novelty is the extension of existing contact formulations to chemical contact, the presented formulation also sheds new light on thermo-mechanical contact, because it is consistently derived from basic principles using only a few assumptions.