An Analytical Model of Phase Changing Chemically Reacting Mixture Flows

2003 ◽  
Author(s):  
George S. Dulikravich ◽  
Marcelo J. Colac¸o
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
Chemical Reactions ◽  
Continuum Mechanics ◽  
Multiphase Flows ◽  
Phase Changes ◽  
Chemically Reacting

A complete and consistent mathematical model of multiphase flows allowing for chemical reactions and/or phase changes has been derived from basic continuum mechanics principles. Comparison of elements of this model with models published by other sources has been elaborated. A set of analytic relations linking mixture and fluid components has been derived. Conclusions about closure of the system have been drawn based on these derivations.

scholarly journals A mathematical model relevant for weakening of chalk reservoirs due to chemical reactions

2009 ◽  
Vol 4 (4) ◽  
pp. 755-788 ◽  
Author(s):  
Steinar Evje ◽  
◽  
Aksel Hiorth ◽  
Merete V. Madland ◽  
Reidar I. Korsnes ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Chemical Reactions

An analytical model for mechanochemical reaction kinetics

2021 ◽  
Author(s):  
Maria Carta ◽  
Francesco Delogu ◽  
Andrea Porcheddu
Keyword(s):  
Reaction Kinetics ◽  
Analytical Model ◽  
Chemical Reactions ◽  
Solvent Free ◽  
Mechanochemical Reaction ◽  
Synthetic Routes ◽  
Chemical Products

With its ability to enable solvent-free chemical reactions, mechanochemistry promises to open new and greener synthetic routes to chemical products of industrial interest. Its practical exploitation requires understanding the relationships...

scholarly journals VIII. On the apparent change in weight during chemical reaction

1913 ◽  
Vol 212 (484-496) ◽  
pp. 227-260
Keyword(s):  
Chemical Reactions ◽  
Chemical Reaction ◽  
Experimental Work ◽  
Total Mass ◽  
Apparent Change ◽  
Chemically Reacting

During the year 1890 the late Prof. Landolt inaugurated his prolonged researches upon the apparent alteration in the total mass of chemically reacting substances. From the time of its inception until it was brought to a conclusion in 1907, the experimental work was freely varied both as regards the conditions and the nature of the chemical reactions involved. The methods and precautions adopted, together with the final results obtained, are to be found embodied and set forth in detail in Landolt’s important memoir, “Über die Erhaltung der Masse hei Chemischen Umsetzungen.”* Before proceeding to deal with my own investigations in this field of research, it may not be inappropriate first very briefly to recall the chief features of Landolt’s work and conclusions.

A Study of Transient Response of Flexible Rotors in High Speed Turbomachinery

1992 ◽  
Author(s):  
V. Pavelic ◽  
R. S. Amano
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Analytical Model ◽  
High Speed ◽  
Angular Speed ◽  
Journal Bearings ◽  
Hydrodynamic Characteristics ◽  
Flexible Assembly ◽  
Lagrange’S Equation ◽  
Equations Of Motions

In many applications the design operating range of the turbomachinery may be well above the rotor first critical speed which leads to the problem of insuring that the turbomachinery performs with a stable, low-level amplitude of vibration. Under certain conditions of high speed and loading the rotor system can start orbiting in its bearing at a rate which is less than the rotor angular speed, and this phenomena is commonly known as whirling or whipping action. This whipping action may produce additional undesirable dynamic loads on the overall flexible assembly and eventually destroy the rotor. Some of this action is also transient in nature. Whirling is a self-exited vibration caused mainly by the fluid bearings and by the internal friction damping of the rotor. To understand this occurrence, a general dynamic mathematical model was derived considering also the complete viscous characteristic of hydrodynamic journal bearings. The general equations of motions of the system are obtained from Lagrange’s equation of motion. The system kinetic, potential, and dissipation functions are determined based on the generalized coordinates of the system. The journal displacements are related to the overall dynamics of the rotor using deformable bearings. The loads acting at the journals of the shaft are integrated from the fluid film pressure distribution in the journal bearings using mobility method. A unique mathematical model is formulated and solved. This model includes the elastic and inertial properties of the flexible rotor, the elastic, damping and inertial properties of supports and the hydrodynamic characteristics of the journal bearings. The equations of motions result in a system of nonlinear second order differential equations which are solved by using finite difference method. The solution of the equations of motions is used to plot maps of motion of journal centers. A computer program was implemented to aid in the solution of the system of equations and to verify analytical model. The computer program used test data available in literature and the results were compared to be very good. The analytical model and results obtained in this study can be of great help to designers of high speed turbomachinery.

Toward the implementation of a multi-component framework in a density-based flow solver for handling chemically reacting flows

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nikhil Kalkote ◽  
Ashwani Assam ◽  
Vinayak Eswaran
Keyword(s):  
Numerical Method ◽  
Chemical Reactions ◽  
Turbulence Model ◽  
Turbulent Combustion ◽  
Reacting Flows ◽  
Content Type ◽  
Flow Solver ◽  
Chemically Reacting Flows ◽  
Chemically Reacting ◽  
Convective Scheme

Purpose The purpose of this study is to present and demonstrate a numerical method for solving chemically reacting flows. These are important for energy conversion devices, which rely on chemical reactions as their operational mechanism, with heat generated from the combustion of the fuel, often gases, being converted to work. Design/methodology/approach The numerical study of such flows requires the set of Navier-Stokes equations to be extended to include multiple species and the chemical reactions between them. The numerical method implemented in this study also accounts for changes in the material properties because of temperature variations and the process to handle steep spatial fronts and stiff source terms without incurring any numerical instabilities. An all-speed numerical framework is used through simple low-dissipation advection upwind splitting (SLAU) convective scheme, and it has been extended in a multi-component species framework on the in-house density-based flow solver. The capability of solving turbulent combustion is also implemented using the Eddy Dissipation Concept (EDC) framework and the recent k-kl turbulence model. Findings The numerical implementation has been demonstrated for several stiff problems in laminar and turbulent combustion. The laminar combustion results are compared from the corresponding results from the Cantera library, and the turbulent combustion computations are found to be consistent with the experimental results. Originality/value This paper has extended the single gas density-based framework to handle multi-component gaseous mixtures. This paper has demonstrated the capability of the numerical framework for solving non-reacting/reacting laminar and turbulent flow problems. The all-speed SLAU convective scheme has been extended in the multi-component species framework, and the turbulent model k-kl is used for turbulent combustion, which has not been done previously. While the former method provides the capability of solving for low-speed flows using the density-based method, the later is a length-scale-based method that includes scale-adaptive simulation characteristics in the turbulence modeling. The SLAU scheme has proven to work well for unsteady flows while the k-kL model works well in non-stationary turbulent flows. As both these flow features are commonly found in industrially important reacting flows, the convection scheme and the turbulence model together will enhance the numerical predictions of such flows.

scholarly journals Suppression of Ground Borne Vibration Induced by High-Speed Lines

2018 ◽  
Vol 152 ◽  
pp. 02001
Author(s):  
Ali Mohamed Rathiu ◽  
Mohammad Hosseini Fouladi ◽  
Satesh Narayana Namasivayam ◽  
Hasina Mamtaz
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
High Speed ◽  
Moving Load ◽  
Ground Vibration ◽  
Harmonic Excitation ◽  
Vibration Response ◽  
Vibration Velocity ◽  
Velocity Response ◽  
The Mathematical Model

Vibration of high-speed lines leads to annoyance of public and lowering real estate values near the railway lines. This hinders the development of railway infrastructures in urbanised areas. This paper investigates the vibration response of an isolated rail embankment system and modifies the component to better attenuate ground vibration. Mainly velocity response is used to compare the responses and the applied force is of 20 kN at excitation frequencies of 5.6 Hz and 8.3 Hz. Focus was made on ground-borne vibration and between the frequency range of 0 and 250 Hz. 3D Numerical model was made using SolidWork software and frequency response was produced using Harmonic Analysis module from ANSYS Workbench software. For analytical modelling MATLAB was used along with Simulink to verify the mathematical model. This paper also compares the vibration velocity decibels (VdB) of analytical two-degree of freedom model mathematical model with literature data. Harmonic excitation is used on the track to simulate the moving load of train. The results showed that modified analytical model gives the velocity response of 75 VdB at the maximum peak. Changes brought to the mass and spacing of the sleeper and to the thickness and the corresponding stiffness for the ballast does not result in significant vibration response. Limitations of two-degree analytical model is suspected to be the cause of this inactivity. But resonance vibration can be reduced with the aid of damping coefficient of rail pad. Statistical analysis methods t-test and ANOVA single factor test was used verify the values with 95% confidence.

Results of Mathematical Modeling of Modified In-Situ Oil Shale Retorting

1984 ◽  
Vol 24 (01) ◽  
pp. 75-86 ◽  
Author(s):  
R.L. Braun ◽  
J.C. Diaz ◽  
A.E. Lewis
Keyword(s):  
Mathematical Model ◽  
Chemical Reactions ◽  
Oil Shale ◽  
Pilot Scale ◽  
Oil Yield ◽  
Particle Sizes ◽  
Physical Processes ◽  
Commercial Scale ◽  
Shale Composition

Abstract Lawrence Livermore Natl. Laboratory (LLNL) has developed a one-dimensional (1D) mathematical model to simulate modified in-situ (MIS) retorting of oil shale. In this paper we discuss application of the model to commercial-scale retorting conditions. The model was tested by comparing calculated values to those measured in experimental retort runs performed at LLNL. There was generally good agreement between the calculated and observed results for oil yield, temperature profiles, and the yields of most gas species. Retorting rates were generally overestimated by as much as 10%. The model is a useful tool for design and control of retort operations and to identify and interpret observations that differ from model predictions. The model was used to predict the results for MIS retorting on a commercial scale, focusing on larger retorts and larger shale particle sizes, focusing on larger retorts and larger shale particle sizes than could be investigated experimentally. Retort bed properties, particularly shale composition and particle size, play an important role in determining the recoverable fraction of oil. For a given shale composition, the inlet-gas properties can be selected to help control retort operations and to maximize oil yield. Extreme variations in oil shale grade that may be encountered as a function of depth can be dealt with by appropriate changes in the composition and flow rate of the inlet gas. In addition, we show that substituting oxygen diluted with steam or CO2 (for air or air diluted with steam) can make significant improvements in the heating value of the effluent gas. Finally, we demonstrate the feasibility of retorting through a substantial interval of very low-grade shale. Introduction LLNL has been developing technology applicable to the MIS process of extracting oil from oil shale.1,2 Our program has involved the experimental measurement of chemical reactions and reaction kinetics,3 the operation of pilot-scale retorts,4 and the development of a mathematical model of an MIS retort.5 The objective is to help establish the technical base required to evaluate and apply the MIS method on a commercial scale. A keystone of our program is the retort model, since it represents our cumulative knowledge of the chemical and physical processes involved in oil shale retorting. The retort model has been used in planning and interpreting pilot-scale retort experiments and has successfully predicted most of the results of those experiments.4 It has also been used in developing an operating strategy for a field MIS oil shale retorting experiment.6 The principal purpose of this work is to apply the retort model to a wide range of conditions for MIS retorting, focusing on larger retorts and larger shale particle sizes than can be investigated in a laboratory experiment. Before the results of those calculations are presented, the model is discussed in terms of its content and validity. Model Description The LLNL retort model is a transient, 1D treatment of a packed-bed retort. In developing the model, we adopted a mechanistic approach based on fundamental chemical and physical properties rather than empirical scaling of pilot retort experiments. The model contains no arbitrarily adjustable parameters. A complete mathematical description of the model has been given elsewhere.5 The important features, therefore, are reviewed here only briefly. Our model includes those processes believed to have the most important effects in either the hot-gas retorting mode or the forward combustion mode. The physical processes are axial convective transport of heat and mass, axial thermal dispersion, gas/solid heat transfer, intraparticle shale thermal conductivity, water vaporization and condensation, and wall heat loss. The chemical reactions within the shale particles are the release of bound water, pyrolysis of kerogen, coking of oil, pyrolysis of char, decomposition of carbonate materials, and gasification of residual organic carbon with CO2, H2O, and O2. The chemical reactions in the bulk-gas stream are the combustion and cracking of oil vapor, combustion of H2, CH4, CHx, and CO, and the water/gas shift. The model permits axial variations of initial shale composition, particle-size distribution, and bed void fraction. It also permits time-dependent variations of the composition, flow rate, and temperature of inlet gas. The governing equations for mass and energy balance are solved numerically by a semi-implicit, finite-difference method. The results of these calculations determine the oil yield, and the composition and temperature of both the gas stream and the shale particles as a function of time and location in the retort.

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