Model Elements and Network Solutions of Heat, Mass and Momentum Transport Processes

260 Pages·2017·10.927 MB·English

by  George L. Danko (auth.)

Heat and Mass Transfer
George L. Danko
Model Elements and
Network Solutions
of Heat, Mass and
Momentum Transport
Processes
Heat and Mass Transfer
Series editors
D. Mewes, Hannover, Germany
F. Mayinger, München, Germany
Heat and mass transfer occur in coupled form in most production processes and
chemical-engineering applications of a physical, chemical, biological or medical
nature. Very often they are associated with boiling, condensation and combustion
processesandalsowithfluidsandtheirflowfields.Hencerheologicalbehaviorand
dissipative heating also play a role.
The increasing interplay of experimental research and computer-assisted
evaluation and analysis methods has led to new results, which not only confirm
empirical representations and their physical interpretation but, in addition, extend
their previously limited applications significantly.
The series covers all fields of heat and mass transfer, presenting the interrela-
tionships between scientific foundations, experimental techniques, model-based
analysisofresultsandtheirtransfertotechnologicalapplications.Theauthorsareall
leadingexpertsin their fields.
Heat and Mass Transfer addresses professionals and researchers, students and
teachers alike. It aims to provide both basic knowledge and practical solutions,
while also fostering discussion and drawing attention to the synergies that are
essential to start new research projects.
More information about this series at http://www.springer.com/series/4247
George L. Danko
Model Elements and Network
Solutions of Heat, Mass
and Momentum Transport
Processes
123
George L. Danko
MackaySchool ofEarth Sciences
andEngineering
University of Nevada, Reno
Reno,NV
USA
ISSN 1860-4846 ISSN 1860-4854 (electronic)
Heat andMassTransfer
ISBN978-3-662-52929-4 ISBN978-3-662-52931-7 (eBook)
DOI 10.1007/978-3-662-52931-7
LibraryofCongressControlNumber:2016950864
©Springer-VerlagGmbHGermany2017
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To Emoke and Reka Danko
Preface
The present publication is the first chapter of the book in development entitled
“Heat, Mass and Momentum Transport Network Models.” The reason for pub-
lishing the first chapter before the completion of the entire book is to serve the
practical need for technical reference for network models in ventilation, climate,
and flow simulation inpipelinesystems. The early publication will also help those
interested in the theory of transport processes and in new methods of network
solutions.
Coupled heat, mass, and momentum transport problems arise in many areas of
science and engineering. With the increasing computational power coupled with
new numerical solution techniques the ambition also grows for solving large-scale
problems involving the flow and transport of scalar or vector substances. For this
reason, network models are becoming widely used in industry, education and
research,suchasVentsim,VnetPC,orVUMA,developedformodelingminesand
interconnected tunneling systems. Such models are accessible to educators, stu-
dents, scientists, or practicing engineers. Many of the new solution methods dis-
cussed in the book are available in a special edition of Ventsim, providing a
user-friendly graphical interface for easy model configuration for the solution of
large-scale, coupled network models.
Thetime-honoredtechniqueofnetworkapplicationisrevisitedinthebookusing
flownetworksolutionsforalltransportprocesscomponentsforacoupledmodeling
task. The conservation laws for mass, energy, and momentum are formulated first
specificallyforthebranchesandnodesoftransportnetworksusingthecombination
of the Eulerian and Lagrangean modeling methods. With the extension of
Bernoulli’s original concept, a new solution is given for the flow field of viscous
and compressible fluids as driven and governed by the balance of mechanical
energy, coupled to the thermodynamics of the transport system. Applicable to
simple or large-scale tasks, the new model elements and methods are built on first
principles. Original formulations, their mathematical derivations, as well as appli-
cations in numerical solution schemes are provided throughout the work.
The numerical solution methods presented have been developed over two dec-
ades starting with ventilation and cooling enhancement studies supported by the
vii
viii Preface
U.S. Department of Energy (DOE), Yucca Mountain Nuclear Waste Repository
Office and continued for the development and qualification of the MULTIFLUX
networkcodeundergrantsfromtheScienceandTechnologyOfficeofDOE.Their
support is gratefully appreciated. I acknowledge with my thanks the long-term
financial support from the National Institute of Safety and Health (NIOSH), U.S.,
for model developments and tests for the improvement in mine safety and health.
Themany research grantsfromotheragenciesandoperating minesstretchingover
a decade from Nye County Natural Resources and Federal Facilities, Nevada;
Barrick Goldstrike Mine and Newmont Gold Corporation, Nevada operations; as
well as the Alpha Foundation are thankfully valued. The support from the
Geothermal Project Office of DOE for opening a new application field for
MULTIFLUX to model Engineered Geothermal Systems is gratefully recognized.
The critical comments from students in the Mine 725: Heat, Mass, and
Momentum Transport Process graduate course over the last few years as well as
from colleagues at the University of Nevada, Reno, Mackay School of Earth
Sciences and Engineering are all acknowledged with my thanks.
Research Assistant Professor Davood Bahrami at the department deserves my
warmest thanks for coding many of the network solution processes and setting up
transport models for numerical tests and applications in various research projects.
His participation in the software qualification of MULTIFLUX has been instru-
mental in the development and commercialization work. The partnership support
from Director Craig Stewart together with other software developers at Chasm
Consulting, Australia, for the integration of the MULTIFLUX model into the
Ventsim Visual software is thankfully recognized.
The cooperative support of Christoph Baumann and others associated with
Springer is also greatly appreciated.
Reno, NV, USA George L. Danko
Contents
1 Introduction... .... .... ..... .... .... .... .... .... ..... .... 1
1.1 Introduction .. .... ..... .... .... .... .... .... ..... .... 1
2 Phenomenological Properties and Constitutive Equations
of Transport Processes .. ..... .... .... .... .... .... ..... .... 5
2.1 Density.. .... .... ..... .... .... .... .... .... ..... .... 5
2.2 Mixture Density, Concentration, Mass Fraction
and Gas Law . .... ..... .... .... .... .... .... ..... .... 7
2.3 Temperature .. .... ..... .... .... .... .... .... ..... .... 8
2.4 Pressure . .... .... ..... .... .... .... .... .... ..... .... 9
2.5 Viscosity in Ideal Gases.. .... .... .... .... .... ..... .... 10
2.6 Viscosity in Real Gases .. .... .... .... .... .... ..... .... 12
2.7 Viscosity in Fluids . ..... .... .... .... .... .... ..... .... 15
2.8 Typical Viscosity Variations... .... .... .... .... ..... .... 16
2.9 Viscosity in Gas Mixtures .... .... .... .... .... ..... .... 17
2.10 Viscous Stresses in Three Dimensions ... .... .... ..... .... 17
2.11 Viscosity and Shear Stress in Turbulent Flow . .... ..... .... 19
2.12 Molecular Thermal Conductivity in Gases .... .... ..... .... 21
2.13 Thermal Conductivity in Gas Mixtures... .... .... ..... .... 25
2.14 Thermal Conductivity in Liquids and Solids... .... ..... .... 25
2.15 Thermal Conductivity and Diffusivity in Turbulent Flow.. .... 26
2.16 Mass Diffusivity in Gases. .... .... .... .... .... ..... .... 27
2.17 Mass Diffusivity in Gas Mixtures... .... .... .... ..... .... 30
2.18 Mass Diffusivity in Liquids ... .... .... .... .... ..... .... 30
2.19 Mass Diffusivity in Solids .... .... .... .... .... ..... .... 31
2.20 Diffusivity in Turbulent Flow.. .... .... .... .... ..... .... 32
2.21 Specific Heat . .... ..... .... .... .... .... .... ..... .... 33
2.22 Compressibility of Gas and Liquid.. .... .... .... ..... .... 34
2.23 Corollary of the Elements of Transport Processes... ..... .... 35
ix
x Contents
3 Conservation of a Scalar Extensive in Integral Form... ..... .... 39
3.1 The Eulerian Shell-Balance Equation .... .... .... ..... .... 39
3.2 Eulerian Balance Equation with Lagrangean
Internal Transport.. ..... .... .... .... .... .... ..... .... 40
3.3 ComparisonoftheEulerianandtheNewEulerian–Lagrangean
Forms... .... .... ..... .... .... .... .... .... ..... .... 44
4 Conservation of a Scalar Extensive in Differential Form..... .... 47
4.1 Differential Species Balance in a Finite Cell... .... ..... .... 47
4.2 Differential Cell Balances with Substance Transport
and Bulk Flow Conservation .. .... .... .... .... ..... .... 49
4.3 Directional, off-Centered Differential Substance
Balance Equations . ..... .... .... .... .... .... ..... .... 51
5 Conservation of a Scalar Extensive in a State-Flux,
Space-Time, Finite-Volume Cell.... .... .... .... .... ..... .... 57
5.1 State-Flux, Finite-Volume Cell for Unit Courant Number . .... 57
5.2 Multiple-Level, State-Flux, Finite-Volume Cell
with Arbitrary Courant Number .... .... .... .... ..... .... 61
5.3 State-Flux, Space-Time Finite-Volume Block Model
with Arbitrary Courant Number .... .... .... .... ..... .... 66
5.4 Extended Applications of the State-Flux, Space-Time
Finite-Volume Block Model... .... .... .... .... ..... .... 72
5.5 Synopsis of the SFST Substance Balance Formulation.... .... 76
6 Conservation of Energy in Integral, Differential,
and State-Flux Forms... ..... .... .... .... .... .... ..... .... 79
6.1 Integral Balance Equation for Energy.... .... .... ..... .... 79
6.2 Separation of the Mechanical and Thermal Components
in the Integral Balance Equation for Energy... .... ..... .... 90
6.2.1 The Case of Zero Stagnant Volume ... .... ..... .... 91
6.2.2 The Case of Nonzero Stagnant Volume .... ..... .... 95
7 Transport Models for Mechanical Energy.... .... .... ..... .... 105
7.1 Differential Form of Mechanical Energy Balance
in a Finite Cell for Unit Courant Number. .... .... ..... .... 105
7.2 State-Flux, Finite-Volume, Mechanical Energy Transport
Model for a Network Branch .. .... .... .... .... ..... .... 108
7.3 State-Flux, Finite-Volume, Mechanical Energy Transport
Model for a Network Junction . .... .... .... .... ..... .... 119
7.3.1 Mass Balance in a Junction Node. .... .... ..... .... 119
7.3.2 Mechanical Energy Balance for a Junction Node .. .... 122
7.4 State-Flux Network Model for Mechanical Energy
Transport in Steady State . .... .... .... .... .... ..... .... 133
7.5 State-Flux Network Model for Time Dependent
Mechanical Energy Transport.. .... .... .... .... ..... .... 140