Multiphase Flow Dynamics 4: Turbulence, Gas Adsorption and Release, Diesel Fuel Properties

337 Pages·2011·4.419 MB·English

by  Nikolay Ivanov Kolev

Multiphase Flow Dynamics 4
Nikolay Ivanov Kolev
Multiphase Flow
Dynamics 4
Turbulence, Gas Adsorption and Release,
Diesel Fuel Properties
ABC
Author
Dr.NikolayIvanovKolev
Möhrendorferstr.7
91074Herzogenaurach
Germany
E-mail:[email protected]
ISBN978-3-642-20748-8 e-ISBN978-3-642-20749-5
DOI10.1007/978-3-642-20749-5
LibraryofCongressControlNumber:2011934153
(cid:2)c 2011Springer-VerlagBerlinHeidelberg
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To Iva, Rali and Sonja with love
Balkan, Bulgaria (painting by Nikolay Ivanov Kolev, 2000)
My first physics teacher, my father Ivan Gutev (drawing
by Nikolay Ivanov Kolev, 2000)
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1983 Sofia
Nikolay Ivanov Kolev, PhD, DrSc
(born 1/8/1951, Gabrowo, Bulgaria)
Summary
This monograph contains theory, methods and practical experience for describing
complex transient multi-phase processes in arbitrary geometrical configurations. It
is intended to help applied scientists and practicing engineers to better understand
natural and industrial processes containing dynamic evolutions of complex multi-
phase flows. It is also intended to be a useful source of information for students in
the high semesters and in PhD programs.
The monograph consists of five volumes:
• Volume 1, Fundamentals.
• Volume 2, Mechanical interactions.
• Volume 3, Thermal interactions.
• Volume 4, Turbulence, gas absorption and release, diesel fuel properties.
• Volume 5, Nuclear thermal hydraulics.
In Volume 1 the concept of three-fluid modeling is presented in detail “from
origin to applications.” This includes the derivation of local volume- and time-
averaged equations and their working forms, the development of methods for their
numerical integration and, finally, a variety of solutions for problems of practical
interest.
Special attention is paid in Volume 1 to the link between the partial differential
equations and the constitutive relations called closure laws, without providing too
much information on the closure laws.
Volumes 2 and 3 are devoted to these important constitutive relations for the
mathematical description of mechanical and thermal interactions. The structure of
these two volumes is in fact a state-of-the-art review and selection of the best
available approaches for describing interfacial transfer processes. In many cases
the original author’s contribution is incorporated in the overall presentation. The
most important aspects of the presentation are that they stem from the author’s
long years of experience developing computer codes. The emphasis is on the prac-
tical use of these relationships: either as stand-alone estimation methods or within
a framework of computer codes.
This book, Volume 4, is devoted to turbulence in multiphase flows as well as
selected subjects in multiphase fluid dynamics that are very important for practical
applications but could not find place in the first three volumes of this work. The
state-of-the-art of turbulence modeling in multiphase flows is presented. First,
some basics of single-phase boundary layer theory, including important scales and
flow oscillation characteristics in pipes and rod bundles, are presented. Then the
scales characterizing dispersed flow systems are presented. The description of the
VIII Summary
turbulence is provided at different levels of complexity: simple algebraic models
for eddy viscosity; algebraic models based on the Boussinesq hypothesis;
modification of the boundary layer shear due to modification of the bulk
turbulence; and modification of the boundary layer shear due to nucleate boiling.
Then the role of the following forces on the mathematical description of turbulent
flows is discussed: the lift force; the lubrication force in the wall boundary layer;
and the dispersion force. A pragmatic generalization of the k-eps models for a
continuous velocity field is proposed, covering flows in large volumes and flows
in porous structures. Its large eddy simulation variant is also presented. A method
of how to derive source and sink terms for multiphase k-eps models is also
presented. A set of 13 single- and two-phase benchmarks for verification of k-eps
models in system computer codes are provided and reproduced with the IVA
computer code as an example of the application of the theory. This methodology is
intended to help other engineers and scientists to introduce this technology step-
by-step into their own engineering practice.
In many practical applications, gases are dissolved in liquids under certain con-
ditions and released under other conditions, and therefore affect technical proc-
esses in many ways, both good and bad. There is almost no systematic description
of this subject in the literature. That is why I decided to collect in Volume 3 useful
information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in
water, valid within a large range of pressures and temperatures, providing appro-
priate mathematical approximation functions and validating them. In addition,
methods for computation of the diffusion coefficients are described. With this in-
formation, the solution and dissolution dynamics of multiphase fluid flows can be
analyzed. For this purpose the non-equilibrium absorption and release on bubble,
droplet and film surfaces under different conditions is mathematically described.
In order to allow the theory from all four volumes to be applied to processes in
combustion engines, a systematic set of internally consistent state equations for
diesel fuel, gas and liquid, valid over a broad range of pressures and temperatures,
are also provided in Volume 4.
Nuclear thermal hydraulics provides a description of the physical processes that
occur in structural materials during the release of fission heat from nuclear reac-
tions. During its release to the environment, the thermal energy can be harnessed
to provide useful mechanical work or heat, or both. Volume 5 is devoted to nu-
clear thermal hydraulics. In a way this is the most essential application of multi-
phase fluid dynamics in analyzing steady and transient processes within nuclear
power plants.
December 2010 Nikolay Ivanov Kolev
Herzogenaurach
Table of Contents
1 Some single-phase boundary layer theory basics..……..............................1
1.1 Flow over plates, velocity profiles, shear forces, heat transfer................1
1.1.1 Laminar flow over one site of a plane..........................................1
1.1.2 Turbulent flow parallel to plane...................................................3
1.2 Steady state flow in pipes with circular cross sections............................4
1.2.1 Hydraulically smooth wall surface....................................................7
1.2.2 Transition region........................................................................16
1.2.3 Completely rough region............................................................17
1.2.4 Heat transfer to fluid in a pipe....................................................18
1.3 Transient flow in pipes with circular cross sections..............................30
Nomenclature........................................................................................................32
References.............................................................................................................34
2 Introduction to turbulence of multi-phase flows.......................................39
2.1 Basic ideas.............................................................................................39
2.2 Isotropy.................................................................................................50
2.3 Scales, eddy viscosity............................................................................51
2.3.1 Small scale turbulent motion......................................................51
2.3.2 Large scale turbulent motion, Kolmogorov-Pandtl
expression...................................................................................52
2.4 k-eps framework....................................................................................54
Nomenclature........................................................................................................59
References.............................................................................................................63
3 Sources for fine resolution outside the boundary layer............................67
3.1 Bulk sources..........................................................................................67
3.1.1 Deformation of the velocity field................................................67
3.1.2 Blowing and suction...................................................................67
3.1.3 Buoyancy driven turbulence generation.....................................68
3.1.4 Turbulence generated in particle traces......................................69
3.2 Turbulence generation due to nucleate boiling......................................73
3.3 Treatment of the boundary layer for non-boiling flows........................74
3.4 Initial conditions....................................................................................79
Nomenclature........................................................................................................80
References.............................................................................................................87
X Table of Contents
4 Source terms for k-eps models in porous structures.................................89
4.1 Single-phase flow.................................................................................89
4.1.1 Steady developed generation due to wall friction......................89
4.1.2 Heat transfer at the wall for steady developed flow...................92
4.1.3 Heat transfer at the wall for non-developed or transient flow....94
4.1.4 Singularities................................................................................94
4.2 Multiphase flow...................................................................................96
4.2.1 Steady developed generation due to wall friction......................96
4.2.2 Heat transfer at the wall for forced convection without
boiling........................................................................................98
4.2.3 Continuum-continuum interaction...........................................103
4.2.4 Singularities.............................................................................104
4.2.5 Droplets deposition at walls for steady developed flow..........106
4.2.6 Droplets deposition at walls for transient flow........................106
Nomenclature......................................................................................................107
References...........................................................................................................110
5 Influence of the interfacial forces on the turbulence structure..............113
5.1 Drag forces.........................................................................................113
5.2 The role of the lift force in turbulent flows........................................113
5.3 Lubrication force in the wall boundary layer.....................................118
5.4 The role of the dispersion force in turbulent flows............................119
5.4.1 Dispersed phase in laminar continuum....................................119
5.4.2 Dispersed phase in turbulent continuum.................................120
Nomenclature......................................................................................................125
References...........................................................................................................126
6 Particle-eddy interactions..........................................................................129
6.1 Three popular modelling techniques...................................................129
6.2 Particle-eddy interaction without collisions........................................130
6.2.1 Response coefficient for single particle....................................130
6.2.2 Response coefficient for clouds of particles.............................132
6.2.3 Particle-eddy interaction time without collisions.....................133
6.3 Particle-eddy interaction with collisions.............................................134
Nomenclature......................................................................................................135
References...........................................................................................................137
7 Two group k-eps models............................................................................139
7.1 Single phase flow................................................................................139
7.2 Two-phase flow...................................................................................140
Nomenclature......................................................................................................141
References...........................................................................................................143
8 Set of benchmarks for verification of k-eps models in system
computer codes...........................................................................................145
8.1 Introduction.........................................................................................145