Table Of ContentTheory and Modeling of Dispersed
Multiphase Turbulent Reacting Flows
Theory and Modeling
of Dispersed
Multiphase Turbulent
Reacting Flows
Lixing Zhou
TsinghuaUniversity, Beijing, China
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Preface
Multiphase, turbulent, and reacting flows are widely encountered in engi-
neering and the natural environment. The basic theory, phenomena, mathe-
matical models, numerical simulations, and applications of multiphase (gas
or liquid flows with particles/droplets or bubbles), turbulent reacting flows
are presented in this book. The special feature of this book is in combining
the multiphase fluid dynamics with the turbulence modeling theory and
reacting fluid dynamics (combustion theory). There are nine chapters in this
book, namely: “Fundamentals of Dispersed Multiphase Flows”; “Basic
Concepts and Description of Turbulence”; “Fundamentals of Combustion
Theory”; “Basic Equations of Multiphase Turbulent Reacting Flows”;
“Modeling of Single-Phase Turbulent Flows”; “Modeling of Dispersed
Multiphase Turbulent Flows”; “Modeling of Turbulent Combustion”; “The
Solution Procedure for Modeling Multiphase Turbulent Reacting Flows”;
and “Simulation of Flows and Combustion in Practical Fluid Machines,
Combustors and Furnaces.” The main difference between this book and pre-
vious books written by the author is that more much better descriptions of
basic equations and closure models of multiphase turbulent reacting flows
are introduced, and recent advances made by the author and other investiga-
torsbetween 1994 and2016 are included.
This book serves as a reference book for teaching, research, and engi-
neering design for faculty members, students, and research engineers in the
fields of fluid dynamics, thermal science and engineering, aeronautical,
astronautical, chemical, metallurgical, petroleum, nuclear, and hydraulic
engineering.
The author wishes to thank Prof. F.G. Zhuang, H.X. Zhang, and C.K. Wu
for their valuable comments and suggestions. Thanks also go to colleagues
and former students: Prof. W.Y. Lin, R.X. Li, X.L. Wang, J. Zhang, B.
Zhou, Y.C. Guo, H.Q. Zhang, L.Y. Hu, Y. Yu, F. Wang, Z.X. Zeng, K. Li,
Y. Zhang; Drs. Gene X.Q. Huang, T. Hong, C.M. Liao, W.W. Luo, K.M.
Sun, Y. Li, T. Chen, Y. Xu, G. Luo, M. Yang, L. Li, H.X. Gu, X.L. Chen,
X.Zhang,andY.Liu.Theirresearch resultsunderthedirectionandcoopera-
tion of the author contributed tothe context ofthis book.
xi
xii Preface
Finally, the author’s gratitude is given to the editors from Elsevier and
the Executive Editor, Dr. Qiang Li from the Tsinghua University Press for
their hard work inthe final editing and publishing ofthis book.
Any comments and suggestions from the experts and readers would be
highly appreciated.
LixingZhou
TsinghuaUniversity,Beijing,China
February,2017
Nomenclature
A area
B preexponentialfactor
c empirialconstants,specificheat
c dragcoefficient
d
d diameter
D diffusivity
E activationenergy
e internalenergy
F force
f mixturefraction
G productionterm
g gravitationalacceleration;meansquirevalueofconcentrationfluctuation
H stagnationenthalpy
h enthalpy
J diffusionfux
k turbulentkineticenergy;reaction-ratecoefficient
l turbulentscale;length
M molecularweight
m mass
N totalparticlenumberflux;particlenumberdensity
n fluctuationofparticlenumberdensity;exponentinparticle-sizedistribution
function;reactionorder;molenumberdensity
Nu Nusseltnumber
p pressure;probabilitydensitydistributionfunction
Pr Prandtlnumber
Q heat;heatingeffect
q heatflux
R universalgasconstant;weightfractioninparticle-sizedistribution
r radius;radialcoordinate
Re Reynoldsnumber
R fluxRichardsonnumber
f
S sourceterm
Sc Schmidtnumber
Sh Sherwoodnumber
T temperature
t time
u,v,w velocitycomponents
V volume;driftvelocity
xiii
xiv Nomenclature
w reactionrate
x,y,z coordinates
X combinedmassfraction;molefraction
Y massfraction
GREEK ALPHABETS
α volumefraction
μ dynamicviscosity
ν kinematicviscosity
λ heatconductivity
ε dissipationrateofturbulentkineticenergy;emissivity
φ generalizeddependentvariable
θ dimensionlesstemperature
τ shearstress
σ Stefan-Boltzmannconstant;generalizedPrandtlnumber
SUBSCRIPTS
A,a air
c rawcoal,reaction
ch reaction;char
d diffusion
e effective;exit
F,fu fuel
f flame;fluid
g gas
h char;heterogeneous
hr heterogeneous
i,in initial;inlet
i,j,k coordinatedirections
k k-thparticlegroup
l liquid
m mixture
Introduction
Dispersed multiphase turbulent reacting flows are widely encountered in
thermal, aeronautical, astronautical, nuclear, chemical, metallurgical, petro-
leum, and hydraulic engineering, and in water and atmosphere environments.
As early as the 1950s, Von Karman and H.S. Tsien suggested using contin-
uum mechanics to study laminar gas reacting flows and combustion, called
“aerothermochemistry” or “dynamics of chemically reacting fluids.”
Multiphase fluid dynamics was first proposed by S.L. Soo in the 1960s for
studying nonreacting multiphase flows. The classical reacting fluid dynamics
and multiphase fluid dynamics do not include the theory of turbulence
modeling. On the other hand, the theory of turbulence modeling was first
proposed by P.Y. Chou in the 1950s, and was fully realized by B.E. Launder
and D.B. Spalding in the 1970s. Within the last 40 years, through worldwide
study and application, it has become the only reasonable and economical
method to solve complex turbulent flows in engineering problems. However,
up until the 1980s, the theory of turbulence modeling was limited to only
single-phasefluidflows themselves, anddidnotconcernthe dispersedphase,
i.e., particles/droplets/bubbles inmultiphase flows.
Since the 1980s, the author has combined multiphase fluid dynamics with
the theory of turbulence modeling, and proposed the concept of multiphase
(two-phase) turbulence models, in particular the turbulence models of the
dispersed phase, i.e., particles/droplets/bubbles. Furthermore, we developed
the turbulence-chemistry models for single-phase and two-phase combustion
using a method similar to turbulence modeling. Hence, the dynamics of mul-
tiphase turbulent reacting flows was developed, where the modeling theory,
numerical simulation, measurements, and their application in combustion
systems were systematically studied. The comprehensive models, basic con-
servation equations, the relationships between slip and diffusion, the energy
distribution between the continuum and dispersed phases, the fluid-particle/
droplet/bubble turbulence interactions, the interactions between particle
turbulence and particle reaction, the gas-phase turbulence-chemistry interac-
tion, and the particle(cid:1)wall interaction were thoroughly studied. A series of
new closure models were proposed, many 2-D and 3-D computer codes were
developed based on the proposed models and some of the simulation results
xv
xvi Introduction
were validated using the laser Doppler velocimeter (LDV), phase Doppler
particle anemometer (PDPA), and particle imaging velocimeter (PIV) mea-
surements and direct numerical simulation (DNS). The research results were
applied to develop innovative swirl combustors, cement kilns, oil(cid:1)water
hydrocyclones, gas(cid:1)solid cyclone separators, and innovative cyclone coal
combustors. This book is written based on the research results of the author,
aswellasthoseobtainedbyotherinvestigatorsinrecentyears.Inthefollow-
ing sections some basic definitions and descriptionsare discussed.
TURBULENT DISPERSED MULTIPHASE FLOWS
Gas/liquid flows containing a vast amount of particles/droplets/bubbles are
called dispersed multiphase flows. This terminology is widely accepted by
the academic and engineering communities in the fields of fluid dynamics,
thermal science and engineering, aeronautical, astronautical, metallurgical,
chemical, petroleum, nuclear, and hydraulic engineering. Frequently, the
concept of “phase” is considered as a thermodynamic state, so multiphase
flows are divided into gas(cid:1)solid (gas(cid:1)particle), liquid(cid:1)solid (liquid(cid:1)parti-
cle), gas(cid:1)liquid (gas(cid:1)spray or bubble(cid:1)liquid), liquid(cid:1)liquid (oil(cid:1)water)
two-phase flows and gas(cid:1)solid(cid:1)liquid, oil(cid:1)water(cid:1)gas three-phase flows.
Also, sometimes the terminologies “suspension flows” and “dispersed flows”
are adopted. Besides, there are nondispersed two-phase flows, such as stratified
and annular gas(cid:1)liquid flows. However, from the multiphase fluid dynamic
point of view, in particular in multifluid models, particles/droplets/bubbles with
differentsizes,velocities,andtemperaturesmayconstitutedifferentphases.This
is the reason why the terminology “multiphase fluid dynamics” was first
proposed by S.L. Soo in the 1960s. In short, although different academic and
engineering communities have different understanding of the above-listed
terminologies, nowadays “multiphase flow” as a general concept of a branch of
scienceandtechnologyiswidelyacceptedwithoutdisagreement.
Most practical fluid flows, maybe more than 99% of flows in the natural
environment and engineering, are laden with particles, droplets, or gas bub-
bles.Puresingle-phaseflowsexist onlyinafewcases such asflowsinartifi-
cial ultraclean environment. There are a variety of multiphase flows, such as
cosmic dust in cosmic space, cloud and fog (rain droplets), dusty-air flow,
sandyrivers,blood flowsinbiologicalbodies,pneumatic/hydraulicconveying,
dust separation and collection, spray coating, drying and cooling, spray/
pulverized-coal combustion, plasma chemistry, fluidized bed, flows in gun
barrels, solid-rocket exhaust, steam-droplet flows in turbines and gas-fiber
flows, steam-water flows in boilers and nuclear reactors, oil(cid:1)water and
gas(cid:1)oil(cid:1)water flows in petroleum pipes, and gas(cid:1)liquid(cid:1)solid flows in
steel making furnaces.
Most fluid flows in engineering facilities, such as flows in hydraulic
channels, gas pipes, heat exchangers, fluid machines, chemical reactors,
