Numerical Modeling of Sootblower Jet Flow
Between Superheater Platens
In a Kraft Recovery Boiler
Kayhan Kermani
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science
Department of Chernical Engineering and Applied Chemistry University of Toronto
O Copyright by Kayhan Kenani 2001
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Canad.
Numerical Modeling of Sootblower Jet Flow Between Superheater Platens in a Kraft Recovery Boiler
Master of Applied Science 2001
Kayhan Kermani
Department of Chernical Engineering and Applied Chemistry University of Toronto
Abstract
Sootblowers are used to control fireside deposit accumulation in kraft
recovery boilers. A sootblower produces high-velocity steam jets which impinge
on deposits and remove them from heat transfer tube surfaces. How the jet
interacts with deposits and tubes is not well understood.
Since direct rneasurement of sootblower jet flow characteristics in a kraft
recovery boiler is difficult, a numerical model has been developed to simulate a
sootblower jet as it propagates between two platens and interacts with deposits.
The numerical model was first used to simulate a scaled laboratory air jet
exerted on a deposit. The numerical results were validated by the experimental
data. The model was subsequently used to simulate a full-scale sootblower jet
under recovery boiler conditions. It shows that the deposit removal efficiency of a
sootblower is a strong function of the distance between the noule and deposit.
pressure, and deposit height.
ACKNOWLEDGMENTS
This work is part of the University of Toronto research program on
"lmproving Recovery Boiler Performance, Emissions, and Safety" jointly
supported by: Alstom Power, Andritz-Ahlstrom Corporation. Aracruz Celulose
S.A., Babcock & Wilcox Company, Boise Casacade Corporation. Bowater
Canada Inc., Cl yde-Bergemann Inc., Daishowa-Marubeni lnternational Ltd.
Domtar Inc.. Domtar Eddy Specialty Papers, Georgia-Pacific Corporation.
International Paper Company, Irving Pulp & Paper Limited, Kvaerner Pulping
Technologies. Potlatch Corporation. Stora Enso Research. Votorantim Celuose
e Papel. Westvaco Corporation, Weyerhaeuser Paper Company, and
VVillamette Industries Inc.
I would like to offer my sincere gratitude to Professors Donald E.
Cormack and Honghi Tran. whose guidance and support made this project a
valuable experience. Special thanks to Professor David C.S. Kuhn for providing
an access to Fluent Code and his comments. I am very grateful to Dr. Andrei
Kaliazine for his comments and support. His expertise was invaluable. My
gratitude goes out to our network administrator. Dan Tomchyshyn, for his
solutions to my cornputer problems. Finally. I would also like to acknowledge
the help and dear friendship of Reza Ebrahimi Sabet.
III
TABLE OF CONTENTS
. . ................................................................................... Abstract II ..- .............................................................. Acknowledgements.. ..-III
Table of Contents.. ........................ ., ....................................... .iv ..
List of Figures.. ...................... ... ... ... Nomenclature .......................................................................... ix
....................................................................... 1 Introduction.. 1 1 .l Motivation and objectives.. ................................................ ..1
.................................................................. 2 Literature Review 4 2.1 The Sootblower Jet ............................................................. 4
2.1.4 FIuid Mechanics of the Sootblower Jet ........................... 4 ................................. 2.1.2 Application of numerical models ..6
2.2 Turbulence rnodeling ................. ... .......................o........e.. 8 2.2.1 Ovewiew.. ............................................................... ..8 2.2.2 Governing equations ............. .... ....... ....................... 9
2.2.2.1 RANS equations .............................................. 1 O 2.2.2.2 Energy equation.. .......................................... ..12
2.2.3 The k - ~ turbulence mode!. ............................................ i 2 2.2.3.1 Standard ke ..............m............m . ~ ~ . m m m ~ 0 ~ e ~ ~ ~ ~ ~ * ~ m . 1 4
............................................................. 2.2.3.2 RNG k-E 16 .............................................................. 2.2.4 Near-wall jet fiow 17
.............................................. 2.3 The numerical solution scheme .18
........................................... 3 Model Description .......................... ... 21 ................................................................................ 3.1 Free jet 21
3.1.1 Gn'd generation .............................................................. -21 3.1.2 Numerical solution method of Fluent ................................. 24 3.1.3 Eggers experiments ......................................................... 25 3.1.4 Computed results and cornparison with experiments ........... 27
3.2 Jet interaction with deposit ..................................................... 31
4 Experimental Procedure .............................................................. 33
4.1 Scaled experimental setup ...................................................... 33 4.2 Experimental results .................... .... .................................... 35 4.3 Numerical solution of the jet applied on a deposit ...................... 38
..................... ....................................... 5 Results and Discussion .. 42 .......... 5.1 Cornparison of simulation results with experimental data 42
............... .............. 5.2 Simulation of a full-scale sootblower .... 43 5.2.1 Effect of lance Steam Temperature ................................ 44
................................................ 5.2.2 Effect of deposit height 45 ............................. 5.2.3 Effect of flue gas and platen temperature 48
5.2.4 Effect of lance steam temperature ................................... 49 ............. 5.2.5 Effect of platen spacing ... ................. A
................... ........ 5.3 Implications for deposit removal process .. 52 5.3.1 Effect of jet force on deposit rernoval ............................... 52
..................... 5.3.2 Effect of mean jet stress on deposit rernoval 54
........................................................................... 6 Conclusions 58
References ............................................................................... 60
Appendices ............................................................................. -62 ......................................... A . Turbulence Model ....-......... ... -62
6 . Modeling Implementation .... ....... .................................. 68 ................................... ................ . C Experimental Data ...... 75
List of Figures and Tables
Overall view of a sootblower
A simplified schematic of a lance head
Hierarchy of the k-E turbulence model
Overview of the coupled numerical solution
A 3D grid of a jet issuing between two platens
Eggers experimental setup
Contours of Mach number of a free jet
Centreline velocity of a free jet
Comparison of two k-E turbulence models
A cornputational domain of a jet applied on a deposit
Scaled experimental setup
A schematic of important dimensions in the setup
Measured pressure and torque.. . .
Measured force, F for M =10
Contours of a simulated jet applied on a deposit
Computed and measured force. F for M =20. and M = 20 cm
Comparison of the computed F with the measured F
Computed F versus lance pressure
Computed F on deposits of different heights
Computed F for different platen spacing
Computed F for different temperature
Cornputed F for different lance temperature
Cornparison of a free jet with a confined jet
Computed PIP and diameter of a sootblower jet
Computed PIP and F
Loaded depositltube contact area
Measured Saah . and computed Siet Flowchart of the turbulence modeling
Computational domain of the iaboratory setup
Computational grid of the laboratory setup
Laboratory setup
Torque sensor layout
Calibration diagram of the torque sensor
Table 1 Combination of M. and X for each experiment
Table 2 Basic parameter of a sootblower
Table C-1 Measured mean drag force for Mi
Table C-2 Measured mean drag force for Mt
Table C-3 Measured mean drag force for Mj
Nomenclature
speed of sound
surface area of a deposit impinged by a jet
a function of turbulent strain and density in RNG k-E equations
coefficient of turbulent viscosity
coefficients of dissipation rate of turbulent energy
specific heat constant
specific heat constant
jet offset
total energy
mean drag force
modeled coefficient in turbulence equations
gravitational acceleration
specific enthalpy
height of a deposit
turbulent kinetic energy
distance between the noule and the entrance of platens
turbulent Mach number
vertical coordinate for boundary layer
pressure
turbulent Prandtl number
gas constant
Reynolds number
mean strain rate
time
temperature
horizontal velocity component in boundary layer equation
dimensionless velocity cornponent in boundary layer equation
velocities in x. y. and z directions
fluctuating velocities in x, y, and z directions
Reynolds stresses
vertical velocity component
normal velocity component
distance between the noule exit and a deposit
boundary layer thickness
dimensionless boundary layer thickness
Greek Symbols
a k , ac coefficients in RNG k-c turbulence equations
P coefficient of thermal expansion
6ij Kronecker function
E dissipation rate of turbulent kinetic energy
4 dependence variable in general discretized equation
6 fluctuating dependence variable
ri j tensor of stresses in momentum equation
rnolecular viscosity
turbulent viscosity
kinetic viswsity
density
shear stress
ratio of specific heats
turbulent Prandtl numbers for k, and E
Chapter 1 - Introduction 1.1 Motivation and objectives
Black liquor is bumed in a kraft recovery boiler to recover inorganic
chemicals used in the pulping process, and to produce steam and power
from the heat of combustion. During the burning process a part of the
inorganic chemicals entrains in the flue gas, and forms fireside deposits on
heat transfer surfaces. If deposits are not sufficiently removed. they may
drastically reduce the boiler thermal performance, and in severe cases.
completely plug the flue gas passages and lead to unscheduled boiler
shutdowns. Effective deposit removal is, therefore. critically important for
maintaining stable boiler operation.
Sootblowers are used to control fireside deposit accumulation in kraft
recovery boilers. Figure 1-1 shows a typical sootblower with a moving
mechanism. It consists of a feed tube, which delivers high-pressure steam
to a lance tube and two opposing noules at the end of the lance tube. As a
sootblower rotates and advances, it produces two high-pressure steam jets
from the noules, which impinge on deposits and remove them from the
tubes. A high efficiency of the sootblowing operation is vitally important for
ensuring continuous boiler operation and for achieving high boiler thermal
performance.
Gpsn?a cabfe /-Raar support bracket Nonle
Figure 1-1 : Overall view of a sootblower (from Diamond Power Co.)
In order to remove deposits from tube surfaces, recovery boilers are
equipped with many sootblowers. Sootblowers consume between 5% to
10% of the boiler steam production.
Much work has been performed so far to examine the
hydrodynamics of a supersonic air jet flowing through a convergent-
divergent nozzle. Jet parameters, in particular the peak impact pressure
(PIP), have been studied experimentally and analytically as a function of
nozzle size, shape. and jet variables. The characteristics of a free jet are
relatively well known. For a nozzle that produces a fully expanded jet. the
jet PIP can be predicted with a high degree of accuracy, if the nouls and
fiuid parameters are .known [3].
However, when a jet propagates between Wo platens or in a bank of
tubes, its flow pattern is greatly affected by the tubes, as well as by deposits
on the tubes. The interaction of the sootblower jet with platens and deposits
is not weil understood. The lack of practical information on sootblower jets
is primarily due to the diffkulty in conducting tests in an operating recovery
boiler where the environment is extremely hostile and uncontrollable.
Meaningful data rnay not be obtained with conventional laboratory test
methods because of the difficulty of providing appropriate sootblower jets
and reproducing the conditions resernbling those found in recovery boilers.
Moreover. it is difficult to measure accurately the jet flow characteristics with
sensors. since they need to be introduced into the jet flow. and thus may
affect the characteristics of the jet.
An alternative approach to both field and laboratory test methods is
to use a numerical model to simulate and predict sootblower jets by a
computational fluid dynamics (CFD) code. This c m also provide a better
understanding of the relationships between the sootblower jet and the
deposit attached to the platen, and ultimately lead to sootblower
performance improvement. Numerical simulation of sootblower jets
between superheater platens has not been attempted to date.
The objectives of this research are as follows: (i) to develop a
numerical model to simulate the sootblower jet impinging on deposits
attached to platens: ( i i ) to conduct laboratory experiments to obtain data
and to compare with the simulation results; and (iii) to use the developed
model to determine major parameters affecting sootblower performance.
Chapter 2 - Literature Review 2.1 The sootblower jet
2.1.1 Fluid mechanics of the sootblower jet
The hydrodynamics of a sootblower jet propagating between
superheater platens is compiex. It is a supersonic, compressible, turbulent.
threedimensional fiow with high velocity and pressure gradients. Figure 2.1
shows a schematic of a sootblower jet operating in a superheater. where the
tubes are arranged into parallel platens. High-pressure steam is delivered to
two noules installed at the end of a long translating and rotating tube called
a lance. The high-pressure steam exgands and accelerates as it passes
through the noules in which two high-velocity jets are finally formed. The jets
have a maximum velocity of two to three times the velocity of sound (Mach
number). They propagate between parallel platens and impinge on deposits.
c
P laten
Figure 2-1: A schematic of a lance head
The purpose of this study is to develop a numerical model to compute
accurately the jet characteristics in a wide range of parameters, including the
operating conditions of most sootblowers.
The sootblower jets flow is turbulent. which means that the basic flow
variables. such as velocity, pressure, density and temperature have a
fluctuating component, and so cannot be simulated without special
techniques. Numerical methods have been developed to compute the
average values of the flow variables from an "averaged" form of the Navier-
Stokes and energy equations. The averaging process introduces new terms
in the Navier-Stokes and energy equations that must be modeled by
additional transport equations. In this work, the k-E turbulence model has
been used for this purpose. it is discussed in some detail in section2.2.3 of
this chapter.
Because of the simple geornetry of superheater platens and high
deposit accumulation on the platens [2], it is desirable to numerically simulate
the sootblower jet flow in this section of a kraft recovery boiler first. This was
the focus of the current study.
2.1.2 Application of numerical models
It is difficult to obtain quantitative measurements of the interaction of
a sootblower jet on a deposit in an operating recovery boiler. Furthermore,
even in the laboratory under controlled conditions measurement techniques
display significant errors due to the supersonic nature of the flow that causes
shock waves in the presence of small flow obstructions.
An alternative is to use numerical models to simulate the sootblower
jets impinged on deposits. This method is a numerical approach to solve the
governing equations of the jet flow behnreen superheater platens by a CF0
computer code. By solving the goveming equations, an approximation of the
jet variables such as velocity, pressure, and temperature is possible.
Moreover. more information is obtainable from a numerical simulation than
from experiments. because geometrical and physical changes can easily be
introduced to the model and their impact on performance can be analyzed.
Very little has been done in the area of numerical modeling of
sootblower jets. This is mainly due to a lack of a universal turbulence model
available in CFD codes. which takes into account both the compressibility
and Mach number effects on a supersonic jet. Recently Sarkar and
Balakrishnan [9] have proposed a rnodified standard k-E turbulence model
applicable to a supersonic compressible jet flow. However, this mode1 has
not been available in commercial CFD codes till a special CFD code.
Rampant. was developed by Fluent Inc. for high-velocity compressible flow
in l996[14].
More recently, Theis and Tam [6] suggested a set of calibrated
coefficients for Sarkar and Balakrishnan k-E turbulence mode1 applicable to
the free supersonic jet exiting to quiescent air. These new coefficients were
validated by comparison of the numerical results of free supersonic jets with
the experirnental results.
This study uses an advanced CFD code, Fluent V5 [14], includes
Sarkar and Balakrishnan standard k-E turbulence mode1 with the set of
coefficients suggested by Theis and Tarn. However. another calibration was
cmducted on the set of coefficients for the numerical modeling of the jets
between two parallel platens.
The rest of this chapter is devoted to define turbulence modeling,
the governing equations of sootblower jet fiow. Aiso, both the standard
RNG k-E turbulence models developed for compressible supersonic jet
are introduced for comparison. A coupled solution scheme defined for so
the governing equations is given at the end.
and
and
flow
lving
2.2 Turbulence modeling
2.2.1 Overview
Turbulence is one of the most important and challenging issues in al1
of computational fiuid dynamics. The fluctuating characteristics of turbulent
flow rnake it highly non-predictable. The turbulent flow tends to be three
dimensional. unsteady. rotational. and highly irregular. The irregularity is
attributed to the non-linearity of the Navier-Stokes equations. This makes the
task of developing universal models exceedingly difficult. There has been
rnuch work done in rhis area over the last two decades and an enormous
amount of empirical relations and phenomenological models have been
developed. Figure 2.2 displays only the hierarchy in the numerical modeling
of the k-E turbulence model for the compressible Row. A detail explanation on
computational effort on turbulence modeling is given in appendix A.
The standard k-E turbulence model has proven over the years to be a
useful engineering approach for the prediction of the mean velocity profiles of
a turbulent compressible subsonic flow [4]. However for high velocity
compressible shearing flow such as a free supersonic air jet. the standard k-E
turbulence model provided numerical results which were not in agreement
with the experirnental data (51. Thus a new turbulence model based on the
standard k-E model was developed by Sakar et al. in 1990 191. For a review of
this subject of turbulence modeling, the remainder of this section is devoted
to the appropriate form (Favre averaged) of goveming equations and
modified k-E turbulence equations for a supersonic compressible jet.
f
Numerical Modeling of the compressible Flow 1 1
Turbulence Mode1
1 Governing Equations (Favre-Averaged Equations) '
Two Equations Models for k - ~ I
Figure 2-2: Hierarchy of the k - ~ turbulence rnodel
2.2.2 Governing equations
A new form of governing equations of turbulent compressible flow
are derived from the Favre-Averaged Navier-Stokes and energy equations.
The derivation is based on the assumption that the jet flow is fully turbulent
when the effects of molecular viscosity are negligible. and the density
fluctuation is the main parameter affecting the jet variables.
2.2.2.1 FANS equations of the compressible turbulent flow
In the turbulence modeling, ail the solution variables in the original
Navier-Stokes and energy equations are decomposed into the mean ( time-
averaged) and fluctuating components. This rnethod is known as "Reynolds
decomposition" and it allows the governing equations to be expressed in the
more desirable time-averaged form where the variables appear as mean
values instead of as Ructuating values.
For compressible turbulent flow. in addition to velocity and pressure
fluctuations. one rnust also account for density and temperature fluctuations
which are negligible in incompressible flow. The effects of these fluctuations
in the tirne averaging equations create triple cornplex correlations involving
density and velocity fluctuation [7]. The appropriate form of the time-
averaged equations can be simplified dramatically by using the density-
weighted averaging procedure suggested by Favre [8]. For velocity
components:
where y and i{,' are the rnean(rnass-averaged) and fluctuating velocity components (i=1,2,3) and
- where P is the conventional Reynolds-averaged density given:
and t, is a tirne interval. which is large when compared to the tirne of the
turbulent oscillations. The overbar over denotes a conventional Reynolds
average, while the overtilde denotes the Favre average. Likewise. for
pressure and other scalars:
In this case 4 denotes general scalars (flow property such as pressure.
temperature. density. etc.) while $ and $'are mean and fluduating
components.
Substituting the expressions of this fwm for the flow variables into
the instantaneous continuity and momentum equations and taking a Favre
average and dropping the overbar and overtilde on the mean velocity, ,
yields Favre-averaged momentum equations. They can be written in
Cartesian tensor form as:
Continuity
Momenturn
Equations (2-5) and (2-6) are called "Favre Averaged" Navier-Stokes
(FANS) equations, and have the same forms as the instantaneous Navier-
Stokes equations, with the velocities and other solution variables now
representing mass-averaged values. In the FANS equations, effects of
turbulence are represented by the Favre-averaged "Reynolds stresses"
( -pl i l t i r : ) . These Reynolds stresses need to be modeled in order to close
equations (2-6) and (2-7).
2.2.2.2 Energy equation
Finally. the energy transport of a supersonic jet flow was rnodeled by
using a Favre averaging concept similar to momentum transfer. The
"rnodeled" energy equation is thus given by:
Where E is the total energy, H is the specific enthalpy, k is the molecular
conductivity, r,, is the stress tensor. Prt is the turbulent Prandtl number for
temperature or enthalpy. The turbulent heat transfer is dictated by the
turbulent viscosity (pt) and turbulent Prandtl number (Prt). The recommended
default value of the turbulent Prandtl number is 0.85 (1 11.
All the above continuity, momentum, and energy equations which define the
jet flow behavior are called the governing equations.
2.2.3 The k-E turbulence model
To close and solve the governing equations, a turbulence model should
be used. The k-E turbulence model is widely used for jet flow valid only for
fully turbulent flows and is based on Reynolds averages of the governing
equations. In the k-E model. analogous to the Stokes relations for the
viscous stresses. Reynolds stresses in equation (2-7) are modeled using the
Boussinesq hypothesis [1 O]:
Where k is the normal stress or turbulent kinetic energy defined by:
The turbulent normal stresses act like pressure. so when equation (2-9) is
used to eliminate rr:ii'. in the mornentum equations. the normal stresses can
be absorbed into the pressure term and need not be calculated explicitly. 6ii
is the Kronecker function. which equals O for i=j, and 1 for i=j. Due to the
very small scale of turbulent motion and its rapid movement. direct
simulation of the above equations would require an enormous amount of
computer time and storage. and thus is not practical. The "eddy" or turbulent
viscosity, pt, is cornputed using turbulent kinetic energy (k) and its rate of
dissipation (E) from:
r- 2
Where E is the dissipation rate of turbulence kinetic energy, defined by:
2.2.3.1 Standard k-E turbulence model
Turbulent kinetic energy (k) and its rate of dissipation (E) in equation
(2-1 1) are obtained frorn the solutions of their "modeled" transport equations as
in a standard k-E turbulence model [9]:
- - C
- C- ( - u ?k
T ( p k ) + T ( p i l , k ) = - [ ( , U + ~ ) = ] + G , +G, - p & ( 1 + 2 ~ ? ) ( 'f a , hl Crk (Tl
and
- - - 3 C' C' C ' u CE & E' T ( P & ) ~ - ( P , E ) = ;((,U +-) - ]+Cir -(Gi + ( l -Cjr)Gh} -C2,p-(2-14) cWt Lx, X I O, Zx1 k k
Note that for high-Mach number flows. the compressibility affects turbulence
through dilatation dissipation. which is normally neglected in the modeling of
incompressible flow. The turbulent Mach number. Mt, is defined as:
Where a (= dm) is the speed of sound and y is the ratio of specific heats (c&). Mt is changing between 0.1 to 0.5 when convective Mach number. Mc
ranging from 1 to 4 respectively [9]. Gk is the generation of turbulent kinetic
energy, k. due to the turbulent stress, and is given by:
and Gb is the generation of k due to buoyancy:
p: z c;, =pg,-- Pr, ir,
where Pri is the turbulent Prandtl number for temperature or enthalpy, and P
is the coefficient of thermal expansion:
For ideal gases. equation (2-1 5) reduces to
P r L7P c;, =-g,-- Pr, ir,
Since the buoyancy effect is negligible to a sootblower jet. the Gb term will
not be included in the present k-E turbulence equations.
Equations (2-13) and (2-14) constitute the k-E turbulence model. which
together with the wntinuity, momentum. and energy equations (2-5 to 2-7
and 2-8) forrn a closed set of equations describing turbulent flows.
The k-E model contains six empirical model constants (CI, . Ca , C, , o k , and Prt ) . They are determined either from experiment or from
cornputer optimization The generally recommended model constants have
the following default values [11]:
CI,=1.44. Ca=1.92, C, =0.09, ~~=1.0, a. =1.3, Prt ~0.85
These default values have been deterrnined from experiments with air and
water for fundamental turbulent shear flows including homogeneous shear
flows and isotropic turbulence. Although they have been found to work fairly
well for a wide range of wall-bounded and free shear flows. they must be
modified slightly in some cases. For the free jet flow, Thies and Tarn [6]
found modified coeffcients were important to reproduce the experimental
data given by some researcher [6]. They found:
Ci.=1.40, Ch=2.02, C,=0.0874. (rk=0.927, O, 4.131. Pr(z0.844
These coefficients have been used in as default. however eventually they
have been changed slightly to reproduce the laboratory data obtained for this
study.
2.2.3.2 Renormalization group (RNG) k-e turbulence model
Several variants of the k-E model have been proposed in recent
years. A more popular version is the RNG k-E model, developed by Orszag
and Yakhot [12]. It has the same from as the standard model. but the model
constants are derived analytically from a mathematical method referred to as
renormalization group theory. In addition. a second t e n also appears in the
s equation. The RNG k-E model is given by:
A - A -
and
Where S is the modulus of the strain tensor, a k = 1 -393, CI, =1.42, C 2 E 4.68,
and B is a function of turbulent strain and density.
In cornparison with the standard kz, the RNG k-E turbulence mode1
introduces smaller coefficients in the k-s equations. These reduced values
mean that the decay of the turbulent dissipation rate, E, in equation (2-21). is
also reduced. This leads to higher values of E, and. subsequently, lower
values of k and pt; therefore. it is expected that the RNG k-E rnodel gives
better results in regions of the flow where the rnean strain rates are high.
such as near walls. because it is more responsive to the effects of rapid
strain than the standard k-c model [12].
2.2.4 Near-wall jet flow
Because of the no-slip boundary condition at wall surfaces. the
velocity gradients near the wall are especially large. Solving the transport
equations al1 the way to the wall requires a very fine grid to resolve the
boundary layer accurately. In most numerical codes, this is avoided by using
what is referred to as a wall function to bridge the gap between the wall and
the fiow immediately outside the boundary layer. Thus, a cornputationally
expensive mesh is avoided. The most common wall function is the standard
logarithmic law of the wall.
In turbulent flow. the wall boundary layer consists of a laminar
sublayer and a so-called log-law region in which the flow is fully turbulent. It
is derived from the fact that at high Reynolds numbers there is equilibrium
between the production and dissipation of turbulent kinetic energy. The mean
velocity profile near a wall is given by Nallasamy (131. He expressed that in
the log-law region. the boundary layer thickness y is defined by the "log-law"
wall function:
where
u ' = u l ( ~ l ~ ) " * (2-23)
Y '=PY(~I?) ' 2 1 ~ (2-24)
T = p (Fu 1 în) (2-2 5)
For the laminar sublayer the boundary layer thickness can be computed:
u* = y' when y+ c 1 1 (2-26)
Because of the high velocity of jet flow. the thickness of the iaminar sublayer
in cornparison with the log-law region is negligible.
2.3 The numerical solution scheme
Numerical modeling methods are used generaily to solve the
governing equations for the conservation of mass and mornentum. and for
energy and other scalars, such as turbulence and chernical species. In al1
methods, a control-volume-based technique is used that consists of the
following:
division of the domain into discrete control volumes using a computational
grid;
0 integration of the governing equations on the individual control volumes to
construct algebraic equations for the discrete dependent variables
("unknown") such as velocities. pressure. temperature. and conserved
scalars; and
linearization of the discretized equations and solution of the resultant
linear equation system to yield updated values of the dependent
variables.
There are two main numerical rnethods: the segregated solution
method and the coupled solution method. These two numerical methods
employ similar discretization processes (finite-volume), but the approach
used to linearize and solve the discretized governing equations is different.
The first method is recommended for predicting subsonic flows. which is not
the desired case in this study. The coupled method is recommended for
predicting high-speed compressible jet flows. This method numerically solves
the governing equations sirnultaneously, and the equations for additional
scalars such as turbulent kinetic energy and dissipation are solved
sequentially (Le., segregated from one another and from the coupled set.)
[W.
Because the governing equations consisting of continuity, momentum and
energy equations are non-linear and coupled. several iterations of the
solution loop must be performed before a converged solution is obtained.
Each iteration consists of the steps iilustrated in Figure 2-3 and outlined as
foilows:
Fluid properties are updated, based on the current solution. (If the
calculation has just begun. a guess for fluid properties should be
provided)
The equations of continuity, momentum. and energy are solved
simultaneously
Equations for scalars such as turbulence properties are solved using the
previously updated values of the other variables.
A check for convergence of the equation set is made. If the solution has
not converged. the solution process is repeated from step 1 above.
If the solution has not converged in the beginning of calculation.
the fluid properties to be adjusted are checked.
Update properties
Solve turbulence and other scrlar equations u Figure 2-3: Overview of the coupled numerical solution
Chapter 3 - Model Description This chapter outlines the numerical mode1 used to solve the governing partial
differential equations (PDE) and other defined scalar partial equations for
both a free jet and a jet impinging on a deposit. For each case. first the finite
control volume grid is briefly described, then the general solutions computed
by a CFD code, Fluent 5 [14], are presented. For a free jet, the computed
velocity results were compared with the experimental data available in the
literature to validate the code. but there was no data for the jet applied on a
deposit.
3.1 Free jet
The definition of a free jet is a jet exhausting into a large unconfined
volume of quiescent air. The free jet expands and decays as it mixes with the
surrounding media. Walls are far enough from the jet. and cannot affect the
jet.
3.1 .le Grid generation
The solution domain consisted of the finite control volume between
two parallel superheater platens, into which issued a symmetric supersonic
jet spreading from a fully expanded nonle. To ueate a 2D axisymrnetrk and
3D graphical geornetry of the finite control volume, a geometry and grid
generation cornputer code, Gambit [14], was used. However, there are other
computational graphical codes available to generate complicated control
volumes.
To create an appropriate mesh for the jet flow computation, the
computation domain was divided into structured rectangular grids. Grids
were made finer in the core of the jet. and also close to the nozzle exit. A
uniform grid in the x-y plane (parallel to the noule exit) with a larger
concentration of grid in the mixing layer of the jet was used in the
computation. A layout of a grid is shown in Figure 3-1. Fine grids were
ernployed to resolve clearly the thin mixing layers of the jet. However. the
grids were coarsened along the centreline of the jet in the x-direction. as the
jet velocity reduces and becomes weak. This coarsening of the grid did not
compromise the spatial resolution of the computation. but allowed a
reduction in the number of control volumes (cells), which greatly reduced the
overall computation tirne.
In Figure 3-1 a 3D grid is shown where the diameter of the noule exit
is 0.0725 cm. which 1s deliberately identical to that of a scaled fully expanded
laboratory nozzle. The distance of the nou le exit from the entrance of the
platens is considered 10 cm, and other dimensions are taken so that the jet
flows between the platens freely as shown in Figure 3-1.
Two grids for 20 axisymrnetric and 30 jets were generated. There
were 100 cells in the x-direction and 10 cells in the y-direction for the 20
axisymrnetric grid. In contrast, there were 100 cells (for 100 cm length) in x-
direction, 20 cells (for 20 cm width) in y-direction, and 10 cells (for 20 cm
depth) in z-direction for the 3D grid. The difference between the two grids is
obviously in the number of total cells, which are 1000 and 20.000 cells for 2D
axisymmetric and 3D. respectively. The cornputational time for 2D
axisymmetric simulation is far less than the 30 simulation; however, the
solutions are different and will be discussed in the following section.
Figure 3-1: A 3D grid of a jet propagates between two platens
3.1.2. Numerical solution method of Fluent
To solve governing equations of high velocity turbulent jet flow, a
commercial computational fluid dynamics code. Fluent. was selected. Fluent
is capable of producing converged flow solutions for turbulent compressible,
supersonic flows at Reynolds numbers up to at least Re = 10" [14]. Fluent
5.1 uses the finite volume method to solve the governing equations. This
method, which is widely used for fluid flow. will be briefly described below.
When the generated grids introduced in section 3.1.1 are read by
Fluent, the governing equations are discretized over each small control
volume (cell) to produce a set of nonlinear algebraic equations for the values
of the dependent variables at the centre of each cell. Fluent approximates
each of these terms as applied to every cell in the computational grid. The
approximation used to relate the cell face values to cell centre values is
called the discretization scheme. The most commonly used scheme is the
second order accurate central differencing scheme. which assumes that the
face value is a linear interpolation of adjacent cell centre values: this scheme
is given by Patankar [15]. Fluent retains this scheme in al1 the discretized
governing equations.
To solve the equations. a sequential procedure is used where each
equation is solved in succession. treating the other dependent variables as
ternporally known. In Fluent. this is referred to as the coupled implicit solver.
Of course. this procedure requires an iterative process.
To model the free jet flow in the grid illustrated in Figure 3-1. the
turbulent flow field was calculated using both the standard k-E and the RNG
k-E models to solve the governing equations. In order to sirnplify the
calculations, the simulation conditions were:
the jet is produced by a fully-expanded nozzle;
the fiuid is an ideal gas;
the inlets and outlet of the domain are at constant pressure boundaries:
platen surfaces are Rat and at a constant temperature.
The simulation was run on a Windows NT workstation equipped with a single
Pentium 2. 300 MHz processor with 512 Mb RAM. Convergence at each run
required approximately 3 minutes for each iteration and 200 iterations for a
3D grid, and 1 minute for each iteration and 100 iterations for a 2D
axisymmetric grid. The implementation of the numerical simulation used for
this simulation is given in appendix C.
3.1.3. Eggers experiments
In order to validate the numerical model used in this study, the
solution method was first used to simulate the experimental data obtained by
Eggers for a free jet [16].
Eggers carried out experiments on a fully-expanded nozzle to
measure the supersonic air jet velocity as a function of distance from the
nonle exit. A schematic view of Eggers' experimental setup is shown in
Figure 3-2. The pressure of the free jet was measured by a pressure
transducer connected to the traversing device. This system allowed
continuous direct recording of total pressure as a function of distance from
the noule exit. As the pressure transducer was displaced along the
centerline, the corresponding velocity of the jet was measured and recurded
on-line by a data acquisition system. The velocity of the jet exhausting to
quiescent air at the noule exit was equal to 538 mis (Mach number M=
Control Valve Noule Pressure
Traversing Device
Gas Reservoirs
Acauisition Svstem
Figure 3-2: Eggers Experimental setup
3.1.4 Computed results and cornparison with experiments
A numericai solution by Fluent shows that the free jet flow
accelerates in the noule. At the exit of the nozzle, the Mach number of the
jet reaches approximately 2.2 as shown in Figure 3-3. In this figure. each
colour presents a specific range of Mach number, specified in the vertical bar
on the left side. The contours of the different velocities are plotted in the
computational domain by Fluent display mode. For example. red colour
displays Mach number of 2.2 around the noule exit. Smooth expanding
contours indicate that there is no shock wave dong the jet axis. It can also
be seen that the jet potential core length is about 12 noule diameters. The
initial mixing layer thickness of the jet is very thin; this mixing layer develops
very rapidly into a self-similar fiow at atmospheric pressure.
Figure 3-3. Contours of Mach nurnber for a free jet
27
To demonstrate that the numerical calculation can provide reliable jet
flow prediction, a comparison between the numerical result and experimental
rneasurements carried out by Eggers was performed. The data of the
axisymmetric jets with Mach number ranges from 2 to 3 were used for
comparison. The exit diameter of the noule is used as the characteristic
size. In Figure 3-4 the axial profiles of the jet centerline velocity (expressed
in a dimensionless form. U J Uc) versus distance from the nou le exit (also in
a dimensionless form. ND.) are compared with the calculations for 3D and
2D axisymmetric jets. Uc and Ue are the jet centerline velocity and nozzle exit
velocity, respectively. X and De are respectively the distance from the noule
exit and the noule diameter. As can be seen. there is good agreement in
both cases. but the 3D numerical prediction is closer to the experimental
data. For jet flow prediction and validation of the Fluent. the accuracy of the
calculated jet flow is sufficient.
A comparison between the k-E turbulence with standard coefficients
[Il] and RNG k-E was also carried out to examine how a RNG k-E turbulence
mode1 application in numerical results is different from those of the standard
k-s turbulence model. The results of the two numerical models are shown in
figure 3-5. As mentioned eariier in chapter 2. the RNG k-6 turbulent
equations have smaller coefficients in comparison with those of equations in
the standard k-E turbulence model. The dissipation rate of the turbulent rate
is larger. hence the calculated velocity of the jet is lower than the measured
one. As indicated in the literature, the RNG k-E turbulence mode1 is not
applicable for the jets when they are fully developed.
XIDe, Distance from the noule
XIDe, Distance from the nozzie
Figure 3-4: Centerline velocity of a free jet
- 30 Standard k-E * * * 30 RNG k-E
O 5 10 15 20 25 30 35 X I D e
Figure 3-5. Cornparison of two k z turbulence models with the data
from Eggers [16]
3.2 Jet Interaction with a Deposit
In this section. the numerical model was extended to simulate a jet
applied on deposits. The simulation results were compared to the laboratory
data obtained from a physical downscale model of a sootblower jet between
two parallel platens. This comparison was used to validate both the
numerical simulation carried by Fluent code and the physical simulation in
the laboratory.
The model domain consisted of two parallel superheater platens. a
deposit attached to a platen. and an air jet exiting a fully-expanded noule
and propagating along the passage between the two platens. Similar to the
free jet model, the computation domain was divided into rectangular grids.
as given in Figure 3-6. with a finer grid employed to simulate better the jet
fiow between the nou le exit and the deposit surface. For a correct
simulation of the jet flow near a platen and deposit. a 30 grid was required.
A k s turbulence model was applied with the corrected coefficient to solve
the governing equations.
The basic model assumptions were the same as those of the free jet.
A standard wall function was employed to approxirnate the boundary
condition for the platens and deposit surfaces. This wall function
approximated the turbulent boundary layer near the surfaces.
Jet Inlel 1
Figure 3-6: A computational domain of a jet on a deposit
A converged solution of the mode1 determined the velocity, pressure.
temperature. and area of the deposit on which the jet flow impinges. Once
the pressure of the jet around the deposit was found. the mean drag force
applied on the deposit was calculated by multiplying the pressure and the
impinged surface of the deposit:
Chapter 4 - Experimental Procedure
4.1 Scaled experimental setup
To obtain new experirnental data for model validation, a scaled
experiment was set up in the laboratory. The experimental setup shown in
Figure 4-1, wnsisted of a motor-driven linear slide assembly from Velmex
Inc. (171, a fully expanded noule, two parallel platens, and an artificial
deposit attached to a tube of the platen. The deposit on the platen could be
moved in order to change the distance of the deposit from the nozzle. The
slide assembly allowed changing the distance between the noule and the
deposit. Another manual slide was used ta move the noule in the direction
perpendicular to the platen plane. It allowed controlling the distance between
the jet axis and the surface of the platen. This distance is called the offset of
the jet to the deposit. When the centerline was on the surface of the platen
and on the tip of the deposit. the offset was zero and maximum. respectively.
A pressure transducer was used before the nozzle to measure the
air pressure. A torque sensor was conneded to the platen on which the
deposit was mounted to measure the torque exerted on the deposit by the
jet. A pressure regulator was used to adjust cylinder pressure to 900 psi at
which the noule produced a fully developed jet. When the valve was open,
high-pressure air passed through the hoses into the noule. The pressure
transducer measured air pressure immediately before the noule. When air
passed through the noule. it accelerated and produced a high velocity jet
that impacted the deposit attached to a pipe of the platen. This pipe was
connected to a torque sensor at one end while the other end was free to
rotate. When the jet impinged on the deposit. both the deposit and pipe
transferred the torque to the sensor. which produced a srnall voltage
corresponding to the jet force. Two compressed air cylinders were used to
keep the air pressure constant during the experiment.
Jet Torque
nsor
---' . Data Compressed . Acquisition
Air - ~ystem
Figure 4-1 : Scaled experimental setup
By recording the torque and the offset, the force of the jet exerted on
the deposit could be measured. 60th the pressures before the nonle and the
torque on the deposit were collected on-line during 3-second duration
experiments for different offsets and distances of the deposit from the noule.
During the experiment. the pressure of air before entering the nou le was
constant, 900 psi.
The laboratory noule was fully expanded with a 0.742-cm exit diameter
working at a 900 psi (6.12 Mpa) inlet pressure. Important dimensions of the
setup are as follows:
length of the platens 30 cm
distance between the platens 3.7 cm
outside diameter of the platen tube 1.27 cm
Al1 above-mentioned dimensions of the setup were downscaied four times
that of real superheater platens. The shape and thickness of the deposit
were rectangular and 1.6 cm. respectively. The tip of the deposit was made
semi-circular to avoid jet disturbance during the experiments.
4.2 Experimental Results
The distance of the noule from the entrance of the platen (M) and
the offset of the noule to the deposit (D) could be changed by the slide
assembly. The deposit attached to the platen could also move in the setup to
change the distance of the deposit from the non le (X) as shown in Figure 4-
Offset Dj 1
Jet --+ -rx~eposit height , H
Figure 4-2. Dimensions in the expenmental setup
The variations of the distances of the noule from the entrance of the platen
and the deposit chosen in experiments are given in Table 1. The force
exerted on the deposit was rneasured for each variation.
Table 1: Combinations of M, and X for each experirnent
M (Distance of the noule from the platen entrance)
1 M I 20 (cm)
I O (cm)
1 X (Noule-deposit distance) l
f 10 20 25 30 40 (cm) ,
l ! 30 (cm)
4
1
i
1 30 40 45 50 60 (cm) 1
C
I
20 30 35 40 50 (cm)
For each pair of M and X mentioned in Table 1, the tests were performed for
three offsets (Di) of 0. 0.8. and 1.6 cm. The pressure of the air before entering
the nou le and the torque exerted on the deposit were recorded by the data
acquisition system simultaneously. A sarnple of recorded data is shown in
Figure 4-3.
+Pressure M e a n torque
Y .I
O Seconds
Figure 4-3: Measured pressure and torque for M = I O , X = 20, and Dj = 0.8 cm
The recorded voltages of the torque sensor and pressure transducer could
be converted into torque and pressure by using the calibration tables given in
Appendix B. The measured torque is a fundion of the output voltage of the
torque sensor recorded by a data acquisition system given as:
Torque = f (output voltage of the torque sensor)
The force exerted on the deposit was equated to the measured torque
divided by the sum of the offset and the radius of the platen pipe,r as follows:
F = Torque/(Dj + r)
The measured force versus X is plotted in Figure 4-4 for different Dj. In this
figure, force was measured when M was constant at 10 cm. All measured
torque and corresponded force are given for M=10 cm in Tables
Appendix B.
60
0.8 cm offset 50 - O cm offset
4 rn A 1.6 cm offset 40 =
Z A + $30 - 0 U O A + LL A
20 - A 0 10 - A
Figure 4-4: Measured force, F for M = 10 cm
4.3 Numerical simulation of the jet on the deposit
In this part. dimensions of the experimental setup are used in a
computational domain for the numerical model. Then the boundary
conditions, which are identical to those in the experiments, are applied to the
domain in order to simulate the experiments. Each numerical test reproduces
the conditions, identical to an experiment when values of Mt X, and Di are the
same. A sample of this simulation is shown in figure 4-5 as contours of
veiocity and pressure when M = 30, X = 30. and Di = 0.8 cm. Each colour
represents a value for the velocity or pressure of the jet in the computational
domain. It shows that the jet has a high velocity, 1000 mls, and a high PIP,
90 psi (630 KPa). at the exit of the nozzle. However, the jet decays rapidly
when it mixes with the ambient air.
Velocity Contours, mis
Pressure Contours, psi
0m.m / FLUENT 6 1 (32. m. coupM W. hl
- - --
Figure 4-5: Contours of a simulated jet on the 1.6cm deposit
From the pressure contours around the deposit. the mean drag force was
calculated by multiplying the pressure and the surfaces of the deposit given
as:
Where Pi is pressure and A, is a face of surface of the deposit.
The mean drag force has been computed and plotted in Figure 4-6 in
order to be ccrnpared with the measured force given in Figure 4-4. The solid
lines are the results of the numerical computation, while the markers show
the experimental data. same as those in Figure 4-4. As shown in Figure 4-6.
the numerical rnodel reproduced the experirnental data based on a standard
k-c turbulence model and the correction coefficients found for this study as:
- Predicted by the rnodel a I
Measured
Figure 4-6: Cornputed and measured mean drag force
Similarly for other values of M. the mean drag force was computed by the
same correction coefficients of the standard k-E turbulence model, and
compared with the measured drag force. The cornparisons are shown in
Figure 4-7.
- Model
- Model 2
30 4
E h
U,
20 4
Offset:
10 a
Figure 4-7: Cornparison of the computed force with the measured force
for M= 20 and M=30
Chapter 5 - Results and Discussion 5.1 Corn parison of simulation results with
experimental data
Cornparison of the simulation results with the experimental data shows
good agreement in Figures 4-6 and 4-7. Three sets of the data in these
figures are given for different offsets, Dj. Maximum force was observed when
the jet was directed at the mid-point (Di = H12) of the deposit. For example. in
Figure 4-6 F is maximum for the curve of D, = 0.8 cm (half of the deposit
height). If the offset is large or small, the mean drag force, F. exerted on the
deposit decreases. When the offset is large, the major part of the Row passes
above the deposit. When the offset is small, the jet is disturbed and partially
diverted by the platen. The curve for Dj = O cm indicates a higher force than
the curve by D, = 1.6 cm (height of the deposit). In al1 cases. the drag force
decreases with X. the distance of the deposit from the noule. It is consistent
with the contours of pressure in Figure 4-5 which shows that the pressure
decreases with X. However, F depends not only on pressure but also on the
size of the deposit. Figure 4-7 also shows good agreement between the
computed and measured mean drag force, F, for M = 20, and 30 cm. These
comparisons validate the numerical mode1 developed for the scaled
sootblower jets defined for a range of dimensionless parameters such as Re
and Mach numbers, same as those of full-scale sootblower jets in a kraft
recovery boiier. Hence, the numerical mode1 can be appiied to sootblowers
operating in recovery boiler conditions. On the other hand, when
experimental data agreed with the numerical results, one may conclude that
scaled air jet experiments are a good approximation to full-scale sootblower
jets in the boiler conditions.
5.2 Simulation of a full-scale sootblower
By using the numerical rnodel of the jet fiow in the superheater platens, a
parametric study is performed to compute the sootblower jet force, F. applied
on a deposit as a function of different parameters such as deposit height (H).
lance steam pressure. and temperature. Table 2 shows the values of the
basic parameters used in the study.
Table 2: Basic parameters of a sootblower
Noule type l Fully expanded I 1
L
Nozzle exit diameter i 29 mm (1, 118") 1 i Lance steam pressure , 1.75 - 2.8 MPa (250 - 450 psi) 1 I
Lance stearn temperature ; 325 - 425 O C 1
1
Flue gases temperature i 600 - 900 O C i
.. Platen tube diameter 1 t 50.8 mm (2 )
l 1 ,. 1 Distance between platens 150 -250 mm(26 - 10 ) 1 l 1 P.
Platen length 1200 mm (24 tubes) _ - ------- - - _ _ - - - - -- -_ . l Platen temperature 400 - 700 O C
ln this study. the nozzle exit diameter was kept constant. 29 mm, while the
lance steam pressure and temperature were changed to examine the steam
jet force exerted on the deposits of different heights, 2.4 to 6.4 cm. The
following assumptions were made during this study:
s team is an ideal gas;
the jet impinged on the middle of the deposit. Di = H12;
adeposit temperature is the same as platen temperature; and
l the surfaces are moderately smooth.
5. 2.1 Effect of lance steam pressure
First. the effect of the lance steam pressure on the mean drag force.
F applied on a deposit of 6.4-cm height was estimated by the numerical
method. For this purpose the F was calculated for the various lance
pressures in the range from 250 psi (1.75 MPa) to 450 psi (2.8 MPa). The
results indicate that the F increases proportionally to lance pressure
increase. as shown in Figure 5-1. In other words, F is a linear function of the
lance pressure. Figure 5-1 shows that the dope of the lines is greatest for
deposits near the noule. and is moderately decreased at larger distances. It
indicates that increasing the lance pressure is effective on the deposit near to
the sootblower. but not for the deposits located far frorn the noules.
1 1.5 2 2.5 3 3.5
Lance pressure, MPa
Figure 5-1: Computed mean drag force exerted on a deposit
5.2.2 Effect of deposit height (H)
Deposition of particles on the superheater platens depends on the
properties of particies such as stickiness, velocity, temperature, etc.. which
are beyond the scope of this research. However, the deposit height (H) is a
key parameter affecting F: the larger the H, the greater the F.
When the deposition of particles occurs. the height or thickness of the
deposit on the platens increases in time. Each time a sootblower jet irnpinges
on a deposit, the height of the deposit may be different. Generally. when a
deposit is thicker. the affected area of the deposit is larger, so the force, F.
applied by the sootblower jet, is greater.
O 40 80 120 160
?Cl cm
Figure 5-2: Computed F for different heights of a deposit (H)
The computed results for different deposit heights are given in Figure 5-2. In
this figure the force, F, for four different heights is plotted versus the distance
of the deposit from the nozzle, X. Each curve presents a deposit height. H.
and indicates that the F decreases with X. It also shows a change in the
slope of the curves at X = 70 - 80 cm. This happens because at this distance
the diameter of the spreading jet is approximately equal to the spacing
between the platens. When X is less than 70 cm, the jet behaves as a free
jet, and after that it is confined by the platen. In other words, the mean drag
force, F, is decreasing moderately after X= 70 cm because the platens
protect the jet from further spreading and mixing with surrounding media.
If the diameter of the jet is smaller than the deposit height, an
increase in deposit size does not affect the F, because the affected deposit
area does not increase with further growth of the deposit height. Therefore.
at a small X. where the jet diameter is small, the effect of the deposit height
is less pronounced: at X=40 cm the difference in the F for 2.4 cm and 8.4 cm
heights is only 60%.
O X, cm 160
Figure 5-3: Computed F for different platen spacing
The computed results for platens spaced 25 cm apart shows that the
break point of the mean drag force curve, where the curve slope is changed,
shifts to 96 cm, as shown in Figure 5-3. This is consistent with the idea that
the break point occurs where the jet diameter grows to fiIl the inter-platen
gap. For the wider spacing this break point occurs at a greater distance.
5.2.3 Effect of flue gas and platen temperature
In the recovery boiler. the sootblower jet is surrounded by the high
temperature flue gas. To investigate how the temperature of the flue gas and
platen temperature may affect the sootblower jet, the temperatures were
changed from 600 to 900 O C and 400 to 700 OC respectively. Figure 5-4
shows the computed results for the mean drag force, F for 700 to 900 O C flue
gas temperature. Only a small change (3 to 5%) of the F was observed. This
is due to a small change of the flue gas density in the range of 700 to 900 O C .
Platen temperature has a negligible effect on the mean drag force, F (less
than 1 Oh).
\. - Corn puted drag force at 700 C \ - - Cornputed drag force at 9W C
Figure 5-4: Computed F for different flue gas temperature
5.2.4 Effect of lance steam temperature
Sootblowers work with superheated steam at a high temperature to
avoid condensation during the expansion process inside the sootblower
noule. However, the temperature of the superheated steam may affect
performance of the sootblower jet applied on a deposit. In a recovery boiler,
to avoid any possible condensation during sootblowing, the lance steam
temperature is kept between 325 to 425OC.
In the model, it was assumed the superheated steam is an ideal gas. so
steam cannot be condensed under any circumstance. The rnodel results for
the mean drag force are shown in Figure 5-5 for two lance steam
temperatures. The effect of steam temperature ranging 325 to 42% is less
than 5% as given in Figure 5-5. This effect may be attributed to the steam
density variations. which do not exceed 10% for the temperature range, if the
lance steam expansion process is isotropie. Moreover, the surrounding Rue
gas mixes with the jet so rapidly that the changing of lance steam
temperature has a small effect on the jet force. However. steam density
changes more significantly if steam condensation is taken into account.
Figure 5-5: Computed mean drag force for different lance temperatures
5.2.5 Effect of platen spacing
So far the effects of the boundary conditions and deposit thickness on
the sootblower jet have been discussed. However. the effect of platen
geometry, in particular platen spacing, has not been considered as an
important parameter in sootblower design. In this section, the effect of platen
spacing which confines the sootblower jet will be discussed.
The sootblower jet propagating in a passage between two parallel
platens is confined by the platens. In theory, a confined jet decays slower
when compared with a free jet. That is because a free jet can mix freely with
surrounding ambient. and the jet decays as far as it mixes. In contrast. the
mixing of the confined jet is limited to the platen spacing.
The cornparison of the computed peak impact pressure (PIP) of a
free jet which is equivalent to the dynamic pressure with that of the confined
jet between two platens is shown in Figure 5-6. The PIP of a confined jet is
calculated for two different spacing between platens, 15 and 25 cm. It shows
that when the two platens are closer. the PIP is bigger, and the drag force
exerted on a deposit is larger.
As Figure 5-6 also shows. this effect is more important at a larger distance,
X, from the non le exit where the free jet PIP is about two times less than
that of a jet propagating between two platens with 15 cm spacing, because of
intense mixing with the ambient gas.
P I P of a jet betwsen two platans. d = 15 cm
- -PIP of a free jet 8 PlP of a jet between two pbtens. d = 25 cm
O 50 100 150 200
X, cm
Figure 5-6: Cornparison of the PIP of a free jet with the PIP of a confined jet
5.3 Implications for deposit removal process
5.3.1 Effect of mean drag force on deposit removal
When a jet strikes on a deposit, the jet PIP is the most important
parameter in the deposit removal process: the bigger the PIP, the better the
deposit rernoval. Although the computed results show that the PIP reduces
drastically with X. the diameter of the jet increases as shown in Figure 5-7.
So the mean drag force, which is defined by multiplying the PIP and the
impinged surface of the deposit, decreases less than the PIP as shown in
Figure 5-8. This suggests that the sootblower-cleaning radius could actually
be greater than that estimated on the basis of the PI? of a free jet.
Figure 5-7: PIP and diameter of a sootblower jet
Figure 5-8: Computed PIP and mean drag forceof a sootblower jet
applied on a deposit
5.3.2 Effect of the Sjat on a deposit removal process
In the last section. it was shown that the mean drag force. F exerted on
a deposit by a jet is a key parameter governing the efficiency of the jet in
deposit removal. When the jet irnpinges on a deposit. the F causes a
shearing stress on the deposit-tube interface which may remove the deposit.
If the deposit-tube interface is A, then the stress on A caused by the jet. S ,el
expressed by:
On the other hand, the adhesion strength Sadh of the deposit attached
to a tube can be defined as the minimum stress needed to remove the
deposit applied by a sootblower. If the deposit adhesion strength is greater
than the stress caused by the jet (S jet) the deposit will continue to grow. In
this case. the thickness of the deposit increases till the stress. S ,et exceeds
the adhesion strength. For instance. consider a deposit attached to a single
tube. with a diameter D = 5 cm. Although the deposit rnay cover the tube
over al1 its length. a jet applied on the deposit at a certain point. and the
stress. S ,=t, will be concentrated around the point of jet contact as shown in
Figure 5-9. In this case. the loaded tubedeposit interface is approximately:
Figure 5-9. Loaded tube-deposit interface
As shown in Figure 5-2 mean drag force. F depends on the deposit thickness
and the distance between nozzle and deposit. X. For instance. F at X=120
cm for a deposit of 2.4 cm thickness is about 300 N. From equation 5-1 the
stress can be estimated as:
S j e t = FI D~
= 0.12 MPa
If the deposit cannot be removed by this stress (Sjet < Sadh), Ït fernains and
grows to a greater thickness. When the thickness of the deposit increases, a
greater drag force is exerted on the deposit. In Figure 5-2, if thickness of the
deposit increases from 2.4 cm to 6.4 cm, F increases from 300 N to 475 N.
Hence the S applied on the loaded tube-deposit interface increases from
0.12 MPa to 0.19 MPa This larger Sjet rnay overcome the adhesion strength.
Sadh However. some deposits with high adhesion strength may not be
removed and may continue to grow until they plug the passage between the
platens.
The deposit adhesion strength. Saah depends generally on deposit
composition and temperature. For a given deposit composition, it is possible
to measure the Saah as a function of deposit temperature. A typical diagram
of the measured Saan versus the deposit temperature for deposit is given in
Figure 5-1 0 [18]. Simiiarly. it is possible to show the computed S,,, versus X
in Figure 5-10 where the S,et and Saan values (both in MPa) are given in the y-
axis. but the deposit temperature value (in O C ) and X value (in cm) are given
in different x-axis.
As shown in Figure 5-10, at 425 O C the measured Sadh is greater than
the computed Sja exerted on a 2.4-cm thickness deposit located at X=120
cm. If the deposit grows to 6.4-cm thickness, the Siet can increase and rnay
remove the deposit. The difference between the Sjet and Sadh values could
provide a simple verification of the sootblower jet efficiency in a deposit
rernoval process when the jet irnpinged on a deposit.
Model
Thickness: 6.4 cm 4
400 450
Deposit temperature,OC
Figure 5-10: Measured Sadt,( r[l8])and computed S j e t b )
Chapter 6 - Conclusions A computational fluid dynamics code, Fluent 5, was used to predict the
fiow characteristics of a sootblower jet propagating between superheater
platens in a recovery boiler. The cornputed jet force exerted on a deposit, F,
compared well with the measured force in a scaled experimental setup. This
comparison indicates that the laboratory scaled air jet is a reliable
approximation, and the numerical simulation is valid and applicable for a full-
sale sootblower je: between superheater platens.
A full-scale boiler numerical simulation was conducted to examine how
the drag force, F. generated by a sootblower was affected by the basic
operational parameters including the distance between the noule and
deposit. noule offset. deposit çize, surrounding temperature, sootblower
lance steam pressure. and temperature.
This study shows that mean drag force, FI is proportional to deposit
size. It also indicates that F is proportional to lance steam pressure. but the
effects of flue gas, platen, and steam temperatures are much smaller.
The numerical calculations demonstrated that the peak impact
pressure, PIPI of a sootblower jet propagating between platens is higher than
that of a free jet. A full-scaie numerical simulation also showed that the jet
PIP decreases rapidly with the distance between the noule and a deposit. X,
M i l e the jet force, FI decreases at a moderate rate. It indicates that a jet
penetration and its effed on deposits at larger distances may be greater than
those estimated by a PI? oniy.
The numerical simulation allows a calculation of the jet stress applied
on the deposiUtube contact area, generated by the jet impact. The
cornparison of predicted stress with the adhesion strength of a deposit, if
available, can verify whether a deposit could be removed by a sootblower jet.
The numerical simulation is entirely dependent on Fluent code in
which the detailed solution procedure and associated error of approximation
is not given. Any effort to create a custom-made code demands a long-term
investment and a challenging task.
The last. but not the least, requirernent for a numerical modeling
procedure is reliable cornputer hardware with a high memory capacity and
fast processor for a long computational the.
References
H. Tran, "Kraft Recovery Boiler Plugging and Prevention", TAPPl Kraft Recovery Operation Short Course, TAPPl Press, 1992, pp.247-282
H. Tran, D. Barham. and D.W. Reeve, "Sinter~ng of Fireside Deposits and Its Impact on Plugging in Kraft Recovery Boilers", TAPPl Journal, Volume 70, NO. 5, 1988. pp. 109-1 1 1
M.I. Jameel, D.E. Cormack. H. Tran, and T.E. Moskal, "Sootblower optimization" Part 1 : Fundamental hydrodynamiw of a sootblower nozzle and jet, TAPPI Journal. Volume 77. No. 5, 1993, pp.135-142
B.E. Launder and D.B. Spalding, "The Numerical Computation of Turbulent Fiowsn, Computer Methods in Applied Mechanics and Engineering, Vol. 3, 1974, pp. 269-289
D. Papamoschou, and A. Roshko. "The Compressible Shear Layer: an Experimental Study,' Journal of Fluid Mechanics, V. 197. 1988, pp. 453-477
A.T. Thies, and C. K.W. Tam. "Computation of Turbulent Axisymmetric and Nonaxisymmetric Jet Flows Using the k-E Model", AlAA Journal. Volume 34, No. 2, Febuary 1996, pp.309-3'i6
S. Sarkar, G. Erlebacher. M.Y. Hussaini, and H.O. Kreiss, "The Analysis and Modeling of Dilatational Terms in Compressible Turbulence", Inst. For Computer Applications in Science and Engineering, NASA Langly Research Center, ICASE Rept. 89-79, Hampton, VA, 1989
A. Favre, " Equations des Gaz Turbulents Compressibles," Journal de Mecanique, Vol. 4, No. 3, 1965, pp. 361 -390
S. Sarkar and L. Balakrishnan, "Application of a Reynolds-Stress Turbulence Model to the Compressible Shear Layef, ICASE Report 90-18. NASA CR 182002,1990
10. J.O. Hinze, "Turbulence". McGraw-Hill Publishing Co.. New York. 1975
1 1.6.E. Launder and 0. B. Spalding, "Lectures in Mathematical Models of Turbulencen, Acadamic Press, London, England, 1972
12.V. Yakhot. and S.A. Orszag, " Renonalization Group Analysis of Turbulence: 1. Basic Theofy", Journal of Scientîfic Cornputing, 7 ( A ):A-54 , 1986
13. M. Nallasamy, "Turbulence Models and their applications to the prediction of interna1 fiows: A review", Computer & Fluids, 1 5(2), 1987, p. 151 -1 94
14. Fluent Inc. "User's Guide for FLUENT", Release 5.0, Volume 3, June 1998, pp. 13-1 1 - 13-21
15. S. V. Patankar, "Numerical Heat Transfer and Fluid Flow", Hemisphere, Washington CD, 1980
16. J.M. Eggers, 'Velocity Profiles and Eddy Viscosity Distributions Downstream of a Mach 2.22 Noule Exhausting to Quiescent Air", NASA TV-3601, Sept. 1 966
17. Velmex, Inc., "UniSIide Motor Driven Positioning System", Catalog M-99, pp.32
18. A. Kaliazine, D. Cormack. A. Ebrahimi-Sabet, and H. Tran, "The Mechanics of Deposit Removal in Kraft Recovery Boilers", Journal of Pulp and Paper Science, Vol. 25, No. 12. 1999, pp. 41 8-424
19. C. J. Chen, and S. Y. Jaw, "Fundemamental of Turbulence Modelingr', Taylor & Francis, 1998
20. H. Tennekes, and J. L. Lumley, "A First Course in Turbulencen, The MIT Press, 1972
Appendices
Appendix A - Turbulence Modeling It is important to understand that the turbulent jet flow is always three-
dimensional, unsteady, rotational, and. most importantly, irregular. The
irregularity of jet motion is due to the inherent nonlinear nature of the Navier-
Stokes equations where the Reynolds number is beyond the critical value. In
order to predict the average behavior of jet flow, a numerical turbulence
model must be established. Figure A-1 shows a flowchart of the art in the
turbulence model ing . Excellent reviews and descriptions of turbulence
modeling are given by Chen and Jaw [Ag]. This section presents the
numerical turbulence models that rnay be applicable to a sootblower jet.
A.l Direct numerical simulation (DNS)
A complete description of a turbulent Row can be obtained by solving
the time dependent Navier-Stokes equations and continuity equation. For the
compressible fiow of a Newtonian fluid, these are given by, and written in
conservative form, as
1 Turbulence Modeling
/ Navier-Stokes Equations I Direct numerical simulation
( D W l I Large eddy simulation 1 (LES) Favre averaged Navier-Stokes equations
(FANS)
/ k - ~ turbulence rnodel l
[-1 [] [J Realizable k - ~
Figure A-1: Flowchart of the turbulence modeling
These equations. which model the flow as a continuum, are valid for
turbulent flow because the smallest length scales in turbulence contain
enough molecules to al1 statistically significant point averages of velocity,
density, etc., which cari Vary continuously in space (201. Of course, to resolve
ail motion, from the largest eddies dictated by the flow enclosure to the
smallest scales dictated by the viscosity, a computational grid of exceedingly
large size would have to be constructed. However, it was proved [20) that the
number of grid cells is proportional to the turbulent Reynolds number to the
9/4* exponent, which is higher than the rnemory capacity of an available
cornputer. For example, the turbulent Row of a sootblower jet, the relevant
Reynolds number is 100,000 based on the diameter of the nonle exit. Using
the 9/4" rule, this would require 3.16 x lot3 computational cells for a
complete description of this ffow. Clearly, DNS is not applicable to flow with
high Reynolds numbers
A-2 Large eddy simulation (LES)
Large eddy simulation represents a compromise between direct
solution and modeling. In this approach. the unsteady Navîer-Stokes
equations are filtered to produce a set of equations that govem the large-
scale motion, and the small scales are modeled. The justification for using
LES is that the large scales tend to be more anistropic and dependent on
the initial and boundary conditions, whereas the small scales tend to be
more isotopic and. hence, universal. The large scales also transport most of
the energy, so they represent the more relevant scales in a turbulent flow.
LES, then, is involved directly for large scales and modeling the small
scales.
A filtered variable is given as,
where D is the computational domain and G is the filter function [21].
According to the definition, the srnallest scale that is resolved directly is equal
to the size of the cell in the grid. All other scales srnaller that the size of the
cell must be rnodeled.
The Navier-stokes equations in LES give
-- where 'ij = ~mu~ - 'Jiuj) is the S U ~ - ~ c a l e stress. which must be modeled. The usual model used is an eddy viscosity model defined as
where p, is the sub-scale turbulent viscosity and
- i aü, au, sij
is the rate of strain tensor.
This model is analogous to the prandtl mixing length model used for
the Reynolds stresses in chapter 2. It is mainly recommended for modeling
the Row with a low Reynolds number enwuntered in the near wall region to
detemine the large-scale turbulent motion. Although LES is less
computational intensive than DNS, it still requires a fairly large grid and is
very time-consuming. Moreover, it produces much more information than is
required for engineering purposes. An alternative, and in fact a much more
widely used approach in engineering, is to use the k-E turbulence model [19].
This rnodel is used to solve the Favre averaged Navier-Stokes equations
(FANS) which were defined in chapter 2.
A-3 k-E turbulence model
ln this model. al1 scales of turbulent motion are modeled. The
unsteadinesç of the flow is removed. or filtered, leaving an equation for the
Reynolds averaged flow variables. A steady state solution can be obtained
despite the unsteadiness of the Row. Also. a much larger cell can be used
since the average flow variables Vary much more gradually in space than
the instantaneous variables.
As mentioned in chapter 2. when Navier-Stokes equations are
averaged over time (t,) and over a density (p), the resulting form of the
FANS equations is the same as given in equations 2-5, 2-6. and 2-7.
II The Favre averaged Reynolds stress tensor (-pu,u,) appears in equation 2-
7 as a result of the non-linearity of the Navier-Stokes equations, and since
it is unknown. the equations cannot be solved. The K-E turbulence model
was used for the Reynolds stress tensor in order to close the equations.
In the k-E turbulence model, Reynolds stress tensors are rnodeled. as in
equation 2-7, where non-linear fluctuation components are replaced by the
mean components.
Note that the solution of FANS equations by using the k-E turbulence model
yield only the mean quantities, and give no detail about the turbulent . ,
components, i.e. u. v , w', etc. To recover this information. transport
equations must be used for k and E. It requires sub models inside the k-E
turbulence model, which were defined as standard k-E, RNG k-E and
realizable modes. All these models define two "modeled" transport
equations for k and E by which fluctuation components could be calculated.
Standard k-E and RNG k-E modes have been discussed in chapter 2, and a
realizable k e model was not considered in this study.
Appendix B- Numerical lmplementation
B-1 Grid generation
The jet flow in the 3 dimensional (30) computational domain shown
in Figure B-1 was created by a graphical amputer code, Gambit introduced
by Fluent V5. This geometry is simplified by fiatting the surfaces of the
parallel platens and neglecting the circular tip of the platen which is farther
to the jet. The dimensions of the geometry were set to be exactly equal to
the dimensions of the experimental setup described in chapter 3. However.
the depth of the geometry in the Figure B-1 is shortened to 40 cm which is
large enough to capture al1 mixing layers of the jet flow. Also the width of the
geometry is shortened to 25 cm which is much larger than the spacing
between the platens (3.7 cm) to take into account the effect of the jet flow
passing over the platen.
A grid was generated by dividing the computational domain into
small hexahedral control volumes (cells). Grid density was made slightly
greater near the jet inlet boundary and deposit surfaces impinged by the jet.
However. care was taken not to create large aspect ratios (skews) in the
cells far downstream of the grid. For instance. near the jet inlet boundary the
growth factor of 1.25 was assumed for the grid lines parallel to the jet inlet. It
means that the grid lines parallel to the ydirection were compressed toward
the jet inlet. lt was also assumed a growth factor of 1.2 for the grid lines
parallel to the centerline of the jet. It means that the parallel grid iines in x-
direction were compressed toward the jet centerline. In general, 30 grids
used in this study have 100 grid points in the x-direction. 20 in the y-
direction, and 10 in the z-direction for 20.000 cells. A sample grid was given
in Figure 8-2.
Figure 6-?. Computational domain of the laboratory setup
Figure 8-2. Cornputational grid for the laboratory setup
8-2 Boundary conditions
The boundary conditions applied to the computational dornain in
Figure B-1 are constant pressure inlet for al1 flow inlets and constant
temperature wall for all surfaces. Pressure inlet boundary conditions were
used to define the fluid pressure at flow inlets. Pressure inlet boundary
conditions were used because the inlet pressure was known but the flow
rate was not known. Pressure inlet boundary conditions were also used to
define a free boundary in ail extemal flow. In Fluent, the following
information must be entered for a pressure inlet boundary:
- total(stagnati0n) pressure, Po
- total (stagnation) temperature
- flow direction - static pressure at the exit of the boundary, Ps
Total pressure for a compressible fluid defined as
where M = Mach number and 7 = ratio of specific heats (c&).
The jet inlet was considered a fully expanded noule in which upstream total
pressure and total temperature were constant (Le. 900 psi and 20 O C )
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