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

National Libraiy of Canada

Bibliothèque nationale du Canada

Acquisitions and Acquisitions et Bibliogaphic Services services bibliographiques

395 Wellington Street 395, rue Wellington Ottawa ON K I A ON4 ûüawa ON K1A ON4 Canada Canada

The author has granted a non- exclusive licence allowing the National Library of Canada to reproduce, loan, distribute or sell copies of this thesis in microform, paper or electronic formats.

L'auteur a accordé une licence non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/film, de reproduction sur papier ou sur format électronique.

The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation.

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 )