a computational analysis of the effects of the input … · 2018-08-24 · university of maribor...

UNIVERSITY OF MARIBOR

FACULTY OF MECHANICAL ENGINEERING

Master Thesis

A COMPUTATIONAL ANALYSIS OF THE EFFECTS OF THE INPUT PROCESS PARAMETERS ON THE

FINAL PRODUCT PROPERTIES IN THE SPRAY DRYER FOR TANNIN PARTICLES

July, 2009 Bojan KRAJNC

Master Thesis

A COMPUTATIONAL ANALYSIS OF THE EFFECTS OF THE INPUT PROCESS PARAMETERS ON THE

FINAL PRODUCT PROPERTIES IN THE SPRAY DRYER FOR TANNIN PARTICLES

July, 2009 Author: Bojan KRAJNC, B. Sc.

Mentor: Prof. Dr. Matjaž HRIBERŠEK

Co-Mentor: Prof. Dr. Leopold ŠKERGET

Vložen original sklepa o potrjeni

temi podiplomskega dela

Vložen original sklepa o imenovanju komisije za oceno

podiplomskega dela

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I Z J A V A

Podpisani Bojan KRAJNC izjavljam, da:

• je bilo predloženo magistrsko delo opravljeno samostojno pod mentorstvom red. prof.

dr. Matjaž HRIBERŠKA in somentorstvom red. prof. dr. Leopolda ŠKERGETA;

• predloženo magistrsko delo v celoti ali v delih ni bilo predloženo za pridobitev

kakršnekoli izobrazbe na drugi fakulteti ali univerzi;

• soglašam z javno dostopnostjo dela v Knjižnici tehniških fakultet Univerze v Mariboru.

Maribor, 1. julij 2009 Podpis:

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ZAHVALA

Zahvaljujem se mentorju red. prof. dr. Matjažu

HRIBERŠKU in somentorju red. prof. dr. Leopold

ŠKERGETU za pomoč in vodenje pri magistrskem

študiju. Zahvaljujem se tudi spoštovanim kolegom in

prijateljem dr. Mateju Zadravcu, dr. Zoranu Žuniču in

dr. Sanibu Bašiču za številne koristne nasvete pri

pripravi magistrskega dela.

Posebna zahvala velja mojim najdražjim za ljubezen,

razumevanje in vzpodbudo.

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A COMPUTATIONAL ANALYSIS OF THE EFFECTS OF THE INPUT PROCESS PARAMETERS ON THE FINAL PRODUCT PROPERTIES IN THE SPRAY DRYER FOR TANNIN PARTICLES

Key words: computational fluid dynamics, finite volume method, multiphase flow, Euler-

Lagrange approach, spray drying, rotary disk atomizer, tannin, maltodextrin

UDK: 532.511:532.525:66.047

ABSTRACT

The design of spray dryers is typically optimized for the unique operating conditions. How-

ever, users sometimes need to use the same spray dryer chamber with some modifications due

to the requirements of different products and/or production rates. Additionally, modification

of operating conditions is very often used in order to improve thermal efficiency of the overall

spray drying process.

In this work results of a computational fluid dynamic (CFD) analysis of the effects of in-

put process parameters on final product properties in the spray dryer for tannin particles are

presented. Commercial CFD code ANSYS CFX 11.0 SP1 and spray dryer model template

supplied with have been used. Model template has been modified and utilized (a) for simple

hexahedral spray dryer of tannin water mixture in order to initially analyze the behaviour of

the model, and (b) for reference lab-scale spray dryer of both maltodextrin water mixture in

order to validate the model by comparison to Huang et al. (2006) and tannin water mixture in

order to analyze the effect of decreased inlet temperature of drying air.

Results of steady state simple spray dryer simulations are presented. Particle trajecto-

ries are presented that reveal intensive droplet evaporation for high inlet temperature of

drying air and only poor volatilization accompanied with droplet cooling for inlet tempera-

ture being too low. Transient reference spray dryer simulations have been performed for two

different mesh sizes and particle rates for maltodextrin mixture. Presented time averaged

profiles at different levels in the drying chamber reveal reasonable matching of velocity

profiles. Additional transient tannin mixture simulations for two different inlet temperatures

reveal reasonable matching of temperature and humidity profiles too, yet for different initiali-

zation and longer physical run time. Thus, a numerical model capable to handle full-scale

industrial spray drying process has been built up, which has to be improved further, however.

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RAČUNALNIŠKA ANALIZA VPLIVA VSTOPNIH PROCESNIH PARAMETROV NA LASTNOSTI KONČNEGA PRODUKTA V RAZPRŠILNEM SUŠILNIKU TANINSKIH DELCEV

Ključne besede: računalniška dinamika tekočin, metoda končnih volumnov, večfazni tok,

večsestavinski tok, Euler-Lagrange pristop, razpršilno sušenje, razpršilno

kolo, tanin, maltodextrin

UDK: 532.511:532.525:66.047

POVZETEK

Konstrukcija razpršilnega sušilnika je prilagojena značilnim obratovalnim pogojem, včasih

pa je treba zaradi zahtev po drugi vrsti produkta in/ali spremenjeni proizvodni kapaciteti

uporabiti isti razpršilni sušilnik in ga modificirati. Pogosto pa je treba spremeniti obratovalne

pogoje zaradi izboljšanja energetske učinkovitosti celotnega postopka razpršilnega sušenja.

V tem delu so predstavljeni rezultati analize vpliva vstopnih procesnih parametrov na

lastnosti končnega produkta v razpršilnem sušilniku taninskih delcev z uporabo programske-

ga paketa za računalniško dinamiko tekočin (RDT). Uporabljen je bil paket ANSYS CFX 11.0

SP1 in predloga tega programa namenjena modeliranju razpršilnega sušenja. Predloga je

bila najprej prilagojena in uporabljena za (a) enostavni kvadratast razpršilni sušilnik vodne

zmesi tanina z namenom preučitve vedenja modela, nato pa še za (b) referenčni primer labo-

ratorijskega razpršilnega sušilnika za vodno zmes maltodextrina z namenom validacije

modela s primerjavo s Huang et al (2006) in za vodno zmes tanina z namenom analizirati

vpliv znižane vstopne temperature sušilnega zraka.

Predstavljeni so rezultati časovno neodvisnih simulacij enostavnega razpršilnega

sušilnika. Predstavljene trajektorije reprezentativnih delcev razkrivajo intenzivno uparjanje

pri višji vstopni temperaturi sušilnega zraka ter ohlajanje in zgolj izhlapevanje za prenizko

vstopno temperaturo. Časovno odvisne simulacije referenčnega razpršilnega sušilnika so bile

izvedene za dve gostoti računske mreže in dva vrednosti števila reprezentativnih delcev zmesi

maltodextrina. Predstavljeni časovno povprečni profili na različnih višinah v sušilniku se v

primeru hitrosti dobro ujemajo. Dodatne časovno odvisne simulacije za zmes tanina pa

pokažejo dobro ujemanje tudi za profile temperatur in vlažnosti, vendarle za spremenjene

začetne pogoje in daljši fizikalni čas računanja. Tako je bil zgrajen numerični model za obrav-

navo industrijskih razpršilnih sušilnikov, ki pa ga je treba še izboljšati.

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CONTENTS

1 INTRODUCTION ................................................................................1

1.1 PROBLEM DESCRIPTION...............................................................................................1

1.2 PREVIOUS WORK .........................................................................................................1

1.3 OBJECTIVE...................................................................................................................3

1.4 ASSUMPTIONS..............................................................................................................4

1.5 OUTLINE......................................................................................................................4

2 BASIC PHYSICAL PRINCIPLES OF SPRAY DRYING ....................6

2.1 INTRODUCTION ............................................................................................................6

2.2 SPRAY DRYING FUNDAMENTALS...............................................................................12

2.3 ATOMIZATION ...........................................................................................................32

2.4 SPRAY-AIR CONTACT (MIXING AND FLOW)..............................................................35

2.5 DRYING OF DROPLETS/SPRAYS .................................................................................42

3 PHYSICAL-MATHEMATICAL MODELING OF SPRAY DRYING...53

3.1 INTRODUCTION ..........................................................................................................53

3.2 MODELLING OF EULERIAN PHASE .............................................................................54

3.3 MODELLING OF PARTICLE TRANSPORT......................................................................74

4 DISCRETIZATION AND SOLUTION THEORY ...............................82

4.1 NUMERICAL DISCRETIZATION ...................................................................................82

4.2 SOLUTION STRATEGY - THE COUPLED SOLVER.........................................................85

5 NUMERICAL MODELS....................................................................88

5.1 SIMPLE CASE .............................................................................................................88

5.2 REFERENCE CASE ......................................................................................................89

6 RESULTS AND DISCUSSION.........................................................91

6.1 SIMPLE CASE .............................................................................................................91

6.2 1ST REFERENCE CASE ...................................................................................................97

6.3 2ND REFERENCE CASE ..............................................................................................103

6.4 3RD REFERENCE CASE ..............................................................................................105

University of Maribor – Faculty of Mechanical Engineering Master Thesis

IX

7 CONCLUSIONS AND PERSPECTIVE ..........................................107

REFERENCES .....................................................................................108

APPENDIX A.............................................................................................I

APPENDIX B.............................................................................................I

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NOMENCLATURE

Latin Letters

A … area

bw … wall thickness of particle

C … concentration

CA … area coefficient

Cd … vapour concentration at the vapour interface

CD … discharge coefficient (atomization) or drag coefficient (droplet air flow)

CDS … heat capacity of dry solids

CP … specific heat at constant pressure

CS … humid heat

CV … velocity coefficient in equation (6.24)

Cw … heat capacity of moisture

m … meter

d … disc, wheel, cup or bowl diameter of rotary atomizer, also linear distance

dd … liquid distributor diameter

dm … mean diameter

dn … nozzle orifice diameter

do … jet diameter or effective diameter of nozzle orifice

D … droplet diameter

Dch … drying chamber diameter

Df … most frequent droplet diameter

DAM … arithmetic mean droplet diameter

Dav … average droplet diameter


XI

DC … droplet diameter at critical point (evaporation)

DD … droplet diameter in dried form (particle diameter)

DGM … geometric mean droplet diameter

DHM … harmonic mean droplet diameter

DM … median droplet diameter

Dmax … maximum droplet diameter

DMMD … geometric mass medium droplet diameter

D0 … capillary diameter

DSM … surface mean droplet diameter

DV … diffusivity

DVM … volume mean droplet diameter

DVS … volume surface droplet diameter (Sauter mean)

Dw … droplet diameter in wet form

D … mean droplet diameter

RD … Rosin-Rammler mean droplet diameter

f … acceleration or frequency of vibration

fN(D) … percentage occurrence of a given size in a sample (number basis)

F … frictional force

FF … force

FR … Froude number

FN … flow number

g … gravitational constant

h … vane height in rotary atomizer wheel or pressure head in nozzle atomizer

hc … heat transfer coefficient

H … humidity or enthalpy

Ha … absolute humidity of air


XII

HC … enthalpy of condensate

HM … percentage moisture in feed (dry solids basis)

Hrel … relative humidity

HS … enthalpy of steam entering air heater

HW … absolute humidity at saturated droplet surface

J … mechanical equivalent of heat

kg … kilogram

K … constant

Kd … thermal conductivity

Kg … mass transfer coefficient

La … air-flow rate

m … mass, droplet mass

m … metre

M … feed rate

MA … mass air rate

Mc … condensate rate

Mf … combustion rate of oil/gas

ML … mass liquid feed rate

Mm … mean molecular weight of gas-vapour mixture in boundary layer around droplet

MP … mass feed rate per unit wetted periphery

MS … dry solids entering dryer/unit time

N … rotary atomizer speed (r.p.m.)

N … newton

Nd … number of droplets in size group

Nu … Nusselt number (hcD/Kd)

N’ … molar diffusion per unit area


XIII

Pf … partial pressure of air in boundary layer

pw … partial pressure of water vapour in air

ΔP … pressure drop

Pa … Pascal

Pd … dynamic pressure

PF … dimensionless average value of vapour pressure of non diffusing gaseous

component surrounding an evaporating droplet

PK … power requirement

PR … power requirement at reference atomizer wheel speed

PS … vapour pressure at droplet surface

PT … total pressure

PW … vapour pressure of water

PWB … saturated vapour pressure of water vapour at droplet wet surface

Patmos … atmospheric pressure

Pr … Prandtl number

q … dispersion coefficient

Q … volumetric feed rate

Qa … enthalpy of air

QH … calorific value

Q’H … heat transferred per unit area

QL … heat loss

QS … enthalpy of feed

QV … volumetric feed rate per vane on atomizer wheel

QVP … volumetric feed rate per unit wetted periphery on rotary atomizer disc/wheel

r … radius

r1 … inlet feed channel radius


XIV

r2 … nozzle orifice radius

rc … radius of air core at the orifice

rd … rotary atomizer disc/wheel radius

ro … radius of liquid feed point on a rotary atomizer disc/wheel or orifice radius of

nozzle atomizer

R … swirl chamber radius, or radial distance

Rc … drying chamber radius

RK … gas constant

Re … Reynolds number

RF … force per unit area

r.p.m. … revolutions per minute

SG … geometric standard deviation

SH … droplet travel in the horizontal direction

SN … number standard deviation

SV … droplet travel in the vertical direction

Sc … Schmidt number

Sh … Sherwood number

t … time

T … temperature

ΔT … temperature difference

Ta … air temperature

Tabs … absolute temperature

Tav … average temperature

Tg … gas temperature

Tr … reference temperature

Td … droplet surface temperature


XV

U … overall heat transfer coefficient

Uf … droplet velocity relative to air

Uh … droplet velocity in the horizontal direction

Ur … droplet velocity in the radial direction

Ut … droplet velocity in the tangential direction

UT … tangential velocity component (nozzle atomizer)

UV … axial velocity (nozzle atomizer)

v … volume

V … velocity

Va … air velocity

Vf … terminal velocity

Vj … liquid jet velocity

Vm … mean velocity at Venturi throat or orifice plate

VM … velocity of atomizing air at the nozzle orifice

Vo … axial velocity of liquid at nozzle orifice

Vr … radial liquid velocity (rotary atomizer)

Vrel … velocity of droplet relative to air or gaseous flow

Vres … resultant velocity

Vs … velocity of sound

Vt … velocity in the tangential direction

VT … peripheral speed of rotary atomizer disc wheel, liquid tangential velocity

component

Vv … release velocity

VD … volume percentage oversize

W … moisture content

WC … critical moisture content


XVI

WE … equilibrium moisture content

WS … weight of moisture/unit weight dry solids

We … Weber number

t

c

dd

WW … evaporation rate

x … horizontal co-ordinate

xw … weight fraction

y … distance from nozzle orifice

Y … vertical co-ordinate

Ye … expansion factor

Z’ … ratio We/Re

Greek Letters

α … dispersion factor or spray angle

δ … boundary layer thickness

η … efficiency

tddθ … rotation speed of liquid

λ … latent heat of vaporization

ν … kinematic viscosity

ρa … density of air

ρD … density of particle

ρl … density of liquid

ρs … density of solids

ρw … density of droplet

σ … surface tension

ω … angular velocity


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1 INTRODUCTION

1.1 Problem Description

Over the past decade, research in the field of spray dryer modeling has primarily dealt with

the practical utility of spray dryers in various industries. These designs are mainly empirical

in nature. However, experiments on full-scale spray dryer present major difficulties, not only

because of their large sizes and massive costs involved, but also because of the complex and

hostile environment in which to measure flow, temperature and humidity, etc. within the

drying chamber. On the other hand, it is essential to understand the spray drying process well.

This will lead to a good productivity, low energy consumption and high final product quality.

Full-scale spray dryer simulations using computational fluid dynamics (CFD)

technology is one possible solution to this problem. However, the lack of experimental data in

the public domain adds to the uncertainty when building enhanced physical models

representative of real spray dryers, which is a major impediment to innovation in spray drying

area.

Therefore, industrial CFD codes have to be validated on small-scale spray dryers before

using them on full-scale industrial spray dryers.

1.2 Previous Work

Much work has been done in the past decade on the performance simulation of spray dryers

based on computational fluid dynamics (CFD) techniques using available commercial

software such as the different versions of Fluent and ANSYS CFX.

In an early work, Southwell et al. (2001) used CFD codes to simulate the inlet region of

a co-current pilot-scale spray dryer to come up with a solution for uneven air distribution,

which is known to affect spray dryer performance and air flow patterns.

Kadja and Bergeles (2003) investigated heat, mass and momentum transfer between a

slurry droplet and a gas flow numerically. They developed a model which can be applied to

assess drying and combustion properties of slurries inside spray dryers or combustors and to

estimate the time needed to reach ignition of the solid component in slurry fuels. The model


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developed was applied to coal water droplet slurries the properties of which are available in

the literature but can also be used for study of drying of any other slurry such as that

encountered in flue gas desulfurization systems or in food industry. The parametric study

revealed that the most important factor in slurry drying is the ambient temperature and that the

injection velocity, the ambient pressure of the flowing medium or the particle initial

temperature affect very little the drying rate.

Goula et al. (2004) investigated the influence of spray drying conditions on residue

accumulation and fouling using CFD simulation. They concluded that residue accumulation

increased with decreases in drying air flow rate.

Huang et al. (2004) simulated a spray dryer fitted with a rotary disk atomizer using a

three-dimensional CFD model. They investigated the interaction between droplets or particles

with the drying air within the drying medium, which is difficult to model reliably. They used

and compared four different turbulence models to simulate the swirling two-phase flow with

heat and mass transfer in the drying chamber and concluded the RNG k-ε model to be the best

based on comparison with limited available experimental data.

Huang et al. (2006) presented results of a computational fluid dynamic study carried out

to investigate the possibility of multi-functional applications of a specific spray dryer

chamber. The volumetric evaporation rate values, heat transfer intensity and thermal energy

consumption per unit evaporation are computed and compared for drying of a 42.5% solids

maltodextrin suspension in a spray chamber 2.2 m in diameter with a cylindrical top section

2.0 m high and a bottom cone 1.7 m high. A three-dimensional computational fluid dynamic

model for pressure nozzle and rotating disc spray dryers was developed and investigated.

Good agreement with limited experimental data was obtained considering complexity of the

system studied. It also shows that a three-dimensional model is more suitable for such a spray

drying system than a two-dimensional axi-symmetric model presented by Kieviet (1997).

Oakley (2004) used four different models, namely, heat and mass balances, equilibrium-

based models, rate-based models, and CFD models for comparing spray dryer modeling in

theory and practice. The value of each technique was demonstrated in different scenarios.

Li and Zbiciński (2005) performed a sensitivity analysis on CFD modeling of a co-

current spray-drying process. They determined the initial parameters of the discrete and

continuous phases experimentally to be used in the model. Their results showed that the


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applied gas turbulence model, drying kinetics, effect of atomizing air, and turbulent particle

dispersion are crucial parameters controlling the accuracy of the CFD model.

In a continuing work, Zbiciński and Li (2006) presented conditions for accurate CFD

modeling of a spray-drying process. The material critical moisture content and the drying

curves were determined experimentally in a previous lab-scale work. Based on the

comparison of the CFD modeling results and the experimental data, they concluded that a

maximum error of 20% in predictions based on the discrete phase parameters, which is

probably close to the current capacity of the CFD technique for modeling spray-drying

processes, is achievable.

Montazer-Rahmati and Ghafele-Bashi (2007) presented a mathematical model for the

description of the drying mechanism and verified its validity using industrial data. In order to

make the model match actual system results, they considered a third stream besides the

climbing hot air and the falling droplet streams that represent part of the sprayed droplets that

exhibit a different behaviour from the rest. Often in model idealizations and for preliminary

estimates, this stream has not been taken into account. But the fact is that the consideration of

this third stream is essential for increasing the accuracy of the model and cannot be neglected.

The major difference in this work compared with previous work is the development of a

mathematical model to consider the effect of the swirling motion of the dried particles instead

of using CFD models. A counter-current spray dryer has been modelled in this work as

opposed to the co-current dryer used in previous work. The amount of entrainment and its

effect on the performance of this type of dryer has been determined with good accuracy.

1.3 Objective

The objective of this work is to present and discuss different sets of numerical results obtained

using the commercial CFD code ANSYS CFX 11.0 SP1 for (a) simple quadratic spray dryer

of tannin water mixture for two different inlet temperatures of drying air aiming to understand

spray dryer model behaviour and capability, and for (b) fully three-dimensional cylinder-on-

cone spray dryer in co-current flow configuration, fitted with a rotary disk atomizer, air outlet

placed by side and product exit placed at the cone bottom, for different combinations ov

drying mixtures, meshes, particle rates and inlet temperatures of drying air. The RNG k–ε

turbulence model was selected in this work based on the work of Huang et al. (2004).

Comparison with limited experimental data presented in Huang et al. (2006) is also included.


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1.4 Assumptions

The main assumptions in this work are:

• The two-phase flow is dilute; i.e., compared with the volume of the drying medium,

the particle volume occupies a very small fraction.

• No agglomeration, collision or breakup occurs among the particles.

• No wall deposition of the particles occurs.

• No temperature gradient exists within the droplet or particle (small Biot number).

• Both phases, i.e. continuous (drying air) and dispersed (particles), are ideal mixtures,

i.e. material properties depends on mass fractions of the constituting components

only.

• No repeated moistening of particles occurs during spray drying, i.e. after some

portion of the moisture has been dried out of the particles it is not possible to be

transferred back to particles again.

• Whole moisture contained in particles is treated to be surface moisture, not anyhow

physically or chemically bounded inside particles.

• Particles are assumed to be spherical, even after they would have been dried out.

1.5 Outline

Chapter 2 describes basic physical principles of spray drying. In Section 2.1 an introduction to

basic physical principles of spray drying is given, including definition of spray drying process

itself, everyday and tannin industry applications, short outline of process stages involved in

spray drying and profits and drawbacks of spray drying. In Section 2.2 spray drying fundamen-

tals including basic description of all three process stages, i.e. atomization of feed into a

spray, spray-air contact (mixing and flow) and drying of spray (moisture/volatiles evapora-

tion) are given. Furthermore, effect of operating variables when meeting dried-product

requirements is addressed, representation of sprays with different methods and common terms

and principles in spray drying are described. In upcoming sections process stages, i.e.

atomization (Section 2.3), spray-air contact (Section 2.4) and drying of droplets (Section 2.5)

are addressed in detail.

Chapter 3 describes physical-mathematical modelling of spray drying. In Section 3.1 a

brief introduction has been made to CFD. Section 3.2 addresses modelling of Eulerian phase


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presenting governing equations, equations of state, buoyancy assumption, multicomponent

flow representation and modelling, wall function theory and turbulence models. Section 3.3

addresses modelling of Lagrangian phase presenting Lagrangian tracking implementation,

integration, interphase transfer through source terms, momentum transfer, turbulence in

particle tracking, heat and mass transfer.

Chapter 4 describes discretization and solution theory. In section 4.1 discretization of

governing equations and coupled system of algebraic equations re presented and in Section

4.2 solution strategy used by coupled solver, general solution and linear equation solution are

presented.

Chapter 5 presents numerical models details for simple case (Section 5.1) and reference

case (Section 5.2). Appendices A and B containing computer program listings and providing

complete reference to numerical settings for all case calculated are related to this chapter.

Chapter 6 presents results and discussion for all available numerical models and combi-

nations of numerical settings.

Chapter 7 presents conclusions based on results presented in previous chapter and

suggested work worthwhile to be undertaken in the future.


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2 BASIC PHYSICAL PRINCIPLES OF SPRAY DRYING

2.1 Introduction

Definition

Spray drying is by definition the transformation of feed from a fluid state into a dried

particulate form by spraying the feed into a hot drying medium. It is a one-step, continuous

particle-processing operation involving drying. The feed can either be a solution, suspension

or paste. The resulting dried product conforms to powders, granules or agglomerates, the form

of which depends upon the physical and chemical properties of the feed and the dryer design

and operation. Spray drying is a procedure which in many industries meets dried product

specifications most desirable for subsequent processing or direct consumer usage. Intensive

research and development during the last four decades has resulted in spray drying becoming

a highly competitive means of drying a wide variety of products. The range of product

applications continues to expand, so that today spray drying has connections with many things

we use daily. The extent of this is worth summarizing as part of the introduction.

Everyday Applications

Spray drying has moved into all major industries ranging from production in the most delicate

of conditions laid down in food and pharmaceutical manufacture right through to the high-

tonnage outputs within such heavy chemical fields as mineral ores and clays. There are many

products and articles in use around us each day to exemplify the extensive usage of spray

drying. This is apparent if we consider just one aspect of common interest to us all, namely

our domestic life.

From foodstuffs to home fittings, spray drying has many associations. Each product

requires different powder requirements to be met during manufacture. For example, we may

be concerned only with the taste and price of the foodstuffs we buy and the quality of the


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household aids we use, but it is most likely one would find a wide range of food stuffs,

equipment and fittings within our homes having direct and indirect connections with the

spray-drying operation. These foodstuffs may well include instant tannin, tannin whitener,

dried eggs, milk, soups, baby foods, perhaps even powdered cheese and fruits. These are

examples of products with direct connections. Spray-dried foodstuffs appeal to the eye, retain

nutritive contents, and arc easy to use because they are readily dry mixed and reconstituted.

This is irrespective of their dried forms, which are highly diverse. Milk powders can be in

agglomerated (instant) form, whereas eggs, soup. Tannin whitener have powdery, and fruits

granular, forms. Apart from dried foodstuffs that are consumed directly, there are many spray-

dried products used in cooking. Examples include condiments (garlic, pimento), flavouring

compounds, rennet, and ingredients in biscuits and cakes. Meat, vegetables and fresh fruit are

foodstuffs with indirect connections with spray drying. Meat may be from a slaughtered

animal reared on feeds based upon spray-dried skim milk, whey or fat-enriched milk

(replacer) or proteins. Whereas appearance might not be so crucial here, particle size and

consistency must be conducive to animal digestion. All vegetables and fruit can be connected

with spray-dried fertilizers and pesticides used in cultivation. For this application the powders

must have good spreading characteristics, with emphasis on particle-size distribution and

moisture content of the powder.

Passing from foodstuffs to general household commodities, many examples can be

cited. Perhaps the best-known spray-drying application is household detergents: but also

spray-dried soaps and other surface active agents are available. In the bathroom cabinet,

spray-dried pharmaceutical products, and even cosmetics, are likely to be found.

Pharmaceuticals, e.g., antibiotics, are produced under the most aseptic of conditions as finely

divided powders, which are often made into tablets prior to marketing. The spray-dried

powder form is ideal for rapid assimilation into the body organs. Many cosmetics rely on

spray drying to provide constituents in such articles as face powders and lipsticks.

Applications to home fittings and furnishings are also extensive. Wall tiling is formed by

pressing coloured spray dried clays. Paints contain spray-dried pigments. Electrical insulation

material is spray dried prior to pressing into parts for electronics and electric power supplies.

Also in the electronics field spray-dried ferrites enjoy wide use, being found in pressed form

in telephones, radio, television, etc. Many household aids are powered by an electric motor

with a ferrite rotor. All these pressing operations demand strict particle-size distributions that

can be met by the spray-drying operation.


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No such survey of spray-dried products in the home is complete without mention of (a)

plastics, as many household plastic utensils originate from a manufacturing process that

includes a spray-drying stage, (b) fabrics, as spray-dried dyestuffs provide the vivid colours of

furnishings and clothing; (c) stationery, as spray drying provides many materials for printing

while spray-dried kaolin is used in papermaking itself; (d) shoes, bags and leather wear, as

spray-dried tannin is closely associated with the curing of leather; (e) starches, as the

extensive processing of this, one of mankind's most basic materials, often includes a spray-

drying stage. Spray-dried starch and its derivatives (sugar, syrup) are widely used in ice-

cream, confectionery, desserts, jellies, preserves, frozen fruit, soft drinks. In non-food

manufacture, spray-dried starch is used in textiles, papermaking, printing and adhesives.

Application of Spray Drying in Tannin Industry

Tannin is a water-soluble mixture of polyhydroxy-benzoic acid that find versatile application

in numerous industries. The most important and well-known application is the curing of

leather, where the tannin is used to precipitate gelatine from animal hides and skins to form a

stable insoluble leather. Other important uses include (a) a dispersant in oil-drilling muds, (b)

an anti-oxidant for use in steam-boiler feeds, (c) rope preservative, (d) cement and (e) a

compounding agent in certain types of inks, dyes, resins, adhesives and medicaments. Tannin

is used in these applications as spray-dried powder. Natural tannins are recovered from

woods, barks and fruits. One of the world's leading sources of natural tannin is from the wood

sweetened chestnut.

The trees, after debarking, are reduced to sawdust in high-duty shredding machines. The

sawdust is conveyed to pressure-extraction units where water is added. The extraction takes

place at 125-130 °C at 25 kPa pressure. The extract is dilute and is concentrated to 80%

extract by vacuum evaporation. The resultant concentrate can be cooled to obtain a common

solid extract, but it is usual to take the extract one stage further to form a special dustless

tannin powder by spray drying. In this case the liquid from the extractors is treated. While still

hot, the dilute extract is transferred to a mixing tank and chemically reacted with sodium

bisulphite, aluminium sulphate, formic and sulphuric acids under closely controlled

conditions. Once the reaction is terminated, vacuum evaporation is carried out or dilute

extract is fed directly to the dryer. The feed temperature to the dryer is 80 °C. A spray dryer

with a high-speed rotating vaned wheel atomizer is used. Inlet and outlet drying air

temperatures arc of the order 250-90 °C. Tannin fines are recovered in cyclones.


- 9 -

What is Involved in Spray Drying?

Spray drying involves atomization of feed (in this work aqueous feed is a matter of

discussion) into a spray and contact between spray and drying medium (in this work drying

medium is air) resulting in moisture evaporation. The drying of the spray proceeds until the

desired moisture content in the dried particles is obtained and the product is then recovered

from the air (in this work product recovery is not a matter of discussion). These three stages

are illustrated by reference to the open-cycle, co-current spray-dryer layout (see Figure 2.1),

the most common type of spray dryer in industry.

The word 'atomization' can be confusing initially. 'Atomization' has no association with

atoms and nuclear physics but covers the process of liquid bulk break-up into millions of

individual droplets forming a spray. A cubic metre of liquid forms approximately 2 x 1012

uniform 100 μm droplets. The energy necessary for this process is supplied by centrifugal,

pressure, kinetic or sonic effects. During spray-air contact, droplets meet hot air and moisture

evaporation takes place from the droplet surfaces. Evaporation is rapid, due to the vast surface

area of droplets in a spray, e.g., the 2 x 1012 droplets of 100 μm diameter mentioned above

offer a total surface area of over 60,000 m2. If the spray drying-plant is properly designed the

outcome will be dried particles suspended in the drying air from which an efficient particle

removal is essential.

Any form of dryer provides means of moisture removal by the application of heat to the

feed product and control of the humidity of the drying medium. A spray dryer is no exception.

Figure 2.1 The process stages of spray drying illustrated by the open-cycle co-current layout


- 10 -

Heat is applied as a heated atmosphere and evaporation is promoted by spraying the feed into

this atmosphere. Humidity control is by air flow and temperature regulation. Although the

vast majority of cases employ hot atmosphere to drive moisture from each spray droplet, there

are cases in which the delicacy of the operation demands that drying medium is first

dehumidified and then just warmed over atmospheric temperatures. This is a variation of the

basic spray-drying concept, and is termed low temperature spray drying.

In introducing the subject, emphasis has been given to the ability of the spray-drying

process to handle a wide range of products, and meet the specifications laid down by

diversified industries. Such a range of application has led to dryer designs becoming less

standardized as each product has to be treated individually and handled in specialized ways to

meet the required specifications. Whatever design of dryer the product demands, the

advantageous features of spray drying are retained.

Advantages and Disadvantages of Spray Drying

Of all the industrial dryer types available, there are few that accept pumpable fluids as the

feed material at the dryer inlet and discharge a dry particulate at the outlet. Of the few, spray

drying is unique in being able to produce powders of specific particle size and moisture

content irrespective of dryer capacity and product heat sensitivity (Figure 2.2).

Figure 2.2 Dried-powder forms produced by spray drying: (a) fine particles (dusty) (non-instant skim milk)

(b) spheres (aluminium oxide) (c) agglomerates (instant skim milk)

(a)

(c)(b)


- 11 -

These characteristics are of such importance to many industrial operations that spray drying

becomes the only rational choice to dry fluid feedstocks even though, being a convectional

type dryer, its thermal efficiency is lower than competing direct-contact dryers that also

receive fluid feed materials.

With spray dryers operating in industries that range from aseptic pharmaceutical

processing through to mining operations and handling feed rates that range from a few

kilograms per hour to well over 100 tonnes per hour per dryer, it is obvious there are many

positive aspects that have led to establishing spray drying as a most important industrial

drying system today. For example:

• Powder quality remains constant throughout the entire dryer operation irrespective of

the length of the dryer run when drying conditions are held constant.

• Spray dryer operation is continuous and easy, operation is adaptable to full automatic

control, response times are fast. One operator can handle more than one

automatically controlled spray dryer if located together in one complex.

• A wide range of dryer designs are available. Products specifications are readily met

through selection of the appropriate spray-dryer design and its operation.

• Spray drying is applicable to both heat-sensitive and heat-resistant materials.

• Feedstocks in solutions, slurry, paste or melt form can be handled if pumpable,

whether they be corrosive, abrasive or not.

• Spray dryers can be designed to any individual capacity requirement. The largest

spray drying complex in operation today handles 2.5 million m3 of gas per hour.

• There is extensive flexibility in spray-dryer designs. Designs are available to handle:

- evaporation of organic solvent-based feedstocks without explosion and fire risks;

- evaporation of aqueous feedstocks that form powders that are potentially

explosive when mixed in air;

- evaporation of aqueous feedstocks where the drying process gives odour

discharge;

- drying of toxic materials;

- drying of feedstocks that require handling in aseptic/hygienic drying conditions.

Spray drying is disadvantaged by high installation costs. Industrial units are physically

larger per unit powder output than other dryer types. This makes spray dryers expensive to fa-

bricate. Furthermore their large diameter or tall drying chambers require expensive buildings

and/or supporting structures.


- 12 -

The spray dryer, being a convection dryer, has a poor thermal efficiency unless very

high inlet drying temperatures can be used. This is possible only in the minority of cases due

to product heat degradation effects by high temperature spray drying.

Drying-air exhausted from spray dryers contains large amounts of low grade waste heat.

It is expensive to remove this heat in heat-exchange equipment since such equipment must

handle powder-laden air at saturated or near saturated conditions, and this leads to the need

for sophisticated heat-exchanger design. Development towards more compact lower energy-

consuming dryer designs is a prime activity of spray-dryer manufacturers, aiming to use a

CFD as a helping aid. Such a development has done much to counteract the most often cited

disadvantage of spray drying, i.e. its relatively poor thermal efficiencies at inlet temperatures

up to 350 °C: the inlet temperature range that covers the vast majority of industrial spray-

drying operations.

2.2 Spray Drying Fundamentals

Process Stages

Spray drying consists of four process stages (see earlier: Figure 2.1):

• Atomization of feed into a spray.

• Spray-air contact (mixing and flow).

• Drying of spray (moisture/volatiles evaporation).

• Separation of dried product from the air (not considered in this work).

Each stage is carried out according to dryer design and operation, and, together with the

physical and chemical properties of the feed, determines the characteristics of the dried

product. The spray homogeneity following atomization and the high rates of moisture

evaporation (spray-air mixing and flow) enable the temperature of the dry product to be

considerably lower than the drying air leaving the drying chamber. The product is thus not

subjected to high temperatures, and when separated from the drying air is devoid of any heat

degradation. The basic physical principle of 'evaporation causes cooling' is very pertinent to

the operation.


- 13 -

• Atomization of feed into a spray

The formation of a spray (atomization) and the contacting of the spray with air are the

characteristic features of spray drying. The selection and operation of the atomizer is of

supreme importance in achieving economic production of top quality products. The

atomization stage must create a spray for optimum evaporation conditions leading to a dried

product of required characteristics.

Rotary atomizers and nozzles are used to form sprays. With rotary atomizers centrifugal

energy is utilized. There are two categories of rotary atomizers: (a) atomizer wheels, (b)

atomizer discs. Wheel designs are available to handle feed rates up to 200 t/h. With nozzle

atomization, pressure, kinetic or (less common) sonic energy is utilized. There is a wide range

of nozzle sizes and designs to meet spray-drying needs. Feed capacities per nozzle are lower

than per rotary atomizer, leading to nozzle duplication to meet high feed-rate requirements.

Rotary Atomizers (Utilization of Centrifugal Energy)

Feed is introduced centrally on to a wheel or disc rotating at speed. The feed flows outwards

over the surface, accelerating to the periphery. Feed, on leaving the periphery, readily

disintegrates into a spray of droplets. Rotary atomizers form a low-pressure system. A wide

variety of spray characteristics can be obtained for a given product through combinations of

feed rate, atomizer speed and atomizer design. Designs of atomizer wheels have vanes or

bushings. Vanes are high, wide, straight or curved; bushings circular or square.

Vaned atomizer wheels are used in many and varied industries, producing sprays of

high homogeneity. Atomizer wheels with bushings are used in more specialized fields, e.g.,

for handling abrasive feeds. Wheels can be operated to produce sprays in the fine to medium-

coarse size range (see Figure 2.2). Peripheral velocities can reach 300 m/s in industry in

specialised cases. Designs of disc include vaneless plates (discs), cups, and inverted bowls.

Rotary atomizers are reliable, easy to operate and can handle fluctuating feed rates. Atomizer

wheels have negligible clogging tendencies due to large flow ports. Feed systems for rotary

atomizers operate at low pressure, and hence they are simple to operate and maintain. One of

the most important features is the ease of particle-size control merely through wheel-speed

control. Rotary atomizers are used in spray drying to produce sprays of mean size 30-120 μm.

The mean size is directly proportional to feed rate and feed viscosity and inversely

proportional to wheel speed and wheel diameter.


- 14 -

Rotary atomization is discussed in detail later. The spray form leaving a rotary atomizer

(vaned wheel) is shown in Figure 1.3a.

Pressure Nozzles (Utilization of Pressure Energy)

The feed concentrate is fed to the nozzle under pressure. Pressure energy is converted to

kinetic energy, and feed issues from the nozzle orifice as a high-speed film that readily

disintegrates into a spray as the Film is unstable. The feed is made to rotate within the nozzle,

resulting in cone-shaped spray patterns emerging from the nozzle orifice. Sprays from

pressure nozzles handling high feed rates are generally less homogeneous and coarser than

sprays from vaned wheels (see Figure 2.4). At low feed rates, spray characteristics from

nozzles and wheels are comparable. Duplication of nozzles allows fine sprays to be obtained

in nozzle dryers, but nozzles are generally used to form coarse particle powders (mean size

120-250 μm) having good free flowability. The spray form leaving a pressure nozzle is shown

in Figure 1.3b. Variation of pressure gives control over feed rate and spray characteristics.

Mean size of spray is directly proportional to feed rate and viscosity, and inversely

proportional to pressure. Pressure nozzles have recorded operating pressures up to 680 atm.

Atomizer Selection

The selection of the atomizer type depends upon the nature of the feed and desired

characteristics of the dried product. In all atomizer types, increased amounts of energy

available for liquid atomization result in sprays having smaller droplet sizes. If the available

atomization energy is held constant but the feed rate is increased, sprays having larger droplet

sizes will result. The degree of atomization depends also upon the fluid properties of the feed

material, where higher values of viscosity and surface tension result in larger droplet sizes for

the same amount of available energy for atomization.

Figure 2.3 Atomizers in operation (a) rotary atomizer (vaned wheel)

(b) nozzle atomizer (pressure nozzle)

(a) (b)


- 15 -

Where a desired particle size distribution can be met by either a rotary or a nozzle

atomizer, the rotary atomizer is normally selected due to its greater flexibility and use of

operation. Rotary atomizers are used to produce a fine to medium-coarse product (mean size

30-150 μm). Coarser sprays can be produced, but medium-to-large industrial capacity would

require a very large-diameter chamber for drying. Nozzle atomizers are used to produce a

coarse product (mean size 150-300 μm). Microphotos of typical rotary atomizer and pressure

nozzle atomizer powders are shown in Figure 2.4.

Figure 2.4 Particle size of powder produced on rotary and nozzle atomizer spray dryers (a) powder produced on rotary atomizer dryer (mean size approximately 70 μm, peripheral

speed approximately 120 m/s) (b) powder produced on pressure-nozzle atomizer dryer (mean size approximately 220 μm,

nozzle pressure approximately 14 atmospheres)

(b)

(a)


- 16 -

• Spray-Air Contact (Mixing and Flow)

The manner in which spray contacts the drying air is an important factor in spray dryer

design, as this has great bearing on dried product properties by influencing droplet behaviour

during drying. Spray-air contact is determined by the position of the atomizer in relation to

the drying air inlet. Many positions are available.

The spray can be directed into hot air entering the drying chamber as shown in Figure

2.5a. Product and air pass through the dryer in 'co-current' flow, i.e. they pass through the

dryer in the same direction (although spray-air movement in reality is often far from co-

current, e.g. at the point of actual spray-air initial contact and in any areas of back mixing in

the drying chamber). This arrangement is widely used, especially if heat-sensitive products

are involved. Spray evaporation is rapid, the drying air cools accordingly, and evaporation

times are short. The product is not subject to heat degradation. Product temperature is low

during the time the bulk of the evaporation takes place, as droplet temperatures approximate

to wet-bulb temperature levels. When the desired moisture content is being approached, each

particle of the product does not rise substantially in temperature as the particle is then in

contact with much cooler air. In fact, low-temperature conditions prevail virtually throughout

the entire chamber volume, in spite of very hot air entering the chamber. The temperature

distribution does depend upon whether the air disperser creates plug-flow or swirling air

conditions in the chamber. The greater the swirling motion, the more uniform the temperature

distribution throughout the drying chamber.

Figure 2.5 Product-air flow in spray dryers


- 17 -

Alternatively, the spray can be contacted with air in 'counter-current' flow (Figure 2.5b).

Spray and air enter at the opposite ends of the dryer. This arrangement offers dryer

performance with excellent heat utilization, but it does subject the driest powder to the hottest

air stream. It readily meets granular powder requirements of non-heat-sensitive products.

Counter-current flow is used with nozzle atomization, since an upward streamline flow of

drying air reduces the downward velocity of the large droplets in the spray, permitting

sufficient residence time in the drying chamber for completion of evaporation.

There are dryer designs that incorporate both 'co-current' and 'counter-current' layouts,

i.e., mixed flow dryers (Figure 2.5c). In this type, coarse free-flowing powder can be pro-

duced in relatively small chambers but the powder is subjected to high particle temperature.

In all cases, the movement of air predetermines the rate and degree of evaporation by

influencing (a) the passage of spray through the drying zone, (b) the concentration of product

(particle population) in the region of the dryer walls, and (c) the extent to which semi-dried

droplets re-enter the hot areas around the air disperser. Air flow in the drying chamber is

discussed in Section 2.4.

• Drying of Spray (Moisture/Volatiles Evaporation)

As soon as droplets of the spray come into contact with the drying air, evaporation takes place

from the saturated vapour film which is quickly established at the droplet surface. The

temperature at the droplet surface approximates to the wet-bulb temperature of the drying air.

Evaporation takes place in two stages. At first there is sufficient moisture within the droplet to

replenish that lost at the surface. Diffusion of moisture from within the droplet maintains

saturated surface conditions and as long as this lasts, evaporation takes place at a constant

rate. This is termed the constant rate period or first period of drying. When the moisture

content becomes too low to maintain saturated conditions, the so-called critical point is

reached and a dried shell forms at the droplet surface. Evaporation is now dependent upon the

rate of moisture diffusion through the dried surface shell. The thickness of the dried shell

increases with time, causing a decrease in the rate of evaporation. This is termed the falling

rate period of second period of drying.

Thus a substantial part of the droplet evaporation takes place when the droplet surfaces

are saturated and cool. Drying chamber design and air flow rate provide a droplet residence

time in the chamber, so that the product is removed from the dryer before product

temperatures can rise to the outlet drying air temperature of the chamber.


- 18 -

During evaporation, the atomized spray distribution undergoes change. Different

products exhibit different evaporation characteristics. Some tend to expand, others collapse,

fracture or disintegrate, leading to porous, irregularly shaped particles. Others maintain a

constant spherical shape or even contract, so that the particles become denser. The extent of

any change in particle shape, and hence the dried-powder characteristics, are closely

connected to the drying rate, and it follows that to meet desired powder characteristics close

consideration must be given to the drying-chamber design.

Effect of Operating Variables when Meeting Dried-Product Requirements

To meet the requirements of the dried product close attention must be given to all four process

stages, since each stage affects the properties of the product to some degree. Atomization

technique and feed properties have a bearing on particle-size distribution, bulk density,

appearance, and moisture content. Spray-air contact and resulting evaporation in the drying

operation have a bearing on bulk density, appearance, moisture content, friability and

retention of activity, aroma and flavour. Techniques for product-air separation will determine

the degree of comminution the powder undergoes following completion of drying. Many

operational variables associated with atomization and the drying operation offer means of

altering the characteristics of the dried product.

• Energy Available for Atomization

Increase in energy available for atomization will create smaller droplet sizes at constant feed

conditions. Increase in rotary atomizer speed, nozzle pressure, or air-liquid flow ratio in two-

fluid nozzles will decrease the mean size of the spray droplets. The spread of droplet sizes in

the spray distribution may not be appreciably changed. Producing greater amounts of Fine

particles can often form a product of higher bulk density. The greater numbers of smaller

particles fill the voids between the larger, and smaller particles may well be more dense.

• Feed Properties

Increase in feed viscosity through increase in feed solids or reduction in feed temperature will

produce coarser sprays on atomization at fixed atomizer operating conditions. Surface-tension

effects appear minor. Increase in feed solids affects evaporation characteristics where

generally an increase in particle and bulk density results.


- 19 -

• Feed Rate

Increasing feed rate produces coarser sprays and dried products.

• Selection of Atomizer Equipment

Rotary atomizers and nozzles exhibit different spray-forming characteristics which can be

utilized to meet necessary product requirements. Selection can only be made with reference to

the product concerned. Modern rotary atomizer and nozzle designs are flexible and can

produce similar spray characteristics. However, rotary atomizers are generally used to

produce fine-medium-coarse powders, and pressure nozzles to produce coarse powders.

Rotary atomizers are preferred for all larger dryer capacities (i.e. feed rates > 5 t/h).

• Design of Atomizer Equipment

This is closely connected with the energy available for atomization, discussed above. If the

energy available is made to act on reduced feed bulk, finer sprays result. Many spray

properties can be achieved by altering the vane design of an atomizer wheel, since the

number, height, width and length of vanes determines the amount of liquid at the point of

atomization at the wheel periphery.

• Air Flow

The rate of air flow controls to a certain extent the residence time of the product in the drying

chamber. Increased residence time leads to a greater degree of moisture removal. Reducing air

velocity assists product recovery from the drying chamber. Air flow has a bearing on the

product being handled and on its dried properties.

• Drying Temperatures

- Inlet

Increase in inlet temperature increases the dryer evaporative capacity at constant air rate.

Higher inlet temperatures mean a more thermally efficient dryer operation. Increased

temperature often causes a reduction in bulk density, as evaporation rates are faster, and

products dry to a more porous or fragmented structure.


- 20 -

- Outlet

For a fixed moisture content and dryer design, outlet temperature must be kept within a

narrow range to maintain the powder packing and flow requirements. Increase in outlet

temperature decreases moisture content at constant air-flow and heat-input conditions.

Operation at low outlet temperature to produce powder of high moisture content is used

when agglomerated forms of powder are required.

Representation of Sprays

Spray droplets and dried particles are an inherent part of spray drying. It is vitally important

that droplets and particles can be represented in a manner suitable for easy reference.

Accepted terminology is available to express mean size and size distributions. Particle-size

distribution features as a most important dried-product specification. Particle size is closely

related to droplet size, but they are rarely equal, due to droplet behaviour during drying.

• Terminology

- Droplet

This refers to the state of subdivision of feed on being sprayed from the atomizer. As long

as the surface moisture remains in the spray, the spray is said to be composed of droplets.

- Particle

This refers to the state of subdivision of dried product. The shape of the particle depends

upon how the droplet was formed during atomization and how the droplet/particle

behaved during drying.

- Agglomerate

An agglomerate is composed of two or more particles adhering to each other.

Agglomerates can be formed through two or more droplets coalescing in the proximity of

the atomizer or through partially dried droplets adhering to each other in the lower

regions of the chamber. Agglomerates when specifically desired are created in the drying

chamber by (a) contacting the evaporating spray with dry product fines, or (b) installing

special agglomerating equipment directly to the drying chamber.


- 21 -

- Size

The size of a particle/droplet/agglomerate is the representative dimension that expresses

the degree of comminution. For spherical particles the diameter represents its size. For

non-spherical particles, its size can be represented by an 'apparent' diameter. This is the

mean distance between extremities of the particle measured through the centre of gravity

of the particle. Size can also be based on area, volume or weight.

- Particle Shape

The complexity of the atomization mechanism and the distortions a droplet undergoes

during drying result in many spray-dried products consisting of non-spherical particles.

Wide variations in shape are often evident. The ratio of measured maximum to minimum

particle diameters often defines shape. To express divergence from sphericity a shape

factor is used, defined as the ratio between the actual surface or volume of the particles

and the total surface or volume obtained from size-measurement techniques, e.g.

microscopic analysis or sieving, assuming the particles are spherical.

• Size Distribution

Droplets and particles comprising sprays and dried products are never of one size. The

atomizer cannot form totally homogeneous sprays. Spray droplets are subjected to different

shape distortions depending upon their drying characteristics and travel within the dryer.

Dried particles and droplets from a spray have a range of sizes termed their size distribution.

A great number of methods have been devised over the years for measuring size distributions.

Microscopic analysis (with manual or automatic counting), sieving, sedimentation, elutriation,

light absorption and automatic sensing equipment are the established methods. Counting

procedures express the number of droplets or particles within a suitable size group

(increment). Size distributions can be represented by a frequency or cumulative distribution

curve. If occurrence is given by number, a number distribution results, or if given by area

volume weight corresponding to a given diameter, area volume weight distributions result.

Number size distribution is the outcome of microscopic analysis - weight distribution the

outcome of sieving.


- 22 -

• Mean Size

The mean droplet or particle size represents a single value, most suited to be representative of

the whole distribution. No value is adequate to express a size distribution, and other

parameters must be used with the mean size for full definition of size characteristics. There

are many types of mean-diameter parameters. The type selected depends upon the information

required about the spray or product, i.e. length, area, volume, shape, etc. The pertinent

characteristic varies according to how the droplet or particle data are to be used.

• Methods of Data Presentation

There are two basic forms of representation available to express the characteristics of size

and size distribution; these forms are summarized below.

- Tabular Form

This is the most precise and general method of presenting droplet size data Tables can

show a listing of size against one or more ways of expressing their distributions, e.g. size

frequency or size cumulation. However, large amounts of data can make tabular form

unwieldy and difficult to interpret.

- Graphical Form

The use of graphical presentation offers many advantages in spite of the accuracy of

tabular presentation. Graphs present data in a form whereby approximate values of devi-

ation and skewness of data from a given mean can be assessed quickly. Graphs are more

manageable than long list; of data in tabular form. The relationship of a size distribution

to a certain mathematical function can be seen at a glance from graphical representation.

Histograms

The histogram is the simplest way of representing size distribution of a spray. It is a plot

of the percentage number of droplets or particles in a given size range (size increment).

The histogram gives an immediate indication of the droplet size, which constitutes the

majority of the distribution. A typical histogram is shown in Figure 2.6.


- 23 -

Size-frequency Curves

Curves are more practical when a large number of size increments are used to express the

size distribution. Size-frequency curves can be considered a smoothed out form of

histogram (Figure 2.6) and give the relative frequency of a variable within a certain group

of data (measurements of diameter, volume surface area, etc.). The frequency curve

shown in Figure 2.7 is a plot of frequency of droplet occurrence against droplet diameter

within certain size increments (fN(D)) against diameter (D). The subscript N indicates a

frequency of occurrence according to number. The frequency of droplet occurrence is

generally stated as a percentage diameter. The frequency curve is expressed as

(2.1)

If the ordinate of the plot is the volume or surface area corresponding to a given diameter

the resulting curve is skewed due to the weighting influence in the large-diameter range.

Figure 2.6 Droplet size distribution represented in histogram form

Figure 2.7 Frequency and cumulative curves showing mean droplet values


- 24 -

Cumulative Plots

A further method of representing size distribution is the cumulative distribution plot

formed by plotting the cumulative frequency percentage of particles or droplets greater or

less than a given size, against the size. Cumulative percentage can be represented on

linear or probability paper. Cumulative plot is shown in Figure 2.7. Particle or droplet

diameter, surface, area, volume, weight can form the basis of the curve.

- Mathematical Form

This is the representation of data in a manner most suitable for size prediction.

Mathematical functions express the form of distribution.

• Analysis of Data

A distribution function and two parameters can be used to represent spray data. These

parameters consist of a mean diameter of some form, and a measure of the size range of

particles involved.

- Mean Diameters

A mean diameter is a mathematical value that represents the complete spray. This value

can be a measure of number, length, area, or volume. A general equation that defines a

mean diameter is given

(2.2)

where D is the mean diameter and p, q are integers (or zero). )(Df is the function

representing the spray size. For arithmetic mean: p=0, q=1; surface mean p=0, q=2,

volume surface mean p=2, q=3; DΔ is the size class increment and is usually taken as

uniform.


- 25 -

The two mean diameters commonly used in the spray drying operation are the median

diameter ( MD ) and the Sauter mean diameter ( VSD ) defined as

(2.3)

The median diameter is that diameter above or below which lies 50% of the number or

volume of droplets/particles. The Sauter mean diameter is that droplet or particle having

the same surface-to-volume ratio as the entire spray or powder sample. The parameters

pre-suppose spherical droplets or particles.

• Distribution Functions

Many authors have prepared mathematical relationships to represent size distributions. The

existence of varying forms illustrates that no one mathematical distribution fits the size range

of droplets or dried particles produced in the spray dryer operation.

In this work only Rosin-Rammler empirical distribution function is discussed in detail.

It is widely quoted to express size distributions. It is empirical, and relates the volume per

cent oversize ( DV ) to droplet diameter (D). The mathematical reads as following

(2.4)

Rearranging equation (2.17) we obtain

(2.5)

or

(2.6)


- 26 -

For a spray distribution to follow this function, the plot of ( )DV100log against (D) will give a

straight line on log-log paper. This is shown in Figure 2.8.

The slope represents the dispersion coefficient (q). The higher the value of (q), the more

uniform the distribution. The Rosin-Rammler mean RD can be obtained directly from the

curve as it is the droplet diameter above which lies 36.8% of the entire spray volume.

Thus it follows that the value on the ordinate of Figure 2.7 corresponding to RD equals

Common Terms and Drying Principles

In the spray-drying operation, the liquid to be removed is almost invariably water, although

the removal of organic solvents in closed-cycle operations is becoming more widespread. The

drying principles involved for both water and non-water systems are the same, and thus in this

chapter the case of water evaporation into air will be taken to illustrate the drying principles

involved.

Figure 2.8 Rosin-Rammler size distribution


- 27 -

The removal of water from a feed to the extent of leaving its solids content in a

completely or nearly moisture-free state is termed drying. The moisture in the feed can be

present in two forms: bound and unbound moisture. The nature of the solids and

accompanying moisture determines the drying characteristics. The bound moisture in a solid

exerts an equilibrium vapour pressure lower than that of pure water at the same temperature.

Water, retained in small capillaries in the solid, adsorbed at solid surfaces, as solutions in cell

or fibre walls, or chemically combined with the solids (product water of crystallization) falls

in the category of bound moisture. The unbound moisture in a hygroscopic material is that

moisture in excess of the bound moisture. All water in a non-hygroscopic material is unbound

water, which exerts an equilibrium vapour pressure equal to that of pure water at the same

temperature. The equilibrium moisture is the moisture content of a product when at

equilibrium with the partial pressure of water vapour of the surroundings. The free moisture is

the moisture in excess of the equilibrium moisture and consists of unbound and some bound

moisture. Only free moisture can be evaporated.

The mechanism of moisture flow through a droplet during spray drying is diffusional,

supplemented by capillary flow. The drying characteristics of the droplet depend upon

whether bound or unbound moisture is evaporated, as each has distinct features. As long as

unbound moisture exists, drying proceeds at near constant rate, and will continue while the

rate of moisture diffusion within the spray droplet is fast enough to maintain saturated surface

conditions. When diffusion and capillary flow can no longer maintain these conditions, the

critical point is reached and the drying rate will decline until the equilibrium moisture content

is attained. The equilibrium moisture content will remain unchanged while product is exposed

to the same atmospheric humidity and temperature.

Figure 3.1 relates these terms to the drying of a spray droplet in a constant humidity air

medium. Other terms used frequently in describing mechanisms are outlined in what follows.

Figure 2.9 Graphical relation between common drying terms


- 28 -

Dry air is atmospheric air exclusive of accompanying water vapour, as distinct from wet

air, which is inclusive of water vapour. The water-vapour content varies considerably from

day to day and from place to place. Properties of wet air are given by enthalpy-humidity

(psychrometric) charts.

Humidity defines the moisture content of the air. The amount of water vapour present in

the air is independent of the air pressure (PT) but it does depend upon the temperature of the

air with which it is mixed, i.e., according to Dalton's law. Thus for air-water systems, the

absolute humidity (Ha) is related to the partial pressure (pw) of the water vapour in the air in

the following way:

(2.7)

where H, is expressed as

Absolute humidities for air-water systems at atmospheric pressure are read directly from

psychrometric charts. Absolute humidities at pressures other than atmospheric, i.e., Ha at

pressure B, are given approximately by

(2.8)

where wP′ =vapour pressure of water at wet bulb temperature. Relative humidity (Hrel) is the

water vapour content expressed relative to the water content at saturation at the temperature of

the mixture. The mixture humidity it saturation is designated 100%. Alternatively, the relative

humidity can be expressed as the ratio

(2.9)

The addition of heat to a wet droplet is insufficient by itself to promote satisfactory

drying. Removal of moisture depends upon the humidity of the surrounding drying air. To

maintain high drying rates, cool humid air must be moved from around a droplet and replaced

with hot low humid air.


- 29 -

The partial pressure of water in air is the pressure it would exhibit if existing alone in

the same volume and at the same air temperature. The sum of partial pressures of components

in a gaseous mixture equals the total mixture pressure. The partial pressure of vapour is the

vapour pressure at dew-point temperature (see equation 2.9). Alternatively, from Dalton's law,

the partial pressure is the multiple of total pressure and mol fraction of vapour. The

significance of partial pressure concerns the reverse driving force it provides resisting drying.

Vapour pressure is governed solely by temperature, and is directly related to drying rates. The

vapour pressure of water at any temperature provides the forward driving force for drying. For

the air-water systems, the vapour pressure at a saturated surface (PwB) is related to that of

water in the surrounding air (Pw) by equation (2.10). The equation can be used to calculate

wet-bulb temperatures;

(2.10)

where Cp = specific heat of vapour at constant pressure, λ = latent heat of vaporization at wet-

bulb temperature, ΔT temperature difference between surface and air (i.e., wet and dry bulb

temperatures).

The dew point (saturation temperature) is the temperature to which wet air must be

cooled at constant pressure before liquid will form through condensation. At the dew point,

the saturation vapour pressure equals the partial pressure of water vapour in the air mixture.

The dew point is not the temperature where all water vapour is condensed to leave dry air. If

the air is cooled below the dew point, condensation continues. The amount of condensation

depends upon the degree of cooling. The air is at a state of saturation at lower temperatures

and the absolute humidity decreases by the quantity of water condensed. The dew point is

related to vapour pressure data where the vapour pressure at dew point is

(2.11)

where PwDB = vapour pressure at dry bulb temperature, Hrel = relative humidity expressed as a

decimal.


- 30 -

The dry-bulb temperature of air is recorded by an ordinary thermometer when in

thermal equilibrium with the air surroundings. The wet-bulb temperature is recorded under

steady-state conditions by a thermometer whose surface is saturated with liquid water and

simultaneously exposed to a mixture of air and water vapour. The usual technique is to place a

clean cloth around the thermometer bulb and thoroughly moisten the cloth. The thermometer

must be placed in a strong air current (velocity greater than 4.5 m/s).

The wet-bulb temperature is lower than the dry-bulb temperature. The difference (or

depression) is proportional to the moisture evaporation from the wet cloth surface. The wet-

bulb temperature, in fact, corresponds to the temperature at which the air would normally be

saturated without any change in its heat content. The upper limit of wet-bulb temperature is

the dry-bulb temperature. The lower limit is the dew point. For saturated mixtures of air, wet-

and dry-bulb and dew-point temperatures are the same. The wet-bulb temperature does not

represent conditions of thermal equilibrium. It represents simultaneous heat and mass transfer:

the dynamic equilibrium between the rate of heat transfer to the thermometer bulb and the rate

of mass transfer from the bulb.

The driving force for moisture evaporation from a saturated surface is the difference

between the water vapour pressure at the temperature of the surface and the partial pressure of

water vapour in the surrounding air (PwB - pw). The driving force can equally well be

expressed in terms of the difference in humidity at the saturated surface (Hw) and the humidity

of the air (Ha), i.e., Hw - Ha. Equation (2.7) relates the partial pressure of water vapour in the

surrounding air to Ha. At the saturated surface, the partial pressure of water equals its vapour

pressure and thus substitution of pw for Pw in equation (2.7) gives the expression for Hw. The

rate of mass transfer from a saturated surface is

(2.12)

For dynamic equilibrium the rate of heat transfer is equal to the product of the rate of

mass transfer and latent heat of vaporization (λ). The rate of heat transfer from a saturated

surface is

(2.13)

combining equations (2.12) and (2.13)


- 31 -

(2.14)

The coefficients hc, kc are incorporated with the humid heat (Cs) in the Lewis number. This is

unique in being unity for air water vapour systems, which results in the adiabatic cooling line

and wet-bulb line coinciding on the psychrometric chart. This greatly simplifies dryer

calculations for solids containing water dried in air.

The humid heat (Cs) is the heat required to raise the temperature of a unit mass of air

and its vapour for 1 °C at constant pressure. It is expressed by

(2.15)

The humid heat is used to calculate the heat for raising the temperatures of air-water vapour

mixtures where

(2.16)

Equation (3.10) is valid so long as condensation or vaporization does not take place.

The enthalpy (heat) of a mixture of air and its water vapour is the sum of the air

enthalpy and vapour enthalpy. Enthalpies are relative to a given reference level (Tr) taken as

air and saturated liquid water at 0 °C. For air-water vapour systems

(2.17)

where λ is at reference temperature.

Drying characteristics of droplets during spray drying are best illustrated by plotting the

variations in evaporation rate and accompanying changes in droplet temperature and vapour

pressure as droplet moisture decreases. Figure 3.5 illustrates the change in droplet temperature

for a droplet containing 50% of moisture contacted with hot air.

The plot shows that although a spray-dried product comes into contact with hot air, at

no stage during the process does the product temperature become high enough to cause

product degradation. The product is removed from the dryer long before the product

temperature has time to rise to approach the temperature of the exhaust drying air. Figure 3.5

also shows the change in vapour pressure during the droplet drying. The vapour pressure

during the initial drying period is that at the wet-bulb temperature.


- 32 -

2.3 Atomization

Introduction

The atomization stage in spray drying produces from liquid bulk a spray of droplets having a

high surface-to-mass ratio. The dried product that results from moisture evaporation of

atomized spray can be made to possess the desired particle size distribution through control of

the atomization variables.

The ideal spray is one of small individual droplets of equal size. Heat and mass transfer

rates and drying times are then the same for all droplets in the spray, ensuring uniform dried-

product characteristics. Droplets of a spray evaporate quickly and the short drying times

involved maintain low droplet temperatures due to the cooling effect that accompanies

evaporation. No product deterioration can take place due to heat, if correct atomization is

combined with a suitable drying-chamber design to give a product residence time just

sufficient for completion of moisture removal. The ideal requirement of an atomizer is to

product homogeneous sprays. Such sprays have not yet been obtained at industrial feed rates,

although atomizer types are available producing sprays that closely approach homogeneity,

when operating with liquids of certain physical characteristics at low feed rates.

In rotary atomization, the feed liquid is centrifugally accelerated to high velocity before

being discharged into an air-gas atmosphere. The liquid is distributed centrally on the

wheel/disc/cup. The liquid extends over the rotating surface as a thin film. Rotary atomization

is often termed centrifugal atomization, but this can be a little misleading as centrifugal

energy is also utilized to a certain degree in centrifugal pressure nozzles, where liquid is given

rotational motion.

The degree of rotary atomization depends upon peripheral speed, feed rate, liquid

properties and atomizer design. Maximum centrifugal energy is imparted to the liquid when

the liquid acquires the peripheral speed of the wheel or disc prior to discharge. If a flat smooth

disc is rotating at high speed and liquid is fed on to its top surface, severe slippage occurs

between the feed liquid and the disc. The velocity of liquid from the edge of the disc is much

lower than peripheral speed of the disc. Conditions of no slippage occur at very low speeds,

but the available centrifugal energy permits only the smallest of feed rates to be satisfactorily

atomized. To prevent slippage in commercial atomizers, radial vanes are used. The liquid is

confined to the vane surface, and at the periphery the maximum liquid release velocity


- 33 -

possible is attained. The maximum release velocity is the resultant of radial and tangential

components acquired by the liquid. Alternatively slippage can be reduced by increasing

friction between the liquid and the rotating surface. This is often done by feeding liquid on to

the lower surface of a disc shaped as an inverted plate, bowl or cup. As the liquid is flung

outwards due to centrifugal force, the liquid Film is pressed against the disc surface. Both

techniques are used to handle large feed rates, although the vaned designs (atomizer wheel)

are selected in cases where fine sprays are required. However, many spray-dryer operations

call for large particle sizes, and thus the inverted disc types enjoy wide usage.

Smooth flat vaneless discs (with feed on the top surface) are rarely used in spray-drying.

Vaneless discs of the plate and cup type are also not discussed. Atomizer wheel designs are

the most widely applied of rotary atomizers and are the subject of this work.

Wheel Atomization (Atomizer Wheels)

At low speeds and feed rates, viscous and surface-tension forces predominate to give direct

droplet formation. For intermediate speeds, the disintegration of liquid ligaments extending

out from the edge of the vane is by centrifugal and to a lesser extent by gravitational forces. In

the commercial range of conditions (high liquid flows at high wheel peripheral speeds), liquid

disintegration occurs right at the wheel edge by frictional effects between air and the liquid

surface as liquid emerges as a thin Film from the vane. The mechanism does not lend itself to

the formation of homogeneous spray, although sprays of small droplet sizes can be produced.

Increasing the viscosity and surface tension of the liquid acts to increase the uniformity of the

spray, but at the expense of a low mean droplet size. However, for general operational

circumstances in spray drying, adjustment to the feed liquid properties is not possible or

desirable.

• Flow over a Vaned Wheel

Liquid fed on to a wheel moves across the surface until contained by the rotating vane. Liquid

flows outwards under the influence of centrifugal force and spreads over the vane, wetting the

vane surface as a thin Film. At very low liquid vane loadings, the thin film can split into

streams.


- 34 -

No liquid slippage occurs on a wheel once liquid has contacted the vane. The vanes,

whether radial or curved, prevent transverse flow of liquid over the surface.

Droplet travel from a wheel is shown in Figure 2.10. The liquid film on leaving the vane

edge has radial (yx) and tangential (yz) velocities giving a resultant component (yw). The

angle of release is less than 45° to the wheel edge. Early work suggested for commercial

atomizer wheels, the radial velocity component is much smaller than the tangential, and

release velocity approximates to the peripheral wheel velocity, and at an angle of release

approaching the tangent to the wheel edge as indicated by equations (2.18)-(2.21):

- Radial velocity (Vr) (for industrial conditions where liquid acceleration along vane has

ceased upon reaching wheel edge).

(2.18)

where ρ1 = density (kg/m3), d = diameter (m), Q = feed rate (m3/h), N = speed of

rotation (r.p.m.), μ = viscosity (cP), n = number of vanes, h = height of vanes.

- Tangential velocity (Vt)

The vanes prevent slippage and the liquid acquires the peripheral velocity of the wheel

on release

(2.19)

Figure 2.10 Liquid flow to and from edge of atomizer wheel


- 35 -

- Resultant release velocity (Vres)

The resultant release velocity is the square root of the sum of the squares of the radial

and tangential components.

(2.20)

- Angle of liquid release (α)

The angle of liquid release follows from equation (2.20) by basic geometry.

(2.21)

In practice it is very small, and Vres approximates to the peripheral speed of the atomizer

wheel.

However, today's mathematical analysis and ability to view liquid conditions at the wheel

edge indicates radial velocities are much larger and related to wheel design.

2.4 Spray-Air Contact (Mixing and Flow)

Introduction

The prediction and control of spray-air movement within the spray-drying chamber are

important requirements for dryer design and performance. The manner in which the spray, on

leaving the atomizer, combines with the drying air determines the rate and extent of drying.

The resulting spray-air movement determines the time each droplet remains in the chamber.

Drying-chamber and air-disperser design must create a flow pattern which prevents the

deposition of partially dried product at the wall and on the atomizer. Wall deposits are caused

by droplets travelling too rapidly to the wall, thereby not allowing sufficient drying time to

elapse. Atomizer deposits result from local eddies. Eddies cause re-entry of dried particles

back into the hottest air regions of the dryer, and even into the air disperser where particles

become scorched, leading to contamination of the finished dried product.

Much has still to be understood about how operating and design variables can best be

combined to produce the spray-air movement from optimum drying conditions. The range of

dryer designs and the unknown in interdependence of the variables prevents a general relation

being formed to express their combined effect on spray-air movement. General reviews of

spray-air movement in spray dryers suggest that fine sprays can be considered to move under


- 36 -

the complete influence of the air flow throughout most of the dryer volume. Once small

droplets have left the atomizer, they attain the velocity of the surrounding air in the proximity

of the atomizer. How far droplets travel until fully influenced by the air flow depends upon

the droplet size, shape and density. However, few data are available relating operating

variables (air rate, feed rate, atomizer operation and location) to the distance small droplets

travel prior to attaining local air velocities. Coarse sprays are more independent of the air

flow. Droplet/particle size form and density determine how the product falls through the air.

The amount of published data on spray-air movement is limited and is applicable

mainly to small dryers. Air-flow determination depends upon a suitable experimental

technique, and few are considered successful. Any probing device automatically interferes

with normal flow conditions, especially in small-diameter dryers. Data for small-diameter

dryers have mostly been obtained from visual observations of light powder suspended in air

streams. Powder movement was then considered representative of conditions existing during

dryer operation.

The common approach to droplet movement is to calculate droplet trajectory from the

atomizer to the chamber wall using stepwise methods. Air flow data are required and these are

either predicted or obtained experimentally in equipment having analogous flow

characteristics. Air-velocity measurements in pilot-plant-size dryers have been conducted

using anemometer methods. In industrial-size dryers gas tracer techniques and holography

have been shown possible. Recent published work on flow patterns includes counter-current

pilot-plant dryer studies using gas tracer techniques and tall-form tower dryers.

Spray-air movement is classified according to the dryer chamber layout, i.e. as a co-

current, counter-current or mixed-flow dryer with associated atomizer. The designation of co-

current, counter-current or mixed flow to spray-air movement in a dryer is in fact not a true

representation of actual conditions. For the case of a co-current flow dryer with rotary

atomizer the spray leaves the atomizer to be contacted obliquely by the entering drying air.

Furthermore, eddies within the drying chamber, around the air disperser, and at the walls

create local areas of counter-current flow between spray and air.

Spray-air movement is governed by air-disperser location and design, atomizer location

and operation, spray-droplet behaviour when drying, chamber dimensions, and method of

powder-air discharge. However, it is the air disperser that determines spray-air movement

during the critical first period of droplet drying. Correct air dispersing stands out as an

essential for obtaining a successful spray-dryer operation.


- 37 -

Figure 7.1 shows three arrangements in co-current-flow dryers with rotary atomizers. In

Figure 2.11 a the air enters directly above the atomizer wheel. The air flow is divided within

the air disperser to give (a) rotational flow around the atomizer and (b) a local flow down

around the wheel edge to depress the spray into an 'umbrella' cloud formation. This air

disperser design gives a good control over radial droplet trajectory, although precise

adjustment of the air-disperser vanes is required to prevent pronounced recirculation of air

into the top corners of the chamber. Alternative air-disperser designs shown are (1) tangential

air entry at the top corners of the chamber, giving high wall velocities (Figure 2.11b), and (2)

the entry of air vertically upwards underneath the wheel (Figure 2.11c). Introduction of air

under the atomizer wheel is particularly advantageous in drying operations involving very

high inlet air temperatures, i.e. of the order 750-850 °C. Hot air can be readily introduced into

the drying chamber without resorting to refractory lined ductwork. The atomizer drive and

chamber roof are also protected, as neither is directly exposed to the high air temperature.

Atomizer cooling and roof construction of the drying chamber are simplified. The air

disperser in Figure 7.1c is a vaned apex placed on top of an air-cooled duct. The vanes create

strong circulating air flow around the atomizers. Without the vaned apex even higher

temperatures can be used (1200 °C) (i.e. riser duct disperser).

Figure 2.11 Air disperser for rotary atomizers in co-current flow dryers (a) Ceiling air disperser, volute inlet for hot air. Air rotation controlled by angled vanes.

Spray pattern controlled by straightening cone. Rotary air flow in chamber. (b) Ceiling air disperser, volute inlet for hot air. Tangential inlet for hot/cool air around

walls. Rotary air flow in chamber. (c) Central air disperser, air rotation controlled by angled vanes. Rotary air flow in

chamber.

(b)(a)

(c)


- 38 -

The initial contact between air and spray can be co-contact (i.e. atomizer wheel and air

rotation in the same direction) or counter-contact (rotations in the opposite direction). A more

controlled air flow results from co-contacting, but the greater mixing created by counter-

contact enables coarser sprays to be dried per given chamber size. Wall impingement of

product often decreases, as counter-contact acts to further reduce the radial trajectory of the

spray. This increases fractionally the time the spray droplets remain suspended in the air flow.

Such advantage is offset to a degree by the greater tendency for deposit formation on the

surfaces of the atomizer.

General Principles

The manner of spray-air flow characterizes the droplet population throughout the chamber

and bears important relation to the evaporation rate of the spray, the optimum residence time

of droplets in a hot atmosphere and the extent of wall deposit formation.

Whatever the mode of atomization, each droplet in the resulting spray is ejected at a

velocity greatly in excess of the air velocities within the chamber However, droplet kinetic

energy is soon dissipated by air friction, and direct penetration is limited to short distances

from the atomizer. In industrial-sized dryers, wall deposits are rarely caused by direct throw

of product to the wall unless atomization has been incomplete. The droplets become

influenced by the surrounding air flow, and movement is governed by the design of the ail

disperser. Any attempt to calculate chamber dimension requirements is dependent on droplet

path data and rate of drying.

Droplet travel in cylindrical (vertical) spray dryers from the time of release from the

atomizer to the point of contact with the chamber wall can be regarded as one- or two-

dimensional motion from a nozzle atomizer operating in a non-rotary air flow, and as three-

dimensional motion from a rotary atomizer operating in a rotary air flow.

It is possible to derive theoretical correlations to represent droplet motion. The simplest

correlations consider droplet mass and sphericity constant, but as droplet mass and shape

change during passage through the dryer, actual travel is far from that predicted. Droplet

motion under evaporating conditions must be considered by taking into account factors which

affect droplet trajectory and heat and mass transfer. This leads to complex correlations.

Certain assumptions to the spray drying process are made to render these correlations more

workable. These include (a) heat transfer between droplet and air is by forced convection, (b)

droplets constituting the spray are spherical, (c) spray is homogeneous, (d) the chance of


- 39 -

coalescence and break-up of droplets during trajectory is disregarded, (e) for dryers with

rotary air flow, the air proceeds through the dryer as a perfect cyclone (velocity is constant in

the axial direction but varies in the tangential direction), (f) for dryers with non-rotary air flow

the air proceeds through the dryer in parallel streamline flow.

For droplets moving relative to air there is a resisting force due to friction between the

air and the surface of the droplets (friction drag) and a drag force related to droplet shape. The

resulting relative movement between droplet and air is dependent upon the variant in the

resisting force and is controlled by the extent of change of the droplet's physical properties

during evaporation.

The basic principles of spray movement in spray dryers can be illustrated with reference

to a single droplet. At any given instant of droplet travel in a vertical plane the forces acting

on the droplet can be expressed as

(2.22)

where D = droplet diameter, Cd =drag coefficient, ρw, ρa = densities of droplet and air, A =

area (= πD2/4 for spherical droplets), Vrel = droplet velocity relative to air.

When gravitational forces and drag forces are equal, droplet acceleration becomes zero and

the droplet velocity is constant. The constant velocity is termed the terminal settling velocity.

Under these conditions the total resisting force (F) can be expressed in terms of particle size,

air density and drag coefficient:

(2.22)

The value of the drag coefficient is dependent upon the droplet Reynolds number

(Re)=(DVρa/ μa), as shown in Table 2.1.

Table 2.1 Relation between Reynolds number (Re) and drag coefficient (CD) (for spherical droplets)


- 40 -

Droplet Trajectory Characteristics From Rotary Atomizers (Atomizer Wheels)

Droplet trajectory, following horizontal release from the atomizer, is affected initially by the

air swirl around the wheel (caused by wheel rotation) and finally by the drying air flow. In

small test dryers, wheel rotation contributes greatly to the overall flow pattern and droplet

trajectory in the chamber but this is not so in industrial dryers as the influence of wheel

rotation declines rapidly with radial distance. Air flow and droplet trajectory are governed

primarily by the air disperser.

The radial travel of droplets depends upon wheel design and speed, feed rate, air-

disperser design and location. The effect of the operating variables (atomizer dimensions and

speed, feed rate) on radial trajectory of sprays has been studied by various workers. Relations

are available for expressing radial trajectory distance expressed as a maximum distance or

distance a given percentage of spray falls a given distance under the atomizer wheel. These

relations are of limited interest to industrial conditions as they neglect the effect of the

containing wall, relate only to the experimental air- disperser design used in the study, and do

not consider reduction in droplet density during evaporation or the effect of drying-air flow.

Comparison between predicted trajectory and actual dryer performance indicates predicted

trajectories to be a conservative estimate of droplet penetration.

Droplet Movement in Drying Chambers

Droplet movement in the drying chamber consists of (1) droplet release from the atomizer, (2)

droplet deceleration and (3) free falling motion or motion under the influence of the drying air

flow in the chamber.

Droplet Release Velocity

Droplet release from rotary and nozzle atomizers is described in previous chapter.

Droplet Deceleration

Droplets leaving an atomizer at velocities in excess of the surrounding air decelerate rapidly

due to frictional forces acting on the droplet surfaces. The rate of deceleration determines the

penetration of droplets through the air surrounding the atomizer. According to Masters (1985)

drew up deceleration equations for single droplets, discharged into still-air conditions, with


- 41 -

gravity neglected. Once the droplet has been discharged from the atomizer, the droplet

velocity decreases, and the droplet passes first through a turbulent, then a semi-turbulent to a

laminar-flow region. If the droplet diameter is large, a laminar flow might not be experienced,

due to a high terminal velocity.

Deceleration in each flow region is given by

(2.24a)

(2.24b)

(2.24c)

Integration of equations (2.24a, b, c) yields the deceleration time and droplet penetration

during each flow region. The above equations are often quoted but they have limited practical

use, owing to the simple system they describe.

More precise methods (though still having important practical limitations) are available

to describe droplet deceleration from rotary atomizers. Interested readers are referred to

Masters (1985).

Terminal Velocity (Spherical Droplets)

Terminal velocity conditions occur when the force of gravity acting on the droplet is counter-

balanced by the air frictional forces. The left-hand side of equation (2.22) becomes zero, and

equating the two forces

(2.25)

The terminal velocity Vf is expressed by

(2.26)

When values of Vf correspond to a droplet Reynolds number less than 0.2, air friction (drag)

forces (F) can be expressed:

(2.27)


- 42 -

The terminal velocity in terms of measurable variables

(2.28)

When droplet motion at terminal velocity corresponds to a Reynolds number within the range

0.2-500, the air frictional (drag) forces (F) equal

(2.29)

Droplets formed during spray drying rarely feature sizes and densities to give terminal

velocity at high Reynolds numbers. Terminal velocities can well be within the semi-turbulent

flow region, in which case equation (2.30) may be applied:

(2.30)

where K = 0.225.

Terminal velocities of droplets in spray-drying chambers deviate from those in the ideal

conditions assumed above. Interested readers are referred to Masters (1985).

2.5 Drying of Droplets/Sprays

Introduction

The evaporation of volatiles (usually water) from a spray involves simultaneous heat and

mass transfer. With the contact between atomized droplets and drying air, heat is transferred

by convection from the air to the droplets, and converted to latent heat during moisture

evaporation. The vaporized moisture is transported into the air by convection through the

boundary layer that surrounds each droplet. The velocity of droplets leaving the atomizer

differs greatly from the velocity of the surrounding air and, simultaneously with heat and

mass transfer, there is an exchange of momentum between the droplets and surroundings.

The rate of heat and mass transfer is a function of temperature, humidity and transport

properties of the air surrounding each droplet. It is also a function of droplet diameter and

relative velocity between droplet and air. Models to describe the droplet drying are to be

found in many publications on drying. Drying principles, factors controlling drying rates and

drying characteristics of droplets have already been introduced (p. 26).


- 43 -

The evaporation history for spray droplets commences with moisture removal at near

constant rate, constant droplet surface temperature and constant partial pressure of vapour at

droplet surface (first period of drying) followed by a decline in removal rate until drying is

complete (second or falling rate drying period). The rate begins to fall off once the droplet

moisture content is reduced to a level known as the critical moisture content.

The majority of droplet moisture is removed during the first period of drying. Moisture

migrates from the droplet interior at a rate great enough to maintain surface saturation. The

wet-bulb temperature represents the droplet temperature. The evaporation rate can be

considered constant, although this is not strictly true. In the spray-drying operation droplet

evaporation commences with the immediate spray-air contact, and the rapid transfer of

moisture into the air is accompanied by lowering of the air temperature. Any decrease in air

temperature reduces the driving force for heat transfer, and the evaporation rate can begin to

fall off even though surface saturation is being maintained. However, it is common to refer to

the initial phase of droplet drying as the constant-rate drying period.

Moisture migration lowers the moisture level within the droplet and a point is

eventually reached when the rate of migration to the surface becomes the limiting factor in the

drying rate. Surface wetness can no longer be maintained, and a falling-off in drying rate

results. The rate of moisture migration is affected by the temperature of the surrounding air.

If the air temperature is so high that the temperature driving forces permit evaporation

to commence at a rate at which migration of moisture cannot maintain surface wetness from

the start, the droplet will experience little constant-rate drying. A dried layer will form

instantaneously at the droplet surface.

This dried layer presents a formidable barrier to moisture transfer, and acts to retain

moisture within the droplet. Thus inlet drying temperatures can readily influence the dried-

product characteristics. Increase in inlet air temperature often results in a rapid formation of

the dried outer layer. This submits the droplet to higher surface temperature than when lower

inlet air temperatures are used. A lower air temperature would mean a lower initial drying

rate, with the maintenance of a surface temperature (equivalent to the wet-bulb temperature)

over longer time periods.

The actual evaporation time for droplets contacted at a fixed air temperature depends

upon droplet shape, chemical composition, physical structure and solids concentration. The

actual time is the sum of the constant rate and the falling-rate periods until the desired

moisture level is reached.


- 44 -

The general drying characteristics are illustrated by a drying-rate curve, Figure 2.12.

In phase AB, the drying rate is established immediately the droplet contacts the drying

air. There follows a slight increase in droplet surface temperature, and the drying rate increa-

ses in the milliseconds required for heat transfer across the droplet-air interface to establish

equilibrium.

In phase BC, conditions of dynamic equilibrium are represented. Drying proceeds at

constant rate, which is the highest rate achieved during the entire droplet evaporation history.

Droplet surface is maintained saturated by adequate migration of moisture from within the

droplet to the surface.

In phase CD, at point C, the critical point is reached and moisture within the droplet can

no longer maintain surface saturation. Drying rate begins to fall, initiating the falling-rate

drying period. This period can form more than one phase, if local areas of wetness remain on

the droplet surface. Phase CD continues until no areas of wetness remain.

In phase DE, resistance to mass transfer is wholly in the solid layer. Evaporation conti-

nues at a decreasing rate until the droplet acquires a moisture content in equilibrium with the

surrounding air. Approach to the equilibrium moisture content E is slow. In the spray-drying

operation, product is usually removed from the dryer before the equilibrium moisture content

is reached. Droplet temperature rises throughout the two phases of the falling-rate period.

Figure 8.1 is schematic. Drying curves in reality have no sharply defined points. Some

of the drying zones as shown may not even occur. For example, in the spray drying of

products that are heat-sensitive, the applied air temperatures are low and the phase AB can

well extend until the critical point is reached. The drying in this case can be said not to feature

the customary constant-rate period.

Figure 2.12 Drying rate curve


- 45 -

Evaporation of Pure Liquid Droplets

Conclusions drawn from studies on the evaporation of pure liquid droplets form the basis for

understanding the spray-drying evaporation mechanisms. The ideal case of evaporation of

single pure liquid droplets can be modified to deal with the deviations in the basic theory

necessary to include the presence of dissolved or insoluble solids.

The extent of moisture removal from a droplet present in a spray dryer depends upon

the mechanism governing the rate of evaporation and the residence time during which

evaporation takes place. The residence time results from the spray-air movement set up in the

drying chamber. For the greater part of droplet travel in the chamber, the droplets are

completely influenced by the air flow, and the relative velocity between droplet and air is very

low. The boundary-layer theory states that evaporation rates for a droplet moving with zero

relative velocity is identical to evaporation in still-air conditions. Thus the mechanism of

evaporation for still-air, based upon boundary-layer theory, can be justifiably applied to many

spray-drying conditions.

In the case of droplets moving relative to the surrounding air, the resulting flow

conditions around the moving droplet influence the evaporation rate. In calculating transfer

rates, these flow conditions plus the properties of the droplet are represented in combinations

of the dimensionless groups indicated in Table 2.2.

Table 2.2 Dimensionless groups


- 46 -

Evaporation of Single Droplets

(a) Droplet Evaporation under Negligible Relative Velocity Conditions

Experimental data of Marshall (1955) have shown that heat transfer to a spherical droplet in

still air can be expressed as

Nu = 2.0 (2.31a)

Likewise has it been established that the mass transfer from a spherical droplet in still air can

be expressed as

Sh = 2.0 (2.31a)

following the heat and mass transfer analogy.

For pure liquid droplets, equation (2.31 ) predicts that the rate of change of the droplet surface

will remain constant during evaporation.

The evaporation rate (dW/dt) in terms of mass transfer can be expressed from equations (2.12)

and (2.31), by substituting

(2.32)

where PwB = water vapour pressure at temperature of saturated droplet surface, pw partial

pressure of water vapour in surrounding air.

The evaporation rate in terms of heat transfer can be expressed from equations (2.12) and

(2.31) by substituting hc = 2KD/D

(2.33)

where Ta = air temperature, Ts = droplet surface temperature.

Conclusions can be drawn from equations (2.32) and (2.33) as to the characteristics of pure

liquid droplet evaporation. (a) The evaporation rate is proportional to diameter and not

surface, (b) Absolute evaporation rates from large droplets are greater than from small

droplets. (c) Evaporation is proportional to the square of initial diameter.

The evaporation time can be deduced from a heat balance over a spray droplet. From equation

(3.7)


- 47 -

Now

Therefore

(2.44)

The term -(λρ1/2ΔT) remains constant during the majority of droplet residence time in the

dryer, and integration of equation (2.44) yields the evaporation time (t) (D0 = initial droplet

diameter).

(2.45)

ΔT is the mean temperature difference between the droplet surface and surrounding air. It is

best to apply the logarithmic mean difference (LMTD) as defined by

(2.46)

ΔT0 and ΔT1 are the temperature differences between droplet and air at the beginning and end

of the evaporation period.

Equation (2.45) can further be simplified where for negligible relative velocity conditions hc =

2KD/D (equation (2.31))

(2.47)


- 48 -

(b) Droplet Evaporation under Relative Velocity Conditions

Evaporation rates increase with increase in relative velocity between droplet and air due to the

additional evaporation caused by the convection in the boundary layer around the droplet. The

total transfer coefficients for the transfer from a spherical droplet can be expressed in terms of

the dimensionless groups where for mass transfer

(2.48)

and for heat transfer

(2.49)

Equations (2.48) and (2.49) reduce to equation (2.31) when the relative velocity is zero. There

has been much discussion over the power values of (x), (y), (x’), (y’), and constants K1, K2.

The value of x accepted generally for evaporation conditions in spray drying is 0.5. This is

applicable to a Reynolds number range between 100 and 1000. Motion of small droplets in

this range occurs only in the first fractions of a second of travel, and thus much of the

evaporation occurs at droplet Reynolds number far below 100. The form most widely applied

for equations (8.9) and (8.10) is the Ranz and Marshall (1952) equation:

(2.50a)

(2.50b)

When applying the above equations, certain limitations must be taken into consideration:

- Steady-state drag coefficients apply. It is convenient to apply the drag equations at steady

state to the case of accelerating or decelerating droplets. In reality the drag coefficients (CD)

for accelerated motion can be 20-60 % higher than values at constant velocity.

- Heat transfer to evaporated moisture is neglected. For drying conditions at high temperatures,

much heat is taken up in heating the vapour as it is transported outwards from the droplet surface.

- Droplet internal structure is stable. Any internal circulation, oscillation or surface distortion

of the droplet will increase heat and mass transfer rates due to variations in the thickness of

the boundary layer.

- Droplets are stable in air flow. Droplets in a spray dryer are often subjected to a swirling air

flow, which causes in turn droplet rotation, reduces boundary layer, increased evaporation rates.


- 49 -

(c) Evaporation under High Air-temperature Conditions

For droplet evaporation at high air temperatures heat transfer to the droplets no longer solely

provides the latent heat of vaporization. Heat is also transferred to the vapours moving away

from the droplet interface into the air flow. This can lead to decisive errors when calculating

evaporation times by the equations mentioned above. The evaporation time could well be

invalid because the evaporation is conducted at high temperature, and here the assumptions

for the computation are no longer relevant.

The effect of high temperature on evaporation mechanism has been analysed mathematically

by Marshall (1955). For an evaporating droplet, the differential equation for conduction of

heat through the surrounding vapour layer can be drawn up. Interested readers are referred to

Masters (1985).

Evaporation of Sprays of Pure Liquid Droplets

The evaporation characteristics of droplets within a spray differ from evaporation

characteristics of single droplets. Although basic theory applies in both cases, it is difficult to

apply this theory to the case of a large number of droplets evaporating close to the atomizer.

Any analysis of spray evaporation depends upon defining the spray in terms of a

representative mean diameter and size distribution, the relative velocity between droplet and

its surrounding air, droplet trajectory and the number of droplets present at any given time per

given volume of drying air. Furthermore there are grave difficulties in determining these

factors in the vicinity of the atomizer and spray evaporation data are subsequently limited. For

sprays moving at low velocities in low-velocity air (counter-current flow dryers) or at low

relative velocities with high-velocity air (co-current flow dryers), the following points can be

made:

(1) Spray evaporation causes reduction in air temperature and evaporation rate decrease.

(2) Sprays of wide distribution evaporate initially more quickly than more homogeneous

sprays of the same chosen mean diameter. The increased evaporation is due to the smaller

droplet sizes in the distribution. The larger droplets evaporate much slower, and thus the

overall spray evaporation time is longer.

(3) No mean diameter parameter can adequately represent the droplets during evaporation of spray.


- 50 -

(4) The size distribution gives the best representation of droplets during the evaporation of spray.

(5) Size distribution of droplets in a spray changes during evaporation.

(6) For homogeneous sprays, the droplet diameter parameter decreases during evaporation.

(7) For non-homogeneous sprays the droplet mean diameter generally shows an initial

increase prior to decrease until completion of evaporation.

Evaporation of sprays of which the droplets move at pronounced relative velocities (for

example, coarse nozzle atomization in co-current flow) shows additional features:

(1) The droplets travel greater distances before a given fraction is evaporated.

(2) Influence of relative velocity between droplet and air is more significant on evaporation

rates at higher release velocities from the atomizer and at higher drying temperatures.

(3) For droplet release from atomizers at high velocities, the relative error of neglecting

droplet velocity is greatest for the smallest droplet sizes in the spray distribution. Small

droplets evaporate virtually instantaneously, and a large proportion of the evaporation is

accomplished in the period of droplet deceleration.

Important features of any spray evaporation history are as follows:

(1) The majority of spray evaporation is completed in a short time interval. For example, 90%

of the evaporation is completed during the first 1.5 s.

(2) Rapid decrease in air temperature accompanies the evaporation.

(3) The mean size of the pure liquid spray increases with time due to the rapid completion of

evaporation of the smaller droplet sizes in the spray. In actual spray-drying operations, the

variation of mean size with time will depend upon the solid content in the spray droplets and

whether drying characteristics lead to particle expansion or retraction during evaporation.

Evaporation of Droplets Containing Insoluble Solids

Feeds of insoluble solids form slurries and pastes (hereafter referred to as suspensions). There

are negligible vapour-pressure lowering effects in droplets containing insoluble solids and the

temperature can be put equal to the wet bulb temperature of pure liquid droplets during the

first period of drying.


- 51 -

Total drying times of droplets containing insoluble solids can be evaluated by dealing

separately with the two drying periods. Drying times for the first period of drying are short

compared with the following second period, but in calculations where the first period is not

considered negligible, Ranz and Marshall (1952) have reported equation (2.47) applicable,

where Kd is the thermal conductivity of the evaporating liquid.

The drying time for the falling-rate drying period cannot be reliably expressed in equation

form. It depends upon the nature of the solid phase. Ranz and Marshall (1952) however, have

proposed a relationship in terms of the critical moisture content (Wc),

(2.51)

where W2 = final moisture content of the dried particle, Kd thermal conductivity of drying

medium.

For drying of droplets at low Reynolds number and negligible vapour pressure effects, the

total time according to Marshall (1955) can be expressed by adding equations (2.47) and

(2.51).

(2.52)

Equation (8.47) represents the evaporation history in its most simplified case. However,

calculated values give close agreement with actual evaporation times in many instances and

thus the equation is useful for obtaining data for spray-dryer chamber design. For a known

flow pattern within the chamber, the minimum residence time for spray evaporation can be

calculated, i.e. the time to evaporate the droplets to a state of dryness for prevention of semi-

wet product build-up on the dryer walls.

In applying equation (2.52) the thermal conductivity is calculated at the mean film

temperature surrounding the evaporating droplet. The film temperature can conveniently be

taken as the average between the exhaust drying air temperature and the droplet surface

temperature. The droplet surface temperature is the adiabatic saturation temperature of the

suspension spray. The surrounding air temperature at the end of the first period of drying is

usually unknown. The driving force (ΔT) over the entire period is most conveniently taken as

the logarithmic mean temperature difference between the inlet air temperature and the slurry

feed temperature, and the exhaust air temperature and the droplet surface temperature at the

critical point. The driving force (ΔT) for the falling-rate period can be taken as the difference


- 52 -

between the exhaust air temperature and the droplet surface temperature at the critical point

although the surface temperature will rise during the falling-rate period. Alternatively air

temperature at the droplet critical point and droplet temperature rise during the falling-rate

period can be assumed. The logarithmic mean temperature difference is applied to both

periods of drying. The droplet diameter at the critical point (Dc) is usually an unknown value.

Ideally this value requires data on the evaporation characteristics of the suspension droplet to

permit determination of droplet size change before solids form at the surface. In the absence

of such data, the methods for determination of evaporation times for droplets containing

dissolved solids can be applied. The factor is taken to express the percentage decrease in

droplet diameter during the first period of drying. Droplet size change is then considered

negligible during the second period of drying.


- 53 -

3 PHYSICAL-MATHEMATICAL MODELING OF SPRAY DRYING

3.1 Introduction

What is Computational Fluid Dynamics?

Computational Fluid Dynamics (CFD) is a computer-based tool for simulating the behaviour

of systems involving fluid flow, heat transfer, and other related physical processes. It works

by solving the equations of fluid flow (in a special form) over a region of interest, with

specified (known) conditions on the boundary of that region.

The History of CFD

Computers have been used to solve fluid flow problems for many years. Numerous programs

have been written to solve either specific problems, or specific classes of problems. From the

mid-1970’s, the complex mathematics required to generalize the algorithms began to be

understood, and general purpose CFD solvers were developed.

These began to appear in the early 1980’s and required what were then very powerful

computers, as well as an in-depth knowledge of fluid dynamics, and large amounts of time to

set up simulations. Consequently, CFD was a tool used almost exclusively in research.

Recent advances in computing power, together with powerful graphics and interactive

3D manipulation of models have made the process of creating a CFD model and analyzing

results much less labour intensive, reducing time and, hence, cost. Advanced solvers contain

algorithms which enable robust solutions of the flow field in a reasonable time.

As a result of these factors, Computational Fluid Dynamics is now an established

industrial design tool, helping to reduce design time scales and improve processes throughout

the engineering world. CFD provides a cost-effective and accurate alternative to scale model

testing, with variations on the simulation being performed quickly, offering obvious

advantages.


- 54 -

The Mathematics of CFD

The set of equations which describe the processes of momentum, heat and mass transfer are

known as the Navier-Stokes equations. These partial differential equations were derived in the

early nineteenth century and have no known general analytical solution but can be discretized

and solved numerically.

Equations describing other processes, such as combustion, can also be solved in

conjunction with the Navier-Stokes equations. Often, an approximating model is used to

derive these additional equations, turbulence models being a particularly important example.

There are a number of different solution methods which are used in CFD codes. The

most common, and the one on which ANSYS CFX is based, is known as the finite volume

technique.

In this technique, the region of interest is divided into small sub-regions, called control

volumes. The equations are discretized and solved iteratively for each control volume. As a

result, an approximation of the value of each variable at specific points throughout the domain

can be obtained. In this way, one derives a full picture of the behaviour of the flow.

3.2 Modelling of Eulerian Phase

This chapter describes the mathematical equations used to model the physics of fluid flow,

heat and mass transfer in ANSYS CFX for single-phase and multi-component flow without

combustion or radiation.

Governing Equations

The cornerstone of computational fluid dynamics are the fundamental governing

equations of fluid dynamics - the continuity, momentum and energy equations. These

equations speak physics. They are the mathematical statements of three fundamental physical

principles upon which all of fluid dynamics is based:

• Mass is conserved;

• Momentum is conserved, i.e., F = ma (Newton's second law);

• Energy is conserved.


- 55 -

In obtaining the basic equations of fluid motion, the following philosophy is always

followed:

• Choose the appropriate fundamental physical principles from the laws of physics

(stated above).

• Apply these physical principles to a suitable model of the flow.

• From this application, extract the mathematical equations which embody such

physical principles

The definition of a suitable model of the flow is not a trivial consideration. In order to

apply the fundamental physical principles to a moving continuum fluid one of the two

following models have to be applied, the finite control volume model and the infinitesimal

fluid element model.

Based on these, governing equations can be obtained in various different forms. For

most fluid dynamics theory, the particular form of the equations makes little difference.

However, for CFD, the use of the equations in one form may lead to success, whereas the use

of an alternate form may result in oscillations (wiggles) in the numerical results, or even

instability. Therefore, in the world of CFD, the various forms of the equations are of vital

interest. Namely, experience in using CFD has shown that the conservation form of the

governing equations should be used. Complete derivation of governing equations in all

different forms can be found in

Governing Transport Equations

The set of equations solved by ANSYS CFX are the unsteady Navier-Stokes equations in

their conservation form. For all the following equations, static (thermodynamic) quantities are

given unless otherwise stated.

In this section, the instantaneous equation of mass, momentum, and energy conservation

are presented. For turbulent flows, the instantaneous equations are averaged leading to

additional terms. These terms, together with models for them, are discussed in chapter

Turbulence and Wall Function Theory.

The instantaneous equations of mass, momentum and energy conservation can be

written as follows in a stationary frame:


- 56 -

• The Continuity Equation

(3.1)

• The Momentum Equations

(3.2)

Where the stress tensor, , is related to the strain rate by

(3.3)

• The Total Energy Equation

(3.4)

Where is the total enthalpy, related to the static enthalpy by:

(3.5)

The term represents the work due to viscous stresses and is called the

viscous work term. The term represents the work due to external momentum

sources and is currently neglected.

- The Thermal Energy Equation

An alternative form of the energy equation, which is suitable for low-speed flows, is

also available. To derive it, an equation is required for the mechanical energy .

(3.6)

The mechanical energy equation is derived by taking the dot product of with the

momentum equation (3.3):

(3.7)

Subtracting this equation from the total energy equation (3.4) yields the thermal

energy equation:

(3.8)


- 57 -

The term is always negative and is called the viscous dissipation. Finally,

the static enthalpy is related to the internal energy by:

(3.9)

So the equation(3.8) can be simplified to:

(3.10)

The term is currently neglected, although it may be non-zero for variable-

density flows. This is the thermal energy equation solved by ANSYS CFX.

Equations of State

In ANSYS CFX, the flow solver calculates pressure and static enthalpy. Finding density

requires that you select the thermal equation of state and finding temperature requires that you

select the constitutive relation. The selection of these two relationships is not necessarily

independent and is also a modeling choice.

The thermal equation of state is described as a function of both temperature and

pressure:

(3.11)

The specific heat capacity, , may also be described as a function of temperature and

pressure:

(3.12)

For an ideal gas, the density is defined by the ideal gas law and, in this case, can be a

function of only temperature:

(3.13)

When ρ or cp are also functions of an algebraic additional variable, in addition to

temperature and pressure, then changes of that additional variable are neglected in the

enthalpy and entropy functions. However, if that additional variable is itself only dependent

on pressure and temperature, then the effects will be correctly accounted for.


- 58 -

• Ideal Gas Equation of State

For an Ideal Gas, the relationship is described by the Ideal Gas Law:

(3.14)

where is the molecular weight of the gas, and is the universal gas constant.

Buoyancy

For buoyancy calculations, a source term is added to the momentum equations as follows:

(3.15)

The density difference is evaluated using either the full buoyancy model or the

Boussinesq model, depending on the physics.

When buoyancy is taken into account, the pressure in the momentum equation excludes

the hydrostatic gradient due to . This pressure is related to the absolute pressure as

follows:

(3.16)

where is a reference location. The reference location option can be set by the user, the

solver defaults it to the centroid of a pressure-specified boundary (if one exists), or to the

pressure reference location (if no pressure-specified boundary exists). Absolute pressure is

used to evaluate fluid properties which are functions of pressure.

Buoyancy is not taken into account in this work.

Multicomponent Flow

• Multicomponent Notation

Components are denoted using capital letters etc. In general, a quantity subscribed

with etc., refers to the value of the quantity corresponding to etc. For

example, the density of component would be written .


- 59 -

• Scalar Transport Equation

For a multicomponent fluid, scalar transport equations are solved for velocity, pressure,

temperature and other quantities of the fluid. However, additional equations must be solved to

determine how the components of the fluid are transported within the fluid.

The bulk motion of the fluid is modelled using single velocity, pressure, temperature

and turbulence fields. The influence of the multiple components is felt only through property

variation by virtue of differing properties for the various components. Each component has its'

own equation for conservation of mass. After Reynolds-averaging this equation can be

expressed in tensor notation as:

(3.17)

where:

is the mass-average density of fluid component in the mixture, i.e., the mass of the

component per unit volume,

is the mass-average velocity field,

is the mass-average velocity of fluid component ,

is the relative mass flux,

is the source term for component which includes the effects of chemical reactions.

Note that if all the equations (3.17) are summed over all components, the result is the

standard continuity equation,

(3.18)

since the reaction rates must sum to zero.

The relative mass flux term accounts for differential motion of the individual

components. This term may be modelled in a number of ways to include effects of

concentration gradients, a pressure gradient, external forces or a temperature gradient. Of


- 60 -

these possible sources of relative motion among the mixture components, the primary effect is

that of concentration gradient. The model for this effect gives rise to a diffusion-like term in

equation (3.17).

(3.19)

The molecular diffusion coefficient, , is assumed to be equal to , where is the

kinematic diffusivity.

Now, define the mass fraction of component to be:

(3.20)

Note that, by definition, the sum of component mass fractions over all components is 1.

Substituting equations (3.20) and (3.19) into equation (3.17), you have:

(3.21)

The turbulent scalar fluxes are modelled using the eddy dissipation assumption as:

(3.22)

where is the turbulent Schmidt number. Substituting equation (3.22) into equation (3.21)

and assuming now that you have mass weighted averages of :

(3.23)

where:

(3.24)

equation (3.23) is simply a general advection-diffusion equation of the form common to the

equations solved for each of the other dependent variables in the fluid flow calculation. Thus,

it is convenient to solve for the in order to establish the composition of the fluid mixture.


- 61 -

Constraint Equation for Components

The ANSYS CFX-Solver solves mass fraction equations (either transport equations or

algebraic equations) for all but one of the components. The remaining component is known as

the constraint component because its mass fraction is determined by the constraint equation:

(3.25)

The performance of the ANSYS CFX-Solver will not be affected by the choice of constraint

component.

Multicomponent Fluid Properties

The physical properties of general multicomponent mixtures are difficult to specify. The

default treatment in ANSYS CFX, Release 11.0 SP1 makes the assumption that the

components form an ideal mixture. An ideal mixture is a mixture of components such that the

properties of the mixture can be calculated directly from the properties of the components and

their proportions in the mixture. In this work all mixtures are assumed to be ideal.

Now consider a given volume of the fluid mixture. Let be the mass of component

present in this volume, then . The partial volume of component is defined to

be the volume, , that would be occupied by the given mass of the component at the same

(local) temperature and pressure as the mixture. The “thermodynamic density” of the

component, which results from evaluating its equation of state at the mixture temperature and

pressure, may be expressed as . Since the partial volumes of all components

must sum to the total volume, , you have:

(3.26)

or:

(3.27)


- 62 -

Thus, the mixture density may be calculated from the mass fractions and the

thermodynamic density of each component, which may require knowledge of the mixture

temperature and pressure, as well as an appropriate equation of state for each component.

Note carefully the distinction between and . The component mass density, , is

a quantity relating to the composition of the mixture, while the thermodynamic density, ,

is a material property of the component.

An arbitrary constitutive fluid property may be calculated from:

(3.28)

where is the property value for fluid component . While it may appear anomalous at first

sight that density does not conform to this expression, the specific volume (volume per unit

mass, i.e., ) does indeed conform, as can be seen by considering equation (3.28).

Properties that may be evaluated for a multicomponent mixture using equation (3.28) include

the laminar viscosity , the specific heat at constant volume , the specific heat at constant

pressure , and the laminar thermal conductivity .

• Energy Equation

Recall that equation (3.38)

(3.38)

is the Reynolds-averaged conservation equation for energy of a single component fluid.

Extending this equation for multicomponent fluids involves adding an additional diffusion

term to the energy equation:

(3.29)

For turbulent flow, this term is Reynolds-averaged giving:

(3.30)


- 63 -

This expression introduces several terms involving the fluctuations of diffusion coefficient,

component enthalpy and species concentration. Under certain circumstances, the fluctuating

components could be an important component of the diffusion process. However, adequate

models are not available within the existing turbulence model to account for these effects.

Thus, only the mean component is retained in the current version of ANSYS CFX.

The implemented conservation of energy equation for multicomponent fluids involves only

mean scalar components and is expressed as:

(3.31)

Multicomponent Energy Diffusion

The energy equation can be simplified in the special case that all species diffusivities are the

same and equal to thermal conductivity divided by specific heat capacity,

(3.32) This equation (3.32) holds when the Lewis number is unity for all components:

For turbulent flow, assuming for all components is usually just as good as the

common practice of using the fluid viscosity for the default component diffusivity (unity

Schmidt number, ). For , the energy equation (3.31) simplifies

exactly to the following:

(3.33)

This equation (3.33) has the advantage that only a single diffusion term needs to be

assembled, rather than one for each component plus one for heat conduction. This can

significantly reduce numerical cost, in particular when the fluid consists of a large number of

components.


- 64 -

Turbulence and Wall Function Theory

Turbulence consists of fluctuations in the flow field in time and space. It is a complex

process, mainly because it is three dimensional, unsteady and consists of many scales. It can

have a significant effect on the characteristics of the flow. Turbulence occurs when the inertia

forces in the fluid become significant compared to viscous forces, and is characterized by a

high Reynolds Number.

Turbulence Models

In principle, the Navier-Stokes equations describe both laminar and turbulent flows without

the need for additional information. However, turbulent flows at realistic Reynolds numbers

span a large range of turbulent length and time scales, and would generally involve length

scales much smaller than the smallest finite volume mesh, which can be practically used in a

numerical analysis. The Direct Numerical Simulation (DNS) of these flows would require

computing power which is many orders of magnitude higher than available in the foreseeable

future.

To enable the effects of turbulence to be predicted, a large amount of CFD research has

concentrated on methods which make use of turbulence models. Turbulence models have

been specifically developed to account for the effects of turbulence without recourse to a

prohibitively fine mesh and direct numerical simulation. Most turbulence models are

statistical turbulence model, as described below. The two exceptions to this in ANSYS CFX

are the Large Eddy Simulation model and the Detached Eddy Simulation model.

Statistical Turbulence Models and the Closure Problem

When looking at time scales much larger than the time scales of turbulent fluctuations,

turbulent flow could be said to exhibit average characteristics, with an additional time-

varying, fluctuating component. For example, a velocity component may be divided into an

average component, and a time varying component.

In general, turbulence models seek to modify the original unsteady Navier-Stokes equations

by the introduction of averaged and fluctuating quantities to produce the Reynolds Averaged

Navier-Stokes (RANS) equations. These equations represent the mean flow quantities only,

while modeling turbulence effects without a need for the resolution of the turbulent


- 65 -

fluctuations. All scales of the turbulence field are being modeled. Turbulence models based

on the RANS equations are known as Statistical Turbulence Models due to the statistical

averaging procedure employed to obtain the equations.

Simulation of the RANS equations greatly reduces the computational effort compared to a

Direct Numerical Simulation and is generally adopted for practical engineering calculations.

However, the averaging procedure introduces additional unknown terms containing products

of the fluctuating quantities, which act like additional stresses in the fluid. These terms, called

‘turbulent’ or ‘Reynolds’ stresses, are difficult to determine directly and so become further

unknowns.

The Reynolds (turbulent) stresses need to be modelled by additional equations of known

quantities in order to achieve “closure.” Closure implies that there is a sufficient number of

equations for all the unknowns, including the Reynolds-Stress tensor resulting from the

averaging procedure. The equations used to close the system define the type of turbulence

model.

Reynolds Averaged Navier-Stokes (RANS) Equations

As described above, turbulence models seek to solve a modified set of transport equations by

introducing averaged and fluctuating components. For example, a velocity may be divided

into an average component, , and a time varying component, .

(3.34)

The averaged component is given by:

(3.35)

where is a time scale that is large relative to the turbulent fluctuations, but small relative

to the time scale to which the equations are solved. For compressible flows, the averaging is

actually weighted by density (Favre-averaging), but for simplicity, the following presentation

assumes that density fluctuations are negligible.

For transient flows, the equations are ensemble-averaged. This allows the averaged equations

to be solved for transient simulations as well. The resulting equations are sometimes called

URANS (Unsteady Reynolds Averaged Navier-Stokes equations).


- 66 -

Substituting the averaged quantities into the original transport equations results in the

Reynolds-averaged equations given below. In the following equations, the bar is dropped for

averaged quantities, except for products of fluctuating quantities.

(3.36)

(3.37)

where is the molecular stress tensor.

The continuity equation has not been altered but the momentum and scalar transport equations

contain turbulent flux terms additional to the molecular diffusive fluxes. These are the

Reynolds stress, , and the Reynolds flux, . These terms arise from the non-linear

convective term in the un-averaged equations. They reflect the fact that convective transport

due to turbulent velocity fluctuations will act to enhance mixing over and above that caused

by thermal fluctuations at the molecular level. At high Reynolds numbers, turbulent velocity

fluctuations occur over a length scale much larger than the mean free path of thermal

fluctuations, so that the turbulent fluxes are much larger than the molecular fluxes.

The Reynolds-averaged energy equation is:

(3.38)

This equation contains an additional turbulence flux term, compared with the

instantaneous equation. The term in the equation is the viscous work term that can

be included by the user.

The mean total enthalpy is given by:

(3.39)

Note that the total enthalpy contains a contribution from the turbulent kinetic energy, , given by:

(3.40)

Similarly, the additional variable equation becomes

(3.41)


- 67 -

Turbulence models close the Reynolds-averaged equations by providing models for the

computation of the Reynolds stresses and Reynolds fluxes. ANSYS CFX models can be

broadly divided into two classes: eddy viscosity models and Reynolds stress models.

Eddy Viscosity Turbulence Models

One proposal suggests that turbulence consists of small eddies which are continuously

forming and dissipating, and in which the Reynolds stresses are assumed to be proportional to

mean velocity gradients. This defines an ‘eddy viscosity model.’

The eddy viscosity hypothesis assumes that the Reynolds stresses can be related to the mean

velocity gradients and Eddy (turbulent) Viscosity by the gradient diffusion hypothesis, in a

manner analogous to the relationship between the stress and strain tensors in laminar

Newtonian flow:

(3.42)

where is the eddy viscosity or turbulent viscosity. This has to be modelled.

Analogous to the eddy viscosity hypothesis is the eddy diffusivity hypothesis, which states

that the Reynolds fluxes of a scalar are linearly related to the mean scalar gradient:

(3.43)

where is the eddy diffusivity, and this has to be prescribed. The eddy diffusivity can be

written as:

(3.44)

where is the turbulent Prandtl number. Eddy diffusivities are then prescribed using the

turbulent Prandtl number.

The above equations can only express the turbulent fluctuation terms of functions of the mean

variables if the turbulent viscosity, , is known. Both the and two-equation

turbulence models provide this variable.

Subject to these hypotheses, the Reynolds averaged momentum and scalar transport equations

become:

(3.45)


- 68 -

where is the sum of the body forces, and is the effective viscosity defined by:

(3.46)

and is a modified pressure, defined by:

(3.47)

By default, the solver actually assumes that , but the contribution can be activated

by the user. In equation (3.45) above, there is a term which although included in

the fundamental form of the equation is neglected in the solver and thus not included here.

The Reynolds averaged energy equation becomes:

(3.48)

Note that although the transformation of the molecular diffusion term may be inexact if

enthalpy depends on variables other than temperature, the turbulent diffusion term is correct,

subject to the eddy diffusivity hypothesis. Moreover, as turbulent diffusion is usually much

larger than molecular diffusion, small errors in the latter can be ignored.

Similarly, the Reynolds averaged transport equation for additional variables (non-reacting

scalars) becomes:

(3.49)

Eddy viscosity models are distinguished by the manner in which they prescribe the eddy

viscosity and eddy diffusivity.

Two Equation Turbulence Models

Two-equation turbulence models are very widely used, as they offer a good compromise

between numerical effort and computational accuracy. Two-equation models are much more

sophisticated than the zero equation models. Both the velocity and length scale are solved

using separate transport equations (hence the term ‘two-equation’).


- 69 -

The and two-equation models use the gradient diffusion hypothesis to relate the

Reynolds stresses to the mean velocity gradients and the turbulent viscosity. The turbulent

viscosity is modelled as the product of a turbulent velocity and turbulent length scale. In two-

equation models, the turbulence velocity scale is computed from the turbulent kinetic energy,

which is provided from the solution of its transport equation. The turbulent length scale is

estimated from two properties of the turbulence field, usually the turbulent kinetic energy and

its dissipation rate. The dissipation rate of the turbulent kinetic energy is provided from the

solution of its transport equation.

The k-epsilon model in ANSYS CFX

is the turbulence kinetic energy and is defined as the variance of the fluctuations in velocity.

It has dimensions of ; for example, . is the turbulence eddy dissipation (the rate

at which the velocity fluctuations dissipate), and has dimensions of per unit time ; for

example, .

The model introduces two new variables into the system of equations. The continuity

equation is then:

(3.50)

and the momentum equation becomes:

(3.51)

where is the sum of body forces, is the effective viscosity accounting for turbulence,

and is the modified pressure as defined in equation (3.48) above.

The model, like the zero equation model, is based on the eddy viscosity concept, so that:

(3.52)

where is the turbulence viscosity. The model assumes that the turbulence viscosity is

linked to the turbulence kinetic energy and dissipation via the relation:

(3.53)

where is a constant.

The values of and come directly from the differential transport equations for the turbulence


- 70 -

kinetic energy and turbulence dissipation rate:

(3.54)

(3.55)

where are constants.

is the turbulence production due to viscous and buoyancy forces, which is modelled using:

(3.56)

For incompressible flow, is small and the second term on the right side of equation

(3.56) does not contribute significantly to the production. For compressible flow, is only

large in regions with high velocity divergence, such as at shocks.

The term in equation (3.56) is based on the “frozen stress” assumption. This prevents the

values of and becoming too large through shocks, a situation that becomes progressively

worse as the mesh is refined at shocks.

The RNG k-epsilon Model in ANSYS CFX

The RNG model is based on renormalization group analysis of the Navier-Stokes

equations. The transport equations for turbulence generation and dissipation are the same as

those for the standard model, but the model constants differ, and the constant is

replaced by the function .

The transport equation for turbulence dissipation becomes:

(3.57) where:

(3.58) and:

(3.59)


- 71 -

Modeling Flow Near the Wall

This section presents the mathematical details of how flow near to a no-slip wall is modeled

in ANSYS CFX. An introduction to near-wall flow, modeling details and guidelines on using

wall functions are presented.

• Mathematical Formulation

The wall-function approach in ANSYS CFX is an extension of the method of Launder and

Spalding (1974). In the log-law region, the near wall tangential velocity is related to the wall-

shear-stress, , by means of a logarithmic relation.

In the wall-function approach, the viscosity affected sublayer region is bridged by

employing empirical formulas to provide near-wall boundary conditions for the mean flow

and turbulence transport equations. These formulas connect the wall conditions (e.g., the wall-

shear-stress) to the dependent variables at the near-wall mesh node which is presumed to lie in

the fully-turbulent region of the boundary layer.

The logarithmic relation for the near wall velocity is given by:

(3.60) where:

(3.61)

(3.62)

where is the near wall velocity, is the friction velocity, is the known velocity tangent

to the wall at a distance of from the wall, is the dimensionless distance from the wall,

is the wall shear stress, is the von Karman constant and is a log-layer constant

depending on wall roughness (natural logarithms are used).

A definition of in the different wall formulations is available. For details, see p. 72.

Scalable Wall Functions

Equation (3.60) has the problem that it becomes singular at separation points where the near

wall velocity, , approaches zero. In the logarithmic region, an alternative velocity scale,

can be used instead of :


- 72 -

(3.63)

This scale has the useful property that it does not go to zero if goes to zero (in turbulent

flow is never completely zero). Based on this definition, the following explicit equation for

can be obtained:

(3.64)

The absolute value of the wall shear stress , is then obtained from:

(3.65)

where:

(3.66) and is as defined earlier.

One of the major drawbacks of the wall-function approach is that the predictions depend

on the location of the point nearest to the wall and are sensitive to the near-wall meshing;

refining the mesh does not necessarily give a unique solution of increasing accuracy (Grotjans

and Menter). The problem of inconsistencies in the wall-function, in the case of fine meshes,

can be overcome with the use of the scalable wall function formulation developed by ANSYS

CFX. It can be applied on arbitrarily fine meshes and allows you to perform a consistent mesh

refinement independent of the Reynolds number of the application.

The basic idea behind the scalable wall-function approach is to limit the value used in the

logarithmic formulation by a lower value of . 11.06 is the intersection

between the logarithmic and the linear near wall profile. The computed is therefore not

allowed to fall below this limit. Therefore, all mesh points are outside the viscous sublayer

and all fine mesh inconsistencies are avoided.

Solver Yplus and Yplus

In the solver output, there are two arrays for the near wall spacing. The definition for the

Yplus variable that appears in the post processor is given by the standard definition of

generally used in CFD:

(3.67)

where is the distance between the first and second grid points off the wall.


- 73 -

In addition, a second variable, solver Yplus, is available which contains the used in the

logarithmic profile by the solver. It depends on the type of wall treatment used, which can be

one of three different treatments in ANSYS CFX. They are based on different distance

definitions and velocity scales. This has partly historic reasons, but is mainly motivated by the

desire to achieve an optimum performance in terms of accuracy and robustness:

• Standard wall function (based on )

• Scalable wall function (based on )

• Automatic wall treatment (based on )

The scalable wall function is defined as:

(3.68)

and is therefore based on of the near wall grid spacing.

Note that both the scalable wall function and the automatic wall treatment can be run on

arbitrarily fine meshes.


- 74 -

3.3 Modelling of Particle Transport

Introduction

Multiphase flow refers to the situation where more than one fluid is present. Each fluid may

possess its own flow field, or all fluids may share a common flow field. Unlike multicompo-

nent flow, the fluids are not mixed on a microscopic scale in multiphase flow. Rather, they are

mixed on a macroscopic scale, with a discernible interface between the fluids. ANSYS CFX

includes a variety of multiphase models to allow the simulation of multiple fluid streams,

bubbles, droplets, solid particles and free surface flows.

Two distinct multiphase flow models are available in ANSYS CFX: an Eulerian–

Eulerian multiphase model and a Lagrangian Particle Tracking multiphase model.

Particle transport modeling is a type of multiphase model, where particulates are tracked

through the flow in a Lagrangian way, rather than being modelled as an extra Eulerian phase.

The full particulate phase is modelled by just a sample of individual particles. The tracking is

carried out by forming a set of ordinary differential equations in time for each particle,

consisting of equations for position, velocity, temperature and masses of species. These

equations are then integrated using a simple integration method to calculate the behaviour of

the particles as they traverse the flow domain. The following section describes the

methodology used to track the particles

Lagrangian Tracking Implementation

Within the particle transport model, the total flow of the particle phase is modelled by

tracking a small number of particles through the continuum fluid. The particles could be solid

particles, drops or bubbles.

The application of Lagrangian tracking in ANSYS CFX involves the integration of

particle paths through the discretized domain. Individual particles are tracked from their

injection point until they escape the domain or some integration limit criterion is met. Each

particle is injected, in turn, to obtain an average of all particle tracks and to generate source

terms to the fluid mass, momentum and energy equations. Because each particle is tracked

from its injection point to final destination, the tracking procedure is applicable to steady state

flow analysis. The following section describes the methodology used to track the particles.


- 75 -

Integration

The particle displacement is calculated using forward Euler integration of the particle velocity

over timestep, .

(3.69)

where the superscripts o and n refer to old and new values respectively and is the particle

velocity. In forward integration, the particle velocity calculated at the start of the timestep is

assumed to prevail over the entire step. At the end of the timestep, the new particle velocity is

calculated using the analytical solution to equation (3.72):

(3.70)

The fluid properties are taken from the start of the timestep. For the particle momentum, f0

would correspond to the particle velocity at the start of the timestep.

In the calculation of all the forces, many fluid variables, such as density, viscosity and

velocity are needed at the position of the particle. These variables are always obtained

accurately by calculating the element in which the particle is travelling, calculating the

computational position within the element, and using the underlying shape functions of the

discretization algorithm to interpolate from the vertices to the particle position.

Interphase Transfer Through Source Terms

According to equation (3.72), the fluid affects the particle motion through the viscous drag

and a difference in velocity between the particle and fluid. Conversely, there is a

counteracting influence of the particle on the fluid flow due to the viscous drag. This effect is

termed coupling between the phases. If the fluid is allowed to influence trajectories but

particles do not affect the fluid, then the interaction is termed one-way coupling. If the

particles also affect the fluid behaviour, then the interaction is termed two-way coupling.

The flow prediction of the two phases in one-way coupled systems is relatively

straightforward. The fluid flow field may be calculated irrespective of the particle trajectories.

One-way coupling may be an acceptable approximation in flows with low dispersed phase

loadings where particles have a negligible influence on the fluid flow. Two-way coupling

requires that the particle source terms are included in the momentum equations. The

momentum sources could be due to turbulent dispersion forces or drag. The particle source

terms are generated for each particle as they are tracked through the flow.


- 76 -

Particle sources are applied in the control volume that the particle is in during the timestep.

The particle sources to the momentum equations are obtained by solving transport equations

for the sources. The generic equation for particle sources is:

(3.71)

Where are the contributions from the particles that are linear in the solution variable and

contains all other contributions. This equation has the same form as the general particle

transport and is solved in the same way as outlined above.

The source to be added to the continuous phase is then S multiplied by the number flow rate

for that particle, which is the mass flow rate divided by the mass of the particle. In ANSYS

CFX, the particle source terms are recalculated each time particles are injected. The source

terms are then retained in memory in order that they may be applied each time the fluid

coefficients are calculated. Thus, the particle sources may be applied even though particles

have not been injected in the current flow calculation.

Momentum Transfer

Consider a discrete particle travelling in a continuous fluid medium. The forces acting on the

particle which affect the particle acceleration are due to the difference in velocity between the

particle and fluid, as well as to the displacement of the fluid by the particle. The equation of

motion for such a particle was derived by Basset, Boussinesq and Oseen for a rotating

reference frame:

(3.72)

which has the following forces on the right hand side:

• : drag force acting on the particle.

• : buoyancy force due to gravity. The buoyancy force is the force on a particle immersed

in a fluid.

• : forces due to domain rotation (centripetal and Coriolis forces).

• : virtual (or added) mass force. This is the force to accelerate the virtual mass of the

fluid in the volume occupied by the particle. This term is important when the displaced fluid

mass exceeds the particle mass, such as in the motion of bubbles.


- 77 -

• : pressure gradient force. This is the force applied on the particle due to the pressure

gradient in the fluid surrounding the particle caused by fluid acceleration. It is only

significant when the fluid density is comparable to or greater than the particle density.

• : Basset force or history term which accounts for the deviation in flow pattern from

a steady state. This term is not implemented in ANSYS CFX.

• Drag Force

The aerodynamic drag force on a particle is proportional to the slip velocity, , between the

particle and the fluid velocity:

(3.73)

Where is the drag coefficient and is the effective particle cross section. The drag

coefficient, , is introduced to account for experimental results on the viscous drag of a

solid sphere. The coefficient is calculated in the same way as for Eulerian-Eulerian

multiphase flow.

• Interphase Drag

The following general form is used to model interphase drag force acting on phase due to

phase :

(3.74)

Note that and . Hence, the sum over all phases of all interphase transfer

terms is zero.

The total drag force is most conveniently expressed in terms of the dimensionless drag

coefficient:

(3.75)

where is the fluid density, is the relative speed, is the

magnitude of the drag force and is the projected area of the body in the direction of flow.

The continuous phase is denoted by and the dispersed phase is denoted by .


- 78 -

• Interphase Drag for the Particle Model

For spherical particles, the coefficients may be derived analytically. The area of a single

particle projected in the flow direction, , and the volume of a single particle are given

by:

(3.76)

where is the mean diameter. The number of particles per unit volume, , is given by:

(3.77)

The drag exerted by a single particle on the continuous phase is:

(3.78)

Hence, the total drag per unit volume on the continuous phase is:

(3.79)

Comparing with the momentum equations for phase , where the drag force per unit volume

is:

(3.80)

you get:

(3.81)

which can be written as:

(3.82)

This is the form implemented in ANSYS CFX.

Sparsely Distributed Solid Particles

At low particle Reynolds numbers (the viscous regime), the drag coefficient for flow past

spherical particles may be computed analytically. The result is Stokes’ law:

CD = 24/Re, Re << 1 (3.83)


- 79 -

For particle Reynolds numbers,

(3.84)

where is the viscosity of the continuous phase, which are sufficiently large for inertial

effects to dominate viscous effects (the inertial or Newton’s regime), the drag coefficient

becomes independent of Reynolds number:

(3.85)

In the transitional region between the viscous and inertial regimes, for

spherical particles, both viscous and inertial effects are important. Hence, the drag coefficient

is a complex function of Reynolds number, which must be determined from experiment.

This has been done in detail for spherical particles. Several empirical correlations are

available. The one available in ANSYS CFX is due to Schiller and Naumann (1933).

Schiller-Naumann Drag Model

(3.86)

ANSYS CFX modifies this to ensure the correct limiting behaviour in the inertial regime by

taking:

(3.87)

Turbulence in Particle Tracking

The calculation of the instantaneous fluid velocity, , depends on the flow regime and the

type of particle tracking desired (mean or with turbulent dispersion). In laminar flows or in

flows where mean particle tracking is calculated, is equal to the mean local fluid velocity,

, surrounding the particle. The path of a particle is deterministic, i.e., there is a unique path

for a particle injected at a given location in the flow.

In turbulent tracking, the instantaneous fluid velocity is decomposed into mean, , and

fluctuating, , components. Now particle trajectories are not deterministic and two identical

particles, injected from a single point, at different times, may follow separate trajectories due

to the random nature of the instantaneous fluid velocity. It is the fluctuating component of the

fluid velocity which causes the dispersion of particles in a turbulent flow. Turbulent

dispersion has not been taken into account in this work.


- 80 -

Heat and Mass Transfer

• Heat Transfer

The rate of change of temperature is governed by three physical processes: convective heat

transfer, latent heat transfer associated with mass transfer, and radiative heat transfer. The last

is neglected in this work.

The convective heat transfer is given by:

(3.88)

where is the thermal conductivity of the fluid, and are the temperatures of the fluid

and of the particle, and is the Nusselt number given by:

(3.89)

where is the specific heat of the fluid.

The heat transfer associated with mass transfer is given by the relation:

(3.90)

where the sum is taken over all components of the particle for which heat transfer is taking

place. The latent heat of vaporization is temperature dependent, and is obtained directly

from the material properties information for the liquid in the particle and its vapour.

The rate of change of temperature for the particle is then obtained from:

(3.91)

where the sum in this equation is taken over all components of the particle including those not

affected by mass transfer.

• Mass Transfer

For particles with heat transfer and one component of mass transfer, and in which the

continuous gas phase is at a higher temperature than the particles, liquid evaporation model is

used. The model uses two mass transfer correlations depending on whether the droplet is

above or below the boiling point. This is determined through the Antoine equation and is

given by:


- 81 -

(3.92)

where are user-supplied coefficients. The particle is boiling if the vapour pressure,

, is greater than the gaseous pressure.

When the particle is above the boiling point, the mass transfer is determined by the

convective heat transfer:

(3.93)

When the particle is below the boiling point, the mass transfer is given by the formula:

(3.94)

Here WC and WG are the molecular weights of the vapour and the mixture in the continuous

phase, while X and XG are the molar fractions in the drop and in the gas phase. In either case,

the rate of mass transfer is set to zero when all of the non-base substances in the particle has

evaporated.


- 82 -

4 DISCRETIZATION AND SOLUTION THEORY

4.1 Numerical Discretization

Analytical solutions to the Navier-Stokes equations exist for only the simplest of flows under

ideal conditions. To obtain solutions for real flows, a numerical approach must be adopted

whereby the equations are replaced by algebraic approximations which may be solved using a

numerical method.

Discretization of Governing Equations

This approach involves discretizing the spatial domain into finite control volumes using a

mesh. The governing equations are integrated over each control volume, such that the relevant

quantity (mass, momentum, energy, etc.) is conserved in a discrete sense for each control

volume.

The figure below shows a typical mesh with unit depth (so that it is two-dimensional),

on which one surface of the control volume is represented by the shaded area.

It is clear that each node is surrounded by a set of surfaces that define the control

volume. All the solution variables and fluid properties are stored at the element nodes.

Consider the mean form of the conservation equations for mass, momentum and a passive

scalar, expressed in Cartesian coordinates:

Figure 4.1 Control volume surface


- 83 -

(4.1)

(4.2)

(4.3)

These equations are integrated over a control volume, and Gauss’ Divergence Theorem

is applied to convert some volume integrals to surface integrals. If control volumes do not

deform in time, then the time derivatives can be moved outside of the volume integrals and

the equations become:

(4.4)

(4.5)

(4.6)

where V and s respectively denote volume and surface regions of integration, and dnj are the

differential Cartesian components of the outward normal surface vector. The volume integrals

represent source or accumulation terms, and the surface integrals represent the summation of

the fluxes.

The first step in the numerical solution of these exact differential equations is to create a

coupled system of linearized algebraic equations. This is done by converting each term into a

discrete form. Consider, for example, an isolated mesh element like the one shown below.

Volumetric (i.e., source or accumulation) terms are converted into their discrete form by

approximating specific values in each sector and then integrating those values over all sectors

that contribute to a control volume. Surface flow terms are converted into their discrete form

by first approximating fluxes at integration points, ipn, which are located at the centre of each

surface segment in a 3D element surrounding the control volume. Flows are then evaluated by

integrating the fluxes over the surface segments that contribute to a control volume.

Figure 4.2 Mesh element


- 84 -

Many discrete approximations developed for CFD are based on series expansion

approximations of continuous functions (such as the Taylor series). The order-accuracy of the

approximation is determined by the exponent on the mesh spacing or timestep factor of the

largest term in the truncated part of the series expansion. This is often the first term excluded

from the approximation. Increasing the order-accuracy of an approximation generally implies

that errors are reduced more quickly with mesh or timestep size refinement. Unfortunately, in

addition to increasing the computational load, high-order approximations are also generally

less robust (i.e., less numerically stable) than their low-order counterparts.

The discrete form of the integral equations becomes:

(4.7)

(4.8)

(4.9)

where V is the control volume, is the timestep, is the discrete outward surface vector,

the subscript ip denotes evaluation at an integration point, and summations are over all the

integration points of the control volume. Note that the first order backward Euler scheme has

been assumed in this equation, although a second order scheme is also available as discussed

below. The superscript refers to the old time level. The discrete mass flow through a

surface of the control volume, denoted by , is given by:

(4.10)

The Coupled System of Equations

The linear set of equations that arise by applying the finite volume method to all elements in

the domain are discrete conservation equations. The system of equations can be written in the

form:

(4.11)

where is the solution, the right hand side, the coefficients of the equation, is the

identifying number of the control volume or node in question, and means “neighbour”, but


- 85 -

also includes the central coefficient multiplying the solution at the th location. The node may

have any number of such neighbours, so that the method is equally applicable to both

structured and unstructured meshes. The set of these, for all control volumes constitutes the

whole linear equation system. For a scalar equation (e.g., enthalpy or turbulent kinetic

energy), , and are each single numbers. For the coupled, 3D mass-momentum

equation set, they are a (4 x 4) matrix or a (4 x 1) vector, which can be

expressed as:

(4.12)

and

(4.13)

(4.14)

It is at the equation level that the coupling in question is retained and at no point are any

of the rows of the matrix treated any differently (e.g., different solution algorithms for

momentum versus mass). The advantages of such a coupled treatment over a non-coupled or

segregated approach are several: robustness, efficiency, generality and simplicity. These

advantages all combine to make the coupled solver an extremely powerful feature of any CFD

code. The principal drawback is the high storage needed for all the coefficients.

4.2 Solution Strategy - The Coupled Solver

Segregated solvers employ a solution strategy where the momentum equations are first

solved, using a guessed pressure, and an equation for a pressure correction is obtained.

Because of the ‘guess-and-correct’ nature of the linear system, a large number of iterations are

typically required in addition to the need for judiciously selecting relaxation parameters for

the variables.


- 86 -

ANSYS CFX uses a coupled solver, which solves the hydrodynamic equations (for u, v,

w, p) as a single system. This solution approach uses a fully implicit discretization of the

equations at any given timestep. For steady state problems, the time-step behaves like an

‘acceleration parameter’, to guide the approximate solutions in a physically based manner to a

steady-state solution. This reduces the number of iterations required for convergence to a

steady state, or to calculate the solution for each timestep in a time dependent analysis.

General Solution

The flow chart shown below illustrates the general field solution process used in the ANSYS

CFX-Solver. The solution of each set of field equations shown in the flow chart consists of

two numerically intensive operations. For each timestep:

1. Coefficient Generation: The non-linear equations are linearized and assembled into the

solution matrix.

2. Equation Solution: The linear equations are solved using an Algebraic Multigrid method.

When solving fields in the ANSYS CFX-Solver, the outer- or timestep-iteration is controlled

by the physical time scale or timestep for steady and transient analyses, respectively. Only

one inner (linearization) -iteration is performed per outer-iteration in steady state analyses,

whereas multiple inner-iterations are performed per timestep in transient analyses.


- 87 -

Linear Equation Solution

ANSYS CFX uses a Multigrid (MG) accelerated Incomplete Lower Upper (ILU) factorization

technique for solving the discrete system of linearized equations. It is an iterative solver

whereby the exact solution of the equations is approached during the course of several

iterations.

The linearized system of discrete equations described above can be written in the

general matrix form:

(4.15)

where is the coefficient matrix, the solution vector and the right hand side.

The above equation can be solved iteratively by starting with an approximate solution,

, that is to be improved by a correction, , to yield a better solution, , i.e.,

(4.16)

where is a solution of:

(4.17)

with , the residual, obtained from:

(4.18)

Repeated application of this algorithm will yield a solution of the desired accuracy. By

themselves, iterative solvers such as ILU tend to rapidly decrease in performance as the

number of computational mesh elements increases. Performance also tends to rapidly

decrease if there are large element aspect ratios present. The performance of the solver can be

greatly improved by employing a ‘multigrid’ technique.


- 88 -

5 NUMERICAL MODELS

5.1 Simple Case

Geometry

Computational Mesh

Boundary Conditions

For details on boundary conditions and other numerical settings refer to Appendix A.

Inlet

Outlet Wall

0.1 m

0.05 m

0.05 m

0.025 m0.025 m


- 89 -

5.2 Reference Case

Geometry

Computational Meshes


- 90 -

Boundary Conditions

In order to model spray ejected from the rotary disc atomizer sixteen ‘‘injection’’ conditions

are defined on the edge of the atomizer vaned wheel (Figure 2).

For details on boundary conditions and other numerical settings refer to Appendix B.


- 91 -

6 RESULTS AND DISCUSSION

6.1 Simple Case

Figure 6.2 Particle trajectories representing particle temperature for Tin, low = 373.15 K

Figure 6.1 Particle trajectories representing particle temperature for Tin, high = 573.15 K


- 92 -

Comparing Figure 6.1 and Figure 6.2 the effect of decreased inlet temperature of drying

air on the effectiveness of spray drying process can be clearly revealed. For both inlet tempe-

ratures of drying air, i.e. Tin, high = 573.15 K and Tin, low = 373.15 K, tannin mixture is ente-

ring this simple spray dryer at 323.15 K (for details on numerical settings for simple case refer

to Appendix A), which is decreasing after that, however, i.e. dispersed liquid mixture is

actually cooling down while being in contact with drying air. This means that evaporation

Figure 6.4 Scalar field representing temperature of continuous phase for Tin, low = 373.15 K

Figure 6.3 Scalar field representing temperature of continuous phase for Tin, high = 573.15 K


- 93 -

does not occur at all for low inlet temperature of drying air, so the only driving force for the

mass transfer of water from tannin mixture to drying air is difference in its concentration, i.e.

poor volatilization is taking place solely. Despite this fact, the well known effect of all drying

processes can be observed on Figures 6.3-6.4, i.e. temperature of drying air decreases in the

region where extensive drying take place. Considering these temperature conditions it can be

easily explained that the reduction of liquid water mass fraction in tannin mixture occurrs

Figure 6.6 Particle trajectories representing H2Ol mass fraction for Tin, low = 373.15 K

Figure 6.5 Particle trajectories representing H2Ol mass fraction for Tin, high = 573.15 K


- 94 -

much more intensively for inlet temperature of drying air being high enough. Respective

scalar fields of liquid water mass fraction in continuous phase, depicted on Figures 6.7-6.8,

reveal the same situation. In case of Tin, high mass fraction is highest in the region where most

of the tannin mixture spray particle trajectories are present, so the mass fraction gradient away

from the spray is quite high. There can be only very small increase of water mass fraction in

continuous phase and related gradient observed for Tin, low.

Figure 6.8 Scalar field representing H2Ol mass fraction for Tin, low = 373.15 K

Figure 6.7 Scalar field representing H2Ol mass fraction for Tin, high = 573.15 K


- 95 -

According to the temperature conditions described above the changes of total particle

mass and mean particle diameter can be explained also. Both quantities are decreasing much

more rapidly in case of Tin, high then in case of Tin, low, which is depicted on Figure 6.9 – 6.12.

Figure 6.10 Particle trajectories representing total particle mass for Tin, low = 373.15 K

Figure 6.9 Particle trajectories representing total particle mass for Tin, high = 573.15 K


- 96 -

Figure 6.12 Particle trajectories representing mean particle diameter for Tin, low = 373.15 K

Figure 6.11 Particle trajectories representing mean particle diameter for Tin, high = 573.15 K


- 97 -

-x- 0.3m-X-disk CFX -+- 0.3m-Y-disk CFX




6.2 1st Reference Case

Comparison of velocity profiles at no spray conditions

Figure 6.13 compares the velocity

profiles at different levels within the

chamber between the predicted [pre-

sent] and measured results of Kieviet

(1997) under no spray condition.

Good agreement is obtained consi-

dering the complexity of the process

and measurement results. It is noted

that there is a non-uniform velocity

distribution in the core region of the

chamber. The highest velocity magni-

tude is about 8.0 m/s at the 0.6 m le-

vel. The velocity is reduced as the air

streams downwards in the chamber. It

is also found that the air flow patterns

are nearly symmetric upstream of the

1.0 m level. However, the asymmetric

velocity profiles at 2.0 m level are

found in Fig. 6.13d. It is due to the

internal exit bent pipe which reduces

the area for air to go through at one

side of the drying chamber. It may

also be because of the turbulent flow

in the drying chamber. This indicates

that the symmetric CFD models in

Kieviet’s (1997) assumptions may

lead to some inaccuracies in the pre-

dicted results for such spray drying

geometry. Figure 6.13 Comparison of velocity profiles between prediction with CFX and measurements

of Kieviet (1997) at no spray condition


- 98 -

Comparison of velocity profiles

The velocity magnitude and axial velocity profiles for a spray dryer fitted with a rotating disk

are shown in Figures 6.14 and 6.15, respectively. Generally, it is found that the high variation

of velocity is located at the center core of diameter of 0.3 m as what we found at no spray

condition (Figure 6.13).

In Figure 6.14, it is noted that the velocity profiles are nearly symmetric at both 0.3 and

1.4 m level. However, asymmetric velocity profiles were found by Huang et al. (2006) in this

case. It seems that the air high swirl induced by the rotating disc has not been captured.


-x- 1.4m-X-disk CFX

-+- 1.4m-Y-disk CFX

Figure 6.14 Comparison of velocity profiles between present prediction and prediction of Huang et al. (2006)


- 99 -


-x- 0.6m-X-disk CFX

-+- 0.6m-Y-disk CFX

-x- 1.4m-X-disk CFX

-+- 1.4m-Y-disk CFX

Comparison of axial velocity profiles

If the axial velocity profiles in Figure 6.15 are considered, it is observed that there is a reverse

flow at 0.3 m level. It is due to the rotating disk which pulls the air below the disk upwards.

This phenomenon was also observed by Masters (1985) and was named as air pumping effect.

These reverse flows disappeared rapidly as the drying air proceeds downwards, e.g., at 0.6 m

level (Figure 6.15b). However, at the same time, there is a reverse flow formed near the

chamber wall as shown in Figure 6.15b and c. This shows that air recirculation appears at this

level. The radial and tangential velocity profiles (not shown here) show that the flows are too

complex to identify typical flow patterns.

Figure 6.15 Comparison of axial velocity profiles between present prediction and prediction of Huang et al. (2006)


- 100 -

-x- 0.3m-X-disk CFX

-+- 0.3m-Y-disk CFX


-x- 1.4m-X-disk CFX

-+- 1.4m-Y-disk CFX

Figure 6.16 Comparison of temperature profiles between present prediction and prediction of Huang

et al. (2006)

Comparison of temperature profiles

The temperature profiles are shown in Figure 6.16. It was found that the temperatures in the

central core of diameter of 0.2 m are almost the same at 0.3 m level (Figure 6.16a). Beside

this also the maximum temperatures in the central have been found to be in good agreement

with Huang et al. (2006) at all levels. However, temperatures profiles does not match at all

outside central core region. It is due to numerical model and numerical settings chosen for this

1st reference case. Coarse mesh, low rate of representing particles injected into drying

chamber, escape boundary condition for particles colliding with walls and a heat transfer

through the walls have been

chosen to be appropriate

numerical settings. Later on

different numerical settings

have been chosen to obtain the

results presented in next

section. Fine mesh, high rate

of representing particles

injected into drying chamber,

no-escape boundary condition

for particles colliding with

walls and no heat transfer

through the walls have been

chosen. While there is almost

no difference in velocity profi-

les presented, temperature pro-

files at different time instances

(Figure 6.21) reveal the fact

that the temperature level in-

creases through the time. This

observation had a critical

impact on numerical settings

chosen later to obtain the

results for 3rd reference case

which will be discussed later.


- 101 -

Comparison of humidity profiles

Even bigger differences have been found for humidity profiles than for the temperature

profiles (Figure 6.17). However, the effect of altered numerical settings for 2nd reference case

was the same, humidity profiles are developing slowly while the physical simulation time

rises (Figure 6.22).

-x- 0.3m-X-disk CFX

-+- 0.3m-Y-disk CFX

-x- 0.6m-X-disk CFX

-+- 0.6m-Y-disk CFX


Figure 6.17 Comparison of absolute humidity profiles between present prediction and prediction of Huang et al. (2006)


- 102 -

Particle trajectories

Figure 6.18 Predicted instantaneous particle trajectories presenting H2Ol mass fraction


- 103 -

6.3 2nd Reference Case

Comparison of velocity profiles

Comparison of axial velocity profiles

Velocity [m/s]Z=-0.3 [m]

0

2

4

6

8

10

12

-1.1 -0.9 -0.7 -0.4 -0.2 0.0 0.2 0.5 0.7 0.9

Radial position [m]

Velo

city

[m/s

]

1000_full.trn1100_full.trn1200_full.trn1300_full.trn1400_full.trn1500_full.trn

Figure 6.19 Comparison of velocity profiles at different time instances

Axial Velocity Z [m/s]Z=-0.3 [m]

-4

-2

0

2

4

6

8

10

-1.1 -0.9 -0.7 -0.4 -0.2 0.0 0.2 0.5 0.7 0.9

Radial position [m]

Axi

al V

eloc

ity [m

/s]


Figure 6.20 Comparison of axial velocity profiles at different time instances


- 104 -

Comparison of temperature profiles


Temperature [K]Z=-0.3 [m]

300

320

340

360

380

400

420

440

460

480

-1.1 -0.9 -0.7 -0.4 -0.2 0.0 0.2 0.5 0.7 0.9

Radial position [m]

Tem

pera

ture

[K]


Figure 6.21 Comparison of axial velocity profiles at different time instances

HumidityZ=-0.3 [m]

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

-1.1 -0.9 -0.7 -0.4 -0.2 0.0 0.2 0.5 0.7 0.9

Radial position [m]

Hum

idity

[kg/

kg]

1000_full.trn1100_full.trn1200_full.trn1300_ful.trn1400_full.trn1500_full.trn

Figure 6.22 Comparison of absolute humidity profiles at different time instances


- 105 -

- - 0.6m-X-disk Huang et al. (2006) - - 0.6m-Y-disk Huang et al. (2006)


Figure 6.23 Comparison of humidity profiles

Radial position [m]

Radial position [m]

Radial position [m]

Absolute humidity [kg/kg]



-x- 0.3m-X-disk CFX - Thigh

-+- 0.3m-Y-disk CFX - Thigh

-x- 0.3m-X-disk CFX - Tlow

-+- 0.3m-Y-disk CFX – Tlow










6.4 3rd Reference Case


Numerical settings chosen for the 3rd reference case are chosen to be as follows: fine mesh,

tannin mixture, high rate of representing particles injected into drying chamber, no-escape

boundary condition for particles colliding with walls and no heat transfer through the walls.

However, in comparison to the

previous reference cases two

main changes were made (1)

the initialization of the water

mass fraction in drying medi-

um was increased from the 0

(zero) to the water mass frac-

tion in drying air, i.e.

0.0138067, and (2) physical

simulation end time was

increased from 5 seconds to 40

seconds. Humidity profiles

obtained in this way corre-

spond much better to the

predictions of Huang et al.

(2006), though, tannin mixture

properties have been used

here.


- 106 -

Instantaneous velocity scalar fields

Figure 6.24 Velocity scalar fields at different cuts through spray dryer


- 107 -

7 CONCLUSIONS AND PERSPECTIVE

The influence of decreased inlet temperature of drying air has been confirmed completely

with the simple spray dryer for tannin mixture. Desired product quality will not be achieved in

case of to low inlet temperature of drying air, i.e., the liquid mixture is not able to evaporate

and actually cools down during drying process which is based on volatilization mechanism

solely. Outgoing particles still contains remarkable moisture amount. To decrease the droplet

size and increase the temperature of the feed would most probably help to solve this problem,

however, additional investigation has to be done concerning this.

Initially, two different numerical models have been set up for the spray drying of the

maltodextrin mixture. Simulation results predicted for the 1st and 2nd case have been

completely validated for the velocity profiles only, however, not for the temperature and

humidity profiles. After that several attempts were made to improve the result accuracy by

altering numerical model and numerical settings. Finally, humidity profiles could be validated

with the 3rd case, which was set up for the simulation of spray drying of tannin mixture,

therefore the matching to Fluent 6 CFD predictions of Huang et al. (2006), which were made

for the maltodextrin mixture, isn’t perfect, however, trends of humidity profiles have been

found to be in good accordance with this reference.

So, spray drying process inside the spray dryer fitted with rotary disk atomizers was

successfully simulated for several different settings in time dependent mode, which has not

been documented very often in the open literature. Easy-to-follow workflow for numerical

modelling of the industrial spray dryers fitted with a rotary disc atomizer using commercial

CFD package has been established. As there was very little open literature presenting

experimental and numerical results for comparison found, much more experimental work in

the field of spray drying is needed in the future.


- 108 -

REFERENCES

Bird, R. B., Stewart, W. E. and Lightfoot, E. N., Transport Phenomena, John Wiley & Sons,

Inc., 1960.

Goula, A. M. and Adamopoulos, K. G., Influence of spray drying conditions on residue

accumulation – simulation using CFD. 2004 Drying Technology. 22, 1107–1128.

Grotjans, H. and Menter, F. R. , Wall functions for general application CFD codes, in:

Papailiou K. D. et al., (Ed.), ECCOMAS 98 Proceedings of the Fourth European

Computational Fluid Dynamics Conference, pages 1112-1117. John Wiley & Sons, 1998.

Huang, L. X., Kumar, K. and Mujumdar, A. S., Simulation of a spray dryer fitted with a

rotary disk atomizer using a 3D computational fluid dynamic model. Drying Technology

2004. 22 (6), 1489-1515.

Huang, L. X., Kumar, K. and Mujumdar, A. S., A comparative study of a spray dryer with

rotary disc atomizer and pressure nozzle using computational fluid dynamic simulations.

Chemical Engineering and Processing 2006. 45 (6), 461-470.

Kadja, M. and Bergeles, G. Modelling of slurry droplet drying. Applied Thermal Engineering

2003. 23 (7), 829–844

Kieviet, F. G., Modeling Quality in Spray Drying, Ph.D. thesis, Eindhoven University of

Technology, the Netherlands, 1997.

Kieviet, F. G., Modeling Quality in Spray Drying, Ph.D. Thesis, T. U. Eindhoven, The

Netherlands, 1997.

Launder, B. E. and Spalding, D. B., The numerical computation of turbulent flows,

Computational Methods in Applied Mechanical Engineering, 3:269-289, 1974.

Li, X. and Zbicinski, I. A Sensitivity Study on CFD Modeling of Cocurrent Spray-Drying

Process. Drying Technology 2005. 23 (8), 1681-1691.

Marshall, W. R., Trans. Amer. Soc. Mech. Eng., 77, No. 11, 1377 (1955)

Masters, K., Spray Drying Handbook, 4th ed., Halsted Press, New York, 1985.


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Montazer-Rahmati, M. M. and Ghafele-Bashi, S. H. Improved Differential Modeling and

Performance of Slurry Spray Dryers as Verified by Industrial Data. Drying Technology 2007.

25 (9), 1447-1458.

Oakley, D. E. Spray Dryer Modeling in Theory and Practice. Drying Technology 2004. 22

(6), 1371-1402.

Ranz, W. E. and Marshall, W. R., Chem. Eng. Prog., 48, No. 3, 141 (1952)

Raw, M. J. Robustness of Coupled Algebraic Multigrid for the Navier-Stokes Equations.

AIAA 96-0297, 34th Aerospace and Sciences Meeting & Exhibit, January 15-18 1996, Reno,

NV.

Schiller, L. and Naumann, A., VDI Zeitschrift, 77, p. 318, 1933.

Southwell, D. B., Langrish, T. A. G. and Fletcher, D. F., Use of computational fluid dynamics

techniques to assess design alternatives for the plenum chamber of a small spray dryer, in:

Abdullah, K., Tambunan, A. H. and Mujumdar, A. S. (Editors.), Proc. First Asian-Australian

Drying Conference, Bali, Indonesia, 1999, 626-633.

von Wendt, J. F. (Ed.), Computational Fluid Dynamics: An Introduction, 2nd ed., Springer-

Verlag, Berlin Heidelberg New York, 1995.

Zbicinski, I. and Li, X. Conditions for accurate CFD modeling of spray-drying process.

Drying Technology 2006. 24 (9), 1109-1114.


- A-I -

APPENDIX A

Simple Model CCL (CFX Command Language) File Listing FLOW: DOMAIN:Domain 1 Coord Frame = Coord 0 Domain Type = Fluid Fluids List = Gas mixture Location = B16 Particles List = Tannin mixture BOUNDARY:Inlet Boundary Type = INLET Location = Inlet BOUNDARY CONDITIONS: COMPONENT:H2O Mass Fraction = 0.014 Option = Mass Fraction END FLOW REGIME: Option = Subsonic END HEAT TRANSFER: Option = Static Temperature Static Temperature = 573.15 [K] (§6.1: 373.15) END MASS AND MOMENTUM: Normal Speed = 1.0 [m s^-1] Option = Normal Speed END TURBULENCE: Option = Medium Intensity and Eddy Viscosity Ratio END END FLUID:Tannin mixture BOUNDARY CONDITIONS: END END END BOUNDARY:Outlet Boundary Type = OUTLET Location = Outlet BOUNDARY CONDITIONS: FLOW REGIME: Option = Subsonic END MASS AND MOMENTUM: Option = Average Static Pressure Relative Pressure = 0 [Pa] END PRESSURE AVERAGING:


- A-II -

Option = Average Over Whole Outlet END END END BOUNDARY:Wall Boundary Type = WALL Location = F17.16,F18.16,F20.16,F22.16 BOUNDARY CONDITIONS: HEAT TRANSFER: Heat Transfer Coefficient = 1.8 [W m^-2 K^-1] Option = Heat Transfer Coefficient Outside Temperature = 293.15 [K] END WALL INFLUENCE ON FLOW: Option = No Slip END WALL ROUGHNESS: Option = Smooth Wall END END FLUID:Tannin mixture BOUNDARY CONDITIONS: VELOCITY: Option = Restitution Coefficient Parallel Coefficient of Restitution = 0 Perpendicular Coefficient of Restitution = 0 END END END END DOMAIN MODELS: BUOYANCY MODEL: Option = Non Buoyant END DOMAIN MOTION: Option = Stationary END MESH DEFORMATION: Option = None END REFERENCE PRESSURE: Reference Pressure = 1 [atm] END END FLUID:Tannin mixture FLUID MODELS: HEAT TRANSFER MODEL: Option = Particle Temperature END MORPHOLOGY: Option = Dispersed Particle Transport Fluid END END END FLUID:Gas mixture FLUID MODELS: COMPONENT:Air Ideal Gas Option = Constraint END COMPONENT:H2O Option = Transport Equation


- A-III -

END HEAT TRANSFER MODEL: Option = Thermal Energy END MORPHOLOGY: Option = Continuous Fluid END END END FLUID MODELS: COMBUSTION MODEL: Option = None END HEAT TRANSFER MODEL: Option = Fluid Dependent END THERMAL RADIATION MODEL: Option = None END TURBULENCE MODEL: Option = k epsilon END TURBULENT WALL FUNCTIONS: Option = Scalable END END FLUID PAIR:Gas mixture | Tannin mixture Particle Coupling = Fully Coupled COMPONENT PAIR:H2O | H2Ol Option = Liquid Evaporation Model LATENT HEAT: Option = Automatic END END INTERPHASE HEAT TRANSFER: Option = Ranz Marshall END MOMENTUM TRANSFER: DRAG FORCE: Option = Schiller Naumann END PRESSURE GRADIENT FORCE: Option = None END TURBULENT DISPERSION FORCE: Option = None END VIRTUAL MASS FORCE: Option = None END END END PARTICLE INJECTION REGION:Particle Injection Region 1 FLUID:Tannin mixture INJECTION CONDITIONS: COMPONENT:Tannin Mass Fraction = 0.525 Option = Value END COMPONENT:H2Ol Mass Fraction = 0.475


- A-IV -

Option = Value END INJECTION METHOD: Cone Angle = 45 [deg] Injection Centre = 0.025 [m], 0.025 [m], 0 [m] Injection Velocity Magnitude = 2 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -1 Injection Direction Y Component = -1 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time and Mass Flow Rate = 10000 [kg^-1] Option = Proportional to Mass Flow Rate END END PARTICLE DIAMETER DISTRIBUTION: Diameter = 0.0001 [m] Option = Specified Diameter END PARTICLE MASS FLOW RATE: Mass Flow Rate = 1e-03 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 323.15 [K] END END END END END OUTPUT CONTROL: PARTICLE TRACK FILE: Option = All Track Positions END RESULTS: File Compression Level = Default Option = Standard END TRANSIENT RESULTS:Transient Results 1 File Compression Level = Low Speed Most Compression Option = Standard OUTPUT FREQUENCY: Option = Timestep Interval Timestep Interval = 50 END END END SIMULATION TYPE: Option = Transient EXTERNAL SOLVER COUPLING: Option = None END INITIAL TIME: Option = Automatic with Value Time = 0 [s] END TIME DURATION: Option = Total Time


- A-V -

Total Time = 2 [s] END TIME STEPS: Option = Timesteps Timesteps = 0.01 [s] END END SOLUTION UNITS: Angle Units = [rad] Length Units = [m] Mass Units = [kg] Solid Angle Units = [sr] Temperature Units = [K] Time Units = [s] END SOLVER CONTROL: ADVECTION SCHEME: Option = Upwind END CONVERGENCE CONTROL: Maximum Number of Coefficient Loops = 10 Timescale Control = Coefficient Loops END CONVERGENCE CRITERIA: Residual Target = 0.000001 Residual Type = RMS END PARTICLE CONTROL: PARTICLE INTEGRATION: First Iteration for Particle Calculation = 100 Iteration Frequency = 10 Number of Integration Steps per Element = 100 Option = Forward Euler END END TRANSIENT SCHEME: Option = Second Order Backward Euler TIMESTEP INITIALISATION: Option = Automatic END END END END LIBRARY: MATERIAL:Air Ideal Gas Material Description = Air Ideal Gas (constant Cp) Material Group = Air Data, Calorically Perfect Ideal Gases Option = Pure Substance Thermodynamic State = Gas PROPERTIES: Option = General Material ABSORPTION COEFFICIENT: Absorption Coefficient = 0.01 [m^-1] Option = Value END DYNAMIC VISCOSITY: Dynamic Viscosity = 1.831E-05 [kg m^-1 s^-1] Option = Value END EQUATION OF STATE:


- A-VI -

Molar Mass = 28.96 [kg kmol^-1] Option = Ideal Gas END REFERENCE STATE: Option = Specified Point Reference Pressure = 1 [atm] Reference Specific Enthalpy = 0. [J/kg] Reference Specific Entropy = 0. [J/kg/K] Reference Temperature = 25 [C] END REFRACTIVE INDEX: Option = Value Refractive Index = 1.0 [m m^-1] END SCATTERING COEFFICIENT: Option = Value Scattering Coefficient = 0.0 [m^-1] END SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 1.0044E+03 [J kg^-1 K^-1] Specific Heat Type = Constant Pressure END THERMAL CONDUCTIVITY: Option = Value Thermal Conductivity = 2.61E-2 [W m^-1 K^-1] END END END MATERIAL:Tannin Material Group = Particle Solids Option = Pure Substance Thermodynamic State = Solid PROPERTIES: Option = General Material EQUATION OF STATE: Density = 470 [kg m^-3] Molar Mass = 1.0 [kg kmol^-1] Option = Value END REFERENCE STATE: Option = Specified Point Reference Temperature = 25 [C] END SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 1300 [J kg^-1 K^-1] END END END MATERIAL:Tannin mixture Material Group = Particle Solids,Water Data Materials List = Tannin,H2Ol Option = Variable Composition Mixture Thermodynamic State = Liquid END MATERIAL:Gas mixture Material Group = Air Data, Gas Phase Combustion Materials List = Air Ideal Gas,H2O Option = Variable Composition Mixture Thermodynamic State = Gas


- A-VII -

END MATERIAL:H2O Material Description = Water Vapour Material Group = Gas Phase Combustion, Interphase Mass Transfer Option = Pure Substance Thermodynamic State = Gas PROPERTIES: Option = General Material ABSORPTION COEFFICIENT: Absorption Coefficient = 1.0 [m^-1] Option = Value END DYNAMIC VISCOSITY: Dynamic Viscosity = 9.4E-06 [kg m^-1 s^-1] Option = Value END EQUATION OF STATE: Molar Mass = 18.02 [kg kmol^-1] Option = Ideal Gas END REFERENCE STATE: Option = NASA Format Reference Pressure = 1 [atm] Reference Temperature = 25 [C] END REFRACTIVE INDEX: Option = Value Refractive Index = 1.0 [m m^-1] END SCATTERING COEFFICIENT: Option = Value Scattering Coefficient = 0.0 [m^-1] END SPECIFIC HEAT CAPACITY: Option = NASA Format LOWER INTERVAL COEFFICIENTS: NASA a1 = 0.03386842E+02 [] NASA a2 = 0.03474982E-01 [K^-1] NASA a3 = -0.06354696E-04 [K^-2] NASA a4 = 0.06968581E-07 [K^-3] NASA a5 = -0.02506588E-10 [K^-4] NASA a6 = -0.03020811E+06 [K] NASA a7 = 0.02590233E+02 [] END TEMPERATURE LIMITS: Lower Temperature = 300 [K] Midpoint Temperature = 1000 [K] Upper Temperature = 5000 [K] END UPPER INTERVAL COEFFICIENTS: NASA a1 = 0.02672146E+02 [] NASA a2 = 0.03056293E-01 [K^-1] NASA a3 = -0.08730260E-05 [K^-2] NASA a4 = 0.01200996E-08 [K^-3] NASA a5 = -0.06391618E-13 [K^-4] NASA a6 = -0.02989921E+06 [K] NASA a7 = 0.06862817E+02 [] END END THERMAL CONDUCTIVITY: Option = Value


- A-VIII -

Thermal Conductivity = 193E-04 [W m^-1 K^-1] END END END MATERIAL:H2Ol Material Description = Water Liquid (H2O) Material Group = Liquid Phase Combustion, Water Data Option = Pure Substance Thermodynamic State = Liquid PROPERTIES: Option = General Material DYNAMIC VISCOSITY: Dynamic Viscosity = 0.00028182 [Pa s] Option = Value END EQUATION OF STATE: Density = 958.37 [kg/m^3] Molar Mass = 18.02 [kg kmol^-1] Option = Value END REFERENCE STATE: Option = Specified Point Reference Pressure = 3.169 [kPa] Reference Specific Enthalpy = -1.5866449E+7 [J/kg] Reference Specific Entropy = 2.82482E+03 [J/kg/K] Reference Temperature = 298.15 [K] END SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 4215.6 [J/kg/K] Specific Heat Type = Constant Pressure END THERMAL CONDUCTIVITY: Option = Value Thermal Conductivity = 0.67908 [W m^-1 K^-1] END END END MATERIAL:H2Ovl Binary Material1 = H2O Binary Material2 = H2Ol Material Description = Water (H2O) Binary Mixture Material Group = Gas Phase Combustion, Liquid Phase Combustion, Water Data Option = Homogeneous Binary Mixture SATURATION PROPERTIES: Option = General PRESSURE: Antoine Enthalpic Coefficient B = 1687.54 [K]*ln(10) Antoine Pressure Scale = 1 [bar] Antoine Reference State Constant A = 5.11564*ln(10) Antoine Temperature Offset C = (230.23-273.15) [K] Option = Antoine Equation END TEMPERATURE: Option = Automatic END END END


- C-I -

APPENDIX B

Reference Model CCL (CFX Command Language) File Listing FLOW: DOMAIN:Default Domain Modified Coord Frame = Coord 0 Domain Type = Fluid Fluids List = Gas mixture Location = B243 Particles List = Maltodextrin mixture (§6.4: Tannin mixture) BOUNDARY:Air_Inlet Boundary Type = INLET Location = Air_Inlet BOUNDARY CONDITIONS: COMPONENT:H2O Mass Fraction = 0.0138067 Option = Mass Fraction END FLOW DIRECTION: Option = Cylindrical Components Unit Vector Axial Component = -7.5 Unit Vector Theta Component = 0 Unit Vector r Component = -5.25 AXIS DEFINITION: Option = Coordinate Axis Rotation Axis = Coord 0.3 END END FLOW REGIME: Option = Subsonic END HEAT TRANSFER: Option = Static Temperature Static Temperature = 195 [C] (§6.4: 240 and 120) END MASS AND MOMENTUM: Mass Flow Rate = 0.336 [kg s^-1] Option = Mass Flow Rate END TURBULENCE: Epsilon = 0.37 [m^2 s^-3] Option = k and Epsilon k = 0.027 [m^2 s^-2] END END FLUID:Maltodextrin mixture BOUNDARY CONDITIONS: END END END


- B-II -

BOUNDARY:Air_Outlet Boundary Type = OUTLET Location = Air_Outlet BOUNDARY CONDITIONS: FLOW REGIME: Option = Subsonic END MASS AND MOMENTUM: Option = Average Static Pressure Relative Pressure = -100 [Pa] END PRESSURE AVERAGING: Option = Average Over Whole Outlet END END END BOUNDARY:Default Domain Modified Default Boundary Type = WALL Location = F241.243,F242.243,F245.243,F246.243,F247.243,F248.243,F249.243,F250.243,F251.243,F252.243,F254.243,F255.243 BOUNDARY CONDITIONS: HEAT TRANSFER: Option = Adiabatic END WALL INFLUENCE ON FLOW: Option = No Slip END WALL ROUGHNESS: Option = Smooth Wall END END FLUID:Maltodextrin mixture BOUNDARY CONDITIONS: VELOCITY: Option = Restitution Coefficient Parallel Coefficient of Restitution = 1.0 Perpendicular Coefficient of Restitution = 1.0 END END END END BOUNDARY:Product_Exit Boundary Type = OUTLET Location = Product_Exit BOUNDARY CONDITIONS: FLOW REGIME: Option = Subsonic END MASS AND MOMENTUM: Option = Average Static Pressure Relative Pressure = -100 [Pa] END PRESSURE AVERAGING: Option = Average Over Whole Outlet END END END DOMAIN MODELS: BUOYANCY MODEL: Option = Non Buoyant


- B-III -

END DOMAIN MOTION: Option = Stationary END MESH DEFORMATION: Option = None END REFERENCE PRESSURE: Reference Pressure = 1 [atm] END END FLUID:Gas mixture FLUID MODELS: COMPONENT:Air Ideal Gas Option = Constraint END COMPONENT:H2O Option = Transport Equation END HEAT TRANSFER MODEL: Option = Thermal Energy END MORPHOLOGY: Option = Continuous Fluid END END END FLUID:Maltodextrin mixture (§6.4: Tannin mixture) FLUID MODELS: HEAT TRANSFER MODEL: Option = Particle Temperature END MORPHOLOGY: Option = Dispersed Particle Transport Fluid END END END FLUID MODELS: COMBUSTION MODEL: Option = None END HEAT TRANSFER MODEL: Option = Fluid Dependent END THERMAL RADIATION MODEL: Option = None END TURBULENCE MODEL: Option = RNG k epsilon END TURBULENT WALL FUNCTIONS: Option = Scalable END END FLUID PAIR:Gas mixture | Maltodextrin mixture (§6.4: Tannin mixture) Particle Coupling = Fully Coupled COMPONENT PAIR:H2O | H2Ol Option = Liquid Evaporation Model LATENT HEAT: Option = Automatic END


- B-IV -

END INTERPHASE HEAT TRANSFER: Option = Ranz Marshall END MOMENTUM TRANSFER: DRAG FORCE: Option = Schiller Naumann END PRESSURE GRADIENT FORCE: Option = None END TURBULENT DISPERSION FORCE: Option = None END VIRTUAL MASS FORCE: Option = None END END END PARTICLE INJECTION REGION:Particle Injection Region 01 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0.05250 [m], 0 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 0.6962 Injection Direction Y Component = 9.9757 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END


- B-V -

PARTICLE INJECTION REGION:Particle Injection Region 02 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0.0485037 [m], 0.0200909 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -3.1743 Injection Direction Y Component = 9.4828 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 03 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0.0371231 [m], 0.0371231 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -6.5616 Injection Direction Y Component = 7.5462


- B-VI -

Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 04 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0.0200909 [m], 0.0485037 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -8.9499 Injection Direction Y Component = 4.4608 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C]


- B-VII -

END END END END PARTICLE INJECTION REGION:Particle Injection Region 05 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0 [m], 0.0525 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -9.9757 Injection Direction Y Component = 0.6962 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 06 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = -0.0200909 [m], 0.0485037 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1]


- B-VIII -

Option = Cone INJECTION DIRECTION: Injection Direction X Component = -9.4828 Injection Direction Y Component = -3.1743 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 07 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = -0.0371231 [m], 0.0371231 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -7.5462 Injection Direction Y Component = -6.5616 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1]


- B-IX -

END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 08 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = -0.0485037 [m], 0.0200909 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -4.4608 Injection Direction Y Component = -8.9499 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 09 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END


- B-X -

INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = -0.0525 [m], 0 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = -0.6962 Injection Direction Y Component = -9.9757 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 10 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = -0.0485037 [m], -0.0200909 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 3.1743 Injection Direction Y Component = -9.4828 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05


- B-XI -

Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 11 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = -0.0371231 [m], -0.0371231 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 6.5616 Injection Direction Y Component = -7.5462 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 12 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END


- B-XII -

COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = -0.0200909 [m], -0.0485037 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 8.9499 Injection Direction Y Component = -4.4608 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 13 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0 [m], -0.0525 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 9.9757 Injection Direction Y Component = -0.6962 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END


- B-XIII -

END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 14 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0.0200909 [m], -0.0485037 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 9.4828 Injection Direction Y Component = 3.1743 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 15 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS:


- B-XIV -

COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0.0371231 [m], -0.0371231 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 7.5462 Injection Direction Y Component = 6.5616 Injection Direction Z Component = 0 Option = Cartesian Components END NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END PARTICLE INJECTION REGION:Particle Injection Region 16 FLUID:Maltodextrin mixture (§6.4: Tannin mixture) INJECTION CONDITIONS: COMPONENT:H2Ol Mass Fraction = 0.575 Option = Value END COMPONENT:Maltodextrin (§6.4: Tannin) Mass Fraction = 0.425 Option = Value END INJECTION METHOD: Cone Angle = 0 [deg] Injection Centre = 0.0485037 [m], -0.0200909 [m], -0.229 [m] Injection Velocity Magnitude = 110.16732228 [m s^-1] Option = Cone INJECTION DIRECTION: Injection Direction X Component = 4.4608 Injection Direction Y Component = 8.9499 Injection Direction Z Component = 0 Option = Cartesian Components END


- B-XV -

NUMBER OF POSITIONS: Number per Unit Time = 10000 [s^-1] Option = Direct Specification END END PARTICLE DIAMETER DISTRIBUTION: Option = Rosin Rammler Rosin Rammler Power = 2.05 Rosin Rammler Size = 70.5 [micron] END PARTICLE MASS FLOW RATE: Mass Flow Rate = 0.00086875 [kg s^-1] END TEMPERATURE: Option = Value Temperature = 27 [C] END END END END END SIMULATION TYPE: Option = Transient EXTERNAL SOLVER COUPLING: Option = None END INITIAL TIME: Option = Automatic END TIME DURATION: Option = Total Time Total Time = 15 [s] (§6.4: 40) END TIME STEPS: Option = Timesteps Timesteps = 0.01 [s] (§6.4: 0.1) END END SOLUTION UNITS: Angle Units = [rad] Length Units = [m] Mass Units = [kg] Solid Angle Units = [sr] Temperature Units = [K] Time Units = [s] END SOLVER CONTROL: ADVECTION SCHEME: Blend Factor = 1.0 Option = Specified Blend Factor END CONVERGENCE CONTROL: Maximum Number of Coefficient Loops = 10 Minimum Number of Coefficient Loops = 1 Timescale Control = Coefficient Loops END CONVERGENCE CRITERIA: Residual Target = 0.00001 Residual Type = RMS END EQUATION CLASS:energy


- B-XVI -

ADVECTION SCHEME: Blend Factor = 1.0 Option = Specified Blend Factor END END EQUATION CLASS:mf ADVECTION SCHEME: Blend Factor = 1.0 Option = Specified Blend Factor END END PARTICLE CONTROL: PARTICLE INTEGRATION: Iteration Frequency = 10 Option = Forward Euler END END TRANSIENT SCHEME: Option = Second Order Backward Euler TIMESTEP INITIALISATION: Option = Automatic END END END END LIBRARY: MATERIAL:Air Ideal Gas Material Description = Air Ideal Gas (constant Cp) Material Group = Air Data, Calorically Perfect Ideal Gases Option = Pure Substance Thermodynamic State = Gas PROPERTIES: Option = General Material ABSORPTION COEFFICIENT: Absorption Coefficient = 0.01 [m^-1] Option = Value END DYNAMIC VISCOSITY: Dynamic Viscosity = 1.831E-05 [kg m^-1 s^-1] Option = Value END EQUATION OF STATE: Molar Mass = 28.96 [kg kmol^-1] Option = Ideal Gas END REFERENCE STATE: Option = Specified Point Reference Pressure = 1 [atm] Reference Specific Enthalpy = 0. [J/kg] Reference Specific Entropy = 0. [J/kg/K] Reference Temperature = 25 [C] END REFRACTIVE INDEX: Option = Value Refractive Index = 1.0 [m m^-1] END SCATTERING COEFFICIENT: Option = Value Scattering Coefficient = 0.0 [m^-1] END


- B-XVII -

SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 1.0044E+03 [J kg^-1 K^-1] Specific Heat Type = Constant Pressure END THERMAL CONDUCTIVITY: Option = Value Thermal Conductivity = 2.61E-2 [W m^-1 K^-1] END END END MATERIAL:Gas mixture Material Group = Air Data, Gas Phase Combustion Materials List = Air Ideal Gas,H2O Option = Variable Composition Mixture Thermodynamic State = Gas END MATERIAL:H2O Material Description = Water Vapour Material Group = Gas Phase Combustion, Interphase Mass Transfer Option = Pure Substance Thermodynamic State = Gas PROPERTIES: Option = General Material ABSORPTION COEFFICIENT: Absorption Coefficient = 1.0 [m^-1] Option = Value END DYNAMIC VISCOSITY: Dynamic Viscosity = 9.4E-06 [kg m^-1 s^-1] Option = Value END EQUATION OF STATE: Molar Mass = 18.02 [kg kmol^-1] Option = Ideal Gas END REFERENCE STATE: Option = NASA Format Reference Pressure = 1 [atm] Reference Temperature = 25 [C] END REFRACTIVE INDEX: Option = Value Refractive Index = 1.0 [m m^-1] END SCATTERING COEFFICIENT: Option = Value Scattering Coefficient = 0.0 [m^-1] END SPECIFIC HEAT CAPACITY: Option = NASA Format LOWER INTERVAL COEFFICIENTS: NASA a1 = 0.03386842E+02 [] NASA a2 = 0.03474982E-01 [K^-1] NASA a3 = -0.06354696E-04 [K^-2] NASA a4 = 0.06968581E-07 [K^-3] NASA a5 = -0.02506588E-10 [K^-4] NASA a6 = -0.03020811E+06 [K] NASA a7 = 0.02590233E+02 [] END TEMPERATURE LIMITS:


- B-XVIII -

Lower Temperature = 300 [K] Midpoint Temperature = 1000 [K] Upper Temperature = 5000 [K] END UPPER INTERVAL COEFFICIENTS: NASA a1 = 0.02672146E+02 [] NASA a2 = 0.03056293E-01 [K^-1] NASA a3 = -0.08730260E-05 [K^-2] NASA a4 = 0.01200996E-08 [K^-3] NASA a5 = -0.06391618E-13 [K^-4] NASA a6 = -0.02989921E+06 [K] NASA a7 = 0.06862817E+02 [] END END THERMAL CONDUCTIVITY: Option = Value Thermal Conductivity = 193E-04 [W m^-1 K^-1] END END END MATERIAL:H2Ol Material Description = Water Liquid (H2O) Material Group = Liquid Phase Combustion, Water Data Option = Pure Substance Thermodynamic State = Liquid PROPERTIES: Option = General Material DYNAMIC VISCOSITY: Dynamic Viscosity = 0.00028182 [Pa s] Option = Value END EQUATION OF STATE: Density = 958.37 [kg/m^3] Molar Mass = 18.02 [kg kmol^-1] Option = Value END REFERENCE STATE: Option = Specified Point Reference Pressure = 3.169 [kPa] Reference Specific Enthalpy = -1.5866449E+7 [J/kg] Reference Specific Entropy = 2.82482E+03 [J/kg/K] Reference Temperature = 298.15 [K] END SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 4215.6 [J/kg/K] Specific Heat Type = Constant Pressure END THERMAL CONDUCTIVITY: Option = Value Thermal Conductivity = 0.67908 [W m^-1 K^-1] END END END MATERIAL:H2Ovl Binary Material1 = H2O Binary Material2 = H2Ol Material Description = Water (H2O) Binary Mixture Material Group = Gas Phase Combustion, Liquid Phase Combustion, Water Data Option = Homogeneous Binary Mixture


- B-XIX -

SATURATION PROPERTIES: Option = General PRESSURE: Antoine Enthalpic Coefficient B = 1687.54 [K]*ln(10) Antoine Pressure Scale = 1 [bar] Antoine Reference State Constant A = 5.11564*ln(10) Antoine Temperature Offset C = (230.23-273.15) [K] Option = Antoine Equation END TEMPERATURE: Option = Automatic END END END MATERIAL:Maltodextrin (§6.4: Tannin) Material Group = Particle Solids Option = Pure Substance Thermodynamic State = Solid PROPERTIES: Option = General Material EQUATION OF STATE: Density = 1000 [kg m^-3] (§6.4: 470) Molar Mass = 1.0 [kg kmol^-1] Option = Value END REFERENCE STATE: Option = Specified Point Reference Temperature = 0 [C] (§6.4: 25) END SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 4219 [J kg^-1 K^-1] (§6.4: 1300) END END END MATERIAL:Maltodextrin mixture Material Group = Particle Solids,Water Data Materials List = H2Ol,Maltodextrin (§6.4: H2Ol,Tannin) Option = Variable Composition Mixture Thermodynamic State = Liquid END


Življenjepis

Osebni podatki Bojan Krajnc

Datum in kraj rojstva: 25. avgust 1971, Maribor

Podatki o izobrazbi Srednješolska izobrazba

Ustanova: Srednja kovinarska, strojna in metalurška šola Maribor.

Pridobljeni naziv: Strojni tehnik.

Univerzitetna izobrazba

Ustanova: Univerza v Mariboru, Fakulteta za strojništvo.

Pridobljeni naziv: u.d.i.s. za energetiko in procesno strojništvo.

Delovne izkušnje 09/1997 – 04/1998

Podjetje: Dostava plina, Ploj Aleksander s.p.

Naziv delovnega mesta: Dostavljavec

04/1998 – 04/2000

Podjetje: Strojne inštalacije Krajnc, Krajnc Stanko s.p.

Naziv delovnega mesta: Prokurist

04/2000 – 04/2002

Podjetje: Viessmann d.o.o., Cesta XIV. divizije 116a, Maribor

Naziv delovnega mesta: Vodja prodaje

04/2002 – 09/2002

Podjetje: Bell d.o.o., Ptujska cesta 11, Miklavž na Dravskem polju

Naziv delovnega mesta: Vodja prodaje

09/2002 – 04/2002

Podjetje: Inometal d.o.o., Zagrebška cesta 20, Maribor

Naziv delovnega mesta: Vodja kontrole kakovosti

04/2002 – 09/2005

Podjetje: Strojne inštalacije Krajnc, Krajnc Stanko s.p.

Naziv delovnega mesta: Prokurist

Od 09/2005 – ...

Podjetje: AVL-AST d.o.o., Trg Leona Stuklja 5, Maribor

Naziv delovnega mesta: Razvojni inženir


BOJAN KRAJNC [91012]

Osebna bibliografija za obdobje 1986-2009

ČLANKI IN DRUGI SESTAVNI DELI

1.08 Objavljeni znanstveni prispevek na konferenci

1. GREIF, David, KRAJNC, Bojan, WANG, De Ming, SCHREFL, Michael. Multi-phase

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MONOGRAFIJE IN DRUGA ZAKLJUČENA DELA

2.11 Diplomsko delo

2. KRAJNC, Bojan. Analiza tokovnih razmer v mešalni posodi s pomočjo PIV tehnike :

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2.25 Druge monografije in druga zaključena dela

3. KRAJNC, Bojan, KRIŽAN, Aleš, MEGLIČ, Dejan, PODBOJEC, Milko, VOLER, Boštjan.

Slogi vzgajanja - začetna faza. Maribor: Srednja kovinarska, strojna in metalurška šola, 1988.

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Vir bibliografskih zapisov: Vzajemna baza podatkov COBISS.SI/COBIB.SI, 24. 6. 2009

http://cobiss.izum.si/scripts/cobiss?command=DISPLAY&base=COBIB&RID=11371286




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