hello welcome to this class on spray theory

and application there are two parts to this class that we are going to focus on they will

sort of the in that order of sequence the first part related to the theory of what is

spray is and the what to why do we need a spray and where would be a good place to use

it that is a segway into a talking more about the applications

although as users i am sure everyone of us has seen a spray you know the simplest of

the household sprays ah perfume or a or a water cleaner that you used to clean glass

there are you know sort of more obvious uses of where you probably encountered sprays ah

what we want to do is actually build upon that we don’t want to take that away instant

start of on a on a theoretical note i want to sort of see what we already know from common

knowledge and really what we see but what we look but we don’t see in other

words we look at something but we don’t completely understand what’s happening that’s going to

be our first objective for the next few lectures ok so we will take a typical ah perfume spray ok let us say a typical perfume spray is about

two hundred milliliters in volume so that’s how much perfume the manufacturer has promised

you and there are some adds i see on tv where

they say they also promise six hundred ah squirts

ok so this whole bottle they promise six hundred of those little ah waves of spray ok ah so

what we want to do is understanding what this really means as engineers and fluid mechanicians

ok so what we ah and also gain a feel for some numbers around these sprays how complicated

are there or how simple are there both ways ok

so what i wanted to is start from this and just say volume per spray volume per squirt

will be this two hundred milliliters divided by six hundred that is about one third of

a milliliter that is how much ah volume of perfume is being deliver to you in one depression

of the plunger ok now again from common observation we know what this looks like so here is your

plunger this is the rest of the bottle that’s usually fairly artistically shaped and there

is a tiny whole from which you get your spray the spray itself has is a collection of drops

some big some small but there is a general periphery of sorts ok so this one third m

l is distributed in this spatial region as soon as i have squirted one delivery of ah

of the perfume i have deliver i have ah i have dispersed one third milliliter of volume

in to this spatial region now in a typical spray we will come to see

this towards end in a lot more detail but in a typical spray say such as a perfume

the mean drop size ok that mean drop size is on the order of let us say fifty micro

meters that is on average these drops are fifty let’s say hundred micro meters ok typically

less than hundred micro meter in diameter so this is also called the average diameter

we will come to talk about this later on in some more detail has to what we mean by an

average diameter ok but let us say it is like an indication of the size of the drops so

from this information and i will use this hundred micro meters only because it’s easier

easy to do the multiplications we want to calculate the volume in one drop ok and from

here on i am going to drop the equality in place for ah the order of so this is same

on the order of so this symbol here is going to be used to mean on the order of now essentially

what this means is i am not really interested in the specific numbers as much as the power

of ten so ten micrometers is ten power two micrometers or ten power minus four meters

that’s all i am interested in for now ok so if i take this the volume in one drop is

this average diameter cubed which would be ten power minus four the cubed meter cubed

ok that’s the volume in one drop so just to complete the calculation it’s ten power minus

twelve meter cubed the volume in one squirt is on the or of i will say one m l

because one third m l is on the order of one m l so it’s on the order of one m l which

is ten power minus three liters which thousand liters make a meter cubed

so this is ten power minus six meter cubed ok so how many drops have i produced that

is simple that is the volume in each squirt divided the volume per drop that gives me

the number so this is ten power minus six meter cubed

divided by ten power minus twelve meter cubed so n is on the order of ten power six ok this

is a simplest of sprays one that we have a probably all familiar with and every squirt

produces a million drops each drop having a size on average about hundred micrometers

ok and that is the purpose of a spray nozzle the objective of a spray nozzle is to do just

this i mean we ok but let us ask the next deeper question why would we want to do this

in the case of a perfume if we understand how a perfume works where all most there to

understanding how an i c engine works or how a gas turbine works because essentially we

are moving a long in the same direction although the magnitudes of some of these number would

be different ok so why would we want to take start with approximately

one m l of perfume ok and from there create ten power six drops each hundred micrometers

in diameter ok so that’s what the nozzle has just done the objective of doing this is essentially

to take perfume that sitting in the bottom of my bottle and disperse it in to an area

see my skin or a piece of clothing that can benefit as a whole

there are many ways of doing it ok we will again stick the perfume and show how a spray

is much more efficient then other ways of doing it i can take a little bit of the perfume

and sp[ear]- it i can take perfume and sprinkle it these are all also available designs but

we all know the is with which a perfume spray works especially in the context of uniform

delivery so if i want to deliver a product uniformly

in a certain space ok performing that delivery hydro dynamically in other words using fluid

mechanics to deliver this product is is what is the most beneficial as far as most as for

as producing a uniform delivery of the of the ah product that you want that you intend

to delivery ok now what have we also done in the process of taking one milliliter and

creating ten power six drops each that is hundred micrometers in diameter on average

ok the biggest increase has been in the total surface area that is available to the drops

ok so the single reason we do this ok we will make an estimate of that but essentially what

we have done is this is not so obvious with with the human use of perfume but if i want

to deodorize a room like this then i want to maximize the area of contact between the

air in this room and the perfume itself ok and this is the most efficient way of doing

it as far as increase the surface area so let us see what we have done so the easiest

easiest way to understand this is to look at surface area

before spray and surface area after spray we will do the after spray part first ok so

essentially if i take the total surface area we call this a l v ok standing for the interfacial

area ok so if i try to estimate this a l v it is

n times the surface area of a given drop ok so i again i have only interested in order

of magnitude so n is the on the order of ten power six

the area of the drop is ten power minus four the squared ok and the units on this is meter

squared so if i look at this that is ten power minus two meter squared

that is ten power minus one centimeter so essentially if i actually look at it it is

about ten centimeters this way ten centimeters this way

this is the actual area that is available so this is ten centimeters or point one meters

this is ten centimeters point one meters ok it is like i have taken one m l of liquid

and smeared it over an area about this big imagine the rate at which that perfume would

now evaporate if i just took one m l of liquid and you know i have not even done the calculation

of the surface area before ah spray but you can see how even if i take a ten centimeter

by ten centimeter window the actual content of a small cuvette with one m l and the the

top area on there would be negligible compare to this so we are already at a point where

we know we have increase the area so much that the initial condition doesn’t even [map

/matter] matter as far as the subtraction is concerned ok so we have taken one m l which

is about a tiny volume of liquid and create it and spread it uniformly relatively speaking

over an area about that big with the simple action of pressing down on

a plunger and you can imagine that if you actually did this whether it is water or perfume

imagine the rate of evaporation because you now increased the surface area available for

all this transport to happen so the net the single biggest reason why spray is find application

in many different areas and we will talk about ah few of those talk about a few of those

later on today is because you have this drastic increase in the surface area going from the

before to the after condition so all your surface area linked transport

properties be it evaporation be it drag droplets are dragged by the air around and that drag

is going to be much higher if you had a higher surface area between the ah dragging medium

and the dragged body so you can imagine how you can take a sphere would have a certain

drag if i took the same volume and created spikes on it i have essentially increase the

surface area and the higher this surface area the higher would be the the drag on this body

that is non spherical ok so you a this increase in surface area has

all these other repercussions with several transport ah phenomena be it momentum be it

mass through evaporation or energy through heat transfer if i want to if i want to evaporate

this fluid i can heat it up but i can only heat the fluid up as fast as the interfacial

area will allow me to so if i can increase the interfacial area i can increase the rate

of evaporation by simply making it by increasing the interfacial area the rate of evaporation

goes up at the same temperature condition ok

so these are the wind falls associated with with increasing the number of drops increasing

the interfacial area that we are all interested in that is that actually drives these spray

applications ok all right so this is sort of the the ah basic sort of so we want to

understand what it is that we are talking about when we call a spray so at least as

far as our definition is concerned till now spray is a collection of drops formed from

a bulk liquid source ok so i have created this collection of drops

through some mechanical action in the case of a perfume spray we will talk about those

as we go a long those are all the details that we will get in to but at this point we

want understand what it is that we are talking about so at least we are talking about a collection

of about million drops ok these numbers that we saw or on we will see later on or on the

lower end of what a commercial spray or an industrial spray or an aerospace spray would

be like some of those sprays could run in to ten power

to twelve ten power fifteen drops being produced per milliliter so huge increase in the surface

area if i took for example that hundred micrometers as the average diameter and i decrease that

to i had a way to decrease it down to ten micrometers i have come down one order of

magnitude on the diameter which means three orders of magnitude more in number ok

so essentially i can take the same volume of liquid and disperse it in to a much larger

number depending on some mechanical design of the of the nozzle ok so essentially what

we are talking about is a collection of drops now if you are a ah dynamists you are a you

are a mechanical engineers and aerospace engineers so if you are a a dynamists so you are looking

at the dynamics of a systems so let’s take a very simple system a cylinder rolling down

and inclined plane ok let us say if there is no slip here how

many degrees of freedom would the system have essentially that cylinder can only go up or

down the inclined plane it’s a one degree of freedom system a particle in air ok single

point particle can move in three different spatial directions it’s three degrees of freedom

so if i tell you the position and velocity of a particle in space that is i have to give

you six numbers i have told you everything there is to know about the present condition

of this particle ok so that is that is what we that is what we

need to know to completely determine the system of one particle i need six numbers so if i

want to know the instantaneous state of a spray what do i need to know i need to know

the position and velocity of every point particle or every drop in the spray so we are talking

of about six times million from the order of ten million pieces of information ten million

numbers to just know the instantaneous state ok

in fact that is not the complete story every particle could be of a slightly different

size correct so just as i want to talk about this idea of dimensionality in sprays this

is now an exercise to identify what are all the what is like the most complicated way

to look at a spray and then see what it see how intractable that is and how we try to

simplify our own understanding of spray that’s the idea of that’s the objective of this next

few minutes here ok so this let’s understand this idea of dimensionality

spatial dimensionality the something that is known to all of us three dimensions in

space if i include time that’s four dimensions right if i include velocities so i need to

know where it is now and where it is headed so that’s three more components of velocity

in space assuming this drop is not big enough to have an identifiable rotation so if i say

rotation is also identifiable on the drop that’s three more degrees of freedom ok

if i say ok i am not going to go near rotation i will said drop is a spherical entity that’s

all most like a point particle so now if we look at what dimensionality means so the first

thing spatial let’s three position plus three velocity dimensions so i have six dimensions

in space in in the ah in the phase space to completely identify one particle

but i also need to know another dimension which is size so every particle in this spray

could be and in general is a different size it is just it is a real number between say

some lower limit of what is possible you will talk about those also like let say point one

micron ok there is no way conceivable that this perfume spray would produce a drop less

than that and there is also an upper limit ok or the upper limit could be infinity the

simplest understanding there is that our upper limit is as big as the whole on the perfume

bottle i cannot produce a drop much bigger than the whole on the perfume bottle

so i have a natural upper limit from in a perfume spray so between this lower limit

and upper limit my diameter on any one drop could be a real number so in that sense it

is no different from a spatial dimension if i put up if i place a perfume bottle here

and spray the perfume spray is starting here heading towards the camera and essentially

all of the drops are constrained between these two lower and upper limits ok

so the spatial coordinate in this direction is is bounded likewise the diameter coordinate

so i want you to start thinking about the size has being another coordinate it is no

different from a spatial coordinate as far as our idea of dimensionality is concerned

there are real differences between size being called a coordinate and space in the way we

write our equations we will come to those later

but the point here is that at the moment if i want to completely describe this spray then

i have to define one more dimension which is the droplet size ok now if this spray if

i am let us say i will switch has and i want to now talk about a jet a fuel ok it’s gas

turbine aircraft spray where i am spraying jet a fuel jet a is not single component fuel

it’s a multi component fuel so if i want to understand what is inside

this drop some drops could have more of the heaver component some drops could have more

of the thinner component or the less ah less viscous component ok so i have now introduced

another dimension and minds you these are all in some

sense orthogonal dimensions in other words if i tell you the position and velocity you

don’t have any idea of what the size is if i tell you the size and position and velocity

you have no idea what is made up a what the drop is made up of so they are all independent

directions to describe the spray so if i now add one more even if i am looking if i am

looking at the binary mixture i have one component direction percentage of component a for example

it’s between zero and hundred percent so they are all nice and bounded so very quickly

we can see that we are on the order of ten times n or ten power seven degrees of freedom

if i want to completely describe and instantaneous snap shot of this spray i have to give you

ten power seven numbers ok and then if i want to describe the evolution at to the next instant

of time i have to somehow come up with these ten power seven numbers of all over again

correct because the next instant could be related

to the previous instant through some mathematically equations but but as far as i am concerned

if i am making measurements they are completely new set of ten power seven numbers so this

is the order of information that you need to before you can say i know everything about

this spray clearly it is out of our reach ok in fact it is not just out of our reach

it is no were within our future reach not just that is this level of detail important

ok so that is the question that we have often ask ourselves not just as engineers of course

you know do why really need to know the position and velocity of every drop in this spray in

order to use it as certainly did need all of this last twenty

minutes of information to use of a perfume spray ok but if i want to use an air blast

atomizer in an aircraft i need a little more information but not to this level ok that

is where comes our next level of approximations so what would some of these approximations

look like instead of me telling you the diameter of

every drop at every point in the spray if i told you one number that is indicative ok

would you have you would have some idea about what the spray is going to feel like

but not to the level of detail that the full dimensionality would allow you it will also

and give you an estimate of the other things like of surface area we were able to estimate

a lot of the macroscopic parameters by simpler estimates ok so bulk of the time at least

in the first one third will be spent looking at these estimates trying to understand what

it is that the what makes a spray and what sort of descriptors can i applied to these

sprays that would make sense and that would be sufficient

ten power seven is like is not is sufficient but it’s like way out of the reach we don’t

need that much so what are the necessary descriptors what is sufficient how much information is

necessary for me to start using a spray ok so this is this is just to give you an idea

of what it is that you are look calling a spray ok we are calling on the order of about

ten power six to ten power ten drops sitting together in a very close spatial region doing

something to the liquid that could not have been done without that sort of a morphology

for that same amount of liquid ok what it does why it does and what are the

uses of it would be the topics of discussion going forward yes so i think like we said

some sort of an approximation is required as we move forward ok and before we start

looking at what those approximations are that will tell us enough about the spray to start

using it let us look at some of the uses of these sprays ok so like we said one of the

objectives is to increase interfacial area that’s quite sort of the most ah overriding

principle on which sprays are applied ok so let us look at the few different applications

of sprays one of the biggest uses i want to start with

something that is not very obvious ok which is called spray drying ok say for example

if you take your coffee powder granules or tide or surf granules a typical manufacturing

process that produces a stride or ah coffee powder granules is where you first create

the product in the form of a slurry a slurry is ah is like a liquid with these particles

not in suspend it’s are they are only in suspension not in solution and these this slurry is sprayed

following up the usually fairly a large bank of nozzles

so like i could have several several nozzle that produce that spray this slurry

and you have on the bottom side we have fan that blows hot air so this slurry this slurry spray as it ah

settles down to the bottom of ah of ah kiln of some kind essentially loses it’s solvent

typically water and you start to get agglomerated granules so whatever particles where in a

single drop now sort of a agglomerate to form a cluster which gives you the feel of a of

coffee granules so you can take a single granule and crush

it and get powder but if i sold you powder it won’t taste as well as granules ok so ah

this is the process by which most of most granulated materials of powder is manufacturing

spray drying is very efficient you are talking several thousands of pounds per hour or flow

rates extremely high flow rates and several nozzles because productivity and production

rates depend on on on that so these are commercially used quite widely and so this is an area where

again the what determines the height of my kiln the drop size

if i can make the drops smaller the water in them evaporates faster because for the

same volume have increase the surface area by decrease in the diameter ok so the faster

evaporation means that faster rate of evaporation means that the ah i get powder i recover powder

from my slurry much faster which means i i don’t need to make the kiln as long as as

or otherwise in also another way of looking at the same thing is that if i make the droplets

too small then i start to get in to granules which are not what my customer is used to

see take the granules feel more like powder ok

so there is also a lower limit on drop size that i don’t desire ok so the point of this

is to show you that very often there are conflicting requirements in any design process ok in the

case of sprays these are in the case of spray drying these are the conflicting requirements

that i don’t want drops much smaller than a certain critical size because they produce

product that is not what the customer is use to see on the other hand if i produce too

large a drop i may get wet product coming out at the bottom of my kiln ok

so these two extremes ah essentially dictate how the kiln design works a spray dryer design

works and this is the basic principle of operation ok now another application these of course

in spray combustion we will talk about this in some detail because there is ah lot more

to lot learn theoretically from looking at the spray combustion has an application again

spray combustion is area ah a area where sprays are applied but the actual applications range

from aircraft engines i c engines as well as land based power generation i have all

these different ah applications where i create a spray of some liquid fuel burn it and from

the products recover heat to run a turbine or run a an engine or some sort ok

again the objective of this is to increase the surface area so really speaking i want

to go as small as possible on the drop size but the conflicting part of the requirement

comes from the geometry of how you want to design this combustor say for example i don’t

want a combustor that is too short and flabby ok i want a slightly longer combustor which

means if i create a missed at my spray nozzle that is very very fine these drops may not

penetrates in sufficiently far in to my combustor as the result i could get hotspots very close

to the nozzle itself so i don’t desire complete pulverization of my liquid i want some large

drops in there as well give me just spray this flame geometry i want that flame itself

to have a certain designable length associated with it ok

so these sorts of conflicting requirements you will see in everyone of these applications

and we will talk about how to resolve them as we go long as well ok another application

is in simple evaporation dispersion and evaporation this is where my perfume spray comes in right

i want to just disperse the perfume and i want to evaporate it that’s how i deodorize

a space so ah again the conflicting requirements are that if i if i spray a perfume here i

want the far end of this room also to see some effect or at least i don’t want the effect

to be completely localized in a small region right adjust in to the nozzle ok

and these sorts ah so and again i want some large drops that will remain in flight for

a little while to give me this ah this spray this length and penetration to the spray because

i don’t want to be walking around every look and cranny of this room to be spray ok so

these are the different conflicting requirements as far as dispersion and evaporation is concerned

so as you see the overriding theme in all these three applications that we just wrote

down is that there is a typical lower end of drop that i don’t desire bellow there is

also low upper end of drop size that i don’t desire ah above as well ok

and a spray nozzle designer and manufacturer has to take these in to account and we able

to design spray nozzles that fit these constraints that is a challenge ok all right so now so

we talked about three or four of these ah three of these applications let’s look in

to one of them some detail and see what is happening just the physics of spray combustion so the first part is where i take the bulk

liquid i atomize this is the first time i am using

this word in to produce the collection of drops ok you will see this word atomize used

in a context of sprays very often nozzles are called atomizers it only it comes from some old british engineers

who have use to colorful language that they started calling nozzles atomizers

although we are nowhere near the atomic limit of these liquids ok we are not atomizing the

liquid in that sense we are heading in that direction but we are far far away from that

ok just to give you an estimate again one drop of this liquid is about let us say ten

power eighteen meter cubed ok and eighteen grams of water contains ten power twenty three

molecules again order of magnitude right eighteen grams is a atomic weight of water eighteen

gram is the eighteen milliliters eighteen milliliters contains ten power twenty three

molecules of water so we need to sort of understand that this

drop is no were near the atomic limit so we are talking of each drop containing on the

order of you know ten power ten molecules still ten power ten or even more you should

ok do the number but it’s they are no were near the atomic limit ok but will see you

see this use quite a bit the collection of drops then evaporate and that evaporation gives rise to vapour

phase fuel that is now mixed in with with your oxidizer your vapour phased fuel that

is mixed in with your oxidizer so this is where reaction happens reaction is essentially you know let us say

if i were to simply approximate ah the liquid fuel by say hexane or octane

you have a certain reaction between octane vapour and oxygen in the air giving rise to

carbon dioxide water vapour and a lot of other by products but essentially that’s the reaction

the reason you have reaction happening the reason we facilitate reaction is because i

have heat release ok that’s what i am after in all these application at least the combustion

applications i have want to somehow convert the chemical energy in this fuels in to heat

so this gives me heat release now the heat release is not going to keep quite it is going

to further affect this evaporation process for sure it is going to affect the reaction

process also because the same pair of molecules say octane

and oxygen have a different rate of reaction at different temperatures so as the mixture

temperature goes up the reaction rates go up typically so you start to see different

rate of reaction and therefore different an increased rate of heat release now there is

also a possibility that this heat release affects the atomization process itself ok

this atomization is essentially what is happening close to the nozzle that is the process of

converting bulk liquid in to a dispersion of drops or collection of drops ok

so that process itself is is a fluid mechanic process there is some some motion happening

and it is quite possible that that fluid mechanic process is affected by the temperature environment

it is embedded in ok so this this heat release could also affect your atomization this is

a simple sort of arrow diagram indicating the different physical ah interactions that

could take place between the spray and the environment ok now the atomization clearly

affects evaporation through the drop size the evaporation is also affected by ah by

the reaction is the affected by the evaporation rate

because if the rate of evaporation is faster the reaction rates depend of course on the

concentrations of the two reactants so the higher the rate of evaporation those concentrations

are now different so you essentially have a highly coupled problem in a simple process

like spray combustion ok so this from an applications perspective this is what makes the design

of spray combustors very challenging ok all right

so with the spray dryer all of the above are still true except the reaction part so you

have one piece of this block removed but the rest of it is essentially the same likewise

with ah with droplet dispersion and evaporation i have at the same atomization and evaporation

part that come in ok so you have we looked at a few different applications so let’s quickly

recap what we learn today so first thing we understood spray morphology

or dimensionality some feel for numbers associated with the real spray ok and then we listed

a few different applications i wrote down the different challenges in each of these

applications ok and then we started to study the coupled nature of any spray application

so if we have to apply these sprays intelligently in any application we really need to get a

hold of at least the third part we need to really get a hold of the coupled nature of

these applications