 Hello, welcome to this class on spray theory and applications. There are two parts to this class that we are going to focus on. It will sort of be in that order of sequence. The first part related to the theory of what a spray is and why do we need a spray and where would be a good place to use it that is a segue into talking more about the applications. Although as users I am sure every one of us has seen a spray. You know the simplest of the household sprays a perfume or a water cleaner that you use to clean glass. There are you know sort of more obvious uses of where you have probably encountered sprays. What we want to do is actually build upon that. We do not want to take that away and start off 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 do not see. In other words we look at something but we do not completely understand what is happening. That is going to be our first objective for the next few lectures. So we will take a typical perfume spray. Let us say a typical perfume spray is about 200 milliliters in volume. So that is how much perfume the manufacturer has promised you. And there are some ads I see on TV where they also promise 600 squirts. So this whole bottle they promise 600 of those little whiffs of spray. So what we want to do is understand what this really means as engineers and fluid machinations. So what we and also gain a feel for some numbers around these sprays. How complicated are they or how simple are they both ways. So what I want to do is start from this and just say volume per spray, volume per squirt will be this 200 milliliters divided by 600 that is about one third of a milliliter. That is how much volume of perfume is being delivered to you in one depression of the plunger. Now again from common observation we know what this looks like. So here is your plunger. This is the rest of the bottle that is usually fairly artistically shaped and there is a tiny hole 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. So this one third ml is distributed in this spatial region as soon as I have squirted one delivery of the perfume. I have dispersed one third milliliter of volume into this spatial region. Now in a typical spray we will come to see this towards the end in a lot more detail but in a typical spray say such as a perfume the mean drop size that mean drop size is on the order of let us say 50 micrometers that is on average these drops are 50 let us say 100 micrometers typically less than 100 micrometer in diameter. So this is also called the average diameter. We will come to talk about this later on in some more detail as to what we mean by an average diameter but let us say it is like an indication of the size of the drops. So from this information and I will use this 100 micrometers only because it is easier easy to do the multiplications. We want to calculate the volume in one drop okay and from here on I am going to drop the equality side in place for the order of. So this is saying 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 10. So 10 micrometers is 10 power 2 micrometers or 10 power minus 4 meters that is all I am interested in for now okay. So if I take this the volume in one drop is this average diameter cubed which would be 10 power minus 4 the cubed meter cubed okay that is the volume in one drop. So just to complete that calculation that is 10 power minus 12 meter cubed the volume in one squirt is on the order of I will say 1 ml because one third ml is on the order of 1 ml. So it is on the order of 1 ml which is 10 power minus 3 liters which 1000 liters make a meter cubed. So this is 10 power minus 6 meter cubed okay. 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 10 power minus 6 meter cubed divided by 10 power minus 12 meter cubed. So n is on the order of 10 power 6 okay. This is the simplest of sprays one that we are probably all familiar with and every squirt produces a million drops each drop having a size on average about 100 micrometers okay and that is the purpose of a spray nozzle the objective of a spray nozzle is to do just this I mean we okay 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 we are almost there to understanding how an IC engine works or how a gas turbine works because essentially we are moving along in the same direction although the magnitudes of some of these numbers would be different okay. So why would we want to take start with approximately one ml of perfume okay and from there create 10 power 6 drops each 100 micrometers in diameter okay that is what the nozzle has just done the objective of doing this is essentially to take perfume that is sitting in the bottom of my bottle and disperse it into an area say my skin or a piece of clothing that can benefit as a whole there are many ways of doing it okay we will again stick to perfume and show how a spray is much more efficient than other ways of doing it. I can take a little bit of the perfume and smear it I can take perfume and sprinkle it these are all also available designs but we all know the ease 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 okay performing that delivery hydrodynamically in other words using fluid mechanics to deliver this product is what is the most beneficial as far as producing a uniform delivery of the product that you intend to deliver okay. Now what have we also done in the process of taking one ml and creating 10 power 6 drops each that is 100 micrometers in diameter on average okay the biggest increase has been in the total surface area that is available to the drops okay. So the single reason we do this okay we will make an estimate of that but essentially what we have done is this is not so obvious with human use of perfume but if I want to de-orderize a room like this then I want to maximize the area of contact between the air in this room and the perfume itself okay 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 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 okay. So essentially if I take the total surface area I will call this a l v okay standing for the interfacial area okay. So if I try to estimate this a l v it is n times the surface area of a given drop okay. So again I am only interested in order of magnitude so n is on the order of 10 power 6 the area of the drop is 10 power minus 4 the square okay and the units on this is meter square. So if I look at this that is 10 power minus 2 meter squared that is 10 power minus 1 centimeter. So essentially if I actually look at it it is about 10 centimeters this way 10 centimeters this way this is the actual area that is available so this is 10 centimeters or 0.1 meters this is 10 centimeters 0.1 meters okay it is like I have taken 1 ml of liquid and smeared it over an area about this big. Imagine the rate at which that perfume would now evaporate I just took 1 ml of liquid and you know I have not even done the calculation of the surface area before spray but you can see how I mean if I take a 10 centimeter by 10 centimeter window the actual content of a small cuvette with 1 ml and the top area on there would be negligible compared to this. So we are already at a point where we know we have increased the area so much that the initial condition does not even matter as far as the subtraction is concerned. So we have taken 1 ml which is about a tiny volume of liquid and spread it uniformly relatively speaking over an area about that big with a 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 have now increased the surface area available for all this transport to happen. So the net the single biggest reason why sprays find application in many different areas and we will talk a 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 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 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 increased the surface area and the higher the surface area the higher would be the drag on this body that is non spherical. So you this increase in surface area has all these other repercussions with several transport 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. So these are the windfalls associated with increasing the number of drops increasing the interfacial area that we are all interested in that is that actually drives these spray applications. So this is sort of the 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. 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 along those are all the details that we will get into but at this point we want to understand what it is that we are talking about. So at least we are talking about a collection of about a million drops can these numbers that we saw around we will see later on around 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 into 10 power 12 10 power 15 drops being produced per milliliter. So huge increase in the surface area if I took for example that 100 micrometers as the average diameter and I decrease that I had a way to decrease it down to 10 micrometers I have come down one order of magnitude on the diameter which means 3 orders of magnitude more in number. So essentially I can take the same volume of liquid and disperse it into a much larger number depending on some mechanical design of the nozzle. So essentially what we are talking about is a collection of drops. Now if you were a dynamisist you are all mechanical engineers and aerospace engineers so if you were a dynamisist so you are looking at the dynamics of a system. So let us take a very simple system a cylinder rolling down an inclined plane let us say if there is no slip here how many degrees of freedom would this system have essentially that cylinder can only go up or down the inclined plane it is a one degree of freedom system. A particle in air single point particle can move in 3 different spatial directions it is 3 degrees of freedom. So if I tell you the position and velocity of a particle in space that is I have to give you 6 numbers I have told you everything there is to know about the present condition of this particle. So that is what we need to know to completely determine the system of one particle I need 6 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 6 times million on the order of 10 million pieces of information 10 million numbers to just know the instantaneous state. 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 sprays that is the idea that is the objective of this next few minutes here. So this let us understand this idea of dimensionality spatial dimensionality is something that is known to all of us 3 dimensions in space for include time that is 4 dimensions right. If I include velocity so I need to know where it is now and where it is headed. So that is 3 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 is 3 more degrees of freedom okay. If I say okay I am not going to go near rotation I will say drop is a spherical entity that is almost like a point particle. So now if you look at what dimensionality means so the first thing spatial that is 3 position plus 3 velocity dimensions. So I have 6 dimensions in space 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 we will talk about those also like let us say 0.1 micron okay. There is no way conceivable that this perfume spray would produce a drop less than that and there is also an upper limit okay or the upper limit could be infinity. The simplest understanding there is that our upper limit is as big as the hole on the perfume bottle I cannot produce a drop much bigger than the hole 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 starting here heading towards the camera and essentially all of the drops are constrained between these two lower and upper limits okay. So the spatial coordinate in this direction is bounded likewise the diameter coordinate. So I want you to start thinking about the size as 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 a droplet size okay. Now if this spray if I am let us say I will switch hats and I want to now talk about a jet A fuel okay. It is a gas turbine aircraft spray where I am spraying jet A fuel jet A is not a single component fuel it is a multi component fuel. So if I want to understand what is inside this drop some drops could have more of the heavier component some drops could have more of the thinner component or the less viscous component okay. So I have now introduced another dimension and mind you these are all in some sense orthogonal dimensions in other words if I tell you the position and velocity you do not 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 what the drop is made up of. So they are all independent directions to describe this spray. So if I now add one more even if I am looking if I am looking at a binary mixture I have one component direction percentage of component A for example it is between 0 and 100 percent. So they are all nice and bounded. So very quickly you can see that we are on the order of 10 times n or 10 power 7 degrees of freedom. If I want to completely describe an instantaneous snapshot of this spray I have to give you 10 power 7 numbers okay and then if I want to describe the evolution to the next instant of time I have to somehow come up with these 10 power 7 numbers all over again correct. Because the next instant could be related to the previous instant through some mathematical equations but as far as I am concerned if I am making measurements they are completely new set of 10 power 7 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 okay in fact it is not just out of our reach it is nowhere within our future reach not just that is this level of detail important. So that is the question that we often ask ourselves not just as engineers of course you know do I really need to know the position and velocity of every drop in this spray in order to use it I certainly did not need all of this last 20 minutes of information to use up a fume spray okay but if I want to use an air blast atomizer in an aircraft I need a little more information but not to this level okay 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 okay 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 give you an estimate of the other things like surface area we were able to estimate a lot of the macroscopic parameters by simpler estimates okay. 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 apply to these sprays that would make sense and that would be sufficient 10 power 7 is like is not is sufficient but it is like way out of the reach we do not need that much. So what are the necessary descriptors what is sufficient how much information is necessary for me to start using a spray okay. So this is this is just to give you an idea of what it is that we are calling a spray okay we are calling on the order of about 10 power 6 to 10 power 10 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 okay. 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 okay 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 okay. So like we said one of the objectives is to increase interfacial area that is quite sort of the most overriding principle on which sprays are applied okay. So let us look at a few different applications of sprays one of the biggest uses I want to start with something that is not very obvious okay which is called spray drying okay say for example if you take your coffee powder granules or tide or surf granules a typical manufacturing process that produces this tide or coffee powder granules is where you first create the product in the form of a slurry a slurry is like a liquid with these particles not in suspend it is there only in suspension not in solution and these this slurry is sprayed following a usually a fairly large bank of nozzles. So like I could have several nozzles that produce that spray this slurry and you have on the bottom side you have a fan that blows hot air. So this slurry spray as it settles down to the bottom of a kiln of some kind essentially loses its solvent typically water and you start to get agglomerated granules. So whatever particles were in a single drop now sort of 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 would not taste as well as granules okay. So this is the process by which most of most granulated materials of powder is manufactured spray drying is very efficient you are talking several thousands of pounds per hour of flow rates extremely high flow rates and several nozzles because productivity and production rates depend 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 drop smaller the water in them evaporates faster because for the same volume I have increased the surface area by decreasing the diameter okay. So the faster evaporation means that faster rate of evaporation means that the I get powder I recover powder from my slurry much faster which means I do not need to make the kiln as long as otherwise. You know also another way of looking at the same thing is that if I make the drop let us too small then I start to get into granules which are not what my customer is used to see the granules feel more like powder okay. So there is also a lower limit on drop size that I do not desire okay. So the point of this is to show you that very often there are conflicting requirements in any design process okay in the case of sprays these are in the case of spray drying these are the conflicting requirements that I do not want drops much smaller than a certain critical size because they produce product that is not what the customer is used to seeing on the other hand if I produce too large a drop I may get wet product coming out at the bottom of my kiln okay. So these two extremes essentially dictate how the kiln design works spray dryer design works and this is the basic principle of operation okay. Now another application is of course in spray combustion we will talk about this in some detail because there is a lot more a lot to learn theoretically from looking at the spray combustion as an application again spray combustion is an area where sprays are applied but the actual applications range from aircraft engines IC engines as well as land based power generation I have all these different applications where I create a spray of some liquid fuel burn it and from the products recover heat to run a turbine or run an engine of some sort okay 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 do not want a combustor that is too short and flabby okay I want a slightly longer combustor which means if I create a mist at my spray nozzle that is very very fine these drops may not penetrate in sufficiently far into my combustor as a result I could get hot spots very close to the nozzle itself so I do not desire complete pulverization of my liquid I want some large drops in there as well to give me this spray this flame geometry I want the flame itself to have a certain discernible length associated with it okay so these sorts of conflicting requirements you will see in every one of these applications and we will talk about how to resolve them as we go along as well okay 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 is how I deodorize the space so 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 do not want the effect to be completely localized in a small region right adjacent to the nozzle okay and these sorts so again I want some large drops that will remain in flight for a little while to give me this spray this length and penetration to the spray because I do not want to be walking around every nook and cranny of this room to be spray okay 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 do not desire below there is also a upper end of drop size that I do not desire above as well okay and a spray nozzle designer and manufacturer has to take these into account and be able to design spray nozzles that fit these constraints that is a challenge okay alright so now so we talked about three or four of these three of these applications let us look into one of them in 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 into produce a collection of drops you will see this word atomize used in the context of sprays very often nozzles are called atomizers it only it comes from some old British engineers who were used to colorful language that they started calling nozzles atomizers although we are nowhere near the atomic limit of these liquids okay we are not atomizing the liquid in that sense we are heading in that direction but we are far far away from that okay just to give you an estimate again one drop of this liquid is about let us say 10 power 18 meter cubed okay and 18 grams of water contains 10 power 23 molecules again order of magnitude right 18 grams is the atomic weight of water 18 grams is 18 milliliters 18 milliliters contains 10 power 23 molecules of water so we need to sort of understand that this drop is nowhere near the atomic limit we are talking of each drop containing on the order of you know 10 power 10 molecules still 10 power 10 or even more we can do the number but it is nowhere near the atomic limit okay but we will see you will see this used quite a bit the collection of drops then evaporate and that evaporation gives rise to vapor phase fuel that is now mixed in with with your oxidizer you have vapor phase 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 a liquid fuel by say hexane or octane you have a certain reaction between octane vapor and oxygen in the air giving rise to carbon dioxide water vapor and a lot of other by products but essentially that is the reaction the reason you have reaction happening the reason we facilitate reaction is because I have heat release okay that is what I am after in all these applications at least the combustion applications I want to somehow convert the chemical energy in these fuels into heat so this gives me heat release now the heat release is not going to keep quiet 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 okay this atomization is essentially what is happening close to the nozzle that is the process of converting bulk liquid into a dispersion of drops a collection of drops okay so that process itself is a fluid mechanic process there is some motion happening and it is quite possible that that fluid mechanic process is affected by the temperature environment it is embedded in okay so this this heat release could also affect your atomization this is a simple sort of a arrow diagram indicating the different physical interactions that could take place between the spray and the environment okay now the atomization clearly affects evaporation through the drop size the evaporation is also affected by the reaction is 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 okay so this from an applications perspective this is what makes the design of spray combustors very challenging okay alright 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 with droplet dispersion and evaporation I have the same atomization and evaporation part that come in okay so you have we looked at a few different applications so let us quickly recap what we learned today so first thing we understood spray morphology or dimensionality some feel for numbers associated with the real spray okay and then we listed a few different applications and wrote down the different challenges in each of these applications okay 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