 Towards the end of the last lecture we started to draw some conclusions about where the energy that is input into a spray going or input into a spray nozzle going. So we started to say that there is two forms of energy in the spray itself the bulk kinetic energy available in each and every drop that is moving added over all the drops that are moving is a substantial amount of the total energy in the spray. The second aspect is this increased interfacial area of the drops themselves from their parent configuration where I had imagine all the liquid in one drop and I had some mechanical grater that grated these this big drop into a bunch of smaller drops as it turns out that grating process we will call it atomizing process cannot happen without increasing the kinetic energy of the drops themselves the daughter drops themselves. Which means that there is some amount of energy that is stored in the half m v squared of every drop and then on top of that there is an increase in the interfacial area and therefore the interfacial energy as it turns out while we set out to increase the interfacial energy that was our interfacial area and we said that in order for me to increase the interfacial area there is a cost associated with that interfacial energy. But that cost was very very small in comparison to the actual energy that we that we typically put into a spray and the reason for that is that the kinetic energy of all the drops moving is very high in comparison to the increased interfacial area this increase in kinetic energy is the reason why is basically the biggest reservoir of all the energy that we input into the spray nozzle itself. So, essentially we started to look we will start to look at some spray nozzle designs and look at this underlying principle of kinetic energy versus interfacial energy. So, a spray nozzle we started to say converts is sort of a crude definition, but as it turns out it increases a spray nozzle does both of these in differing magnitudes. So, we need to understand why it does this and what are the what is the reason why the increase in increase in kinetic energy is usually much higher than the increase in the interfacial energy. We will look at these two reasons today in a typical spray. So, we are now looking at the mechanics of a typical spray nozzle the first step is to convert the first step in any in most spray nozzles is to take a pressurized source of liquid. If it is not already pressurized it is then pressurized this is this is our initial source of energy the plunger pushing like before I push the plunger chances are the perfume inside is that atmospheric pressure the act of pushing the plunger down causes the pressure to go up slightly. So, the first thing is I have this pressure energy we look at that in some quantitative terms later on, but essentially there is this idea that fluid at a higher pressure has some capacity to do work which is nothing, but energy. That pressure energy is converted into kinetic energy inside the nozzle we are not yet where we have atomized it. So, just bulk liquid inside the spray nozzle is moving faster than it is then of course, the rest condition where it is just sitting at the bottom of a reservoir that increase kinetic energy is a first step in this spray process. And then that increase liquid kinetic energy I will call this bulk kinetic energy of the bulk liquid here let me actually do it like be a little more precise with this. So, essentially I will call the pressure energy is converted into bulk liquid kinetic energy. So, it is still bulk liquid I use the word bulk the phrase bulk liquid to denote non atomized liquid. So, it is still in the form of a contiguous medium basically this bulk liquid then goes through some other process to give rise to atomized liquid. So, now this is in the form of drops the kinetic energy of the bulk liquid inside if I have to go to my real ideal spray that we started to describe that I use an I input energy that energy is goes to increase interfacial area. So, I put in 10 power minus 6 joules of energy I get 10 micron fragments of liquid that is my dream atomizer. But if I go through this route this mechanistic route I have already accelerated the bulk liquid to some kinetic energy. That kinetic energy cannot go back into the liquid as interfacial energy because that is also going against this idea of quality of energy. Moving liquid is like a very refined highest source of highest form of energy interfacial energy is also not is a lower quality energy source than mechanical moving parts moving entities. So, this kinetic energy cannot go back into interfacial energy alone with 100 percent efficiency cannot spontaneously go back to interfacial to interfacial energy is everybody with me on this that I have mechanical energy which cannot for it cannot spontaneously go back to become interfacial energy. It is sort of like saying heat spontaneously becoming work or heat spontaneously becoming a mechanical shaft it cannot happen at 100 percent efficiency it could happen. But surely not at 100 percent efficiency therefore, you are always going to be left with some kinetic energy of this drops plus interfacial energy. So, actually I cannot say that it cannot happen at 100 percent efficiency although it can thermodynamically there is no reason to believe that process cannot be 100 percent efficient because this is not a cyclic process because all of our ideas of second law are only valid for cyclic processes this is not a at least I have drops in motion let us say some fast motion can I get stationary tiny fragments out of it no reason to believe that cannot happen. But unlikely we will see in a moment in most instances you get some remnant kinetic energy in the drops and that kinetic energy is still substantial in comparison to this increased interfacial energy. So, this is the route in which most mechanical atomizers work I will give you just a simple thought example of a non-mechanical atomizer if I take a drop of liquid and imagine I have embedded a tiny amount of some power in it some explosive at the center of this blob of liquid and I explode it. So, there was a chemical energy in that explosive at the end of it if I can create stationary blobs without any dissipation then all of the chemical energy in the explosive is completely converted into interfacial energy if I can do it through that route. But as it turns out fluid mechanically the only route to creating an atomized spray is through increasing the bulk kinetic energy and then using that kinetic energy and some sort of an instability in that flow field to give rise to tiny drops. We will look at this in great detail later on. So, essentially this route is what is called primary atomization this route of taking pressurized liquid increasing the kinetic energy of that bulk liquid and some fluid mechanic process in the middle typically some sort of an instability in the fluid mechanic flow field we will see this later on gives rise to atomized liquid that has kinetic energy and some increased interfacial energy. This is the this process of breaking up contiguous liquid into fragments is called primary atomization. To distinguish this from obviously, if I call this primary atomization I better define a secondary atomization otherwise the word primary has no meaning I will use the word blobs the blobs form from the second primary atomization phase undergo further break up. So, somehow these blobs of liquid at themselves not stable and therefore are likely to break up this process is what we call secondary atomization. So, from nozzle to nozzle we look at in just a moment we look at about a dozen different designs of these pre nozzles the common theme is going to be I need a source of energy I need a source of liquid I need a process by which that energy source interacts with the liquid source and causes the liquid to break up that is primary break up. After the break up has happened the primary break up has happened these blobs of liquid that are formed blobs could be tiny drops or big blobs you know I just use a word interchangeably these blobs of liquid could be more unstable could be unstable still and break up to smaller drops or blobs later on that later on process we will come to later the later on process is relatively insensitive to these nozzle designs. So, in other words the blob a blob of liquid breaking up sort of depends on the local flow field around that blob of liquid and it has in some sense forgotten the design of the nozzle through which it has come because it now only depends on its local environment versus the primary break up process where I have an energy source I have a source of bulk liquid I bring these two together inside my nozzle and cause them to exchange energy to the point where the bulk liquid breaks up that is my primary objective in the primary instability process and I am going to facilitate that through this nozzle design that is the objective of trying to actively engineer a design in a spray nozzle right as opposed to just sort of let them come together alright. So, the objective of a spray nozzle is to allow interaction between a an energy source and b a bulk liquid source different atomizer designs do this differently different atomizer designs work with different energy sources different atomizer designs are intended to work with different kinds of bulk liquids. So, therefore, so many different choices for a and b as many different designs for spray nozzles alright. So, we will now look at starting with some fairly simple designs we will look at a few different designs here. This is sort of a it is actually a diesel injector that is shown in this schematic the diesel injector has a source of fuel as you can see the fuel flows through this passage and is and usually fills this gap here or this area this volume and there is a rocker mechanism the that is released by storing energy into a spring and this imagine it just abruptly comes pushes this liquid out of of this injector. So, this is like a pulse of liquid that comes out and the morphology of the liquid coming out if I zoom out on this side here what does that look like this whole thing is still bulk liquid this bulk liquid is now accelerated through this orifice it is just it is just a through hole it is just a drilled hole basically what comes out is a jet this jet is moving at some velocity. So, I have taken the spring energy converted first into pressure energy in the liquid and that pressure is act that pressurized liquid is accelerated through this converging passage to give me a fast moving source of liquid this fast moving source of bulk fast moving bulk liquid has some kinetic energy in it. Now, what is the source of I need some source of energy to break this up right as it turns out in this case it is the air around that is at rest. So, imagine you can think of it in many ways, but the way I think is sort of the most intuitive is the liquid is moving very fast, but if you are moving with the air with the liquid it is the air that is moving back very fast right in a relative frame of reference. So, it is as though I have taken a stationary column of liquid and I moving air back in this direction at a very high velocity. And that is the if you want imagine a source of energy the air is a the kinetic energy of the air is a source of energy that source of energy destabilizes this interface and in turn strips of drops. So, I might create some drops stripping off from the side and as these drops are stripped from the side this core diameter decreases and essentially I get. So, if you will imagine this meniscus is now unstable because one part of the if I take a profile across some section like that this part is moving at a high velocity this part is relatively at rest. So, there is a shear layer here that develops that shear layer in some classical fluid mechanics sense has an inflection point an inflection point in a velocity profile is sufficient to call that velocity to ensure that the velocity profile is unstable. And because of that you create and you create a growth of that instability essentially shedding these drops. So, what is the area over which the fluid which is in this case the bulk liquid let us say diesel and air which is around interact it is the area of that interfacial area of the cylinder. So, if I want to increase that interfacial area essentially to facilitate this interaction in a more intimate fashion for the same volume of that liquid column I should increase the surface area of interaction. So, as it turns out a circle has the least perimeter for a given area a cylindrical column has the least surface area for a given height of the cylinder of liquid per unit volume right. So, it is going the other way around. So, ideally I should make the whole like a star shape or something that would increase the interfacial area for this energy in the air stream to interact with the liquid. Now, I pose the problem as though the air is atomizing the liquid which is in fact the correct way to think of it, but really speaking even if this liquid was injected into vacuum the liquid by virtue of it is own inertia also breaks up. But in a specific design that we are looking at here which is a diesel injector it is essentially a shear driven instability that causes this drops to be sheared from the surface area of the cylinder where I get tiny drops and sort of an experimental evidence that you can use as testament to my argument is that the drops formed are typically much smaller than the diameter of the hole itself. And we will see examples where they are on the order of the diameter of the hole. In fact the simplest example of a spray is a dripping faucet if I take a tie my bathroom faucet and allow it to just drip. Volume goes into the atomizer or my nozzle or the faucet itself comes out in the form of a drip. Inside the nozzle water is in a contiguous form it is it is one continuum. Once it comes out it is now discrete set of drops there is an increase in the interfacial energy in this process that is facilitated by gravity in that particular instance. So that is the source of energy the faucet which is my atomizer is bringing it to bringing them together in some sense although it is a very trivial case to think of. But even in this in this instance the atomizer is introducing the liquid in a way that the air can destabilize the liquid now and break up break the liquid up into drops. So this is the simplest form of a of an atomizer that I have taken pressure energy in the liquid. So it is in the energy here is in the form of a pressurized liquid that pressurized liquid allows some of the pressure energy to be converted into kinetic energy in the liquid through when it accelerates through this passage. And that kinetic energy in the liquid when is when it comes in contact with the air around which is now at rest creates this inflection point in the in the velocity profile between stagnant air here and fast moving liquid here. And that inflection point is sufficient to cause this flow field to be unstable and cause drops to be sheared from the side. So I have a cylindrical column it breaks it is a basic principle of operation of a diesel injector. Now if I want to increase the interfacial area between the liquid and the air like I said I have to go to some weird shape like a star. As it turns out a star is not as weird the way people engineer a star into a diesel injector is by having multiple holes. That is the reason for having multiple holes in a diesel injector. Instead of having one star shaped hole I can take six holes or five holes as many different designs have different ways of looking at it. Essentially I have taken the volume flow rate going into each of these orifices is 1 over n where n is the number of holes in relation to having all the flow rate go through one orifice. So you can clearly see that the interfacial area available for the air to destabilize the liquid is now higher. So in some sense the efficiency of atomization is better with multiple holes. How far do I take this argument can I go to 100 holes on a diesel injector sure you can except the hole size then becomes extremely small. So manufacturability is the bottom line constraint in all of this. Actually not completely the constraint manufacturability is one of two constraints the other constraint is the fuel quality itself. Diesel as clean as I can get from a gas station has tiny particles in it. So if I make the hole if I have a way of drilling one micron holes 100 of them at the bottom of a diesel injector tip I will clog it up in no time. So that is the other side of this the whether you get the clogging process to be initiated from the combustion side. So some should particles coming and clogging it up or from the fuel side particles in the fuel that come and get themselves embedded in this little orifice. One way or the other it is not good for the atomizer. So owing to these two I can increase the number of holes to the point where to some judicious point where I still am not encountering clogging as a problem and manufacturability is not the issue. That is how a diesel injector works the simplest of the kind. As it turns out it is very inefficient at creating interfacial area. So we will go to the one that is actually most widely used which is called a simplex swirl atomizer. Simplex swirl atomizer is by far the most commonly used of any spray nozzle design. The basic principle of operation is this. So imagine this is my nozzle instead of injecting the liquid straight through from the top and allowing it to accelerate through a converging passage. What is done is it is the fluid is injected through a set of tangential slots. I will call this fuel or liquid. Liquid is injected through a set of tangential slots and what I have essentially done now this is the cross section at some at this section db. This is sort of the view shown here. So essentially you can see the orifices shown as two circles here. Really speaking they are sort of just shown there to give you the idea that that they are tangential orifices. So they are better shown. So this is the tangential injection passage and what I what that does is I create a swirl inside here. So this chamber is very often called a swirl chamber and the liquid is swirling say in this particular instance the way I have shown the view. When I look from top the swirl is clockwise. So the fluid is swirling inside and when the swirling fluid goes through this converging passage I accelerate the swirl just like simply using the principle of conservation of angular momentum just like ice skater with the hands wide apart spins when the hands are drawn in the angular velocity of the ice skater goes up. So in a very analogous manner the angular velocity of the fluid goes up and that increased angular velocity also has an increased centrifugal force of the liquid. So all of the liquid because of this very high swirl velocity is now sticking to the walls of this exit orifice. So this part is called the exit orifice it is just a straight hole except if I look at if this whole orifice was filled with liquid and the liquid is swirling essentially it is just like a spinning bucket you know I create a void in the middle because of that all of this is essentially air it is exactly like a spinning bucket. The liquid is spinning it is also moving in the downward direction the way I have shown the picture because the volume of the swirl chamber is constant and I am introducing more liquid from the tangential slots. So the liquid inside the swirl chamber has no choice but to come out the point the reason I am going through this gory explanation of this is because it has nothing to do with gravity this can be oriented anyway it is the incompressibility of the liquid that is causing the fuel the fuel to flow in the axial direction. So this incompressibility of the fuel causes a small axial velocity but a very high swirl velocity notice how I can well will come to the ratio of the two velocities in a moment but essentially I have created a very high swirl velocity of this liquid and that high swirl velocity causes a low pressure region in the center line causing this air to be drawn in. So there is a low pressure there and that just like a spinning bucket you know how if I take a bucket I start with a meniscus if I spin it around the center line I spread this out into a parabola. So that point is now come down so the water now occupies a shape where the meniscus is a parabola right a part of a parabola. This decrease in the meniscus level is exactly analogous to where the meniscus should have been here it is now back here because of this spin. Now the what I have essentially done here is I have taken this liquid and spread it out into a thin swirling film. So this is my liquid this schematic is not actually to scale the thickness the thickness is usually less than 10% of the actual diameter the diameter of the orifice. So if d orifice is the diameter of the orifice itself the thickness is very very small thickness of the liquid. So most of the orifice is just interfacial is just air basically see how this is fundamentally different from the diesel case. The diesel atomizer the diesel injector was a situation where the orifice was completely flooded with liquid. The only interfacial area there was the surface area of the cylinder exiting the injector. Here the interface is now two fold there is an interface on the inside here and an interface on the outside. So I get twice the benefit for the same orifice size and because I have spread it out into a very thin film the film thickness is one of two determinants of the final drop size. The film thickness is very small we will see the benefits of this in a moment but the interfacial area of interaction between the air and the liquid is now twice as much as I have I had the chance to create in the diesel injector. In addition this is swirling the swirling film is naturally going to expand outwards once it exits the atomizer that is what you see here which is depicted in the form of this cone. So I had a wall inside which the swirling film was sticking as soon as the liquid exits from the other side because the swirl creates an additional centrifugal force that is now unbalanced from the wall reaction it is going to further expand outwards. And this further expansion outwards does two things one it increases the interfacial area between the air and the liquid even more and two it slows down the acts it slows down the swirl of the liquid it is just now the reverse of the ice cater problem. The objective of the swirl was two fold a to spread it out into a thin film spread the liquid out into a thin film and b increase the interfacial area of interaction and c because the actual kinetic energy remember we said this kinetic energy thing is a bad thing I do not want drops to be moving very fast or let us say if I have an application where I am only interested in increasing the interfacial energy of this liquid I really do not want a fast moving spray. But and like I said earlier like we said earlier that is a cost that we have to bear and I want to see if I can minimize it here is a way to minimize it the axial velocity of this liquid is only determined by the flow rate right. So, for the same flow rate I can increase the number of tangential orifices through which I inject the liquid into the swirl chamber causing a high tangential velocity. But low axial velocity the axial velocity being the same I can increase the tangential velocity of the motion the tangential velocity is what is responsible for this water to liquid to go stick to the walls creating a very thin film. So, I can create a as thin a film as I want for whatever be your flow rate by changing the design the diameters of the tangential orifices the tangential the injection orifices and the number of those orifices. This is an added degree of freedom I did not have in the diesel injector I can now control the axial motion which is set by my mass flow rate independent of the film thickness which like I am like I am going to show you is going to be one of the main determinants of the droplet size. A simplex design allows you to control droplet size relatively independent of the mass flow rate that you put in. In the previous diesel injector design if I increase the mass flow rate for the same orifices diameter I have essentially increase the velocity of the few of the liquid coming out which means I have increased the nature of the instability at the inflection point I am likely to get smaller drops. So, over in fact going back the other way in this injector design the only way to get smaller drops is to increase the velocity of the bulk liquid which if I do not change the orifices size means I am stuck with the same orifices flow rate. So, one way to overcome it is to have multiple orifices injecting the fuel. So, for the same mass flow rate while in this particular design you only have one degree of freedom which is your orifices size. Here you have two degrees of freedom which is this tangential orifices diameter and their number as well as this orifices size. Both of these put together allow us independent control of the mass flow rate and the drop size to over a fairly large operating region and that is I think the main reason why this particular nozzle design is widely used. In fact the real reason it is found wide commercial applicability is because I am not constrained by this orifices size you know this d orifices which is my orifices size can be a fairly large value. I can have a fairly large sized hole that I drill and I am fluid mechanically causing the cross sectional area through which the liquid flows out to become small. I am using fluid mechanic processes to decrease the cross sectional area through which the fluid flows swirl. So, that is the reason I can create as tiny a film as thin a film as I want to while having as relatively speaking again as bigger hole as I can. So, from a manufacturability perspective it is always a good thing when I do not have to drill tiny holes in metal parts it is always a good thing. When I have to go to a plastic molded component it is an even better benefit that I do not have to work with tiny features molding tiny features in plastic is always a pain. So, this is a simple design that provides two degrees of freedom. Now, when the film that spills out of the nozzle itself now is going to expand outwards and because you have a similar fluid mechanic instability so this film is now moving in this direction with the air being relatively speaking stationary. So, I have essentially if I take a cross section here I have the same inflection point in velocity profile. So, if I zoom that out on the side here this is my film this film is moving in this direction it may also have a small swirl component, but that would have died out by the section that I have drawn. So, if I take this section c c c the air outside is at rest, but the liquid is moving at some velocity again I have the same inflection point in the velocity profile I think that is spelt inflection sorry not with an x. This inflection point again is sufficient to assure us that that velocity profile is unstable because of which you get a certain kind of instability we will look at that in some detail later on. So, this again causes this liquid film to further break up. So, downstream of here I will change my pen color just to show you drops in blue these drops in blue are formed from this film from the break up of this film. We will look at we will look at this in some more detail in the next class, but there is some break up processes have processes that are causing this film to break up into drops this is our primary break up process. Now, some of these drops may be further unstable and later on they may break down into even smaller drops, but and that is our secondary process, but we are only going to focus on the primary process which is what the nozzle is responsible for. Now, a problem with this is that I create drops let us say if I take a further section downstream we are still talking about the simplex nozzle design. If I have let us say one of those simplex nozzles that I showed in that schematic and I create this film that is spilling out this is the liquid film I am going to create these drops like I showed in that same schematic here. If I take a section down here and call this d d I am going to have more drops let us say this is my spray now I am going to have more drops in this region and less drops here. So, essentially that section d d if I was to take an image of the liquid itself liquid drops it is going to be like a doughnut like a vada with a hole in the middle because there is going to be less mass flow rate of the drops in the middle there is going to be more mass flow rate through that cross sectional area. So, it is really going to look like a diffuse vada in other words I cannot tell when the hole appeared, but then it suddenly appears that is because just like the spray edge it is not a sharp sharply defined edge it is not like the edge of a pen we discussed this it is a relatively speaking a diffuse region over which you had a spray and now there is no spray similarly on the inside you had a spray here and in the middle you have less density of drops. So, this is called a holocone spray. So, a simplex nozzle by design delivers a holocone spray. So, in other words all the drops are distributed into a nice holocone there are applications where it is actually good to have a holocone spray there are other applications where I would rather not have a holocone spray, but more of a spray where I have a nice uniform distribution of drops unfortunately a simplex nozzle is a bad choice when I want a nice uniform distribution of drops we will look at how to solve that problem a little later on. So, let us quickly recap what we have done today we looked at the energy budget for a spray nozzle and said it does two things it increases the kinetic energy it increases the interfacial energy while this is my objective I cannot do without this as you saw from the case of a diesel injector where I am increasing the kinetic energy in order to facilitate that inflection point in order to cause the break up to happen. So, this is as opposed to let us say a mechanical carrot grater where I control the break up process by the frequency at which the greater approaches the carrot and the flow rate is how fast I move they can be unrelated, but in this case they are coupled all right. So, with that we said simple design we looked at two separate designs one is a diesel injector which is essentially also called a through hole atomizer it is like a pressure jet atomizer the other example is a simplex design. So, also called a pressure swirl atomizer we looked at these two designs we have at least another ten such nozzle designs to look at depending on remember we said there is an energy source there is a bulk liquid source the objective of a nozzle is to introduce the two to each other and cause the liquid to break up here are two ways of doing it we will find another at a few different ways in the next class.