 Hello, welcome back, we are going to continue our discussion of sprays and atomization. Hello, welcome back, we are going to continue our discussion of sprays and atomization, but we are going to move on to a little more practical, a few more practical aspects and look at external spray characteristics and their measurement. So let us take a simple example of a spray, you know we looked at what the morphology of the spray is like in the earlier lectures, what we want to do today is understand how one could characterize these sprays. Now we did actually go through and make a list of a few different properties, external properties of sprays, we will start with the first one, we will start by making this distinction between the spray cone angle and the liquid cone angle. The liquid cone angle if I zoom into this near nozzle region, what I have essentially is a flapping liquid sheet of sorts, we have seen videos of this and then you start to get a spray where these drops form. This cone angle subtended by the liquid sheet itself is what is often referred to as the liquid sheet cone angle and the measurement that you can make of the spray part itself slightly downstream is what we will often called the spray cone angle. Now how do you measure these two properties? The liquid cone angle can be measured from a high speed image, a snapshot of the spray at this magnification as shown and it is fairly straight forward and very clearly defined because this is a liquid sheet that is formed at the exit and the angle made by the liquid sheet is very clearly defined. As opposed to the angle made by the liquid sheet, the angle made by the spray is not as clearly defined because the spray itself is essentially a bunch of drops and you have a lot of mist on the outside and it is not like a rigid object that has a clearly defined edge. So, measuring spray cone angle is always a matter of subject, bit of a subjective decision but in the industry typically one could use what is called a blade protractor. So, measurement devices for each of these, so first the liquid cone angle, your best bet is a high magnification image. The spray cone angle can be measured with what is called a blade protractor, this is a technique that is widely employed in the industry. Essentially if you imagine a device that has got two metal blades that are allowed to swing back and forth and you and an operator brings these in to touch the so called edge of the spray. Now, one person's edge is another person's periphery, is another person's mist. So, there is subjectivity in what one would call the edge of a spray. So, one of the basic problems with using blade protractor is poor repeatability or actually more precisely poor reproducibility. So, operator to operator, while one operator working on one spray nozzle may be able to reproduce the same result, may be able to actually repeat the same value of measurement. If you bring in several operators and have them test the same spray nozzle, you are likely to get high variability. So, this is a device that potentially has high repeatability, but poor reproducibility. Reproducibility is important if I want to convey my results to a fellow engineer and have him verify my findings. So, that is where the challenge lies with these blade protractor, but it is a very simple device cheap and it is widely used. An alternate way is again going back to imaging and using image analysis. So, one way that imaging is often employed is if I take an edge of image of a spray, let us say I take an image that is a sufficiently large spatial representation of the spray cone angle. So, the liquid part is the liquid cone is very close to the nozzle here and then when I take the image, I do see all the mist and everything on the edge and if I take a line going across the spray and plot the intensity in the image as a function of the position from the center line. So, if this is a center line, if I plot the intensity in this particular photograph, intensity of the drops of the image itself, one would see that there is a sharp rise right around the point that you would call the edge. And this point here where the gradient is the highest also known as inflection point is one possible measure of what the edge should be like. So, essentially I look at the whiteness of this pixels of these line of this line array of pixels. So, in whiteness as in a grayscale and it goes from nearly pitch black on the outside of the spray to where the liquid drops reflecting light back towards the camera look whitish at a higher grayscale number. And when I plot that quantitatively, I get a plot that looks like this. And from these two inflection points, I can get the width of the spray at this axial location. So, typically what is done is that you could get the width at a couple of different axial locations and through a curve fit figure out what the cone angle would be. So, that 2 theta is calculated knowing what the spray width is here, spray width is at another axial location. And the fact that I have the nozzle here using these three points using these three data points you one could reach one could essentially reconstruct the spray. Now, a simpler variant of this is to just make this measurement at one axial location. So, if I know this width I will call this 2 w and if I know this height if I call this h, I can define this theta to be h over w or w over h. But this is going to give you a higher source of error in comparison to making the measurements at two positions primarily because most of the time the spray is sort of collapsing on to itself due to air entrainment not due to gravity due to air entrainment. So, this problem is not going to go away if you try to orient the spray upwards or horizontally it is essentially due to the fact that air from the outside is being entrained into the spray that there is a small collapse of the diameter of the cross sectional area over which the drops are distributed. And then the last technique that you can use to measure spray cone angle is what is called a patternation process. So, if I take a spray and place beneath this spray a series of tubes the liquid column in each of these tubes is going to be slightly higher and lower. So, if I were to quantitatively plot that again as the tube height h. So, if that is h is a function of r from the center line or replace this as the center line. So, I have what looks like this from knowing this peak value of the volume flux and saying say if this is v peak I am going to go to a point where the volume flux is one tenth of the v peak and call that my spray edge. So, the point where the volume flux is one tenth of v peak is denoted as the spray edge. So, in other words I have to figure out some way to convert an otherwise blurred edge into a quantitatively repeatable sharp edge. And in this is a case where I take this series of tubes insert them underneath the spray and collect volume in these tubes from the spray over a fixed period of time. And that gives me the tube levels and notice how that notice how I have intentionally drawn the peaks to have different values on either side of the center line. So, in a real spray there is no reason to expect symmetry in the spray. There is geometric symmetry in the nozzle, but very often your spray itself could be slightly off and there is no theoretical reason that they should always be exactly the same in a practical when applied to a practical spray nozzle. So, I could take let us say the average of these two peaks as my peak value and the edge is where the volume in a given tube is one tenth the volume of the peak. So, essentially the edge is being defined as the point where the volume flux is an order of magnitude smaller than the volume in any one given tube. So, once I know this I can essentially do what we did with the image. So, I get a pattern at one axial location pattern at another axial location and from that knowing the spray edge at the two axial locations and knowing the origin of the spray I can fit a second order curve to these three points and from that calculate a spray angle. It is always good to do this at two axial locations again because of this feature that spray edges are not linear entities. So, if you look at what we have just done the difference between doing it via the pattern nation process versus the image analysis process that I discussed earlier is that the image analysis gives us a snapshot in time distributed over space. So, I am using spatial information, but at one instant of time whereas the pattern nation process is where you are accruing the information over time at one axial location. So, it is the old spatial versus temporal measurement techniques, but for this particular spray characteristic that we are interested in both of these give reasonably the same answer. Size velocity correlation is not really was the reason why spatial and temporal measurements are independent whereas when it comes to spray cone angle as a as an entity it gives approximately the same values even if they are not quantitatively the same the techniques are very close the yield very similar results. So, that brings us to the second spray the first spray characteristic is this cone angle. So, spray cone angle and liquid cone angle and the next spray characteristic is what we call spray pattern. Spray pattern is an indication of the distribution of volume flux in a cross section of a spray. Now, depending on the internal flow in the nozzle I could get different spray patterns and like we discussed in the very early part of our discussion the example I have here would be called a hollow cone spray pattern on the other hand something like that would be called a solid cone spray pattern. Now, for the duration of today's lecture like we started we are only going to restrict ourselves to mechanical measurements measurement systems there are optical equivalents of these in of course imaging is optical, but it is a fairly inexpensive tool to use in a in a in a any measurement setting. So, we will stick to mechanical measurement systems for the most part because they are A inexpensive and B they give us reasonably accurate figures for the most part where optical tools give us better estimates the the degree of the quality of the measurement in an optical system is it is not justified by the cost incurred in many instances. So, we will I think these are still valuable research tools and certainly design level tools that one needs to be familiar with. So, we will go to spray pattern one of the tools that is often used is what is called a patternator we have already seen what this patternator is there is three kinds of patternators one is called an in line patternator the other is a circular patternator the third is called a sector patternator we will see what each of these are and what pieces of information these yield. The one I described in the context of measuring course spray angle is what we would often called is what is called the in line patternator as you can see the tubes are all arranged in a straight line the circular patternator is where the tubes are all arranged as points on a circle which with each one of these collection points draining into. So, the ith collection point drains into an ith tube. So, I can this actually if I look at the top view of this these are all circles. So, the middle one may be a circle this outside one will be an annulus of sorts. So, the ith collection annulus is a better way to put it actually. So, except the one right in the middle all other collection regions are shaped on an annulus except they are arranged in a circular pattern where I could place this patternator concentric with the orifice on the spray nozzle. Now, the advantage of this is that each of these collection annuli are at the same distance from the spray nozzle. So, you are likely to collect. So, essentially the cross section a cross sectional area of this annulus that is facing the nozzle is exactly the same as the geometric area. Let us make sure we understand this point if I did the same exact thing in an inline setting and I had a spray nozzle that is spraying let us say I will intentionally draw a wide spray. The collection going into this sector has a mean velocity in this direction which automatically means that the collection area is not this area, but more like the area perpendicular to the velocity vector. So, essentially v dot d a is what is responsible for the mass getting collected into the ith chamber. So, in an inline design the v dot d a the angle between the velocity vector and the d a and the area vector are different and that causes even though I am thinking that I have I am exposing the liquid to the same cross sectional area. The cross sectional area that is that the flow actually sees is different depending on how far out away from the center line that particular sector is located. Whereas, if I have them all arranged in the form of a circle then the area that the then v the angle between the area vector and the velocity vector are is essentially close to being 0. So, before I go much further what do these patternators measure they measure volume flux. So, let us see let us make sure we get the units right on this say I run one of this for a minute and in that minute I collect so many cc of fuel or liquid. If I divide this by the area and then by the time I have taken to collect the liquid this is this forms the units of measurement. So, if the area of cross section of the ith annulus is a i if v i is the volume collected let me write it on this side here. If v i is the volume collected in the tube if a i is the cross sectional area of the of the annulus and if t is the time then the volume flux called q dot double prime is given by v i divided by a i t. So, it is in this quantity a i that the problem arises. If I have 20 annuli at you know across the circle and if I want to calculate a i for the ith annulus by the geometry of that annulus. So, the inner radius of the annulus the outer radius of the annulus I am essentially assuming that the flow is is entering the annulus nearly perpendicularly. Which will be the case if I have them on a circular arrangement if I have them on an annular arrangement then it does not necessarily be the case. And for what kind of sprays does this error become higher and higher the wider the spray angle you can see the angle between the velocity vector in the area vector increases. And the farther away I am from the spray from the spray origin the angle also is likely to increase. So, these are so, if I am interested in measuring large sprays patternation on large sprays in line patternator is a bad choice I have to go to what looks like a circular patternator. Whereas, if I am looking at a small spray that is say I am only 3 inches away the entire spray width is only let us say 2 or 3 inches in diameter and I have a sufficient resolution of cubes in that region. Then an in line patternator may not be very far off from the circular patternator, but you do have the source of error. The third is what is called a sector patternator. So, this is essentially like a circular patternator, but except if I look at the top view of this circular patternator it is not a series of annual I, but a series of sectors. So, each of these sectors is responsible for collecting volume in that sector. So, if V i is the volume collected in the ith sector, A i is the cross sectional area of that sector as the flow sees it and if t is the time of collection I can define the same Q i double prime which is given by V i divided by A i t and I expect Q i double prime over all the sectors to be the same if I have a relatively uniform spray. So, this is a patternator that measures the degree of axis symmetry of the spray or degree of uniformity of the spray in the azimuthal direction. Now again you can create an equivalent of this that is that does not have this sector that does not have the curved nature to the surface, but it could be flat. But again you run into the same issue of the area visible to the flow except that it does not really matter in this case because the error due to the angle between velocity vector and the area vector is the same for all sectors. So, it really you essentially still are able to measure the degree of azimuthal uniformity in the spray, but this is a typical construction. So, these are all mechanical or intrusive methods of measurement I take this device stick it underneath the spray and from knowing the volume collected in each of these 8 sectors each of these 8 sectors then drains into a separate measuring tube. And by knowing the volume collected in each of the separate tubes I am able to estimate the degree of non uniformity in the spray. The last quantity that we want to talk about we will define we will call mean drop size. Mean drop size is a parameter that really is very difficult to measure, but it is an important parameter especially when I want to estimate like the rates of evaporation or the rates of mixing of some vapor phase. These are all phenomena that are greatly influenced by the by the rate of evaporation itself. So, if you look at by the drop size. So, if you look at mean drop size the oldest way of measuring mean drop size is what is called the wax plate method. Now you will probably not find anybody using this today because there are optical tools that will do this for you, but I still think there is value in this it is a very simple technique that you can use that in a days time you can build something on your own and get an estimate of what the drop size may be. So, how does this work you essentially take a plate let us say like a glass plate and coat it with candle wax. So, it is a simple candle wax and this could be like a glass plate glass or some kind of a metal plate or something that you can easily heat and then you insert this plate you first heat it up slightly until you have the wax in some molten state and then cover this plate with a piece of plastic and expose it to the spray itself. So, essentially you have the wax the liquid wax now because the plate is slightly warm you only need like 50 degrees c heat to melt wax. So, you have molten wax on this glass plate and on top of that you have a cover of some kind the cover is removed for removed and replaced back for a very short period of time. So, what you create on the glass plate are indentations wherever your liquid drops heat the wax and just by the liquid heating the wax it immediately solidifies right around where the liquid has heat that is the only piece that is the only place where you do not want further flow of the liquid wax. So, as soon as the water drop hits the wax surface it causes the wax to freeze at that point with the indentation in it. So, once you have recovered this plate with all these indentations on it you can then go to each one of these indentations and measure the size either under a microscope or in a or just by simple by placing it against a known measure like a ruler. So, how can you finally, get drop size from this what you need to do is that this instrument now requires some sort of a calibration. So, what I have at the end of the day is the size of this indentation, but not the size of the drop. So, if I take a known source of drops. So, the calibration process starts with a known source of drops. So, you know the diameter what is the simplest such source of drops it is essentially your old dripping faucet you can analytically calculate the size of the drops that will result from this. Once I know the size of the drops that are impacting the plate in my calibration experiment I can establish a correlation between the size of the indentation and the size of the drop itself. And typically this is a linear correlation so knowing the slope of the curve you can go to an unknown sized indentation and establish the size of the drop. So, this is actually like I said a very simple and reasonably accurate measure, but like in every other case we need to understand the limitations of these measurement techniques. So, what are the limitations of the wax plate technique first is there is a lower limit below which it would not work. Now, where does this come from essentially as soon as I take a spray and place an obstruction in the way of the spray the smaller drops in the spray are likely to just follow the air stream which is going to go around this way and that air stream is going to carry the smaller drops with it. So, you essentially require the drop to be of a certain size before which it will not make this turn with the with the air, but in fact come and form an indentation. You do not want the drop to be carried away by the air, but instead impact the plate and cause an indentation. This lower limit is one reason why you will only tend to overestimate the drop size. So, if you have some fine particles in your spray those will not be measured by this and so you will only tend to overestimate the drop size. So, you do have an upper bound. So, this provides an upper bound and over the real drop size. The second problem is the velocity dependence of the indentation. So, in other words I can take the same dripping faucet in my calibration experiment and I can get indentations at different heights below the faucet and get different indentation sizes depending on how far below the faucet my wax plate is placed. Just because the same size drop is now impacting the plate with a higher velocity. So, the size of the indentation is now not just a function of the size of the drop, but also a function of the velocity with which the drop hits the wax surface. So, if I want to know I only have the indentation spot size as a measure, but I can get the same indentation size by a larger drop that is moving slower or a smaller drop that is moving faster and I do not have enough information to tell one from the other. So, there is we do know that there is a velocity dependence of this slope. So, this slope here is velocity dependent, but how does that really cause a problem in our measurement system? It comes from the fact that if I have different sized drops in the spray moving at different velocities, then I am likely to get into this issue of not knowing what the indentation size is meaning for a given velocity the slope is fixed the indentation size versus drop size slope which means that as long as all of my drops are moving at relatively speaking a similar velocity I am likely to get a good correlation back from the between the indentation size and the drop size. So, as simple a technique as this is this is an exceptionally useful way and it is fairly robust it is withstood the test of time for almost 40 to 50 years before the advent of lasers. So, this is this was the first way by which drop sizes are measured and I think there is still value in performing these kinds of measurements. So, that is the story as far as mechanical patternation systems go. Now, as you found from both of those instances both from the cone angle, patternation and the drop size they are all intrusive measurement techniques whether it is your circular patternator or sector patternator they are all they have an intrusion error associated with their presence. In other words the spray pattern in the undisturbed spray is not the same as the spray pattern with the patternator inserted. This is what we will call intrusion error and it is very often difficult to characterize and quantify the intrusion error, but it is possible to estimate the direction of that intrusion error which is sufficient. So, if I know whether I am over estimating or under estimating my volume flux in let us say the in line patternator I can use the measurement as either an upper bound or a lower bound and that may be sufficient for most engineering applications specifically for the case of the in line patternator. Again if I place a tube in a spray I am assuming that all the drops passing through a certain area of cross section go into the tube and become deposited and I measure that as volume in cc terms. But if some of these drops were to meander away due to the air currents I am only going to measure the ones that actually went in and got deposited in the bottom of the nozzle bottom of the test tube which means that the in line patternator or for that matter any patternator underestimates the volume flux just as we said the indenter on the drop size overestimates the drop size this the mean drop size because it is going to leave out some of the smaller drops. So, these are ways of bounding the measurement or bounding the error on the measurement which is which is always a useful exercise. We will stop here we will continue this discussion and sort of become more current in the next few classes where we are going to discuss optical and non-intrusive measurement devices for a measuring external spray characteristics. Thank you.