 The last class we had looked at how vaporization times are determined by the droplet diameters right and we had said injectors are the devices that are used to optimize the propellants. Now let us look at what are the various kinds of injectors that are used and how do they operate and what are the difficulties in operation. Now injectors are devices that put the propellant into a fine jet of liquid okay now what happens to this jet of liquid I am sure most of you would have played with a garden hose right when you reduce the area it comes out like a thin sheet and then breaks up into droplets why should it break up into droplets yes what is causing that instability now if you look at what are the forces that are at play in this process one is inertia force then there is a surface tension of the liquid right the other thing is the viscous forces because there is an ambient atmosphere that is still right and therefore you have viscous forces that are trying to slow it down and that breaks it up into a very fine droplets okay. So that is what also actually happens in a liquid rocket motor so you use you bring out the propellant in a fine jet then it will break up and become very fine droplets the size of the droplets has a relationship to the size of the injector we will see what that is in a short while now the basic job of the injector is to break up the propellants into fine spray or fine droplets right so it has to be designed such that firstly we need stable combustion okay if the combustion is unstable then we are into problem first we need stable combustion then we need high combustion efficiency that is we are looking at excess of 92% if the combustion efficiency is small although we are using propellants we are not getting a maximum benefit out of it only a fraction of it is being utilized okay so we would want the combustion efficiency to be as high as possible now we also want this to make sure that the combustion chamber length is small please remember this is a pressure vessel that we are talking about combustion chamber is a pressure vessel and if you have a larger length then it means weight so we want it to be as short as possible we want to have very high combustion efficiencies also so there are two things that are running in opposite directions right I mean one is forcing it to be longer you want higher combustion efficiencies you want it longer but then if you have it very long then your weights will go up so designing it is a challenge and lastly this also has to ensure that combustion temperatures what do we mean by this there is a spray that is there we do not want any kind of hot spots okay we do not want some places to be very very hot then the other places to be not so hot because that would in turn mean that the cooling problem becomes more acute in some region and the motor might give way in some portion okay so we do not want that and therefore we want the combustion temp temperature to be within limits this is in some sense if some of you have studied aircraft engines there is something called as pattern factor which the which is talked about in gas turbine combustors also at the end of it you want a nearly uniform distribution because then you are feeding it into the turbine you do not want hot spots then so all these things needs to be ensured by a proper injector design now let us look at the different kinds of injectors that have used in the industry for this purpose one as a straight hole injector then there are swirl injectors now in the straight hole injectors there are three types one is shower head and unlike like and unlike impinging and lastly coaxial let us look at how these are as you can see here the first one is the shower head injector this is nothing but very similar to the shower that we use every day right these are straight holes and there is fuel and oxidizer that is coming now notice that they are going parallel to each other right so therefore in a sense you are not utilizing the possibility of using the momentum of these jets to break them up right one is as I said if you push a jet into quiescent air there is viscous forces and surface tension these interact and make it into fine droplets but in addition to that you could make the jets interact with each other and therefore break up into a fine spray in a much shorter distance right so in this shower head it has not done whereas in a light doublet this is utilized that is you have either an oxidizer or fuel jet coming here and either oxidizer or fuel jet coming here the name like is there because you are using either fuel on fuel or oxidizer on oxidizer okay so these jets interact and they break up break up into very fine droplets in a much shorter distance whereas if you look at this this is an unlike jet unlike impingement that is you have oxidizer coming and impinging on fuel okay this kind of arrangement people would not use in when they are using hypergolic fields right hypergolic fields if you remember they do not need any injection and once they see each other they start reacting so in this case you would have heat release very very close to the injector head which sometimes might not be recommended and therefore whenever people use hypergolic fields they use this kind of combination that is like combination that is fuel on fuel or oxidizer on oxidizer now if you look at like or unlike doublet the jets come here right we will be able to show something if you to take a look at like or unlike doublet it is something like this you have either fuel or oxidizer coming here and either fuel or oxidizer coming in here right if you look at these jets interact at some point and the resultant direction in which the jet goes off is given like this so this angle if we call it beta injector and this let us say this is a f o x vf we can show that if there is any problem with one of the jets right in this case we are going to have a change in the direction of the result in jet and sometimes it might go and impinge against the wall the hot gases so we would not want that so if we calculate the tan of the angle beta injector this can be expressed as this is from purely momentum balance now if due to any reason the mass flow rate or one of the parameters of one of the jets varies then the resultant direction will also change which is not a very good thing right it will also result in changes to the mixture ratio locally the mixture ratio might also get affected we do not want that and therefore use of an unlike triplet as shown here is more recommended in this case the direction does not change and it is more robust and you also can use something like an unlike pentad as shown here that is we are only seeing a section here which will show three there will be one more on the two more on the either side okay in addition to this we have looked at shower head and like an unlike impinging I said there are coaxial injectors which is shown here coaxial injectors are typically used for cases where you have liquid oxygen and liquid hydrogen because if you remember hydrogen would already be a gas so then it is easier to have this kind of injectors wherein it is coaxial you will have the liquid in the core and the gas on the periphery you could also swirl it the inner fluid that is the liquid and you will get a swirl injector so coaxial injectors you will have many of these repeated right there each is one unit and you can repeat it to get your overall injector now let us look at the various advantages and disadvantages of these injectors firstly let us take the shower head now shower head if you look at it it is also very good for film cooling remember we probably are going to use film cooling because you need a layer of fuel on the walls injected on the walls it is easier to get that with a shower head but as I said we are not using the momentum of the jets to break up into very fine droplets so the optimization is poor and hence it will require a very large volume for combustion chamber design so although this is good for film cooling then the like doublet right in this case the mixing is a lot better because you are using the momentum of the jets to break them up so it also leads to a stabler combustion and the volume of the combustion chamber is also very small but it will have a larger control volume a larger combustion volume compared to unlike doublet but it is also very simple to design the manifold you will see what is the manifold in a short time what you see here is the design of the manifold the portion that is upstream of the injector is called the manifold now if you are wanting to have unlike injection unlike doublet you see that the fuel and oxidizer must be I mean you should have one fuel manifold and then oxidizer and then fuel and then oxidizer so it is not easy to design the pipeline and other things upstream of this right it becomes very complicated but whereas if you have a like doublet it is a lot more easier because you are going to have only fuel on fuel or oxidizer on oxidizer this has very good mixing so faster combustion and smaller volume of the combustion chamber it is also not very difficult to design this manifold but as we said earlier we we should not be using this when we are using hyperbolic fluids both these designs as we discussed earlier are I mean the design is very sensitive and prone to changes in mixture ratio because of what we discussed here the angle at which they come in and interact so they are very sensitive to mixture ratio changes if you take a look at what unlike triplet that we discussed this would have very good mixing properties and as well as it is not sensitive to changes in mixture ratio but the design of the manifold could be a lot more troublesome in this because you want fuel oxidizer and then again fuel so very similar to unlike pentad is also very similar to this okay then lastly the swirl burner now in the case of a swirl burner it is probably going to be very difficult to use film cooling simply because if you look at this figure here as I said earlier there are going to be a number of elements of this so you have to kind of make sure that on the periphery you take care to ensure that you have only fuel being injected something similar to what is shown here all this has coaxial injectors in the center right if you look at it there are a large number of coaxial injectors in the center but on the periphery you have holes wherein only hydrogen is injected so this will have good mixing and faster combustion but it might have issues with film cooling now all these injectors one of the troublesome issues with liquid rocket engines is if you look at a liquid rocket engine it is very very manufacturing intensive it has firstly it has if you are looking at turbo pump fed systems you have to design pumps you have to design turbines and all that there are a lot more moving parts firstly and if you come to the thrust chamber of the combustor itself the design is very very intensive in terms of manufacturing if you have cooling regenerative cooling then those coolant tubes need to be very carefully done manufacturing is a very critical thing there because you are looking at very fine tube sizes and the total tolerances that you can give is not very large so it really you need to have very good manufacturing skills in order to make sure that you have a very good liquid rocket system if you look at the injectors also all of them are very small holes and you need to take special care to ensure that the design is very good right one of the things that people take care is what should be the L by D ratio length to diameter of each injector it is typically something between 4 to 5 and you need to ensure on the manifold side right manifold side it has a manifold side entry smooth rounded entry and on the combustor side it has a sharp edged exit now one of the troubles is if you look at how to make this rocket motor right there are some designs which allow you to make the injector first and then weld the entire injector plate to the manifold such designs are called accessible and there are designs wherein in this case accessible design you can remove whatever burst that are there due to manufacturing before you finally weld it but if there are birds that are there on the injector right then the mass flow rate of one particular injector might change so that creates a problem in the functioning right and that needs to be taken care of so that is why I said manufacturing is a big problem in terms of liquid rocket motors so there are three kinds of injector heads one is accessible that is you can make the injector head and then weld it on to the rest of the motor so both sides you can now see and remove the birds that are there on while manufacturing this that is possible in this there are semi accessible and then blind also that is you will not be able to access it at all so in that case you have to look at some different kinds of ways to remove the birds okay like electro polishing and other techniques otherwise you cannot remove these birds through mechanical means right okay now we have kind of understood how injectors work and we also know what is the mass flow rate expression for mass flow rate through an injector we had said that m dot is equal to Cd into a injector under root 2 ? L ? P right so if you want to change the mass flow rate remember liquid rocket motors we can throttle the thrust that is we can increase or decrease the thrust so if you want to change the mass flow rate if you look at this expression CD is fixed density of the liquid is fixed injector area is fixed so the only thing that is available for changing the mass flow rate is the ? P so therefore you can change the upstream pressure of the combustor that is the manifold pressure and get a higher or lower injector where ? P across the injector and get the required mass flow rate through the injector while doing that one needs to be a little more careful as I said while doing the change in the mass flow rate one needs to be a little more careful simply because there is a region where in the CD the coefficient of discharge if we plot the ? P across the injector and CD coefficient of discharge the coefficient of discharge remains constant over some region and then drops and then goes like this like right but there is no guarantee that if you are reducing the ? P injector it might follow the same path okay it could follow a different path something like this while coming back this is known as hysteresis okay that is while going in one direction it takes a particular path while coming back it does not come back along the same path so if you are operating the motor in this you need to be very careful and it would be advisable not to operate the motor in this region and to avoid it completely because while doing the operations in one way it will have some mass flow rate while coming back it could have a different mass flow rate ? P you can change by either changing the pump output pressure this is possible probably only in a if turbo pump in the other one you have a pressure regulator so you can regulate the pressure that is acting in the tank okay in a turbo pump you have to change the pump power out input then you can get a lower or higher ? P across the pump and therefore the pressure at the manifold but in the case of pressure fed system you have to operate the pressure regulator to get the required throttling at partly this happens because if you look at it the fluid is going through a path right there could be flow separation and other things now if you are reducing the injector pressure the processes might not the flow separation process might not follow the same path while you are coming back right and that is why this kind of hysteresis is observed so we have now learned what is the mass flow rate through an injector and if you remember we can calculate based on the thrust and ISP what is the mass flow rate of fuel right now what the other information that we need is what is the area of injector that we need to use in order to design a particular liquid rocket motor right if we know this area or the diameter then we can design these injectors now how to go about designing this injector size now as I said earlier if you look at what are the things that control the droplet size one is the injected diameter and the other is the interplay between inertia forces viscous forces and surface tension okay so if you put this down in terms of non-dimensional numbers then the non-dimensional numbers that are of relevance here would be we said one is Reynolds number and the other one is Weber number Reynolds number you know is inertia force by viscous force similarly the Weber number and they defined as ratio of inertia to surface tension so we can express Reynolds number of the I put the suffix j to indicate jet this we can write it as rho L VL rho L VJ then sigma here indicates surface tension forces okay so using this we can come up with an expression for something known as shorter mean diameter to the jet diameter what is shorter mean diameter any idea heard of it before shorter mean diameter okay shorter mean diameter is nothing but the ratio of volume to surface area okay if you take that ratio you will get the dimension as 1 meter so that is something that is used ratio of volume to this is more relevant in some sense because we said heat transfer depends on surface area right larger the surface area then better will be the heat transfer so surface area to volume is what is known as shortening diameter and this dsmd by dj is given as okay this is the expression for Reynolds number and Weber number connecting the diameter of the jet to the sort of mean diameter so if we want a particular sort of mean diameter right if you want the combustion to be complete within some length we would want a particular sort of mean diameter right we if you remember in the previous class we discussed about how vaporization times are affected by the diameters of the droplets so we will know what kind of diameters to use and therefore using this we can calculate what kind of jet diameters we would need right fine typically the range of Reynolds number and Weber number would be of the order of for rocket engines 10 power 5 to 10 power 6 so we would get dsmd to be approximately equal to something like dj okay so if you have a 1 millimeter jet diameter or an injector diameter of 1 millimeter then your sort of mean diameter will be something like 90 microns right so you can now based on this you can design the number of injectors to be used I mean the injector diameter and then to get the required mass flow rate of fuel and oxidizer you can decide on the number of injectors and then on the injector plate you cannot have all of them with a very small gap between the two so you need to have a sufficient clearance between one and the other so using that you can now inject design the entire injector plate right they do not diverge at an angle the resultant jet will go at an angle the dj you are talking about dj is nothing but we are simply assuming dj is nothing but equal to the injector diameter okay so we have now learnt how to design the injector now the only part that is remaining is how to size the entire engine right I said we can now using this design the injector diameter and the number of injectors and how to arrange them and all that so we now can design the overall thrust chamber if you remember AT right AT we had got from what considerations trust and mass flow rate considerations right this is fixed then what we are left with is how to design this length of the motor and what should be the cross-sectional area of the motor or the engine in this case so this is AC and this is length if you remember we had defined something called L star with respect to solid rockets right we had said L star is nothing but we see by AT so this L is very similar to this now one way to look at this L is the gases will have some mean velocity let us call that as you mean so L star should be greater than you mean into time of vaporization right if we have to have we discuss this in the previous class that the vaporization time is probably the slowest process is the vaporization process and this is the time that will be the largest other times are smaller than this so if you design a motor such that L star is greater than this then you are going to have chamber where in the combustion is going to be nearly complete okay so we have now looked at what is the length now this is a chamber in which you are adding heat so therefore the pressure from head end to nozzle end is going to drop right but for all our calculations of thrust and other things what we are interested in is this pressure right this is the pressure that if you look at the thrust equation PC 80 CF PC 80 right this is the one that governs this so we need to ensure that the pressure drop from the head end to the nozzle end is as small as possible right so then this sizing needs to be also done primarily this AC is determined on how many injectors and how do we house them that is the one that drives how we choose AC okay so if we have different AC by 80 if we have AC by 80 is equal to 1.2 then P2 by P1 this ratio would be 0.85 and if we have AC by 80 is equal to 3 will be larger because you now have a larger area to have a mass flow through so with this we complete our discussions on liquid rocket motors right we have learnt how to go about designing pressure fed systems pump fed systems and then also how to look at what is the droplet size and also look at what is the length of the combustion chamber we need to have okay this finishes our discussions on liquid rocket motors in the next classes so we will look at hybrid rocket motors thank you.