 So, good morning folks, welcome back. Today we have day 9 of our workshop. Today the topic is topic 13 and that is introduction to cycles, goes by the name quite often used cycle analysis. I should warn you that this is a course for workshop on thermodynamics. So, we could say that what we are doing is we are looking at thermodynamic analysis of cycle. Because if you see we have basic thermodynamics on one side, you have applied thermodynamics or power plants, refrigeration plants and many other type of plants cycles along with other things like heat transfer fluid mechanics, combustion, cyclometry all. Link basic thermodynamics on one side to power plants, refrigeration plants and other equipment of tremendous interest to engineers, particularly mechanical engineers on the other side. Consequently, what we have is something like science at one end and technology at the other end. Being engineers, we are supposed to be comfortable with both, but this being a course in thermodynamics, we would remain more on the science side than on the technology side. Otherwise there is no end to which we can go into the details of cycles. Because after doing thermodynamic analysis of cycles, we will go to the implementation of cycles. Then we will go to the hardware which is used in the implementation. Then we will go to the analysis of the processes inside the hardware. Then analysis of materials used to create the hardware. Analysis of the actual physical situation in the hardware. And you can go into almost any detail. You can go into machine design, fatigue, fracture, material science, reliability, safety, detailing of each and every component. You can say that look what you are doing is essentially studying and doing the engineering of cycles. We do not want to go into that detail. We only have a few hours, but that is not the main restriction. The main restriction is we are going to look at cycles essentially from a thermodynamic point of view. So if you look up our scheme of things, we will talk about classification of cycles. Then we will talk about implementation of cycles. Then we will talk about performance parameters, some typical performance parameters of cycles. Then we will essentially be describing and looking at the thermodynamics of power cycles and refrigeration cycles. Not in very great detail, but the basic idea, basic principle behind these cycles. Cycles are implemented in various equipment and plants. Then it is difficult for us to keep away from the technology used to implement those. Particularly when it comes to internal engine cycles, autocycle and diesel cycles and to some extent vapor compression cycles, there is a very thin line which can easily transgressible line. Although we would like to keep away from technology and emphasize the basic thermodynamic principles, when it comes to some types of cycles, particularly auto diesel cycles and to some extent the vapor compression cycles, technology is not very far away from the details of the cycle. There is a very thin line which can easily be crossed. Sometimes you want to explain the cycle and the details of the cycle needs to be crossed to study those cycles and wherever necessary, we will do that. Then we will spend some time on the modifications of cycles to improve certain performance parameters and finally to the combination of cycles. But what we should remember is that any cycle finally is implemented in a number of components and if you analyze the cycle, it will be various thermodynamic processes either in a typical float system like a cylinder piston arrangement or a typical open system about which we have already seen. And if you go back to your exercises on open systems, you will find that there are some exercises which are essentially pertaining to parts of a cycle. For example, we look at exercise OS24. This exercise OS24 is essentially part of a cycle, but here we will, we have to analyze it as a combination of components, each one of them is a thermodynamic open system. So although perhaps you have solved this, you will notice that there is one component which is a pump, which is a work transfer device, another component which is a boiler, which is a heat transfer device, third component which is a turbine, another work component. Then there are two components which are a bit odd. One of them M is the mixer which takes in two streams, mixes them and gives out a mixed stream. Whereas this S is a separator, which takes the wet steam at 4 and converts it into two streams, one of almost dry saturated steam at 5 and another at almost saturated liquid at 6. I think as specified, state 6 is 2 bar dry saturated vapor and state 5 is 2 bar saturated liquid. So if they are not approximately dry saturated and saturated vapor, they are exactly as specified. And on cycles, if you look at your exercise sheet, we have a set of 33 exercises and you can create many more. And actually as you do this, you will notice that we are not very far away from technology in many of these exercises on cycles. So let us first look at the classification of cycles. First we should realize that cycles are used for our plants and refrigeration plants. And the importance of cycles is we started getting introduced to cycles right at the beginning when we started studying the second law of thermodynamics. And although we did a large number of theoretical exercises there, now we have come to a stage where we are going to really implement. And the first question that arises is why not always use the Carnot cycle when we know that given certain situation the Carnot cycle is the base cycle. We delayed that discussion a bit and let us first look at the classification of cycles. There are a number of ways by which we can look at cycles. For example, one method of classifying cycles is the base typically on the type of usage. This would be a power cycle or a refrigeration cycle. Then another classification is essentially for power cycles. This is whether it is external combustion or internal combustion. Of course, now there are cycles where the energy is not supplied by the process of combustion, but by nuclear decay or solar concentration. But the classification of external combustion and internal combustion with a generalization of combustion to heat source or heat supply, it is still valid. We will generalize it when we come to that. Then the third way is whether it is what is known as an open cycle or a closed cycle. A fourth way of classifying cycles would be whether it is based on a single piece of equipment, what I call single equipment cycle or multi equipment cycle. Actually this order can be in any order except that two should follow one. Unless you talk of power cycles, you cannot classify power cycles further into external combustion and internal combustion. Fifth is whether it is a gas cycle or it is a vapor cycle. One thing I should say that whenever I use pertaining to cycles, the word refrigeration that includes extensions of refrigeration as air conditioning, cryogenics, freezing and all those. Let us look at these classifications in some detail and what their implementation implies. What are the implications of those adjectives used in this classification? Let us say the first one is based on types of usage. Here we have power cycle and refrigeration cycle. We can say power cycle produces or delivers power. That is its main purpose. Whereas refrigeration cycle is produces what we call refrigeration effect. With one proviso here that although it is not a refrigeration cycle, if you have a heat pumping cycle, you can say instead of a refrigeration effect you can say or heating effect. So these are power producers whereas these are power consumers. I should not write positive or negative here. There is nothing positive or nothing negative about this cycle. Here W dot cycle would be greater than 0 and this is the main purpose of producing power in these cycles. Out here W dot cycle would be, so these are power producers, these are power consumers. But the main purpose is to provide either a refrigeration effect or a heat supply effect. If you look at the T S diagram where T is on the Y axis and S is on the X axis, a power cycle would typically be clockwise whereas a refrigeration cycle essentially would be anti-clockwise. That is the result because of, let us look at some typical cycle diagrams. By that I mean let me draw a line that is indicating the surroundings provide us a large thermal reservoir to be used either as a source or a sink. A typical power cycle will have an energy source which is higher than T ambient and the power cycle will work by consuming energy in the form of heat, heat absorbed and heat rejected. This is typically an engine producing a W dot net which is greater than 0 in the direction shown. Now of course if you have a source when you absorb it the temperature will have to be slightly lesser than the source. When you reject it, you have to reject it at a temperature slightly higher than the ambient so that we have certain temperature difference available for the good heat transfer. So this is the typical situation of a power cycle and for a power cycle quite often we will define the efficiency, definitions of these parameters we will come when we come to the item three. When it comes to refrigeration cycle there are typically two types of refrigeration cycles which we consider. One is the standard refrigeration cycle whose job is to maintain a system at a low temperature, at a temperature which is T ref lower than the ambient temperature. And the job of this cyclic device is to absorb heat known as the refrigeration effect from that low temperature system doing one of two things perhaps both one. Maybe initially the refrigerated space is at ambient temperature and we want to reduce its temperature to below ambient. The second one is to maintain it below ambient we will have to still extract certain amount of heat because we cannot have perfect insulation. So there will be some transfer of heat just because of temperature difference from the surroundings to the refrigerated space. And if we want to maintain the state of that space at the low temperature we will have to keep on extracting an equivalent amount of heat. So the refrigerator will extract heat will consume power look at the direction if the other way for this W dot and we will reject the required amount of heat to the ambient. Obviously if this is the refrigeration temperature while extracting heat you will have to be at a temperature slightly below that and the heat rejection will have to be at a temperature slightly above ambient. This is the typical schematic of a refrigeration cycle. We have another type of refrigeration cycle or what we call the reversed cycle if you feel like. So maybe I should write here that sometimes these are known as direct cycles and these are known as reversed cycles. But nothing special about this terminology. The other type of cycle is used to maintain the temperature of some system at a value higher than the ambient. It could be an incubator, an oven or something like that. So now we have a refrigerator like system. We call it a heat pump. It consumes power. The main job is to deliver the required amount of heat at the required rate to the hot system. And for that it can absorb the required amount of heat from the ambient consuming an appropriate amount of power. So what we have on the left side is the power plant. On the right side we have the refrigeration plant and the heat pump plant. In the engine this is what we need and this is what is required to be done to produce that. In the refrigerator cycle this is what we need and W dot is required to be consumed to produce that refrigeration effect. Whereas in the heat pump this is what we need. We set up the heat pump to supply this heat and this is what we have to provide power input to produce that much amount of heat. So this is the first level of classification or the first type of classification. And all of us have seen all three types of plant. This type of plant and this type of plant are very common. These types of plants we generally do not come across, but there are enough illustrations of these plants. Now we go to the second type of classification and that pertains to power cycles. Now when it comes to power cycles we will need to know that you cannot produce any power unless you absorb certain amount of heat from a high temperature source. The second classification is for power cycles type of. Traditionally the heat source used to be produced by combustion of fuel. But nowadays instead of combustion of fuel of any kind, of course the idea of fuel has expanded. Instead of combustion of fuel you could have nuclear reactions of some kind fusion or fusion. Fusion is common, fusion is still in the lab. You could have a natural source like solar energy, you could even have geothermal energy. And since we are always short of power we will be looking at various other sources. But finally these are heat sources. Now this classification of so called external combustion versus internal. Although it pertains to classically combustion we can say now pertains to the heat source. Now the difference is if you have external combustion, then the energy release, I will use the word release which is not a good word to use, occurs outside the working fluid and heat transfer is across some physical boundary like a wall. So what you have is you have a working fluid going through some passage. You have some other system in which so called combustion quote unquote or the heat release takes place and the heat is transferred across a boundary. This is the intervening boundary across which this q dot is transferred. As a result of this the temperature of the heat source needs to be high to provide a certain amount of delta T. And since that will be limited by some technical consideration the temperature to which we can heat up the working fluid is also limited. However the advantage of external combustion is that the process of combustion separated from the cyclic process. So you can optimize this independently of what happens in the cycle that is one. The second one is the working fluid does not undergo any change in its composition. So if it is a precious working fluid you do not have to worry about it getting contaminated or chemically modified in any way. If it is demineralized water well it will get converted to steam back to water but water remains water. So most of our steam plants I would say most of them because we will have an illustration may be rarely where it will not be so but almost all our steam plants are of the external combustion kind. Even when they are nuclear plants where there is a reactor which generates heat and it is transferred across some boundary some physical boundary physical barrier to the fluid. We tend to call it an external combustion plant even though no real process of combustion is involved. Now when it comes to internal combustion the combustion reactions within the working fluid consequently no heat transfer another system is involved. Consequently higher temperatures can be achieved but the disadvantage is composition of working fluid changes and not only that because the combustion reaction take place within the working fluid the process of combustion and the cyclic process they get entangled into each other. You cannot optimize one and say let us worry about the other one independently that is something you cannot do because combustion now becomes an integral part of the cycle. And the main disadvantage of another disadvantage is that the composition of the working fluid changes and this will have to be taken care of appropriating. So that brings us to the second classification essentially for power cycle. Now we come to the third classification open cycle and closed cycle. Now this is an implementation detail a closed cycle the working fluid in general does not equipment all processes of the cycle executed within the plant. Example is our household refrigeration plant household refrigerator everybody says that it has a sealed unit of certain kind. It uses a working fluid earlier it used to be R12 now it may be R134 some ABC or something like that. We are getting newer and newer working fluids for ice plant ammonia is a reasonably common working fluid. But whatever is the working fluid it never leaves the equipment in which it moves never comes in contact unless there is some accident or you have to do it for replacing it or cleaning the whole thing or maintenance or repass. In the general scheme of things the working fluid remains inside the piece or pieces of equipment which execute that cycle. A household refrigerator is a typical example in fact the technical name for that equipment is the sealed unit of the refrigerator even our household air conditioners are of that kind. When it comes to power plant typically our steam power plants are closed cycle power plants where the steam water generally does not leave the plant except that the water because of the large area to which it is exposed of metals it is move the impurities we take out through blow down some part of the water and replenish it at some place. But it is to maintain the health of the plant not for thermodynamic working of the plant. So in spite of that small amount of blow down and replenishment of water we consider the steam power plant to be a closed cycle. An open cycle on the other hand is something in which at least one process outside the plant and here we depend on nature. The working fluid leaves the plant new fluid is inducted. The examples of this for example the example of closed cycles are steam power plants refrigeration typical steam power plants and typical refrigeration plant. Open cycles are our auto or we talk instead of cycles let us say petrol, diesel engines and of course gas engines, CNG engines, LPG engines and all that. Jet engines and similar devices in which we take in typically the ambient air as the working fluid execute some processes and then throw it out. So if we say this is the open cycle plant the working fluid goes in at some P0 T0 which is near ambient and after the executing some processes it is thrown out at some P exit T exit which is different. And this process of reducing the temperature reducing the pressure and may be even modifying the composition back to it is the fresh one at the ambient it is supposed to be done by nature. We do not worry about it we throw we take in air we take in petrol in our car engine and we throw out the exhaust. Let nature worry about converting nitrogen oxides back into nitrogen and oxygen convert carbon dioxide back into carbon sorry carbon and oxygen create a new fuel for us whatever other pollutants the nature should get rid of and of course if it is at a higher temperature it will create some noise but that noise will get dissipated and nature will bring it back to its own ambient pressure and well although the surroundings will become hot for some time nature will take care the heat will get dissipated and we will get back our ambient fluid at the temperature T0. So the disadvantage of an open cycle is that we are loading nature without asking for its permission for at least part of the part of the execution of the cycle. Now that brings me to the end of the third type of classification the fourth type of classification let me go back is whether it is a single equipment cycle and multi equipment cycle. Instead of equipment sometimes the word component is used and as the classification says here it depends on see any cycle will have a number of processes. Now if it is a single equipment cycle all processes executed in a single equipment cycle are the same. The first one is a piece of which is typically cylinder piston with associated mechanism valves either piston rod or direct crank shaft connecting rod crank shaft through of the crank all those paraphernalia. So whether it is a heating process whether it is a cooling process whether it is a heat generation process whether it is just expansion compression process all processes in a single piece of equipment and that piece of equipment is almost invariably a cylinder piston arrangement and the various processes then we say are executed in various different strokes or combination of strokes or parts of strokes because the piston goes from one end one extreme position to another extreme position when we come to auto and diesel cycles we will see about that. The advantage of this is well you have to essentially design one piece of equipment very well. However the requirement on that piece of equipment is tremendous because even a simple compression process almost adiabatic it has to execute the simple adiabatic process it has to execute it has to suck in the working fluid it has to push out the working fluid or it has to heat the working fluid by means of either combustion or some other means it has to cool the working fluid by some other means. Even in refrigeration plants there are some cryogenic pieces of equipment which are in a very complex cylinder piston arrangement for example the sterling engine. In fact the sterling engine is so complicated that depending on the layout you can make it consider it a single piece of equipment or you can consider it as a multi piece of equipment because the regenerator etc sometimes is made part of the piston called it a displacer and externally it simply looks like a cylinder piston arrangement but internally there could be various components. The multi equipment plant on the other hand almost always each process has associated with a piece of equipment that means different processes has different pieces of equipment. So for compression there is a piece of equipment like compressor for expansion there is a piece of equipment called expander or turbine for heating up there is either a heater or a boiler for cooling there is a cooler or a condenser for pumping there is a pump for compressing there is a compressor. Each one a specialized piece so there is specialization possible and because there are different pieces of equipment the working fluid is working fluid flows from one component or equipment to another and connecting ducts are used for this purpose. The advantage here is that you can have for each process in the cycle a very specialized component to execute that process consequently each process can be executed in a much better way than in a single piece of equipment because you cannot optimize it is very difficult to optimize a single piece of equipment to execute all the processes with equal thinning. Whereas in a multi piece of equipment you take there is a specialized equipment called compressor for compression another specialized equipment called turbine for expansion specialized equipment for condensing specialized equipment for boiling specialized equipment for each and every purpose. The disadvantages now the plant will not be very compact it will have to be laid out with all interconnecting ducts and valves and control equipment. But the comparison again between single piece of equipment and the multi equipment type single piece of equipment tends to become compact but the sizes are consequently restricted. Take for example our power plants when it comes to power plants the auto and diesel type of cycles petrol, diesel, gas engines they are good for a range of power from say roughly a few kilowatts to 100 kilowatts perhaps a few megawatts that is the limit. But if you want something like 30 megawatt, 50 megawatt a single piece of equipment is just out of question. Now if you take a single piece of equipment to mean just one cylinder then you are even still restricted you can have a 4 megawatt engine but that will have may be 32 or 36 cylinders each producing 136th of the power. So if you see one cylinder piston arrangement and say that is one unit all you have to do is like slices in a bread you have stacked it up to make a multi cylinder engine then one unit is may be good for a few tens of kilowatt or may be of the order of 100 kilowatt not more than that. Whereas when it comes to multi equipment each equipment can be scaled as required. So when it comes to large power almost all our plants whether power plants internal combustion, external combustion they are all multi equipment plants and because multi equipment plants have individual pieces of equipment to execute their processes each equipment can be designed exactly to do what it needs to do and in the overall health and efficiency and robustness of the plant increases even the life of that plant is higher tends to be higher. Finally let us go back to the 5th classification I do not want to come back here we have finished 4th and we will finish the 5th one and just I wrote them down as 1, 2, 3, 4, 5 because that is how I remembered them all that I remembered that there are 5 of this kind you can put them up and down as needed except that external combustion and internal combustion plant you cannot classify before you classify power and refrigeration plant. Now let us go to the final 5th classification and that is gas cycle or gas power plant or gas refrigeration plant and vapor cycle or vapor plant power plant or refrigeration. This classification depends on the type of working fluid and as the name says the working fluid could either be a gas or the working fluid could be a vapor. For gas cycles as the name says always the working fluid always in the gaseous phase no change of phase is ever expected. The advantage is analysis is simple and in fact analysis is so simple that if you assume that the gas behaves like an ideal gas and that too with constant specific heats then approximate if needed analytical expressions for cycle parameters like efficiency etcetera can be derived. For example, you have this famous expression that efficiency of an Otto cycle is 1 minus 1 over r v to the power gamma minus 1 something like this you can derive and many of our teachers take great interest in the ability of a student to derive such equations for Otto cycle, diesel cycle, dual cycle and with their various combinations and modifications. However, there are certain restrictions of gas cycles. The restriction on gas cycle is whenever you change whenever you absorb heat or whenever you reject heat there has to be a change in temperature. Consequently, if you want to have a gas getting heated start from some temperature more heat means a higher temperature so that is a disadvantage and the higher temperature quite often is restricted from the equipment point of view material point of view. Vapor cycles on the other hand the vapor cycle as the name suggests does not mean that we use the vapor as the working fluid that is true. But in a vapor cycle it is a vapor and it is condensate together form the working phase and part of the cycle it will be in the vapor or gaseous phase, part of the cycle it will be in the liquid phase or the condensed phase and because of this change of phase particularly this change boiling and condensation boiling or evaporation or vapor generation is an essential part essential part of the cycle. You can have a gas cycle or a vapor cycle using steam but if it never condenses as implemented in the cycle well we will not call it a vapor cycle. If it remains always in the super heated zone comes nowhere near a state where it is likely to get condensed then we will call it a vapor cycle, we will call it a gas cycle, we will not call it a vapor cycle. In fact this classification is one of the funny things in general we do not make much of a difference between a gas and a vapor they are more or less synonymous term but when it comes to classification we have a distinction between what constitutes a gas cycle and what constitutes a vapor cycle. The advantage of a vapor cycle is because some fluids like ammonia, water have large latent heats you can make the fluid absorb heat make the fluid reject heat without any significant change in temperature that is one great advantage of this. So, latent heat of the working fluid is important but you will need specialized equipment to make use of this in terms of boilers and condensers but the disadvantage is because there is no simple equation of state for say water M H 3 refrigerants etcetera, etcetera no this implies no expressions for parameter. For example we have seen that for an auto cycle or for a diesel cycle or for a Brayton cycle which are gas cycles or even the reverse Brayton cycle which is the joule cycle you can write the efficiency or the coefficient of performance or any other parameter like for example the for auto cycle we can calculate the mean effective pressure those can be written down in terms of certain pressures, certain temperatures and certain ratios pertaining to either geometry or ratios of pressure or ratios of temperature. Something like that just cannot do for a power plant of the vapor which works on the vapor cycle. For example, if I tell you that an auto cycle works with these ambient conditions and there are a volumetric compression ratio of say 8 say that it works the working fluid which is air then all that you have to do is use the volumetric compression ratio r v, guess or use an appropriate value of gamma for the working fluid and substitute that in this formula and get an expression for the so called efficiency. Such relations analytical expressions are or this derivation is what is sometimes known as standard analysis whereas for vapor cycles there is no standard analysis. If I tell you that I have a steam power plant which works with condenser exit at say 40 degrees C saturated liquid and boiler exit at say 70 bar and dry saturated vapor and if I tell you that the turbine and the pump are both isentropic determine the cycle efficiency. There is no formula in which you can substitute these values and get a cycle efficiency. You will have to go to steam tables lay out your first you have to lay out your plant on paper draw the T s diagram or H s diagram as you feel appropriate and then use the steam table to extract all those parameters. If I change one of the parameters again there is no formula in which you can substitute I mean you have to do all the calculations again. The process and the procedure remains the same but the numerical values will all be different and they will have to be computed out. So, just the way the auto cycle efficiency or the standard efficiency of an auto cycle can be written in terms of just two parameters R v and gamma. You cannot do that for a steam power plant or a vapor refrigeration plant. Now, at this stage it is just to take some examples. People are for example let us take the household refrigerator. What type of a cycle is it? First thing it is a refrigeration cycle. Since it is a refrigeration cycle there is no question of it being classified as external combustion or external internal combustion. Second one we can say it is a vapor cycle. The third one is that it is a multi equipment cycle and another characteristic is that it is a closed cycle. Now I am going to take a break but I will break for five minutes but I will ask you to classify the cycles used in the following pieces of equipment. Car engine, steam power plant, jet engine and the classical steam locomotive. Classify these on the all our power plants. So, classify them as on the five parameters that we have discussed so far. I will be back with you in a few minutes.