 Welcome back after lunch, we were looking at schematic of a single Rankine cycle plant. In a course on thermodynamics when we do cycle analysis, it is necessary to emphasize the following thing, understanding what the plant is, understanding the appropriate state space on either the TS or any other appropriate diagram. One thing should be emphasized that although other diagrams are okay, whenever it comes to a multi-equipment cycle, whether it is Rankine cycle, Brayton cycle, the TS diagram is one diagram which is always relevant, it will not become irrelevant although for some purposes HS is used, in some cases PS is used. So one should have the students be familiar with sketching a cycle first as a block diagram, so you know what the equipments are and two, on an appropriate pair of properties, the common pairs are TS, HS, PV and PH, but of course if you want you can have a PS diagram and SV diagram, it is left to you, the student should be confident of sketching this on any pair that you dictate. Now at this stage we have looked at the PSPS type power generation cycle, if it is gas then we call it Brayton and if it is vapor we call it Rankine. I would prefer to introduce the students at this stage to the use of such a cycle as a refrigerator cycle and we will now look at the gas cycle corresponding to the reversed Brayton cycle called the Joule cycle and the reversed Rankine with appropriate modifications which is known as the vapor compression cycle. Let us look at the gas refrigeration cycle, we will introduce this on the TS diagram, but here one thing is important, you have to sketch the ambient temperature and you have to sketch the refrigerated space temperature and now remember that we have to absorb heat from the refrigerated space. So one isobar of the cycle in which heat is absorbed must be at temperatures not exceeding the refrigeration space. So let us say that this is the process 1 to 2 in which heat is absorbed from the refrigerated space. Now we have a compression process by which temperature has to be raised and it has to be raised above the ambient temperature and from there till such a point that if at pH if we cool it isobarically from here an isentropic expansion should bring it back to the process diagram sorry the plant diagram would look like this. Notice that on the TS diagram unlike the Brayton and Rankine cycle, this cycle known as the Joule cycle which uses a gas as a working fluid it is seen to move anticlockwise. The compressor expander or turbine the cold heat exchanger and the heat rejecting hot heat exchanger the cooler if you want or heat absorber and the heat rejection mechanism. So this from the turbine goes as 1 goes at 2 to compressor goes as 3 to the heat exchanger comes as 4 inlet to the turbine. The flows will be heat absorbed from the refrigerated space W dot C, W dot T and this is heat rejected to the ambient. And using our ideal gas approximation for the working fluid with constant specific heats you can do a standard analysis and determine the COP of this cycle leave it as an exercise to the student it will again be a function only of R p the ratio of pH and PL and gamma. What is important at this stage to demonstrate to them emphasize on them that unlike the Brayton cycle Brayton power cycle which is shown here you will notice that you can run it with a very small pressure ratio and you can run it with a still larger pressure ratio all that will happen is the points 3 and 2 will change 2, 3 and 4 will change accordingly. When it comes to refrigeration cycle the Brayton refrigeration or joule cycle emphasize that once you have this after heat rejection the minimum temperature that the working fluid which will that will be reached will be 4. Now we want to expand it and bring it down to a temperature which is lower than T ref this difference must be positive in the sense that temperature at 1 should be lower than the refrigerated space temperature. So, that some energy can be absorbed as heat from in during the isobaric process 1 to 2. If we do not have a high enough pressure ratio then the adiabatic expansion or isentropic expansion from 4 to 1 will not be reducing the temperature low enough for the exit temperature to be below T ref. So, the requirement is that T 4 after expansion T 4 pH after expansion to T L should reach a temperature T 2 which should be less than T ref and since T 2 by T 4 is given by P L by pH raise to gamma minus 1 by gamma. We have the requirement that T 2 which is this into T 4 should be less than or equal to T ref and that means your pressure ratio pH by P L should be such that pH by P L raise to gamma minus 1 by gamma should be greater than 4 let me see yes I have turned it around should be greater than T 4 by T ref. So, this gives you an idea of the minimum pH by P L needed to make the cycle work for refrigeration. Such a restriction does not exist on the Brayton power cycle, but on the Joule refrigeration cycle such a restriction does not exist on the Brayton power cycle, but on the Joule refrigeration cycle such a restriction exists. So, that should be emphasized otherwise once that is noted everything else can be done by applying first law to various components and extracting the required parameters. Now, we have seen the Brayton cycle, gas power cycle, Rankine cycle which is a vapor power cycle, then the refrigeration cycle, the gas cycle which is the sort of reverse of Brayton which is Joule cycle, but where we have also seen the requirement that the pressure ratio pH to P L needs to have a minimum value depending on the ratio of the ambient temperature and the refrigerated space temperature. Now, it is time for us to look at the reverse cycle related to the vapor power cycle or reverse Rankine cycle in some crude sense which we call the vapor compression cycle. For this we first look at the look at A T S diagram and let us say let us now write sketch over temperatures. Let us say this is the temperature of the ambient and let us say this is the temperature of the refrigerated space. We must have a heat absorption process at the refrigerated space temperature or below it. So, let us say that on this line we will have the heat absorption process. Heat rejection process should be at the ambient temperature or above it. So, let us say that on this line we should have the heat rejection process. Notice that we cannot go below this line because that would make the heat rejection process take place below ambient which is not applicable. So, the heat rejection can go only up to this point. So, in principle I can now have a turbine which expands it from this point say 1 to this point 2 and I can do the compression from say this point 3 to this point 4 giving me a refrigeration cycle which is a reversed Carnot cycle working between T ref and T ambient. Now, as a principle of thermodynamics it is ok, but when it comes to actual application two things must be noted. First this turbine here from 3 to 4 sorry compressor here from 3 to 4 will be compressing wet steam which is not good for a compressor whether a reciprocating compressor or a turbo compressor. So, what we do is instead of absorbing heat only up to this point we will say that we will not do any heat absorption here. We will absorb heat right up to the point where the refrigerator refrigerant becomes the working fluid becomes dry saturated steam call this 3 then we will compress it I am assuming adiabatic reversible or isentropic compression till you reach a pressure which is the saturation pressure at ambient. So, this is now my P H and this is my P L. So, my compression process is like this 3 to 4 then the heat rejection to the ambient is done from point 4 first desuperating and then condensing to 1 and then instead of having a turbine from 1 to 2 which would be a turbine which will produce only a small amount of power and which will have to handle again 2 phase flow. We replace that by a very simple component known as a throttling device. The job of that component is to just reduce the pressure and do nothing else. The block diagram looks like this heat rejection heat exchanger known as the condenser heat absorption from the cold space known as the evaporator. We have a compressor and we have a throttling device the states condenser exit 1 evaporator inlet 2 evaporator exit 3 compressor exit 4. The interactions evaporator absorbs the refrigeration effect from the cold space. The compressor consumes power w dot c the condenser rejects heat to the ambient q dot reject. The throttling device has no interaction with the ambient. The throttling device is usually a capillary tube in household refrigerators and air conditioners or for larger capacity plant it could be a throttle valve. The advantage of a throttle valve is nothing but the crudest version of a throttle valve will be our water tap which is only slightly open. So, even a small amount of flow requires a large amount of pressure drop. The advantage of a throttle valve is that you can design it easily for various capacities. As the load changes and the flow rate changes you can even have an adjustable throttle valve or an automatically controlled throttle valve. Once you realize this and understand the T S diagram and the block diagram all these interactions w dot c q dot reject q dot ref can be determined using our principles of thermodynamics. Each one of these components is a simple open thermodynamic system and usually 3 is dry sat vapor and 1 is saturated liquid. These are the default states, but we may have some other specification for the vapor which may be a few degrees superheated or the condensate which may a few degrees c sub cooled. At this stage it is perhaps usual to introduce them that this cycle which is known as the vapor compression cycle is often shown on P H diagram. The advantage of using H as one of the axis is that since most of the components are open thermodynamic systems the differences in H or the increase or decrease of H across a component can be directly related to when multiplied by mass flow rate to either the heat transfer or the power absorbed or the power delivered. If you want we can even sketch the Rankine cycle on the P H diagram, but that is for some reason is not done. So, the cycle will be bounded by two pressure lines the P H and the P L. The vapor dome usually looks like this. Sometimes this line is depending on the refrigerant this line is slope to the right or sometimes it slopes inwards that is a minor detail. Assuming state one condenser exit to be saturated liquid and state three the evaporator exit to be dry saturated vapor the cycle now looks like this. This is a constant entropy process in the ideal situation brings it to state two compressor exit then condensation from two to one first desuperheating and then condensation. Then one to two is a throttling process in which the enthalpy at the inlet and the exit are the same that reduces the pressure and finally two to three is the heat absorption and now you will notice here that H two minus H three is the heat sorry the enthalpy rise in the compressor multiply this by m dot and you will get compressor power H three minus H two is delta H across the evaporator which when multiplied by m dot gives you the refrigeration effect. So, from this diagram even visually you can look up the you can visualize the C O P as refrigeration effect divided by the power consumed because the throttling device does not produce any power we have the net power just equal to the compressor power consumption. This is the advantage of using H as one of the coordinates that delta H immediately gives us the visual idea of the heat transfer rate or the power involved with this. Now at this stage we have looked at the basic power cycles and refrigeration cycles all of the essentially of the PSPS kind. So, we have looked at Rankine, we have looked at Brayton, we have looked at Rankine, we have looked at reversed Brayton which is June and a reversed vapor cycle used for refrigeration known as the vapor compression cycle. In a course in thermodynamics if you are introducing them to cycles it is not necessary to get into the details of the technology involved that is the type of compressors, the type of evaporators, the type of throttling devices and so on. Now the cycles which we have seen so far are cycles which are essentially multi-equipment cycles and the basic idea is the PSPS cycle that means two isovaric processes typically for heat absorption and heat rejection and two isentropic processes which are also which are actually reversible adiabatic processes which do the job of increasing the pressure from the lower value to the upper value, decreasing the pressure from the upper value to the lower value and providing the required amount of power input and power output. Now we come to cycles in which we use a single piece of equipment and those are now what are known as although they are traditionally known as IC engine cycles. The IC engine cycle also includes the Brayton cycle when it is implemented as a gas turbine cycle. So, see to it that the students do not get under an impression that an IC engine cycle only means either auto cycle or diesel cycle or their minor modification. Brayton cycle is also an IC engine cycle but here we are going to talk of two major cycles the auto cycle and the diesel cycle. Of course there are other cycles which are the you know there is a dual cycle I think there may be an exercise on this one dual cycle. There is an Atkinson cycle which is a modification of the auto cycle and if you want you can include that but then the number of cycles which we have is actually a very large number of cycles. In a course on thermodynamics the teacher has to decide how much is to be included and how much is to be left for the second course which would be applied thermodynamics or power plants and refrigeration. Now these auto and diesel cycles are typically used in vehicle engines. So, these are mainly required for transportation and hence these cycles need to be compact because they are always on the move the engines which implement this cycle are always or almost always on the move unlike a large steam plant or a large refrigeration plant which would essentially be stationary. Consequently these cycles are for small power capacity comparatively small power capacity and they are characterized by these they are single equipment cycle, they are power cycles, they are gas cycles, they are internal combustion and they are open cycles. Naturally internal combustion means we have no choice, we have to have an open cycle. We have been talking about the Carnot cycle as a TS, TS cycle, the Brayton cycle and other cycles as PS, PS cycles. So, from in that terminology we can say that the auto cycle is perhaps an SV, SV cycle and the diesel cycle is an SP, SV cycles, but this is the idealization of these cycles. And the single piece of equipment which is used for this cycle is a cylinder piston arrangement and hence although we are in a course in thermodynamics some details need to be mentioned and the student informed properly. For example, we should explain in simple words using simple sketches the mechanism of the cylinder and the piston which has a reciprocating motion then rarely piston rod, but definitely a connecting rod. Then the crank, crankshaft and other peripherals like flywheel etcetera which go with the crank shaft. We should also talk about the inlet and exit ports and valves which open or close those valves as needed. If you want we can talk about camshaft and other things but if you start doing that we end up with a lot of peripheral information which needs to be provided. What we really need to understand is for simple almost an air standard type analysis that is assuming air as the working fluid and other standardized thing. All that we need to know is that we have a cylinder in which a piston moves from one extreme which makes the gas occupy the least amount of volume to another extreme in which the gas occupies the largest possible amount of volume. We should have this nomenclature ready. When the cylinder is at the innermost position it is known as the top dead center or inner dead center. The other position with the largest volume is the bottom dead center. The inner dead center and outer dead center are not so common terms the top dead center and bottom dead center are common terms. The clearance volume is a volume which will never be passed over by the piston that is the guaranteed volume which will always remain in the cylinder whereas the stroke volume or the swept volume is the volume which is swept by the piston as it goes from top dead center to bottom dead center or vice versa. We say that the movement of the piston from TDC to BDC is known as a stroke. So to execute one cycle we need a minimal of two strokes. However it is up to our choice to execute a cycle in either two strokes or four strokes or six strokes or eight strokes because cycle means it has to come back to its original position. So if a cycle begins from TDC it has to end at the situation where the piston is back at TDC. So we must have either two or four or an even number of strokes. Common cycles have two strokes or four strokes. Four stroke cycles are very common. Two stroke cycles are not uncommon. Six stroke cycles are very rarely used. We say that we have two valves typically two valves. If you have more than two valves there those are parallel paths. One is the inlet valve which can be opened or closed by means of an inlet mechanism and then exit valve IV and EV. There are mechanisms which open the inlet valve allowing gas to come in. If the exhaust valve is open and if the conditions are appropriate the gas can go out. We will look at the idealized cycles in which the working fluid will be assumed to be an ideal gas with constant specific heats and all the processes will be idealized. For example a process of compression or expansion would be considered adiabatic and reversible and hence isentropic. Similarly as we describe we will describe that some processes of combustion and movement of fluid will be idealized at either constant volume process or constant pressure process. Both the Otto cycle and the diesel cycle in their standard version are implemented in four strokes and the four strokes are from TDC to BDC first, BDC to TDC second and two more of this kind. Now the Otto cycle is the typical cycle for petrol engines also for CNG and similar engines. The characteristic of this is air plus fuel is mixed it is called premixed because this mixing occurs outside the cylinder. Earlier it used to occur in a carburetor where using a venturi the required amount of fuel and main working fluid which is air were mixed. Since the fuels are either in the gaseous form or are in a very volatile liquid form like petrol the spray simply evaporates and you have an air and petrol vapor mixture which is available for our engine. Since the engines work in a cylinder piston arrangement it is very common to show these on the PV diagram. We have one stroke in which the piston moves from TDC to BDC. So, stroke one piston moves from TDC to BDC inlet valve is open. So, when that happens air fuel mixture is sucked in essentially at ambient temperature ambient pressure. This is known as the induction stroke let us say this goes from 0 to 1. The second stroke is from BDC to TDC no valve open the air gets compressed this is assumed to be adiabatic and reversible and hence as a centriple air and fuel mixture gets compressed. Now at this state two this is stroke two this is state two we have a high pressure and reasonably high temperature mixture of air and fuel. So, a spark is used to initiate combustion because it is premixed and petrol is used very highly volatile highly reactive fuel. The combustion takes place and it takes place pretty fast. Although it takes a finite amount of time the movement of the piston is so small during this period that we idealize that the combustion leads to heat release and the state goes to 3. So, here the state goes from 1 to 2 here the state goes from 2 to 3 sorry induction is let me put I missed something I forgot to write that this is induction stroke state from 1 to 2 this is compression this line I missed 2 to 3 sorry induction is 0 to 1 compression is 1 to 2 at 2 spark using a spark plug initiates combustion and 2 to 3 the combustion process is modeled as a constant volume process because it is a premixed highly reactive mixture. Now the third stroke then is an expansion stroke combustion is over so 3 to 4. The third stroke is again from TDC to BDC again no valve open and this is the expansion stroke or power stroke and finally at 4 this is 3 to 4 at 4 exhaust valve opens and when exhaust valve opens this gas because it is now combustion products they suddenly find a passage open to the atmosphere. So, although the pressure at 4 is higher than the pressure at 1 because of the sudden discharge of gases there is a noisy outflow of these gases we need a silencer to take care of this noise the pressure in the ideal case reduces to 1 and this is the third stroke the pressure reduces from 4 to 1 and finally the fourth stroke where we go from BDC to TDC with EV open IV closed this is known as the exhaust stroke where the air fuel mixture after combustion. So, reacted gases they are thrown out so 4 to 1 and then 1 to we can say 4 to 5 shouldn't call it 4 to 1 because 5 is a different state the composition will be different this will be 5 to 6 where 6 is again essentially 0. So, this is 0 to 1 and this is 6. So, we have look at it there are 6 different processes 0 to 1, 1 to 2, 2 to 3, 3 to 4 and 4 to 5, 5 to 6, but there are actually 4 strokes because these 2 processes 2 to 3 and 4 to 5 are assumed to occur essentially at constant volume. Now, under these simplifying assumptions of idealized processes that things play take place at constant pressure during inlet and exhaust these 2 processes 1 to 2 and 3 to 4 assumed as reversible isentropic the reversible adiabatic and hence isentropic and if you assume 2 to 3 and 4 to 5 are constant volume processes and model them as constant volume heating and cooling then we can do for the auto cycle a standard analysis and the standard analysis we should be able to show that the efficiency of an auto cycle turns out to be 1 over 1 minus r v raise to gamma minus 1 where gamma as usual is the ratio of specific heats and r v is what is known as the volumetric compression ratio it is defined as the volume at BDC total volume at BDC divided by the total volume at TDC the volume occupied by the gas when it is at the bottom dead center divided by volume occupied by the gas which is at the top dead center this turns out to be v stroke plus v clearance divided by v clearance and the next cycle and perhaps if you want to introduce the diesel cycle not the last cycle but otherwise the last cycle in a basic introduction should be the diesel cycle you may mention to the students that for a typical auto cycle the compression ratio would usually be in this range and you should explain to them quickly without going into much detail how does 6 come across come about and how does 10 come about but actually that is a part of the power plant or IC engine scores not really a thermodynamics course when it comes to a diesel cycle explain in or explain using differences from auto cycle and may be in this case it is a good idea to sketch the p v diagram first and then talk about the differences because the students remember tend to remember the p v diagram of the auto cycle very well so have it side by side and compared to that the sketch the diesel cycle this is p ambient and you say the first stroke 0 to 1 is the induction stroke so stroke 1 0 to 1 induction as in petrol only but tell them that only air it sucked in then sketching it like this but the process is actually like this the second stroke 1 to 2 is compression again air only so at state 2 we do not have a air fuel mixture but compressed air and usually the compression ratios are larger typically of the order of 15 so this pressure is high this temperature is also high at state 2 because we have idealized the compression to be reversible adiabatic that is isentropic. Now at state 2 for some period in the next process 2 to 3 we have injection which leads to combustion injection of fuel so here in the hot air at 2 we spray the liquid fuel sometimes preheated sometimes not now because it is a liquid fuel it has to split into droplets then by heat transfer from the hot gas the droplets have to become hot and evaporate the evaporated fuel vapor has to mix with the air finding appropriate amount of oxygen for combustion and then the combustion has to proceed the temperature is high enough for the combustion to get initiated on its own but it takes time for the processes of heating up evaporation and mixing before the combustion proceeds this is a multi step process and it requires time and it requires some finite time in which we cannot by default make the assumption which we made in the auto cycle that the combustion takes place so fast that we can essentially assume that it is occurring at a constant volume when the piston is at or very near the TDC. In diesel the actual process of combustion is neither constant volume nor constant pressure but for idealization very crude idealization we assume that the combustion can be more modded from 2 to 3 when the injection is on as a constant pressure heat addition process this is a model this is assumed and then at 3 the injection stops and this is known as cut off so this is the cut off point and the ratio of volumes at 3 to 2 is also known as the cut off ratio then the remaining part 3 to 4 is expansion without combustion. So the third stroke actually begins at 2 but includes 2 to 3 injection and combustion and 3 to 4 which is expansion so the so called power stroke is 2 to 3 constant pressure part 3 to 4 an adiabatic expansion and beyond that it is very similar to the auto cycle 4 to 5 4 exhaust valve opens here inlet valve is open here no valve is open in this process also no valve is open expansion also no valve is open exhaust valve opens pressure valve drops to ambient 4 to 5 and finally 4th stroke 5 to 6 is the exhaust stroke. So we have 4 strokes and 6 processes some processes are similar to the auto engine and some processes are different from the auto engines particularly the differences are in the way the combustion process is modelled and you should now tell them that if you neglect the induction stroke and the exhaust stroke the auto cycle is made up of the idealized auto cycle is made up of a constant entropy process a constant volume process a constant entropy process and another constant volume process whereas the diesel cycle is made up of neglecting the induction and exhaust strokes a constant entropy process a constant pressure process a constant entropy process another one and a constant volume process and of course you can do a standard analysis of diesel cycle and I find always it is a good idea that I do the derivation of the standard efficiency of the auto cycle on the board the diesel cycle I leave it as a classroom exercise to the students because it is important that it derive something on their own slightly more complex stuff than the auto cycle because unless they do that if you give some modification for example the dual cycle in the examination they will not be prepared for that at all and here you should be able to show them that efficiency of a diesel cycle is a simple not very complex function of gamma r v and r c where the gamma as earlier is the C p by C v ratio of the working fluid r v is as earlier the volume in the cylinder at B dc divided by the volume in the cylinder at T dc and r c is v 3 by v 2 this is known as the cut off ratio. Now at this stage and after this stage what I prefer is bring up the exercises use these for the following purposes number one students should get a feel for numbers for example whatever you do for a typical rank in cycle whatever with the modification the efficiency will hardly exceed 50 percent in spite of reheat regeneration and things like that. But if the students do not solve a reasonable number of problems and realize that the efficiency the way we use steam today typical parameters is unlikely to exceed 50 percent and that too with a great number of modifications otherwise typically it will be between 35 40 percent. In an examination if they solve a problem and make a mistake and you end up with an efficiency of 70 percent they will not realize that they have made a mistake one of the things in growing up as a engineer particularly a mechanical engineers to have a feel for numbers and feel for typical parameters typical values. So see to it that the students get a feel by solving some exercises and two use this exercise to introduce modifications for example we have typical modifications of reheat regeneration intercooling intercooling is used only in some Brayton cycles it is not very rare and it is rather rare. I am taking a break.