 The specific power of the spark ignition IC engine that we discussed in the previous two lectures is not very high. We can actually see that in this diagram. So, you can see that the specific power which is nothing but W net over MCV T1 that is the dimensionless specific power you can see is in the lower side of this curve. So, this is the compression ignition diesel engine that we are going to discuss next, but you can see that this value is not high. Of course, the value can be increased by increasing T3 over T1, but T3 over T1 equal to 7 is usually about the maximum value that we are generally using in practical applications. It cannot be increased much beyond that. So, there is no scope for doing that and as you can see from this diagram, it is not sensitive to compression ratio also for a given T3 over T1 as I mentioned earlier the specific power asymptotes beyond the compression ratio of about 4 or 5. Of course, one strategy that we can think of is to add more cylinders. So, if the specific power from one cylinder is less, of course, more cylinders may be added. The disadvantage with this strategy, this is used in many practical applications, but the disadvantage with this strategy is that the power to weight ratio of the engine deteriorates. So, as you add more cylinders, you are adding more weight. So, the power developed per unit weight of the engine deteriorates as you add more cylinders, but this can be practiced up to a point we can increase the number of cylinders, but the fundamental limitation that the specific power output from spark ignited internal combustion engine is small that still remains. Now, to address this, the compression ignition engine was developed. Basically, the compression ignition engine uses a heavier fuel like diesel in contrast to the spark ignition engine which uses a lighter fuel like petrol or gasoline. The compression ignition engine uses higher compression ratios and the temperatures, the maximum temperatures seen in the engine may be of the same order as the spark ignition engine, but because of the higher compression ratios and the way the compression is achieved, the specific power produced by the compression ignition engines are higher. Now, in addition, compression ignition engines also generally offer higher thermal efficiency when compared to spark ignition engines. You must bear in mind that in the case of the spark ignition engine, we are limited to compression ratios below 10. So, that means we are also limited in the compression in the thermal efficiency that we can realize. Whereas, in the case of a compression ignition engines, the compression ratios are much higher and they generally exhibit higher thermal efficiency. So, this was also clear from the previous diagram. So, in the spark ignition engine, we are limited to compression ratios less than 10 in order to avoid the docking phenomenon. Whereas, in the case of a compression ignition engine, the compression ratios can be higher. So, consequently, these engines also have higher thermal efficiency. So, these are the advantages of the compression ignition engine, higher specific power and higher thermal efficiency. On the downside, however, is the fact that because compression ignition engines use a heavier fuel like diesel, the emissions from the engine also worsen. For instance, compression ignition engines tend to put out pollutants like unburned hydrocarbons and soot, which are typically not present in the case of a spark ignited IC engine because it uses a lighter fuel like gasoline. So, there is an additional disadvantage that comes from using compression ignition engine, which itself comes from the factor it uses a heavier fuel like diesel. Of course, these sorts of issues will be discussed in great detail in a course on internal combustion engines. So, we must confine our attention to the air standard cycles, efficiencies and so on. We will not pay too much attention to these complications, but I will mention them wherever it is required so that you have a perspective on the effect that the parameters have on the overall performance of the engine and other attributes of the engine. So, in the case of the compression ignition engine, air is taken into the engine in the intake stroke in contrast to the SI engine, where air and fuel mixture is taken into the engine here, air is taken into the engine. The air is then compressed to compression ratios higher than 15 typically 20 or so. Because we are taking in only air, the danger of knocking does not arise in this case. So, the air can be compressed to much higher compression ratios and also much higher temperatures at the end of the compression stroke. So, generally the temperature at the end of the compression stroke is actually higher than what we saw in the case of an SI engine. Remember SI engine, we said that we cannot go much above T3 over T1 of 7. Whereas, in the case of compression ignition engine, we can go above that and we do go above that. In fact, this temperature is higher than the auto ignition temperature of the diesel fuel. But since air around is compressed, there is no danger of knocking in the case of the SI engine. So, at the end of the compression stroke, fuel is sprayed into the cylinder. So, there is a fuel injector which sprays the fuel into the cylinder at the end of the compression stroke. Because the air is already at a temperature higher than the auto ignition temperature of the fuel, a separate ignition mechanism such as a spark plug is not required in the case of a SI engine. The sprayed fuel evaporates, mixes with the air and begins to burn. Now, in the case of the compression ignition engine, the heat release is much more gradual. In fact, the heat release is such that the pressure remains more or less constant as the temperature, maximum temperature increases as the fuel undergoes combustion. So, here we can actually treat the heat release as a constant pressure process in contrast to the SI engine where it was actually treated as a constant volume process. So, during the power stroke or at the end of the compression process. So, remember this is a situation where the piston is still moving down. So, in the intake stroke, the piston moves from BDC to TDC or top dead center. I am sorry, in the case of the intake, the piston moves from top dead center to bottom dead center. And in the case of the compression stroke, it goes from bottom dead center to top dead center. And combustion now in the case of the CI engine is part of the power stroke, is part of the downward motion of the piston. So, here the piston actually starts moving from the top dead center to bottom dead center. Whereas, in the case of the SI engine, the combustion actually was a constant pressure constant volume process. So, it took place instantaneously without any movement of the piston because it was constant volume. So, whereas here because it is a constant pressure process, piston begins to move down and a combustion process also accompanies the downward motion of the piston. So, for part of the downward motion of the piston, heat release occurs and for the rest of the downward motion of the piston, we have power stroke. And the fuel supply is cut off at some point. So, after a certain amount of fuel is sprayed, the fuel supply is cut off. So, from this point onwards, there is no fuel and the fuel that is already in the cylinder continues to burn, expand and push the piston down and produces work. So, there is a cut off point at which during the downward movement of the piston at which the fuel supply is cut off. So, in the exhaust stroke, the piston moves from bottom dead center to top dead center and pushes the combustion gases out and the cylinder is then ready to receive a fresh charge of air. So, the main difference, of course, there are several differences, but probably one of the most important difference is the fact that combustion takes place at constant pressure. The other important difference is that the compression ratio is much higher than what we normally see in the case of an SI engine. So, the PV diagram of an air standard diesel cycle may be depicted like this. So, here a certain amount of air is present. Remember, this is an air standard cycle. So, this works with a fixed mass of air in the cylinder. So, a certain mass of air is present in the cylinder at state 1, which is then compressed from 1 to 2, from bottom dead center to top dead center. Of course, as we did before, this ratio V1 over V2 is called the compression ratio denoted R, like what we did for the SI engine. It remains the same. Then, fuel is sprayed or in the case of the air standard cycle, heat is added while maintaining the pressure constant. So, from 2 to 3, we have heat addition. So, this is of course, compression. So, this is constant pressure heat addition. Now, the heat addition is stopped once we reach certain value for the specific volume or once we reach a certain cutoff value for the volume. So, V3 over V2 is called the cutoff ratio and denoted Rc. Now, from state 3 to state 4, we have expansion process where the combustion gases expand and produce work. Notice that the work is non-zero during 2, 3 also because the piston is moved down, pushed down. There is displacement work during 2, 3 also in this case. It is not a constant volume process. It is a constant pressure process. 4 to 1, as before, heat rejection process takes place at constant volume. Notice that the number of stroke in the case of air standard diesel cycle is still 2, just like what we had for the air standard auto cycle. So, this is one stroke from bottom dead center to top dead center and then this is another stroke from top dead center to bottom dead center because this takes place at constant volume. There is no movement of the piston. Now, the actual compression ignition engine that uses a diesel fuel, as I mentioned earlier, utilizes 4 strokes whereas the air standard diesel cycle utilizes only 2 strokes. Now, first law applied to process 1, 2 which is a compression process gives us this. Here we have assumed the process to be isentropic in the ideal case. Of course, isentropic efficiency can be added to the analysis. So, there is no loss of generality in assuming the process to be isentropic. So, we take Q to be 0. So, this is the work that is put into the engine during process 1, 2. 2, 3 is constant pressure heat addition process. Again, application of first law gives us this. Notice that this is the displacement work which is norm 0 and during the constant pressure heat addition process. So, 3, 4 again is isentropic expansion process and 4, 1 is constant volume heat rejection process. So, this is isentropic and this is of course, constant volume. So, net work output during each cycle is work that is produced positive work minus the work that is put into the cycle. So, here we have expansion work which is this term here and we also have displacement work during the constant pressure heat addition process which is this term here. So, the thermal efficiency of the cycle is nothing but W net divided by Q n and this may be written like this. And so, if we combine, so if we rewrite this, we may actually combine this term with this term. So, these two may be combined and so, since h is equal to u plus p v, we may write this as h 3. Similarly, we may combine this term with this term and write it as h 2. So, we end up with an expression like this for the thermal efficiency of the cycle. Now, suppose we assume the working substance which remembered in the case of an air standard cycle working substance is air, suppose we assume it to be calorically perfect. So, that u is equal to c v times t and h is equal to c p times t, then the expression for network may be simplified like this. Notice that we have non-dimensionalized the network in the same manner as was done for the SI engine. We have non-dimensionalized using m c v t 1, so that fair comparison between the auto cycle and diesel cycle is possible. That is why we have done it like this. So, work is non-dimensionalized with m c v t 1. And the thermal efficiency of the cycle may be written like this. So, here as I mentioned before, the compression ratio r is equal to v 1 over v 2 and the cutoff ratio r c is v 3 over v 2. So, this shows that the performance matrix of the cycle namely w net eta and we will also develop an expression for the second law efficiency. So, the performance matrix, these are the three performance matrix. So, these are controlled by the parameters r c and r. So, these two parameters control the performance of the cycle. In the case of the auto cycle, the compression ratio and t 3 over t 1 were the two parameters which control the performance of the cycle. In this case, we have r c and r. Remember, r c is the cutoff ratio. So, it indirectly controls the peak temperature because r c controls the amount of heat that is added, it indirectly controls the peak temperature in the cycle. So, in that sense, it is similar to the auto cycle. So, let us see how the two performance matrix vary with different values for these parameters. The specific work output of the diesel engine, I am sorry, the air standard diesel cycle is certainly higher than what we saw for the auto cycle. Even for r c equal to 2, you can see that for a compression ratio of 20, the specific power of a diesel cycle is comparable to the specific work output of an auto cycle for the highest value of t 3 over t 1. And as we increase r 3, the specific work output increases. And notice that the specific work output of the air standard diesel cycle also increases with compression ratio. So, as we increase the compression ratio, the specific work output increases in contrast to the auto cycle, where the specific power no longer varies with the compression ratio for values of compression ratio beyond 5. Whereas here, it continues to increase almost linearly with compression ratio for a given value of r c. So, you may recall that this was one of the objectives that we started out with, that we wanted higher specific power from the engine higher than what we had for the auto cycle. So, since the specific power output is higher, the diesel engine is diesel engine or compression ignition engine is used typically for heavy duty applications, whereas the spark ignition IC engine is typically used for light duty vehicles or light duty applications. All heavy duty applications use the compression ignition diesel engine extensively. Now, if you look at efficiency, you can see that for typical compression ratio of 20 or so, you can see that the efficiency of the air standard diesel cycle is already higher than the highest value that we saw for the auto cycle for an r c of 2. However, as r c increases, you can see that the efficiency comes down for a given compression ratio as r c increases, the efficiency of the cycle comes down. So, the specific power goes up with r c, whereas the efficiency comes down with r c. So, you can see that the requirements are conflicting, you would like to have high value for specific power and the high value for efficiency. But fortunately, the variation of efficiency with the compression ratio is relatively mild. And also the drop in the value for efficiency with r c does not appear to be very large. So, with reasonable values of compression ratios, we should be able to get good thermal efficiency in the air standard diesel cycle also. Now, let us go and take a look at the second law efficiency for the air standard diesel cycle. Now, before we do that, let us take note of the following points. The thermal efficiency of the diesel cycle at r equal to 20, which is a typical value for production diesel engines is almost the same as the highest value possible for auto cycle corresponding to about r equal to 10 or 9 or so. Another interesting thing is that the expression for the efficiency of the cold air standard diesel cycle becomes identical to its counterpart for auto cycle as r c goes to 1. So, here as you can see, if you look at this expression as you let r c go to 1. If you use Lopital's rule, you will notice that as r c goes to 1, this efficiency tends to 1 minus 1 minus 1 over r raise to gamma minus 1, which is identical to the expression that we had for the auto cycle. So, it is somewhat erroneously said that as r c goes to 1, the diesel cycle approaches the auto cycle. It is erroneously mentioned in many places, so you need to be careful about that because if you look at this illustration, it becomes clear that this is erroneous. As r c goes to 1, remember r c is v 3 over v 2. So, as r c goes to 1, so as r c goes to 1, you can see that 0.3 moves towards 0.2 and when r c becomes identically equal to 1, 0.3 sits right over 0.2, which means that the cycle actually looks like this. So, we start from 1, the air is compressed to 2 and then there is no heat addition, so the air expands again from 3 to 4 along the same path. So, the air expands from 3 to 1 along the same path. So, which means that it is actually a motoring cycle. The air is alternately compressed and expanded with 0 work output. So, although the expression is identical to that of the auto cycle, the cycle is not because if you look at the expression for w net, if you set r c equal to 1 in the expression for w net, you set r c equal to 1 in the expression for w net, you can see that this term goes to 0 and this also goes to 0. So, the power, the work output from the engine goes to 0. So, it becomes a motoring cycle, there is no net work output from the cycle. So, that is very important. So, q h goes to 0 as r c goes to 1 and so the cycle becomes a motoring cycle. So, the expression between the air, cold air standard diesel cycle and the auto cycle are identical, but that is only coincidental because other things are different. Now, the exergy that is supplied during the cycle is the work that is put into the engine. So, that is the first part. So, let us see. So, this is the work that is put in the cycle during the compression stroke and this is the heat supplied. So, this is the exergy that is supplied during the cycle and for a cold air standard analysis, this may be simplified to read like this finally. Notice that we have done non-dimensionalized the exergy supplied as well in the same manner as we did for the specific work output. Now, the exergy that is recovered from the cycle is the work that is done during the power stroke plus the displacement work during heat addition process. And this for a cold air standard analysis, this expression may be simplified to read like this. And the second law efficiency of course is exergy recovered divided by exergy supplied. And if we look at the variation of the second law efficiency with the parameters in the cycle, it looks like this. Again, it is the second law efficiency is plotted on the same graph for both the cycles to enable fair comparison. So, you can see that the second law efficiency is fairly insensitive to the compression ratio, fairly insensitive for Rc equal to 2, it is almost insensitive for Rc equal to 4, it is mildly sensitive to compression ratio. And more importantly, the second law efficiency decreases with increasing Rc or with increasing peak temperature in the cycle just like what we saw for auto cycle. With increasing peak temperature, the second law efficiency comes down for both auto and diesel cycles. And as I mentioned before, this is due to the fact that as the temperature of the reservoir which supplies heat increases, the external irreversibility during the heat addition process. And remember the gas or the air is at a the air is at a lower temperature when we have state 2. So, the external irreversibility during process 2-3 causes the second law efficiency to come down. So, you can see that second law efficiency comes down with increasing Rc, same manner as auto cycle. However, the diesel cycle expresses much less sensitivity to R, the second law efficiency of the cycle expresses much or displays much less sensitivity to R when compared to the auto cycle. So, you can see that the cold air standard analysis although it is highly ideal, it allows us to get these sorts of insights into the cycle. Most importantly, as I mentioned at the beginning of the discussion on air standard cycle, the cold air standard analysis allows us to understand, identify different parameters that control the performance of the cycle or the performance matrix. Not only that, it also allows us to get an idea on how these parameters affect the performance matrix. So, that is also very important. Although it is an ideal analysis, these variations and insights that you are able to get carry over into the real cycle also. So, and these effects may be taken into account when designing the real engine.