Consider one cylinder of a spark-ignition, internalcombustion engine. Before the compression str

Consider one cylinder of a spark-ignition,...

Key Concepts

Internal Combustion Engine Cycles

This concept involves understanding the thermodynamic cycle in engines that convert chemical energy from fuel into mechanical work. In spark-ignition engines, the cycle includes intake, compression, power (combustion), and exhaust strokes. The analysis requires applying the laws of thermodynamics to different stages of the cycle as the gas mixture is compressed and then undergoes combustion, directly affecting pressure, temperature, and efficiency.

Adiabatic Processes

An adiabatic process is one in which no heat is exchanged with the surroundings. When such a process is reversible, it is isentropic, meaning that the entropy of the system remains constant. In the context of an internal combustion engine, the compression stroke is often modeled as a reversible adiabatic process to determine the resulting changes in temperature and pressure, using relationships derived from the first law of thermodynamics.

Compression Ratio

The compression ratio is the ratio of the maximum to the minimum volume in the cylinder of an engine. It is a critical parameter for determining the efficiency and performance of an internal combustion engine. A higher compression ratio generally leads to higher temperatures and pressures at the end of the compression stroke which affects the combustion process and the engine's overall thermodynamic efficiency.

Combustion Process

This concept involves the rapid chemical reaction (combustion) of the fuel and air mixture, typically occurring at top dead center in a spark-ignition engine. In thermodynamic analyses, the combustion process is often idealized as taking place at constant volume and under adiabatic conditions. This idealization helps in determining the post-combustion temperature and pressure by accounting for the energy released during the reaction.

Entropy Change and Irreversibility

Entropy is a measure of disorder or randomness in a system, and its change indicates whether a process is reversible or not. In an ideal reversible process, entropy remains constant; however, in real combustion processes, entropy increases due to irreversibilities such as rapid heat release and friction. Quantifying this entropy change is crucial for understanding the efficiency losses and the degree of irreversibility in the engine cycle.

Excess Air in Combustion

Excess air refers to the use of more air than is required for complete stoichiometric combustion of the fuel. Using an air-fuel mixture with excess air affects the combustion process, as it influences the final temperature and pressure reached during combustion. Additionally, it plays a role in controlling the emissions and affects the thermal efficiency of the engine, making it an important factor in engine design and performance analysis.

Transcript

00:01 So we have a, we're going to look at one cylinder of a spark ignition internal combustion engine.

00:07 Before the compression stroke, the cylinder is filled with the mixture of air and methane.

00:12 110 % theoretical air is used.

00:16 Before compression, we're at reference conditions, and the compression ratio is 9 to 1.

00:24 So, let's see here.

00:25 Here's our reaction, or, oops, here's our chemical formula for the reaction.

00:33 We have ch4.

00:36 We're going to, got some xx oxygen here.

00:42 We're at reference conditions initially, and again, the volume in the compressed state is one -ninth of that of the volume in the initial state.

00:52 And we're totally assumed that it is isotropic.

00:56 Well, we have an isotropic process because it's reversible and abatic.

01:01 So what we need to do is if we're going to use, let's use, heat capacities here, assuming that these are roughly ideal gases.

01:14 And well, what we need to do is if we want to get a little more accurate calculation, we can use the kind of the heat capacity at an elevated temperature.

01:28 So we can, we'll assume that our secondary temperature is about 400, 650 calvin.

01:37 So it give us an average temperature, average with the reference temperature of about 475 kelvin.

01:46 And so from that, we can look up the heat capacities for the methane, for the oxygen, and for the nitrogen.

01:55 And then for the mix, we wind up with 31 .0 kilojoules per kilowal of fuel carbon per kelvin.

02:04 And so, again, we're just, we're going to guess this, and we're going to guess this.

02:09 Average here and then we'll figure out what this is and see if our guess was any good.

02:13 And so we're just basically trying to adjust these hay capacities because using reference conditions, we could use reference conditions, but that would give us a less accurate result.

02:25 Once we know this, we can subtract the ideal gas constant, get the key capacity constant volume, and then we can get the ratio.

02:37 And the ratio turns out to be about 1 .3 .3 so now we know we have an isotropic process.

02:45 So we can get the temperature after compression.

02:48 We know this ratio here.

02:50 This is one, this is actually nine.

02:53 We know this temperature.

02:55 So we get 666 kelvin as our final temperature.

02:58 And we guessed 650.

03:00 Obviously i did a little iteration here and guess this wasn't my first guess, but again got pretty close here.

03:10 And so we got it.

03:11 Get this value here.

03:15 So you could guess basically you could use the reference state here and get a value and then get that that would be in the ballpark and then you know use that value to find an average and then go through and iterate the process.

03:28 Then we also get a pressure because we know the volume ratio here.

03:33 And so the pressure is about two megapascals after we've compressed the fuel air mixture.

03:42 With the cylinder, with the piston.

03:47 So then we were asked to assume that the complete combustion takes place while the piston is at top dead center, so at a volume, at a minimum volume, in an adiabatic process, determine the temperature and the pressure after combustion and the increase in entropy during the combustion process.

04:05 Okay, so here's our energy formula.

04:10 Again, we're assuming that this happens all.

04:15 Before while the piston is at the top, so the volume is not changing, so we're doing no mechanical work and assuming that it's adiabatic also.

04:25 So we basically have, this is the internal energy, so the internal energy from before combustion to after should be the same.

04:36 Now we can look up the for, let's see here, we need for h2.

04:45 That is before combustion, so that is the entropy of the reactants.

04:51 And so we have the entropy of formation for the methane, and then the adjustment.

05:01 Again, we'll assume that it's using this heat capacity for the mixture and the adjustments to this temperature here.

05:09 And so we adjust, and then we get the entropy of the reactants is 56 .2 megajoules per kilomol of fuel.

05:17 Now for the products, we have, or for in the after combustion, we have the enthalpy contained in the carbon dioxide that contained in the water, the oxygen, and the nitrogen.

05:35 Now, let's see here, we have, we can plug everything into here, and we know some of these values.

05:44 Let's see here.

05:48 We know, let's see here, we know, we don't know this, well we have to, again, that is going to be an unknown because we don't know t3.

05:59 We know this, so plugging everything in, we get that, we need this thing here.

06:12 Why did i do here? i missed a term here.

06:19 Yeah, so let's see here.

06:23 When i copied this over, i missed.

06:26 This should not be zero.

06:28 Well, we could say this is, let's say that that is minus, let's see here, 8 -6 -870 megajoules per kilomole calvin...

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