A Google search yields hundreds of graphs of measured exhaust temperature, many as a function of rpm. This is often part of dynamometer testing and emissions data collected.
It is most fortunate to have both theory and experimental data in this case. The approach I would suggest is to begin with rather simple theory (Otto cycle), incorporating crankshaft angle. Then add a reasonable approximation of the valve timing. You wouldn't need to specifically model the camshaft, lifters, pushrods, and valves, only the finite opening over time, producing a time-variant flow area for the exhaust. Then numerically tune the combustion to match experimental data (simple calculations often don't work here for reasons I discuss elsewhere). Now you would be ready to consider the exhaust process with minimal detail. Look for experimental data that come from one sensor in the combustion chamber plus another in the exhaust manifold near the valve. When you can roughly match the measured values, refine the calculations. A stepped approach from simplistic to complex will give you some encouraging results along the way and also provide insight as to which factors are more important than others. I would implement this entire process in an Excel spreadsheet, such as the one attached. Starting with a 3D transient CFD model of the combustion chamber with Fluent might make some pretty pictures, but won't produce much in the way of insight.
The amount of oxygen in the exhaust gas is used as an indirect measurement of the intake air/fuel ratio. automotive engine sensors in use today is the exhaust gas oxygen (EGO) sensor. This sensor is often called a lambda sensor from the Greek letter lambda (λ)which is commonly used to denote the equivalence ratio.
λ = (air/fuel) / (air/fuel@stoichiometry )
Whenever the air/fuel ratio is at stoichiometry, the value for λ is 1. When the air-fuel mixture is lean, the condition is represented by λ > 1. Conversely, when the air-fuel mixture is rich, the condition is represented by (λ < 1).
Exhaust gas temperature is a function of many variables.
Engines with lower BSFC values typically have lower exhaust gas temperatures because more of the fuels energy is used in the cylinder.
Another important factor is the air/fuel ratio. If excess oxygen is in the exhaust the temperature will be higher.
Camshaft timing, ignition timing, and IN/EX flow ratios during valve overlap are factors too.
I suspect trying to get an accurate exhaust gas temperature will be difficult without having a lot of specific engine parameters.
I have personally experienced exhaust gas temperature variation between cylinders on the same engine of 50C or more.
This is not difficult to calculate all what you need, if to use Lotus Engine Simulation (LES) software - you can download a freeware multi-cylinder version of Lotus Engine Simulation here https://www.lotuscars.com/engineering-software/. The operating manual is here - https://lotusproactive.files.wordpress.com/2013/08/getting-started-with-lotus-engine-simulation.pdf , this seems complicated, but for your task it is simple, because it is enough to read the first chapters only.
At least, when I need to get some data concerning ICE parameters, I always use LES software. In the case as you have, I would calculate exhaust gas temperature (with all other parameters) for different rpm using the dimensions of studied engine. This is 30 min of work maximum.
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