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Calculate the net work done per cycle for each case and

Vehicle Power-Train Technologies

Engine modelling assignment:

The pressure increment dP due to combustion and piston work was derived in class for an ideal engine cycle with a finite period of heat release. This can be used to determine the pressure-time history of the engine and consequently, the cycle work done and thermal efficiency. Use any numerical method you prefer (e.g., spreadsheet, Mathcad, C++ etc.) to solve the equation and estimate the engine performance. For this analysis, use the Wiebe function shown in class to model the mass-burned fraction as a function of crank angle. Use the following assumptions:

A compression ratio CR of 10:1

A single cylinder engine with displacement of 500 cc

The combustion being modelled is of a stoichiometric mix of octane and air; 14.7 kg air to every 1 kg of air

The pressure and temperature at the start of compression is 101325 Pa and 20^{o} C respectively

A specific heat ratio of 1.3 can be used for compression and expansion

The engine is operating at wide open throttle (WOT) with no pumping losses

The pressure and temperature in the cylinder drops instantly to pre-compression conditions at the end of the stroke at bottom dead centre (BDC)

PART A

Run your calculations for a range of combustion start times ?? from -60^{o} to +30^{o} and for the following burn duration angles?: 30^{o}, 60^{o}, 90^{o}, 120^{o}

Hint: solve the differential equation numerically using crank-angle increments that are small enough.

Plot a P-V diagram for the case of ?? = -30^{o} and ?? = 90^{o} and compare to the ideal Otto cycle diagram. Please show the start point and end point of combustion in the diagram. There is no need to plot the exhaust and intake strokes.

Calculate the net work done per cycle for each case and then plot the thermal efficiency against? on the same plot for each the four values of? Explain why there is an optimum? for each burn duration case. Based on your data, state a rule of thumb for setting the optimum?

PART B

Using equations 9.60 and 9.62 in Heywood`s text (which are explained in class) and your estimates of the pressure and temperature histories of the unburnt charge in the engine, estimate the CR needed to just cause knock for a given fuel Octane Number (ON) as defined in equation 9.62.

Hint: the onset of knock occurs when autoignition takes place just before all the fuel-air charge is burnt in an engine cycle. The integral in equation 9.60 becomes 1 at that point. Change your CR by changing the clearance volume only.

Plot this critical compression ratio CCR against ON for the following ON values: 65, 75, 85, 95, 105, 115, 125. Place the ON values on the horizontal axis. Use ?? = 90^{o} and the corresponding ?? for maximum thermal efficiency.

How does the graph in III change if ?? = 30^{o} instead of 90^{o}? Explain your findings. How does the graph in III change if the start of combustion occurs well before the optimum value for ??? Explain your findings.

Please work in pairs. One student does part A and the other does part B. On the cover page of your report, please name the person who worked on part A and the person who worked on part B. Provide student numbers as well.

Please write a proper and concise report (around 15 pages in total) including introduction with aims, method, discussion and conclusion. Please do not state in your objectives that you want to learn things as this is obvious.

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