Figure 9-12 Actual and ideal cycles in spark-ignition engines and their P-v diagrams.

Four-stroke cycle
1 cycle = 4 stroke = 2 revolution

Two-stroke cycle
1 cycle = 2 stroke = 1 revolution

1-2 Isentropic compression
2-3 Constant-volume heat addition
3-4 Isentropic expansion
4-1 Constant-volume heat rejection

9.21-1.png

Figure 9-15 T-s diagram of the ideal Otto cycle.

The two-stroke engines are generally less efficient than their four-stroke counterparts but they are relatively simple and inexpensive, and they have high power-to-weight and power-to-volume ratios.

9.24-1.png

Schematic of a two-stroke reciprocating engine

9.25-1.png

Figure 9-14 Two-stroke engines are commonly used in motorcycles and lawn mowers.

Air enters the cylinder through the open intake valve at atmospheric pressure P0 during process 0-1 as the piston moves from TDC to BDC.

The intake valve is closed at state 1 and air is compressed isentropically to state 2. Heat is transferred at constant volume (process 2-3); it is expanded isentropically to state 4; and heat is rejected at constant volume (process 4-1).

Air is expelled through the open exhaust valve (process 1-0).

Work interactions during intake and exhaust cancel each other, and thus inclusion of the intake and exhaust processes has no effect on the net work output from the cycle.

However, when calculating power output from the cycle during an ideal Otto cycle analysis, we must consider the fact that the ideal Otto cycle has four strokes just like actual four-stroke spark-ignition engine.

$W_{o u t, 0 - 1} = P_{0} (v_{1} - v_{0})$

$W_{i n, 1 - 0} = P_{0} (v_{1} - v_{0})$

9.26-1.png

Figure 9-16 P-v diagram of the ideal Otto cycle that includes intake and exhaust strokes.

$(q_{i n} - q_{o u t}) + (w_{i n} - w_{o u t}) = h_{e x i t} - h_{i n l e t}$

$q_{i n} = u_{3} - u_{2} = c_{v} (T_{3} - T_{2})$

$q_{o u t} = u_{4} - u_{1} = c_{v} (T_{4} - T_{1})$

$η_{t h, O t t o} = \frac{w_{n e t}}{q_{i n}} = 1 - \frac{q_{o u t}}{q_{i n}} = 1 - \frac{T_{4} - T_{1}}{T_{3} - T_{2}} = 1 - \frac{T_{1} (T_{4} / T_{1} - 1)}{T_{2} (T_{3} / T_{2} - 1)}$

$\frac{T_{1}}{T_{2}} = {(\frac{v_{2}}{v_{1}})}^{k - 1} = {(\frac{v_{3}}{v_{4}})}^{k - 1} = \frac{T_{4}}{T_{3}}$

$r = \frac{V_{max}}{V_{min}} = \frac{V_{1}}{V_{2}} = \frac{v_{1}}{v_{2}}$

9.29-1.png

Figure 9-17 Thermal efficiency of the ideal Otto cycle as a function of compression ratio (k= 1.4).

$η_{t h, O t t o} = 1 - \frac{1}{r^{k - 1}}$

In SI engines, the compression ratio is limited by autoignition or engine knock.
9.30-1.png

Figure 9-18 The thermal efficiency of the Otto cycle increases with the specific heat ratio k of the working fluid.

Ex.9-2 (Part 1).png Ex.9-2 (Part 2).png Ex.9-2 (Part 3).png Ex.9-2( Part 4).png

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