Otto Cycle

Facts:

Key operating facts:

Power control
- More air $\Rightarrow$ More Power
Fuel Injection
- Intake Stroke

Combustion:

Constant air/fuel ratio
- Close to stoichiometric
Premixed mode
- Start of combustion controlled by spark ignition
- Front propagation

Pros/Cons:

Subject to knocking $\Rightarrow$ need high octane # fuel

Ideal Otto Cycle:

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Process:

Intake Stroke:

$0 \to 1$ : constant pressure

Compression Stroke:

$1 \to 2$ : isentropic
$2 \to 3$ : combustion, constant volume

Power Stroke:

$3 \to 4$ : isentropic

Exhaust Stroke:

$4 \to 1$ : constant volume
$1 \to 0$ : contant pressure

System:

Unit mass inside combustion chamber
Intensive/specific quantities
Compression ratio $r = \frac{V_{1}}{V_{2}}$

First Law of Thermodynamics:

$1 \to 2$ : $Δ u_{12} = - w_{12}$
$2 \to 3$ : $Δ u_{23} = C_{v} (T_{3} - T_{2}) = q_{i n}$
$3 \to 4$ : $Δ u_{34} = - w_{34}$
$4 \to 1$ : $Δ u_{45} = C_{v} (T_{1} - T_{4}) = q_{o u t}$

Second Law of Thermodynamics:

$1 \to 2$ : $T_{2} = T_{1} r^{γ - 1}$ $P_{2} = P_{1} r^{γ}$
$3 \to 4$ : $T_{3} = T_{4} r^{γ - 1}$ $P_{3} = P_{4} r^{γ}$

Specific heat added:

Heat released by combustion $q_{i n} = C_{v} T_{1} (\frac{T_{3}}{T_{1}} - r^{γ - 1})$

Specific work produced:

Power Stroke - Compression Stroke $w_{n e t} = w_{12} + w_{34} = \int_{1}^{2} P d v + \int_{3}^{4} P d v = C_{v} T_{1} (\frac{T_{3}}{T_{1}} - r^{γ - 1}) (1 - r^{γ - 1})$

Thermal Efficiency:

$η_{t h} = \frac{w_{n e t}}{q_{i n}} = 1 - \frac{1}{r^{γ} - 1} = 1 - \frac{T_{1}}{T_{2}}$

Not a function of any temperature
Independent of any heat added

Sources of Irreversibility:

Combustion: $2 \to 3$
Uncontrolled expansion: $4 \to 1$