What do you understand by thermodynamics analysis of CI engine combustion process. Explain in detail giving a governering equations.

 

Thermodynamic Analysis of CI Engine Combustion Process

The thermodynamic analysis of a Compression Ignition (CI) engine (commonly called a diesel engine) involves understanding how pressure, temperature, volume, and heat release change during the engine cycle, especially during combustion. This analysis helps in predicting performance, efficiency, and emissions.

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Phases of CI Engine Combustion

In a CI engine, combustion occurs in multiple stages after fuel is injected into high-temperature, high-pressure air. The main phases are:

1. Ignition Delay: Time between the start of injection and start of combustion.

2. Premixed Combustion: Rapid burning of fuel that has mixed with air during delay.

3. Diffusion Combustion: Controlled burning of remaining fuel as it mixes with air.

4. Late Combustion: Final stages of burning as pressure and temperature fall.

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Thermodynamic Modeling of Combustion

To analyze the process, the First Law of Thermodynamics is applied to the control volume of the cylinder contents:

Governing Equation (First Law for Open System):

$$\frac{dQ}{d\theta} = \frac{dU}{d\theta} + p\frac{dV}{d\theta}$$

Where:

• $\frac{dQ}{d\theta}$ = heat released per crank angle degree

• $\frac{dU}{d\theta}$ = change in internal energy

• $p$ = cylinder pressure

• $V$ = cylinder volume

• $\theta$ = crank angle

For ideal gases:

$$dU = m c_v dT$$

So the heat release rate becomes:

$$\frac{dQ}{d\theta} = m c_v \frac{dT}{d\theta} + p\frac{dV}{d\theta}$$

This is the basic thermodynamic equation used to calculate the rate of heat release (ROHR) during combustion from in-cylinder pressure data.

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Wiebe Function (Heat Release Model)

The Wiebe function is often used to model the fraction of fuel burned $x_b$ over crank angle $\theta$:

$$x_b(\theta) = 1 - \exp\left[-a\left( \frac{\theta - \theta_0}{\Delta \theta} \right)^m\right]$$

Where:

• $a$, $m$ = empirical constants

• $\theta_0$ = start of combustion

• $\Delta \theta$ = combustion duration

• $x_b$ = mass fraction of fuel burned

Then:

$$\frac{dx_b}{d\theta} = \text{Heat release rate (HRR) model}$$

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Assumptions in Thermodynamic Analysis:

• Air-standard cycle or single-zone combustion.

• Ideal gas behavior.

• No mass loss or gain during combustion.

• Homogeneous air-fuel mixture (simplified case).

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Applications of Thermodynamic Analysis:

• Estimating indicated power and efficiency.

• Designing combustion chambers.

• Predicting in-cylinder pressure and temperature profiles.

• Optimizing injection timing and fuel burn rate.

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Conclusion:

Thermodynamic analysis of CI engine combustion provides deep insight into combustion behavior, performance, and efficiency. Using the First Law of Thermodynamics and empirical models like the Wiebe function, engineers can predict heat release, pressure variations, and optimize engine parameters for better performance and reduced emissions.