Thermochemistry

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Thermochemistry is the branch of thermodynamics that deals with the heat and energy changes during chemical reactions. In aircraft propulsion, thermochemistry is crucial for analyzing fuel combustion, heat release, and energy conversion in engines.

1. Fundamental Concepts

Thermochemistry focuses on enthalpy changes during chemical reactions. The key quantity is the heat of reaction (or enthalpy of reaction), which represents the energy absorbed or released when reactants convert to products at constant pressure.

Enthalpy of Reaction

\Delta H_{reaction} = H_{products} - H_{reactants}

  • Exothermic reactions: \Delta H < 0, heat is released.
  • Endothermic reactions: \Delta H > 0, heat is absorbed.

Combustion of hydrocarbon fuels in engines is highly exothermic, releasing significant energy to power turbines.

2. Standard States and Reference Conditions

Enthalpy values are often tabulated at standard state conditions:

  • Pressure: 1 atm (or 1 bar)
  • Temperature: usually 298.15 K (25 °C)

Standard enthalpy of formation, \Delta H_f^\circ, is defined for forming 1 mole of a compound from its elements in their standard states.

Example:

\Delta H_f^\circ (CO_2) = -393.5 \text{ kJ/mol}

3. Enthalpy of Combustion

The enthalpy of combustion is the energy released when one mole of fuel burns completely in oxygen under standard conditions.

For a generic hydrocarbon fuel:

C_xH_y + \left( x + \frac{y}{4} \right) O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O + \text{heat}

Example for methane:

CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O

Standard enthalpy of combustion for methane:

\Delta H_{comb}^\circ = -890.3 \text{ kJ/mol}

4. Heating Values of Fuels

Aircraft fuels are characterized by their heating value:

  • Higher Heating Value (HHV): Includes latent heat of vaporization of water in products.
  • Lower Heating Value (LHV): Excludes latent heat; assumes water is vapor.

For aviation kerosene (Jet-A):

  • LHV ≈ 43 MJ/kg
  • HHV ≈ 46 MJ/kg

In propulsion analysis, LHV is commonly used because exhaust products are hot gases with water vapor.

5. Hess’s Law

Hess’s Law states:

The total enthalpy change of a reaction is the same, no matter how it occurs.

This allows calculation of enthalpy changes using standard enthalpies of formation:

\Delta H_{reaction} = \sum \nu_p \Delta H_f^\circ (products) - \sum \nu_r \Delta H_f^\circ (reactants)

Where:

  • \nu_p, \nu_r = stoichiometric coefficients of products and reactants.

Example:

Combustion of octane:

2 C_8H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O

\Delta H_{comb}^\circ = [16 \Delta H_f^\circ (CO_2) + 18 \Delta H_f^\circ (H_2O)] - [2 \Delta H_f^\circ (C_8H_{18})]

6. Adiabatic Flame Temperature

Adiabatic flame temperature is the maximum temperature achieved by combustion with no heat loss to surroundings. It’s a critical design parameter in propulsion:

  • Higher flame temperatures increase turbine inlet temperatures and efficiency.
  • Limited by material capabilities and NOx emissions.

Energy balance for adiabatic combustion:

\sum n_{reactants} h_{reactants} = \sum n_{products} h_{products}

Assuming no heat loss:

Q = 0

All chemical energy converts to thermal energy of products.

7. Specific Heat and Enthalpy Changes

During combustion analysis, the specific heat latex[/latex] of gases is used to evaluate enthalpy changes with temperature:

\Delta h = \int_{T_{ref}}^{T} c_p(T) , dT

For approximate calculations:

\Delta h \approx c_p \Delta T

This relationship helps determine exit temperatures in combustors.

8. Chemical Equilibrium

Combustion products may not be fully oxidized if the process is incomplete or at high temperatures. Equilibrium calculations predict species concentrations:

  • At high temperatures, dissociation of CO2 and H2O may occur.
  • Equilibrium shifts with pressure and temperature.

Understanding equilibrium is essential for accurate predictions of:

  • Flame temperatures
  • Emissions (e.g., CO, NOx)
  • Engine performance

9. Relevance to Aircraft Propulsion

Thermochemistry is foundational for:

  • Determining fuel requirements
  • Predicting combustor exit temperature
  • Modeling heat release in cycle analysis
  • Designing low-emission combustors

By applying thermochemical principles, engineers can improve efficiency, control emissions, and ensure safe operation of propulsion systems.

Thermochemistry provides the quantitative basis for analyzing and optimizing the combustion process that powers aircraft engines.

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