Presentation Transcript

1. ME 525: Combustion Session 2

   Today Review of Property Relations Conservation of Mass and First Law of Thermodynamics (Conservation of Energy) Control Mass Control Volume Air Standard Processes and Cycles
2. Intensive and Extensive Property Relations: Ideal Gas in an Engine Cyl. Volume at top dead center (TDC) Cylinder (Cyl.) Volume at bottom dead center (BDC) Volume is equal to mass times specific volume and Equal to number of mols times molar specific volume. Piston Review equations 2.1, 2.2, 2.3 for other property relations
3. Calorific Equation of State (For a given composition and phase), the state of a “pure” working substance is defined by two independent properties corresponding to the mechanical work and heat transfer modes of energy transport. Internal energy is related to temperature and specific volume Enthalpy is related to temperature and pressure For ideal gases, u and h are functions of temperature alone.
4. Ideal Gas Mixtures Combustion involves mixtures of ideal gases with significant variation in molecular weights. H atom as well as C7H16 and other heavier hydrocarbons. Combustion may also involve multiple phases including solid, liquid, and gas phases. Since, free electrons also exist, combustion media are sometimes analyzed as plasmas. Important for igniters but in general limited to three phases with gas phase being most prevalent.
5. Phase Change Processes in Combustion In many combustion applications, fuel enters the combustor as a liquid or even as a solid and phase change processes are important. Products of combustion often contain sufficient amount of water vapor to condense in the exhaust system or on emission to the environment. Higher heating value (HHV) of fuels is defined assuming water leaves the combustor as a liquid. Fire suppression often involves water sprays that vaporize and reduce the temperature sufficiently to suppress combustion. Phase change to solid particulate phase is responsible for soot emissions from combustors. Enthalpy of vaporization and Clausius-Chapeyron equations help include liquid phase change processes in basic combustion calculations.
6. Conservation of energy statement for control mass Use appropriate sign convention for heat and work interactions Heat transfer into system positive; heat transfer from system negative Work into system negative; work out of system positive Control Mass Energy Balance for “pure working substance”
7. Control Volume Energy Balance for “pure working substance” Conservation of energy statement for control volume Mass flow rate entering the open system increases energy content while that leaving the system decreases energy content Use appropriate sign convention for heat and work interactions Heat transfer into system positive; heat transfer from the system- negative Work into system negative; work from the system- positive h = u + Pvwhere Pvis the flow work
8. Equation of State with Phase Change (For a given composition but with phase change), the state of a “pure” working substance is still defined by two independent properties. Temperature and pressure are no longer independent properties! Enthalpy and all other properties are now related to T, x or P, x, or T, v Consider Enthalpy: Note the equations that were written for ideal gases do not apply! Examples: For phase change processes In fact Is not even defined!
9. Enthalpy Change with Combustion (For a given phase but with composition change), two independent thermodynamic properties and the composition change define changes in all properties. Enthalpy and all other properties are now related to T, P, Yi Consider Enthalpy: Ideal Gas
10. Control Volume Energy Balance for “pure working substance” with Combustion (?) Conservation of energy statement for control volume For air standard analysis the working substance is still maintained as “air,” and the enthalpy change occurring because of combustion is treated as if it was heat addition from an external source leading to a change in the temperature of the “pure” working substance. “Heat added,” is then calculated as Heating Value multiplied by the mass of fuel burned. The mass of fuel is usually much smaller than the mass of air and hence air standard analysis provides approximately correct answers.
11. Control Volume Energy Balance for “pure working substance” with Combustion Conservation of energy statement for control volume with appropriate assumptions, the energy equation can be: The number of mol of products in the reactor and the number of mol of reactants in the reactor depend on the conservation of mass equations for each species which also involve the rates of reaction. For now, let us assume steady state and
12. Example Problems (Try to read ahead of time, will solve these together in class) Coal approximated as Carbon (C) burns with pure oxygen (O2) to produce CO2. Write an equation for the reaction and find the mass in kg of the product gases per mol of oxygen consumed in the combustion process. Repeat 1 for hydrogen and carbon monoxide considered as fuel gases. Write a chemically balanced equation for combustion of a generic paraffin CnH2n+2 with air. Find the mass of product gases if one mol of heptane is burned with stoichiometrically correct amount of air. Find mass fractions and mole fractions in reactants and products. Check that the mass is conserved in the reaction. Are the mol conserved? What is the consequence of this in practical combustor designs?
13. Example Problems Find stoichiometrically correct air to fuel mol and mass ratio for heptane combustion. Find mass and mole fractions of reactant and product species for complete combustion of heptane with 50% excess air. Find the equivalence ratio. Partial pressures of CH₄, C₂H₆, C₃H₈ and C4H₁₀ in a fuel mixture of these 4 paraffins are 0.5 atm, 0.3 atm, 0.15 atm and 0.05 atm. Find the stoichiometric Air/Fuel ratio, mass and mole fractions of products resulting from complete combustion, mole fractions of CO₂, N₂ in the products if the water vapor is completely condensed out, mole fraction of H₂O, CO₂ and N₂ in the products if exhaust gas temperature is reduced to 50˚C and the water condensation process reaches equilibrium. Click here to see solution to example problem.