Applied thermodynamics ppt

Thermodynamics, Flame Temperature and Equilibrium and metallurgical thermodynamics ppt
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Dr.TomHunt,United States,Teacher
Published Date:23-07-2017
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Thermodynamics, Flame Temperature and Equilibrium CEFRC Combustion Summer School 2014 Prof. Dr.-Ing. Heinz Pitsch Copyright ©2014 by Heinz Pitsch. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Heinz Pitsch. Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Thermodynamic quantities • Thermodynamics, flame • Flame temperature at complete conversion temperature, and equilibrium • Chemical equilibrium • Governing equations • Laminar premixed flames: Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 2 Thermodynamic Quantities First law of thermodynamics - balance between different forms of energy • Change of specific internal energy: du specific work due to volumetric changes: dw = -pdv , v=1/r specific heat transfer from the surroundings: dq • Related quantities specific enthalpy (general definition): specific enthalpy for an ideal gas: • Energy balance: 3 Multicomponent system • Specific internal energy and specific enthalpy of mixtures • Relation between internal energy and enthalpy of single species 4 Multicomponent system • Ideal gas  u and h only function of temperature • If c is specific heat capacity at constant pressure and h is reference pi i,ref enthalpy at reference temperature T , temperature dependence of partial ref specific enthalpy is given by • Reference temperature may be arbitrarily chosen, most frequently used: T = 0 K or T = 298.15 K ref ref 5 Multicomponent system • Partial molar enthalpy H is i and its temperature dependence is where the molar heat capacity at constant pressure is • In a multicomponent system, the specific heat capacity at constant pressure of the mixture is 6 Determination of Caloric Properties • Molar reference enthalpies of chemical species at reference temperature are listed in tables • Reference enthalpies of H , O , N and solid carbon C were chosen as zero, 2 2 2 s because they represent the chemical elements • Reference enthalpies of combustion products such as CO and H O are 2 2 typically negative 7 Determination of Caloric Properties • Temperature dependence of molar enthalpy, molar entropy, and molar heat capacities may be calculated from polynomials • Constants a for each species i are listed in tables j 8 Determination of Caloric Properties NASA Polynomials for two temperature ranges and standard pressure p = 1 atm 9 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Thermodynamic quantities • Thermodynamics, flame • Flame temperature at complete conversion temperature, and equilibrium • Chemical equilibrium • Governing equations • Laminar premixed flames: Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 10 Flame Temperature at Complete Conversion • First law of thermodynamics for an adiabatic system at constant pressure (dq = 0, dp = 0) with only reversible work (dw = -pdv) • From first law with follows • Integrated from the unburnt (u), to burnt (b) gives or 11 Flame Temperature at Complete Conversion • With and follows • Specific heats to be calculated with the mass fractions of the burnt and unburnt gases 12 Flame Temperature at Complete Conversion • For a one-step global reaction, the left hand side of may be calculated by integrating which gives / h i,ref and finally 13 Flame Temperature at Complete Conversion • Definition: Heat of combustion • Heat of combustion changes very little with temperature • Often set to: • Simplification: T = T and assume c approximately constant u ref p,b • For combustion in air, nitrogen is dominant in calculating c p,b • Value of c somewhat larger for CO , somewhat smaller for O , while that pi 2 2 for H O is twice as large 2 • Approximation for specific heat of burnt gas for lean and stoichiometric mixtures c = 1.40 kJ/kg/K p 14 Flame Temperature at Complete Conversion • Assuming c constant and Q = Q , the flame temperature at complete conversion p ref for a lean mixture (Y = 0) is calculated from F,b  Coupling function between fuel mass fraction and temperature • With n = - n' follows F F 15 Flame Temperature at Complete Conversion • For a rich mixture should be replaced by • One obtains similarly for complete consumption of the oxygen (Y = 0) O ,b 2 16 Flame Temperature at Complete Conversion • Equations and may be expressed in terms of the mixture fraction • Introducing and and specifying the temperature of the unburnt mixture by where • T is the temperature of the oxidizer stream and T that of the fuel stream 2 1 • c assumed to be constant p 17 Flame Temperature at Complete Conversion • Equations and then take the form • The maximum temperature appears at Z = Z : st 18 Flame Temperature at Complete Conversion Burke-Schumann Solution: Infinitely fast, irreversible chemistry 19 Flame Temperature at Complete Conversion • The table shows for combustion of pure fuels (Y = 1) in air (Y = 0.232) F,1 O ,2 2 with T = 300 K and c = 1.4 kJ/kg/K u,st p - stoichiometric mixture fraction - stoichiometric flame temperatures for some hydrocarbon-air mixtures 20