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Unformatted text preview: AAE 439 5. COMBUSTION AND THERMOCHEMISTRY Ch5 1 AAE 439 Overview Definition & mathematical determination of chemical equilibrium, Definition/determination of adiabatic flame temperature, Prediction of composition and temperature of combusted gases as a function of initial temperature, Prediction of amounts of fuel & oxidizer, Thermochemical changes during expansion process in nozzle. Performance Parameters: CF = 2 2 -1 +1 2 +1 -1 -1 pe p -p 1- + e a p p0 0 c* = RT0 +1 2 +1 -1 Performance depends on: T, MW, p0, pe, pa, Ch5 2 AAE 439 Overview Important Concepts & Elements of Analysis Conversion of Chemical Energy to Heat Simple Treatment of Properties of Gases Balancing Chemical Reactions - Stoichiometry Adiabatic Flame Temperature Chemical Equilibrium and Gibbs Free Energy Nozzle Expansion Effects Thermochemical Calculations Ch5 3 AAE 439 5.1 THERMODYNAMICS OF GAS MIXTURES Ch5 4 AAE 439 Perfect Gas Perfect Gas Law relates pressure, temperature and density for a perfect gas/ mixture of gases : p V = n T = mR T Universal Gas Constant: Gas Constant: Calorically Perfect Gas: Internal Energy Enthalpy pv = RT = 8.314 R= M J mol K du = c v dT dh = c p dT u2 - u1 = c v (T2 - T1 ) h 2 - h1 = c p (T2 - T1 ) Specific Heat Relationships: Definition of "Mole": cp - cv = R = cp cv A mole represents the amount of gas, which contains Avogadro's number of gas molecules: 6.021023 molecules/mol. Ch5 5 AAE 439 Gibbs-Dalton Law Properties of a mixture is determined by the properties of constituents according to GibbsDalton Law: The pressure of a mixture of gases is equal to the sum of the pressure of each constituent when each occupies alone the volume of the mixture at the temperature of the mixture. The internal energy and the entropy of a mixture are equal, respectively, to the sums of the internal energies and the entropies of its constituents when each occupies alone the volume of the mixture at the temperature of the mixture. Temperature Pressure Volume Energy Entropy Enthalpy Tmix = T1 = T2 = ... = TN pmix = p1 + p2 + p3 ...+ pN = pi i=1 N Vmix = m mix v mix = m1v1 = m2 v2 = ... = m N v N E mix = m mix emix = m1e1 + m2 e2 +...+ m N eN = m i ei i=1 N Smix = m mix smix = m1 s1 + m2 s2 + ... + m N sN H mix = m mix h mix = m1h1 + m2 h 2 + ... + m N h N smix = Smix n mix h mix = H mix n mix Ch5 6 AAE 439 Mixture of Gases Mass Based p i V = m i R i T = n i T p = pi i=1 N Definitions by Molar Based p Vi = m i R i T = n i T V = Vi i=1 N PG Law Pressure Fraction of Species Enthalpy Entropy m M yi = i = x i i m mix Mmix h mix = yi h i i y i=1 N i =1 n M x i = i = yi mix n mix Mi x i=1 N i =1 h mix = x i h i i smix (T, p) = yi si (T, p) pi si (T, p i ) = si (T, p ref ) - R ln p ref i smix (T, p) = x i si (T, p) pi si (T, p i ) = si (T, p ref ) - ln p ref i Equivalent Molecular Weight Mmix equiv m = = n m = N mi M i=1 i 1 yi M i=1 i N Mmix equiv m = = n n M i=1 i N i n = x i Mi i=1 Ch5 7 N AAE 439 Mixture of Gases Vi p i M = = x i = yi mix V p Mi c p,mix = c p,i yi i=1 N Definitions: Relationship Specific Heat Ratio of Specific Heat mix = c p,mix c v,mix = c p,mix c p,mix - R mix Ch5 8 AAE 439 5.2 1st LAW OF THERMODYNAMICS Ch5 9 AAE 439 1st LTD - Fixed Mass First law of thermodynamics embodies the fundamental principle of conservation of energy. Q and W are path functions and occur only at the system boundary. E is a state variable (property), E is path independent. System Boundary enclosing Fixed Mass Q m, E W Q Heat added to system in going from state 12 - W Work done by system on surrounding in going from state 12 = E12 Change in total system energy in going from state 12 Q q - - W w = = dE dt de dt 1 2 E = m u + v + g z 2 Ch5 10 AAE 439 1st LTD - Control Volume Control Surface (CS) enclosing Control Volume (CV) Conservation of energy for a steady-state, steady-flow system. m e + pv ( ) inlet dmCV dt =0 dE CV dt =0 m e + pv ( ) outlet QCV Rate of heat transferred across the CS, from the surrounding to the CV. - WCV QCV = m eoutlet Rate of energy flowing out of CV. WCV - m einlet Rate of energy flowing into CV. + m po v o - p i v i ( ) Rate of all work done by CV, including shaft work but excluding flow work. 1 QCV - WCV = m h o - h i + v2 - v2 + g zo - z i 2 o i ( ) ( ) ( ) Net rate of work associated with pressure forces where fluid crosses CS, flow work. Assumptions: Control Volume is fixed relative to the coordinate system. Eliminates any work interactions associated with a moving boundary, Eliminates consideration of changes in kinetic and potential energies of CV itself. Properties of fluid at each point within CV, or on CS, do not vary with time. Fluid properties are uniform over inlet and outlet flow areas. There is only one inlet and one exit stream. Ch5 11 AAE 439 THERMODYNAMIC PROCESSES E = U + E potential + E kinetic = Q - Wshaft - Wflow Energy Equation (1st Law of TD) Energy Change due to a process going from State 1 to State 2: U = U 2 - U1 = Q - Wflow = Q - p V ConstantVolume (Isochoric) Process: U = Q ConstantPressure (Isobaric) Process: U = Q - p V U + p V = Q H = Q Ch5 12 AAE 439 5.3 THERMOCHEMISTRY BASICS Ch5 13 AAE 439 Energies in Chemical Reactions QCV Enthalpy of Combustion (Reactions): H in = H reactant REACTANTS Stoichiometric fuel-oxidizer (air) mixture at standard state conditions: Tref and pref. H out = H product PRODUCTS Complete combustion at standard state conditions: : Tref and pref. h rxn qCV = h prod - h reac H rxn = H prod - H reac Graphical Interpretation Heat of Combustion: h C = -h rxn Ch5 14 ...
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