Energy Systems Analy&Dgn
Energy Systems Analy&Dgn ME 4315
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This 0 page Class Notes was uploaded by Chloe Reilly on Monday November 2, 2015. The Class Notes belongs to ME 4315 at Georgia Institute of Technology - Main Campus taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/234251/me-4315-georgia-institute-of-technology-main-campus in Mechanical Engineering at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
M6 LISIS ESSENTIALS OF COMBUSTION COMPLETE COMBUSTION OF HYDROCARBONS CxHy WITH OXYGEN 02 Cx x02 xCO2 1 172 2102 gt H20 2 Adding 1 and 2 CxHy x02 gtxC02 H20 3y Cz dc M5301 0 2602 341 0 For gasoline approximated by octane CgH18 M1142 C8H18l 12502 gt 8002 9H20g Where 1 stands for the liquid state and g the gaseous state COMPLETE COMBUSTION WITH THEORETICAL AIR The volume composition of dry air is 7808 nitrogen 2095 oxygen 093 argon plus about fourteen other substances to complete the whole To a close approximation air may be modeled as 7809 nitrogen 2095 oxygen 093 argon and 003 carbon dioxide2 This breakdown gives an apparent molecular weight for dry air of 28965 For use in analysis a molar overbar and massbased air re ratio for octane are de ned as 2 m0 4123mm2 m0 5967molamoz e molfue mol e 02095m 102 AF m 28965le 5967mp la maz e mm W1 m l e 1142le 15131b1bm COMPLETE COMBUSTION WITH EXCESS AIR Excess air is used to ensure complete combustion and to reduce the ame temperature to that compatible with materials as those for nozzles and blades of gas turbines Note that dissociation and loss of thermal energy to the surroundings will also lower the ame temperature Let I actual fuel air ratio moles ofdry air per mole of fuel Then ExcessEZ ii 100 34 100 AF AF 1 The equation is formulated such that the re coef cient is unity Analysis thereafter will base all terms of the energy equation per mole of fuel 2 Bathie Table 42 p 71 Theoretical Air TZ 100 AF EQUIVALENCE RATIO 5 ratio of the actual fuelair ratio to the theoretical fuelair ratio A ratio greater than 1 is said to be rich less than I lean COMPLETE COMBUSTION OF NOCTANE WITH THEORETICAL DRY AIR CBH18 5967DA gt 8C02 9H20 5967DA 12502 For combustion with other than theoretical air we can write a J Va bk 01718 X DA gt 8C0 9H0 X DA 12502 Note that some texts model air using just the two substances 0 and N2 21 02 and 79 N2 thus lmolO2 376molN2 476molsai The corresponding chemical equation for theoretical air is 08H 12502 376N2 gt 8C0 9H20 47N2 ANALYSIS OF COMBUSTION CHAMBERS FURNACES AND INTERNAL COMBUSTION ENGINES The general energy equation for cnb q w 2 quotshe producm nihi reaetants Where n moles of substance per mole of fuel h enthalpy of formation hf change in enthalpy to account for departures from the standard reference state de ned by a pressure of one atmosphere and a temperature of 25 C or 77 F The enthalpy of formation is the heat energy released exothermic reaction or absorbed endothermic reaction when one mole 3unit mass of fuel is formed at standard reference conditions om the elements in their most stable form hhfAh AhhTP hTefPef 3 See eg Bathie 43 p 72 or Moran and Shapiro 1321 p 707 ENTHALPY 0F COMBUSTION Rewriting equation 4 to separate the enthalpies of formation from the changes in enthalpy from the standard reference state SRS we get equation 5 q w quot2 hf eproducts ni hf irwmnm Ely Ahepmductx nquot Ahireactants The enthalpy of combustion is de ned as the di erence between the enthalpies of formation of the products and reactants It is the term in braces For combustion of a fuel it is merely the heat energy released from a system when the products have been cooled to the SRS Ifthe enthalpies of formation are not known as for eg fuel oil and coal the enthalpy of combustion can be used instead as in equation 5 HEATING VALUE absolute value of the enthalpy of combustion The higher heating value HHIO implies that the water in the products is in the liquid phase The lower heating value LHIO implies that the water in the products is in the vapor phase The di erence between these two quantities is the latent heat of vaporization ADIABATIC FLANIE TEMPERATURE the temperature resulting when q and w are set to zero in equations 4 or 5 T Ah f CPAr HVoJos MuteP ch Tm 39 TI H HV 395 L HV JP QM REFERENCES l 010 H7 0 l Bathie W W Fundamentals of Gas Turbines 2 ed John Wiley amp Sons Inc 1996 2 Moran M J and Shapiro H N Fundamentals of Engineering Thermodynamics 4 ed John Wiley amp Sons Inc 2000 3 Black W Z and Hartley J G Thermodynamics EnglishSI Version 3 ed HarperCollins 1996 Al rx n39b l Tlraft Alf ycPAT 39T m 4 3 2 l 0LT bTCrAT6 M t Mil AL A M Kim a W Zl we 2L U M 2 tum I C quot quot i GAS TURBINE ANALYSIS AND DESIGN NOMENCLATURE mg rha mass rate of air mass rate of gas CCCombustion Chamber C compressor GT gas turbine drives compressor PT power turbine r compression ratio 139 isentropic process a actual process WC compressor work 39 WGT gas turbine work WPT power turbine work 17m mechanical ef ciency Note small quot wquot stands for work per unit mass The diagram below shows the principal components of a gas turbine for power production The gases exiting state 5 may be diverted to a sick or to heat recovery components Also shown is a Ts diagram of the thermodynamic W cycle k W L01 lt2 StatelisknownPl and I State 2 For a given pressure ratio state2i is known 139 P2 Pl S2 S1 The actual state leaving the compressor 2a is found from the de nition of compressor ef ciency which can be estimated with reasonable accuracy h h2i hr hm Neglecting potential and kinetic energies the actual compressor work per unit mass is WC hlh2a 77c State 3 is found by estimating the percent pressure drop in the combustion chamber P3 P2 AP and selecting the highest temperature for best ef ciency compatible with the turbine nozzleblade material State 4 The ideal work of the gas turbine is found from the de nition of turbine ef ciency The actual work is equal to that of the compressor but opposite in sign W GT1 won quot 7701 Furthermore an 113 h From this relation and the knowledge that S4 13 state 4i is found The enthalpy of state 4a is found from the de nition of turbine ef ciency and knowledge of Rt I73 h4a ha Thu 770T State Si is found from the power turbine exit pressure which will depend on any components installed for noise abatement or heat recovery and the enthalpy 35 s4 State 5a is then found 39om the estimated power turbine ef ciency h4a 11511 nquot h4a h5i The work of the power turbine is WPT h4a hSa The heat energy added in the combustion chamber is 4 ha 3912 The thermal ef ciency is wPT nth q Two use ll quantities for comparing engines are the speci c fuel consumption SF C and the heat rate HR The SF C is mass rate of fuel divided by the power 711 lbmf 3413 lbmf 2545 lb SFC f W 17hmfLHV Btu nth LHV kWh 77 hLHVhph The heat rate is the rate of heat energy added divided by the power output g 3413 Btu z 2545 Btu HR nthQ 77m kWh 7731 kph TURBINE DIlVIENSIONS Turbine dimensions are determined largely by the required mass rate Starting with the client s requirement for power at the generator bus estimate the generator ef ciency and calculate the required brake power WPT quotdrake 17m mgWPT The required area of the turbine nozzle and blade rings can be calculated for each stage from VA mg T REFERENCE
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