19open_cycle - Open Cycle mf_dot fuel combustor QH_dot 2...

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Open Cycle compressor turbine ma_dot air QH_dot 1 2 3 4 W_dotnet= Wt_dot+Wc_dot mf_dot fuel combustor = = power . .. compressor . .. W c_dot m a_dot ( h 2 h 1 ) m a_dot c p_air ( T 2 T 1 ) turbine . .. = + = 1 + W t_dot ( m a_dot m f_dot ) ( h 3 h 4 ) m a_dot m f_dot c p_prod ( T 3 T 4 ) Jet engine m a_dot as a side note: if the net work were converted to velocity via a nozzle (jet engine) the relationships would be W net_dot = W t_dot W c_dot determines state 4 out of turbine at p 4 > p 1 atmosphere is state 5 T 4 determined from equation for net work = c p ( T 3 T 4 ) w net γ− 1 1 1 T 4 p 4 γ T 5 p 5 γ T 5 p 5 γ could determine p 4 from = determine T 5 from = or . .. = T 3 p 3 T 3 p 3 T 4 p 4 nozzle anlysis: 2 V First law, Q = W = 0 h 4 = h 5 + determines V, thrust from momentum change 2 combustor . .. 1 = atmosphere . .. adiabatic combustion Q = W = 0 0 = H R2 H P3 0 = Enthaply of reactants at combustor inlet, compressor outlet - Enthalpy of products out of combustor - first law rewrite using LHV . .. 0 = H R2 H R0 ( H P3 H P0 ) + LHV rewrite using specifi enthalpy and mass flows . .. on a per unit mass flow of fuel . .. 0 = h f2 h f0 + m a_dot ( h a2 h a0 ) 1 + m a_dot ( h p3 h p0 ) + LHV m f_dot m f_dot to account for incomplete combustion introduce combustion efficiency . .. only obtain η comb HV 12/19/2005 1
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Given 0 = h f2 h f0 + m a_dot ( h a2 h a0 ) 1 + m a_dot ( h p3 h p0 ) + η comb LHV m f_dot m f_dot can solve for m a_dot /m f_dot Find m a_dot ) h f2 h f0 h p3 + h p0 + η comb LHV ) m f_dot ( ( h a2 + h a0 + h p3 h p0 + m a_dot = η comb LHV ( h f2 h f0 ) ( h p3 h p0 ) m f_dot h p3 h p0 ( h a2 h a0 ) introduce average specific heat . .. = h a2 h a0 = h p3 h p0 h f2 h f0 c p_bar_air T 2 T 0 c p_bar_prod T 3 T 0 c p_bar_fuel = T 2 T 0 + m a_dot = η comb LHV c p_bar_fuel ( T 2 T 0 ) c p_bar_prod ( T 3 T 0 ) m f_dot c p_bar_prod ( T 3 T 0 ) c p_bar_air ( T 2 T 0 ) m f_dot c p_bar_prod ( T 3 T 0 ) c p_bar_air ( T 2 T 0 ) or . .. inverting = m a_dot η comb LHV + c p_bar_fuel ( T 2 T 0 ) c p_bar_prod ( T 3 T 0 ) gas turbine efficiency efficiency dividing by m a_dot m f_dot W net_dot W t_dot + W c_dot 1 + m a_dot c p_bar_prod ( T 3 T 4 ) c p_bar_air ( T 2 T 1 ) η = = = m f_dot LHV m f_dot LHV m f_dot LHV m a_dot fuel kg SFC = hr = kg = lb not equality . ..
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19open_cycle - Open Cycle mf_dot fuel combustor QH_dot 2...

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