17polytropic_eff

# 17polytropic_eff - Polytropic Efficiency consider a two...

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Polytropic Efficiency kJ := 1000J consider a two stage compressor with a stage efficiency = 0.9 kJ p 1 := 1bar p 2 := 5bar p 3 := 20bar s 1 := 1 η stage := 0.9 kg K calculations the states resulting are plotted . .. 0.95 1 1.05 1.1 1.15 200 400 600 800 Temperature entropy using the gas laws and stage effiiciency = η stage , after the first stage the states will be kJ T 2 = 491.556 K s 2 = 1.04 p 2 = 5 bar kg K after the second stage the states will be T 3 = 756.994 K s 3 = 1.076 kJ p 3 = 20 bar kg K now if we calculate efficiency of the compressor T s T 3s T 1 T 3s T 1 T 33s T 2 T 2s T 1 η comp = T = T 3 T 1 T 3 T 1 = 0.88 as a check . .. T 3 T 2 = 0.9 T 2 T 1 = 0.9 This effect can be accounted for by using polytropic efficiency - or small stage efficiency. reset variables T, s, p h 2s h 1 T 2s T 1 T s = = = η c h 2 h 1 T 2 T 1 T compressor 11/9/2005 1

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as the pressure ratio approaches unity T s d d = T s define . .. η pc = T s T dT dT => dT s = η pc dT for simple compressible substance Tds = dh (7.7) v dp ds = dh v dp = dT R dp ideal gas and definition of c po T T c po T p isentropic ds = 0 dT s = R dp c po T p dT dp T 2 R p 2 substitute dT s = dT = R rearrange and ln = ln η pc c po η pc T p integrate . .... T 1 c po ⋅η pc p 1 c po c po R γ − 1 γ = c vo c vo := γ R := c po c vo η pc c po simplify γη pc γ− 1 T 2s 1 1 raise to exponents T 2 p 2 pc use in definition T 2s T 1 T
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## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.611 taught by Professor Davidburke during the Fall '06 term at MIT.

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17polytropic_eff - Polytropic Efficiency consider a two...

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