hw_Rankine_Q_A

hw_Rankine_Q_A - Problem Set: Rankine Cycles Problem 1:...

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Center for Advanced Energy Systems Michael R. Muller, Director 640 Bartholomew Road, Piscataway NJ 08854 (908) 644-8469 FAX: (732) 445-0730 mullerm@rci.rutgers.edu http://caes.rutgers.edu Problem Set: Rankine Cycles Problem 1 : Calculate the thermal efficiency of a simple Rankine cycle for which steam leaves the boiler as saturated vapor at 3 x 10 6 N/m 2 and is condensed to saturated liquid at 7000 N/m 2 . The pump and turbine have isentropic efficiencies of 0.6 and 0.8, respectively. The pump inlet is saturated liquid. Solution : () 73 . 0 7167 . 7 559 . 0 1878 . 6 1878 . 6 s J/g 2636 168 04 28 h h Q Pa M SAT.VAP.@3 2804 J/g 168 3 6 . 0 007 . 1 163 ; J/g 163 3 , 4 3 2 3 in 3 2 1 2 1 = = + = = = = = = = = + = Δ + = = χ fg f s s x s h h W h h P v h h h so ( ) ( )( ) ( ) ( ) % 5 . 26 2636 / 5 704 704 8 . 0 880 1924 2804 8 . 0 J/g 1924 2572 73 . 0 163 27 . 0 4 3 4 = = = = = = = + = η h h W h Problem 2 : A Rankine-cycle power plant has one stage of reheat. The turbine inlet is 3 x 10 6 N/m 2 at 500 ° C. After expansion to 0.5 x 10 6 N/m 2 the steam is reheated to 500 ° C and expanded in a second turbine to a condenser pressure of 0.007 x 10 6 N/m 2 . The steam leaves the condenser as saturated liquid. Calculate the cycle efficiency, using a pump efficiency of 0.6 and turbine efficiencies of 0.8. Solution : 1)
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Center for Advanced Energy Systemt Michael R. Muller, Director J/g 5 6 . 0 3 J/g 3 3 007 . 1 J/g 163 2 3 3 1 = = = = Δ = = W m MN x Mg M P v W h 2) h 2 = 168 3) J/g 3288 J/g 2346 . 7 ; 3456 2 3 1 3 3 = = = = h h Q K s h 4) () J/g 397 496 8 . 0 J/g 496 2960 3456 240 J/g, 2960 ; 5 . 0 at 4 3 1 , 4 3 4 2 = = = = = ° = W h h W C T h s s m MN s s s 5) h 5 = 3483.9 500 ° C ( ) s 5 = 8.0873 Q 2 = h 5 h 4 = 423.9 Q = Q 1 + Q 2 = 3288 + 423.9 3712 J / g 6) s 6 = s 5 = 8.0873 P 6 = 0.007 MPa X 6,5 = s s f s fg = 8.0873 0.559 7.7167 = 0.975 h 6, s = 0.025 163 + 0.975 2572 = 2514 W 2, s = h 5 h 6 = 970 J / g ; W = 0.8 970 = 776 J / g W total = 397 + 776 = 1173 J / g η = 1173 5 3712 = 31.4%
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Center for Advanced Energy Systemt Michael R. Muller, Director Problem 3 : Determine the energy-conversion efficiency for a supercritical steam power plant where condensation occurs at 100 ° F and the high-pressure side is at 4000 psia. Assume that the maximum system temperature is 1000 ° F and that the overall isentropic efficiency of the turbines (several used in series) is 0.90. The pump efficiency is 0.60. Specify the heating rate and steam- flow rate for 100 MW of power output. Solution : () = = = = = = = = = = = = = + = + = = = = = = = = Δ = = = = = = = = ° ° ° ° . / 10 68 . 8 393 . 0 / 10 413 . 3 / , / 10 60 . 6 517 / 10 413 . 3 / 393 . 0 1315 / 517 / / 1315 88 1403 / 88 20 68 / 517 20 537 20 6 . 0 / 12 . 12 778 144 9 . 0 4000 016 . 0 537 596 9 . 0 / 810 / 1403 6 . 596 / 97 . 67 8 8 5 8 2 3 1 2 4 , 3 4 3 , 1 hv Btu x x W Q hv lbm x x W W M Q W lbm Btu h h Q lbm Btu W h h lbm Btu W W W lbm Btu W lbm Btu v W lbm Btu W lbm Btu h W W lbm Btu h h h W lbm Btu h B B NET B p p T NET p p ps T s s T T s s T η Problem 4 : The geothermal plant operated by a utility company in northern California utilizes steam produced by natural means underground. Steam wells are drilled to tap this steam supply which is available at 65 psia at 350 ° F. The steam leaves the turbine at 4-in Hg absolute pressure.
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This note was uploaded on 02/08/2011 for the course ME 650:462 taught by Professor Muller during the Fall '10 term at Rutgers.

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hw_Rankine_Q_A - Problem Set: Rankine Cycles Problem 1:...

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