Introducton to Terodynacs, Lecture -5 Pro. G. Cccarell (0 Applcaton o Control olue Energy Analyss Most terodynac devces consst o a seres o coponents operatng n a cycle, e.g., stea power plant Man coponents o te above cycle are: Boler (stea generator eat excanger Turbne generates work Condenser eat excanger Pup Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0
Oters coponents nclude: nozzles, dusers, trottlng devces Nozzles and Dusers Devces tat ncrease or decrease te low velocty by passng te low troug a varable area duct, A A Applyng conservaton o ass assung steady low: dm C dt A A A A Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0
For low subsonc low ( = A A Subsonc Nozzle: A < A > Subsonc Duser: A > A < Arcrat gas turbne duser nozzle Applyng te energy equaton (assung steady, no eat loss, PE=0: de dt q w s ( / gz ( e e / gz e 0 Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0
Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0 ( / / For a rocket nozzle >> (
Turbne A devce n wc sat work s generated as a result o gas passng troug a set o blades attaced to a reely rotatng sat Te rotatng blades redrect te low o axs, so you need a set o xed blades tat stragten out te low beore te next set o rotatng blades Rotatng blades Fxed blades Rotatng blades Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 5 o 0
In ts course we are not nterested n te detals o te low troug eac blade, or row o blades. We are nterested n te overall energy balance Flow T W Applyng Frst Law (steady-state, neglect eat transer 0 q w ( ( w ( ( work per unt ass Oten te cange n KE s sall copared to cange n.e., w Note: work output ( w 0 Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 6 o 0
Power s work output per unt te W w ( EXAMPLE Stea enters a turbne operatng at steady-state wt a ass low rate o 600 kg/. Te turbne develops a power output o 000 kw. At te nlet te pressure s 60 bars, te teperature s 00C and te velocty s 0 /s. At te ext te pressure s 0. bar, te qualty s 0.9 and te velocty s 50 /s. Calculate te rate o eat transer between te turbne and te surroundngs, n kw. stea = 600 kg/r P = 60 bar T = 00C = 0 /s T W lqud/vapor x = 0.9 P= 0. bar = 50 /s T 00C 76C 60 bar 0. bar v Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 7 o 0
Assue steady-state and PE s neglgble 0 q w ( ( q w ( ( Need entalpy at states and State : Fro saturated water Table A- Tsat (60 bar= 75.6C snce T>Tsat at sae pressure ave supereated vapor Fro supereated water vapor Table A- (60bar, 00C= 77. kj/kg State : Fro saturated water Table A- (0. bar= 9.8 kj/kg g(0. bar= 58.7 kj/kg = + x(g- = 9.8 + 0.9(9.8= 5. kj/kg so - = 5. - 77. = -8.8 kj/kg Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 8 o 0
0.5 = 0.5(50 00 s -0 =00 N kg /s /s J N 00 J kg Collectng ters: q w ( ( Q W ( ( 000 kw 600 kg r r 600 s 8.8 kj kg. kj kg Q 6. kw Negatve sgn ples eat loss ro turbne Note: Derence n agntude between and ke Magntude o eat loss Q (6 kw copared to agntude o power output W (000 kw Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 9 o 0
Copressor/pup A devce n wc sat work nput s used to rase te pressure o a lud (lqud or vapor Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 0 o 0
Agan we are not nterested n te detals o te low troug eac blade or row o blades. We are nterested n te overall energy balance Flow C W Applyng Frst Law (steady-state, neglect eat transer and PE 0 q w ( ( w ( ( work per unt ass Oten te cange n KE s sall copared to cange n.e., w Note: work nput ( w 0 Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0
Trottlng Devce A devce tat generates a sgncant pressure drop va a low restrcton, e.g., partally closed valve. Applyng Frst Law (steady-state, neglect eat transer and PE 0 q w ( ( / I te state s taken ar downstrea ro te blockage te cange n velocty s neglgble,.e., Trottlng process s caracterzed by constant entalpy Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0
Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0 Heat Excangers Tese are devces tat transer energy between lud streas at derent teperatures cool or eat one o te luds. Te ollowng s a tube-n-tube eat excanger Can ave cross-low or parallel-low type Applyng Frst law to above cross low eat excanger assung steady low, no eat loss to te envronent and KE and PE s neglgble ( ( ( ( 0 gz gz gz gz W Q Steady low so and ( ( 0
Solvng we get To get te rate o eat transer ro one strea to te oter peror C analyss on only te nner-tube (assue nner-strea s otter tan outer-strea Q Agan Applyng Frst Law wt sae assuptons 0 ( Q ( Q ( Snce Q 0, so T > T (lud cools down Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page o 0
Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 5 o 0 A C analyss o te outer-strea would gve ( ( ( 0 Q Q o o Snce 0 Q o, so T > T (lud eats up Note, te agntude o te energy transer rate ro te nner strea Q equals te agntude o te energy transer rate nto te outer-strea o Q Q Q o Qo
Note we recover te sae relatonsp obtaned usng te global energy balance Anoter coon type o eat excanger s a drect contact eat excanger, e.g., open eed water eater. Hot strea, War strea, Cold strea, Ts type o eat excanger conssts o a vessel were a ot strea and cold strea o te sae lud are xed and ext at an nteredate teperature troug a sngle outlet. Apply conservaton o ass and Frst Law to te C and assung steady state, neglgble KE and PE cange to get: dm C dt 0 Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 6 o 0
de C dt Q W ( ( ( 0 Transent Control olue Analyss Apples wen te C as only one nlet or one ext Reservor: constant T constant P valve C Consderng te llng o a rgd tank o volue cv wt a gas suppled at a constant pressure and teperature Applyng conservaton o ass dm dt C e Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 7 o 0
Applyng Frst Law, neglectng eat transer to envronent, KE and PE de dt C du dt C Q W ( / gz e (... Note: constant entalpy across te valve (trottlng devce gas specc entalpy,, nto te C equals te gas specc entalpy n te reservor, R du dt C R Substtutng Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 8 o 0
du dt C R dm dt C Integratn g ro te ntal state ""to te nal state "" U du U R M dm M U U ( M M R M u M u ( M M R Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 9 o 0
I te tank s ntally epty (vacuu = 0 M u M R c T c P T R T c c P T R kt R Work done gettng gas nto te C results n a nal tank gas teperature ger tan te reservor teperature Source URL: ttp://e.queensu.ca/courses/0/lecturenotes.tl Saylor URL: ttp://www.saylor.org/courses/me0/#.. Cccarcell/Queens Unversty (www.queens.ca Saylor.org Used by persson. Page 0 o 0