P04 237

Equations

Thermodynamics - An Engineering Approach (5th Ed) - Cengel, Boles - Mcgraw-Hill (2006) - pg.

Turbina cu abur, curgere stationara

Un debit de abur cu 10 MPa si 550 C intra intr-o turbina cu 60 m/s, curge stationar si iese cu 25 kPa si un titlude vapori de 95 %. In timpul procesului are loc o cedare de caldura de 30 kJ/kg. Sectiunea de curgere la intrareain turbina e de 150 cm2, iar cea de iesire e de 1400 cm2. Sa se determine:(a) debitul masic de abur(b) viteza de iesire(c) puterea produsa de turbinaSa se studieze influenta marimii sectiunii de curgere la iesire asupra vitezei la iesire si a puterii produse deturbina.

$UnitSystem kPa C

Marimi de intrare:

A1 = 150[cm2

]; V el1 = 60 [m/s] (1)

T1 = 550 [C] ; P1 = 10000 [kPa] (2)

qout = 30 [kJ/kg] (3)

x2 = 0.95 (4)

1

$IfNot ParametricTable

A2 = 1400[cm2

]A[2]= 1000:1000:3000 [cm2] (5)

P2 = 25 [kPa] P[2]= 10:10:50 kPa (6)

$EndIf

Rezolvare:

s1 = s (steam, T = T1, P = P1) (7)

h1 = h (steam, T = T1, P = P1) [kJ/kg] (8)

v1 = v (steam, T = T1, P = P1)[m3/kg

]specific volume of steam at state 1 (9)

m = A1 ·V el1v1

·∣∣∣∣∣1× 10·4

m2

cm2

∣∣∣∣∣ [kg/s] (10)

h2 = h (steam, P = P2, x = x2) [kJ/kg] (11)

s2 = s (steam, P = P2, x = x2) (12)

T2 = T(steam, P = P2, x = x2) [C] not required, but good to know (13)

v2 = v (steam, P = P2, x = x2)[m3/kg

]specific volume of steam at state 2 (14)

V el2 = m · v2(A2 ·

∣∣∣1× 10·4 m2

cm2

∣∣∣) [m/s](15)

Conservarea energiei pentru curgerea stationara:

For steady-flow, δE˙= 0

For the turbine as the control volume, neglecting the PE of each flow steam:

Ein = Eout [kW] (16)

Ein = m ·(h1 +

V el212

·∣∣∣∣∣0.001 kW

W

∣∣∣∣∣)

[kW] (17)

Eout = m ·(h2 +

V el222

·∣∣∣∣∣0.001 kW

W

∣∣∣∣∣)+ m · qout + Wout [kW] (18)

Power = Wout ·∣∣∣∣0.001 MW

kW

∣∣∣∣ [MW] (19)

Qout = m · qout [kW] (20)

Data$ = Date$ (21)

Solution

2

Data$ = ‘2014-02-06’ Ein = 88472 [kW] Eout = 88472 [kW] m = 25.26 [kg/s]

Power = 10.25 [MW] Qout = 757.7 [kW] qout = 30 [kJ/kg] Wout = 10248 [kW]

Arrays

Row Pi Ti hi si vi xi Ai V eli[kPa] [C] [kJ/kg] [kJ/kg-C] [m3/kg] [cm2] [m/s]

1 10000 550 3501 6.756 0.03563 150 602 25 64.95 2500 7.483 5.901 0.95 1400 1065

Viteza iesire

Puterea produsa

3