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A steam power plant design consists of an ideal Rankine cycle with regeneration.

ID: 1842826 • Letter: A

Question

A steam power plant design consists of an ideal Rankine cycle with regeneration. Steam enters Turbine 1 at P1 and T1 at the rate of m1 and exits at P2. A fraction (y') of the steam exiting Turbine 1 is diverted to a closed feedwater heater while the remainder enters Turbine 2. A portion (y") of the steam exiting Turbine 2 at P3 is diverted to an open feedwater heater while the reaminder enters Turbine 3. The exit of Turbine 3 is fed into a condenser that operates at P4. Saturated liquid exits the condenser and is fed to Pump 1. The outlet of Pump 1 is fed into the open feedwater heater. Saturated liquid exits the open feedwater heater and is fed to Pump 2. The outlet of pump 2 is fed to the closed feedwater heater. Saturated liquid exits the low pressure output of the closed feedwater heater and is fed through a steam trap to the open feedwater heater. Both exits of the closed feedwater heater are at the same temperature. All turbines and pumps are isentropic.

Given Values: m1 = 45 kg/s, P1 = 140 bar, T1 = 520 C, P2 = 10 bar, P3 = 1 bar, P4 = 0.06 bar

Find :

The specific enthalpy at the inlet of turbine 1 inlet

The specific entropy at the inlet of turbine 1 inlet

The specific enthalpy at the exit of turbine 1

The specific enthalpy at the exit of turbine 2

The specific enthalpy at the exit of turbine 3

The specific enthalpy at the condenser exit

The specific enthalpy at the exit of the low pressure pump

The specific enthalpy at the exit of the open feedwater heater

The specific enthalpy at the exit of the high pressure pump

The specific enthalpy at hte low pressure exit of the closed feedwater heater

The specific enthalpy at the exit of the steam trap

The specific enthalpy at the inlt to the boiler

Determine the fraction of flow (y') diverted to the closed feedwater heater

The power (MW) produced by turbine 1

The power (MW) produced by turbine 2

Determine the fraction of flow (y") diverted to the open feedwater heater

The power (MW) produced by turbine 3

The power (kW) required bu the low pressure pump

The power (kW) required by the high pressre pump

The total rate of heat transfer (MW) supplied to the boiler

The thermal efficiency (%) of the pwer plant

Explanation / Answer

solution:

1)here given that steam entering turbine1 at T1=520 c and p1=140 bar has enthaphy as

h1=3379.8091 kj/kg

s1=6.4642 kj/kg k

2)this steam is exiting turbine 1 at point 2 with isentropic expansion so we can write

s1=s2

for P2=10 bar

sf=2.1384 and sg=6.5849 and cp=2.7149

s1=sf+x(sg-sf)

6.4642=2.1384+x(6.5849-2.1384)

x=.9728

h2=hf2+x(hg2-hf2)

hf2=762.68,hg2=2777.1195

h2=2722.43 kj/kg

as liquid at exit of closed heater is saturated liquid

hf2=h9=h10=762.68 kj/kg

,steam at exit of turbine 1

2)from that steam certain mass bleeded to closed heater and remaining at pressure P2=10 bar get enter in turbine 2 entry as

for turbine 2 exit,p3=1 bar

sf=1.3025,sg=7.3588

s1=s3

6.4642=1.3025+x(7.3588-1.3025)

x=.8522

h3=hf3+x(hg3-hf3)

hf3=417.43,hg3=2674.94

h3=417.43+.8522*(2674.94-417.43)

enthalphy at turbine 2 exit=h3=2341.47kj/kg

enthalphy at turbine 2 exit h3=2341.47 kj/kg

when this steam enters turbine 3 and exited at p4=.06 bar,so we get that

s1=s4

s1=sf4+x(sg4-sf4)

sf4=.5208,sg4=8.3291

6.4642=.5208+x(8.3291-.5208)

x=.7611

h4=hf4+x(hg4-hf4)

hf4=151.49.hg4=2566.66

enthalphy at turbine3 exit=h4=1989.83 kj/kg

enthalphy at condenser exit is nothing but saturated liquid at p4=.06 bar,so we get that

h5=hf4=151.49 kj/kg

where work done in pump 1 is

h6=h5+(p3-p4/10)=151.49+((1-.06)/10)=151.584 kj/kg

where enthalphy at open heater is saturated liquid at p3=1 bar sowe get that

h7=hf3=417.43 kj/kg

where enthalphy at closed heater again saturated liquid at p2=10 bar

enthalphy to steam trap=enthalphy to boiler=h9=h10=762.68 kj/kg

work done in high pressure pump is

enthalphy at high pressure pump exit=h8=h7+((p2-p3)/10)=417.43+((10-1)/10)=418.33 kj/kg

8)in this way we get all enthalpies and entropy as per question and for getting steam fraction y' and y'' we have equation at point 7 and 9 as

(1-y')y''m1h3+(1-y')(1-y'')m1h6+m1h10y'=m1h7

and

m1y'h2+m1h8=m1y'h10+m1h9

on putting value we get y' as

y'=.175711 of m1

and putting value of y' in first equation at point 7 we get

y''=.08779 of (1-y')m1

9)in this way we haev calculated all enthalpies and entropies and fraction of steam bleeded so from that we can easily calculated workdone in turbine and heat supplied in reheater.

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