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taurus [48]
3 years ago
14

A steam power plant operates on an ideal Rankine cycle with two stages of reheat and has a net power output of 120 MW. Steam ent

ers all three stages of the turbine at 500°C. The maximum pressure in the cycle is 15 MPa, and the minimum pressure is 5 kPa. Steam is reheated at 5 MPa the first time and at 1 MPa the second time. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle and (b) the mass flow rate of the steam.

Engineering
1 answer:
uysha [10]3 years ago
7 0

Answer:

a) 40.6%

b)72.19kg/s

Explanation:

The Rankine cycle with two reheat stages has 9 stages in total.

The maximum pressure will be at the first inlet stage of the HP turbine which is stage 3. The minimum pressure will be the exit stage of the condenser because the condenser operates under vacuum pressure which is stage 1.

The following assumptions can be made:

1 - Each component in the cycle is analyzed as an open system operating at steady-state.

  2 - All of the processes are internally reversible.

  3 - The turbine and pump operate adiabatically and are internally reversible, so they are also isentropic.

   4 - Condensate exits the condenser as saturated liquid.

  5 - The effluent from the HP turbine is a saturated vapor.

  6 - No shaft work crosses the system boundary of the boiler or condenser.

   7 - Changes in kinetic and potential energies are negligible

a) The thermal efficiency of the cycle is defined as the work of the cycle divided by the total heat input to the system. The stages that have heat input is stages 2-3, 4-5, 6-7.

For stage 2:

s₁=s₂ assuming isentropic

s_1=0.4762 @ P_1=15MPa

enthalpy will be a compressed liquid so after interpolation

h_2=97.93+(0.4762-0.2932)((180.77-97.93)/(0.5666-0.2932))=153.38kJ/kg

For stage 3:

Superheated steam @ T=500⁰C and P=15MPa

h_3=3310.8kJ/kg

Stage 4:

superheated vapor

P=5MPa

s₃=s₄=6.3480 kJ/kg, we must use interpolation to find h₄

h_4=2925.7-(6.348-6.2111)((3069.3-2925.7)/(6.4516-6.2111))=3007.44kJ/kg

Stage 5:

Superheated steam @ T=500⁰C and P₄=P₅=5 MPa

h_5=3434.7kJ/kg

Stage 6:

Superheated steam at P₆= 1MPa

s₅=s₆

s_6=6.9781

We find h₆ using interpolation from the steam tables:

h_6=2943.1-(6.9781-6.9265)((3051.6-2943.1)/(7.1246-6.9265))=2970.67kJ/kg

Stage 7:

P₇=P₆=1MPa

T=500⁰C superheated steam

h_7=3479.1kJ/kg

The heat into the cycle is:

=(h_3-h_2)+(h_5-h_4)+(h_7-h_6)

=(3310.8-153.38)+(3434.7-3007.44)+(3479.1-2970.67)=4108.74kJ/kg

We can determine the work out by the condenser from stage 9 to stage 1:

Stage 1:

saturated liquid P=5kPa

h_1=137.75kJ/kg

Stage 9:

We assume that its a saturated liquid with quality of 1 at 5kPa and

s₇=s₉ and after interpolation

h_9=2568.53kj/kgK

Qout = [/tex]2568.53-137.75=2430.79kJ/kg[/tex]

The thermal efficiency can be written in terms of qin and qout:

n=1-(q_o/q_i)=1-2430.79/4093.11=0.4061

Efficiency of 40.61%

b)

The mass flow rate can be calculated from the Wnet:

W_n=W_t-W_p

Work of the turbines minus the work of the pumps:

W_n=m((h_3-h_4)+(h_5-h_6)+(h_7-h_9)-(h_1-h_2)

120000=m(1662.33)

m=72.19

mass flow rate of steam is 72.19 kg/s

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1. (5 pts) An adiabatic steam turbine operating reversibly in a powerplant receives 5 kg/s steam at 3000 kPa, 500 °C. Twenty per
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Answer:

temperature of first extraction 330.8°C

temperature of second extraction 140.8°C

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Explanation:

Hello!

To solve this problem we must use the following steps.

1. We will call 1 the water vapor inlet, 2 the first extraction at 100kPa and 3 the second extraction at 200kPa

2. We use the continuity equation that states that the mass flow that enters must equal the two mass flows that leave

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As the problem says, 20% of the flow represents the first extraction for which 5 * 20% = 1kg / s

solving

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3.

we find the enthalpies and temeperatures in each of the states, using thermodynamic tables

Through laboratory tests, thermodynamic tables were developed, these allow to know all the thermodynamic properties of a substance (entropy, enthalpy, pressure, specific volume, internal energy etc ..)  

through prior knowledge of two other properties

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5.we find the enthalpy and the temperature in the second extraction with the pressure 200 kPav y the entropy of state 1

h3=Enthalpy(Water;s=s1;P=P3)

h3=2750KJ/kg

T3=Temperature(Water;P=P3;s=s1)

T3=140.8°C

6.

Finally, to find the power of the turbine, we must use the first law of thermodynamics that states that the energy that enters is the same that must come out.

For this case, the turbine uses a mass flow of 5kg / s until the first extraction, and then uses a mass flow of 4kg / s for the second extraction, taking into account the above we infer the following equation

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