Question

Steam at a pressure of 13.73 bar, and temperature of 250^∘C is expanded through a turbine to a pressure of 4.12 bar, it is then reheated at a constant pressure to a temperature of 200^∘C and then it completes its expansion through the turbine to an exhaust pressure of 0.206 bar.

(a) Draw the expansion and reheating process on T-s and h-s (Mollier diagram), respectively

(b) Calculate the efficiency of the plant and the work done: (i) taking the reheating into account (ii) if the steam is expanded direct to the exhaust pressure without reheating.

Answer 1

We're given the following information in the problem:

• Initial pressure, P₁=13.73 bar

• Initial temperature, T₁=250∘C

• Reheat pressure, P₂=4.12 bar

• Final pressure, P₄=0.206 bar

Using the superheated steam table at P = 13.73 bar and T₁=250^∘C

The specific enthalpy at the initial state is, h₁=2929 kJ/kg

The specific entropy at the initial state is, s₁=6.7594 kJ/kg⋅K

Using the saturated steam table at P = 13.76 bar, we get

The specific enthalpy of the saturated liquid is, h_f=824 kJ/kg

Process 1-2 is an isentropic process, therefore,

s₂=s₁=6.7594 kJ/kg⋅K

Using the saturation table bar we get:

s_g=6.8864 kJ/kg⋅K>s₂=6.7594 kJ/kg⋅K

Thus, the steam is in a saturated liquid-vapor phase at the intermediate state.

Quality of the saturated liquid-vapor phase at the intermediate state:

The specific enthalpy of the steam at the intermediate state is,

Using the superheated steam table at P = 4.12 bar and T₂=200^∘C

The specific enthalpy at the intermediate state 3 is, h₃=2860.4 kJ/kg

The specific entropy at the intermediate state 3 is, s₃=7.1577 kJ/kg⋅K

Process 3-4 is an isentropic process, therefore,

s₃=s₄=7.1577 kJ/kg⋅K

Using the saturation table at P = 0.206 bar we get:

s_g=7.9 kJ/kg⋅K>s₄=7.1577 kJ/kg⋅K

Thus, the steam is in a saturated liquid-vapor phase at the intermediate state.

Quality of the saturated liquid-vapor phase at the final state:

The specific enthalpy of the steam at the intermediate state is,

a) The expansion and reheating process on T-s and h-s is shown below:

Comments

Thank you, much clearer now.