Rankine Cycle

Ideal cycle for vapor power plants

isentropic compression in a pump

constant pressure heat addition in a boiler

isentropic expansion in a turbine

constant pressure heat rejection in a condenser

NO!

• enters as - saturated liquid
• during: compressed isentropically; T increases, brought to operating pressure of boiler
• leaves as - compressed liquid

• enters as - compressed liquid
• during: heat exchanger, T increase, no P change
• leaves as - superheated vapor

• enters as - superheated vapor
• during - expands isentropically; T and P drop
• leaves as - saturated liquid-vapor mix

• enters as - saturated liquid-vapor mix
• during - Heat exchanger, reject heat to cooling medium, no P change
• dropleaves as - saturated liquid

(q_in-q_out) + (w_in-w_out) = h_e-h_i

• (q=0)
• w_pump,in=h₂-h₁ = v(P₂-P₁)
• h₁=h_f@P1 and v=v₁=v_f@p1

• (w = 0)
• q_in=h₃-h₂

• (q=0)
• w_turb,out = h₃-h₄

• (w=0)
• q_out=h₄-h₁

n_th=w_net/q_in =1 - q_out/q_in

w_net = q_in-q_out=w_turb,out-w_pump,in

• saturated liquid
• Find h and v - given P, look @ Table A-5 (saturated water)

• compressed liquid
• Find h - apply conservation of energy eq.

• wpump,in = wturb,out
• h₂-h₁=v(P₂-P₁)
• h₂ = v(P₂-P₁)+h₁

• superheated vapor
• Find h and s - given T and P, look @ Table A-6 (superheated water)

• saturated liquid-vapor mix
• Find h - given P; apply quality equations
• get values from A-5

• x_# = x_# - s_f / s_fg
• h_# = h_f+x_#h_fg
• h_# = h_f + (s_# - s_f / s_fg)h_fg

w_turb,out = n_tw_{s turb,out}

w_pump,in = w_{s, pump in} / n_p

• y = y₀ + (x-x₀)(y₁-y₀ / x₁-x₀)
• x - given
• 0 and 1; table #'s

• Using ex. from hw
• 1) Btwn two P's, linear interpolation for each T, get h_a and h_b
• 2) Btwn two T's, linear interpolate with h_a and h_b for final h

W*dot*_net = (mass flow rate)W_net

• increase T for superheated steam
• increase boiler pressure, at same T (but quality decreases)
• decrease T heat is rejected from condenser

two stage turbine to solve excessive moisture problem after increasing boiler pressure

q_in = q_primary + q_reheat = (h₃-h₂) + (h₅-h₄)

w_turb,out = w_turb,I + w_turb,II = (h₃-h₄)+(h₅-h₆)

= P₅ = P₄

• T₃ = T₅ - to maintain heat
• find entropy at state 6 - s₆ = s_f + x₆s_fg
• use T₅ and s_5/6 , look @ Table A-6 to find P

• saturated liquid
• find h and v = given P, look @ table A-5

• compressed liquid
• apply conservation of energy eq. (use h₁ and v₁)

• superheated vapor
• find h₃ and s₃, given P and T look @ Table A-6

• saturated liquid-vapor mix
• Calculate P₄, s₄ (s₃)
• Look @ Table A-6

• Superheated vapor
• Given T and s₅(s₄), look @ Table A-6

• Saturated mixture
• Given P, look @ A-5
• apply quality equations, h₆ = h_f + x₆h_fg

FHW - device that heats feedwater by regeneration

transfer heat to the feedwater from the expanding steam, in counterflow exchanger built into the turbine

q_in = h₅-h₄

q_out = (1-y)(h₇-h₁)

w_turb,out = (h₅-h₆) + (1-y)(h₆-h₇)

w_pump,in = (1-y)w_pumpI,in + w_pumpII,in

y = m₆/m₅ (mass flow) = h₃-h₂ / h₆-h₂

• saturated liquid
• Find h and v - given P, look @ Table A-5

• compressed liquid
• apply conservation energy
• Find h

• saturated liquid
• find h and v, given P (same as 2 and 6), look @ Table A-5

• compressed liquid
• apply conservation energy
• find h

• superheated vapor
• find h and s, given P and T, look @ Table A-6

• saturated liquid-vapor mix
• find h, given P, apply quality equation

• saturated liquid-vapor mix
• find h, given P appy quality equation