带有T-s图和h-s图的联合[二元]循环热效率-优快云博客

作者：Valery Ochkov [http://twt.mpei.ac.ru/ochkov/v_ochkov.htm]

介绍

restart;

with(ThermophysicalData);

with(Units[Standard]);

图示为最简单的理想联合[二元]循环方案，即使用过热蒸汽的汽轮机循环[6-7]。在该装置中，锅炉[6-9]的燃烧器被燃气轮机装置[布雷顿循环：1-4]所取代，该燃气轮机装置配备了空气压缩机[1-2]、燃烧室[2-3]、燃气轮机[3-4]和另一台发电机。

计算

蒸汽轮机循环

输入数据：

t_6 := (480 + 273.15) * K; p_6 := 9 * MPa; p_7 := 4.76 * kPa;

t_6 := 753.15 K

p_6 := 9 MPa

p_7 := 4.76 kPa [2.1.1]

新蒸汽（汽轮机入口）的比熵：

s_6 := Property(entropy, pressure = p_6, temperature = t_6, water);

6.593 kJ/(kg·K) [2.1.2]

新蒸汽（汽轮机入口）的比焓：

h_6 := Property(enthalpy, pressure = p_6, temperature = t_6, water);

3336.4 kJ/kg [2.1.3]

汽轮机出口蒸汽比熵（理想的蒸汽膨胀过程）：

s_7 := s_6;

汽轮机出口处蒸汽的干度：

x_7 := Property(Q, pressure = p_7, entropy = s_7, water);

77.13 % [2.1.4]

汽轮机出口湿蒸汽温度：

t_7 := Property(temperature, pressure = p_7, Q = 1, water): t_7 - 273.15 * K;

32.00 °C [2.1.5]

汽轮机出口湿蒸汽的比焓：

h_7 := Property(enthalpy, temperature = t_7, Q = x_7, water);

2004.4 kJ/kg [2.1.6]

蒸汽在汽轮机中的比功：

w_st := h_6 - h_7;

1332.0 kJ/kg [2.1.7]

冷凝器温度下饱和线上水的比焓：

hw_7 := Property(enthalpy, temperature = t_7, Q = 0, water);

134.1 kJ/kg [2.1.8]

冷凝器温度下饱和线上水的比熵：

sw_7 := Property(entropy, temperature = t_7, Q = 0, water);

0.4643 kJ/(kg·K) [2.1.9]

凝结水的比焓

h_8 := hw_7;

给水压力

p_9 := p_6;

给水的比熵（泵中的理想过程）：

s_9 := sw_7;

给水温度：

t_9 := Property(temperature, pressure = p_9, entropy = s_9, water): t_9 - 273.15 * K;

32.22 °C [2.1.10]

给水的比焓：

h_9 := Property(enthalpy, pressure = p_9, temperature = t_9, water);

143.1 kJ/kg [2.1.11]

给水泵的比有用功：

w_p := h_9 - hw_7;

9.023 kJ/kg [2.1.12]

供给锅炉的比热：

q_b := h_6 - h_9;

3193.3 kJ/kg [2.1.13]

因此，蒸汽轮机循环的热效率为：

η_tst := (w_st - w_p) / q_b;

41.43 % [2.1.14]

燃气轮机循环

输入数据：

t_1 := (15 + 273.15) * K; p_1 := 0.1 * MPa; p_2 := 1 * MPa; t_3 := (1100 + 273.15) * K; t_5 := (130 + 273.15) * K;

t_1 := 288.15 K

p_1 := 0.1 MPa

p_2 := 1 MPa

t_3 := 1373.15 K

t_5 := 403.15 K [2.2.1]

新鲜空气的比焓

h_1 := Property(enthalpy, pressure = p_1, temperature = t_1, air);

414.38 kJ/kg [2.2.2]

新鲜空气的比熵

s_1 := Property(entropy, pressure = p_1, temperature = t_1, air);

3.8500 kJ/(kg·K) [2.2.3]

压缩机出口空气的比熵、温度和比焓

s_2 := s_1:

t_2 := Property(temperature, pressure = p_2, entropy = s_2, air): t_2 - 273.15 * K;

279.46 °C [2.2.4]

h_2 := Property(enthalpy, pressure = p_2, temperature = t_2, air);

683.60 kJ/kg [2.2.5]

进入燃气轮机的气体压力、比熵和比焓

p_3 := p_2:

s_3 := Property(entropy, pressure = p_3, temperature = t_3, air);

4.867 kJ/(kg·K) [2.2.6]

h_3 := Property(enthalpy, pressure = p_3, temperature = t_3, air);

1610.34 kJ/kg [2.2.7]

燃气轮机出口气体压力、比熵、温度和比焓

p_4 := p_1:

s_4 := s_3:

t_4 := Property(temperature, pressure = p_4, entropy = s_4, air): t_4 - 273.15 * K;

498.01 °C [2.2.8]

h_4 := Property(enthalpy, pressure = p_4, temperature = t_4, air);

916.82 kJ/kg [2.2.9]

供给燃烧室的比热：

q_1 := h_3 - h_2;

926.74 kJ/kg [2.2.10]

燃气轮机的比功：

w_gt := h_3 - h_4;

693.52 kJ/kg [2.2.11]

空气压缩机的比功：

w_c := h_2 - h_1;

269.23 kJ/kg [2.2.12]

因此，燃气轮机循环的热效率为：

η_tgt := (w_gt - w_c) / q_1;

45.78 % [2.2.13]

联合[二元]循环

蒸汽锅炉出口气体压力和比焓

p_5 := p_4:

h_5 := Property(enthalpy, pressure = p_5, temperature = t_5, air);

530.5 kJ/kg [2.3.1]

气体与蒸汽的质量流量比

m := (h_6 - h_9) / (h_4 - h_5);

8.265 [2.3.2]

供给燃烧室的比热：

q_1 := m * (h_3 - h_2);

7659.4 kJ/kg [2.3.3]

燃气轮机循环的比功

w_gtc := (h_3 - h_4) - (h_2 - h_1);

424.3 kJ/kg [2.3.4]

蒸汽轮机循环的比功

w_stc := (h_6 - h_7) - (h_9 - h_8);

1323.0 kJ/kg [2.3.5]

因此，联合[二元]循环的热效率高于单独的蒸汽或燃气轮机循环：

η_tbc := (m * w_gtc + w_stc) / q_1;

63.06 % [2.3.6]

T-s 图

静态图

t__triple := 273.16*Unit('K');
t__critical := 647.096*Unit('K');

水在饱和线上的比熵随温度变化函数

wspSSWT := T → Property(entropy, temperature = T, Q = 0, H2O):

p1 := plot([wspSSWT(t), t, t = (t_triple / K) .. (t_critical / K)], color = "Blue", thickness = 1, linestyle = "solid", legend = "Water on saturated line"):

蒸汽在饱和线上的比熵随温度变化函数

wspSSST := T → Property(entropy, temperature = T, Q = 1, H2O):

p2 := plot([wspSSST(t), t, t = (t_triple / K) .. (t_critical / K)], color = "Red", thickness = 1, linestyle = "solid", legend = "Steam on saturated line"):

s_9 := Property(entropy, pressure = p_9, temperature = t_7, water):

wspTPS := (p, s) → Property(temperature, pressure = p, entropy = s, H2O):

p3 := plot([s, wspTPS(p_6 / Pa, s), s = (s_9 / (Jkg^(-1)K^(-1))) .. (s_6 / (Jkg^(-1)K^(-1)))], thickness = 1, color = "Black", legend = "Boiler"):

p4 := plots:-pointplot([[(s_6 / (Jkg^(-1)K^(-1))), (t_6 / K)], [(s_6 / (Jkg^(-1)K^(-1))), (t_7 / K)]], connect = true, thickness = 1, color = ["Red", "Blue"], legend = "Steam expansion in turbine"):

p5 := plots:-pointplot([[(s_6 / (Jkg^(-1)K^(-1))), (t_7 / K)], [(s_9 / (Jkg^(-1)K^(-1))), (t_7 / K)]], connect = true, thickness = 1, color = ["Red", "Blue"], legend = "Condenser"):

p6 := plots:-pointplot([[(s_1 / (Jkg^(-1)K^(-1))), (t_1 / K)], [(s_1 / (Jkg^(-1)K^(-1))), (t_2 / K)]], connect = true, thickness = 3, color = "Brown", legend = "Compressor"):

p7 := plots:-pointplot([[(s_4 / (Jkg^(-1)K^(-1))), (t_4 / K)], [(s_4 / (Jkg^(-1)K^(-1))), (t_3 / K)]], connect = true, thickness = 3, color = "Green", legend = "Gas turbine"):

wspgTPS := (p, s) → Property(temperature, pressure = p, entropy = s, air):

p8 := plot([s, wspgTPS(p_2 / Pa, s), s = (s_2 / (Jkg^(-1)K^(-1))) .. (s_3 / (Jkg^(-1)K^(-1)))], thickness = 3, color = "Orange", legend = "Combustion chamber"):

p9 := plot([s, wspgTPS(p_1 / Pa, s), s = (s_2 / (Jkg^(-1)K^(-1))) .. (s_3 / (Jkg^(-1)K^(-1)))], thickness = 3, color = "Gold", legend = "Atmosphere"):

动态图：

h-s 图

作为温度函数的饱和线上水的比焓

wspHSWT := T → Property(enthalpy, temperature = T, Q = 0, H2O):

p10 := plot([wspSSWT(t), wspHSWT(t), t = (t_triple / K) .. (t_critical / K)], thickness = 1, linestyle = "solid", legend = "Water on saturated line"):

作为温度函数的饱和线上蒸汽的比焓

wspHSST := T → Property(enthalpy, temperature = T, Q = 1, H2O):

p11 := plot([wspSSST(t), wspHSST(t), t = (t_triple / K) .. (t_critical / K)], color = "Red", thickness = 1, linestyle = "solid", legend = "Steam on saturated line"):

wspHPS := (p, s) → Property(enthalpy, pressure = p, entropy = s, H2O):

p12 := plot([s, wspHPS(p_6 / Pa, s), s = (s_9 / (Jkg^(-1)K^(-1))) .. (s_6 / (Jkg^(-1)K^(-1)))], thickness = 1, color = "Black", legend = "Boiler"):

p13 := plots:-pointplot([[(s_6 / (Jkg^(-1)K^(-1))), (h_6 / (Jkg^(-1)))], [(s_6 / (Jkg^(-1)K^(-1))), (h_7 / (Jkg^(-1)))]], connect = true, thickness = 1, color = ["Red", "Blue"], legend = "Steam expansion in turbine"):

p14 := plot([s, wspHPS(p_7 / Pa, s), s = (s_9 / (Jkg^(-1)K^(-1))) .. (s_6 / (Jkg^(-1)K^(-1)))], thickness = 1, color = "Blue", legend = "Condenser"):

p15 := plots:-pointplot([[(s_1 / (Jkg^(-1)K^(-1))), (h_1 / (Jkg^(-1)))], [(s_1 / (Jkg^(-1)K^(-1))), (h_2 / (Jkg^(-1)))]], connect = true, thickness = 3, color = "Brown", legend = "Compressor"):

p16 := plots:-pointplot([[(s_4 / (Jkg^(-1)K^(-1))), (h_4 / (Jkg^(-1)))], [(s_4 / (Jkg^(-1)K^(-1))), (h_3 / (Jkg^(-1)))]], connect = true, thickness = 3, color = "Green", legend = "Gas turbine"):

wspgHPS := (p, s) → Property(enthalpy, pressure = p, entropy = s, air):

p17 := plot([s, wspgHPS(p_2 / Pa, s), s = (s_2 / (Jkg^(-1)K^(-1))) .. (s_3 / (Jkg^(-1)K^(-1)))], thickness = 3, color = "Orange", legend = "Combustion chamber"):

p18 := plot([s, wspgHPS(p_1 / Pa, s), s = (s_2 / (Jkg^(-1)K^(-1))) .. (s_3 / (Jkg^(-1)K^(-1)))], thickness = 3, color = "Gold", legend = "Atmosphere"):