| 1 |
REQUIRE "johnpye/fprops/rankine_fprops.a4c"; |
| 2 |
|
| 3 |
(*------------------------------------------------------------------------------ |
| 4 |
REGENERATIVE RANKINE CYCLE |
| 5 |
*) |
| 6 |
(* |
| 7 |
Add a boiler feedwater heater and two-stage turbine. |
| 8 |
*) |
| 9 |
MODEL rankine_regen_water; |
| 10 |
|
| 11 |
BO IS_A boiler_simple; |
| 12 |
TU1 IS_A turbine_simple; |
| 13 |
BL IS_A tee; (* bleed *) |
| 14 |
TU2 IS_A turbine_simple; |
| 15 |
CO IS_A condenser_simple; |
| 16 |
HE IS_A heater_open; |
| 17 |
PU1 IS_A pump_simple; |
| 18 |
PU2 IS_A pump_simple; |
| 19 |
|
| 20 |
BO.cd.component :== 'water'; |
| 21 |
|
| 22 |
(* main loop *) |
| 23 |
BO.outlet, TU1.inlet ARE_THE_SAME; |
| 24 |
TU1.outlet, BL.inlet ARE_THE_SAME; |
| 25 |
BL.outlet, TU2.inlet ARE_THE_SAME; |
| 26 |
TU2.outlet, CO.inlet ARE_THE_SAME; |
| 27 |
CO.outlet, PU1.inlet ARE_THE_SAME; |
| 28 |
PU1.outlet, HE.inlet ARE_THE_SAME; |
| 29 |
HE.outlet, PU2.inlet ARE_THE_SAME; |
| 30 |
PU2.outlet, BO.inlet ARE_THE_SAME; |
| 31 |
|
| 32 |
(* bleed stream *) |
| 33 |
BL.outlet_branch, HE.inlet_heat ARE_THE_SAME; |
| 34 |
phi ALIASES BL.phi; |
| 35 |
p_bleed ALIASES TU1.outlet.p; |
| 36 |
|
| 37 |
p_bleed_ratio IS_A fraction; |
| 38 |
p_bleed_ratio * (TU1.inlet.p - TU2.outlet.p) = (TU1.outlet.p - TU2.outlet.p); |
| 39 |
|
| 40 |
mdot ALIASES BO.mdot; |
| 41 |
cd ALIASES BO.inlet.cd; |
| 42 |
|
| 43 |
T_H ALIASES BO.outlet.T; |
| 44 |
T_C ALIASES CO.outlet.T; |
| 45 |
|
| 46 |
eta IS_A fraction; |
| 47 |
eta_eq:eta * (BO.Qdot_fuel) = TU1.Wdot + TU2.Wdot + PU1.Wdot + PU2.Wdot; |
| 48 |
|
| 49 |
Wdot_TU1 ALIASES TU1.Wdot; |
| 50 |
Wdot_TU2 ALIASES TU2.Wdot; |
| 51 |
Wdot_PU1 ALIASES PU1.Wdot; |
| 52 |
Wdot_PU2 ALIASES PU2.Wdot; |
| 53 |
Qdot_fuel ALIASES BO.Qdot_fuel; |
| 54 |
|
| 55 |
eta_carnot IS_A fraction; |
| 56 |
eta_carnot_eq: eta_carnot = 1 - T_C / T_H; |
| 57 |
|
| 58 |
eta_turb_tot IS_A fraction; |
| 59 |
TU_out_is IS_A stream_state; |
| 60 |
TU_out_is.cd, TU1.inlet.cd ARE_THE_SAME; |
| 61 |
TU_out_is.p, TU2.outlet.p ARE_THE_SAME; |
| 62 |
TU_out_is.s, TU1.inlet.s ARE_THE_SAME; |
| 63 |
eta_turb_eq:eta_turb_tot * (TU1.inlet.h - TU_out_is.h) = (TU1.inlet.h - TU2.outlet.h); |
| 64 |
|
| 65 |
(* some checking output... *) |
| 66 |
|
| 67 |
phi_weston IS_A fraction; |
| 68 |
phi_weston_eq:phi_weston * (TU1.outlet.h - PU1.outlet.h) = (PU2.inlet.h - PU1.outlet.h); |
| 69 |
phi_eq:phi_weston = phi; |
| 70 |
|
| 71 |
q_a IS_A specific_energy; |
| 72 |
q_a_eq: q_a = TU1.inlet.h - PU2.outlet.h; |
| 73 |
|
| 74 |
Wdot IS_A energy_rate; |
| 75 |
Wdot_eq: Wdot = TU1.Wdot + TU2.Wdot + PU1.Wdot + PU2.Wdot; |
| 76 |
|
| 77 |
cons_en: HE.inlet.mdot * HE.inlet.h + HE.inlet_heat.mdot * HE.inlet_heat.h = HE.outlet.mdot * HE.outlet.h; |
| 78 |
|
| 79 |
x_turb_out ALIASES TU2.outlet.x; |
| 80 |
METHODS |
| 81 |
METHOD default_self; |
| 82 |
RUN BO.default_self; |
| 83 |
RUN TU1.default_self; |
| 84 |
RUN TU2.default_self; |
| 85 |
RUN CO.default_self; |
| 86 |
RUN PU1.default_self; |
| 87 |
RUN PU2.default_self; |
| 88 |
BO.outlet.h := 4000 {kJ/kg}; |
| 89 |
p_bleed := 37 {bar}; |
| 90 |
TU1.outlet.h := 2300 {kJ/kg}; |
| 91 |
BL.cons_mass.included := FALSE; |
| 92 |
(*HE.cons_mass.included := FALSE;*) |
| 93 |
HE.cons_en.included := FALSE; |
| 94 |
cons_en.included := FALSE; |
| 95 |
HE.inlet.v := 100 {m^3/kg}; |
| 96 |
HE.inlet.p.nominal := 40 {bar}; |
| 97 |
HE.inlet.v.nominal := 1 {L/kg}; |
| 98 |
HE.inlet.h.nominal := 100 {kJ/kg}; |
| 99 |
END default_self; |
| 100 |
METHOD solarpaces2010; |
| 101 |
RUN ClearAll; |
| 102 |
RUN default_self; |
| 103 |
(* component efficiencies *) |
| 104 |
FIX BO.eta; BO.eta := 1.0; |
| 105 |
FIX TU1.eta; TU1.eta := 0.85; |
| 106 |
FIX TU2.eta; TU2.eta := 0.85; |
| 107 |
FIX PU1.eta; PU1.eta := 0.8; |
| 108 |
FIX PU2.eta; PU2.eta := 0.8; |
| 109 |
FIX Wdot; Wdot := 100 {MW}; |
| 110 |
(* |
| 111 |
(* FIX CO.outlet.p; CO.outlet.p := 10 {kPa};*) |
| 112 |
FIX CO.outlet.T; CO.outlet.T := 40 {K} + 273.15 {K}; |
| 113 |
FIX CO.outlet.x; CO.outlet.x := 1e-6; |
| 114 |
FIX PU1.outlet.p; PU1.outlet.p := 7 {bar}; |
| 115 |
FIX PU2.outlet.p; PU2.outlet.p := 150 {bar}; |
| 116 |
PU2.outlet.p.upper_bound := 150 {bar}; |
| 117 |
FIX BO.outlet.T; BO.outlet.T := 580 {K} + 273.15 {K}; |
| 118 |
*) |
| 119 |
(* turbine conditions *) |
| 120 |
FIX TU1.inlet.p; TU1.inlet.p := 150 {bar}; |
| 121 |
FIX TU1.inlet.T; TU1.inlet.T := 580 {K} + 273.15 {K}; |
| 122 |
FIX TU1.outlet.p; TU1.outlet.p := 7 {bar}; |
| 123 |
FIX CO.outlet.T; CO.outlet.T := 40 {K} + 273.15 {K}; |
| 124 |
(* heater conditions *) |
| 125 |
TU2.outlet.p := 10 {kPa}; |
| 126 |
(* FIX HE.outlet.p; HE.outlet.p := 0.7 {MPa}; *) |
| 127 |
FIX CO.outlet.x; CO.outlet.x := 1e-6; |
| 128 |
FIX HE.outlet.x; HE.outlet.x := 1e-6; |
| 129 |
END solarpaces2010; |
| 130 |
METHOD on_load; |
| 131 |
RUN solarpaces2010; |
| 132 |
(* |
| 133 |
This model needs to be solved using QRSlv with convopt set to 'RELNOMSCALE'. |
| 134 |
*) |
| 135 |
SOLVER QRSlv; |
| 136 |
OPTION convopt 'RELNOM_SCALE'; |
| 137 |
OPTION iterationlimit 400; |
| 138 |
END on_load; |
| 139 |
METHOD set_x_limit; |
| 140 |
FREE PU2.outlet.p; |
| 141 |
PU2.outlet.p.upper_bound := 150 {bar}; |
| 142 |
FIX TU2.outlet.x; TU2.outlet.x := 0.9; |
| 143 |
END set_x_limit; |
| 144 |
METHOD cycle_plot; |
| 145 |
EXTERNAL cycle_plot_rankine_regen2(SELF); |
| 146 |
END cycle_plot; |
| 147 |
METHOD moran_ex_8_5; |
| 148 |
RUN default_self; |
| 149 |
(* |
| 150 |
This is Example 8.5 from Moran and Shapiro, 'Fundamentals of |
| 151 |
Engineering Thermodynamics', 4th Ed. |
| 152 |
*) |
| 153 |
RUN ClearAll; |
| 154 |
(* component efficiencies *) |
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FIX BO.eta; BO.eta := 1.0; |
| 156 |
FIX TU1.eta; TU1.eta := 0.85; |
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FIX TU2.eta; TU2.eta := 0.85; |
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FIX PU1.eta; PU1.eta := 1.0; |
| 159 |
FIX PU2.eta; PU2.eta := 1.0; |
| 160 |
(* turbine conditions *) |
| 161 |
FIX TU1.inlet.p; TU1.inlet.p := 8. {MPa}; |
| 162 |
FIX TU1.inlet.T; TU1.inlet.T := 480 {K} + 273.15 {K}; |
| 163 |
FIX TU1.outlet.p; TU1.outlet.p := 0.7 {MPa}; |
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FIX TU2.outlet.p; TU2.outlet.p := 0.008 {MPa}; |
| 165 |
(* heater conditions *) |
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(* FIX HE.outlet.p; HE.outlet.p := 0.7 {MPa}; *) |
| 167 |
FIX CO.outlet.x; CO.outlet.x := 0.0001; |
| 168 |
FIX HE.outlet.x; HE.outlet.x := 0.0001; |
| 169 |
FIX Wdot; Wdot := 100 {MW}; |
| 170 |
END moran_ex_8_5; |
| 171 |
METHOD self_test; |
| 172 |
(* solution values to the Moran & Shapiro example 8.5 problem *) |
| 173 |
ASSERT abs(eta - 0.369) < 0.001; |
| 174 |
ASSERT abs((TU1.Wdot+TU2.Wdot)/mdot - 984.4{kJ/kg}) < 1 {kJ/kg}; |
| 175 |
ASSERT abs(mdot - 3.69e5 {kg/h}) < 0.05e5 {kg/h}; |
| 176 |
ASSERT abs(CO.inlet.h - 2249.3 {kJ/kg}) < 1.0 {kJ/kg}; |
| 177 |
END self_test; |
| 178 |
METHOD weston_ex_2_6; |
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(* |
| 180 |
The scenario here is example 2.6 from K Weston (op. cit.), p. 55. |
| 181 |
*) |
| 182 |
RUN ClearAll; |
| 183 |
|
| 184 |
(* all ideal components *) |
| 185 |
FIX BO.eta; BO.eta := 1.0; |
| 186 |
FIX TU1.eta; TU1.eta := 1.0; |
| 187 |
FIX TU2.eta; TU2.eta := 1.0; |
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FIX PU1.eta; PU1.eta := 1.0; |
| 189 |
FIX PU2.eta; PU2.eta := 1.0; |
| 190 |
|
| 191 |
(* mass flow rate is arbitrary *) |
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FIX mdot; |
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mdot := 10 {kg/s}; |
| 194 |
|
| 195 |
(* max pressure constraint *) |
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FIX PU2.outlet.p; |
| 197 |
PU2.outlet.p := 2000 {psi}; |
| 198 |
PU2.outlet.h := 1400 {btu/lbm}; (* guess *) |
| 199 |
|
| 200 |
(* boiler max temp *) |
| 201 |
FIX BO.outlet.T; |
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BO.outlet.T := 1460 {R}; |
| 203 |
BO.outlet.h := 1400 {btu/lbm}; (* guess *) |
| 204 |
|
| 205 |
(* intermediate temperature setting *) |
| 206 |
FIX TU1.outlet.p; |
| 207 |
TU1.outlet.p := 200 {psi}; |
| 208 |
(* FIX TU1.outlet.T; |
| 209 |
TU1.outlet.T := 860 {R}; (* 400 °F *) |
| 210 |
TU1.outlet.h := 3000 {kJ/kg}; (* guess *) *) |
| 211 |
|
| 212 |
(* minimum pressure constraint *) |
| 213 |
FIX CO.outlet.p; |
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CO.outlet.p := 1 {psi}; |
| 215 |
|
| 216 |
(* condenser outlet is saturated liquid *) |
| 217 |
FIX CO.outlet.h; |
| 218 |
CO.outlet.h := 69.73 {btu/lbm}; |
| 219 |
|
| 220 |
(* remove the redundant balance equations *) |
| 221 |
HE.cons_mass.included := TRUE; |
| 222 |
HE.cons_en.included := TRUE; |
| 223 |
BL.cons_mass.included := FALSE; |
| 224 |
phi_weston_eq.included := TRUE; |
| 225 |
phi_eq.included := FALSE; |
| 226 |
cons_en.included := FALSE; |
| 227 |
|
| 228 |
(* fix the bleed ratio *) |
| 229 |
FIX BL.phi; |
| 230 |
BL.phi := 0.251; |
| 231 |
|
| 232 |
(* FIX BL.outlet.h; |
| 233 |
BL.outlet.h := 355.5 {btu/lbm}; *) |
| 234 |
|
| 235 |
(** |
| 236 |
these values seem to be from another problem, need to check which ... |
| 237 |
ASSERT abs(TU1.inlet.s - 1.5603 {btu/lbm/R}) < 0.01 {btu/lbm/R}; |
| 238 |
ASSERT abs(TU1.outlet.s - 1.5603 {btu/lbm/R}) < 0.01 {btu/lbm/R}; |
| 239 |
ASSERT abs(TU2.outlet.s - 1.5603 {btu/lbm/R}) < 0.01 {btu/lbm/R}; |
| 240 |
ASSERT abs(PU1.inlet.s - 0.1326 {btu/lbm/R}) < 0.001 {btu/lbm/R}; |
| 241 |
ASSERT abs(PU1.outlet.s - 0.1326 {btu/lbm/R}) < 0.002 {btu/lbm/R}; |
| 242 |
ASSERT abs(PU2.inlet.s - 0.5438 {btu/lbm/R}) < 0.002 {btu/lbm/R}; |
| 243 |
ASSERT abs(PU2.outlet.s - 0.5438 {btu/lbm/R}) < 0.002 {btu/lbm/R}; |
| 244 |
|
| 245 |
ASSERT abs(TU1.inlet.h - 1474.1 {btu/lbm}) < 1.5 {btu/lbm}; |
| 246 |
ASSERT abs(TU1.outlet.h - 1210.0 {btu/lbm}) < 1.5 {btu/lbm}; |
| 247 |
ASSERT abs(TU2.outlet.h - 871.0 {btu/lbm}) < 1.5 {btu/lbm}; |
| 248 |
ASSERT abs(PU1.inlet.h - 69.73 {btu/lbm}) < 0.001 {btu/lbm}; |
| 249 |
ASSERT abs(PU1.outlet.h - 69.73 {btu/lbm}) < 1.0 {btu/lbm}; |
| 250 |
ASSERT abs(PU2.inlet.h - 355.5 {btu/lbm}) < 1.5 {btu/lbm}; |
| 251 |
ASSERT abs(PU2.outlet.h - 355.5 {btu/lbm}) < 8 {btu/lbm}; |
| 252 |
|
| 253 |
ASSERT abs(w_net - 518.1 {btu/lbm}) < 0.3 {btu/lbm}; |
| 254 |
|
| 255 |
ASSERT abs(w_net * mdot - (TU1.Wdot + TU2.Wdot)) < 1 {W}; |
| 256 |
|
| 257 |
ASSERT abs(q_a - 1118.6 {btu/lbm}) < 7 {btu/lbm}; |
| 258 |
|
| 259 |
ASSERT abs(eta - 0.463) < 0.003; |
| 260 |
|
| 261 |
ASSERT abs(phi - 0.251) < 0.001; |
| 262 |
*) |
| 263 |
END weston_ex_2_6; |
| 264 |
END rankine_regen_water; |
| 265 |
|
| 266 |
|
| 267 |
MODEL rankine_regen_common; |
| 268 |
BO IS_A boiler_simple; |
| 269 |
TU IS_A turbine_simple; |
| 270 |
CO IS_A condenser_simple; |
| 271 |
HE IS_A heater_closed; |
| 272 |
PU IS_A pump_simple; |
| 273 |
|
| 274 |
(* main loop *) |
| 275 |
BO.outlet, TU.inlet ARE_THE_SAME; |
| 276 |
TU.outlet, HE.inlet_heat ARE_THE_SAME; |
| 277 |
HE.outlet_heat, CO.inlet ARE_THE_SAME; |
| 278 |
CO.outlet, PU.inlet ARE_THE_SAME; |
| 279 |
PU.outlet, HE.inlet ARE_THE_SAME; |
| 280 |
HE.outlet, BO.inlet ARE_THE_SAME; |
| 281 |
|
| 282 |
mdot ALIASES BO.mdot; |
| 283 |
cd ALIASES BO.inlet.cd; |
| 284 |
|
| 285 |
T_H ALIASES BO.outlet.T; |
| 286 |
T_C ALIASES CO.outlet.T; |
| 287 |
|
| 288 |
eta IS_A fraction; |
| 289 |
eta_eq:eta * (BO.Qdot_fuel) = TU.Wdot + PU.Wdot; |
| 290 |
|
| 291 |
Wdot_TU ALIASES TU.Wdot; |
| 292 |
Wdot_PU ALIASES PU.Wdot; |
| 293 |
Qdot_fuel ALIASES BO.Qdot_fuel; |
| 294 |
|
| 295 |
eta_carnot IS_A fraction; |
| 296 |
eta_carnot_eq: eta_carnot = 1 - T_C / T_H; |
| 297 |
|
| 298 |
Wdot IS_A energy_rate; |
| 299 |
Wdot_eq: Wdot = TU.Wdot + PU.Wdot; |
| 300 |
|
| 301 |
DE_cycle "cycle energy balance, should be zero" IS_A energy_rate; |
| 302 |
DE_cycle = BO.Qdot + CO.Qdot - TU.Wdot - PU.Wdot; |
| 303 |
|
| 304 |
x_turb_out ALIASES TU.outlet.x; |
| 305 |
METHODS |
| 306 |
METHOD default_self; |
| 307 |
RUN BO.default_self; |
| 308 |
RUN TU.default_self; |
| 309 |
RUN CO.default_self; |
| 310 |
RUN PU.default_self; |
| 311 |
RUN HE.default_self; |
| 312 |
BL.cons_mass.included := FALSE; |
| 313 |
HE.cons_en.included := FALSE; |
| 314 |
END default_self; |
| 315 |
METHOD cycle_plot; |
| 316 |
EXTERNAL cycle_plot_rankine_regen1(SELF); |
| 317 |
END cycle_plot; |
| 318 |
END rankine_regen_common; |
| 319 |
|
| 320 |
MODEL rankine_regen_toluene REFINES rankine_regen_common; |
| 321 |
|
| 322 |
BO.cd.component :== 'toluene'; |
| 323 |
|
| 324 |
METHODS |
| 325 |
METHOD on_load; |
| 326 |
FIX BO.outlet.T; BO.outlet.T := 580 {K} + 273.15 {K}; |
| 327 |
FIX PU.outlet.p; PU.outlet.p := 150 {bar}; |
| 328 |
FIX CO.outlet.T; CO.outlet.T := 40 {K} + 273.15 {K}; |
| 329 |
FIX CO.outlet.x; CO.outlet.x := 1e-6; |
| 330 |
FIX HE.outlet.T; HE.outlet.T := 300 {K} + 273.15 {K}; |
| 331 |
|
| 332 |
FIX BO.eta; BO.eta := 1.0; |
| 333 |
FIX TU.eta; TU.eta := 0.85; |
| 334 |
FIX PU.eta; PU.eta := 0.8; |
| 335 |
|
| 336 |
SOLVER QRSlv; |
| 337 |
OPTION convopt 'RELNOM_SCALE'; |
| 338 |
OPTION iterationlimit 200; |
| 339 |
END on_load; |
| 340 |
METHOD default_self; |
| 341 |
RUN rankine_regen_common::default_self; |
| 342 |
PU.inlet.h := 400 {kJ/kg}; |
| 343 |
BO.outlet.h := 400 {kJ/kg}; |
| 344 |
CO.outlet.h := 400 {kJ/kg}; |
| 345 |
CO.outlet.p := 10 {kPa}; |
| 346 |
END default_self; |
| 347 |
END rankine_regen_toluene; |
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