| 1 |
REQUIRE "atoms.a4l"; |
| 2 |
REQUIRE "johnpye/thermo_types.a4c"; |
| 3 |
|
| 4 |
IMPORT "freesteam"; |
| 5 |
|
| 6 |
(* Model of simple Rankine cycle with boiler, turbine, condenser, pump *) |
| 7 |
|
| 8 |
(*------------------------------------------------------------------------------ |
| 9 |
BACKGROUND STUFF |
| 10 |
*) |
| 11 |
|
| 12 |
(* |
| 13 |
Thermo properties -- IAPWS-IF97 |
| 14 |
*) |
| 15 |
MODEL steam_state; |
| 16 |
p IS_A pressure; |
| 17 |
h IS_A specific_enthalpy; |
| 18 |
|
| 19 |
T IS_A temperature; |
| 20 |
v IS_A specific_volume; |
| 21 |
s IS_A specific_entropy; |
| 22 |
x IS_A fraction; |
| 23 |
|
| 24 |
props: freesteam_Tvsx_ph( |
| 25 |
p,h : INPUT; |
| 26 |
T,v,s,x : OUTPUT |
| 27 |
); |
| 28 |
METHODS |
| 29 |
METHOD default; |
| 30 |
p := 10{bar}; |
| 31 |
p.nominal := 42 {bar}; |
| 32 |
h := 2000 {kJ/kg}; |
| 33 |
|
| 34 |
T := 400 {K}; |
| 35 |
v.nominal := 10 {L/kg}; |
| 36 |
s := 4 {kJ/kg/K}; |
| 37 |
x := 0.8; |
| 38 |
END default; |
| 39 |
METHOD solve; |
| 40 |
EXTERNAL do_solve(SELF); |
| 41 |
END solve; |
| 42 |
METHOD on_load; |
| 43 |
RUN default_all; |
| 44 |
FIX p, h; |
| 45 |
END on_load; |
| 46 |
END steam_state; |
| 47 |
|
| 48 |
(* a simple connector that includes calculation of steam properties *) |
| 49 |
MODEL steam_node; |
| 50 |
state IS_A steam_state; |
| 51 |
p ALIASES state.p; |
| 52 |
h ALIASES state.h; |
| 53 |
v ALIASES state.v; |
| 54 |
T ALIASES state.T; |
| 55 |
s ALIASES state.s; |
| 56 |
x ALIASES state.x; |
| 57 |
mdot IS_A mass_rate; |
| 58 |
METHODS |
| 59 |
METHOD default; |
| 60 |
mdot.nominal := 2 {kg/s}; |
| 61 |
END default; |
| 62 |
METHOD solve; |
| 63 |
EXTERNAL do_solve(SELF); |
| 64 |
END solve; |
| 65 |
METHOD on_load; |
| 66 |
RUN default_all; RUN reset; RUN values; |
| 67 |
FIX p,h; |
| 68 |
END on_load; |
| 69 |
END steam_node; |
| 70 |
|
| 71 |
MODEL steam_equipment; |
| 72 |
inlet "in: inlet steam stream" IS_A steam_node; |
| 73 |
outlet "out: outlet steam stream" IS_A steam_node; |
| 74 |
|
| 75 |
cons_mass:inlet.mdot = outlet.mdot; |
| 76 |
mdot ALIASES inlet.mdot; |
| 77 |
END steam_equipment; |
| 78 |
|
| 79 |
(*------------------------------------------------------------------------------ |
| 80 |
PUMP COMPONENT |
| 81 |
*) |
| 82 |
|
| 83 |
MODEL pump_simple REFINES steam_equipment; |
| 84 |
NOTES |
| 85 |
'block' SELF {Simple model of a pump using isentropic efficiency} |
| 86 |
END NOTES; |
| 87 |
|
| 88 |
dp IS_A delta_pressure; |
| 89 |
inlet.p + dp = outlet.p; |
| 90 |
|
| 91 |
outlet_is IS_A steam_state; |
| 92 |
outlet_is.p, outlet.p ARE_THE_SAME; |
| 93 |
|
| 94 |
outlet_is.s, inlet.s ARE_THE_SAME; |
| 95 |
eta IS_A fraction; |
| 96 |
|
| 97 |
eta_eq:eta * (inlet.h - outlet.h) = (inlet.h - outlet_is.h); |
| 98 |
|
| 99 |
(* work done on the environment, will be negative *) |
| 100 |
Wdot IS_A energy_rate; |
| 101 |
Wdot_eq:Wdot = eta * mdot * (inlet.h - outlet.h); |
| 102 |
|
| 103 |
w IS_A specific_energy; |
| 104 |
w_eq:w = eta * (outlet.h - inlet.h); |
| 105 |
|
| 106 |
(* |
| 107 |
NOTES |
| 108 |
'inline' inlet {in:} |
| 109 |
'inline' outlet {out:} |
| 110 |
END NOTES; |
| 111 |
*) |
| 112 |
END pump_simple; |
| 113 |
MODEL pump_simple_test REFINES pump_simple; |
| 114 |
(* no equations here *) |
| 115 |
METHODS |
| 116 |
METHOD on_load; |
| 117 |
FIX inlet.p; |
| 118 |
FIX inlet.h; |
| 119 |
FIX outlet.p; |
| 120 |
FIX eta; |
| 121 |
FIX mdot; |
| 122 |
|
| 123 |
inlet.p := 5 {bar}; |
| 124 |
inlet.h := 400 {kJ/kg}; |
| 125 |
outlet.p := 100 {bar}; |
| 126 |
eta := 0.65; |
| 127 |
mdot := 900 {t/d}; |
| 128 |
END on_load; |
| 129 |
END pump_simple_test; |
| 130 |
|
| 131 |
(*------------------------------------------------------------------------------ |
| 132 |
TURBINE COMPONENT |
| 133 |
*) |
| 134 |
|
| 135 |
MODEL turbine_simple REFINES steam_equipment; |
| 136 |
NOTES |
| 137 |
'block' SELF {Simple turbine model} |
| 138 |
END NOTES; |
| 139 |
|
| 140 |
dp IS_A delta_pressure; |
| 141 |
inlet.p + dp = outlet.p; |
| 142 |
|
| 143 |
outlet_is IS_A steam_state; |
| 144 |
outlet_is.p, outlet.p ARE_THE_SAME; |
| 145 |
outlet_is.s, inlet.s ARE_THE_SAME; |
| 146 |
|
| 147 |
eta IS_A fraction; |
| 148 |
eta_eq:eta * (inlet.h - outlet_is.h) = (inlet.h - outlet.h); |
| 149 |
|
| 150 |
(* work done on the environment, will be positive *) |
| 151 |
Wdot IS_A energy_rate; |
| 152 |
Wedot_eq:Wdot = mdot * (inlet.h - outlet.h); |
| 153 |
|
| 154 |
w IS_A specific_energy; |
| 155 |
w_eq:w = inlet.h - outlet.h; |
| 156 |
|
| 157 |
END turbine_simple; |
| 158 |
|
| 159 |
MODEL turbine_simple_test REFINES turbine_simple; |
| 160 |
(* no equations here *) |
| 161 |
METHODS |
| 162 |
METHOD on_load; |
| 163 |
FIX inlet.p; |
| 164 |
FIX inlet.h; |
| 165 |
FIX outlet.p; |
| 166 |
FIX eta; |
| 167 |
FIX mdot; |
| 168 |
|
| 169 |
inlet.p := 100 {bar}; |
| 170 |
inlet.h := 3000 {kJ/kg}; |
| 171 |
outlet.p := 5 {bar}; |
| 172 |
eta := 0.85; |
| 173 |
mdot := 900 {t/d}; |
| 174 |
END on_load; |
| 175 |
END turbine_simple_test; |
| 176 |
|
| 177 |
(*------------------------------------------------------------------------------ |
| 178 |
BOILER COMPONENT |
| 179 |
*) |
| 180 |
|
| 181 |
(* |
| 182 |
simple model assumes no pressure drop, but heating losses due to |
| 183 |
flue gas temperature |
| 184 |
*) |
| 185 |
MODEL boiler_simple REFINES steam_equipment; |
| 186 |
NOTES |
| 187 |
'block' SELF {Simple boiler model} |
| 188 |
END NOTES; |
| 189 |
|
| 190 |
inlet.p, outlet.p ARE_THE_SAME; |
| 191 |
Qdot_fuel IS_A energy_rate; |
| 192 |
Qdot IS_A energy_rate; |
| 193 |
|
| 194 |
Qdot = mdot * (outlet.h - inlet.h); |
| 195 |
|
| 196 |
eta IS_A fraction; |
| 197 |
Qdot = eta * Qdot_fuel; |
| 198 |
END boiler_simple; |
| 199 |
|
| 200 |
MODEL boiler_simple_test REFINES boiler_simple; |
| 201 |
(* nothing here *) |
| 202 |
METHODS |
| 203 |
METHOD on_load; |
| 204 |
FIX inlet.p; |
| 205 |
FIX inlet.h; |
| 206 |
FIX eta; |
| 207 |
FIX outlet.h; |
| 208 |
FIX mdot; |
| 209 |
|
| 210 |
inlet.p := 100 {bar}; |
| 211 |
inlet.h := 500 {kJ/kg}; |
| 212 |
|
| 213 |
eta := 0.8; |
| 214 |
outlet.h := 3000 {kJ/kg}; |
| 215 |
mdot := 900 {t/d}; |
| 216 |
END on_load; |
| 217 |
END boiler_simple_test; |
| 218 |
|
| 219 |
(*------------------------------------------------------------------------------ |
| 220 |
CONDENSER COMPONENT |
| 221 |
*) |
| 222 |
|
| 223 |
(* |
| 224 |
this is really simple (fluid props permitting): just work out the heat |
| 225 |
that must be expelled to get the water down to a certain state |
| 226 |
*) |
| 227 |
MODEL condenser_simple REFINES steam_equipment; |
| 228 |
NOTES |
| 229 |
'block' SELF {Simple condenser model} |
| 230 |
'inline' inlet {in: yahoooo} |
| 231 |
END NOTES; |
| 232 |
|
| 233 |
inlet.p, outlet.p ARE_THE_SAME; |
| 234 |
Qdot IS_A energy_rate; |
| 235 |
|
| 236 |
cons_en: Qdot = mdot * (outlet.h - inlet.h); |
| 237 |
|
| 238 |
END condenser_simple; |
| 239 |
|
| 240 |
MODEL condenser_simple_test REFINES condenser_simple; |
| 241 |
(* nothing here *) |
| 242 |
METHODS |
| 243 |
METHOD on_load; |
| 244 |
FIX inlet.p, inlet.x; |
| 245 |
FIX outlet.h; |
| 246 |
FIX mdot; |
| 247 |
|
| 248 |
inlet.p := 5 {bar}; |
| 249 |
inlet.x := 0.95; |
| 250 |
outlet.h := 500 {kJ/kg}; |
| 251 |
mdot := 900 {t/d}; |
| 252 |
END on_load; |
| 253 |
END condenser_simple_test; |
| 254 |
|
| 255 |
(*------------------------------------------------------------------------------ |
| 256 |
FEEDWATER HEATER |
| 257 |
*) |
| 258 |
|
| 259 |
(* |
| 260 |
open heater does not have inlet.mdot==outlet.mdot, so not a refinement |
| 261 |
of 'steam_equipment'. |
| 262 |
*) |
| 263 |
MODEL heater_open; |
| 264 |
NOTES |
| 265 |
'block' SELF {Simple open feedwater heater model} |
| 266 |
END NOTES; |
| 267 |
|
| 268 |
inlet "in:" IS_A steam_node; |
| 269 |
inlet_heat "in:" IS_A steam_node; |
| 270 |
outlet "out:" IS_A steam_node; |
| 271 |
|
| 272 |
inlet_heat.p, inlet.p, outlet.p ARE_THE_SAME; |
| 273 |
|
| 274 |
(* cons. mass *) |
| 275 |
cons_mass: inlet.mdot + inlet_heat.mdot = outlet.mdot; |
| 276 |
|
| 277 |
(* cons. energy *) |
| 278 |
cons_en: inlet.mdot * inlet.h + inlet_heat.mdot * inlet_heat.h = outlet.mdot * outlet.h; |
| 279 |
|
| 280 |
END heater_open; |
| 281 |
|
| 282 |
MODEL heater_open_test REFINES heater_open; |
| 283 |
(* nothing here *) |
| 284 |
METHODS |
| 285 |
METHOD on_load; |
| 286 |
FIX inlet.p, inlet.h; |
| 287 |
inlet.p := 40 {bar}; |
| 288 |
inlet.h := 634 {kJ/kg}; |
| 289 |
FIX inlet_heat.h; |
| 290 |
inlet_heat.h := 2960 {kJ/kg}; |
| 291 |
|
| 292 |
FIX outlet.mdot; |
| 293 |
outlet.mdot := 900 {t/d}; |
| 294 |
|
| 295 |
FIX inlet.mdot; |
| 296 |
inlet.mdot := 700 {t/d}; |
| 297 |
END on_load; |
| 298 |
END heater_open_test; |
| 299 |
|
| 300 |
(*------------------------------------------------------------------------------ |
| 301 |
TEE PIECE |
| 302 |
*) |
| 303 |
|
| 304 |
(* |
| 305 |
it's not a car :-) |
| 306 |
*) |
| 307 |
MODEL tee; |
| 308 |
NOTES |
| 309 |
'block' SELF {Model of a branching of two flow streams} |
| 310 |
END NOTES; |
| 311 |
|
| 312 |
inlet "in:" IS_A steam_node; |
| 313 |
outlet "out:" IS_A steam_node; |
| 314 |
outlet_branch "out:" IS_A steam_node; |
| 315 |
|
| 316 |
inlet.p, outlet.p, outlet_branch.p ARE_THE_SAME; |
| 317 |
inlet.h, outlet.h, outlet_branch.h ARE_THE_SAME; |
| 318 |
|
| 319 |
(* cons. mass *) |
| 320 |
cons_mass: inlet.mdot = outlet.mdot + outlet_branch.mdot; |
| 321 |
|
| 322 |
phi IS_A fraction; |
| 323 |
phi_eq: phi * inlet.mdot = outlet_branch.mdot; |
| 324 |
|
| 325 |
END tee; |
| 326 |
|
| 327 |
(*------------------------------------------------------------------------------ |
| 328 |
OVERALL CYCLE |
| 329 |
*) |
| 330 |
|
| 331 |
(* |
| 332 |
simplest possible rankine cycle |
| 333 |
*) |
| 334 |
MODEL rankine; |
| 335 |
|
| 336 |
BO IS_A boiler_simple; |
| 337 |
TU IS_A turbine_simple; |
| 338 |
CO IS_A condenser_simple; |
| 339 |
PU IS_A pump_simple; |
| 340 |
|
| 341 |
BO.outlet, TU.inlet ARE_THE_SAME; |
| 342 |
TU.outlet, CO.inlet ARE_THE_SAME; |
| 343 |
CO.outlet, PU.inlet ARE_THE_SAME; |
| 344 |
PU.outlet, BO.inlet ARE_THE_SAME; |
| 345 |
|
| 346 |
Qdot_loss ALIASES CO.Qdot; |
| 347 |
|
| 348 |
T_H ALIASES BO.outlet.T; |
| 349 |
T_C ALIASES CO.outlet.T; |
| 350 |
|
| 351 |
eta IS_A fraction; |
| 352 |
eta * (BO.Qdot_fuel - PU.Wdot) = TU.Wdot; |
| 353 |
|
| 354 |
eta_carnot IS_A fraction; |
| 355 |
eta_carnot = 1 - T_C / T_H; |
| 356 |
|
| 357 |
mdot ALIASES TU.mdot; |
| 358 |
x_turb_out ALIASES TU.outlet.x; |
| 359 |
METHODS |
| 360 |
(* first test case: just some plausible values *) |
| 361 |
METHOD specify_1; |
| 362 |
RUN ClearAll; |
| 363 |
FIX PU.inlet.p; |
| 364 |
FIX PU.inlet.h; |
| 365 |
FIX PU.outlet.p; |
| 366 |
FIX BO.outlet.h; |
| 367 |
FIX TU.eta; |
| 368 |
FIX PU.eta; |
| 369 |
FIX BO.eta; |
| 370 |
FIX mdot; |
| 371 |
END specify_1; |
| 372 |
METHOD values_1; |
| 373 |
PU.inlet.p := 1 {bar}; |
| 374 |
PU.inlet.h := 104.9 {kJ/kg}; |
| 375 |
PU.outlet.p := 250 {bar}; |
| 376 |
BO.outlet.h := 3772 {kJ/kg}; |
| 377 |
TU.eta := 0.85; |
| 378 |
PU.eta := 0.65; |
| 379 |
BO.eta := 0.9; |
| 380 |
mdot := 900 {t/d}; |
| 381 |
END values_1; |
| 382 |
(* |
| 383 |
second test case: numbers from Example 2.1, K Weston, 'Energy Conversion', |
| 384 |
1992, http://www.personal.utulsa.edu/~kenneth-weston/ |
| 385 |
*) |
| 386 |
METHOD specify; |
| 387 |
RUN ClearAll; |
| 388 |
FIX PU.outlet.p; |
| 389 |
FIX BO.outlet.T; |
| 390 |
FIX PU.inlet.p; |
| 391 |
FIX PU.inlet.h; |
| 392 |
FIX TU.eta; |
| 393 |
FIX PU.eta; |
| 394 |
FIX BO.eta; |
| 395 |
FIX mdot; |
| 396 |
END specify; |
| 397 |
METHOD values; |
| 398 |
PU.outlet.p := 2000 {psi}; |
| 399 |
BO.outlet.T := 1460 {R}; BO.outlet.h := 3400 {kJ/kg}; |
| 400 |
PU.inlet.p := 1 {psi}; |
| 401 |
PU.inlet.h := 69.73 {btu/lbm}; |
| 402 |
TU.eta := 1.0; |
| 403 |
PU.eta := 1.0; |
| 404 |
BO.eta := 1.0; |
| 405 |
mdot := 900 {t/d}; |
| 406 |
END values; |
| 407 |
METHOD on_load; |
| 408 |
RUN specify; |
| 409 |
RUN values; |
| 410 |
END on_load; |
| 411 |
METHOD self_test; |
| 412 |
(* check the results against those from K Weston's book *) |
| 413 |
(* note that we have NOT neglected pump work in this case! *) |
| 414 |
ASSERT abs(eta - 0.4294) < 0.0005; |
| 415 |
ASSERT abs(eta_carnot - 0.6152) < 0.0005; |
| 416 |
ASSERT abs(TU.outlet.x - 0.7736) < 0.0005; |
| 417 |
ASSERT abs(TU.w - 603.1 {btu/lbm}) < 0.7 {btu/lbm}; |
| 418 |
END self_test; |
| 419 |
END rankine; |
| 420 |
|
| 421 |
(*------------------------------------------------------------------------------ |
| 422 |
REHEAT RANKINE CYCLE |
| 423 |
*) |
| 424 |
MODEL rankine_reheat; |
| 425 |
|
| 426 |
BO1 IS_A boiler_simple; |
| 427 |
BO2 IS_A boiler_simple; |
| 428 |
TU1 IS_A turbine_simple; |
| 429 |
TU2 IS_A turbine_simple; |
| 430 |
CO IS_A condenser_simple; |
| 431 |
PU IS_A pump_simple; |
| 432 |
|
| 433 |
BO1.outlet, TU1.inlet ARE_THE_SAME; |
| 434 |
TU1.outlet, BO2.inlet ARE_THE_SAME; |
| 435 |
BO2.outlet, TU2.inlet ARE_THE_SAME; |
| 436 |
TU2.outlet, CO.inlet ARE_THE_SAME; |
| 437 |
CO.outlet, PU.inlet ARE_THE_SAME; |
| 438 |
PU.outlet, BO1.inlet ARE_THE_SAME; |
| 439 |
|
| 440 |
BO1.eta, BO2.eta ARE_THE_SAME; |
| 441 |
|
| 442 |
(* boiler peak temperature is reached for both main and reheat... *) |
| 443 |
BO1.outlet.T, BO2.outlet.T ARE_THE_SAME; |
| 444 |
|
| 445 |
mdot ALIASES PU.mdot; |
| 446 |
|
| 447 |
T_H ALIASES BO1.outlet.T; |
| 448 |
T_C ALIASES CO.outlet.T; |
| 449 |
|
| 450 |
eta IS_A fraction; |
| 451 |
eta * (BO1.Qdot_fuel + BO2.Qdot_fuel - PU.Wdot) = TU1.Wdot + TU2.Wdot; |
| 452 |
|
| 453 |
eta_carnot IS_A fraction; |
| 454 |
eta_carnot = 1 - T_C / T_H; |
| 455 |
|
| 456 |
METHODS |
| 457 |
(* |
| 458 |
The on_load scenario reproduces the same calculation from |
| 459 |
K Weston, op. cit., Example 2.5, p. 51. |
| 460 |
*) |
| 461 |
METHOD on_load; |
| 462 |
FIX BO1.eta; |
| 463 |
BO1.eta := 1.0; |
| 464 |
FIX TU1.eta, TU2.eta; |
| 465 |
TU1.eta := 1.0; |
| 466 |
TU2.eta := 1.0; |
| 467 |
FIX PU.eta; |
| 468 |
PU.eta := 1.0; |
| 469 |
FIX PU.inlet.p; |
| 470 |
PU.inlet.p := 1 {psi}; |
| 471 |
FIX PU.inlet.h; |
| 472 |
PU.inlet.h := 69.73 {btu/lbm}; |
| 473 |
FIX BO1.outlet.T; |
| 474 |
BO1.outlet.T := 1460 {R}; |
| 475 |
BO1.outlet.h := 3000 {kJ/kg}; (* guess *) |
| 476 |
TU1.outlet.h := 3000 {kJ/kg}; (* guess *) |
| 477 |
FIX PU.outlet.p; |
| 478 |
PU.outlet.p := 2000 {psi}; |
| 479 |
FIX mdot; |
| 480 |
mdot := 900 {t/d}; |
| 481 |
|
| 482 |
(* this value here is what defines the intermediate pressure *) |
| 483 |
FIX TU1.outlet.T; |
| 484 |
TU1.outlet.T := 860 {R}; |
| 485 |
|
| 486 |
TU2.inlet.h := 3000 {kJ/kg}; (* guess *) |
| 487 |
END on_load; |
| 488 |
METHOD self_test; |
| 489 |
ASSERT abs(eta - 0.443) < 0.0005; |
| 490 |
ASSERT abs(TU2.outlet.x - 0.926) < 0.0015; |
| 491 |
ASSERT abs(TU1.w + TU2.w) - 763.1 {btu/lbm} < 1 {btu/lbm}; |
| 492 |
END self_test; |
| 493 |
END rankine_reheat; |
| 494 |
|
| 495 |
(*------------------------------------------------------------------------------ |
| 496 |
REGENERATIVE RANKINE CYCLE |
| 497 |
*) |
| 498 |
(* |
| 499 |
Add a boiler feedwater heater and two-stage turbine. |
| 500 |
|
| 501 |
This model is hard to solve! One solution seems to be to |
| 502 |
1. load it, run on_load. |
| 503 |
2. attempt to solve |
| 504 |
3. disable equation HE.cons_en |
| 505 |
4. free HE.outlet.x |
| 506 |
5. solve again. |
| 507 |
*) |
| 508 |
MODEL rankine_regen; |
| 509 |
|
| 510 |
BO IS_A boiler_simple; |
| 511 |
TU1 IS_A turbine_simple; |
| 512 |
BL IS_A tee; (* bleed *) |
| 513 |
TU2 IS_A turbine_simple; |
| 514 |
CO IS_A condenser_simple; |
| 515 |
HE IS_A heater_open; |
| 516 |
PU1 IS_A pump_simple; |
| 517 |
PU2 IS_A pump_simple; |
| 518 |
|
| 519 |
(* main loop *) |
| 520 |
BO.outlet, TU1.inlet ARE_THE_SAME; |
| 521 |
TU1.outlet, BL.inlet ARE_THE_SAME; |
| 522 |
BL.outlet, TU2.inlet ARE_THE_SAME; |
| 523 |
TU2.outlet, CO.inlet ARE_THE_SAME; |
| 524 |
CO.outlet, PU1.inlet ARE_THE_SAME; |
| 525 |
PU1.outlet, HE.inlet ARE_THE_SAME; |
| 526 |
HE.outlet, PU2.inlet ARE_THE_SAME; |
| 527 |
PU2.outlet, BO.inlet ARE_THE_SAME; |
| 528 |
|
| 529 |
(* bleed stream *) |
| 530 |
BL.outlet_branch, HE.inlet_heat ARE_THE_SAME; |
| 531 |
phi ALIASES BL.phi; |
| 532 |
p_bleed ALIASES TU1.outlet.p; |
| 533 |
|
| 534 |
mdot ALIASES BO.mdot; |
| 535 |
|
| 536 |
T_H ALIASES BO.outlet.T; |
| 537 |
T_C ALIASES CO.outlet.T; |
| 538 |
|
| 539 |
eta IS_A fraction; |
| 540 |
eta_eq:eta * (BO.Qdot_fuel) = TU1.Wdot + TU2.Wdot + PU1.Wdot + PU2.Wdot; |
| 541 |
|
| 542 |
Wdot_TU1 ALIASES TU1.Wdot; |
| 543 |
Wdot_TU2 ALIASES TU2.Wdot; |
| 544 |
Wdot_PU1 ALIASES PU1.Wdot; |
| 545 |
Wdot_PU2 ALIASES PU2.Wdot; |
| 546 |
Qdot_fuel ALIASES BO.Qdot_fuel; |
| 547 |
|
| 548 |
eta_carnot IS_A fraction; |
| 549 |
eta_carnot = 1 - T_C / T_H; |
| 550 |
|
| 551 |
(* some checking output... *) |
| 552 |
|
| 553 |
phi_weston IS_A fraction; |
| 554 |
phi_weston_eq:phi_weston * (TU1.outlet.h - PU1.outlet.h) = (PU2.inlet.h - PU1.outlet.h); |
| 555 |
phi_eq:phi_weston = phi; |
| 556 |
|
| 557 |
w_net IS_A specific_energy; |
| 558 |
w_net_eq: TU1.mdot * w_net = TU1.mdot * (TU1.inlet.h - TU1.outlet.h) + TU2.mdot * (TU2.inlet.h - TU2.outlet.h); |
| 559 |
|
| 560 |
q_a IS_A specific_energy; |
| 561 |
q_a = TU1.inlet.h - PU2.outlet.h; |
| 562 |
|
| 563 |
Wdot IS_A energy_rate; |
| 564 |
Wdot = TU1.Wdot + TU2.Wdot + PU1.Wdot + PU2.Wdot; |
| 565 |
|
| 566 |
cons_en: HE.inlet.mdot * HE.inlet.h + HE.inlet_heat.mdot * HE.inlet_heat.h = HE.outlet.mdot * HE.outlet.h; |
| 567 |
|
| 568 |
METHODS |
| 569 |
METHOD default_self; |
| 570 |
BO.outlet.h := 4000 {kJ/kg}; |
| 571 |
p_bleed := 37 {bar}; |
| 572 |
TU1.outlet.h := 2300 {kJ/kg}; |
| 573 |
CO.cons_en.included := FALSE; |
| 574 |
CO.cons_mass.included := FALSE; |
| 575 |
END default_self; |
| 576 |
METHOD on_load; |
| 577 |
RUN moran_ex_8_5; |
| 578 |
(* note: |
| 579 |
acheived solution with the following variables fixed: |
| 580 |
BO.eta |
| 581 |
TU1.eta |
| 582 |
TU2.eta |
| 583 |
PU1.eta |
| 584 |
PU2.eta |
| 585 |
BO.outlet.p = TU1.inlet.p |
| 586 |
TU2.outlet_is.p = TU2.outlet.p |
| 587 |
PU2.inlet.x = HE.outlet.x |
| 588 |
Wdot |
| 589 |
|
| 590 |
REMOVE TU1.outlet.T = p_bleed |
| 591 |
REMOVE HE.outlet.p (redundant) |
| 592 |
*) |
| 593 |
END on_load; |
| 594 |
METHOD moran_ex_8_5; |
| 595 |
RUN default_self; |
| 596 |
(* |
| 597 |
This is Example 8.5 from Moran and Shapiro, 'Fundamentals of |
| 598 |
Engineering Thermodynamics', 4th Ed. |
| 599 |
*) |
| 600 |
RUN ClearAll; |
| 601 |
(* component efficiencies *) |
| 602 |
FIX BO.eta; BO.eta := 1.0; |
| 603 |
FIX TU1.eta; TU1.eta := 0.85; |
| 604 |
FIX TU2.eta; TU2.eta := 0.85; |
| 605 |
FIX PU1.eta; PU1.eta := 1.0; |
| 606 |
FIX PU2.eta; PU2.eta := 1.0; |
| 607 |
(* turbine conditions *) |
| 608 |
FIX TU1.inlet.p; TU1.inlet.p := 8. {MPa}; |
| 609 |
FIX TU1.inlet.T; TU1.inlet.T := 480 {K} + 273.15 {K}; |
| 610 |
FIX TU1.outlet.p; TU1.outlet.p := 0.7 {MPa}; |
| 611 |
FIX TU2.outlet.p; TU2.outlet.p := 0.008 {MPa}; |
| 612 |
(* heater conditions *) |
| 613 |
(* FIX HE.outlet.p; HE.outlet.p := 0.7 {MPa}; *) |
| 614 |
FIX HE.outlet.x; HE.outlet.x := 0.001; |
| 615 |
FIX Wdot; Wdot := 100 {MW}; |
| 616 |
END moran_ex_8_5; |
| 617 |
METHOD weston_ex_2_6; |
| 618 |
(* |
| 619 |
The scenario here is example 2.6 from K Weston (op. cit.), p. 55. |
| 620 |
*) |
| 621 |
RUN ClearAll; |
| 622 |
|
| 623 |
(* all ideal components *) |
| 624 |
FIX BO.eta; BO.eta := 1.0; |
| 625 |
FIX TU1.eta; TU1.eta := 1.0; |
| 626 |
FIX TU2.eta; TU2.eta := 1.0; |
| 627 |
FIX PU1.eta; PU1.eta := 1.0; |
| 628 |
FIX PU2.eta; PU2.eta := 1.0; |
| 629 |
|
| 630 |
(* mass flow rate is arbitrary *) |
| 631 |
FIX mdot; |
| 632 |
mdot := 10 {kg/s}; |
| 633 |
|
| 634 |
(* max pressure constraint *) |
| 635 |
FIX PU2.outlet.p; |
| 636 |
PU2.outlet.p := 2000 {psi}; |
| 637 |
PU2.outlet.h := 1400 {btu/lbm}; (* guess *) |
| 638 |
|
| 639 |
(* boiler max temp *) |
| 640 |
FIX BO.outlet.T; |
| 641 |
BO.outlet.T := 1460 {R}; |
| 642 |
BO.outlet.h := 1400 {btu/lbm}; (* guess *) |
| 643 |
|
| 644 |
(* intermediate temperature setting *) |
| 645 |
FIX TU1.outlet.p; |
| 646 |
TU1.outlet.p := 200 {psi}; |
| 647 |
(* FIX TU1.outlet.T; |
| 648 |
TU1.outlet.T := 860 {R}; (* 400 °F *) |
| 649 |
TU1.outlet.h := 3000 {kJ/kg}; (* guess *) *) |
| 650 |
|
| 651 |
(* minimum pressure constraint *) |
| 652 |
FIX CO.outlet.p; |
| 653 |
CO.outlet.p := 1 {psi}; |
| 654 |
|
| 655 |
(* condenser outlet is saturated liquid *) |
| 656 |
FIX CO.outlet.h; |
| 657 |
CO.outlet.h := 69.73 {btu/lbm}; |
| 658 |
|
| 659 |
(* remove the redundant balance equations *) |
| 660 |
HE.cons_mass.included := TRUE; |
| 661 |
HE.cons_en.included := TRUE; |
| 662 |
BL.cons_mass.included := FALSE; |
| 663 |
phi_weston_eq.included := TRUE; |
| 664 |
phi_eq.included := FALSE; |
| 665 |
cons_en.included := FALSE; |
| 666 |
|
| 667 |
(* fix the bleed ratio *) |
| 668 |
FIX BL.phi; |
| 669 |
BL.phi := 0.251; |
| 670 |
|
| 671 |
(* FIX BL.outlet.h; |
| 672 |
BL.outlet.h := 355.5 {btu/lbm}; *) |
| 673 |
|
| 674 |
END weston_ex_2_6; |
| 675 |
METHOD self_test; |
| 676 |
ASSERT abs(TU1.inlet.s - 1.5603 {btu/lbm/R}) < 0.01 {btu/lbm/R}; |
| 677 |
ASSERT abs(TU1.outlet.s - 1.5603 {btu/lbm/R}) < 0.01 {btu/lbm/R}; |
| 678 |
ASSERT abs(TU2.outlet.s - 1.5603 {btu/lbm/R}) < 0.01 {btu/lbm/R}; |
| 679 |
ASSERT abs(PU1.inlet.s - 0.1326 {btu/lbm/R}) < 0.001 {btu/lbm/R}; |
| 680 |
ASSERT abs(PU1.outlet.s - 0.1326 {btu/lbm/R}) < 0.002 {btu/lbm/R}; |
| 681 |
ASSERT abs(PU2.inlet.s - 0.5438 {btu/lbm/R}) < 0.002 {btu/lbm/R}; |
| 682 |
ASSERT abs(PU2.outlet.s - 0.5438 {btu/lbm/R}) < 0.002 {btu/lbm/R}; |
| 683 |
|
| 684 |
ASSERT abs(TU1.inlet.h - 1474.1 {btu/lbm}) < 1.5 {btu/lbm}; |
| 685 |
ASSERT abs(TU1.outlet.h - 1210.0 {btu/lbm}) < 1.5 {btu/lbm}; |
| 686 |
ASSERT abs(TU2.outlet.h - 871.0 {btu/lbm}) < 1.5 {btu/lbm}; |
| 687 |
ASSERT abs(PU1.inlet.h - 69.73 {btu/lbm}) < 0.001 {btu/lbm}; |
| 688 |
ASSERT abs(PU1.outlet.h - 69.73 {btu/lbm}) < 1.0 {btu/lbm}; |
| 689 |
ASSERT abs(PU2.inlet.h - 355.5 {btu/lbm}) < 1.5 {btu/lbm}; |
| 690 |
ASSERT abs(PU2.outlet.h - 355.5 {btu/lbm}) < 8 {btu/lbm}; |
| 691 |
|
| 692 |
ASSERT abs(w_net - 518.1 {btu/lbm}) < 0.3 {btu/lbm}; |
| 693 |
|
| 694 |
ASSERT abs(w_net * mdot - (TU1.Wdot + TU2.Wdot)) < 1 {W}; |
| 695 |
|
| 696 |
ASSERT abs(q_a - 1118.6 {btu/lbm}) < 7 {btu/lbm}; |
| 697 |
|
| 698 |
ASSERT abs(eta - 0.463) < 0.003; |
| 699 |
|
| 700 |
ASSERT abs(phi - 0.251) < 0.001; |
| 701 |
END self_test; |
| 702 |
END rankine_regen; |
| 703 |
|
| 704 |
MODEL rankine_compare; |
| 705 |
simple IS_A rankine; |
| 706 |
regen IS_A rankine_regen; |
| 707 |
simple.BO.inlet.p, regen.BO.inlet.p ARE_THE_SAME; |
| 708 |
simple.BO.inlet.h, regen.BO.inlet.h ARE_THE_SAME; |
| 709 |
simple.BO.Qdot_fuel, regen.BO.Qdot_fuel ARE_THE_SAME; |
| 710 |
simple.CO.outlet.T, regen.CO.outlet.T ARE_THE_SAME; |
| 711 |
simple.BO.eta, regen.BO.eta ARE_THE_SAME; |
| 712 |
simple.TU.eta, regen.TU1.eta, regen.TU2.eta ARE_THE_SAME; |
| 713 |
simple.PU.eta, regen.PU1.eta, regen.PU2.eta ARE_THE_SAME; |
| 714 |
simple.mdot, regen.mdot ARE_THE_SAME; |
| 715 |
METHODS |
| 716 |
METHOD on_load; |
| 717 |
RUN ClearAll; |
| 718 |
RUN regen.on_load; |
| 719 |
END on_load; |
| 720 |
END rankine_compare; |
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