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Contents of /trunk/models/solar/cylindrical_absorber.a4l

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Revision 2573 - (show annotations) (download) (as text)
Mon Feb 20 23:03:16 2012 UTC (10 years, 5 months ago) by jpye
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Merging models from Vikram Kadam. Awaiting checking.
1 REQUIRE "atoms.a4l";
2 REQUIRE "solar/solar_types.a4l";
3 REQUIRE "johnpye/thermo_types.a4c";
4
5 REQUIRE "johnpye/sunpos.a4c";
6
7 IMPORT "johnpye/fprops/helmholtz";
8
9 MODEL helmholtz_conf;
10 component IS_A symbol_constant;
11 component :== 'water';
12 END helmholtz_conf;
13
14 MODEL sunpos_tracker2 REFINES sunpos;
15 (* The collector is rotated about a horizontal east-west axis with continuous adjustment to minimize the angle of incidence *)
16
17 sin(delta) * ( sin(phi)*sin(beta) + cos(phi)*cos(beta)*cos(gamma) ) = cos(delta) * cos(omega) * ( sin(phi) * cos(beta) * cos(gamma) - cos(phi) * sin(beta) ) + cos(delta) * cos(beta) * sin(gamma) * sin(omega);
18
19 METHODS
20 METHOD specify;
21 FIX t, L_st, L_loc, phi; (* time and location *)
22 FIX gamma; (* surface orientation *)
23 END specify;
24
25 METHOD bound_self;
26 beta.lower_bound := 0 {deg};
27 beta.upper_bound := 90 {deg};
28 END bound_self;
29
30 METHOD values;
31 L_st := -90{deg};
32 L_loc := -89.4{deg};
33 phi := +43{deg};
34 (* t := 32.4375 {d}; *)
35 t := 32{d} + 10{h}+30{min};
36 gamma := 15{deg}; (* surface orientation *)
37 END values;
38
39 METHOD default_self;
40 beta := 45{deg};
41 END default_self;
42
43 METHOD on_load;
44 RUN specify;
45 RUN values;
46 RUN bound_self;
47 RUN default_self;
48 END on_load;
49 END sunpos_tracker2;
50
51
52 MODEL hconv_c_a(
53 D WILL_BE distance;
54 V WILL_BE speed;
55 T_amb WILL_BE temperature;
56 );
57
58 r IS_A mass_density;
59 u IS_A viscosity;
60 Re IS_A factor;
61 (* Reynolds Number *)
62 Nu IS_A factor;
63 k IS_A thermal_conductivity;
64 value IS_A heat_transfer_coefficient;
65
66 Re*u = r*V*D;
67 Nu = 0.40 + 0.54 * Re^0.52;
68 value*D = Nu*k;
69
70 METHODS
71 METHOD specify;
72 FIX r;
73 FIX u;
74 FIX k;
75 END specify;
76
77 METHOD values;
78 r := 1.2466 {kg/m^3};
79 u := 1.78e-5 {kg/m/s};
80 k := 0.0253 {W/m/K};
81 END values;
82 END hconv_c_a;
83
84 MODEL test_hconv_c_a();
85 D IS_A distance;
86 V IS_A speed;
87 T_amb IS_A temperature;
88
89 instance IS_A hconv_c_a(D,V,T_amb);
90
91 METHODS
92 METHOD specify;
93 FIX D;
94 FIX V;
95 FIX T_amb;
96 RUN instance.specify;
97 END specify;
98
99 METHOD values;
100 D := 1 {cm};
101 V := 10 {m/s};
102 T_amb := 10 {K} + 273.15 {K};
103 RUN instance.values;
104 END values;
105
106 METHOD on_load;
107 RUN specify;
108 RUN values;
109 END on_load;
110
111 END test_hconv_c_a;
112
113
114
115 MODEL hr_c_a(
116 Tc WILL_BE temperature;
117 T_amb WILL_BE temperature;
118 e WILL_BE fraction;
119 );
120
121 S IS_A stefan_boltzman_constant;
122 S :== 5.670e-8 {watt/m^2/K^4};
123
124 value IS_A heat_transfer_coefficient;
125
126 value = 4*S*e*(Tc+T_amb)^3;
127
128 METHODS
129 METHOD specify;
130 END specify;
131
132 METHOD values;
133 END values;
134 END hr_c_a;
135
136
137 MODEL test_hr_c_a();
138 Tc IS_A temperature;
139 T_amb IS_A temperature;
140 e IS_A fraction;
141
142 instance IS_A hr_c_a(Tc,T_amb,e);
143
144 METHODS
145 METHOD specify;
146 FIX Tc;
147 FIX T_amb;
148 FIX e;
149 RUN instance.specify;
150 END specify;
151
152 METHOD values;
153 Tc := 40 {K} + 273.15 {K};
154 T_amb := 10 {K} + 273.15 {K};
155 e := 0.9;
156 RUN instance.values;
157 END values;
158
159 METHOD on_load;
160 RUN specify;
161 RUN values;
162 END on_load;
163
164 END test_hr_c_a;
165
166
167 MODEL hr_r_c(
168 Tc WILL_BE temperature;
169 Tr WILL_BE temperature;
170 e1 WILL_BE fraction;
171 e2 WILL_BE fraction;
172 Ar WILL_BE area;
173 Aa WILL_BE area;
174 );
175
176 S IS_A stefan_boltzman_constant;
177 S :== 5.670e-8 {watt/m^2/K^4};
178
179 value IS_A heat_transfer_coefficient;
180
181 value = S*(Tc^2+Tr^2)*(Tc+Tr) / (((1-e1)/e1)+1+((1-e2)/e2)*(Ar/Aa));
182
183
184 METHODS
185 METHOD specify;
186 END specify;
187
188 METHOD values;
189 END values;
190 END hr_r_c;
191
192
193 MODEL test_hr_r_c();
194
195 Tc IS_A temperature;
196 Tr IS_A temperature;
197 e1 IS_A fraction;
198 e2 IS_A fraction;
199 Ar IS_A area;
200 Aa IS_A area;
201
202 instance IS_A hr_r_c (Tc,Tr,e1,e2,Ar,Aa);
203
204 METHODS
205 METHOD specify;
206 FIX Tc;
207 FIX Tr;
208 FIX e1;
209 FIX e2;
210 FIX Ar;
211 FIX Aa;
212 RUN instance.specify;
213 END specify;
214
215 METHOD values;
216 Tc := 40 {K} + 273.15 {K};
217 Tr := 100 {K} + 273.15 {K};
218 e1 := 0.9;
219 e2 := 0.88;
220 Ar := 16 {cm^2};
221 Aa := 4 {cm^2};
222 RUN instance.values;
223 END values;
224
225 METHOD on_load;
226 RUN specify;
227 RUN values;
228 END on_load;
229 END test_hr_r_c;
230
231
232
233 MODEL Ul;
234 Tc IS_A temperature;
235 Tr IS_A temperature;
236 T_amb IS_A temperature;
237 e IS_A fraction;
238 e1 IS_A fraction;
239 e2 IS_A fraction;
240 Ar IS_A area;
241 Aa IS_A area;
242 D IS_A distance;
243 V IS_A speed;
244
245
246 hconv_c_a_instance IS_A hconv_c_a(D,V,T_amb);
247
248 hr_c_a_instance IS_A hr_c_a(Tc,T_amb,e);
249
250 hr_r_c_instance IS_A hr_r_c (Tc,Tr,e1,e2,Ar,Aa);
251
252 C IS_A factor;
253
254 value IS_A heat_transfer_coefficient;
255
256
257
258 Tc = (Ar*hr_r_c_instance.value*Tr + Aa*(hr_c_a_instance.value + hconv_c_a_instance.value)*T_amb) / (Ar*hr_r_c_instance.value + Aa*(hr_c_a_instance.value + hconv_c_a_instance.value));
259
260 C * Ar = Aa;
261
262 value * C * hr_r_c_instance.value = (hconv_c_a_instance.value + hr_c_a_instance.value) * (hr_r_c_instance.value - value);
263
264
265 METHODS
266 METHOD specify;
267 FIX Tr;
268 FIX T_amb;
269 FIX e;
270 FIX e1;
271 FIX e2;
272 FIX Ar;
273 FIX Aa;
274 FIX D;
275 FIX V;
276
277 RUN hconv_c_a_instance.specify;
278 RUN hr_c_a_instance.specify;
279 RUN hr_r_c_instance.specify;
280 END specify;
281
282 METHOD values;
283 Tr := 100 {K} + 273.15 {K};
284 T_amb := 10 {K} + 273.15 {K};
285 e := 0.9;
286 e1 := 0.9;
287 e2 := 0.88;
288 Ar := 16 {cm^2};
289 Aa := 4 {cm^2};
290 D := 1 {cm};
291 V := 10 {m/s};
292
293 RUN hconv_c_a_instance.values;
294 RUN hr_c_a_instance.values;
295 RUN hr_r_c_instance.values;
296 END values;
297
298 METHOD on_load;
299 RUN specify;
300 RUN values;
301 END on_load;
302 END Ul;
303
304
305 MODEL S1;
306
307 (* Variables *)
308
309 sp IS_A sunpos_tracker2;
310
311 value IS_A factor;
312
313 DNI IS_A factor;
314 kT IS_A factor;
315
316 IAM IS_A factor;
317
318 f IS_A distance; (* focal length of the concentrator (distance from vertex to the focus) *)
319 L IS_A distance; (* length of collector assembly (same as earlier L, length of receiver tube) *)
320 EndLoss IS_A factor;
321
322 Eta_field IS_A factor; (* field efficiency *)
323 TrkTwstErr IS_A factor; (* twisting and tracking error associated with the collector type *)
324 GeoAcc IS_A factor; (* geometric accuracy of the collector mirrors *)
325 MirRef IS_A fraction; (* mirror reflectivity *)
326 MirCln IS_A fraction; (* mirror cleanliness *)
327
328 Eta_HCE IS_A fraction; (* Heat Collection Element Efficiency *)
329 HCEdust IS_A factor; (* losses due to shading of HCE by dust on the envelope *)
330 BelShad IS_A factor; (* losses from shading of ends of HCEs due to bellows (WHAT is this *)
331 EnvTrans IS_A fraction; (* transmissivity of the glass envelope *)
332 HCEabs IS_A fraction; (* absorbtivity of the HCE selective coating *)
333 HCEmisc IS_A factor; (* miscellaneous factor to adjust for other HCE losses *)
334
335 SFAvail IS_A fraction; (* fraction of the solar field that is operable and tracking the sun *)
336
337
338
339 (* Equations *)
340
341 DNI = 1;
342
343 value = DNI * cos(sp.theta) * IAM * EndLoss * Eta_field * Eta_HCE * SFAvail;
344
345 IAM = 1 + 0.000884 {1/rad} * (sp.theta / cos(sp.theta)) - 0.00005369 {1/rad^2} * (sp.theta / cos(sp.theta))^2;
346
347 EndLoss * L = L - f*tan(sp.theta);
348
349 Eta_field = TrkTwstErr * GeoAcc * MirRef * MirCln; (* Assuming all the collectors (in cases there are more than one) are identical. *)
350
351 Eta_HCE = HCEdust * BelShad * EnvTrans * HCEabs * HCEmisc;
352
353
354 METHODS
355 METHOD specify;
356 FIX kT;
357 FIX f;
358 FIX L;
359
360 FIX TrkTwstErr;
361 FIX GeoAcc;
362 FIX MirRef;
363 FIX MirCln;
364
365 FIX HCEdust;
366 FIX BelShad;
367 FIX EnvTrans;
368 FIX HCEabs;
369 FIX HCEmisc;
370
371 FIX SFAvail;
372
373 RUN sp.specify;
374 END specify;
375
376 METHOD values;
377 kT := 0.75;
378 f := 1{cm};
379 L := 2{cm};
380 RUN sp.values;
381 END values;
382
383 METHOD on_load;
384 RUN specify;
385 RUN values;
386
387 RUN sp.bound_self;
388 RUN sp.default_self;
389 END on_load;
390 END S1;
391
392
393 MODEL water_props(
394 T WILL_BE temperature;
395 );
396 Cp IS_A specific_heat_capacity;
397 Cp_dimless IS_A factor;
398
399 rho IS_A mass_density;
400 mu IS_A viscosity;
401 k IS_A thermal_conductivity;
402
403 T_dimless IS_A factor;
404
405
406 T_dimless * 1{K} = T;
407 Cp_dimless = 4.2204 - 4.2587e-3 + 1.3575e-4*T_dimless^2 - 1.8660e-6*T_dimless^3 + 1.3008e-8*T_dimless^4 - 4.2341e-11*T_dimless^5 + 5.2769e-14*T_dimless^6;
408
409 Cp = Cp_dimless * 1{kJ/kg/K};
410
411 (* Cp = 7.573 {kJ/kg/K}; Cp is assumed constant temporarily *)
412 (*h = 21 {kJ};*)
413
414 rho = 1000 {kg/m^3};
415 mu = 0.152 {N*s/m^2};
416 k = 0.58 {watt/m/K};
417
418 p IS_A pressure;
419 h IS_A specific_enthalpy;
420 u IS_A specific_energy;
421
422
423 conf IS_A helmholtz_conf;
424
425 props1: helmholtz_p(
426 T, rho : INPUT;
427 p : OUTPUT;
428 conf : DATA
429 );
430
431 props2: helmholtz_u(
432 T, rho : INPUT;
433 u : OUTPUT;
434 conf : DATA
435 );
436
437 rho*(h - u) = p;
438
439 METHODS
440 METHOD bound_self;
441 T_dimless.lower_bound := 0;
442 T_dimless.upper_bound := 5000;
443 END bound_self;
444 END water_props;
445
446
447 MODEL test_water_props;
448 T IS_A temperature;
449 wp IS_A water_props(T);
450
451 METHODS
452 METHOD on_load;
453 FIX T;
454 T := 40 {K} + 273.15 {K};
455 RUN wp.bound_self;
456 END on_load;
457 END test_water_props;
458
459
460 MODEL h_fi(
461 Di WILL_BE distance;
462 V_f WILL_BE speed; (* Velocity of fluid in the tube *)
463 wp_f WILL_BE water_props; (* Density of the fluid at T_f *)
464 L WILL_BE distance; (* length of receiver tube (Input) *)
465 Tc WILL_BE temperature;
466 );
467 (* Variables *)
468 value IS_A heat_transfer_coefficient;
469 Nu1 IS_A factor;
470 Re1 IS_A factor;
471 Pr IS_A factor;
472 wp_Tc IS_A water_props(Tc);
473
474
475 (* Equations *)
476
477 value = Nu1 * wp_f.k / Di;
478
479 (* For Re1 less than 10000 *)
480 Nu1 = 1.86/((Re1*Pr)^(2/3)) * ((Di/L)^(1/3)) * ((wp_f.mu/wp_Tc.mu)^0.14);
481 (* For Re more than 10000, Nu1 = 0.023*Re^0.8*Pr^0.4 *)
482
483 Re1 = wp_f.rho * V_f * Di / wp_f.mu; (* Reynolds Number inside the tube *)
484 Pr = wp_f.Cp * wp_f.mu / wp_f.k; (* Prandtl Number *)
485
486 END h_fi;
487
488
489 MODEL Cylindrical_Absorber;
490 (* constants *)
491 e IS_A real_constant;
492 e :== 2.718;
493
494
495 (* Variables *)
496 T_in IS_A temperature;
497 V_f IS_A speed; (* Velocity of fluid in the tube *)
498 L IS_A distance; (* length of receiver tube (Input) *)
499 W IS_A distance; (* Width of aparture *)
500 N IS_A factor; (* Number of solar collector assemblies *)
501 Do IS_A distance; (* Outer diameter of the receiver tube (Input) *)
502 Di IS_A distance; (* Inner diameter of the receiver tube (Input) *)
503 k_tube IS_A thermal_conductivity; (* thermal conductivity of the tube material *)
504
505 Ul_instance IS_A Ul;
506 S1_instance IS_A S1;
507 wp_in IS_A water_props(T_in);
508 wp_f IS_A water_props(T_f);
509 h_fi_instance IS_A h_fi (Di, V_f, wp_f, L, Ul_instance.Tc); (* Heat transfer coefficient inside the tube *)
510
511 Qu IS_A intensity;
512 T_out IS_A temperature;
513 T_f IS_A temperature;
514 FR IS_A factor;
515 F_dash IS_A factor;
516 m_dot IS_A mass_rate;
517 delta_h IS_A specific_enthalpy; (* delta_enthalpy; Change in enthalpy *)
518 Vdot_f IS_A volume_rate;
519 power IS_A factor;
520
521 (* Equations *)
522 Qu * Ul_instance.Aa + FR * Ul_instance.Aa * Ul_instance.Ar * Ul_instance.value * (T_in - Ul_instance.T_amb) = Ul_instance.Aa * S1_instance.value * Ul_instance.Aa;
523 T_f * 2 = (T_in + T_out);
524 FR * (Ul_instance.Ar * Ul_instance.value) = (m_dot * wp_f.Cp) * (1 - e^power);
525 power = -1 * Ul_instance.Ar * Ul_instance.value * F_dash / m_dot * wp_f.Cp;
526 F_dash * ( (h_fi_instance.value*Di) + (Do*Ul_instance.value) + (h_fi_instance.value*Di)*Ul_instance.value*(Do/2*k_tube)*ln(Do/Di)) = (h_fi_instance.value*Di);
527 m_dot * 4 = wp_f.rho * (3.14 * Di^2) * V_f;
528 delta_h = wp_f.h - wp_in.h;
529 delta_h * (Vdot_f * wp_in.rho) = Qu * W * L * N;
530 Vdot_f = 3.14 * Di^2 / 4;
531
532
533 METHODS
534 METHOD specify;
535 FIX T_in;
536 FIX V_f;
537 FIX L;
538 FIX W;
539 FIX N;
540 FIX Do;
541 FIX Di;
542 FIX k_tube;
543
544 RUN Ul_instance.specify;
545 RUN S1_instance.specify;
546 RUN wp_in.specify;
547 RUN wp_f.specify;
548 RUN h_fi_instance.specify;
549 END specify;
550
551 METHOD bound_self;
552 power.lower_bound := -100;
553 power.upper_bound := 100;
554
555 FR.upper_bound := 10000;
556
557 RUN wp_in.bound_self;
558 RUN wp_f.bound_self;
559 END bound_self;
560
561 METHOD other;
562 RUN bound_self;
563 RUN S1_instance.sp.bound_self;
564 RUN S1_instance.sp.default_self;
565
566 RUN Ul_instance.values;
567 RUN S1_instance.values;
568 RUN wp_in.values;
569 RUN wp_f.values;
570 RUN h_fi_instance.values;
571 END other;
572
573 (*
574 METHOD on_load;
575 RUN specify;
576 RUN other;
577
578 SOLVER QRSlv;
579 OPTION convopt 'RELNOM_SCALE';
580 END on_load;
581 *)
582 END Cylindrical_Absorber;
583
584
585 MODEL example_Cylindrical_Absorber REFINES Cylindrical_Absorber;
586
587 METHODS
588 METHOD values;
589 T_in := 10 {K} + 273.15 {K};(* Inlet temperature of water *)
590 V_f := 0.5 {m/s}; (* Velocity of fluid in the tube *)
591 L := 10 {m}; (* length of receiver tube (Input) *)
592 W := 2.5 {m}; (* Width of aparture *)
593 N := 1; (* Number of solar collector assemblies *)
594 Do := 0.06 {m}; (* Outer diameter of the receiver tube (Input) *)
595 Di := 0.055 {m}; (* Inner diameter of the receiver tube (Input) *)
596 k_tube := 16 {watt/m/K}; (* thermal conductivity of the tube material *)
597 END values;
598
599 METHOD on_load;
600 RUN Cylindrical_Absorber::specify;
601 RUN Cylindrical_Absorber::other;
602 RUN values;
603
604 SOLVER QRSlv;
605 OPTION convopt 'RELNOM_SCALE';
606 END on_load;
607 END example_Cylindrical_Absorber;

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john.pye@anu.edu.au
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