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Contents of /trunk/models/steam/dsgsat3.a4c

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Revision 1179 - (show annotations) (download) (as text)
Fri Jan 19 01:14:32 2007 UTC (15 years, 5 months ago) by johnpye
File MIME type: text/x-ascend
File size: 6119 byte(s)
Fixed problem with 'v' (spec vol) verusus 'vel' in one equation!
Added new formulation where (rho*u) equation is rewritten as (u).
1 REQUIRE "ivpsystem.a4l";
2 REQUIRE "atoms.a4l";
3 REQUIRE "johnpye/thermo_types.a4c";
4
5 (*
6 An attempt to model direct steam generation in pipe flow, limited to the
7 saturated regime, and with constant-valued friction factor. External heat
8 loss is also simplified.
9 *)
10 REQUIRE "steam/satsteamstream.a4c";
11
12 MODEL dsgsat3;
13 n IS_A integer_constant;
14 n :== 2;
15
16 (* temporal derivatives *)
17 drho_dt[2..n] IS_A density_rate;
18 dmdot_dt[2..n] IS_A mass_rate_rate;
19 du_dt[2..n] IS_A power_per_volume;
20 dTw_dt[2..n] IS_A temperature_rate;
21
22 (* wall properties *)
23 rho_w IS_A mass_density;
24 D, D_2 IS_A distance;
25 c_w IS_A specific_heat_capacity;
26 A, A_w IS_A area;
27 h_int IS_A heat_transfer_coefficient; (* internal *)
28 h_ext IS_A heat_transfer_coefficient; (* external *)
29 z_A: A = 1{PI}*D^2/4;
30 z_Aw: A_w = 1{PI}*(D_2^2 - D^2)/4;
31 dz IS_A distance;
32 L IS_A distance;
33 z_dz: dz = L / (n - 1);
34
35 (* fluid properties *)
36 node[1..n] IS_A satsteamstream;
37
38 (* flow properties *)
39 vel[1..n] IS_A speed;
40 T_w[2..n] IS_A temperature;
41 T[1..n] IS_A temperature;
42
43 (* constants, for the moment: *)
44 f IS_A positive_factor;
45 (* mu_f IS_A viscosity; *)
46 T_amb IS_A temperature;
47
48 (* system dynamics *)
49 qdot_t[2..n], qdot_l[2..n] IS_A power_per_length;
50 qdot_s IS_A power_per_length;
51
52 FOR i IN [1..n] CREATE
53 z_vel[i]: vel[i] = node[i].v*node[i].mdot/A;
54 END FOR;
55
56 (* some aliases just for easier review of the state of the model *)
57 x[1..n] IS_A fraction;
58 mdot[1..n] IS_A mass_rate;
59 p[1..n] IS_A pressure;
60 FOR i IN [1..n] CREATE
61 x[i], node[i].x ARE_THE_SAME;
62 mdot[i], node[i].mdot ARE_THE_SAME;
63 p[i], node[i].p ARE_THE_SAME;
64 T[i], node[i].T ARE_THE_SAME;
65 END FOR;
66
67 (* differential equations *)
68 FOR i IN [2..n] CREATE
69 z_massbal[i]: A * drho_dt[i] * dz = - (node[i].mdot - node[i-1].mdot);
70
71 z_enbal[i]: dz * (node[i].rho * A * du_dt[i] - qdot_t[i]) =
72 - node[i].mdot * (node[i].u - node[i-1].u)
73 - (node[i].p*node[i].v*node[i].mdot - node[i-1].p*node[i-1].v*node[i-1].mdot);
74
75 z_mombal[i]: dz/A*dmdot_dt[i] = -(node[i].p-node[i-1].p)
76 - f/D/2*node[i].rho*vel[i]^2*(
77 node[i].rho*vel[i]^2 - node[i-1].rho*vel[i-1]^2
78 );
79
80 z_wall[i]: rho_w*A_w*c_w*dTw_dt[i] = qdot_s - qdot_l[i] - qdot_t[i];
81 z_loss[i]: qdot_l[i] = h_ext*(1{PI}*D_2)*(T_w[i] - T_amb);
82 z_trans[i]: qdot_t[i] = h_int*(1{PI}*D) *(T_w[i] - node[i].T);
83
84 (* -- original formulation --
85 z_massbal[i]: A * drho_dt[i] * dz = - (node[i].mdot - node[i-1].mdot);
86 z_mombal[i]: dz/A*dmdot_dt[i] = -(node[i].p-node[i-1].p)
87 - f/D/2*node[i].rho*node[i].v^2*(
88 node[i].rho*vel[i]^2 - node[i-1].rho*vel[i-1]^2
89 );
90 z_enbal[i]: dz * (A * drhou_dt[i] - qdot_t[i]) = - (node[i].Hdot - node[i-1].Hdot);
91 z_wall[i]: rho_w*A_w*c_w*dTw_dt[i] = qdot_s - qdot_l[i] - qdot_t[i];
92 z_loss[i]: qdot_l[i] = h_ext*(1{PI}*D_2)*(T_w[i] - T_amb);
93 z_trans[i]: qdot_t[i] = h_int*(1{PI}*D) *(T_w[i] - node[i].T);
94 *)
95 END FOR;
96
97 t IS_A time;
98 METHODS
99 METHOD bound_self;
100 vel[1..n].upper_bound := 100 {m/s};
101 qdot_l[2..n].lower_bound := 0 {W/m};
102 FOR i IN [1..n] DO
103 RUN node[i].bound_self;
104 END FOR;
105 END bound_self;
106 METHOD default_self;
107 D := 0.06 {m};
108 D_2 := 0.07 {m};
109 A_w := 0.25{PI}*D_2^2 -0.25{PI}*D^2;
110 FOR i IN [1..n] DO
111 RUN node[i].default_self;
112 END FOR;
113 END default_self;
114 METHOD values;
115 L := 50 {m};
116 h_int := 5 {W/m^2/K};
117 h_ext := 10 {W/m^2/K};
118 node[1].mdot := 0.3 {kg/s};
119 node[1].p := 5 {bar};
120 node[1].x := 0.2;
121 qdot_s := 1000 {W/m^2} * D_2 * 10;
122 FOR i IN [2..n] DO
123 dmdot_dt[i] := 0.0 {kg/s/s};
124 du_dt[i] := 0 {W/m^3};
125 node[i].v := 0.2 {L/kg};
126 node[i].rho := 6 {kg/L};
127 node[i].dp_dT := +0.5 {kPa/K};
128 END FOR;
129 END values;
130 METHOD on_load;
131 RUN configure_steady;
132 RUN ode_init;
133 END on_load;
134 (*---------------- a physically sensible steady-state configuration-----------*)
135 METHOD configure_steady;
136 RUN default_self;
137 RUN ClearAll;
138 RUN specify_steady;
139 RUN bound_steady;
140 RUN values;
141 END configure_steady;
142 METHOD bound_steady;
143 RUN bound_self;
144 T_w[2..n].upper_bound := 1000 {K};
145 END bound_steady;
146 METHOD specify_steady;
147 (* change to a proper steady-state problem, with fluid properties FREEd *)
148 FOR i IN [1..n] DO
149 RUN node[i].specify;
150 FIX dTw_dt[i]; FREE T_w[i];
151 END FOR;
152 FIX node[1].p;
153 FREE node[1].T;
154 FIX qdot_s;
155 FIX D, D_2, L;
156 FIX h_int, c_w, rho_w, h_ext;
157 FIX f;
158 (* FIX mu_f; *)
159 FIX T_amb;
160 (* fix derivatives to zero *)
161 FOR i IN [2..n] DO
162 (* FIX dmdot_dt[i]; FREE node[i].mdot; *)
163 FREE node[i].x; FIX node[i].p;
164 FIX drho_dt[i]; FREE node[i].p;
165 FIX du_dt[i]; FREE node[i].T;
166 FREE mdot[i]; FIX dmdot_dt[i];
167 END FOR;
168 END specify_steady;
169 (*------------------------- the dynamic problem ------------------------------*)
170 METHOD configure_dynamic;
171 FOR i IN [2..n] DO
172 FREE drho_dt[i]; FIX node[i].rho;
173 FREE dmdot_dt[i]; FIX node[i].mdot;
174 FREE du_dt[i]; FIX node[i].u;
175 FREE dTw_dt[i]; FIX T_w[i];
176 FREE node[i].x;
177 FREE node[i].T;
178 END FOR;
179 t := 0 {s};
180 END configure_dynamic;
181 METHOD free_states;
182 FOR i IN [2..n] DO
183 FREE node[i].rho;
184 FREE node[i].mdot;
185 FREE node[i].u;
186 FREE T_w[i];
187 END FOR;
188 END free_states;
189 METHOD ode_init;
190 (* add the necessary meta data to allow solving with the integrator *)
191 t.ode_type := -1;
192 t.obs_id := 1;
193
194 FOR i IN [2..n] DO
195 drho_dt[i].ode_id := 4*i; node[i].rho.ode_id := 4*i;
196 drho_dt[i].ode_type := 2; node[i].rho.ode_type := 1;
197
198 dmdot_dt[i].ode_id := 4*i+1; node[i].mdot.ode_id := 4*i+1;
199 dmdot_dt[i].ode_type := 2; node[i].mdot.ode_type := 1;
200
201 du_dt[i].ode_id := 4*i+2; node[i].u.ode_id := 4*i+2;
202 du_dt[i].ode_type := 2; node[i].u.ode_type := 1;
203
204 dTw_dt[i].ode_id := 4*i+3; T_w[i].ode_id := 4*i+3;
205 dTw_dt[i].ode_type := 2; T_w[i].ode_type := 1;
206 END FOR;
207
208 FOR i IN [1..n] DO
209 p[i].obs_id := 1 + 5*i;
210 x[i].obs_id := 2 + 5*i;
211 node[i].mdot.obs_id := 4 + 5*i;
212 END FOR;
213 FOR i IN [2..n] DO
214 qdot_t[i].obs_id := 3 + 5*i;
215 T_w[i].obs_id := 5 + 4*i;
216 END FOR;
217 END ode_init;
218
219 METHOD fix_outlet_quality;
220 FIX x[n];
221 FREE node[1].mdot;
222 END fix_outlet_quality;
223
224 END dsgsat3;
225 ADD NOTES IN dsgsat2;
226 'QRSlv' iterationlimit {50}
227 END NOTES;

john.pye@anu.edu.au
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