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REQUIRE "ivpsystem.a4l"; |
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REQUIRE "atoms.a4l"; |
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REQUIRE "johnpye/thermo_types.a4c"; |
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|
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(* |
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An attempt to model direct steam generation in pipe flow, limited to the |
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saturated regime, and with constant-valued friction factor. External heat |
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loss is also simplified. |
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*) |
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REQUIRE "steam/satsteamstream.a4c"; |
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|
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MODEL dsgsat3; |
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n IS_A integer_constant; |
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n :== 4; |
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|
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(* temporal derivatives *) |
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drho_dt[2..n] IS_A density_rate; |
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dmdot_dt[2..n] IS_A mass_rate_rate; |
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du_dt[2..n] IS_A power_per_volume; |
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dTw_dt[2..n] IS_A temperature_rate; |
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|
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(* wall properties *) |
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rho_w IS_A mass_density; |
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D, D_2 IS_A distance; |
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c_w IS_A specific_heat_capacity; |
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A, A_w IS_A area; |
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h_int IS_A heat_transfer_coefficient; (* internal *) |
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h_ext IS_A heat_transfer_coefficient; (* external *) |
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z_A: A = 1{PI}*D^2/4; |
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z_Aw: A_w = 1{PI}*(D_2^2 - D^2)/4; |
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dz IS_A distance; |
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L IS_A distance; |
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z_dz: dz = L / (n - 1); |
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|
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(* fluid properties *) |
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node[1..n] IS_A satsteamstream; |
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|
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(* flow properties *) |
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vel[1..n] IS_A speed; |
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T_w[2..n] IS_A temperature; |
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T[1..n] IS_A temperature; |
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|
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(* constants, for the moment: *) |
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f IS_A positive_factor; |
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(* mu_f IS_A viscosity; *) |
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T_amb IS_A temperature; |
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|
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(* system dynamics *) |
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qdot_t[2..n], qdot_l[2..n] IS_A power_per_length; |
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qdot_s IS_A power_per_length; |
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|
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FOR i IN [1..n] CREATE |
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z_vel[i]: vel[i] = node[i].v*node[i].mdot/A; |
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END FOR; |
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|
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(* some aliases just for easier review of the state of the model *) |
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x[1..n] IS_A fraction; |
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mdot[1..n] IS_A mass_rate; |
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p[1..n] IS_A pressure; |
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FOR i IN [1..n] CREATE |
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x[i], node[i].x ARE_THE_SAME; |
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mdot[i], node[i].mdot ARE_THE_SAME; |
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p[i], node[i].p ARE_THE_SAME; |
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T[i], node[i].T ARE_THE_SAME; |
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END FOR; |
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|
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(* differential equations *) |
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FOR i IN [2..n] CREATE |
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z_massbal[i]: A * drho_dt[i] * dz = - (node[i].mdot - node[i-1].mdot); |
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|
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z_enbal[i]: dz * (qdot_t[i] - node[i].rho * A * du_dt[i]) = |
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+ node[i].mdot * (node[i].u - node[i-1].u) |
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+ (node[i].p*node[i].v*node[i].mdot - node[i-1].p*node[i-1].v*node[i-1].mdot); |
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|
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z_mombal[i]: - dz/A*dmdot_dt[i] = |
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(node[i].p-node[i-1].p) |
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+ dz * f/D/2 * node[i].rho * vel[i]^2 |
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+ (node[i].rho*vel[i]^2 - node[i-1].rho*vel[i-1]^2); |
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|
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z_wall[i]: rho_w*A_w*c_w*dTw_dt[i] = qdot_s - qdot_l[i] - qdot_t[i]; |
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z_loss[i]: qdot_l[i] = h_ext*(1{PI}*D_2)*(T_w[i] - T_amb); |
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z_trans[i]: qdot_t[i] = h_int*(1{PI}*D) *(T_w[i] - node[i].T); |
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|
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(* -- original formulation -- |
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z_massbal[i]: A * drho_dt[i] * dz = - (node[i].mdot - node[i-1].mdot); |
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z_mombal[i]: dz/A*dmdot_dt[i] = -(node[i].p-node[i-1].p) |
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- f/D/2*node[i].rho*node[i].v^2*( |
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node[i].rho*vel[i]^2 - node[i-1].rho*vel[i-1]^2 |
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); |
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z_enbal[i]: dz * (A * drhou_dt[i] - qdot_t[i]) = - (node[i].Hdot - node[i-1].Hdot); |
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z_wall[i]: rho_w*A_w*c_w*dTw_dt[i] = qdot_s - qdot_l[i] - qdot_t[i]; |
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z_loss[i]: qdot_l[i] = h_ext*(1{PI}*D_2)*(T_w[i] - T_amb); |
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z_trans[i]: qdot_t[i] = h_int*(1{PI}*D) *(T_w[i] - node[i].T); |
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*) |
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END FOR; |
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|
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t IS_A time; |
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METHODS |
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METHOD bound_self; |
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vel[1..n].upper_bound := 100 {m/s}; |
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qdot_l[2..n].lower_bound := 0 {W/m}; |
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FOR i IN [1..n] DO |
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RUN node[i].bound_self; |
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END FOR; |
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END bound_self; |
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METHOD default_self; |
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D := 0.06 {m}; |
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D_2 := 0.07 {m}; |
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A_w := 0.25{PI}*D_2^2 -0.25{PI}*D^2; |
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FOR i IN [1..n] DO |
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RUN node[i].default_self; |
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END FOR; |
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END default_self; |
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METHOD values; |
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L := 1 {m}; |
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h_int := 100 {W/m^2/K}; |
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h_ext := 10 {W/m^2/K}; |
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f := 0.01; |
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node[1].mdot := 0.2 {kg/s}; |
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node[1].p := 7 {bar}; |
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node[1].x := 0.2; |
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qdot_s := 1000 {W/m^2} * D_2 * 10; |
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FOR i IN [2..n] DO |
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dmdot_dt[i] := 0.0 {kg/s/s}; |
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du_dt[i] := 0 {W/m^3}; |
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node[i].v := 0.2 {L/kg}; |
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node[i].rho := 6 {kg/L}; |
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node[i].dp_dT := +0.5 {kPa/K}; |
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node[i].p := 5 {bar}; |
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END FOR; |
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END values; |
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METHOD on_load; |
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RUN configure_steady; |
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RUN ode_init; |
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END on_load; |
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(*---------------- a physically sensible steady-state configuration-----------*) |
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METHOD configure_steady; |
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RUN default_self; |
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RUN ClearAll; |
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RUN specify_steady; |
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RUN bound_steady; |
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RUN values; |
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END configure_steady; |
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METHOD bound_steady; |
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RUN bound_self; |
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T_w[2..n].upper_bound := 1000 {K}; |
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END bound_steady; |
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METHOD specify_steady; |
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(* change to a proper steady-state problem, with fluid properties FREEd *) |
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FOR i IN [1..n] DO |
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RUN node[i].specify; |
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FIX dTw_dt[i]; FREE T_w[i]; |
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END FOR; |
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FIX node[1].p; |
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FREE node[1].T; |
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FIX qdot_s; |
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FIX D, D_2, L; |
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FIX h_int, c_w, rho_w, h_ext; |
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FIX f; |
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(* FIX mu_f; *) |
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FIX T_amb; |
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(* fix derivatives to zero *) |
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FOR i IN [2..n] DO |
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(* FIX dmdot_dt[i]; FREE node[i].mdot; *) |
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FREE node[i].x; FIX node[i].p; |
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FIX drho_dt[i]; FREE node[i].p; |
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FIX du_dt[i]; FREE node[i].T; |
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FREE mdot[i]; FIX dmdot_dt[i]; |
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END FOR; |
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END specify_steady; |
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(*------------------------- the dynamic problem ------------------------------*) |
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METHOD configure_dynamic; |
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FOR i IN [2..n] DO |
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FREE drho_dt[i]; FIX node[i].rho; |
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FREE dmdot_dt[i]; FIX node[i].mdot; |
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FREE du_dt[i]; FIX node[i].u; |
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FREE dTw_dt[i]; FIX T_w[i]; |
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FREE node[i].x; |
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FREE node[i].T; |
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END FOR; |
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t := 0 {s}; |
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END configure_dynamic; |
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METHOD free_states; |
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FOR i IN [2..n] DO |
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FREE node[i].rho; |
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FREE node[i].mdot; |
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FREE node[i].u; |
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FREE T_w[i]; |
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END FOR; |
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END free_states; |
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METHOD ode_init; |
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(* add the necessary meta data to allow solving with the integrator *) |
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t.ode_type := -1; |
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|
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FOR i IN [2..n] DO |
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drho_dt[i].ode_id := 4*i; node[i].rho.ode_id := 4*i; |
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drho_dt[i].ode_type := 2; node[i].rho.ode_type := 1; |
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|
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dmdot_dt[i].ode_id := 4*i+1; node[i].mdot.ode_id := 4*i+1; |
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dmdot_dt[i].ode_type := 2; node[i].mdot.ode_type := 1; |
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|
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du_dt[i].ode_id := 4*i+2; node[i].u.ode_id := 4*i+2; |
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du_dt[i].ode_type := 2; node[i].u.ode_type := 1; |
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|
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dTw_dt[i].ode_id := 4*i+3; T_w[i].ode_id := 4*i+3; |
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dTw_dt[i].ode_type := 2; T_w[i].ode_type := 1; |
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END FOR; |
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|
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FOR i IN [1..n] DO |
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p[i].obs_id := 1 + 10*i; |
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x[i].obs_id := 2 + 10*i; |
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node[i].mdot.obs_id := 4 + 10*i; |
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END FOR; |
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FOR i IN [2..n] DO |
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qdot_t[i].obs_id := 3 + 10*i; |
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T_w[i].obs_id := 5 + 10*i; |
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T[i].obs_id := 6 + 10*i; |
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END FOR; |
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END ode_init; |
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METHOD fix_outlet_quality; |
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FIX x[n]; |
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FREE node[1].mdot; |
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END fix_outlet_quality; |
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|
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END dsgsat3; |
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ADD NOTES IN dsgsat2; |
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'QRSlv' iterationlimit {50} |
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END NOTES; |
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