| 1 |
REQUIRE "atoms.a4l"; |
| 2 |
|
| 3 |
ATOM energy_rate_per_length REFINES solver_var |
| 4 |
DIMENSION M*L/T^3 |
| 5 |
DEFAULT 1000{W/m}; |
| 6 |
lower_bound := -1e50{W/m}; |
| 7 |
upper_bound := 1e50{W/m}; |
| 8 |
nominal := 1000{W/m}; |
| 9 |
END energy_rate_per_length; |
| 10 |
|
| 11 |
ATOM energy_flux REFINES solver_var |
| 12 |
DIMENSION M/T^3 |
| 13 |
DEFAULT 1000{W/m^2}; |
| 14 |
lower_bound := -1e50{W/m^2}; |
| 15 |
upper_bound := 1e50{W/m^2}; |
| 16 |
nominal := 1000{W/m^2}; |
| 17 |
END energy_flux; |
| 18 |
|
| 19 |
ATOM heat_transfer_coefficient REFINES solver_var |
| 20 |
DIMENSION M/T^3/TMP |
| 21 |
DEFAULT 5{W/m^2/K}; |
| 22 |
|
| 23 |
lower_bound := 0{W/m^2/K}; |
| 24 |
upper_bound := 1e50{W/m^2/K}; |
| 25 |
nominal := 5{W/m^2/K}; |
| 26 |
|
| 27 |
END heat_transfer_coefficient; |
| 28 |
|
| 29 |
MODEL cavity; |
| 30 |
W,B,S,N,C,E,D IS_A distance; |
| 31 |
theta, phi, psi IS_A angle; |
| 32 |
|
| 33 |
F_WN, F_WW, F_WB IS_A factor; |
| 34 |
F_NB, F_NW, F_NN, F_BW, F_BN IS_A factor; |
| 35 |
F_WS IS_A factor; |
| 36 |
|
| 37 |
N * sin(theta) = D; |
| 38 |
S * tan(theta) = D; |
| 39 |
B = W + 2 * S; |
| 40 |
E^2 = W^2 + D^2; |
| 41 |
phi = arctan(D/W); |
| 42 |
psi = 1{PI} - phi; |
| 43 |
C^2 = E^2 + S^2 - 2* E * S * cos(psi); |
| 44 |
|
| 45 |
F_WN = (W+N-C)/2/W; |
| 46 |
F_WW = (2*E-2*D)/2/W; (* from top to directly opp part of bottom *) |
| 47 |
F_WB = 1 - 2 * F_WN; |
| 48 |
F_WS = (1 - 2 * F_WN - F_WB)/2; |
| 49 |
F_NB = (N+B-C)/2/N; |
| 50 |
F_NW = (N+W-C)/2/N; |
| 51 |
|
| 52 |
F_BN = F_NB*N/B; |
| 53 |
F_NN = 1 - F_NW - F_NB; |
| 54 |
F_BW = F_WB*W/B; |
| 55 |
|
| 56 |
n IS_A set OF symbol_constant; |
| 57 |
n :== ['W','B','L','R']; |
| 58 |
|
| 59 |
(* Put lengths into a vector *) |
| 60 |
|
| 61 |
A[n] IS_A distance; |
| 62 |
A['W'], W ARE_THE_SAME; |
| 63 |
A['B'], B ARE_THE_SAME; |
| 64 |
A['L'], N ARE_THE_SAME; |
| 65 |
A['R'], N ARE_THE_SAME; |
| 66 |
|
| 67 |
(* View factor matrix *) |
| 68 |
|
| 69 |
F[n][n] IS_A factor; |
| 70 |
|
| 71 |
F['W']['L'], F['W']['R'], F_WN ARE_THE_SAME; |
| 72 |
F['W']['B'], F_WB ARE_THE_SAME; |
| 73 |
F['W']['W'] = 0; |
| 74 |
|
| 75 |
F['B']['L'], F['B']['R'], F_BN ARE_THE_SAME; |
| 76 |
F['B']['W'], F_BW ARE_THE_SAME; |
| 77 |
F['B']['B'] = 0; |
| 78 |
|
| 79 |
F['L']['R'], F['R']['L'], F_NN ARE_THE_SAME; |
| 80 |
F['L']['B'], F['R']['B'], F_NB ARE_THE_SAME; |
| 81 |
F['L']['W'], F['R']['W'], F_NW ARE_THE_SAME; |
| 82 |
F['L']['L'] = 0; |
| 83 |
F['R']['R'] = 0; |
| 84 |
|
| 85 |
(* Radiation equations *) |
| 86 |
q[n] IS_A energy_rate_per_length; |
| 87 |
|
| 88 |
E_b[n] IS_A energy_flux; |
| 89 |
J[n] IS_A energy_flux; |
| 90 |
T[n] IS_A temperature; |
| 91 |
eps[n] IS_A factor; (* emissivity *) |
| 92 |
|
| 93 |
FOR i IN n CREATE |
| 94 |
q[i] = SUM[ (J[i]-J[j])*(A[i]*F[i][j]) | j IN n]; |
| 95 |
END FOR; |
| 96 |
|
| 97 |
FOR i IN n CREATE |
| 98 |
E_b[i] = 1{SIGMA_C} * T[i]^4; |
| 99 |
END FOR; |
| 100 |
|
| 101 |
FOR i IN n CREATE |
| 102 |
q[i] * (1-eps[i]) = (E_b[i] - J[i]) * (eps[i]*A[i]); |
| 103 |
END FOR; |
| 104 |
|
| 105 |
METHODS |
| 106 |
METHOD default_self; |
| 107 |
RUN reset; RUN values; RUN bound_self; |
| 108 |
END default_self; |
| 109 |
|
| 110 |
METHOD bound_self; |
| 111 |
phi.lower_bound := 0 {deg}; |
| 112 |
phi.upper_bound := 90 {deg}; |
| 113 |
psi.lower_bound := 90 {deg}; |
| 114 |
psi.upper_bound := 180 {deg}; |
| 115 |
END bound_self; |
| 116 |
|
| 117 |
METHOD specify; |
| 118 |
FIX T['W', 'B']; |
| 119 |
FIX q['L','R']; |
| 120 |
FIX W,D,theta; |
| 121 |
FIX eps[n]; |
| 122 |
END specify; |
| 123 |
|
| 124 |
METHOD values; |
| 125 |
T['W'] := 550 {K}; |
| 126 |
T['B'] := 373.15 {K}; |
| 127 |
q['L','R'] := 0 {W/m}; |
| 128 |
|
| 129 |
W := 500 {mm}; |
| 130 |
D := 300 {mm}; |
| 131 |
theta := 30 {deg}; |
| 132 |
|
| 133 |
eps['W'] := 0.49; |
| 134 |
eps['B'] := 0.9; |
| 135 |
eps['L','R'] := 0.1; |
| 136 |
|
| 137 |
END values; |
| 138 |
|
| 139 |
END cavity; |
| 140 |
|
| 141 |
(*======================================== |
| 142 |
This model adds external convection |
| 143 |
coefficients to the model, and an |
| 144 |
ambient temperature. |
| 145 |
|
| 146 |
We also calculate the F_rad correlation |
| 147 |
parameter. |
| 148 |
*) |
| 149 |
MODEL cavity_losses REFINES cavity; |
| 150 |
h_B, h_N IS_A heat_transfer_coefficient; |
| 151 |
T_amb IS_A temperature; |
| 152 |
|
| 153 |
- q['B'] = h_B * B * (T['B'] - T_amb); |
| 154 |
- q['L'] = h_N * N * (T['L'] - T_amb); |
| 155 |
- q['R'] = h_N * N * (T['L'] - T_amb); |
| 156 |
|
| 157 |
F_rad IS_A factor; |
| 158 |
F_rad_1 IS_A factor; |
| 159 |
|
| 160 |
- q['B'] = F_rad * eps['W'] * 1{SIGMA_C} * (T['W']^4 - T['B']^4); |
| 161 |
|
| 162 |
- q['B'] = F_rad_1 * 1{SIGMA_C} * (T['W']^4 - T['B']^4) / |
| 163 |
(1/eps['B'] + 1/eps['W'] - 1); |
| 164 |
|
| 165 |
METHODS |
| 166 |
METHOD specify; |
| 167 |
FIX T['W'], T_amb; |
| 168 |
FIX h_B, h_N; |
| 169 |
FIX W,D,theta; |
| 170 |
FIX eps[n]; |
| 171 |
END specify; |
| 172 |
METHOD values; |
| 173 |
T['W'] := 550 {K}; |
| 174 |
T_amb := 290 {K}; |
| 175 |
W := 500 {mm}; |
| 176 |
D := 300 {mm}; |
| 177 |
theta := 30 {deg}; |
| 178 |
eps['W'] := 0.49; |
| 179 |
eps['B'] := 0.9; |
| 180 |
eps['L','R'] := 0.1; |
| 181 |
h_B := 10 {W/m^2/K}; |
| 182 |
h_N := 0.5 {W/m^2/K}; |
| 183 |
(* free values *) |
| 184 |
T['L','R'] := 500 {K}; |
| 185 |
T['B'] := 400 {K}; |
| 186 |
END values; |
| 187 |
END cavity_losses; |
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