XSDAppAB.rst.txt 15 KB
 Batson Iii committed Jan 19, 2021 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 .. _9-1AB: XSDRNPM Appendices A and B ========================== .. _9-1a: XSDRNPM APPENDIX A: Special XSDRNPM Files ----------------------------------------- Three special files that can be optionally produced by XSDRNPM are described in this appendix. (See Sect. 10.1.5 and the discussion of the logical units in the 0$array.) The files will be created with file names of the form **ftNNfXXX.EXT** where **NN** is the 2 digit logical unit number (from the 0$$array), **XXX** is a 3 digit number which is incremented by one starting with one to make the name unique, and **EXT** is an extension identifying which type of file it is (**acf** for activity file, **btf** for balance table file, and **idf** for input and derived data file). .. _9-1a-1: Activity file ~~~~~~~~~~~~~ The data on the activity file depends on what input options are specified. The data is in ASCII sets, which consist of a label record followed by the record(s) of the activity. There will be at most **IAZ** sets ordered as the 49 and 50 arrays. The first sets of data will be the activities by interval (if the input parameter **IAI** was specified). A set will be formatted as below. **activity by interval for nuclide** *nnnnnnnn* **reaction type** *rrrrrrrr* **Activity(first interval)** **.** **.** **.** **.** **Activity(last interval)** The preceding set will be repeated **IAZ** times. Then sets giving the activities by zone will be given. They will be formatted as below. | **activity by zone for nuclide** *nnnnnnnn* **reaction** *rrrrrrrr* | **Activity(first zone)** **.** **.** **.** **.** **Activity(last zone)** .. _9-1a-2: Balance table file ~~~~~~~~~~~~~~~~~~ The contents of the balance table are defined in :numref:tab9-1a-1 and :numref:tab9-1a-2. The structure of the “balance table file” written to **LBTF** is: Record 1 **KEFF, SP** **KEFF** – k\ :sub:effective for problem **SP** – search parameter for case Record 2 – Sets of ASCII data consisting of a label record followed by data records. Record last A set of data is as follows (igp is the total number of groups plus one): **fine(few) group summary for zone** *zzzzz* **set type** **Set type data(group 1)** **Set type data(group 2)** **.** **.** **.** **.** **Set type data(group igp)** The data for a set type will be written for each zone of the problem, plus a system summary if there is more than one zone. After one set type is finished, the next set type will be written. The order of the set types is as follows: **fixed source** **fission source** **absorption rate** **total leakage** **fission rate** **flux** ** rate** **buckling loss** **right current** **left current** **right leakage** **left leakage** The fine group summary data will be written if **LBTF** is > 0. After the fine group data is finished, the few group summary data will follow if a weighting calculation is specified with a broad group collapse. .. _9-1a-3: Input and derived data file ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The contents of the input and derived data file (specified by **LIDF**) is as follows: Record 1 – **title** (80 characters) Record 2 – **1$$ array** (label) Record 3,4 – **data from 1$ array** Record 5 – **2$$array** (label) Record 6 – **data from 2 array** Record 7 – **3$$ array** (label) Record 8,9 – **data from 3\$ array** Record 10 – **4array** (label) Record 11 – **data from 4 array** Record 12 – **5*\* array** (label) Record 13,14 – **data from the 5\* array** Record 15 – **cross section parameters** (label) Record 16 – **total groups, neutron groups, gamma groups, first thermal group** Record 17 – **nuclides on library** (label) Records 17a – **list of nuclides on the cross section library** Record 18 – **mixture numbers** (label) Records 18a – **data from the 13 array** Record 19 – **component numbers** (label) Records 19a – **data from the 14 array** Record 20 – **densities** (label) Records 20a – **data from the 15\* array** Record 21 – **cccc identifiers** (label) Records 21a – **data from the 16 array** Record 22 – **neutron energy group boundaries** (label) Records 22a –- **list of the energy boundaries for the neutron groups** Record 23 – **neutron lethargy group boundaries** (label) Records 23a – **list of the lethargy boundaries for the neutron groups** Record 24 – **neutron weighted velocities** (label) Record 24a – **list of the neutron average velocities** Record 25 – **gamma energy group boundaries** (label) Record 25a – **list of the energy boundaries for the gamma groups** Record 26 – **gamma lethargy group boundaries** (label) Records 26a – **list of the lethargy boundaries for the gamma groups** Record 27 – **gamma weighted velocities** (label) Records 27a – **list of the gamma velocities** Record 28 – **broad group numbers** (label) Records 28a – **list of the broad group numbers by fine group - 51 array** Record 29 – **group band** (label) Records 29a – **group band numbers by fine group** Record 30 – **calculation type** (label) Records 30a – **calculation type by fine group** Record 31 – **right albedo** (label) Records 31a – **list of the right boundary albedos by group - 47\* array** Record 32 – **left albedo** (label) Records 32a – **list of the left boundary albedos by group - 48\* array** Record 34 – **mixture by zone** (label) Records 34a – **data from the 39 array** Record 35 – **order of scattering by zone** (label) Records 35a – **data from the 40 array** Record 36 – **activity materials** (label) Records 36a – **data from the 49 array** Record 37 – **activity reaction types** (label) Records 37a – **data from the 50 array** Record 38 – **quadrature weights** (label) Records 38a – **data from the 43\* array** Record 39 – **quadrature cosines** (label) Records 39a – **data from the 42\* array** Record 40 – **weights x cosines** (label) Records 40a – **product of quadrature weights times quadrature** Record 41 – **reflected directions** (label) Records 41a – **reflected direction index array** Record 42 – **pl scattering constants** (label) Records 42a – **constants for converting from discrete angles to Legendre moments** Record 43 – **interval boundaries** (label) Records 43a – **data from the 35\* array** Record 44 – **interval midpoints** (label) Records 44a – **array containing the midpoints of each interval** Record 45 – **zone by interval** (label) Records 45a – **data from the 36 array** Record 46 – **interval boundary areas** (label) Records 46a – **area of each interval boundary** Record 47 – **interval volumes** (label) Records 47a – **volume of each interval** Record 48 – **interval density factors** (label) Records 48a – **data from the 38\* array** Record 49 – **zone width modifiers** (label) Records 49a – **data from the 41\* array** Record 50 – **source spectrum by interval** (label) Records 50a – **data from the 30 array** .. _tab9-1a-1: .. list-table:: Balance table definitions. :align: center :class: longtable :widths: 30 * - **FS** = Fission Source\ :sub:grp,zone = :math:1 / \lambda \Sigma_{\text {i} \subset \text{zone}}\left[X_{i, \operatorname{grp}} \Sigma_{\operatorname{grp}^{\prime}}\left(v \Sigma_{\text {fgrp }^{\prime}, i} \varphi_{\text {grp }^{\prime}, \mathrm{i}}\right) V_{i}\right] * - **XS** = Fixed Source\ :sub:grp,zone = :math:\Sigma_{1 \subset \text{zone} \text{}}\left[Q_{\text {grp }, i} V_{i}+A_{i} \Sigma_{\mu m>0} B S_{i, \text { grp, } m} \mu_{m} w_{m}-A_{i+1} \Sigma_{\mu m<0} B S_{i, \text { grp }, m} \mu_{m} w_{m}\right] * - **IS** = Inscatter\ :sub:grp,zone = :math:\Sigma_{\text {i} \subset \text{zone}} \sum_{j \neq \operatorname{grp}}\left[\Sigma_{j \rightarrow \operatorname{grp}, i} \varphi_{j, i} V_{i}\right] * - **SS** = Selfscatter\ :sub:grp,zone = :math:\Sigma_{\text {i} \subset \text{zone}}\left[\Sigma_{\text {grp } \rightarrow \operatorname{grp}} \varphi_{\text {grp }, \mathrm{i}} \mathrm{V}_{\mathrm{i}}\right] * - **OS** = Outscatter\ :sub:grp,zone = :math:\Sigma_{\text {i} \subset \text{zone}} \sum_{j \neq \operatorname{grp}}\left[\sum_{\operatorname{grp} \rightarrow j} \varphi_{\text {grp }, i} V_{i}\right] * - **AB** = Absorption\ :sub:grp,zone = :math:\Sigma_{\text {i} \subset \text{zone}}\left[\Sigma_{\text {abs grp }, i} \varphi_{\text {grp }, \mathrm{i}} \mathrm{V}_{\mathrm{i}}\right] * - **LK** = Leakage\ :sub:grp,zone = :math:\left\lbrack A_{\text{zr}}\Sigma_{m}\left( \psi_{m,\mathrm{\mspace{6mu}}\text{zr}}\mu_{m}w_{m} \right)\mathrm{\quad} - \mathrm{\quad}A_{z1}\Sigma_{m}\left( \psi_{m,\mathrm{\mspace{6mu}}z1}\mu_{m}w_{m} \right) \right\rbrack * - **RF** = Right Boundary Flux\ :sub:grp,zone = :math:\Sigma_{\mathrm{m}}\left(\psi_{\mathrm{m}, \mathrm{zr}, \mathrm{grp}} \mathrm{W}_{\mathrm{m}}\right) * - **LF** = Left Boundary Flux\ :sub:grp,zone = :math:\Sigma_{\mathrm{m}}\left(\psi_{\mathrm{m}, \mathrm{zr}, \mathrm{grp}} \mathrm{W}_{\mathrm{m}}\right) * - **RL** = Right Leakage\ :sub:grp,zone = :math:\mathrm{A}_{\mathrm{zr}} \Sigma_{\mathrm{m}}\left(\psi_{\mathrm{m}, \mathrm{zr}, \mathrm{grp}} \mu_{\mathrm{m}} \mathrm{W}_{\mathrm{m}}\right) * - **LL** = Left Leakage\ :sub:grp,zone = :math:A_{z l} \Sigma_{m}\left(\psi_{m, z l, g r p} \mu_{m} W_{m}\right) * - **NN** = n,2n Rate\ :sub:grp,zone = :math:\Sigma_{i \subset \text { zone }} \Sigma_{p \geq 2}\left[p / 2 \Sigma_{n, p n} \varphi_{g r p, i} V_{i}\right] * - **FR** = Fission Rate\ :sub:grp,zone = :math:\sum_{i \subset \text { zone }}\left[\Sigma_{f g r p, i} \varphi_{g r p, i} V_{i}\right] * - **DB** = DB\ :sup:2 Flux\ :sub:grp,zone = :math:\sum_{i \subset zone}\left[D_{g r p, i} B_{g r p, i}^{2} \varphi_{g r p, i} V_{i}\right] * - **TF** = Total Flux\ :sub:grp,zone = :math:\sum_{i \subset z o n e}\left[\varphi_{g r p, i} V_{i}\right] * - **BAL = {FS+XS+IS+NN+max(LL,0)-min(RL,0)} / {OS+AB+max(RL,0)-min(LL,0)}** .. _tab9-1a-2: .. list-table:: Balance table definition symbols. :align: center :class: longtable :width: 30 * - :math:\sum_{\mathrm{i} \subset \mathrm{zone}} is the sum over all intervals i in the zone * - :math:\sum_{\mathrm{grp}} is the sum over all groups grp * - :math:\sum_{j \neq g r p} is the sum over all groups j not equal to group grp * - :math:\sum_{\mathrm{m}} is the sum over the quadrature * - :math:\sum_{\mathrm{p} \geq 2} is the sum over all processes :math:\sum_{\mathrm{n}, \mathrm{pn}} * - :math:\lambda \quad=\text { the eigenvalue } * - :math:\chi \quad=\text { the fission spectrum } * - :math:\mathbf{V} = the average number of neutrons produced in a fission * - :math:\sum_{\mathrm{f}} = the fission cross section * - :math:\varphi = the scalar flux * - V = the volume of a mesh interval * - Q = the volumetric external source in a mesh interval * - A = the area of a boundary of a mesh interval * - BS = the angular flux boundary source on an interval boundary * - :math:\mu_{\mathrm{m}} = the mth discrete angle of the quadrature * - :math:\mathrm{W}_{\mathrm{m}} = the mth weight of the quadrature * - :math:\sum_{j \rightarrow g r p} = the scattering cross section for scattering from group j to group grp * - :math:\sum_{\mathrm{grp} \rightarrow \mathrm{j}} = the scattering cross section for scattering from group grp to group j * - :math:\sum_{\operatorname{grp} \rightarrow \operatorname{grp}} = the scattering cross section for within-group scattering (i.e., from group grp to the same group grp) * - :math:\sum_{\mathrm{abs}} = the absorption cross section * - :math:\psi = the angular flux * - A\ :sub:zr = the area of the right-hand boundary of the zone * - A\ :sub:zl = the area of the left-hand boundary of the zone * - :math:\sum_{\mathrm{n}, \mathrm{pn}} = the cross section for producing p neutrons, p=2,3,...,p an integer * - D = the diffusion coefficient (used in providing a buckling correction for 2 and 3 dimensions) * - B\ :sup:2 = the buckling for the second and third dimensions (includes an extrapolation distance) * - **max(LL,0)** means that a positive Left Leakage is a source into the zone * - **min(RL,0)** means that a negative Right Leakage is a source into the zone. It is included with a minus sign to make it a positive source * - **max(RL,0)** means that a positive Right Leakage is a loss from the zone * - **min(LL,0)** means that a negative Left Leakage is a loss from the zone. It is included with a minus sign to make it a positive loss .. _9-1b: APPENDIX B: XSDRNPM Mixed Cross Sections ---------------------------------------- When **IPRT** (2 array) is set > −1, XSDRNPM prints the mixed reaction rate cross sections that are used in its calculations. The order of the cross sections for each group is given below in :numref:tab9-1b-1. The diffusion coefficient is used in computing buckling corrections, and in some of the options for computing the current used in weighting the transport cross section. The upscatter cross section is used to checking upscatter convergence. The cross section is used in computing the balance for the balance tables. It is actually a weighted sum of all the multiple neutron exit reactions other than fission. These are all treated in XSDRNPM as scattering reactions. Chi is the fission spectrum, and is used to distribute the fission source in energy space. The fission cross section is used to compute the fission rate reported in the balance tables. The absorption cross section is used to compute the absorptions in the balance tables, and to compute the absorption term in the eigenvalue. Nu*fission cross section is used to generate the source term for all except a fixed source calculation. The total cross section is used to determine the neutron transport. .. _tab9-1b-1: .. table:: Order of mixed reaction cross sections :align: center +------------------------------------------------------------+ | 1. Diffusion coefficient (for use in buckling corrections) | +------------------------------------------------------------+ | 2. Upscatter cross section | +------------------------------------------------------------+ | 3. cross section | +------------------------------------------------------------+ | 4. Chi (fission spectrun) | +------------------------------------------------------------+ | 5. Fission cross section | +------------------------------------------------------------+ | 6. Absorption cross section | +------------------------------------------------------------+ | 7. Nu*Fission cross section | +------------------------------------------------------------+ | 8. Total cross section | +------------------------------------------------------------+ ....