|
| 1 | +# 3D JWL Spherical TNT Free-Air Benchmark |
| 2 | + |
| 3 | +This benchmark is a 3D JWL/TNT free-air blast candidate for MFC. A spherical |
| 4 | +region of TNT detonation products expands into ambient air, and native point |
| 5 | +probes record pressure-time histories for arrival time, peak incident |
| 6 | +overpressure, and positive-phase impulse extraction. |
| 7 | + |
| 8 | +Reference values are intentionally not fabricated. The MFC probe extraction is |
| 9 | +implemented and the case runs, but the published reference values still need to |
| 10 | +be filled from the paper/CONWEP table before this should be described as |
| 11 | +completed validation. |
| 12 | + |
| 13 | +## Citation |
| 14 | + |
| 15 | +Giam, Toh, and Tan, "Numerical Review of Jones-Wilkins-Lee Parameters for |
| 16 | +Trinitrotoluene Explosive in Free-Air Blast," Journal of Applied Mechanics, |
| 17 | +2020. DOI: `10.1115/1.4046243`. |
| 18 | + |
| 19 | +The case is motivated by that free-air TNT/JWL review, but this repository does |
| 20 | +not currently include an accessible table of the paper's exact benchmark |
| 21 | +values. Until those values, Kingery-Bulmash/CONWEP values, or another trusted |
| 22 | +numeric free-air TNT reference are added, this is a benchmark candidate rather |
| 23 | +than completed validation. |
| 24 | + |
| 25 | +## Physics Scope |
| 26 | + |
| 27 | +This benchmark initializes TNT detonation products directly and validates 3D JWL product-air blast expansion. It does not model detonation initiation, reaction-zone structure, afterburn, or structural coupling. |
| 28 | + |
| 29 | +The benchmark exercises: |
| 30 | + |
| 31 | +- 3D JWL product-air expansion. |
| 32 | +- Radial free-air blast propagation in a Cartesian grid. |
| 33 | +- Native MFC pressure probes and post-processing. |
| 34 | +- A comparison framework for published or standard free-air blast quantities. |
| 35 | + |
| 36 | +The benchmark does not validate detonation initiation, reaction-zone physics, |
| 37 | +afterburn, structural coupling, confined blast, tunnel blast, or ground |
| 38 | +reflection. |
| 39 | + |
| 40 | +## Why This Is Genuinely 3D |
| 41 | + |
| 42 | +The default case resolves an octant of a spherical products region in a 3D |
| 43 | +Cartesian domain. The shock expands in x, y, and z, with active transverse |
| 44 | +reconstruction and Riemann fluxes. This is not a 1D shock tube extruded through |
| 45 | +the 3D solver path. |
| 46 | + |
| 47 | +Symmetry planes at `x = 0`, `y = 0`, and `z = 0` recover the full spherical |
| 48 | +solution while reducing the cell count by a factor of about eight. The probes |
| 49 | +lie near the positive x radial direction, at the nearest cell centers to the |
| 50 | +target radii. Keeping probes on cell centers avoids boundary and |
| 51 | +MPI-decomposition interpolation artifacts on the coarse default grid. |
| 52 | + |
| 53 | +## Geometry |
| 54 | + |
| 55 | +| Quantity | Value | |
| 56 | +|---|---:| |
| 57 | +| Charge center | `(0, 0, 0) m` in the octant representation | |
| 58 | +| Charge radius | `0.05 m` | |
| 59 | +| TNT/product reference density | `1630 kg/m^3` | |
| 60 | +| Full-sphere TNT mass | `0.853466 kg` | |
| 61 | +| Domain | `x, y, z in [0, 0.5] m` | |
| 62 | +| Final time | `2.0e-4 s` | |
| 63 | + |
| 64 | +The simulated octant contains one eighth of the full sphere. The symmetry |
| 65 | +boundaries make the resolved field equivalent to the full charge, so scaled |
| 66 | +distance uses the full TNT mass: |
| 67 | + |
| 68 | +```text |
| 69 | +W = (4/3) pi (0.05 m)^3 (1630 kg/m^3) = 0.853466 kg |
| 70 | +Z = r / W^(1/3) |
| 71 | +``` |
| 72 | + |
| 73 | +## Grid |
| 74 | + |
| 75 | +Default local grid: |
| 76 | + |
| 77 | +| Quantity | Value | |
| 78 | +|---|---:| |
| 79 | +| `m = n = p` | `63` | |
| 80 | +| Cells in octant | `64^3` | |
| 81 | +| Cell size | `0.0078125 m` | |
| 82 | +| Reconstruction | mapped WENO3 | |
| 83 | +| Riemann solver | HLLC | |
| 84 | +| Time stepper | RK3 | |
| 85 | +| CFL target | `0.3` | |
| 86 | + |
| 87 | +Lower-resolution smoke run: |
| 88 | + |
| 89 | +```bash |
| 90 | +./mfc.sh run benchmarks/3D_jwl_spherical_tnt_free_air_validation/case.py -n 4 -- --grid 31 |
| 91 | +python3 benchmarks/3D_jwl_spherical_tnt_free_air_validation/gauges.py --grid 31 |
| 92 | +``` |
| 93 | + |
| 94 | +The `64^3` octant default gives a visibly cleaner spherical shock than the |
| 95 | +older `32^3` smoke grid, but it takes several minutes and writes larger output |
| 96 | +files. |
| 97 | + |
| 98 | +## Boundary Conditions |
| 99 | + |
| 100 | +| Boundary | MFC value | Meaning | |
| 101 | +|---|---:|---| |
| 102 | +| `bc_x%beg`, `bc_y%beg`, `bc_z%beg` | `-2` | symmetry planes | |
| 103 | +| `bc_x%end`, `bc_y%end`, `bc_z%end` | `-3` | non-reflecting/open boundaries | |
| 104 | + |
| 105 | +## EOS And Initial Conditions |
| 106 | + |
| 107 | +Ambient air fills the full octant before the products sphere is overlaid: |
| 108 | + |
| 109 | +| Parameter | Value | |
| 110 | +|---|---:| |
| 111 | +| Air EOS | ideal gas/stiffened gas, `eos = 1` | |
| 112 | +| Air pressure | `101325 Pa` | |
| 113 | +| Air density | `1.225 kg/m^3` | |
| 114 | +| Air physical gamma | `1.4` | |
| 115 | +| MFC air `fluid_pp(2)%gamma` | `2.5` | |
| 116 | +| Air sound speed | `340.3 m/s` | |
| 117 | +| Air `cv` | `717.5 J/(kg K)` | |
| 118 | + |
| 119 | +TNT products use the JWL constants already present in the MFC JWL examples and |
| 120 | +benchmarks. They are documented here as the repo-local parameter source, not as |
| 121 | +a claim that these are the exact Giam et al. tabulated values: |
| 122 | + |
| 123 | +| Parameter | Value | |
| 124 | +|---|---:| |
| 125 | +| Products EOS | JWL, `eos = 2` | |
| 126 | +| Products density/reference density `rho0` | `1630 kg/m^3` | |
| 127 | +| Products volume-fraction floor | `1.0e-6` | |
| 128 | +| JWL `A` | `3.712e11 Pa` | |
| 129 | +| JWL `B` | `3.231e9 Pa` | |
| 130 | +| JWL `R1` | `4.15` | |
| 131 | +| JWL `R2` | `0.95` | |
| 132 | +| JWL `omega` | `0.30` | |
| 133 | +| Initial specific energy equivalent | `E0/rho0 = 6.1908e6 J/kg` | |
| 134 | +| Initial internal energy density `E0` | `1.0089e10 J/m^3` | |
| 135 | +| JWL cold pressure at `rho = rho0` | `6.2837e9 Pa` | |
| 136 | +| Initial products pressure | `9.3104e9 Pa` | |
| 137 | +| Products `cv` | `613.5 J/(kg K)` | |
| 138 | +| `jwl_air_e0` | `2.5575e5 J/kg` | |
| 139 | +| `jwl_air_rho0` | `1.225 kg/m^3` | |
| 140 | +| air Grüneisen (derived from `fluid_pp(2)%gamma`) | `1/2.5 = 0.4` | |
| 141 | + |
| 142 | +The initialized products pressure is computed in `case.py` from: |
| 143 | + |
| 144 | +```text |
| 145 | +p = A (1 - omega/(R1 V)) exp(-R1 V) |
| 146 | + + B (1 - omega/(R2 V)) exp(-R2 V) |
| 147 | + + omega E0, |
| 148 | +V = rho0 / rho = 1. |
| 149 | +``` |
| 150 | + |
| 151 | +## Probe Locations |
| 152 | + |
| 153 | +The default `--grid 63` run uses the nearest cell centers to target x positions |
| 154 | +`0.15, 0.25, 0.35, 0.45 m`: |
| 155 | + |
| 156 | +| Gauge | x (m) | y (m) | z (m) | r (m) | Z (m/kg^(1/3)) | |
| 157 | +|---:|---:|---:|---:|---:|---:| |
| 158 | +| 1 | 0.152344 | 0.003906 | 0.003906 | 0.152444 | 0.160712 | |
| 159 | +| 2 | 0.253906 | 0.003906 | 0.003906 | 0.253966 | 0.267741 | |
| 160 | +| 3 | 0.347656 | 0.003906 | 0.003906 | 0.347700 | 0.366558 | |
| 161 | +| 4 | 0.449219 | 0.003906 | 0.003906 | 0.449253 | 0.473618 | |
| 162 | + |
| 163 | +MFC's native probe interpolation can write a local initial pressure that differs |
| 164 | +from the analytic ambient state on this coarse octant grid. The reducer therefore |
| 165 | +uses each probe's first sample as its local baseline and reports pressure rise |
| 166 | +relative to that baseline. |
| 167 | + |
| 168 | +Arrival time is the first time the pressure rise exceeds 5 percent of ambient: |
| 169 | + |
| 170 | +```text |
| 171 | +p(t) - p(t=0) > 0.05 p_ambient |
| 172 | +``` |
| 173 | + |
| 174 | +Peak incident overpressure is estimated from the same baseline-corrected trace: |
| 175 | + |
| 176 | +```text |
| 177 | +dp_peak = max(p(t) - p(t=0)) |
| 178 | +``` |
| 179 | + |
| 180 | +Positive-phase impulse is integrated over the baseline-corrected history: |
| 181 | + |
| 182 | +```text |
| 183 | +I = integral max(p(t) - p(t=0), 0) dt |
| 184 | +``` |
| 185 | + |
| 186 | +## Run Commands |
| 187 | + |
| 188 | +From the repository root: |
| 189 | + |
| 190 | +```bash |
| 191 | +./mfc.sh run benchmarks/3D_jwl_spherical_tnt_free_air_validation/case.py -n 4 |
| 192 | +python3 benchmarks/3D_jwl_spherical_tnt_free_air_validation/gauges.py |
| 193 | +./mfc.sh precheck |
| 194 | +``` |
| 195 | + |
| 196 | +The probe reducer reads: |
| 197 | + |
| 198 | +```text |
| 199 | +benchmarks/3D_jwl_spherical_tnt_free_air_validation/D/probe<i>_prim.dat |
| 200 | +``` |
| 201 | + |
| 202 | +and writes: |
| 203 | + |
| 204 | +```text |
| 205 | +benchmarks/3D_jwl_spherical_tnt_free_air_validation/gauge_results.csv |
| 206 | +``` |
| 207 | + |
| 208 | +## Comparison Table |
| 209 | + |
| 210 | +| Gauge | r (m) | Z (m/kg^(1/3)) | MFC arrival (s) | Ref arrival (s) | MFC peak dp (Pa) | Ref peak dp (Pa) | MFC impulse (Pa s) | Ref impulse (Pa s) | Error | |
| 211 | +|---|---:|---:|---:|---:|---:|---:|---:|---:|---:| |
| 212 | +| 1 | 0.152444 | 0.160712 | 8.000000e-06 | pending reference | 9.189414e+06 | pending reference | 1.142617e+03 | pending reference | pending | |
| 213 | +| 2 | 0.253966 | 0.267741 | 3.700000e-05 | pending reference | 7.494431e+06 | pending reference | 3.127588e+02 | pending reference | pending | |
| 214 | +| 3 | 0.347700 | 0.366558 | 7.200000e-05 | pending reference | 5.750937e+06 | pending reference | 2.453974e+02 | pending reference | pending | |
| 215 | +| 4 | 0.449253 | 0.473618 | 1.150000e-04 | pending reference | 4.023872e+06 | pending reference | 3.029903e+02 | pending reference | pending | |
| 216 | + |
| 217 | +Reference values may be filled from Giam et al. if numeric values are available, |
| 218 | +from Kingery-Bulmash/CONWEP free-air TNT data if used for comparison, or from |
| 219 | +another clearly cited spherical free-air TNT reference. If values are digitized |
| 220 | +from a figure, label them as digitized estimates. |
| 221 | + |
| 222 | +## Pass/Fail Expectations |
| 223 | + |
| 224 | +This candidate benchmark passes its local sanity checks when: |
| 225 | + |
| 226 | +- The case completes without NaNs. |
| 227 | +- Density, pressure, and internal energy remain positive. |
| 228 | +- Shock arrival time increases monotonically with radius. |
| 229 | +- Peak incident overpressure decreases monotonically with radius. |
| 230 | +- The pressure histories show a radially reasonable outward blast. |
| 231 | + |
| 232 | +Quantitative error should be reported only after trusted reference arrival, |
| 233 | +peak incident overpressure, and impulse values are added. |
| 234 | + |
| 235 | +## Limitations And Remaining Work |
| 236 | + |
| 237 | +- This is not completed validation until the reference columns are populated. |
| 238 | +- A `32^3` octant run is available as a faster smoke test, but the default is now `64^3`. |
| 239 | +- The products sphere initialization does not model a detonation wave or |
| 240 | + reaction zone. |
| 241 | +- No afterburn, structural coupling, confinement, or ground reflection is |
| 242 | + represented. |
| 243 | +- A higher-resolution run should be used before drawing quantitative |
| 244 | + conclusions. |
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