Table 1
Different tank categories in the SAE J2601.
| PRESSURE CLASS | WATER VOLUME OF CHSS (L) | CHSS CAPACITY CATEGORY |
|---|---|---|
| H35 | 49.7–99.4 | A |
| H35 | 99.4–174 | B |
| H35 | 174–248.6 | C |
| H70 | 49.7–99.4 | A |
| H70 | 99.4–174 | B |
| H70 | 174–248.6 | C |
| H70 | >248.6 | D |
[i] Abbreviation: CHSS: compressed hydrogen storage system.
Adapted from Table 8 from SAE International (2020).
Figure 1
Simplified P&ID of the HRS section between the control valve and the CHSS of the FCEV. The data measured by the dispenser and transmitted by the FCEV are reported in the figure.
Abbreviations: CHSS: compressed hydrogen storage system; FCEV: fuel cell electric vehicle; HRS: hydrogen refueling station; P&ID: piping and instrumentation diagram.
Figure 2
Flowchart of the diabatic formulation.
Table 2
Coefficient table for the polynomial functions Ciso(P, T), Cadia(P, T, Tinj) and Ccp–eff(P, T).
| TERM | Ciso COEFFS | Cp-eff COEFFS | Cadia COEFFS |
|---|---|---|---|
| 1 | 1.1283600E+06 | 8.0916516E+02 | 1.5907225E+06 |
| Tinj | 0.0000000E+00 | 0.0000000E+00 | 5.8152799E+03 |
| Tinj2 | 0.0000000E+00 | 0.0000000E+00 | 1.0473866E+00 |
| Tinj3 | 0.0000000E+00 | 0.0000000E+00 | –4.3391871E–03 |
| Tinj4 | 0.0000000E+00 | 0.0000000E+00 | 8.6699560E–06 |
| Tinj5 | 0.0000000E+00 | 0.0000000E+00 | –2.4108136E–08 |
| T | 4.1345584E+03 | –2.1782544E–01 | –2.2584316E+02 |
| T*Tinj | 0.0000000E+00 | 0.0000000E+00 | –2.9014440E+00 |
| T*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | –5.9850516E–04 |
| T*Tinj3 | 0.0000000E+00 | 0.0000000E+00 | 2.8617328E–06 |
| T*Tinj4 | 0.0000000E+00 | 0.0000000E+00 | –1.9133298E–08 |
| T2 | –3.9128813E–01 | 4.5885629E–02 | 2.3204987E+00 |
| T2*Tinj | 0.0000000E+00 | 0.0000000E+00 | 2.6318857E–02 |
| T2*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | 3.2417329E–06 |
| T2*Tinj3 | 0.0000000E+00 | 0.0000000E+00 | –2.6388874E–08 |
| T3 | 4.8869951E–03 | –1.0613305E–03 | –1.9312110E–02 |
| T3*Tinj | 0.0000000E+00 | 0.0000000E+00 | –2.0154968E–04 |
| T3*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | –9.3200198E–09 |
| T4 | 1.0076258E–06 | 3.0320051E–06 | 2.1059983E–04 |
| T4*Tinj | 0.0000000E+00 | 0.0000000E+00 | 8.5624925E–07 |
| T5 | –1.6012029E–07 | 2.1608048E–08 | –1.0304455E–06 |
| P | 1.3614112E+04 | 8.9668248E+03 | 2.1697410E+04 |
| P*Tinj | 0.0000000E+00 | 0.0000000E+00 | 6.3710870E+01 |
| P*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | –4.5069595E–02 |
| P*Tinj3 | 0.0000000E+00 | 0.0000000E+00 | 5.2637944E–05 |
| P*Tinj4 | 0.0000000E+00 | 0.0000000E+00 | 1.5242998E–07 |
| P*T | 2.2820956E+01 | –2.9038600E+01 | –5.3663267E+01 |
| P*T*Tinj | 0.0000000E+00 | 0.0000000E+00 | –2.7913640E–01 |
| P*T*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | 1.0626895E–05 |
| P*T*Tinj3 | 0.0000000E+00 | 0.0000000E+00 | 8.8698092E–08 |
| P*T2 | –5.4810045E–02 | 6.9133477E–02 | 3.4922958E–01 |
| P*T2*Tinj | 0.0000000E+00 | 0.0000000E+00 | 1.2330859E–03 |
| P*T2*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | –4.7593259E–09 |
| P*T3 | –3.0271457E–04 | –2.8540368E–05 | –1.9932921E–03 |
| P*T3*Tinj | 0.0000000E+00 | 0.0000000E+00 | –2.3767989E–06 |
| P*T4 | 1.3146260E–06 | –2.6105553E–07 | 4.1096764E–06 |
| P2 | 1.6414600E+02 | –5.0523257E+01 | 1.8501464E+02 |
| P2*Tinj | 0.0000000E+00 | 0.0000000E+00 | –3.4170773E–01 |
| P2*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | 7.5245467E–04 |
| P2*Tinj3 | 0.0000000E+00 | 0.0000000E+00 | –9.1746565E–07 |
| P2*T | –1.0389051E+00 | 3.1786849E–01 | –8.8709648E–01 |
| P2*T*Tinj | 0.0000000E+00 | 0.0000000E+00 | 1.3000849E–03 |
| P2*T*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | –1.4771480E–07 |
| P2*T2 | 3.2574499E–03 | –1.0656155E–03 | 1.5205511E–03 |
| P2*T2*Tinj | 0.0000000E+00 | 0.0000000E+00 | –5.3952236E–06 |
| P2*T3 | –1.8807052E–06 | 1.0760745E–06 | 5.8572045E–06 |
| P3 | –1.5591316E+00 | 1.9073393E–01 | –1.9570425E+00 |
| P3*Tinj | 0.0000000E+00 | 0.0000000E+00 | 1.3755835E–03 |
| P3*Tinj2 | 0.0000000E+00 | 0.0000000E+00 | –3.6679280E–06 |
| P3*T | 8.2229225E–03 | –1.6978191E–03 | 9.6192507E–03 |
| P3*T*Tinj | 0.0000000E+00 | 0.0000000E+00 | –1.1676633E–06 |
| P3*T2 | –1.7633706E–05 | 4.5014322E–06 | –1.8160604E–05 |
| P4 | 9.6056237E–03 | 8.2909304E–05 | 1.2227065E–02 |
| P4*Tinj | 0.0000000E+00 | 0.0000000E+00 | –2.6843097E–06 |
| P4*T | –2.4421704E–05 | 3.2439269E–06 | –3.1950194E–05 |
| P5 | –2.7419060E–05 | –2.6875205E–06 | –3.4507177E–05 |
Figure 3
Flowchart of the iterative method.
Figure 4
View of the 243.6 L thermocouple tree. It is placed in front of the tank for visualization but is then inserted inside the tank volume during the refueling tests. A zoomed view at the upper tank part highlights with white circles the presence of the thermocouple probes on the thermocouple tree branches. The thermocouple tree is symmetrical.
Figure 5
Plotting of the experimental data measured during the eight refueling steps of the type IV 243.6 L tank.
Table 3
Numerical applications of the volume estimation formula based on the experimental data.
| TEST # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Ptank(t0) (MPa(g)) | 2.8 | 11.48 | 20.61 | 31.12 | 2.79 | 10.98 | 20.75 | 30.65 |
| Tamb(t0) (°C) | 29.15 | 30.59 | 30.4 | 30.77 | 27.79 | 28.41 | 29.18 | 31.36 |
| Tinj (°C) | –20.05 | –18.75 | –16.54 | –16.7 | –27.45 | –26.03 | –27.94 | –29.06 |
| Δt (s) | 37 | 35 | 34 | 21 | 40 | 37 | 33 | 28 |
| ΔPtank (MPa) | 2.23 | 2.99 | 3.43 | 2.38 | 2.34 | 3.08 | 3.5 | 3.67 |
| Δm (kg) | 0.38 | 0.42 | 0.43 | 0.25 | 0.39 | 0.45 | 0.44 | 0.41 |
| ΔTtank (°C) | 8.01 | 8.20 | 6.55 | 3.40 | 8.55 | 8.32 | 5.98 | 4.89 |
| ΔTSAE (°C) | 23.91 | 15.24 | 10.36 | 8.07 | 23.92 | 15.62 | 10.31 | 8.13 |
| Viso (L) Relative error % | 220.2 –9.6 | 206.4 ⚠ –15.3 | 203.7 ⚠ –16.4 | 192.0 ⚠ –21.2 | 218.5 –10.3 | 208.8 –14.3 | 206.4 ⚠ –15.3 | 202.4 ⚠ –16.9 |
| Viso–FO (L) Relative error % | 217.4 –10.8 | 202.9 ⚠ –16.7 | 199.8 ⚠ –18.0 | 189.5 ⚠ –22.2 | 215.5 –11.5 | 205.1 ⚠ –15.8 | 202.3 ⚠ –16.9 | 198.4 ⚠ –18.6 |
| Vadia (L) Relative error % | 305.7 ⚠ 25.5 | 287.0 ⚠ 17.8 | 283.4 ⚠ 16.3 | 268.8 10.3 | 303.2 ⚠ 24.5 | 290.2 ⚠ 19.1 | 287.1 ⚠ 17.9 | 281.4 ⚠ 15.5 |
| Vdia (L) Relative error % | 249.6 2.5 | 240.5 –1.3 | 242.1 –0.6 | 232.0 –4.8 | 242.1 –0.6 | 238.2 –2.2 | 236.7 –2.8 | 232.5 –4.6 |
| Vdia–approx (L) Relative error % | 252.7 3.7 | 239.2 –1.8 | 242.7 –0.4 | 231.6 –4.9 | 240.7 –1.2 | 240.8 –1.2 | 234.6 –3.7 | 234.9 –3.6 |
| V0D–hotCaseCD (L) Relative error % | 258.9 6.3 | 247 1.4 | 247.6 1.6 | 229.5 –5.8 | 253.1 3.9 | 245.6 0.8 | 242.8 –0.3 | 240.8 –1.2 |
| V0D–hotCaseHD (L) Relative error % | 292.4 ⚠ 20 | 280.5 ⚠ 15.1 | 278.1 14.2 | 260.4 6.9 | 291.8 ⚠ 19.8 | 283 ⚠ 16.2 | 280.1 ⚠ 15 | 279.3 14.7 |
| V0D–coldCaseCD (L) Relative error % | 240.9 –1.1 | 234 –3.9 | 234.6 –3.7 | 217.2 –10.8 | 238.3 –2.2 | 234.8 –3.6 | 232.3 –4.6 | 231.3 –5 |
| VSAE (L) Relative error % | 264.7 8.7 | 269.7 10.7 | 266.6 9.5 | 306.8 ⚠ 25.9 | 261.4 7.3 | 270.6 11.1 | 269.0 10.4 | 269.2 10.5 |
[i] Cells indicate the relative error below the volume value. Volumes with errors greater than 15% are reported with the symbol ⚠ (reference volume 243.6 L).
Figure 6
Plotting of the experimental data measured during the six refueling steps of the type IV 1520 L tank.
Table 4
Numerical applications of the volume estimation formula based on the experimental data.
| TEST # | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Ptank(t0) (MPa(g)) | 2.31 | 9.5 | 2.7 | 10.53 | 2.07 | 8.1 |
| Tamb(t0) (°C) | 12.78 | 23.03 | 18.48 | 22.85 | 12.78 | 25.58 |
| Tinj (°C) | –17.83 | –19.25 | –21.37 | –26.93 | –5.48 | –22.41 |
| Δt (s) | 143 | 146 | 57 | 65 | 935 | 22 |
| ΔPtank (MPa) | 1.42 | 2.42 | 0.71 | 1.06 | 8.47 | 0.25 |
| Δm (kg) | 1.5 | 2.24 | 0.72 | 0.95 | 8.83 | 0.2 |
| ΔTtank (°C) | 18.84 | 11.75 | 11.02 | 5.99 | 30.51 | 1.79 |
| ΔTSAE (°C) | 24.56 | 24.05 | 16.83 | 15.98 | 24.87 | 18.08 |
| Viso (L) Relative error % | 1292.5 ⚠ –15.0 | 1288.9 ⚠ –15.2 | 1268 ⚠ –16.6 | 1249.7 ⚠ –17.8 | 1345.9 –11.5 | 1108.5 ⚠ –27.1 |
| Viso–FO (L) Relative error % | 1281.5 ⚠ –15.7 | 1270.3 ⚠ –16.4 | 1262.6 ⚠ –16.9 | 1241.8 ⚠ –18.3 | 1279.4 ⚠ –15.8 | 1106.9 ⚠ –27.2 |
| Vadia (L) Relative error % | 1805.4 ⚠ 18.8 | 1797.8 ⚠ 18.3 | 1778.1 ⚠ 17.0 | 1758.6 ⚠ 15.7 | 1801 ⚠ 18.5 | 1564.4 2.9 |
| Vdia (L) Relative error % | 1460.4 –3.9 | 1492.2 –1.8 | 1469.4 –3.3 | 1452.7 –4.4 | 1349.3 –11.2 | 1311.8 –13.7 |
| Vdia–approx (L) Relative error % | 1463.0 –3.7 | 1490.8 –1.9 | 1469.7 –3.3 | 1454.8 –4.3 | 1335.9 –12.1 | 1288.8 –15.2 |
| V0D–hotCaseCD (L) Relative error % | 1548 1.8 | 1535 1.0 | 1539 1.3 | 1480 –2.6 | 1584 4.2 | 1335 –12.2 |
| V0D–hotCaseHD (L) Relative error % | 1575 3.6 | 1658 9.1 | 1658 9.1 | 1615 6.3 | 1583 4.1 | 1543 1.5 |
| V0D–coldCaseCD (L) Relative error % | 1352 –11.1 | 1345 –11.5 | 1396 –8.2 | 1305 –14.1 | 1401 –7.8 | 1108.5 ⚠ –27.1 |
| VSAE (L) Relative error % | 1643.2 8.1 | 1763.9 ⚠ 16.0 | 2038.4 ⚠ 34.1 | 2933.8 ⚠ 93.0 | 1489.7 –2.0 | –1156.7 ⚠ –176.1 |
[i] Cells indicate the relative error below the volume value. Volumes with errors greater than 15% are reported with the symbol ⚠ (reference volume 1520 L).