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APPENDIX 1.

Drag values retrieved from ANSYS FLUENT for each of the 11 shells. Drag data are reported in dyne. Columns are labeled with the water velocity corresponding to a drag value. Rows are labeled with the shell to corresponding to a given set of drag data.

Shell ID 1
cm/s
1.75
cm/s
2.5
cm/s
3.75
cm/s
5
cm/s
7.5
cm/s
10
cm/s
15
cm/s
20
cm/s
25
cm/s
50
cm/s
Cardioceras 2.46 5.12 9 16.64 26.16 50.84 83.12 167.78 280.62 429.16 1629.85
Sphenodiscus 1.71 4.22 7.02 13.1 20.81 39.96 64.78 129.43 213.82 315.57 1079.8
Nautilus lifesize 17.59 48.92 95.49 206.07 355.56 772.65 1349.12 2947.88 5097.65 7752.39 25590.25
Nautilus 5cm 3.32 8.42 15.66 32.55 55.46 118.79 205.26 441.78 765.2 1184.07 4408.79
Oppelia 2.38 5.77 .89 18.43 31.58 63.16 102.3 214.78 345.61 545.83 2078.65
Sphereocone 3.83 9.93 18.71 39.29 66.91 141.82 243.82 522.35 908.85 1385.69 5259.64
Serpenticone 2.75 6.45 11.39 22.64 37.01 76.61 129.09 281.02 492.54 767.64 2996.45
Center 3.02 7.08 12.84 25.84 43.12 89.33 149.67 326.62 573.49 885.92 3398.94
Oxycone 2.71 5.99 10.29 19.69 32.07 64.75 107.94 223.86 378.93 576.25 2117.9
Serplaty 2.63 5.79 9.67 17.81 28.37 56.7 94.03 197.37 342.02 527.49 2035.6
Extreme Serpenticone 2.81 6.14 9.98 18.23 29.33 60.03 101.37 219.65 385.84 586.37 2304.58

 

 

APPENDIX 2.

Coefficient of drag values calculated following the equations of Jacobs (1992). Columns are labeled with the water velocity corresponding to a given value. Rows are labeled with the shell to corresponding to a given set of values.

  1
cm/s
1.75
cm/s
2.5
cm/s
3.75
cm/s
5
cm/s
7.5
cm/s
10
cm/s
15
cm/s
20
cm/s
25
cm/s
50
cm/s
Cardioceras 0.971 0.66 0.568 0.467 0.413 0.357 0.328 0.294 0.277 0.271 0.257
Sphenodiscus 0.994 0.801 0.653 0.541 0.484 0.413 0.376 0.334 0.311 0.293 0.251
Nautilus lifesize 0.528 0.48 0.459 0.44 0.427 0.412 0.405 0.393 0.383 0.372 0.307
Nautilus 5cm 0.718 0.595 0.542 0.501 0.48 0.457 0.444 0.425 0.414 0.41 0.382
Oppelia 0.869 0.688 0.578 0.479 0.461 0.41 0.374 0.349 0.316 0.319 0.304
Sphereocone 0.713 0.604 0.557 0.52 0.498 0.469 0.454 0.432 0.423 0.413 0.392
Serpenticone 0.738 0.565 0.489 0.432 0.397 0.365 0.346 0.335 0.33 0.33 0.322
Center 0.73 0.559 0.497 0.444 0.417 0.384 0.362 0.351 0.347 0.343 0.329
Oxycone 0.883 0.637 0.536 0.456 0.418 0.375 0.352 0.324 0.309 0.3 0.276
Serplatyicone 0.966 0.694 0.568 0.465 0.417 0.37 0.345 0.322 0.314 0.31 0.299
Extreme Serpenticone 1.106 0.789 0.629 0.51 0.462 0.42 0.399 0.384 0.38 0.369 0.363

APPENDIX 3.

Drag values retrieved from ANSYS FLUENT for a hemisphere run in each scheme from Table 1. The benchmark data were mathematically derived from coefficient of drag values from Blevins (1984). Columns are named for the water velocity corresponding to a drag value. Row names identify the simulation scheme used to obtain each set of values.

  5 cm/s 10 cm/s 20 cm/s 50 cm/s
Scheme 4 279.66 1138.89 4632.3 29441.13
Scheme 3 294.42 1185.66 4812.26 30393.66
Scheme 2 334.4 1282.26 5176.69 30486.5
Scheme 1 278.98 1185.66 4482.37 28368.43
Baseline 286.59 1146.35 4585.40 28658.76

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