Appendice I
Studio di sensibilità alla griglia, al volume di
calcolo ed al modello di turbolenza per lo studio
del bulbo di una IACC
In previsione di successive simulazioni con Fluent del flusso intorno ad un bulbo, si è effettuato uno
studio di sensibilità alla griglia ed al volume di calcolo della soluzione.
I.1 Generazione della geometria
L’unico vincolo che si ha nel progetto della geometria del bulbo è solo la massa che deve avere.
Tale massa deve essere indicativamente di 20 ton.
Per uno studio di sensibilità, non è necessario avere una geometria raffinata. Anzi è meglio una
geometria indicativa della forma da studiare, ma più tozza, al fine di disturbare maggiormente il
flusso quindi richiedere migliori caratteristiche alla griglia di calcolo.
Il bulbo è stato quindi schematizzato come un ellissoide prolato (ottenuto come rotazione di
un’ellisse intorno al suo asse maggiore) di lunghezza 5.75 m e di raggio massimo 0.385 m.
Queste dimensioni ci garantiscono la massa richiesta (per un peso specifico di
), una
forma ragionevole e non troppo fluidodinamica.
3
11200 /
kg m
La chiglia e le appendici sono state generate con un profilo NACA 64010, la prima con una corda di
0,85 m e le seconde con una corda di 0,2 m. Alla chiglia si è data una lunghezza di circa 3 m ed alle
appendici un’apertura di 0.8 m con una freccia di circa 30° (Fig. I.1).
I.2 Generazione delle griglie
Al fine di meglio simulare la condizione operativa del bulbo, si è posto un angolo di sbandamento
di 15°.
Si è deciso di utilizzare un volume di calcolo cilindrico a base circolare in modo da imporre sulla
superficie laterale la condizione di Velocità inlet e sulle basi, che simulano la superficie dell’acqua
ed il fondale, condizioni di Simmetry.
Per effettuare lo studio di sensibilità al volume di calcolo, si è generato un primo volume di raggio
ed altezza 50 m (Volume 1), successivamente questo è stato inglobato in uno più grande di raggio
ed altezza 75 m (Volume 2).
Fig. I.2 Mesh 1 (Bulbo, Volume 0, Volume 1)
In questo modo la stesa mesh (mesh 1a) utilizzata per il volume interno è stata poi usata come
origine per la mesh del volume esterno, e questo corrisponde correttamente a spostare più lontano la
superficie di applicazione della condizione al contorno (aumento del volume di calcolo) (mesh 2).
Fig. I.3 Mesh 2 (Bulbo, Volume 0, Volume 1,Volume 2)
Per effettuare lo studio di sensibilità alla griglia di calcolo si è invece costruita una nuova mesh per
il Volume 1 più fitta (mesh 1b) in modo da avere un termine di paragone dei risultati al variare
dell’infittimento della griglia a volume di calcolo costante.
In tutte e tre le mesh costruite, si è generato un volume intermedio (interior) per gestire la
diminuizione dell’infittimento della griglia con la distanza dal bulbo (Volume 0).
La generazione delle mesh è partita sempre dalle superfici del bulbo e successivamente i volumi
esterni.
I dettagli delle generazioni e delle mesh sono riportati di seguito.
Spacing
Metodo
Mesh 1a
Mesh 1b
Mesh 2
Bulbo Tri
Pave 0.02 0.015 0.02
Volume 0
Tet/Hybrid Tgrid
0.5
0.4
0.5
Volume 1
Tet/Hybrid Tgrid
2
1.8
2
Volume 2
Tet/Hybrid Tgrid
2.5
N°
celle
Mesh 1a
1.13 10
⋅
6
Mesh 1b
6
1.70 10
⋅
Mesh 2
1.49 10
⋅
6
I.3 Simulazioni
Fig. I.5 Settaggi di Fluent
Questi settaggi portano alla simulazione del flusso intorno al sistema chiglia bulbo, con angolo
rollio di 15°, in incidenza di 5° rispetto ad una corrente asintotica d’acqua.
I coefficienti che di seguito verranno riportati sono riferiti alla sezione massima del bulbo che si
assume pari a
0,0465427 m
2
.
I.4 Risultati
I risultati ottenuti, sono stati confrontati sia in termini di forze globali agenti sul corpo, sia in
termini di forze sulle singole superfici definite.
I.4.1 k-ε realizable
Resistenza
Mesh 1a
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 31.861762 10.512577 42.374339 0.0054864399 0.0018102144 0.0072966542
bulbo_sinistro 343.7787 201.04217 544.82087 0.059197014 0.03461848 0.093815494
bulbo_destro 301.91015 192.78028 494.69043 0.051987454 0.033195823 0.085183277
chiglia_sinistra 885.55632 97.881459 983.43778 0.15248847 0.016854709 0.16934318
chiglia_destra 158.9533 112.02776 270.98106 0.027370982 0.019290634 0.046661616
appendice_destra 22.151779 8.4162939 30.568073 0.0038144282 0.0014492447 0.0052636729
--- --- --- --- --- --- ---
net 1744.212 622.66054 2366.8726 0.30034479 0.10721911
0.4075639
Mesh 1b
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 28.294046 11.017394 39.31144 0.0048720965 0.0018971414 0.006769238
bulbo_sinistro 333.62485 205.63826 539.26311 0.05744857 0.035409904 0.092858474
bulbo_destro 290.46239 197.93232 488.3947 0.050016205 0.034082978 0.084099183
chiglia_sinistra 867.6924 98.807579 966.49998 0.14941239 0.017014183 0.16642658
chiglia_destra 116.05765 112.87718 228.93483 0.019984561 0.019436899 0.03942146
appendice_destra 20.619655 8.8642403 29.483895 0.0035506039 0.0015263789 0.0050769828
--- --- --- --- --- --- ---
net 1656.751 635.13697 2291.888 0.28528443 0.10936748
0.39465191
Mesh 2
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 30.633335 9.699184 40.332519 0.0052749108 0.0016701521 0.0069450629
bulbo_sinistro 320.14827 193.4418 513.59007 0.055127969 0.033309733 0.088437702
bulbo_destro 291.04904 187.56794 478.61698 0.050117224 0.032298283 0.082415507
chiglia_sinistra 875.4571 92.702577 968.15968 0.15074944 0.015962931 0.16671237
chiglia_destra 139.78798 106.75268 246.54067 0.024070808 0.018382291 0.042453099
appendice_destra 21.304317 7.7040106 29.008328 0.0036684994 0.001326593 0.0049950924
--- --- --- --- --- --- ---
net 1678.38 597.86819 2276.2482 0.28900885 0.10294998
0.39195883
Portanza
Mesh 1a
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 104.25973 0.3787789 104.63851 0.017953017 6.5223877e-05 0.018018241
bulbo_sinistro -729.94292 -3.5315522 -733.47447 -0.12569261 -0.00060811606 -0.12630072
bulbo_destro 3668.8168 -2.6156347 3666.2012 0.63175235 -0.00045039952 0.63130195
chiglia_sinistra 1252.4294 -8.3183603 1244.1111 0.21566224 -0.001432381 0.21422985
chiglia_destra 11678.004 -4.0181264 11673.986 2.0108953 -0.00069190175 2.0102034
appendice_destra -32.076194 -0.98760898 -33.063803 -0.005523364 -0.00017006144 -0.0056934255
--- --- --- --- --- --- ---
net 15941.491 -19.092504 15922.398 2.7450469 -0.0032876359
2.7417593
Mesh 1b
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 102.77573 0.36549819 103.14122 0.017697478 6.2937003e-05 0.017760415
bulbo_sinistro -740.50933 -3.5031257 -744.01246 -0.12751209 -0.00060322115 -0.12811531
bulbo_destro 3646.327 -2.7786585 3643.5483 0.6278797 -0.00047847143 0.62740123
chiglia_sinistra 1222.1257 -8.3483086 1213.7773 0.21044407 -0.001437538 0.20900653
chiglia_destra 11718.047 -3.5962174 11714.451 2.0177905 -0.00061925107 2.0171712
appendice_destra -33.140059 -1.073447 -34.213506 -0.0057065563 -0.00018484233 -0.0058913986
--- --- --- --- --- --- ---
net 15915.626 -18.934259 15896.692 2.7405931 -0.0032603869
2.7373327
Mesh 2
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 106.39707 0.35037386 106.74744 0.018321056 6.0332668e-05 0.018381388
bulbo_sinistro -832.29567 -3.036811 -835.33248 -0.14331725 -0.00052292402 -0.14384017
bulbo_destro 3663.6261 -2.7792937 3660.8468 0.63085852 -0.00047858081 0.63037994
chiglia_sinistra 1235.9497 -7.6885547 1228.2611 0.2128245 -0.0013239316 0.21150057
chiglia_destra 11727.026 -4.1407373 11722.885 2.0193366 -0.00071301475 2.0186236
appendice_destra -33.781384 -0.90188792 -34.683272 -0.0058169893 -0.0001553007 -0.00597229
--- --- --- --- --- --- ---
net 15866.922 -18.196911 15848.725 2.7322064 -0.0031334192
2.729073
Momenti
Mesh 1a
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m
--- --- --- --- --- --- ---
appendice_sinistra (191.65788 824.55304 251.41953) (0.039715748 -2.0760889 8.3428869) (191.6976 822.47695 259.76241) (0.0057395742 0.024692871 0.0075292547) (1.1893666e-06 -6.2172587e-05 0.00024984424) (0.0057407636 0.024630698 0.007779099)
bulbo_sinistro (0.047156788 697.22797 -3014.5596) (3.8544793 -12.850685 57.420059) (3.9016361 684.37728 -2957.1395) (1.4122033e-06 0.02087987 -0.090276946) (0.00011543 -0.00038483917 0.0017195572) (0.00011684221 0.020495031 -0.088557389)
bulbo_destro (0.00083621923 257.76093 706.099) (0.63943529 11.915326 65.021042) (0.64027151 269.67625 771.12004) (2.5042238e08 0.0077191605 0.021145531) (1.9149154e05 0.000356828 -0.0019471836) (1.9174196e-05 0.0080759885 -0.023092714)
chiglia_sinistra (-2603.9385 1429.6732 -166.61449) (0.34159276 163.71236 49.141552) (-2603.5969 1593.3856 -117.47293) (-0.077980086 0.042814391 -0.0049896002) (1.0229671e-05 0.0049026902 0.0014716409) (-0.077969856 0.047717081 -0.0035179593)
chiglia_destra (-21054.9 -915.44843 -2321.5034) (-9.6730337 190.04282 43.312431) (-21064.573 -725.40561 -2278.191) (-0.63053062 -0.027414913 -0.06952201) (-0.00028967812 0.0056912078 0.0012970764) (-0.6308203 -0.021723705 -0.068224933)
appendice_destra (42.534904 -187.06927 -79.395592) (0.0056521758 1.327419 -5.0333896) (42.540557 -185.74186 -84.428981) (0.0012737918 -0.0056021593 -0.002377658) (1.6926558e-07 3.9752188e-05 -0.0001507348) (0.0012739611 -0.0055624071 -0.0025283928)
--- --- --- --- --- --- ---
net (-23424.598 2106.6974 -6036.7525) (-4.7921584 352.07114 88.162498) (-23429.39 2458.7686 -5948.59) (-0.7014959 0.06308922 -0.18078249) (-0.00014351066 0.010543466 0.0026402003) (-0.70163941 0.073632687 -0.17814229)
Mesh 1b
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m
--- --- --- --- --- --- ---
appendice_sinistra (192.01868 826.229 245.93497) (0.044498242 -2.1488113 8.6812515) (192.06318 824.08019 254.61622) (0.0057503789 0.024743061 0.0073650088) (1.3325878e-06 -6.4350404e-05 0.00025997724) (0.0057517115 0.02467871 0.007624986)
bulbo_sinistro (0.018127197 675.40088 -2965.9749) (3.9684772 -13.057589 58.849445) (3.9866044 662.34329 -2907.1254) (5.4285476e-07 0.020226215 -0.08882198) (0.0001188439 -0.0003910353 0.001762363) (0.00011938675 0.019835179 -0.087059617)
bulbo_destro (0.0020648045 281.71582 754.86938) (0.6622858 12.306064 66.784714) (0.66435061 294.02188 821.6541) (6.1834654e08 0.0084365372 0.022606056) (1.9833458e05 0.0003685294 -0.0020000003) (1.9895292e-05 0.0088050666 -0.024606056)
chiglia_sinistra (-2539.9468 1395.6945 -155.93419) (0.28810057 164.96692 49.525017) (-2539.6587 1560.6614 -106.40917) (-0.076063727 0.04179683 -0.0046697575) (8.6277411e-06 0.0049402605 0.0014831245) (-0.0760551 0.04673709 -0.003186633)
chiglia_destra (-21134.865 -979.19617 -2389.2532) (-10.487316 191.53716 43.471756) (-21145.353 -787.65901 -2345.7814) (-0.63292532 -0.029323965 -0.07155091) (-0.00031406341 0.0057359588 0.0013018477) (-0.63323938 -0.023588006 -0.070249062)
appendice_destra (46.066006 -202.12303 -81.566956) (0.0089982366 1.4043264 -5.3758841) (46.075004 -200.71871 -86.94284) (0.0013795376 -0.0060529738 -0.0024426837) (2.6946998e-07 4.2055331e-05 -0.00016099148) (0.0013798071 -0.0060109184 -0.0026036752) --- --- --- --- --- --- --- net (-23436.707 1997.721 -6101.6636) (-5.514956 355.00806 88.366872) (-23442.222 2352.729 -6013.2967) (-0.70185853 0.059825703 -0.18272638) (-0.00016515626 0.010631418 0.0026463207) (-0.70202368 0.070457122 -0.18008006)
Mesh 2
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m
--- --- --- --- --- --- ---
appendice_sinistra (196.32913 847.10114 255.18292) (0.036950808 -1.911824 7.6889362) (196.36608 845.18931 262.87186) (0.005879464 0.025368118 0.0076419571) (1.106565e-06 -5.7253349e-05 0.0002302604) (0.0058805705 0.025310865 0.0078722175)
bulbo_sinistro (0.04741282 693.32721 -2909.7915) (3.8029015 -12.12621 55.340195) (3.8503143 681.201 -2854.4513) (1.4198706e-06 0.020763054 -0.087139459) (0.0001138854 -0.00036314334 0.0016572715) (0.00011530527 0.020399911 -0.085482187)
bulbo_destro (0.0010984546 287.81821 -756.85632) (0.69335651 11.312848 -62.901409) (0.69445497 299.13105 -819.75773) (3.2895394e-08 0.0086192852 -0.022665559) (2.0763931e-05 0.0003387856 -0.001883707) (2.0796827e-05 0.0089580708 -0.024549266)
chiglia_sinistra (-2570.5447 1411.7087 -159.75798) (-0.030448748 154.91646 46.459377) (-2570.5751 1566.6252 -113.2986) (-0.076980042 0.042276409 -0.0047842685) (-9.1184795e-07 0.0046392796 0.0013913179) (-0.076980954 0.046915689 -0.0033929506)
chiglia_destra (-21136.803 -947.46039 -2356.4634) (-8.6115751 180.95709 41.330097) (-21145.414 -766.5033 -2315.1333) (-0.63298334 -0.028373574 -0.070568954) (-0.00025789064 0.0054191179 0.0012377115) (-0.63324123 -0.022954456 -0.069331243)
appendice_destra (46.36425 -204.33257 -82.969391) (0.0055307043 1.2107277 -4.5947328) (46.369781 -203.12184 -87.564124) (0.0013884691 -0.0061191426 -0.0024846824) (1.6562787e-07 3.6257634e-05 -0.00013759836) (0.0013886348 -0.006082885 -0.0026222808)
--- --- --- --- --- --- ---
net (-23464.606 2088.1623 -6010.6557) (-4.1032843 334.35909 83.322464) (-23468.709 2422.5214 -5927.3332) (-0.702694 0.062534149 -0.18000097) (-0.00012288096 0.010013044 0.0024952559) (-0.70281688 0.072547193 -0.17750571)
Dalle simulazioni effettuate, si evince che la Mesh 1a è sufficiente per lo studio della
fluidodinamica del bulbo con Fluent utilizzando il modello di turbolenza k
− relizable; infatti, i
ε
risultati che sono stati ottenuti non variano significativamente all’aumentare del volume di calcolo e
dell’infittimento della griglia.
Resistenza
Mesh 1a
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 66.976782 20.171329 87.148111 0.011533075 0.0034734044 0.015006479
bulbo_sinistro 630.43102 249.10968 879.5407 0.10855714 0.04289547 0.15145261
bulbo_destro 440.90543 227.41041 668.31584 0.075921762 0.039158963 0.11508072
chiglia_sinistra 1498.0162 184.41511 1682.4313 0.25795107 0.031755381 0.28970645
chiglia_destra 651.63953 154.37831 806.01784 0.11220914 0.026583191 0.13879234
appendice_destra 38.784384 15.248929 54.033313 0.0066784816 0.0026257911 0.0093042727
--- --- --- --- --- --- ---
net 3326.7533 850.73377 4177.4871 0.57285068 0.1464922
0.71934288
Mesh 1b
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 71.153051 21.078321 92.231371 0.012252208 0.0036295839 0.015881792
bulbo_sinistro 619.24182 248.19864 867.44047 0.10663042 0.042738595 0.14936901
bulbo_destro 432.98914 228.35098 661.34012 0.074558615 0.039320924 0.11387954
chiglia_sinistra 1483.42 177.30871 1660.7287 0.25543768 0.030531693 0.28596937
chiglia_destra 642.97653 151.87583 794.85236 0.11071742 0.026152277 0.13686969
appendice_destra 40.381624 16.104769 56.486393 0.0069535184 0.0027731626 0.0097266811
--- --- --- --- --- --- ---
net 3290.1621 842.91725 4133.0794 0.56654985 0.14514624
0.71169609
Mesh 2
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 65.642787 19.742715 85.385503 0.011303367 0.0033995992 0.014702967
bulbo_sinistro 617.97119 244.7116 862.68279 0.10641162 0.042138143 0.14854976
bulbo_destro 440.1437 224.23893 664.38262 0.075790595 0.038612848 0.11440344
chiglia_sinistra 1486.7218 182.68133 1669.4031 0.25600623 0.031456833 0.28746306
chiglia_destra 648.31356 152.94815 801.26171 0.11163643 0.026336925 0.13797335
appendice_destra 37.354822 14.801102 52.155924 0.0064323179 0.0025486774 0.0089809954
--- --- --- --- --- --- ---
net 3296.1478 839.12383 4135.2717 0.56758056 0.14449303
0.71207359
Portanza
Mesh 1a
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 107.88186 0.94062467 108.82248 0.018576729 0.00016197097 0.0187387
bulbo_sinistro -105.24525 -7.0938744 -112.33912 -0.018122718 -0.0012215305 -0.019344248
bulbo_destro 3683.2121 0.053148569 3683.2653 0.63423115 9.151924e-06 0.6342403
chiglia_sinistra 1658.8489 -22.897031 1635.9519 0.28564568 -0.003942757 0.28170292
chiglia_destra 10741.09 -1.3746389 10739.715 1.8495632 -0.00023670611 1.8493265
appendice_destra -29.370725 -1.8731523 -31.243877 -0.0050574954 -0.00032254769 -0.0053800431
---
---net 16056.417 -32.244924 16024.172 2.7648366 -0.0055524184
2.7592841
Mesh 1b
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 106.70844 0.99394054 107.70238 0.018374673 0.00017115171 0.018545825
bulbo_sinistro -124.94123 -6.7902252 -131.73146 -0.02151427 -0.0011692436 -0.022683514
bulbo_destro 3648.5507 -0.38305969 3648.1677 0.62826262 -6.5961009e-05 0.62819666
chiglia_sinistra 1553.637 -22.344874 1531.2921 0.2675287 -0.0038476781 0.26368102
chiglia_destra 10791.442 -0.5256327 10790.916 1.8582336 -9.0511385e-05 1.8581431
appendice_destra -31.463264 -2.0559012 -33.519166 -0.0054178205 -0.00035401615 -0.0057718367
--- --- --- --- --- --- ---
net 15943.934 -31.105752 15912.828 2.7454675 -0.0053562586
2.7401113
Mesh 2
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 108.06103 0.91987424 108.98091 0.018607582 0.00015839785 0.01876598
bulbo_sinistro -194.14316 -6.8641303 -201.00729 -0.033430504 -0.0011819697 -0.034612474
bulbo_destro 3721.2054 0.073195575 3721.2786 0.6407734 1.2603921e-05 0.640786
chiglia_sinistra 1609.233 -22.690875 1586.5422 0.27710207 -0.0039072578 0.27319481
chiglia_destra 10775.044 -1.3139845 10773.73 1.8554099 -0.00022626172 1.8551837
appendice_destra -29.581605 -1.7985418 -31.380147 -0.0050938079 -0.00030970011 -0.005403508
--- --- --- --- --- --- ---
net 15989.818 -31.674461 15958.144 2.7533687 -0.0054541876
2.7479145
Momenti
Mesh 1a
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m --- --- --- --- --- --- --- appendice_sinistra (179.9234 746.9649 286.76157) (0.034500845 -4.3268962 16.765179) (179.9579 742.63801 303.52674) (0.0053881619 0.022369341 0.008587642) (1.033196e-06 -0.00012957746 0.00050206642) (0.0053891951 0.022239763 0.0090897084) bulbo_sinistro (0.04782664 772.0882 -4180.1392) (4.4730945 -17.490307 71.422852) (4.5209211 754.59789 -4108.7163) (1.4322633e-06 0.023121707 -0.12518253) (0.00013395566 -0.00052378182 0.0021388985) (0.00013538792 0.022597926 -0.12304363)
bulbo_destro (-0.0019176997 -0.26754341 -286.80588) (0.18852481 15.643111 -81.771713) (0.18660711 15.375568 -368.57759) (-5.7429309e-08 -8.0121162e-06 -0.008588969) (5.6457482e-06 0.00046846389 -0.0024488156) (5.5883189e-06 0.00046045177 -0.011037785)
chiglia_sinistra (-3472.188 2524.2893 -256.89398) (14.493128 312.52118 95.804428) (-3457.6949 2836.8105 -161.08955) (-0.10398153 0.075594834 -0.0076931981) (0.00043402536 0.0093590645 0.002869053) (-0.10354751 0.084953898 -0.0048241451)
chiglia_destra (-19459.139 -76.615036 -1532.7815) (-20.765993 263.29672 58.932568) (-19479.905 186.68169 -1473.8489) (-0.58274238 -0.0022943887 -0.045902172) (-0.00062187872 0.0078849409 0.0017648522) (-0.58336425 0.0055905521 -0.04413732)
appendice_destra (23.610548 -96.682526 -80.258812) (0.00022340483 2.5718217 -9.6174917) (23.610771 -94.110704 -89.876304) (0.00070706454 -0.0028953494 -0.0024035088) (6.6902993e-09 7.7018285e-05 -0.0002880148) (0.00070707123 -0.0028183311 -0.0026915236) --- --- --- --- --- --- --- net (-22727.747 3869.7773 -6050.1178) (-1.5765218 572.21563 151.53582) (-22729.323 4441.9929 -5898.5819) (-0.68062731 0.11588813 -0.18118274) (-4.7212061e-05 0.017136128 0.0045380397) (-0.68067452 0.13302426 -0.1766447)
Mesh 1b
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m --- --- --- --- --- --- --- appendice_sinistra (176.47546 731.24622 287.53424) (0.03754206 -4.5303626 17.573774) (176.51301 726.71585 305.10802) (0.0052849066 0.021898614 0.0086107813) (1.1242712e-06 -0.00013567066 0.00052628141) (0.0052860309 0.021762943 0.0091370627) bulbo_sinistro (0.018187186 751.50049 -4131.1729) (4.480866 -17.440088 71.348892) (4.4990531 734.0604 -4059.824) (5.4465123e-07 0.022505168 -0.12371614) (0.00013418839 -0.00052227792 0.0021366836) (0.00013473304 0.02198289 -0.12157945)
bulbo_destro (-0.00011642065 14.449313 -330.81628) (0.22395465 15.576698 -81.855309) (0.22383823 30.026011 -412.67159) (-3.4864464e-09 0.00043271325 -0.0099069476) (6.7067647e-06 0.00046647502 -0.002451319) (6.7032782e-06 0.00089918827 -0.012358267)
chiglia_sinistra (-3281.9651 2503.6252 -226.72688) (14.087442 300.5986 92.226944) (-3267.8776 2804.2238 -134.49994) (-0.098284933 0.074976007 -0.0067897847) (0.00042187631 0.0090020194 0.0027619182) (-0.097863056 0.083978027 -0.0040278666)
chiglia_destra (-19569.564 -82.260277 -1591.7784) (-21.843458 259.11981 57.651287) (-19591.408 176.85954 -1534.1272) (-0.58604929 -0.0024634466 -0.047668952) (-0.00065414554 0.007759855 0.0017264818) (-0.58670344 0.0052964084 -0.04594247)
appendice_destra (26.758194 -109.5308 -85.881371) (0.0031500799 2.750258 -10.315027) (26.761344 -106.78054 -96.196398) (0.00080132702 -0.0032801163 -0.0025718874) (9.4335369e-08 8.2361912e-05 -0.00030890388) (0.00080142135 -0.0031977544 -0.0028807913) --- --- --- --- --- --- --- net (-22648.278 3809.0302 -6078.8416) (-3.010503 556.07492 146.63056) (-22651.288 4365.1051 -5932.211) (-0.67824745 0.11406894 -0.18204293) (-9.0155465e-05 0.016652763 0.004391142) (-0.67833761 0.1307217 -0.17765179)
Mesh 2
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m --- --- --- --- --- --- --- appendice_sinistra (180.89755 753.41315 286.13672) (0.032848075 -4.2365975 16.403839) (180.9304 749.17655 302.54056) (0.0054173348 0.022562446 0.0085689297) (9.8370054e-07 -0.00012687329 0.00049124539) (0.0054183185 0.022435573 0.0090601751) bulbo_sinistro (0.048081506 773.15063 -4149.0459) (4.4352651 -17.080843 70.199905) (4.4833466 756.06979 -4078.846) (1.4398957e-06 0.023153524 -0.12425138) (0.00013282278 -0.00051151961 0.0021022749) (0.00013426268 0.022642005 -0.12214911)
bulbo_destro (-0.0017509161 10.629974 -309.03159) (0.2059972 15.381898 -80.649094) (0.20424628 26.011872 -389.68068) (-5.2434645e-08 0.0003183356 -0.0092545618) (6.1689934e-06 0.00046064134 -0.0024151965) (6.1165587e-06 0.00077897694 -0.011669758)
chiglia_sinistra (-3379.4775 2510.3613 -252.75896) (14.380051 309.57697 94.902786) (-3365.0975 2819.9383 -157.85617) (-0.10120514 0.075177733 -0.0075693666) (0.00043063904 0.0092708942 0.0028420515) (-0.1007745 0.084448627 -0.0047273151)
chiglia_destra (-19514.791 -84.297562 -1541.5011) (-20.644287 260.81772 58.366516) (-19535.435 176.52016 -1483.1346) (-0.584409 -0.0025244571 -0.046163298) (-0.00061823399 0.0078107022 0.0017479007) (-0.58502723 0.0052862451 -0.044415397)
appendice_destra (25.185537 -104.67557 -80.165894) (0.0001744523 2.4843824 -9.2910852) (25.185712 -102.19119 -89.456979) (0.0007542307 -0.0031347168 -0.0024007262) (5.2243191e-09 7.4399742e-05 -0.00027823991) (0.00075423593 -0.0030603171 -0.0026789661)
--- --- --- --- --- --- ---
net (-22688.139 3858.582 -6046.3667) (-1.5899517 566.94352 149.93287) (-22689.729 4425.5255 -5896.4338) (-0.67944118 0.11555286 -0.1810704) (-4.7614246e-05 0.016978245 0.0044900361) (-0.67948879 0.13253111 -0.17658037)
Dalle simulazioni effettuate, si evince che la Mesh 1a è sufficiente per lo studio della
fluidodinamica del bulbo con Fluent utilizzando il modello di turbolenza k
− ; infatti, i risultati
ω
che sono stati ottenuti non variano significativamente all’aumentare del volume di calcolo e
dell’infittimento della griglia.
I.4.3 Reynolds Stress
Resistenza
Mesh 1a
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 28.947142 8.3657996 37.312942 0.0049845566 0.0014405499 0.0064251064
bulbo_sinistro 271.45005 193.19488 464.64492 0.046742373 0.033267215 0.080009587
bulbo_destro 258.78021 190.53376 449.31397 0.044560688 0.032808983 0.077369671
chiglia_sinistra 873.29013 82.61538 955.90551 0.1503763 0.014225965 0.16460226
chiglia_destra 85.402244 92.669679 178.07192 0.014705849 0.015957266 0.030663116
appendice_destra 20.028107 7.1716176 27.199724 0.0034487422 0.0012349175 0.0046836598
--- --- --- --- --- --- ---
net 1537.8979 574.55111 2112.449 0.26481851 0.098934897
0.3637534
Mesh 1b
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 25.360889 8.7164606 34.077349 0.0043670212 0.001500932 0.0058679532
bulbo_sinistro 259.6158 199.58452 459.20032 0.044704573 0.03436748 0.079072053
bulbo_destro 246.78738 196.90765 443.69503 0.042495582 0.033906535 0.076402118
chiglia_sinistra 846.08865 85.271707 931.36036 0.14569234 0.014683372 0.16037571
chiglia_destra 36.045553 96.162703 132.20826 0.0062068683 0.016558748 0.022765616
appendice_destra 18.312766 7.551254 25.86402 0.003153369 0.0013002891 0.0044536581
--- --- --- --- --- --- ---
net 1432.211 594.19429 2026.4053 0.24661975 0.10231736
0.35593771
Mesh 2
Force vector: (0.99619901 0.087112002 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 28.680088 7.65855 36.338638 0.0049385711 0.0013187649 0.006257336
bulbo_sinistro 263.96942 186.70297 450.67239 0.045454245 0.03214934 0.077603585
bulbo_destro 258.78806 186.05107 444.83913 0.044562041 0.032037085 0.076599126
chiglia_sinistra 870.61915 78.396374 949.01553 0.14991637 0.013499473 0.16341584
chiglia_destra 86.718895 87.920599 174.63949 0.01493257 0.015139498 0.030072068
appendice_destra 19.723355 6.5535592 26.276914 0.0033962654 0.0011284909 0.0045247563
--- --- --- --- --- --- ---
net 1528.499 553.28312 2081.7821 0.26320006 0.095272652
0.35847271
Portanza
Mesh 1a
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 111.69793 0.30569808 112.00363 0.019233839 5.2639717e-05 0.019286479
bulbo_sinistro -940.30336 -2.4368161 -942.74017 -0.16191565 -0.00041960783 -0.16233526
bulbo_destro 3573.8433 -3.5526272 3570.2907 0.61539837 -0.00061174507 0.61478662
chiglia_sinistra 1263.5956 -5.787678 1257.8079 0.21758499 -0.0009966099 0.21658838
chiglia_destra 11819.013 -5.4142948 11813.598 2.0351763 -0.00093231513 2.0342439
appendice_destra -36.882756 -0.83990057 -37.722657 -0.0063510306 -0.00014462678 -0.0064956574
--- --- --- --- --- --- ---
net 15790.963 -17.725619 15773.238 2.7191268 -0.003052265
2.7160745
Mesh 1b
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 110.54381 0.29727863 110.84109 0.019035105 5.1189929e-05 0.019086295
bulbo_sinistro -953.31919 -2.4669859 -955.78617 -0.16415691 -0.00042480294 -0.16458171
bulbo_destro 3555.1277 -3.6610604 3551.4666 0.61217563 -0.00063041673 0.61154521
chiglia_sinistra 1235.5466 -5.9351217 1229.6114 0.21275508 -0.001021999 0.21173309
chiglia_destra 11878.016 -5.2994586 11872.716 2.0453364 -0.0009125409 2.0444238
appendice_destra -37.810101 -0.9112637 -38.721365 -0.0065107148 -0.00015691516 -0.00666763
--- --- --- --- --- --- ---
net 15788.105 -17.976612 15770.128 2.7186346 -0.0030954848
2.7155391
Mesh 2
Force vector: (-0.087112002 0.99619901 0)
pressure viscous total pressure viscous total
zone name force force force coefficient coefficient coefficient
n n n
--- --- --- --- --- --- ---
appendice_sinistra 112.54449 0.28391954 112.82841 0.019379612 4.8889558e-05 0.019428502
bulbo_sinistro -1009.3037 -2.012307 -1011.316 -0.17379716 -0.00034650944 -0.17414367
bulbo_destro 3606.3657 -3.6237309 3602.7419 0.62099856 -0.00062398877 0.62037457
chiglia_sinistra 1241.4347 -5.2868303 1236.1479 0.21376899 -0.00091036637 0.21285863
chiglia_destra 11859.077 -5.4867246 11853.59 2.0420751 -0.00094478719 2.0411303
appendice_destra -37.811284 -0.77089129 -38.582176 -0.0065109186 -0.00013274372 -0.0066436623
--- --- --- --- --- --- ---
net 15772.306 -16.896565 15755.41 2.7159142 -0.0029095059
2.7130047
Momenti
Mesh 1a
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m
--- --- --- --- --- --- ---
appendice_sinistra (208.09688 899.41327 265.67526) (0.03859606 -1.6296235 6.6380925) (208.13547 897.78365 272.31335) (0.0062318724 0.026934709 0.007956171) (1.1558353e-06 -4.8802298e-05 0.0001987908) (0.0062330283 0.026885906 0.0081549618)
bulbo_sinistro (0.048476577 637.98267 -2623.126) (3.9521236 -11.738524 55.115944) (4.0006002 626.24414 -2568.01) (1.4517269e-06 0.019105652 -0.078554693) (0.00011835416 -0.00035153332 0.0016505559) (0.00011980588 0.018754119 -0.076904137)
bulbo_destro (0.0044109775 343.07257 -871.77362) (0.80626142 10.802924 -63.072258) (0.8106724 353.87549 -934.84588) (1.3209544e-07 0.010273986 -0.026106985) (2.4145092e-05 0.00032351492 -0.0018888235) (2.4277188e-05 0.010597501 -0.027995808)
chiglia_sinistra (-2631.5173 1399.8252 -139.16165) (-1.8767346 138.66304 41.348782) (-2633.3941 1538.4882 -97.81287) (-0.078805989 0.041920533 -0.0041674708) (-5.6202528e-05 0.0041525389 0.001238271) (-0.078862192 0.046073072 -0.0029291998)
chiglia_destra (-21319.289 -1034.8668 -2452.5063) (-4.2168741 158.22293 36.673523) (-21323.506 -876.64389 -2415.8328) (-0.63844826 -0.030991133 -0.073445151) (-0.00012628263 0.0047382985 0.0010982611) (-0.63857454 -0.026252834 -0.07234689)
appendice_destra (53.501755 -234.54005 -89.596313) (0.0086943945 1.1087782 -4.2563806) (53.510449 -233.43128 -93.852694) (0.0016022158 -0.0070237656 -0.0026831387) (2.6037083e-07 3.3204556e-05 -0.00012746573) (0.0016024762 -0.006993.3204556e-05611 -0.0028106045)
--- --- --- --- --- --- ---
net (-23689.155 2010.8868 -5910.4886) (-1.2879332 295.42953 72.447702) (-23690.443 2306.3164 -5838.0409) (-0.70941858 0.060219982 -0.17700127) (-3.8569707e-05 0.0088472212 0.0021695897) (-0.70945715 0.069067203 -0.17483168)
Mesh 1b
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m
--- --- --- --- --- --- ---
appendice_sinistra (209.10675 904.29724 260.87711) (0.045558129 -1.6623944 6.8627887) (209.15231 902.63485 267.7399) (0.006262115 0.027080969 0.0078124808) (1.3643282e-06 -4.9783687e-05 0.00020551978) (0.0062634794 0.027031185 0.0080180006)
bulbo_sinistro (0.018582484 612.96472 -2570.678) (4.0971866 -12.09437 56.893421) (4.1157691 600.87035 -2513.7846) (5.5648922e-07 0.01835644 -0.076984035) (0.00012269835 -0.00036218982 0.001703786) (0.00012325484 0.017994251 -0.075280249)
bulbo_destro (-0.0014427301 370.55658 -927.45465) (0.81684864 11.308327 -65.290787) (0.81540591 381.86491 -992.74544) (-4.3205405e-08 0.011097049 -0.027774463) (2.4462147e-05 0.00033865021 -0.0019552617) (2.4418942e-05 0.0114357 -0.029729725)
chiglia_sinistra (-2576.3169 1348.1917 -129.2326) (-2.0884421 142.72557 42.550079) (-2578.4053 1490.9173 -86.682521) (-0.077152903 0.040374266 -0.0038701257) (-6.2542528e-05 0.0042741994 0.0012742462) (-0.077215446 0.044648465 -0.0025958795)
chiglia_destra (-21430.443 -1109.8384 -2531.5425) (-4.8874359 164.14774 37.94762) (-21435.33 -945.69066 -2493.5949) (-0.64177698 -0.033236305 -0.075812045) (-0.00014636393 0.0049157286 0.0011364165) (-0.64192335 -0.028320576 -0.074675629)
appendice_destra (56.837082 249.14958 91.375633) (0.01072212 1.1758797 4.5453315) (56.847804 247.9737 95.920964) (0.0017020988 0.0074612767 0.002736424) (3.2109508e07 3.5214042e05 -0.00013611894) (0.0017024199 -0.0074260627 -0.0028725429) --- --- --- --- --- --- --- net (-23740.799 1877.0223 -5989.4063) (-2.0055625 305.60075 74.41779) (-23742.804 2182.623 -5914.9885) (-0.71096516 0.056211143 -0.17936461) (-6.0060534e-05 0.0091518187 0.0022285879) (-0.71102522 0.065362961 -0.17713602)
Mesh 2
Moment Center: (0 0 0)zone name pressure moment viscous moment total moment pressure coefficient viscous coefficient total coefficient n-m n-m n-m
--- --- --- --- --- --- ---
appendice_sinistra (209.76686 907.71399 267.33774) (0.034513839 -1.4956564 6.0768967) (209.80137 906.21833 273.41463) (0.0062818834 0.02718329 0.0080059571) (1.0335851e-06 -4.4790387e-05 0.00018198468) (0.006282917 0.0271385 0.0081879418)
bulbo_sinistro (0.048799381 645.36102 -2609.0925) (3.8898818 -11.180037 53.358589) (3.9386812 634.18099 -2555.7339) (1.4613939e-06 0.019326612 -0.078134434) (0.0001164902 -0.0003348083 0.0015979284) (0.0001179516 0.018991803 -0.076536506)
bulbo_destro (0.0045644785 354.69449 -894.53339) (0.84054583 10.305264 -61.22916) (0.84511031 364.99975 -955.76255) (1.3669233e-07 0.010622028 -0.026788571) (2.5171807e-05 0.00030861149 -0.0018336283) (2.5308499e-05 0.010930639 -0.028622199)
chiglia_sinistra (-2589.0283 1398.1586 -139.28427) (-2.156014 131.50127 39.172615) (-2591.1843 1529.6598 -100.11166) (-0.077533572 0.041870623 -0.0041711429) (-6.4566101e-05 0.0039380654 0.0011731014) (-0.077598138 0.045808688 -0.0029980415)
chiglia_destra (-21388.814 -1037.2739 -2456.1433) (-3.3634572 150.11482 34.887562) (-21392.178 -887.1591 -2421.2557) (-0.64053034 -0.031063218 -0.073554067) (-0.00010072538 0.0044954851 0.001044777) (-0.64063106 -0.026567733 -0.07250929)
appendice_destra (55.351871 -243.25691 -91.599266) (0.0078346794 1.013476 -3.8870904) (55.359706 -242.24344 -95.486356) (0.0016576212 -0.0072848092 -0.0027431211) (2.3462497e-07 3.0350543e-05 -0.00011640661) (0.0016578558 -0.0072544586 -0.0028595277) --- --- --- --- --- --- --- net (-23712.671 2025.3972 -5923.315) (-0.74669497 280.25914 68.379412) (-23713.417 2305.6564 -5854.9356) (-0.7101228 0.060654524 -0.17738538) (-2.2361257e-05 0.0083929139 0.0020477567) (-0.71014517 0.069047438 -0.17533762)
