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
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
|
// 2017 © Raphael Maurin <raphael.maurin@imft.fr>
// 2017 © Julien Chauchat <julien.chauchat@legi.grenoble-inp.fr>
// 2019 © Remi Monthiller <remi.monthiller@gmail.com>
#include "HydroForceEngine.hpp"
#include <lib/high-precision/Constants.hpp>
#include <lib/smoothing/LinearInterpolate.hpp>
#include <core/Scene.hpp>
#include <pkg/common/Sphere.hpp>
#include <preprocessing/dem/Shop.hpp>
#include <core/IGeom.hpp>
#include <core/IPhys.hpp>
#include <boost/optional.hpp>
#include <boost/random/linear_congruential.hpp>
#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>
namespace yade { // Cannot have #include directive inside.
using math::max;
using math::min;
YADE_PLUGIN((HydroForceEngine));
/* Initialize all the necessary variables to run HydroForceEngine. */
void HydroForceEngine::initialization()
{
// Profiles
vxPart = vector<Real>(nCell, 0.0); //Averaged streamwise particle velocity (old version)
vPart = vector<Vector3r>(nCell, Vector3r::Zero()); //Averaged particle velocity (new version)
phiPart = vector<Real>(nCell, 0.0); //Averaged solid volume fraction
averageDrag = vector<Real>(nCell, 0.0); //Averaged drag force
vxFluid = vector<Real>(nCell + 1, 0.0); //Averaged fluid velocity
ReynoldStresses = vector<Real>(nCell, 0.0); //Reynolds stresses
if (convAccOption == false) convAcc = vector<Real>(nCell, 0.0); //Convective acceleration (optional)
turbulentViscosity = vector<Real>(nCell, 0.0); //Turbulent viscosity
taufsi = vector<Real>(nCell, 0.0); //Fluid-particle momentum transfer
// Particle based quantities
size_t lenBody = scene->bodies->size();
vFluctX = vector<Real>(lenBody, 0.0); //Turbulent fluctuations along x
vFluctY = vector<Real>(lenBody, 0.0); //Turbulent fluctuations along y
vFluctZ = vector<Real>(lenBody, 0.0); //Turbulent fluctuations along z
// Compute radiusParts in order to use the averaging function
computeRadiusParts();
}
/* Scans the Bodies and gets all different radius
* and fill a vector of all different radius.
*
* If you 2 different size of particles, the size of
* the resulting vector will be 2.
*/
void HydroForceEngine::computeRadiusParts()
{
radiusParts = vector<Real>();
FOREACH(const shared_ptr<Body>& b, *Omega::instance().getScene()->bodies)
{
if (!b->isClump()) {
const Sphere* sphere = dynamic_cast<Sphere*>(b->shape.get());
if (sphere) {
Real r = sphere->radius;
if (std::find(radiusParts.begin(), radiusParts.end(), r) == radiusParts.end()) { radiusParts.push_back(r); }
}
}
}
}
/////////////////////////////////////////////////////////////////////////////////////////////////
/* Application of hydrodynamical forces */
void HydroForceEngine::action()
{
// Buoyancy, drag, lift and convective acceleration forces application, loop over the particles
Vector3r gravityBuoyancy = gravity;
if (steadyFlow == true) gravityBuoyancy[0] = 0.; // If the fluid flow is steady, no streamwise buoyancy contribution from gravity
FOREACH(Body::id_t id, ids)
{
Body* b = Body::byId(id, scene).get();
if (!b) continue;
if (b->isClump()) continue;
if (!(scene->bodies->exists(id))) continue;
const Sphere* sphere = dynamic_cast<Sphere*>(b->shape.get());
if (sphere) {
Vector3r posSphere = b->state->pos; //position vector of the sphere
int p = int(math::floor((posSphere[2] - zRef) / deltaZ)); //cell number in which the particle is
if ((p < nCell) && (p >= 0)) {
Vector3r liftForce = Vector3r::Zero();
Vector3r dragForce = Vector3r::Zero();
Vector3r convAccForce = Vector3r::Zero();
//deterministic version
Vector3r vRel
= Vector3r(vxFluid[p + 1] + vFluctX[id], vFluctY[id], vFluctZ[id]) - b->state->vel; //fluid-particle relative velocity
//Drag force calculation
if (vRel.norm() != 0.0) {
dragForce = 0.5 * densFluid * Mathr::PI * pow(sphere->radius, 2.0)
* (0.44 * vRel.norm() + 24.4 * viscoDyn / (densFluid * sphere->radius * 2)) * pow(1 - phiPart[p], -expoRZ)
* vRel;
}
//lift force calculation due to difference of fluid pressure between top and bottom of the particle
int intRadius = int(math::floor(sphere->radius / deltaZ));
if ((p + intRadius < nCell) && (p - intRadius > 0) && (lift == true)) {
Real vRelTop = vxFluid[p + 1 + intRadius]
- b->state->vel[0]; // relative velocity of the fluid wrt the particle at the top of the particle
Real vRelBottom = vxFluid[p + 1 - intRadius] - b->state->vel[0]; // same at the bottom
liftForce[2]
= 0.5 * densFluid * Mathr::PI * pow(sphere->radius, 2.0) * Cl * (vRelTop * vRelTop - vRelBottom * vRelBottom);
}
//buoyant weight force calculation
Vector3r buoyantForce = -4.0 / 3.0 * Mathr::PI * pow(sphere->radius, 3.0) * densFluid * gravityBuoyancy;
if (convAccOption == true) { convAccForce[0] = -convAcc[p]; }
//add the hydro forces to the particle
scene->forces.addForce(id, dragForce + liftForce + buoyantForce + convAccForce);
}
}
}
// Lubrication force application, loop over the interactions (more efficient)
if (lubrication == true) {
//loop over the interactions
FOREACH(const shared_ptr<Interaction>& I, *scene->interactions)
{
// Get the two id of the object interacting
const auto id1 = I->getId1();
const auto id2 = I->getId2();
// Get the body caracteristic
const auto b1 = Body::byId(id1, scene).get();
const auto b2 = Body::byId(id2, scene).get();
// Get the sphere caracteristics
const auto sphere1 = dynamic_cast<Sphere*>(b1->shape.get());
const auto sphere2 = dynamic_cast<Sphere*>(b2->shape.get());
//If the two interacting objects are spheres, apply buoyancy force (Need to generalize for any object).
if ((sphere1) && (sphere2)) {
// Evaluate quantities necessary to know if the lubrication force is at stake
const auto deltaPos12 = b2->state->pos - b1->state->pos; // Evaluate the x_12 relative position vector
const auto deltaVel12 = b2->state->vel - b1->state->vel; // Evaluate the v_12 relative velocity vector
const auto deltaPosNorm = deltaPos12.norm(); //Take the norm of the relative position vector
const auto delta_n
= deltaPosNorm - (sphere1->radius + sphere2->radius); //calculation the distance between the two particles surface
// Calculate the normal velocity
const auto velNormal = deltaVel12.dot(deltaPos12) * deltaPos12 / deltaPosNorm;
// Calculate the lubrication force f12
if (deltaVel12.dot(deltaPos12) < 0) {
const auto lubricationForce = 6 * Mathr::PI * viscoDyn / (delta_n + roughnessPartScale)
* pow((sphere1->radius * sphere2->radius) / (sphere1->radius + sphere2->radius), 2) * velNormal;
// Apply the lubrication force to the two particles
scene->forces.addForce(I->id1, lubricationForce); //lubrication = + f12
scene->forces.addForce(I->id2, -lubricationForce); //lubrication = - f12
}
}
}
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////
/* Volume-averaging function, necessary to perform fluid 1D coupling */
void HydroForceEngine::averageProfile()
{
// Total values
vector<Real> phiAverageTot(nCell, 0.0);
vector<Real> dragAverageTot(nCell, 0.0);
vector<Vector3r> vAverageTot(nCell, Vector3r::Zero());
// Multi class vectors
vector<vector<Real>> phiAverageMulti;
vector<vector<Real>> dragAverageMulti;
vector<vector<Real>> vAverageMultiX;
vector<vector<Real>> vAverageMultiY;
vector<vector<Real>> vAverageMultiZ;
// Only ask for memory when Multi average is enable
if (twoSize || enableMultiClassAverage) {
phiAverageMulti = vector<vector<Real>>(radiusParts.size(), vector<Real>(nCell, 0.0));
dragAverageMulti = vector<vector<Real>>(radiusParts.size(), vector<Real>(nCell, 0.0));
vAverageMultiX = vector<vector<Real>>(radiusParts.size(), vector<Real>(nCell, 0.0));
vAverageMultiY = vector<vector<Real>>(radiusParts.size(), vector<Real>(nCell, 0.0));
vAverageMultiZ = vector<vector<Real>>(radiusParts.size(), vector<Real>(nCell, 0.0));
}
//
// Loop over the particles for averaging determination
// Restrict the loop to spheres that are not clumps
//
FOREACH(const shared_ptr<Body>& b, *Omega::instance().getScene()->bodies)
{
if (b->isClump()) continue; //If it is a clump, skip
shared_ptr<Sphere> s = YADE_PTR_DYN_CAST<Sphere>(b->shape); //Take the sphere characteristichs
if (!s) continue; //If it is not a sphere, skip
// Getting radius of particle
const Real rPart = s->radius;
// Computing z the position of the particle (with 0 at zRef).
const Real zPart = b->state->pos[2] - zRef;
// Define the correspondig cell number.
const int nPart = int(math::floor(zPart / deltaZ));
// Computing drag force applied on the particle in order to evaluate the associated momentum transfer
//
Vector3r fDrag = Vector3r::Zero();
if ((nPart >= 0) && (nPart < nCell)) {
const Vector3r uRel = Vector3r(vxFluid[nPart + 1] + vFluctX[b->id], vFluctY[b->id], vFluctZ[b->id]) - b->state->vel;
// Drag force with a Dallavalle formulation (drag coef.)
// and Richardson-Zaki Correction (hindrance effect)
fDrag = 0.5 * Mathr::PI * pow(rPart, 2.0) * densFluid * (0.44 * uRel.norm() + 24.4 * viscoDyn / (densFluid * 2.0 * rPart))
* pow((1 - phiPart[nPart]), -expoRZ) * uRel;
} else {
fDrag = Vector3r::Zero();
}
// Point particle average (volume weighted if not mono-disperse)
//
if (pointParticleAverage == true) {
const Real volPart = 4. / 3. * Mathr::PI * pow(rPart, 3.); //volume of the particle
phiAverageTot[nPart] += volPart; //Add the volume of the particle to phiAverageTot
vAverageTot[nPart] += volPart * b->state->vel; //Weight the velocity by the particle volume
dragAverageTot[nPart] += volPart * fDrag[0]; //Weight the drag force by the particle volume
if (twoSize || enableMultiClassAverage) {
// Getting the radius index of the particle.
const unsigned int i = find(radiusParts.begin(), radiusParts.end(), rPart) - radiusParts.begin();
if (i >= radiusParts.size()) { throw runtime_error("Radius of particlenot found. Did you call computeRadiusParts ?"); }
phiAverageMulti[i][nPart] += volPart;
vAverageMultiX[i][nPart] += volPart * b->state->vel[0];
vAverageMultiY[i][nPart] += volPart * b->state->vel[1];
vAverageMultiZ[i][nPart] += volPart * b->state->vel[2];
dragAverageMulti[i][nPart] += volPart * fDrag[0];
}
}
// Local volume weighted averaged taking into account the extent of the particle accross different averaging layers
//
else {
// Getting minimum and maximum layer reached by the particle.
const int nMinPart = max(0, int(math::floor((zPart - rPart) / deltaZ)));
const int nMaxPart = min(nCell - 1, int(math::floor((zPart + rPart) / deltaZ)));
const Real deltaCenter = zPart - nPart * deltaZ;
// Loop over the cells in which the particle is contained.
int n = nMinPart;
while (n <= nMaxPart) {
// Compute zInf and zSup
Real zInf = (n - nPart - 1) * deltaZ + deltaCenter;
Real zSup = (n - nPart) * deltaZ + deltaCenter;
if (zInf < -rPart) { zInf = -rPart; }
if (zSup > rPart) { zSup = rPart; }
// Analytical formulation of the volume of a slice of sphere.
const Real volPart = Mathr::PI * pow(rPart, 2) * (zSup - zInf + (pow(zInf, 3) - pow(zSup, 3)) / (3 * pow(rPart, 2)));
if (twoSize || enableMultiClassAverage) {
// Getting the radius index of the particle.
const unsigned int i = find(radiusParts.begin(), radiusParts.end(), rPart) - radiusParts.begin();
if (i >= radiusParts.size()) { throw runtime_error("Radius of particle not found. Did you call computeRadiusParts ?"); }
phiAverageMulti[i][n] += volPart;
vAverageMultiX[i][nPart] += volPart * b->state->vel[0];
vAverageMultiY[i][nPart] += volPart * b->state->vel[1];
vAverageMultiZ[i][nPart] += volPart * b->state->vel[2];
dragAverageMulti[i][n] += volPart * fDrag[0];
}
phiAverageTot[n] += volPart;
vAverageTot[n] += volPart * b->state->vel;
dragAverageTot[n] += volPart * fDrag[0];
// Incrementing.
n++;
} //End of the while loop
} //End of the else loop
} //End of the loop over the particles
//
//Normalization of the averaged quantities evaluated
//
for (int n = 0; n < nCell; n++) {
// Normalized the weighted velocity by the volume of particles
// contained inside the cell.
if (twoSize || enableMultiClassAverage) {
// Loop over each radius of particles.
for (unsigned int i = 0; i < radiusParts.size(); i++) {
// Avoiding division by 0
if (phiAverageMulti[i][n] != 0) {
// phiAverage still contains the total solid volume.
vAverageMultiX[i][n] /= phiAverageMulti[i][n];
vAverageMultiY[i][n] /= phiAverageMulti[i][n];
vAverageMultiZ[i][n] /= phiAverageMulti[i][n];
dragAverageMulti[i][n] /= phiAverageMulti[i][n];
// Get the volume fraction from the solid volume.
phiAverageMulti[i][n] /= vCell;
} else {
vAverageMultiX[i][n] = 0.0;
vAverageMultiY[i][n] = 0.0;
vAverageMultiZ[i][n] = 0.0;
dragAverageMulti[i][n] = 0.0;
}
}
}
// phiAverage still contains the total solid volume.
if (phiAverageTot[n] != 0) {
vAverageTot[n] /= phiAverageTot[n];
dragAverageTot[n] /= phiAverageTot[n];
} else {
vAverageTot[n] = Vector3r::Zero();
dragAverageTot[n] = 0.0;
}
// Get the volume fraction from the solid volume.
phiAverageTot[n] /= vCell;
}
// Setting all class attributes.
if (twoSize || enableMultiClassAverage) {
// Multi class :
multiVxPart = vAverageMultiX;
multiVyPart = vAverageMultiY;
multiVzPart = vAverageMultiZ;
multiDragPart = dragAverageMulti;
multiPhiPart = phiAverageMulti;
}
// Tot
vPart = vAverageTot;
averageDrag = dragAverageTot;
phiPart = phiAverageTot;
// Saving for an average over time
phiPartT.push(phiAverageTot);
if (phiPartT.size() > nbAverageT) { phiPartT.pop(); }
// If asked by the user, variables are evaluated in order to make it compatible with former versions of the code
if (compatibilityOldVersion == true) {
vxPart = vector<Real>(nCell, 0.0);
vyPart = vector<Real>(nCell, 0.0);
vzPart = vector<Real>(nCell, 0.0);
if (twoSize) {
phiPart1 = vector<Real>(nCell, 0.0);
phiPart2 = vector<Real>(nCell, 0.0);
vxPart1 = vector<Real>(nCell, 0.0);
vxPart2 = vector<Real>(nCell, 0.0);
vyPart1 = vector<Real>(nCell, 0.0);
vyPart2 = vector<Real>(nCell, 0.0);
vzPart1 = vector<Real>(nCell, 0.0);
vzPart2 = vector<Real>(nCell, 0.0);
averageDrag1 = vector<Real>(nCell, 0.0);
averageDrag2 = vector<Real>(nCell, 0.0);
}
for (int n = 0; n < nCell; n++) {
vxPart[n] = vPart[n][0];
vyPart[n] = vPart[n][1];
vzPart[n] = vPart[n][2];
if (twoSize) {
if (radiusParts.size() != 2)
throw runtime_error("More than two particle size, not compatible with averagedProfile function and twosize option");
phiPart1[n] = phiAverageMulti[0][n];
phiPart2[n] = phiAverageMulti[1][n];
vxPart1[n] = vAverageMultiX[0][n];
vxPart2[n] = vAverageMultiX[1][n];
vyPart1[n] = vAverageMultiY[0][n];
vyPart2[n] = vAverageMultiY[1][n];
vzPart1[n] = vAverageMultiZ[0][n];
vzPart2[n] = vAverageMultiZ[1][n];
averageDrag1[n] = dragAverageMulti[0][n];
averageDrag2[n] = dragAverageMulti[1][n];
}
}
}
}
//////////////////////////////////////////////////////////////////////////////////////////// END OF HydroForceEngine::averageProfile
////////////////////////////////////////////////////////////////////////////////////////////////////////////
// TURBULENT VELOCITY FLUCTUATIONS MODELS
/* Velocity fluctuation determination. To execute at a given (changing) period corresponding to the eddy turn over time*/
/* Should be initialized before running HydroForceEngine */
void HydroForceEngine::turbulentFluctuation()
{
/* check size */
size_t size = vFluctX.size();
if (size < scene->bodies->size()) {
size = scene->bodies->size();
vFluctX.resize(size);
vFluctY.resize(size);
vFluctZ.resize(size);
}
/* reset stored values to zero */
#if (YADE_REAL_BIT <= 64)
memset(&vFluctX[0], 0, size);
memset(&vFluctY[0], 0, size);
memset(&vFluctZ[0], 0, size);
#else
// the standard way, perfectly optimized by compiler.
std::fill(vFluctX.begin(), vFluctX.end(), 0);
std::fill(vFluctY.begin(), vFluctY.end(), 0);
std::fill(vFluctZ.begin(), vFluctZ.end(), 0);
#endif
/* Create a random number generator rnd() with a gaussian distribution of mean 0 and stdev 1.0 */
/* see http://www.boost.org/doc/libs/1_55_0/doc/html/boost_random/reference.html and the chapter 7 of Numerical Recipes in C, second edition (1992) for more details */
static boost::minstd_rand0 randGen((int)TimingInfo::getNow(true));
static boost::normal_distribution<Real> dist(0.0, 1.0);
static boost::variate_generator<boost::minstd_rand0&, boost::normal_distribution<Real>> rnd(randGen, dist);
Real rand1 = 0.0;
Real rand2 = 0.0;
Real rand3 = 0.0;
/* Attribute a fluid velocity fluctuation to each body above the bed elevation */
FOREACH(Body::id_t id, ids)
{
Body* b = Body::byId(id, scene).get();
if (!b) continue;
if (!(scene->bodies->exists(id))) continue;
const Sphere* sphere = dynamic_cast<Sphere*>(b->shape.get());
if (sphere) {
Vector3r posSphere = b->state->pos; //position vector of the sphere
int p = int(math::floor((posSphere[2] - zRef) / deltaZ)); //cell number in which the particle is
// If the particle is inside the water and above the bed elevation, so inside the turbulent flow, evaluate a turbulent fluid velocity fluctuation which will be used to apply the drag.
// The fluctuation magnitude is linked to the value of the Reynolds stress tensor at the given position, a kind of local friction velocity ustar
// The fluctuations along wall-normal and streamwise directions are correlated in order to be consistent with the formulation of the Reynolds stress tensor and to recover the result
// that the magnitude of the fluctuation along streamwise = 2*along wall normal
if ((p < nCell)
&& (posSphere[2] - zRef
> bedElevation)) { // Remove the particles outside of the flow and inside the granular bed, they are not submitted to turbulent fluctuations.
Real uStar2 = ReynoldStresses[p] / densFluid;
if (uStar2 > 0.0) {
Real uStar = sqrt(uStar2);
rand1 = rnd();
rand2 = rnd();
rand3 = rnd();
// Free surface flow: x and z fluctuation are correlated as measured by Nezu 1977 and as expected from the formulation of the Reynolds stress tensor.
if (unCorrelatedFluctuations == false) rand3 = -rand1 + rnd();
vFluctZ[id] = rand1 * uStar;
vFluctY[id] = rand2 * uStar;
vFluctX[id] = rand3 * uStar;
}
} else {
vFluctZ[id] = 0.0;
vFluctY[id] = 0.0;
vFluctX[id] = 0.0;
}
}
}
}
/* Alternative Velocity fluctuation model, same as turbulentFluctuation model but with a time step associated with the fluctuation generation depending on z */
/* Should be executed in the python script at a period dtFluct corresponding to the smallest value of the fluctTime vector */
/* Should be initialized before running HydroForceEngine */
void HydroForceEngine::turbulentFluctuationZDep()
{
int idPartMax = vFluctX.size();
Real rand1 = 0.0;
Real rand2 = 0.0;
Real rand3 = 0.0;
/* Create a random number generator rnd() with a gaussian distribution of mean 0 and stdev 1.0 */
/* see http://www.boost.org/doc/libs/1_55_0/doc/html/boost_random/reference.html and the chapter 7 of Numerical Recipes in C, second edition (1992) for more details */
static boost::minstd_rand0 randGen((int)TimingInfo::getNow(true));
static boost::normal_distribution<Real> dist(0.0, 1.0);
static boost::variate_generator<boost::minstd_rand0&, boost::normal_distribution<Real>> rnd(randGen, dist);
//Loop on the particles
for (int idPart = 0; idPart < idPartMax; idPart++) {
//Remove the time ran since last application of the function (dtFluct define in global)
fluctTime[idPart] -= dtFluct;
//If negative, means that the time of application of the fluctuation is over, generate a new one with a new associated time
if (fluctTime[idPart] <= 0) {
fluctTime[idPart] = 10 * dtFluct; //Initialisation of the application time
Body* b = Body::byId(idPart, scene).get();
if (!b) continue;
if (!(scene->bodies->exists(idPart))) continue;
const Sphere* sphere = dynamic_cast<Sphere*>(b->shape.get());
Real uStar = 0.0;
if (sphere) {
Vector3r posSphere = b->state->pos; //position vector of the sphere
int p = int(math::floor((posSphere[2] - zRef) / deltaZ)); //cell number in which the particle is
if (ReynoldStresses[p] > 0.0) uStar = sqrt(ReynoldStresses[p] / densFluid);
// Remove the particles outside of the flow and inside the granular bed, they are not submitted to turbulent fluctuations.
if ((p < nCell) && (posSphere[2] - zRef > bedElevation)) {
rand1 = rnd();
rand2 = rnd();
rand3 = rnd();
// Free surface flow: x and z fluctuation are correlated as measured by Nezu 1977 and as expected from the formulation of the Reynolds stress tensor.
if (unCorrelatedFluctuations == false) rand3 = -rand1 + rnd();
vFluctZ[idPart] = rand1 * uStar;
vFluctY[idPart] = rand2 * uStar;
vFluctX[idPart] = rand3 * uStar;
// Limit the value to avoid the application of fluctuations in the viscous sublayer
const Real zPos = max(b->state->pos[2] - zRef - bedElevation, 11.6 * viscoDyn / densFluid / uStar);
// Time of application of the fluctuation as a function of depth from kepsilon model
if (uStar > 0.0) fluctTime[idPart] = min(0.33 * 0.41 * zPos / uStar, 10.);
} else {
vFluctZ[idPart] = 0.0;
vFluctY[idPart] = 0.0;
vFluctX[idPart] = 0.0;
fluctTime[idPart] = 0.0;
}
}
}
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////
/* Fluid Resolution */
///////////////////////
// Fluid resolution routine: 1D vertical volume-averaged fluid momentum balance resolution
void HydroForceEngine::fluidResolution(Real tfin, Real dt)
{
//Variables declaration
int i, j, maxiter, q, ii;
Real phi_nodej, termeVisco_j, termeVisco_jp1, termeTurb_j, termeTurb_jp1, viscof, dz, sum, phi_lim, dudz, ustar, fluidHeight, urel, urel_bound, Re, eps,
ff, ffold, delta, dddiv, ejm1, phijm1, upjm1, ejp1, phijp1, upjp1, secondMemberPart;
vector<Real> sig(nCell, 0.0), dsig(nCell - 1, 0.), viscoeff(nCell, 0.), ufn(nCell + 1, 0.), wallFriction(nCell - 1, 0.), viscoft(nCell, 0.),
ufnp(nCell + 1, 0.), a(nCell + 1, 0.), b(nCell + 1, 0.), c(nCell + 1, 0.), s(nCell + 1, 0.), lm(nCell, 0.), ddem(nCell + 1, 0.),
ddfm(nCell + 1, 0.), deltaz(nCell, 0.), epsilon_node(nCell, 0.), epsilon(nCell, 0.);
//Initialisation
Real time = 0;
ufn = vxFluid; //Assign the global variable vxFluid to ufn, i.e. the last fluid velocity profile evaluated
viscof = viscoDyn / densFluid; // compute the kinematic viscosity
dz = deltaZ;
Real imp = 0.5; // Implicitation factor of the lateral sink term due to wall friction
// compute fluid phase volume fraction
for (j = 0; j < nCell; j++) {
epsilon[j] = 1. - phiPart[j];
}
// Mesh definition: regular of step dz
sig[0] = 0.;
dsig[0] = dz;
for (j = 1; j < nCell - 1; j++) {
sig[j] = sig[j - 1] + dsig[j - 1];
dsig[j] = dz;
}
sig[nCell - 1] = sig[nCell - 2] + dsig[nCell - 2];
// Usefull quantities for the staggered grid, i.e. quantities defined at mesh nodes or in between (velocity nodes)
for (j = 0; j < nCell; j++) {
if ((j != 0) && (j != nCell - 1)) {
deltaz[j] = 0.5 * (dsig[j - 1] + dsig[j]); //Space between two velocity nodes, j-1/2 and j+1/2
epsilon_node[j] = 0.5
* (epsilon[j - 1] + epsilon[j]); //Fluid volume fraction extrapolated at the regular mesh node j (evaluated at velocity nodes)
} else if (j == 0) {
deltaz[j] = 0.5 * dsig[j]; //Space between velocity node 0 (boundary) and velocity node 1/2
epsilon_node[j] = epsilon[j]; //Fluid volume fraction at the bottom, taken to be equal to the one at the first step (choice)
} else if (j == nCell - 1) {
deltaz[j] = 0.5 * dsig[j - 1]; //Space between velocity node ndimz-3/2 and velocity node ndimz-1 (boundary)
epsilon_node[j] = epsilon[j - 1]; //Fluid volume fraction at the top, taken to be equal to the one at the last step (choice)
}
}
// compute the fluid height
fluidHeight = sig[nCell - 1];
//////////////////////////////////// // computeTaufsi(dt);
// Compute the fluid-particle momentum transfer associated to drag force, taufsi = phi/Vp*<fd>/rhof/(uf - up), not changing during the fluid resolution
//Initialization
taufsi.resize(nCell);
#if (YADE_REAL_BIT <= 64)
memset(&taufsi[0], 0, nCell); //Resize and initialize taufsi
#else
// the standard way, perfectly optimized by compiler.
std::fill(taufsi.begin(), taufsi.end(), 0);
#endif
Real lim = 1e-5, dragTerm = 0., partVolume = 1.;
vector<Real> partVolumeMulti(radiusParts.size(), 1.);
// Evaluate particles volume
if (twoSize || enableMultiClassAverage) {
for (unsigned int r = 0; r < radiusParts.size(); r++) {
partVolumeMulti[r] = 4. / 3. * Mathr::PI * pow(radiusParts[r], 3);
}
} else {
partVolume = 4. / 3. * Mathr::PI * pow(radiusPart, 3);
}
// Compute taufsi
taufsi[0] = 0.;
for (i = 1; i < nCell; i++) {
if (twoSize || enableMultiClassAverage) {
dragTerm = 0.;
for (unsigned int r = 0; r < radiusParts.size(); r++)
dragTerm += (multiPhiPart[r][i] / partVolumeMulti[r] * multiDragPart[r][i]);
} else {
dragTerm = phiPart[i] / partVolume * averageDrag[i];
}
urel = math::abs(
ufn[i + 1]
- vPart[i]
[0]); // Difference of definition between ufn and vxPart, ufn starts at 0, while vxPart starts at 1/2. The two therefore corresponds for i+1 and i
urel_bound = math::max(urel, lim); //limit the value to avoid division by 0
taufsi[i] = math::max(
0.,
math::min(
dragTerm / urel_bound / densFluid,
pow(10 * dt,
-1.))); //limit the max value of taufsi to the fluid resolution limit, i.e. 1/(10dt) and required positive (charact. time)
}
////////////////////////////////////
// Compute the effective viscosity (due to the presence of particles)
switch (irheolf) {
// 0 : Pure fluid viscosity
case 0: {
for (j = 0; j < nCell; j++)
viscoeff[j] = viscof;
}; break;
// 1 : Einstein's effective viscosity
case 1: {
viscoeff[0] = viscof * (1. + 2.5 * phiPart[0]);
for (j = 1; j < nCell; j++) {
phi_nodej = 0.5 * (phiPart[j - 1] + phiPart[j]); // solid volume fraction at (scalar) node j.
viscoeff[j] = viscof * (1. + 2.5 * phi_nodej);
}
}; break;
//2: fluid volume fraction power-law effective viscosity
case 2: {
viscoeff[0] = viscof * (1. + 2.5 * phiPart[0]);
for (j = 1; j < nCell; j++) {
phi_nodej = 0.5 * (phiPart[j - 1] + phiPart[j]); // solid volume fraction at (scalar) node j.
viscoeff[j] = viscof * pow(1 - phi_nodej, -2.8);
}
}; break;
//default
default: throw std::runtime_error("HydroForceEngine: irheolf should take an integer value between 0 and 2.");
}
////////////////////////////////////
// Compute the mixing length
switch (ilm) {
// ilm = 0 : Prandtl mixing length
case 0: {
lm[0] = 0.;
for (j = 1; j < nCell; j++)
lm[j] = kappa * sig[j];
}; break;
// ilm = 1 : Parabolic profile (free surface flows)
case 1: {
lm[0] = 0.;
for (j = 1; j < nCell; j++)
lm[j] = kappa * sig[j] * sqrt(1. - sig[j] / fluidHeight);
lm[nCell - 1] = 0.;
}; break;
// ilm = 2 : Li and Sawamoto (1995) integral of concentration profile
case 2: {
sum = 0.;
lm[0] = 0.;
//Threshold the value of the solid volume fraction:once the profile reach phiMax,
// the lower part of the bed is considered to be at phiMax. This fully damp the turbulence in the bed.
int nPhiMax = nCell;
while (phiPart[nPhiMax] < phiMax)
nPhiMax -= 1;
for (j = 1; j < nCell; j++) {
if (j - 1 < nPhiMax) phi_lim = phiMax;
else
phi_lim = phiPart[j - 1];
sum += kappa * (phiMax - phi_lim) / phiMax * dsig[j - 1];
lm[j] = sum;
}
}; break;
// ilm = 3 : TODO, TEST : enableMultiClassAverage must be true
case 3: {
const Real cvd = 0.5;
for (j = 0; j < nCell; j++) {
int k = j;
Real lmpj = cvd * computePoreLength(j);
Real zj = sig[j];
Real lmp = lmpj;
Real lmz = 0;
k--;
while (k > 0 and lmp > lmz) {
const Real zvd = (zj - sig[k]);
lmp = cvd * computePoreLength(k);
lmz = kappa * zvd;
k--;
}
lm[j] = lmz;
}
}; break;
// ilm = 4 : Gauthier Rousseau's model, based on phiMax.
case 4: {
const Real viscoKin = viscoDyn / densFluid;
const Real revd = 26.0;
const Real cvd = 0.5;
// computing lp
Real volumeAverage = 0.0;
Real surfaceAverage = 0.0;
for (unsigned int l = 0; l < radiusParts.size(); l++) {
const Real vj = 4.0 / 3.0 * Mathr::PI * pow(radiusParts[l], 3.0);
const Real sj = 4.0 * Mathr::PI * pow(radiusParts[l], 2.0);
volumeAverage += vj;
surfaceAverage += sj;
}
const Real lp = (1.0 - phiMax) / phiMax * volumeAverage / surfaceAverage;
// lp computed
Real zvd = 0.;
lm[0] = 0.;
for (j = 1; j < nCell; j++) {
Real phiLim = std::min(phiPart[j - 1], phiMax);
zvd += sqrt((phiMax - phiLim) / phiMax) * dsig[j - 1];
lm[j] = kappa * zvd * (1 - exp(-sqrt(fabs(zvd * vxFluid[j]) / viscoKin) / revd)) + cvd * lp;
}
}; break;
// ilm = 5 : TODO, TEST : Model based on Ni and Capart 2018 results and Gauthier Rousseau's Thesis results.
case 5: {
// Coefficient given by Gauthier Rousseau.
const Real clp = 0.5;
// Coefficient given by Ni and Capart.
const Real cd = 0.2;
// Computes the position of the bed.
const Real zBed = sig[computeZbedIndex()];
// Computes lm
for (j = 0; j < nCell; j++) {
lm[j] = max(min(clp * computePoreLength(j), cd * computeDiameter(j)), kappa * (sig[j] - zBed));
}
}; break;
// ilm = 6 : TODO, TEST : Model of mixing length for pipe flow, combining Li & Sawamoto and pipe flow Prantl mixing length
case 6: {
//Initialization
vector<Real> lm_bot(nCell, 0.);
vector<Real> lm_top(nCell, 0.);
// Li & Sawamoto mixing length from the bottom
sum = 0.;
//Threshold the value of the solid volume fraction:once the profile reach phiMax,
// the lower part of the bed is considered to be at phiMax. This fully damp the turbulence in the bed.
int nPhiMax = nCell;
while (phiPart[nPhiMax] < phiMax)
nPhiMax -= 1;
for (j = 1; j < nCell; j++) {
if (j - 1 < nPhiMax) phi_lim = phiMax;
else
phi_lim = phiPart[j - 1];
sum += kappa * (phiMax - phi_lim) / phiMax * dsig[j - 1];
lm_bot[j] = sum;
}
//Prantl mixing length from the top
lm_top[nCell - 1] = 0.;
for (j = nCell - 1; j >= 0; j--)
lm_top[j] = kappa * (sig[nCell - 1] - sig[j]);
//Final mixing length as the minimum between the two
for (j = 1; j < nCell; j++)
lm[j] = min(lm_bot[j], lm_top[j]);
}; break;
//default: error
default: throw std::runtime_error("HydroForceEngine: ilm should take an integer value between 0 and 6.");
}
// end switch ilm
///////////////////////////////////////////////
// FLUID VELOCITY PROFILE RESOLUTION: LOOP OVER TIME (main loop)
while (time < tfin) {
// Advance time
time = time + dt;
////////////////////////////////////
// Compute the eddy viscosity depth profile, viscoft
// Eddy viscosity
switch (iturbu) {
// 0 : No turbulence
case 0: {
for (j = 0; j < nCell; j++)
viscoft[j] = 0.;
}; break;
// iturbu = 1 : Turbulence activated
case 1: {
// Compute the velocity gradient and the turbulent viscosity
for (j = 0; j < nCell; j++) {
dudz = (ufn[j + 1] - ufn[j]) / deltaz[j];
viscoft[j] = pow(lm[j], 2) * fabs(dudz);
}
// test on y+ for viscous sublayer for log profile validation
ustar = sqrt(fabs(gravity[0]) * sig[nCell - 1]);
if (viscousSubLayer == 1) {
for (j = 1; j < nCell; j++)
if (sig[j] * ustar / viscof < 11.3) viscoft[j] = 0.;
}
}; break;
//default: error
default: throw std::runtime_error("HydroForceEngine: iturbu should take an integer value between 0 and 1.");
}
//////////////////////////////////// end switch iturbu
//////////////////////////////////
// Compute the lateral wall friction profile, if activated
if (fluidWallFriction == true) {
switch (wallFrictionModel) {
case 0: { //Blasius 1913
for (j = 0; j < nCell - 1; j++) {
Re = max(1e-10, fabs(ufn[j + 1]) * channelWidth / viscof);
wallFriction[j] = fluidFrictionCoef * 0.3164 / pow(Re, 0.25);
}
}; break;
case 1: { //Graf and Altinakar 1998
maxiter = 100; //Maximum number iteration for the resolution
eps = 1e-2; //Tolerance for the equation resolution
for (j = 0; j < nCell - 1; j++) {
Re = max(1e-10, fabs(ufn[j + 1]) * channelWidth / viscof);
ffold = pow(0.32, -2); //Initial guess of the friction factor
delta = 1e10; //Initialize at a random value greater than eps
q = 0;
while ((delta >= eps)
&& (q
< maxiter)) { //Loop while the required precision is reached or the maximum iteration number is overpassed
q += 1;
//Graf and Altinakar 1993 formulation of the friction factor
ff = pow(2. * log10(Re * sqrt(ffold) / 4) + 0.32, -2);
delta = fabs(ff - ffold) / ffold;
ffold = ff;
}
if (q == maxiter) ff = 0.;
wallFriction[j] = fluidFrictionCoef * ff;
}
}; break;
default: throw std::runtime_error("HydroForceEngine: wallFrictionModel should take an integer value between 0 and 1.");
}
}
////////////////////////////////// end wall friction
//////////////////////////////////
// Compute the system of equation in matricial form (Compute a,b,c,s)
// Bottom boundary condition: (always no-slip)
a[0] = 0.;
b[0] = 1.;
c[0] = 0.;
s[0] = 0.;
// Top boundary condition: (0: no-slip / 1: zero gradient)
if (iusl == 0) {
a[nCell] = 0.;
b[nCell] = 1.;
c[nCell] = 0.;
s[nCell] = uTop;
} else if (iusl == 1) {
a[nCell] = -1.;
b[nCell] = 1.;
c[nCell] = 0.;
s[nCell] = 0.;
}
//Loop over the spatial mesh to determine the matricial coefficient, (a,b,c,s), from j+1=1 to j+1=nCell-1 (values 0 and nCell correspond to BC)
for (j = 0; j < nCell - 1; j++) {
//Interesting quantities to compute
termeVisco_j = dt * epsilon[j] / dsig[j] * viscoeff[j] / deltaz[j];
termeVisco_jp1 = dt * epsilon[j] / dsig[j] * viscoeff[j + 1] / deltaz[j + 1];
termeTurb_j = dt / dsig[j] * epsilon_node[j] * viscoft[j] / deltaz[j];
termeTurb_jp1 = dt / dsig[j] * epsilon_node[j + 1] * viscoft[j + 1] / deltaz[j + 1];
if (j == 0) {
ejm1 = epsilon[j];
phijm1 = phiPart[j];
upjm1 = vPart[j][0];
} else {
ejm1 = epsilon[j - 1];
phijm1 = phiPart[j - 1];
upjm1 = vPart[j - 1][0];
}
if (j == nCell - 1) {
ejp1 = epsilon[j];
phijp1 = phiPart[j];
upjp1 = vPart[j][0];
} else {
ejp1 = epsilon[j + 1];
phijp1 = phiPart[j + 1];
upjp1 = vPart[j + 1][0];
}
secondMemberPart = dt * epsilon[j] / dsig[j]
* (viscoeff[j + 1] / deltaz[j + 1] * (phijp1 * upjp1 - phiPart[j] * vPart[j][0])
- viscoeff[j] / deltaz[j] * (phiPart[j] * vPart[j][0] - phijm1 * upjm1));
// LHS: algebraic system coefficients
a[j + 1] = -termeVisco_j * ejm1 - termeTurb_j; //eq. 24 of the manual Maurin 2018
b[j + 1] = termeVisco_jp1 * epsilon[j] + termeVisco_j * epsilon[j] + termeTurb_jp1 + termeTurb_j + epsilon[j] + dt * taufsi[j]
+ imp * dt * epsilon[j] * 2. / channelWidth * 0.125 * wallFriction[j]
* pow(ufn[j + 1], 2); //eq. 25 of the manual Maurin 2018 + fluid wall correction
c[j + 1] = -termeVisco_jp1 * ejp1 - termeTurb_jp1; //eq. 26 of the manual Maurin 2018
// RHS: unsteady, gravity, drag, pressure gradient, lateral wall friction
s[j + 1] = ufn[j + 1] * epsilon[j] + epsilon[j] * dt * math::abs(gravity[0]) + dt * taufsi[j] * vPart[j][0] + secondMemberPart
- (1. - imp) * dt * epsilon[j] * 2. / channelWidth * 0.125 * wallFriction[j] * pow(ufn[j + 1], 2)
- epsilon[j] * dpdx / densFluid * dt; //eq. 27 of the manual Maurin 2018 + fluid wall correction and pressure gradient forcing.
}
//////////////////////////////////
////////////////////////////////////
// Solve the matricial tridiagonal system using Real-sweep algorithm
// downward sweep
dddiv = b[0];
ddem[0] = -c[0] / dddiv;
ddfm[0] = s[0] / dddiv;
for (i = 1; i <= nCell - 1; i++) {
dddiv = b[i] + a[i] * ddem[i - 1];
ddem[i] = -c[i] / dddiv;
ddfm[i] = (s[i] - a[i] * ddfm[i - 1]) / dddiv;
}
// upward sweep
dddiv = b[nCell] + a[nCell] * ddem[nCell - 1];
ddfm[nCell] = (s[nCell] - a[nCell] * ddfm[nCell - 1]) / dddiv;
ufnp[nCell] = ddfm[nCell];
for (ii = 1; ii < nCell + 1; ii++) {
i = nCell - ii;
ufnp[i] = ddem[i] * ufnp[i + 1] + ddfm[i];
}
//////////////////////////////////
// Update solution for next time step
for (j = 0; j < nCell + 1; j++)
ufn[j] = ufnp[j];
}
///////////////////////////// END OF THE LOOP ON THE TIME
//Update Fluid velocity, turbulent viscosity and Reynolds stresses
ReynoldStresses.resize(nCell);
turbulentViscosity.resize(nCell);
vxFluid.resize(nCell + 1);
#if (YADE_REAL_BIT <= 64)
memset(&ReynoldStresses[0], 0, nCell);
memset(&turbulentViscosity[0], 0, nCell);
memset(&vxFluid[0], 0, nCell + 1);
#else
// the standard way, perfectly optimized by compiler.
std::fill(ReynoldStresses.begin(), ReynoldStresses.end(), 0);
std::fill(turbulentViscosity.begin(), turbulentViscosity.end(), 0);
std::fill(vxFluid.begin(), vxFluid.end(), 0);
#endif
for (j = 0; j < nCell; j++) {
vxFluid[j] = ufn[j]; // Update fluid velocity
turbulentViscosity[j] = viscoft[j];
ReynoldStresses[j] = densFluid * epsilon_node[j] * viscoft[j] * (ufn[j + 1] - ufn[j]) / deltaz[j];
}
vxFluid[nCell] = ufn[nCell];
}
//End of fluid resolution
/* Computes the pore length scale
*
*/
Real HydroForceEngine::computePoreLength(int i)
{
const Real lim = 1e-3;
Real lp = 0.0;
Real volumeAverage = 0.0;
Real surfaceAverage = 0.0;
for (unsigned int j = 0; j < radiusParts.size(); j++) {
const Real vj = 4.0 / 3.0 * Mathr::PI * pow(radiusParts[j], 3.0);
const Real sj = 4.0 * Mathr::PI * pow(radiusParts[j], 2.0);
volumeAverage += multiPhiPart[j][i] * vj;
surfaceAverage += multiPhiPart[j][i] * sj;
}
if (phiPart[i] > 0.0) {
volumeAverage /= phiPart[i];
surfaceAverage /= phiPart[i];
}
if (surfaceAverage <= 0.0) {
lp = (1.0 - phiPart[i]) / max(phiPart[i], lim);
} else {
lp = (1.0 - phiPart[i]) / max(phiPart[i], lim) * volumeAverage / surfaceAverage;
}
return lp;
}
/* Gets the position where to start the Prandt model using a dichotomique method.
*
*/
int HydroForceEngine::computeZbedIndex()
{
const vector<Real> averagePhiPartT = computePhiPartAverageOverTime();
int iLeft = 0;
int iRight = phiPart.size() - 1;
int iMiddle;
do {
iMiddle = (iLeft + iRight) / 2;
if (averagePhiPartT[iMiddle] > phiBed) {
iLeft = iMiddle + 1;
} else {
iRight = iMiddle - 1;
}
} while (iRight > iLeft);
return iLeft;
}
/* Computes the diameter
*
*/
Real HydroForceEngine::computeDiameter(int i)
{
Real d = 0.0;
Real volumeAverage = 0.0;
Real surfaceAverage = 0.0;
for (unsigned int j = 0; j < radiusParts.size(); j++) {
const Real vj = 4.0 / 3.0 * Mathr::PI * pow(radiusParts[j], 3.0);
const Real sj = 4.0 * Mathr::PI * pow(radiusParts[j], 2.0);
volumeAverage += multiPhiPart[j][i] * vj;
surfaceAverage += multiPhiPart[j][i] * sj;
}
if (phiPart[i] > 0.0) {
volumeAverage /= phiPart[i];
surfaceAverage /= phiPart[i];
}
if (surfaceAverage <= 0.0) {
d = 0.0;
} else {
d = 6.0 * volumeAverage / surfaceAverage;
}
return d;
}
/* Computes the mean profile over the nbAverageT time.
*
*/
vector<Real> HydroForceEngine::computePhiPartAverageOverTime()
{
if (nbAverageT == 0) {
return phiPart;
} else {
vector<Real> averagePhiPartT(nCell, 0.0);
std::queue<vector<Real>> q = phiPartT;
while (!q.empty()) {
vector<Real> phiTmp = q.front();
for (unsigned int j = 0; j < averagePhiPartT.size(); j++) {
averagePhiPartT[j] += phiTmp[j];
}
q.pop();
}
for (unsigned int j = 0; j < averagePhiPartT.size(); j++) {
averagePhiPartT[j] /= phiPartT.size();
}
return averagePhiPartT;
}
}
///////////////////////////////////////////////////////////////////////// END OF HydroForceEngine::fluidResolutionNEW
} // namespace yade
|
