Week 2 - Flow over a Cylinder.

Phenomenon of Karman Vortex street.

In fluid dynamics, a Karman vortex street is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies.

It is named after the engineer and fluid dynamicist Theodore von Kármán,and is responsible for such phenomena as the "singing" of suspended telephone or power lines and the vibration of a car antenna at certain speeds. Mathematical modeling of von Kármán vortex street can be performed using different techniques including but not limited to solving the full Navier-Stokes equations with k-epsilon, SST, k-omega and Reynolds stress, and large eddy simulation (LES) turbulence models,by numerically solving some dynamic equations such as the Ginzburg-Landau equation, or by use of a bicomplex variable.

A vortex street will form only at a certain range of flow velocities, specified by a range of Reynolds numbers (Re), typically above a limiting Re value of about 90. The (global) Reynolds number for a flow is a measure of the ratio of inertial to viscous forces in the flow of a fluid around a body or in a channel, and may be defined as a nondimensional parameter of the global speed of the whole fluid flow:

`Re_L=(UL)/v_0`

where:

• `U` = the free stream flow speed (i.e. the flow speed far from the fluid boundaries `U_oo` like the body speed relative to the fluid at rest, or an inviscid flow speed, computed through the Bernoulli equation), which is the original global flow parameter, i.e. the target to be non-dimensionalised.
• `L` = a characteristic length parameter of the body or channel
• `v_0` = the free stream kinematic viscosity parameter of the fluid, which in turn is the ratio:

between:

• `rho_0` = the reference fluid density.
• `mu_0`= the free stream fluid dynamic viscosity

This formula will generally hold true for the range 250 < Re_d < 200000:

• f = vortex shedding frequency.
• d = diameter of the cylinder
• U = flow velocity.

Now, simulating the flow over a 2-D cylinder with a velocity of 1m/s form the inlet.

Properties of simulating the flow over the 2-D cylinder :

• Flow over a cylinder is important in many industrial application like cooling of iron or cylindrical pipe.
• Circular pipes have more application in heat exchanger. High temperature flue gases flow over a circular cylinder in a cross flow.
• Depending on flow rate, fluid properties and size of cylinder, the flow can be laminar, transition and turbulent.
• Larger vortexes are found at lower Reynolds number.

Now the geometry of the 2D cylinder :

Here, the length and width of the rectangle 60m and 20m and diameter of the cylinder in 2-D is 2m and remaining details of the geometry is mentioned below.

Details of the geometry:

Geometry of the 2-D strucutre with the above mention detials is shown below:

Now to get the accurate number of result for the cylinder we have to use sizing option in the meshing where we can increase the number of divisions inside the cylinder for the accurate result.

To get the above number of divisions change the parameters to the requirement of the geometry.

After doing the sizing of the cylinder we have to put the layers around the cylinder for better meshing quality.

After changing the inflation option and inserting the layer height and maximum layers as per requirement which have been shown above. The geometry is shown below:

After changing the parameters before the meshing now the meshing properties has to change from the default element size to 0.5m.

When meshing is done we have to simulate geometry with laminar flow and with velocity inlet 1 m/s. We have to simulate the flow at different reynolds number 10 , 100, 1000, 10000, 100000 at the monitor poin which we have to locate at a distance of four times to the dimaeter to right from the axis. After doing all this we have intiliaze it and simulate it and need to find the coefficient of drag and lift for different reynolds number.

Part 1)

Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.

By putting the dynamic viscosity value from the Reynolds Formulae `Re=(rhouL)/mu`

Re=100

`rho`=1

u=1

L=2

From this we can find the dynmaic viscosity of the flow and put the value of dynamic viscosity in the chart.

Steady state:

At steady state with reynolds number=100 we can see the vortex shedding from the given figure of velocity contour and variation of the velocity from the cylinder.

Now, pressure contour of the geometry of steady state flow.

Residuals of the geometry :

Coefficient of lift of the steady state flow from the geometry:

Coefficient of drag for steady state flow of geometry.

Vertex average of the velocity for the geometry.

Vertex average of the velocity from the monitor point of the geometry.

Calculation of Strouhal Nuber for coefficient of lift with 400 iterations.

(title "Spectral Analysis of lift-rfile")
(labels "Strouhal Number" "Magnitude")

((xy/key/label "lift")
0.0000000e+00	6.6773295e-03
3.3333334e-03	1.1412264e-02
6.6666668e-03	1.0351874e-02
9.9999998e-03	9.7052371e-03
1.3333334e-02	8.7320562e-03
1.6666668e-02	7.4809543e-03
2.0000000e-02	5.8109425e-03
2.3333333e-02	4.1736900e-03
2.6666667e-02	4.6537281e-03
2.9999999e-02	6.7380853e-03
3.3333335e-02	6.5433425e-03
3.6666665e-02	1.4780679e-02
3.9999999e-02	1.4757242e-02
4.3333333e-02	8.9079551e-02
4.6666667e-02	8.1655473e-02
5.0000001e-02	1.6596172e-02
5.3333335e-02	1.5356806e-02
5.6666669e-02	7.3536090e-03
5.9999999e-02	7.9789776e-03
6.3333333e-02	5.7733045e-03
6.6666670e-02	5.4370910e-03
7.0000000e-02	4.8015900e-03
7.3333330e-02	4.4271736e-03
7.6666668e-02	4.2064548e-03
7.9999998e-02	3.4331868e-03
8.3333336e-02	3.6623729e-03
8.6666666e-02	2.0610539e-03
9.0000004e-02	3.3696855e-03
9.3333334e-02	3.7754013e-03
9.6666664e-02	2.9838106e-03
1.0000000e-01	2.8464491e-03
1.0333333e-01	2.8562457e-03
1.0666667e-01	2.4112968e-03
1.1000000e-01	2.8487258e-03
1.1333334e-01	2.4961319e-03
1.1666667e-01	2.7725848e-03
1.2000000e-01	2.5450455e-03
1.2333333e-01	2.4679701e-03
1.2666667e-01	2.2780721e-03
1.3000000e-01	2.2030233e-03
1.3333334e-01	7.3226041e-04
1.3666667e-01	3.5774359e-03
1.4000000e-01	3.1867330e-03
1.4333333e-01	2.6058753e-03
1.4666666e-01	2.7081189e-03
1.5000001e-01	2.6283464e-03
1.5333334e-01	2.7652120e-03
1.5666667e-01	2.7985743e-03
1.6000000e-01	2.6085016e-03
1.6333333e-01	2.8241295e-03
1.6666667e-01	2.3952110e-03
1.7000000e-01	2.6772092e-03
1.7333333e-01	2.2396981e-03
1.7666666e-01	2.2834423e-03
1.8000001e-01	2.5895645e-03
1.8333334e-01	3.1477022e-03
1.8666667e-01	2.4521602e-03
1.9000000e-01	2.5662216e-03
1.9333333e-01	2.4492487e-03
1.9666667e-01	2.6077358e-03
2.0000000e-01	2.5147416e-03
2.0333333e-01	2.4338346e-03
2.0666666e-01	2.6336131e-03
2.0999999e-01	2.4375378e-03
2.1333334e-01	2.4696400e-03
2.1666667e-01	2.3575865e-03
2.2000000e-01	2.4392144e-03
2.2333333e-01	2.4770601e-03
2.2666667e-01	2.2191817e-03
2.3000000e-01	2.2516854e-03
2.3333333e-01	2.3672509e-03
2.3666666e-01	2.3250098e-03
2.3999999e-01	2.4144491e-03
2.4333334e-01	2.3663372e-03
2.4666667e-01	2.2008258e-03
2.5000000e-01	2.2884964e-03
2.5333333e-01	2.1894581e-03
2.5666666e-01	2.4549684e-03
2.5999999e-01	2.2245781e-03
2.6333332e-01	2.2612878e-03
2.6666668e-01	2.5278707e-03
2.7000001e-01	2.1807270e-03
2.7333334e-01	1.7979003e-03
2.7666667e-01	2.1545889e-03
2.8000000e-01	2.0940264e-03
2.8333333e-01	2.1452261e-03
2.8666666e-01	1.8166990e-03
2.8999999e-01	2.0531453e-03
2.9333332e-01	1.8668638e-03
2.9666665e-01	1.7080074e-03
3.0000001e-01	2.0510142e-03
3.0333334e-01	1.7449132e-03
3.0666667e-01	1.9562761e-03
3.1000000e-01	1.9300041e-03
3.1333333e-01	1.7998385e-03
3.1666666e-01	1.7616086e-03
3.1999999e-01	1.9191341e-03
3.2333332e-01	1.7436397e-03
3.2666665e-01	1.8450582e-03
3.3000001e-01	1.6611702e-03
3.3333334e-01	1.6786343e-03
3.3666667e-01	1.6914828e-03
3.4000000e-01	1.5680592e-03
3.4333333e-01	2.0743394e-03
3.4666666e-01	1.6646398e-03
3.4999999e-01	1.7592057e-03
3.5333332e-01	1.6395720e-03
3.5666665e-01	1.3352495e-03
3.6000001e-01	1.5808860e-03
3.6333334e-01	1.6291953e-03
3.6666667e-01	1.7158954e-03
3.7000000e-01	1.6313582e-03
3.7333333e-01	1.7566911e-03
3.7666667e-01	1.3380256e-03
3.8000000e-01	1.7882136e-03
3.8333333e-01	1.2597891e-03
3.8666666e-01	1.7366420e-03
3.8999999e-01	1.1249322e-03
3.9333335e-01	1.4486198e-03
3.9666668e-01	1.3709755e-03
4.0000001e-01	9.4269885e-04
4.0333334e-01	1.7546075e-03
4.0666667e-01	1.6386042e-03
4.1000000e-01	1.5342293e-03
4.1333333e-01	1.0365281e-03
4.1666666e-01	1.2754939e-03
4.1999999e-01	2.4475125e-03
4.2333335e-01	1.7056898e-03
4.2666668e-01	1.6051785e-03
4.3000001e-01	1.7807636e-03
4.3333334e-01	1.5607082e-03
4.3666667e-01	7.4045151e-04
4.4000000e-01	1.4865240e-03
4.4333333e-01	8.8273955e-04
4.4666666e-01	1.0777750e-03
4.4999999e-01	2.1542700e-03
4.5333335e-01	1.4817412e-03
4.5666668e-01	1.4894889e-03
4.6000001e-01	6.5783097e-04
4.6333334e-01	1.9313322e-03
4.6666667e-01	2.7676828e-03
4.7000000e-01	1.3785629e-03
4.7333333e-01	2.3301151e-03
4.7666666e-01	2.1829582e-03
4.7999999e-01	1.8460706e-03
4.8333332e-01	1.2554335e-03
4.8666668e-01	2.0338907e-03
4.9000001e-01	1.4478333e-03
4.9333334e-01	9.2105905e-04
4.9666667e-01	2.0985892e-03
5.0000000e-01	8.5562421e-04
)

Calculation of Strouhal Number for coefficient of drag for 400 iterations

"drag-rfile"
"Iteration" "drag"
("Iteration" "drag")
1 86.79098313129825
2 39.48902439825606
3 23.37200698387243
4 15.91923758573352
5 12.10159766162877
6 9.884741775891484
7 8.450441366464513
8 7.373718686451075
9 6.570911103733756
10 5.912675491158868
11 5.383522710271468
12 4.948062671808634
13 4.579929608433548
14 4.265941142595355
15 3.995894478566004
16 3.763275502111935
17 3.563820901801396
18 3.391118189522038
19 3.241885708236989
20 3.111431244648113
21 2.997749139287645
22 2.898765558743616
23 2.814179888958325
24 2.739528503930338
25 2.675082334191965
26 2.620062912521816
27 2.572123226764673
28 2.530515119947947
29 2.495051945799058
30 2.462707892703041
31 2.437397477025818
32 2.412482082462343
33 2.39327167147041
34 2.375301369974697
35 2.361848102851694
36 2.337870830704791
37 2.322776901266944
38 2.311007068014865
39 2.299192312697361
40 2.287647801784953
41 2.277173309443202
42 2.266559538933556
43 2.258068531903268
44 2.250228734591968
45 2.243852709247493
46 2.236628781879062
47 2.229320712480586
48 2.221995266189269
49 2.211626832409491
50 2.204502165087685
51 2.197198404021437
52 2.192249411805434
53 2.184251872326761
54 2.176748478286269
55 2.170935528215553
56 2.164840926932802
57 2.15913922998736
58 2.154680165683771
59 2.150309599433029
60 2.144789945608459
61 2.140787088830022
62 2.13643429549919
63 2.132032512263873
64 2.127497125126755
65 2.123989875017717
66 2.117913350131835
67 2.115615540537912
68 2.112833260998348
69 2.11047855045644
70 2.107891093434441
71 2.10452454400834
72 2.10017284964676
73 2.097319184091242
74 2.095610967240142
75 2.092994445856802
76 2.091280567232146
77 2.0898278292528
78 2.087977533282352
79 2.084198621329386
80 2.082280282350683
81 2.079915870250181
82 2.078464502304059
83 2.075739615296153
84 2.075348700096832
85 2.074100056614463
86 2.071813567202203
87 2.069710847429176
88 2.068032674064926
89 2.065912056514601
90 2.064627275945953
91 2.064134431127353
92 2.06232683122344
93 2.061257887993597
94 2.060051736944269
95 2.058382981382296
96 2.057458050238921
97 2.057244595075182
98 2.056156887563383
99 2.055410744364314
100 2.054538619866002
101 2.053521965020914
102 2.053487207234135
103 2.052867833907734
104 2.052941393065417
105 2.051409493801827
106 2.051739351461933
107 2.052128130075915
108 2.051838788840536
109 2.053124061207397
110 2.053489570049013
111 2.053413261798077
112 2.051860062825769
113 2.0517025968266
114 2.05124185594874
115 2.050360951380298
116 2.048919816638018
117 2.050738595006002
118 2.052406582583041
119 2.052430986196693
120 2.053538033342742
121 2.056905721990759
122 2.057849687329293
123 2.057855493357597
124 2.057604288853653
125 2.057648865885879
126 2.058117072203276
127 2.058989392653951
128 2.061043361173207
129 2.062596203358667
130 2.067101678927582
131 2.070276066065812
132 2.071722395138476
133 2.073202920882379
134 2.073919846393756
135 2.077412859451538
136 2.073488568464206
137 2.077272888537518
138 2.078606711232247
139 2.07743388326059
140 2.080502044550165
141 2.08384054043493
142 2.084185134061813
143 2.082549880663781
144 2.090059093854343
145 2.092226320071773
146 2.093999783471044
147 2.091278999568627
148 2.089835896302858
149 2.091151677885152
150 2.096483544503207
151 2.099573561114819
152 2.100093926534096
153 2.110136059653376
154 2.113684107106267
155 2.115307073066488
156 2.115457032756378
157 2.111695204602033
158 2.11111407619097
159 2.111603093618397
160 2.113460011641529
161 2.114105963641061
162 2.116462010375217
163 2.116210401228436
164 2.111709433454278
165 2.108534803891259
166 2.115417633274596
167 2.122257454109278
168 2.125860546914794
169 2.122758263217615
170 2.122700386604624
171 2.117910081635361
172 2.120765218126859
173 2.114839337456671
174 2.120102839526281
175 2.124234124604228
176 2.134707251698511
177 2.142327891298805
178 2.142267807543179
179 2.13989258577834
180 2.135555757947362
181 2.129216629055478
182 2.128500737432475
183 2.130132038702798
184 2.129971008602334
185 2.132803626891286
186 2.127624357731589
187 2.124209207609058
188 2.127124067046255
189 2.131056802935765
190 2.133605177045265
191 2.135144820357463
192 2.137105841512573
193 2.133568644919337
194 2.129081794421855
195 2.127415600742442
196 2.127272883932652
197 2.129023268490957
198 2.138774135142915
199 2.144263746486388
200 2.151450444571084
201 2.150437687296284
202 2.148201918994496
203 2.141551369782417
204 2.134499741156185
205 2.132530262361112
206 2.135449354384696
207 2.134261764569107
208 2.132984091389919
209 2.126672540251655
210 2.129998718867982
211 2.137931487413207
212 2.140169156659101
213 2.146824193628734
214 2.14069639813971
215 2.133441731731611
216 2.130551012457696
217 2.133537337323228
218 2.131916275596341
219 2.135617582632843
220 2.135590576186273
221 2.150950838901186
222 2.150792903623395
223 2.151294529200711
224 2.146351478570423
225 2.140220206356821
226 2.137594791282459
227 2.139474170714127
228 2.138248251666439
229 2.139278214257679
230 2.137104531352587
231 2.129155949556364
232 2.13003422393014
233 2.135008091693087
234 2.13744242709005
235 2.143403031477835
236 2.146050009231551
237 2.142894228020536
238 2.135514396760543
239 2.136493256996669
240 2.130808441966316
241 2.134553371416733
242 2.136635246726859
243 2.147832125635291
244 2.148160122297262
245 2.146999876316635
246 2.150052942967979
247 2.147580056480418
248 2.144295986077583
249 2.140323323309604
250 2.14042877599825
251 2.13914281306618
252 2.137154621029982
253 2.132746834123569
254 2.130824870595964
255 2.130341092088328
256 2.135869218703922
257 2.141661320829309
258 2.144464533306289
259 2.144587564872222
260 2.139759458282083
261 2.133775885166553
262 2.133926194316644
263 2.134266403200273
264 2.138029551371541
265 2.142562796815878
266 2.149976639541052
267 2.153547417121757
268 2.151507380430407
269 2.146775420957693
270 2.143731257626425
271 2.137616023517474
272 2.134466425093279
273 2.139912532764547
274 2.138938721592811
275 2.133488024616784
276 2.132446313577514
277 2.134412120171111
278 2.141761693318078
279 2.143698395066821
280 2.142646466814742
281 2.140360065087922
282 2.138401206420074
283 2.133099304379339
284 2.137134229188229
285 2.133949749417945
286 2.134522866069613
287 2.136733257863903
288 2.152950774605825
289 2.1527057322301
290 2.149920855140997
291 2.147385162050215
292 2.144073368252154
293 2.140135433517253
294 2.139372285360723
295 2.140444139090314
296 2.138017872910001
297 2.135736846825528
298 2.129578229746745
299 2.127157852939062
300 2.138955380063251
301 2.144840862335517
302 2.14982459280276
303 2.142996756228893
304 2.13714966908777
305 2.131229346546064
306 2.134871265310067
307 2.132737493758548
308 2.139501508648615
309 2.140869401250704
310 2.148528939750038
311 2.149730841834859
312 2.152029119257593
313 2.148396294465235
314 2.143521298783142
315 2.140345685105345
316 2.140123671968205
317 2.142997408449823
318 2.13597355742702
319 2.136440149763174
320 2.131589874283626
321 2.132379893433305
322 2.134858082416806
323 2.139429282066352
324 2.14263465229372
325 2.142191155921334
326 2.144768647375581
327 2.13938220883945
328 2.138870487390521
329 2.135884602630138
330 2.132515144320176
331 2.136304410593962
332 2.142593741254749
333 2.148528139709162
334 2.151426386244938
335 2.153550487426863
336 2.149431362966288
337 2.144054243938748
338 2.139566862153756
339 2.13845780779851
340 2.139397144696894
341 2.137611108293239
342 2.132796630742826
343 2.129640136257431
344 2.13490392642899
345 2.139938403233155
346 2.143981552146869
347 2.14410883301061
348 2.141587813553152
349 2.137424681577524
350 2.135354178990995
351 2.133838364022198
352 2.134378595098855
353 2.138932494900799
354 2.143276234774411
355 2.149213664251282
356 2.153886427788975
357 2.151327924667695
358 2.147667415779993
359 2.143198804886441
360 2.137817104628119
361 2.13515404657711
362 2.139891894113779
363 2.138839188158497
364 2.134757933316517
365 2.131264804630335
366 2.13421607832794
367 2.139507403353624
368 2.142260504448718
369 2.145923178231531
370 2.14343978100305
371 2.140589567377523
372 2.133781755544014
373 2.132246617475121
374 2.130923969967337
375 2.136392291694651
376 2.136656242536639
377 2.152845986081091
378 2.153799760204687
379 2.154648824461637
380 2.146198297655256
381 2.145130014182541
382 2.137577569588291
383 2.138379822158089
384 2.143121699873355
385 2.138874064197867
386 2.136070350522486
387 2.128921028700855
388 2.131821423241451
389 2.137791161856448
390 2.142403170462605
391 2.141473131927888
392 2.143042767170459
393 2.141883571594259
394 2.135067490405672
395 2.135521660718676
396 2.132295237715034
397 2.138582317924858
398 2.138696217829954
399 2.148754609042752
400 2.147964527791672

Unsteady State:

Changing the flow of the geometry from the steady state to the unsteady state from the physics in ansys fluent.

At unsteady state with reynolds number=100 we cannot see the vortex shedding from velocity contour of the given figure and variation of the velocity from the cylinder.

Pressure Contour of the geometry with unsteady flow:

Residuals of the geometry from the unsteady flow:

Coefficient of lift of the geometry from unsteady flow:

Coefficient of lift of the geometry from the unsteady flow:

Vertex average of velocity of geomtry from unsteady flow:

Vertex average of velocity at monitor point of the geometry from the unsteady flow:

As comparing the both the steady flow and unsteady flow we can see the differences between them :

Part 2)

a) Calculating the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000 in stedy state.

Case 1) Re=10

Pressure countour

Velocity Contour:

Residuals:

Average vertex of velocity at monitor point:

Average vertex of velocity of the geometry;

Coefficient of drag:

Coefficient of lift:

Case 2) Re= 100

At steady state with reynolds number=100 we can see the vortex shedding from the given figure of velocity contour and variation of the velocity from the cylinder.

Now, pressure contour of the geometry of steady state flow.

Residuals of the geometry :

Coefficient of lift of the steady state flow from the geometry:

Coefficient of drag for steady state flow of geometry.

Vertex average of the velocity for the geometry.

Vertex average of the velocity from the monitor point of the geometry.

Case 3) Re=1000

Velocity contour for the geometry with reynolds number 1000.

Pressure contour of the geometry with reynolds number 1000

Residuals:

Vertex average of velocity at monitor point

Vertex average velocity of the geometry:

Profile for the coefficient of the drag

Profile for the coefficient of lift:

Case 4) Re=10000

Pressure Contour of the geometry with reynolds number 10000.

Velocity contour of the geometry with reynolds number 10000

Residuals:

Vertex Average of velocity at monitor point

Vertex average of velocity of the geometry

Profile for the coefficient of drag of the geometry:

Profile for the coefficient of lift:

Case 5) Re=100000

Velocity Contour of the geometry with reynolds number 100000

Pressure Contour od the geometry with reynolds number 100000

Residuals:

Vertex average of velocity at monitor point

Vertex average of velocity of the geometry:

Profile for the coefficient of drag:

Profile for the coefficient of lift:

b) The effect of Reynolds number on the coefficient of drag.

As the reynolds number increases the coefficient of decreases or vice-versa.

The lower the Reynolds Number, the lesser the “Inertial Forces” struggling to keep fluid flowing, because the “Weak Flow Energy” loses the fight against “Viscous Forces (Sticky Forces)” which try to the prevent the fluid from flowing.

In other words,

• the smaller the Reynolds Number is, the more the fight between “motion and stickiness” tips over towards the dominance of more stickiness, due to higher Viscous Forces and comperatively smaller Inertial Forces (less kinetic energy of the flow).
• the higher the Reynolds Number is, this fight tips over towards the dominance of higher Inertial forces, due to increased kinetic energy of the flow.

Therefore, an easier description would be like, “The Lower the Reynolds Number, the more the sticky Viscous Forces gain dominance over the motivating energy of Inertial Forces.”

And as anything gets more sticky (Viscous Forces), stickiness causes a higher drag. By the same token, as the kinetic energy of motivating forces (Inertial Forces) increase, the ReN will increase and hence the “Drag due to Viscous Forces” exerted within the fluid flow decreases, because the energetic motivating Inertial Forces increase and finally take over the relative dominance while the Viscous Forces gradually diminish.[1]

When the Reynolds numbers are small the flow behaves like a potential flow. There is no separation. The drag is all due to skin friction. As the Reynolds number is increased this drag decreases.At Reynolds numbers around 2 - 30, there is a separation of boundary layer, but the wake is of a limited length. The eddies formed seem fixed behind the cylinder. For Reynolds numbers close to 40 -70, there is a periodic oscillation of the wake. For higher Reynolds numbers the eddies break off from the cylinder. As the Reynolds number is increased, the eddies are continuously shed from the cylinder and washed downstream. Two rows of vortices are formed called the Vortex Street. Now the pressure drag contributes to almost 90% of the total drag. The value of C_D reaches a minimum of around 0.9 at a Reynolds number of around 2000. Increasing the Reynolds numbers further results in large angular velocities and a degeneration of vortices into turbulence.[2]

Referebces:

[1]:https://www.quora.com/Why-does-the-drag-coefficient-decrease-with-an-increasing-Reynolds-number

[2]:http://www.mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/introvisc/node11.html#:~:text=When%20the%20Reynolds%20numbers%20are,is%20increased%20this%20drag%20decreases.