×

zbMATH — the first resource for mathematics

Large-eddy simulation of the compressible flow past a wavy cylinder. (English) Zbl 1225.76174
Summary: Numerical investigation of the compressible flow past a wavy cylinder was carried out using large-eddy simulation for a free-stream Mach number \(M_{\infty } = 0.75\) and a Reynolds number based on the mean diameter \(Re = 2 \times 10^{5}\). The flow past a corresponding circular cylinder was also calculated for comparison and validation against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including drag reduction and fluctuating force suppression, shock and shocklet elimination, and three-dimensional separation and separated shear-layer instability, have been studied systematically. Because of the passive control of the flow over a wavy cylinder, the mean drag coefficient of the wavy cylinder is less than that of the circular cylinder with a drag reduction up to 26%, and the fluctuating force coefficients are significantly suppressed to be nearly zero. The vortical structures near the base region of the wavy cylinder are much less vigorous than those of the circular cylinder. The three-dimensional shear-layer shed from the wavy cylinder is more stable than that from the circular cylinder. The vortex roll up of the shear layer from the wavy cylinder is delayed to a further downstream location, leading to a higher-base-pressure distribution. The spanwise pressure gradient and the baroclinic effect play an important role in generating an oblique vortical perturbation at the separated shear layer, which may moderate the increase of the fluctuations at the shear layer and reduce the growth rate of the shear layer. The analysis of the convective Mach number indicates that the instability processes in the shear-layer evolution are derived from oblique modes and bi-dimensional instability modes and their competition. The two-layer structures of the shear layer are captured using the instantaneous Lamb vector divergence, and the underlying dynamical processes associated with the drag reduction are clarified. Moreover, some phenomena relevant to the compressible effect, such as shock waves, shocklets and shock/turbulence interaction, are analysed. It is found that the shocks and shocklets which exist in the circular cylinder flow are eliminated for the wavy cylinder flow and the wavy surface provides an effective way of shock control. As the shock/turbulence interaction is avoided, a significant drop of the turbulent fluctuations around the wavy cylinder occurs. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the passive control of the compressible flow past a wavy surface.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
76F50 Compressibility effects in turbulence
76M12 Finite volume methods applied to problems in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1017/S0022112088003325 · doi:10.1017/S0022112088003325
[2] DOI: 10.1017/S0022112001006978 · Zbl 1156.76403 · doi:10.1017/S0022112001006978
[3] DOI: 10.1063/1.870151 · Zbl 1149.76504 · doi:10.1063/1.870151
[4] DOI: 10.2514/3.60135 · doi:10.2514/3.60135
[5] DOI: 10.1146/annurev.fl.25.010193.002543 · doi:10.1146/annurev.fl.25.010193.002543
[6] DOI: 10.1017/S0022112073001114 · doi:10.1017/S0022112073001114
[7] DOI: 10.1017/S0022112094000030 · doi:10.1017/S0022112094000030
[8] DOI: 10.1063/1.1637354 · Zbl 1186.76032 · doi:10.1063/1.1637354
[9] DOI: 10.1007/s003480050098 · doi:10.1007/s003480050098
[10] DOI: 10.2514/3.11365 · doi:10.2514/3.11365
[11] DOI: 10.1063/1.858365 · doi:10.1063/1.858365
[12] DOI: 10.1017/S0022112088001442 · Zbl 0642.76070 · doi:10.1017/S0022112088001442
[13] DOI: 10.1006/jfls.2000.0358 · doi:10.1006/jfls.2000.0358
[14] DOI: 10.1146/annurev.fl.22.010190.002543 · doi:10.1146/annurev.fl.22.010190.002543
[15] DOI: 10.1016/j.jweia.2007.06.016 · doi:10.1016/j.jweia.2007.06.016
[16] DOI: 10.2514/3.60930 · doi:10.2514/3.60930
[17] DOI: 10.1063/1.858164 · Zbl 0753.76074 · doi:10.1063/1.858164
[18] Martin, Theor. Comput. Fluid Dyn. 13 pp 361– (1999)
[19] DOI: 10.1017/S0022112008005697 · Zbl 1171.76402 · doi:10.1017/S0022112008005697
[20] DOI: 10.2514/3.58828 · doi:10.2514/3.58828
[21] DOI: 10.1063/1.1762299 · Zbl 0158.23602 · doi:10.1063/1.1762299
[22] DOI: 10.1017/S0022112073000315 · doi:10.1017/S0022112073000315
[23] DOI: 10.1017/S0022112004002927 · Zbl 1142.76401 · doi:10.1017/S0022112004002927
[24] DOI: 10.1017/S0022112006000930 · Zbl 1177.76163 · doi:10.1017/S0022112006000930
[25] DOI: 10.1063/1.858280 · doi:10.1063/1.858280
[26] Lighthill, Laminar Boundary Layers pp 46– (1963)
[27] DOI: 10.1098/rspa.1952.0060 · Zbl 0049.25905 · doi:10.1098/rspa.1952.0060
[28] DOI: 10.1016/j.fluiddyn.2006.06.003 · Zbl 1178.76036 · doi:10.1016/j.fluiddyn.2006.06.003
[29] DOI: 10.1063/1.858071 · doi:10.1063/1.858071
[30] DOI: 10.1016/j.jfluidstructs.2004.04.004 · doi:10.1016/j.jfluidstructs.2004.04.004
[31] DOI: 10.1016/j.jfluidstructs.2003.12.010 · doi:10.1016/j.jfluidstructs.2003.12.010
[32] DOI: 10.1017/S0022112008004217 · Zbl 1156.76380 · doi:10.1017/S0022112008004217
[33] DOI: 10.1016/j.ijheatfluidflow.2008.01.006 · doi:10.1016/j.ijheatfluidflow.2008.01.006
[34] DOI: 10.2514/1.13690 · doi:10.2514/1.13690
[35] DOI: 10.1017/S0022112095000462 · Zbl 0847.76007 · doi:10.1017/S0022112095000462
[36] DOI: 10.1063/1.1583733 · Zbl 1186.76240 · doi:10.1063/1.1583733
[37] DOI: 10.1007/s00348-005-0981-9 · doi:10.1007/s00348-005-0981-9
[38] DOI: 10.1017/S0022112075002777 · Zbl 0325.76117 · doi:10.1017/S0022112075002777
[39] Zdravkovich, Flow Around Circular Cylinders (1997)
[40] DOI: 10.1017/S0022112006009475 · Zbl 1094.76031 · doi:10.1017/S0022112006009475
[41] DOI: 10.1063/1.865552 · Zbl 0623.76053 · doi:10.1063/1.865552
[42] DOI: 10.1063/1.869458 · doi:10.1063/1.869458
[43] DOI: 10.2514/2.1864 · doi:10.2514/2.1864
[44] DOI: 10.1063/1.868737 · doi:10.1063/1.868737
[45] DOI: 10.1142/S0217984909018084 · doi:10.1142/S0217984909018084
[46] DOI: 10.1146/annurev.fl.23.010191.003125 · doi:10.1146/annurev.fl.23.010191.003125
[47] DOI: 10.1017/S0022112096004326 · doi:10.1017/S0022112096004326
[48] Pope, Turbulent Flows (2000) · Zbl 0966.76002 · doi:10.1017/CBO9780511840531
[49] DOI: 10.1063/1.1637604 · Zbl 1186.76423 · doi:10.1063/1.1637604
[50] DOI: 10.1016/S0376-0421(98)00014-1 · doi:10.1016/S0376-0421(98)00014-1
[51] DOI: 10.1007/s11434-009-0325-x · Zbl 1184.76704 · doi:10.1007/s11434-009-0325-x
[52] DOI: 10.1007/978-3-540-29028-5 · doi:10.1007/978-3-540-29028-5
[53] DOI: 10.1017/S0022112006004551 · Zbl 1110.76016 · doi:10.1017/S0022112006004551
[54] DOI: 10.1017/S002211207200165X · doi:10.1017/S002211207200165X
[55] DOI: 10.1017/S0022112008002760 · Zbl 1147.76015 · doi:10.1017/S0022112008002760
[56] DOI: 10.1016/j.compfluid.2005.07.002 · Zbl 1151.76025 · doi:10.1016/j.compfluid.2005.07.002
[57] DOI: 10.2514/3.11891 · doi:10.2514/3.11891
[58] DOI: 10.1063/1.857955 · Zbl 0825.76334 · doi:10.1063/1.857955
[59] DOI: 10.1016/S0045-7930(01)00022-6 · Zbl 1059.76032 · doi:10.1016/S0045-7930(01)00022-6
[60] DOI: 10.1146/annurev.fluid.36.050802.122128 · Zbl 1125.74323 · doi:10.1146/annurev.fluid.36.050802.122128
[61] DOI: 10.1063/1.868900 · Zbl 1086.76031 · doi:10.1063/1.868900
[62] DOI: 10.1017/S0022112007006155 · Zbl 1116.76047 · doi:10.1017/S0022112007006155
[63] DOI: 10.1017/S0022112000001622 · Zbl 0998.76036 · doi:10.1017/S0022112000001622
[64] DOI: 10.2514/2.895 · doi:10.2514/2.895
[65] DOI: 10.1006/jcph.1999.6238 · Zbl 0955.76045 · doi:10.1006/jcph.1999.6238
[66] DOI: 10.1146/annurev.fluid.38.050304.092036 · Zbl 1100.76058 · doi:10.1146/annurev.fluid.38.050304.092036
[67] DOI: 10.1063/1.869749 · doi:10.1063/1.869749
[68] DOI: 10.1017/S0022112072000515 · doi:10.1017/S0022112072000515
[69] DOI: 10.1063/1.1409968 · Zbl 1184.76133 · doi:10.1063/1.1409968
[70] DOI: 10.1017/S0022112096007525 · Zbl 0875.76159 · doi:10.1017/S0022112096007525
[71] DOI: 10.1063/1.868460 · Zbl 1025.76541 · doi:10.1063/1.868460
[72] Truesdell, The Kinematics of Vorticity (1954) · Zbl 0056.18606
[73] DOI: 10.2322/tjsass.44.229 · doi:10.2322/tjsass.44.229
[74] DOI: 10.1017/S0022112096003631 · doi:10.1017/S0022112096003631
[75] DOI: 10.1063/1.2734996 · Zbl 1182.76190 · doi:10.1063/1.2734996
[76] DOI: 10.1017/S0022112095000310 · doi:10.1017/S0022112095000310
[77] Chorin, Vorticity and Turbulence (1994) · Zbl 0795.76002 · doi:10.1007/978-1-4419-8728-0
[78] DOI: 10.1146/annurev.fluid.39.050905.110149 · Zbl 1136.76022 · doi:10.1146/annurev.fluid.39.050905.110149
[79] DOI: 10.1142/S021798491002344X · Zbl 1195.76207 · doi:10.1142/S021798491002344X
[80] DOI: 10.2514/3.9394 · doi:10.2514/3.9394
[81] DOI: 10.1017/S0022112009991960 · Zbl 1189.76434 · doi:10.1017/S0022112009991960
[82] DOI: 10.1016/S0376-0421(01)00017-3 · doi:10.1016/S0376-0421(01)00017-3
[83] DOI: 10.1098/rspa.1996.0128 · Zbl 0886.76012 · doi:10.1098/rspa.1996.0128
[84] DOI: 10.1175/1520-0493(1963)091&lt;0099:GCEWTP&gt;2.3.CO;2 · doi:10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
[85] DOI: 10.1017/S0022112005004726 · Zbl 1071.76015 · doi:10.1017/S0022112005004726
[86] DOI: 10.1017/S0022112007008129 · Zbl 1125.76350 · doi:10.1017/S0022112007008129
[87] DOI: 10.1063/1.2931682 · Zbl 1182.76111 · doi:10.1063/1.2931682
[88] DOI: 10.1007/BF00910686 · doi:10.1007/BF00910686
[89] DOI: 10.1146/annurev.fluid.36.050802.122110 · Zbl 1081.76038 · doi:10.1146/annurev.fluid.36.050802.122110
[90] DOI: 10.1017/S0022112095000085 · Zbl 0825.76309 · doi:10.1017/S0022112095000085
[91] DOI: 10.1016/S0142-727X(03)00052-3 · doi:10.1016/S0142-727X(03)00052-3
[92] DOI: 10.1017/S0022112091001684 · Zbl 0717.76094 · doi:10.1017/S0022112091001684
[93] DOI: 10.1063/1.1355682 · Zbl 1184.76474 · doi:10.1063/1.1355682
[94] DOI: 10.1063/1.868779 · Zbl 1026.76541 · doi:10.1063/1.868779
[95] DOI: 10.2514/3.8842 · doi:10.2514/3.8842
[96] DOI: 10.1146/annurev.fluid.32.1.137 · doi:10.1146/annurev.fluid.32.1.137
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.