×

zbMATH — the first resource for mathematics

Interaction of two tandem deformable bodies in a viscous incompressible flow. (English) Zbl 1183.76709
Summary: Previous laboratory measurements on drag of tandem rigid bodies moving in viscous incompressible fluids found that a following body experienced less drag than a leading one. Very recently a laboratory experiment [L. Ristroph and J. Zhang, Phys. Rev. Lett. 101, 194502 (2008)] with deformable bodies (rubble threads) revealed just the opposite - the leading body had less drag than the following one. The Reynolds numbers in the experiment were around \(10^{4}\). To find out how this qualitatively different phenomenon may depend on the Reynolds number, a series of numerical simulations are designed and performed on the interaction of a pair of tandem flexible flags separated by a dimensionless vertical distance \((0 \leqslant D \leqslant 5.5)\) in a flowing viscous incompressible fluid at lower Reynolds numbers \((40 \leqslant Re \leqslant 220)\) using the immersed boundary (IB) method. The dimensionless bending rigidity \(\hat K_b\) and dimensionless flag mass density \(\hat M\) used in our work are as follows: \(8.6 \times 10^{-5} \leqslant \hat K_b \leqslant 1.8 \times 10^{-3}, 0.8 \leqslant \hat M \leqslant 1.0\). We obtain an interesting result within these ranges of dimensionless parameters: when \(Re\) is large enough so that the flapping of the two flags is self-sustained, the leading flag has less drag than the following one; when \(Re\) is small enough so that the flags maintain two nearly static line segments aligned with the mainstream flow, the following flag has less drag than the leading one. The transitional range of \(Re\) separating the two differing phenomena depends on the value of \(\hat K_b\). With \(Re\) in this range, both the flapping and static states are observed depending on the separation distance \(D\). When \(D\) is small enough, the flags are in the static state and the following flag has less drag; when \(D\) is large enough the flags are in the constant flapping state and the leading flag has less drag. The critical value of \(D\) depends on \(\hat K_b\).

MSC:
76D99 Incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1002/cpa.3160460602 · Zbl 0741.76103
[2] DOI: 10.1016/0021-9991(90)90103-8 · Zbl 0682.76105
[3] DOI: 10.1103/PhysRevLett.101.194502
[4] DOI: 10.1007/s00466-005-0018-5 · Zbl 1178.74170
[5] DOI: 10.1242/jeb.00209
[6] DOI: 10.1006/jcph.2001.6715 · Zbl 1153.76339
[7] DOI: 10.1006/jcph.2001.6813 · Zbl 1065.76568
[8] DOI: 10.1016/S0045-7930(96)00032-1 · Zbl 0898.76077
[9] DOI: 10.1063/1.1582476 · Zbl 1186.76611
[10] DOI: 10.1016/j.jcp.2008.04.028 · Zbl 1213.76129
[11] Li, The Immersed Interface Method – Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (2006) · Zbl 1122.65096
[12] DOI: 10.1006/jcph.2002.7066 · Zbl 1130.76406
[13] DOI: 10.1126/science.193.4258.1146
[14] DOI: 10.1137/S1064827595282532 · Zbl 0879.76061
[15] DOI: 10.1016/j.cma.2007.11.031 · Zbl 1158.76458
[16] DOI: 10.1137/0731054 · Zbl 0811.65083
[17] DOI: 10.1017/S0022112008002103 · Zbl 1146.76020
[18] DOI: 10.1016/0021-9991(89)90151-4 · Zbl 0681.76030
[19] DOI: 10.1006/jcph.2000.6483 · Zbl 0954.76066
[20] DOI: 10.1016/j.cma.2003.12.044 · Zbl 1067.76576
[21] DOI: 10.1016/j.jcp.2006.11.015 · Zbl 1124.74052
[22] DOI: 10.1080/00140137908924623
[23] DOI: 10.1038/35048530
[24] DOI: 10.1073/pnas.0408383102
[25] DOI: 10.1063/1.2734674 · Zbl 1146.76441
[26] Zdravkovich, J. Fluids Engng 99 pp 618– (1977)
[27] DOI: 10.1038/nature01232
[28] DOI: 10.1017/S0022112007005563 · Zbl 1176.76044
[29] DOI: 10.1016/j.jcp.2005.07.016 · Zbl 1161.76548
[30] DOI: 10.3934/dcdsb.2009.11.519 · Zbl 1277.76132
[31] DOI: 10.1016/0045-7825(81)90049-9 · Zbl 0482.76039
[32] DOI: 10.1006/jcph.1997.5689 · Zbl 0888.76067
[33] DOI: 10.1137/S003614299426450X · Zbl 0920.76056
[34] DOI: 10.1016/j.jcp.2005.02.011 · Zbl 1115.76386
[35] DOI: 10.1137/0732047 · Zbl 0842.76052
[36] DOI: 10.1016/0045-7825(94)90022-1 · Zbl 0845.76069
[37] DOI: 10.1016/j.cma.2003.12.024 · Zbl 1060.74676
[38] DOI: 10.1016/0045-7825(94)90135-X · Zbl 0845.73078
[39] DOI: 10.1615/IntJMultCompEng.v4.i1.90
[40] DOI: 10.1006/jcph.2000.6542 · Zbl 1047.76097
[41] Sulsky, Comput. Phys. Commun. 87 pp 136– (1994)
[42] DOI: 10.1016/0021-9991(88)90003-4 · Zbl 0652.76025
[43] DOI: 10.1016/0045-7825(94)00033-6 · Zbl 0851.73078
[44] DOI: 10.1006/jcph.1999.6236 · Zbl 0957.76052
[45] DOI: 10.1103/PhysRevLett.94.094302
[46] DOI: 10.1006/jcph.2001.6935 · Zbl 1039.76050
[47] DOI: 10.1016/j.compstruc.2007.01.017
[48] DOI: 10.1016/0021-9991(88)90158-1 · Zbl 0641.76140
[49] DOI: 10.1006/jcph.1999.6293 · Zbl 0953.76069
[50] DOI: 10.1016/j.jfluidstructs.2003.10.001
[51] DOI: 10.1063/1.2736083 · Zbl 1146.76370
[52] Peskin, Contemp. Math. 141 pp 161– (1993)
[53] DOI: 10.1016/0045-7825(82)90128-1 · Zbl 0508.73063
[54] DOI: 10.1017/S0962492902000077 · Zbl 1123.74309
[55] DOI: 10.1142/S0218202506001212 · Zbl 1088.74050
[56] DOI: 10.1016/0021-9991(77)90100-0 · Zbl 0403.76100
[57] Cottet, C. R. Acad. Sci. Paris, Ser. I 338 pp 581– (2004) · Zbl 1101.74028
[58] DOI: 10.1006/jcph.1993.1162 · Zbl 0778.76064
[59] DOI: 10.1017/S0022112007005307 · Zbl 1124.76011
[60] DOI: 10.1016/j.cma.2007.05.028 · Zbl 1158.74533
[61] DOI: 10.2307/2004428 · Zbl 0184.20103
[62] DOI: 10.1146/annurev.fluid.37.061903.175743 · Zbl 1117.76049
[63] DOI: 10.2307/2004575 · Zbl 0198.50103
[64] DOI: 10.1006/jcph.1997.5872 · Zbl 0908.76068
[65] DOI: 10.1006/jcph.2002.6993 · Zbl 1130.76392
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.