Hydroelastic instability of viscoelastic fluids in developing flow through a compliant channel

Morteza Safarifard; Zahra Aghaee; Mohammad Pourjafar; Solmaz Bazargan; Kayvan Sadeghy

Korea-Australia Rheology Journal, Vol.32, No.2, 99-119, May, 2020

DOI10.1007/s13367-020-0010-9 Export Citation

Hydroelastic instability of viscoelastic fluids in developing flow through a compliant channel

Morteza Safarifard, Zahra Aghaee, Mohammad Pourjafar¹, Solmaz Bazargan², and Kayvan Sadeghy^†

Center of Excellence in Design and Optimization of Energy Systems (CEDOES), School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran 11155-4563, Iran
¹Department of Mechanical Engineering, University of Tehran, Rezvanshahr 43841-119, Iran
²Satellite Research Institute, Iranian Space Research Center, Tehran 1997994313, Iran

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Linear stability of a viscoelastic fluid obeying the Walters’ B model is analytically and numerically investigated in the entrance region of a plane channel formed between two parallel plates. The plates are compliant and obey the two degree-of-freedom von Karman solid model. Having obtained the base-flow velocity profiles using the boundary-layer theory, their vulnerability to infinitesimally small varicose disturbances is investigated using the temporal, normal-mode, linear stability analysis. The results obtained show that a fluid’s elasticity has a stabilizing effect on the developing velocity profiles. The distance at which the flow becomes unstable shifts further downstream (i.e., towards the fully-developed section) of the channel when the Deborah number is increased. An increase in the flexural rigidity of the plates is shown to have a stabilizing effect on the short waves (i.e., the flutter modes) whereas an increase in its mass can dramatically destabilize such modes. The flow becomes more stable when the stiffness of the soft matter restraining the vertical movement of the plates is increased with the effect being more significant on the long waves (i.e., flow-induced modes). Boosting the dissipating effect of this material is predicted to have a stabilizing effect on the short waves.

Keywords:developing flow;Walters’ B fluid;linear stability;compliant channel;flutter instability;Deborah number

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[3] Beard DW, Walters K, Math. Proc. Camb. Philos. Soc., 60, 667 (1964)

[4] Bewersdorff HW, 6th European Drag Reduction Working Meeting, Eindhoven, Netherlands, 347-368 1991.

[5] Biau D, Eur. J. Mech. B-Fluids, 27, 579 (2008)

[6] Bird RB, Armstrong RC, Hassager O, Dynamics of Polymeric Liquids Vol. 1: Fluid Mechanics, 1987.

[7] Burrell GL, Dunlop NF, Separovic F, Soft Matter, 6, 2080 (2010)

[8] Carpenter PW, Garrad AD, J. Fluid Mech., 155, 465 (1985)

[9] Carpenter PW, Garrad AD, J. Fluid Mech., 170, 199 (1986)

[10] Carpenter PW, Gajjar JSB, Theor. Comput. Fluid Dyn., 1, 349 (1990)

[11] Carpenter PW, Davies C, Lucey AD, Curr. Sci., 79, 758 (2000)

[12] Chen TS, Sparrow EM, J. Fluid Mech., 30, 209 (1967)

[13] Chaudhary I, Garg P, Shankar V, Subramanian G, J. Fluid Mech., 881, 119 (2019)

[14] Chun DH, Schwarz WH, Phys. Fluids, 11, 5 (1968)

[15] Davey A, Q. J. Mech. Appl. Math., 26, 401 (1973)

[16] Davies C, Carpenter PW, J. Fluid Mech., 352, 205 (1997)

[17] Davies C, Carpenter PW, J. Fluid Mech., 335, 361 (1997)

[18] Dervaux J, Ciarletta P, Amar MB, J. Mech. Phys. Solids, 57, 458 (2008)

[19] Draad AA, Kuiken GDC, Nieuwstadt FTM, J. Fluid Mech., 377, 267 (1998)

[20] Drazin PG, Introduction to Hydrodynamic Stability, 2002.

[21] Duan WH, Wang CM, Nanotechnology, 20, 075702 (2009)

[22] Eggleton CD, Ferziger JH, Pulliam TH, Phys. Fluids, 6, 700 (1994)

[23] Garg VK, Gupta SC, Phys. Fluids, 24, 1752 (1981)

[24] Gavriely N, Shee TR, Cugell DW, Grotberg JB, J. Appl. Physiol., 66, 2251 (1989)

[25] Grotberg JB, Davis SH, J. Biomech., 13, 219 (1980)

[26] Hifdi A, Touhami MO, Naciri JK, J. Stat. Mech.-Theory Exp., 2004, P06003 (2004)

[27] Hsiao KW, Dinic J, Ren Y, Sharma V, Schroeder CM, Phys. Fluids, 29, 121603 (2017)

[28] Hwang SH, Litt M, Forsman WC, Rheol. Acta, 8, 438 (1969)

[29] Johnson MW, Urbanik TJ, J. Appl. Mech.-Trans. ASME, 51, 146 (1984)

[30] Labropulu F, Husain I, Chinichian M, Int. J. Math. Math. Sci., 61, 3249 (2004)

[31] Larose P, Grotberg JB, J. Fluid Mech., 331, 37 (1997)

[32] Lucey AD, Carpenter PW, Phys. Fluids, 7, 2355 (1995)

[33] Macosko CW, Rheology 1994.

[34] Madani-Tonekaboni SA, Abkar R, Khoeilar R, Math. Probl. Eng., 2012, 861508 (2012)

[35] Metzner AB, White JL, AIChE J., 11, 989 (1965)

[36] Naebe M, Shirvanimoghaddam K, Appl. Mater. Today, 5, 223 (2016)

[37] Patne R, Shankar V, J. Fluid Mech., 860, 837 (2019)

[38] Prescher S, Polzer F, Yang Y, Siebenburger M, Ballauff M, Yuan JY, J. Am. Chem. Soc., 136(1), 12 (2014)

[39] Quijano G, Couvert A, Amrane A, Bioresour. Technol., 101(23), 8923 (2010)

[40] Sadri RM, Floryan JM, Comput. Fluids, 31, 133 (2002)

[41] Sajid M, Javed T, Abbas Z, Ali N, Int. J. Nonlinear Sci. Numer. Simul., 14, 285 (2013)

[42] Sapir MH, Reiss EL, SIAM J. Appl. Math., 37, 290 (1979)

[43] Shankar V, Kumaran V, Phys. Fluids, 14, 2324 (2002)

[44] Smith FT, Bodonyi RJ, Q. J. Mech. Appl. Math., 33, 293 (1980)

[45] Teipel I, Trans. Can. Soc. Mech. Eng., 12, 57 (1988)

[46] Tsigklifis K, Lucey AD, J. Fluid Mech., 827, 155 (2017)

[47] Weiss E, Abu-Reziq R, J. Mater. Sci., 52(17), 10637 (2017)

[48] Yue YM, Ru CQ, Xu KY, Int. J. Non-Linear Mech., 88, 67 (2017)