Numerical Simulation of Flow in a Wavy Wall Microchannel Using Immersed Boundary Method

Author(s): Mithun Kanchan, Ranjith Maniyeri*

Journal Name: Recent Patents on Mechanical Engineering

Volume 13 , Issue 2 , 2020

Become EABM
Become Reviewer


Background: Fluid flow in microchannels is restricted to low Reynolds number regimes and hence inducing chaotic mixing in such devices is a major challenge. Over the years, the Immersed Boundary Method (IBM) has proved its ability in handling complex fluid-structure interaction problems.

Objectives: Inspired by recent patents in microchannel mixing devices, we study passive mixing effects by performing two-dimensional numerical simulations of wavy wall in channel flow using IBM.

Methods: The continuity and Navier-Stokes equations governing the flow are solved by fractional step based finite volume method on a staggered Cartesian grid system. Fluid variables are described by Eulerian coordinates and solid boundary by Lagrangian coordinates. A four-point Dirac delta function is used to couple both the coordinate variables. A momentum forcing term is added to the governing equation in order to impose the no-slip boundary condition between the wavy wall and fluid interface.

Results: Parametric study is carried out to analyze the fluid flow characteristics by varying amplitude and wavelength of wavy wall configurations for different Reynolds number.

Conclusion: Configurations of wavy wall microchannels having a higher amplitude and lower wavelengths show optimum results for mixing applications.

Keywords: Dirac delta function, fractional-step method, immersed boundary method, momentum forcing, passive mixing, wavy walled microchannel.

Sadlej K, Wajnryb E, Ekiel-Jeżewska ML, Lamparska D, Kowalewski TA. Dynamics of nanofibres conveyed by low Reynolds number flow in a microchannel. Int J Heat Fluid Flow 2010; 31(6): 996-1004.
Lim S, Choi H. Micro channel unit. US006866067 (2005).
Karaki H, Kato K, Sawayashiki Y, Terada H, Wakabayashi A. Intra-microchannel mixing method and apparatus. US20090129198 (2009).
Link D, Weitz D, Cristobal-Azkarte G, Cheng Z, Ahn K. Method for mixing droplets in microchannel. EP2662135 (2013).
Cho CC. A combined active/passive scheme for enhancing the mixing efficiency of microfluidic devices. Chem Eng Sci 2008; 63(12): 3081-7.
Tatsuo N, Shinichiro M, Shingho A, Yuji K. Flow observations and mass transfer characteristics in symmetrical wavy-walled channels at moderate Reynolds numbers for steady flow. Int J Heat Mass Transf 1990; 33(5): 835-45.
Wang GV, Vanka SP. Convective heat transfer in periodic wavy passages. Int J Heat Mass Transf 1995; 38(17): 3219-30.
Bahaidarah HM, Anand NK, Chen HC. Numerical study of heat and momentum transfer in channels with wavy walls. Numer Heat Transf A 2005; 47(5): 417-39.
Aslan E, Taymaz I, Islamoglu Y. Finite volume simulation for convective heat transfer in wavy channels. Heat Mass Transf 2016; 52(3): 483-97.
Mondal B, Mehta SK, Patowari PK, Pati S. Numerical study of mixing in wavy micromixers: Comparison between raccoon and serpentine mixer. Chem Eng Process 2019; 136: 44-61.
Grant Mills Z, Shah T, Warey A, Balestrino S, Alexeev A. Onset of unsteady flow in wavy walled channels at low Reynolds number. Phys Fluids 2014; 26(8): 084104
Aneesh AM, Sharma A, Srivastava A, Chaudhury P. Effects of wavy channel configurations on thermal-hydraulic characteristics of Printed Circuit Heat Exchanger (PCHE). Int J Heat Mass Transf 2018; 118: 304-15.
Karimipour A, Esfe MH, Safaei MR, Semiromi DT, Jafari S, Kazi SN. Mixed convection of copper-water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method. Physica A 2014; 402: 150-68.
Jourabian M, Darzi AA, Toghraie D, Ali Akbari O. Melting process in porous media around two hot cylinders: Numerical study using the lattice Boltzmann method. Physica A 2018; 509: 316-35.
Toghaniyan A, Zarringhalam M, Akbari OA, Shabani GA, Toghraie D. Application of lattice Boltzmann method and spinodal decomposition phenomenon for simulating two-phase thermal flows. Physica A 2018; 509: 673-89.
Najafi MJ, Naghavi SM, Toghraie D. Numerical simulation of flow in hydro turbines channel to improve its efficiency by using of Lattice Boltzmann Method. Physica A 2019; 520: 390-408.
Alipour P, Toghraie D, Karimipour A, Hajian M. Modeling different structures in perturbed Poiseuille flow in a nanochannel by using of molecular dynamics simulation: Study the equilibrium. Physica A 2019; 515: 13-30.
Alipour P, Toghraie D, Karimipour A, Hajian M. Molecular dynamics simulation of fluid flow passing through a nanochannel: Effects of geometric shape of roughnesses. J Mol Liq 2019; 275: 192-203.
Nemati M, Abady AR, Toghraie D, Karimipour A. Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid-vapor for multi-phase flows. Physica A 2018; 489: 65-77.
Tohidi M, Toghraie D. The effect of geometrical parameters, roughness and the number of nanoparticles on the self-diffusion coefficient in Couette flow in a nanochannel by using of molecular dynamics simulation. Physica B 2017; 518: 20-32.
Rezaei M, Azimian AR, Semiromi DT. The surface charge density effect on the electro-osmotic flow in a nanochannel: A molecular dynamics study. Heat Mass Transf 2015; 51(5): 661-70.
Noorian H, Toghraie D, Azimian AR. The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation. Heat Mass Transf 2014; 50(1): 95-104.
Semiromi DT, Azimian AR. Molecular dynamics simulation of nonodroplets with the modified Lennard-Jones potential function. Heat Mass Transf 2011; 47(5): 579-88.
Semironi DT, Azimian AR. Molecular dynamics simulation of liquid-vapor phase equilibrium by using the modified Lennard-Jones potential function. Heat Mass Transf 2010; 46(3): 287-94.
Parsaiemehr M, Pourfattah F, Akbari OA, Toghraie D, Sheikhzadeh G. Turbulent flow and heat transfer of water/Al2O3 nanofluid inside a rectangular ribbed channel. Physica E 2018; 96: 73-84.
Toghraie D, Mokhtari M, Afrand M. Molecular dynamic simulation of copper and platinum nanoparticles Poiseuille flow in a nanochannels. Physica E 2016; 84: 152-61.
Balootaki AA, Karimipour A, Toghraie D. Nano scale lattice Boltzmann method to simulate the mixed convection heat transfer of air in a lid-driven cavity with an endothermic obstacle inside. Physica A 2018; 508: 681-701.
Alipour P, Toghraie D, Karimipour A. Investigation the atomic arrangement and stability of the fluid inside a rough nanochannel in both presence and absence of different roughness by using of accurate nano scale simulation. Physica A 2019; 524: 639-60.
Javadzadegan A, Motaharpour SH, Moshfegh A, Akbari OA, Afrouzi HH, Toghraie D. Lattice-Boltzmann method for analysis of combined forced convection and radiation heat transfer in a channel with sinusoidal distribution on walls. Physica A 2019; 526: 121066
Zarringhalam M, Ahmadi-Danesh-Ashtiani H, Toghraie D, Fazaeli R. Molecular dynamic simulation to study the effects of roughness elements with cone geometry on the boiling flow inside a microchannel. Int J Heat Mass Transf 2019; 141: 1-8.
Toghraie D, Hekmatifar M, Salehipour Y, Afrand M. Molecular dynamics simulation of Couette and Poiseuille water-copper nanofluid flows in rough and smooth nanochannels with different roughness configurations. Chem Phys 2019; 527: 110505
Zarringhalam M, Ahmadi-Danesh-Ashtiani H, Toghraie D, Fazaeli R. The effects of suspending copper nanoparticles into argon base fluid inside a microchannel under boiling flow condition by using of molecular dynamic simulation. J Mol Liq 2019; 293: 111474
Afrouzi HH, Ahmadian M, Moshfegh A, Toghraie D, Javadzadegan A. Statistical analysis of pulsating non-Newtonian flow in a corrugated channel using Lattice-Boltzmann method. Physica A 2019; 535: 122486
Javadzadegan A, Joshaghani M, Moshfegh A, Akbari OA, Afrouzi HH, Toghraie D. Accurate meso-scale simulation of mixed convective heat transfer in a porous media for a vented square with hot elliptic obstacle: An LBM approach. Physica A 2020; 537: 122439
Peng Y, Zarringhalam M, Hajian M, Toghraie D, Tadi SJ, Afrand M. Empowering the boiling condition of Argon flow inside a rectangular microchannel with suspending Silver nanoparticles by using of molecular dynamics simulation. J Mol Liq 2019; 295: 111721
Peng Y, Zarringhalam M, Barzinjy AA, Toghraie D, Afrand M. Effects of surface roughness with the spherical shape on the fluid flow of argon atoms flowing into the microchannel, under boiling condition using molecular dynamic simulation. J Mol Liq 2020; 297111650
Jolfaei NA, Jolfaei NA, Hekmatifar M. Piranfar A, Toghraie D, Sabetvand R, Rostami S. Investigation of thermal properties of DNA structure with precise atomic arrangement via equilibrium and non-equilibrium molecular dynamics approaches. Comput Methods Programs Biomed 2019; 185: 105169
Peskin CS. Flow patterns around heart valves: A digital computer method for solving the equations of motion. IEEE Trans Biomed Eng 1973; (4): 316-7.
Mittal R, Iaccarino G. Immersed boundary methods. Annu Rev Fluid Mech 2005; 37: 239-61.
Horng TL, Hsieh PW, Yang SY, You CS. A simple direct-forcing immersed boundary projection method with prediction-correction for fluid-solid interaction problems. Comput Fluids 2018; 176: 135-52.
Xie F, Zheng H, Deng J, Zheng Y. Vortex induced vibration of a circular cylinder with a filament by using penalty immersed boundary method. Ocean Eng 2019; 186: 106078
Tao S, He Q, Wang L, Huang S, Chen B. A non-iterative direct-forcing immersed boundary method for thermal discrete unified gas kinetic scheme with Dirichlet boundary conditions. Int J Heat Mass Transf 2019; 137: 476-88.
Jianming YA. Sharp interface direct forcing immersed boundary methods: A summary of some algorithms and applications. J Hydrodynamics Ser B 2016; 28(5): 713-30.
Yang X, Zhang X, Li Z, He GW. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J Comput Phys 2009; 228(20): 7821-36.
Tian FB, Luo H, Zhu L, Liao JC, Lu XY. An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J Comput Phys 2011; 230(19): 7266-83.
Cui J, Lin Z, Jin Y, Liu Y. Numerical simulation of fiber conveyance in a confined channel by the immersed boundary-lattice Boltzmann method. Eur J Mech BFluids 2019; 76: 422-33.
Huang WX, Shin SJ, Sung HJ. Simulation of flexible filaments in a uniform flow by the immersed boundary method. J Comput Phys 2007; 226(2): 2206-28.
Kim MJ, Lee JH. Flapping dynamics of a flexible flag clamped vertically in a viscous uniform flow. J Mech Sci Technol 2019; 33(3): 1243-56.
Dash SM, Lee TS, Huang H. A novel flexible forcing hybrid IB-LBM scheme to simulate flow past circular cylinder. Int J Mod Phys C 2014; 25(01): 1340014
Dash SM, Lee TS, Lim TT, Huang H. A flexible forcing three dimension IB-LBM scheme for flow past stationary and moving spheres. Comput Fluids 2014; 95: 159-70.
Dash SM. A flexible forcing immersed boundary-simplified lattice Boltzmann method for two and three-dimensional fluid-solid interaction problems. Comput Fluids 2019; 184: 165-77.
Vasconcelos AG, Albuquerque DM, Pereira JC. A very high-order finite volume method based on weighted least squares for elliptic operators on polyhedral unstructured grids. Comput Fluids 2019; 181: 383-402.
Nezhad JR, Mirbozorgi SA. An immersed boundary-lattice Boltzmann method to simulate chaotic micromixers with baffles. Comput Fluids 2018; 167: 206-14.
Kim W, Choi H. Immersed boundary methods for fluid-structure interaction: A review. Int J Heat Fluid Flow 2019; 75: 301-9.
Kolahdouz EM, Bhalla APS, Craven BA, Griffith BE. An immersed interface method for discrete surfaces. J Comput Phys 2020; 400: 108854
Cai SG, Ouahsine A, Smaoui H, Favier J, Hoarau Y. An efficient implicit direct forcing immersed boundary method for incompressible flows. JPCS 2015; 574(1): 012165
Tschisgale S, Kempe T, Fröhlich J. A general implicit direct forcing immersed boundary method for rigid particles. Comput Fluids 2018; 170: 285-98.
Zhu X, He G, Zhang X. An improved direct-forcing immersed boundary method for fluid-structure interaction simulations. J Fluids Eng 2014; 136(4): 040903
Ji C, Munjiza A, Williams JJ. A novel iterative direct-forcing immersed boundary method and its finite volume applications. J Comput Phys 2012; 231(4): 1797-821.
Zhu L, He G, Wang S. Miller L, Zhang X, You Q, Fang S . An immersed boundary method based on the lattice Boltzmann approach in three dimensions, with application. Comput Math Appl 2011; 61(12): 3506-18.
Yuan HZ, Niu XD, Shu S, Li M, Yamaguchi H. A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating a flexible filament in an incompressible flow. Comput Math Appl 2014; 67(5): 1039-56.
Favier J, Revell A, Pinelli A. Numerical study of flapping filaments in a uniform fluid flow. J Fluids Structures 2015; 53: 26-35.
Roy S, Heltai L, Costanzo F. Benchmarking the immersed finite element method for fluid-structure interaction problems. Comput Math Appl 2015; 69(10): 1167-88.
Falagkaris EJ, Ingram DM, Markakis K, Viola IM. PROTEUS: A coupled iterative force-correction immersed-boundary cascaded lattice Boltzmann solver for moving and deformable boundary applications. Comput Math Appl 2018; 75(4): 1330-54.
Wu J, Cheng Y, Zhang C, Diao W. Simulating vortex induced vibration of an impulsively started flexible filament by an implicit IB-LB coupling scheme. Comput Math Appl 2020; 79(1): 159-73.
Wang Z, Fan J, Luo K. Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles. Int J Multiph Flow 2008; 34(3): 283-302.
Wei A, Zhao H, Jun J, Fan J. A fast, efficient multi-direct forcing of immersed boundary method for flow in complex geometry. SIMULTECH 2012; 1: 309-14.
O’Connor J, Revell A. Dynamic interactions of multiple wall-mounted flexible flaps. J Fluid Mech 2019; 870: 189-216.
Wang L, Tian FB. Numerical study of flexible flapping wings with an immersed boundary method: Fluid-structure-acoustics interaction. J Fluids Structures 2019; 90: 396-409.
Martins DM, Albuquerque DM, Pereira JC. On the use of polyhedral unstructured grids with a moving immersed boundary method. Comput Fluids 2018; 174: 78-88.
Garg H, Soti AK, Bhardwaj R. A sharp interface immersed boundary method for vortex-induced vibration in the presence of thermal buoyancy. Phys Fluids 2018; 30(2): 023603
Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows. J Comput Phys 2005; 209(2): 448-76.
Wang L, Currao GM, Han F, Neely AJ, Young J, Tian FB. An immersed boundary method for fluid-structure interaction with compressible multiphase flows. J Comput Phys 2017; 346: 131-51.
Wang S, Zhang X. An immersed boundary method based on discrete stream function formulation for two-and three-dimensional incompressible flows. J Comput Phys 2011; 230(9): 3479-99.
Thekkethil N, Sharma A, Agrawal A. Unified hydrodynamics study for various types of fishes-like undulating rigid hydrofoil in a free stream flow. Phys Fluids 2018; 30(7): 077107
Silva AL, Silva AR, Silveira Neto AD. Numerical simulation of two-dimensional complex flows around bluff bodies using the immersed boundary method. J Braz Soc Mech Sci Eng 2007; 29(4): 379-87.
Kim J, Kim D, Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries. J Comput Phys 2001; 171(1): 132-50.
Kim B, Chang CB, Park SG, Sung HJ. Inertial migration of a 3D elastic capsule in a plane Poiseuille flow. Int J Heat Fluid Flow 2015; 54: 87-96.
Huang WX, Sung HJ. An immersed boundary method for fluid-flexible structure interaction. Comput Methods Appl Mech Eng 2009; 198(33-36): 2650-61.
Maniyeri R. Numerical study of flow over a cylinder using an immersed boundary finite volume method. IJER 2014; 3: 213-6.
Iaccarino G, Verzicco R. Immersed boundary technique for turbulent flow simulations. Appl Mech Rev 2003; 56(3): 331-47.
Lim S, Peskin CS. Simulations of the whirling instability by the immersed boundary method. SIAM J Sci Comput 2004; 25(6): 2066-83.
Wiens JK, Stockie JM. Simulating flexible fiber suspensions using a scalable immersed boundary algorithm. Comput Methods Appl Mech Eng 2015; 290: 1-8.
Kim Y, Lai MC. Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method. J Comput Phys 2010; 229(12): 4840-53.
Park SG, Chang CB, Kim B, Sung HJ. Simulation of fluid-flexible body interaction with heat transfer. Int J Heat Mass Transf 2017; 110: 20-33.
Su SW, Lai MC, Lin CA. An immersed boundary technique for simulating complex flows with rigid boundary. Comput Fluids 2007; 36(2): 313-24.
Lai MC, Peskin CS. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J Comput Phys 2000; 160(2): 705-19.
Maniyeri R, Kang S. Numerical study on bacterial flagellar bundling and tumbling in a viscous fluid using an immersed boundary method. Appl Math Model 2014; 38(14): 3567-90.
Maniyeri R, Suh YK, Kang S, Kim MJ. Numerical study on the propulsion of a bacterial flagellum in a viscous fluid using an immersed boundary method. Comput Fluids 2012; 62: 13-24.
Maniyeri R, Kang S. Hydrodynamic interaction between two swimming bacterial flagella in a viscous fluid-a numerical study using an immersed boundary method. Prog Comput Fluid Dyn 2014; 14(6): 375-85.
Maniyeri R, Kang S. Numerical study on the rotation of an elastic rod in a viscous fluid using an immersed boundary method. J Mech Sci Technol 2012; 26(5): 1515-22.
Kanchan M, Maniyeri R. Numerical analysis of the buckling and recuperation dynamics of flexible filament using an immersed boundary framework. Int J Heat Fluid Flow 2019; 77: 256-77.
Kanchan M, Maniyeri R. Numerical simulation of buckling and asymmetric behavior of flexible filament using temporal second-order immersed boundary method. Int J Numer Methods Heat Fluid Flow 2019; 77: 256-77.
Kanchan M, Maniyeri R. Computational Study of Fluid Flow in Wavy Channels Using Immersed Boundary Method. In: Bansal JC, Das KN, Nagar A, Deep K, Ojha AK, Eds. Soft Computing for Problem Solving Springer. 2019; pp. 283-93.
Kanchan M, Maniyeri R. Flow analysis for efficient design of wavy structured microchannel mixing devices. AIP Conf Proc 2018; 1943(1): 020042
Kanchan M, Maniyeri R. Fluid-structure interaction study and flow rate prediction past a flexible membrane using IBM and ANN techniques. J Fluids Eng 2020; 142(5): 051501
Gong LJ, Kota K, Tao W, Joshi Y. Thermal performance of microchannels with wavy walls for electronics cooling. IEEE Trans Compon Packaging Manuf Technol 2011; 1(7): 1029-35.
Ahmed MA, Yusoff MZ, Shuaib NH. Numerical Investigation on the Nanofluid Flow and Heat Transfer in a Wavy Channel. In: Shaari KZK, Awang M, Eds. . Engineering Applications of Computational Fluid Dynamics. Springer 2014; pp. 145-67.
Zontul H, Kurtulmuş N, Şahin B. Pulsating flow and heat transfer in wavy channel with zero degree phase shift. Mater Sci 2017; 1(1): 31-8.
Gong L, Kota K, Tao W, Joshi Y. Parametric numerical study of flow and heat transfer in microchannels with wavy walls. J Heat Transfer 2011; 133(5): 051702
Ramgadia AG, Saha AK. Numerical study of fully developed flow and heat transfer in a wavy passage. Int J Therm Sci 2013; 67: 152-66.

Rights & PermissionsPrintExport Cite as

Article Details

Year: 2020
Page: [118 - 125]
Pages: 8
DOI: 10.2174/2212797613666200207111629
Price: $25

Article Metrics

PDF: 12