Abstract
The paper studies the two-dimensional roller-type viscous micropumps design problem using a level set based topology optimization method. The flow in the viscous micropumps is considered as non-Newtonian flow approximated by the power-law constitutive model. The optimization objective is to minimize the flow viscous dissipation and maximize the flow rate subject to the area constraint. Topology optimization of several roller-type viscous micropumps is numerically investigated by using the presented level set based optimization method. The results show that (1) the optimal long viscous micropump has a higher flow rate; (2) the optimal short viscous micropumps with different flow rates can achieve lower viscous dissipations; (3) the optimal design of the non-Newtonian fluid viscous micropump with a bigger power-law index has a wider gap on the top of the rotor to accommodate a higher flow rate.
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References
Abdelgawad M, Hassan I, Esmail N (2004) Transient behavior of the viscous micropump. Microscale Thermophys Eng 8:361–381
Abdelgawad M, Hassan I, Esmail N, Phutthavong P (2005) Numerical investigation of multistage viscous micropump configurations. J Fluids Eng 127:734–742
Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393
Amstutz S (2005) The topological asymptotic for the Navier–Stokes equations. ESAIM: Contrl Optim Calc Var 11:401–425
Andreasen CS, Gersborg AR, Sigmund O (2009) Topology optimization of microfluidic mixers. Int J Numer Meth Fluids 61:498–513
Bataineh KM, Al-Nimr MA (2009) 2D navier–stokes simulations of microscale viscous pump with slip flow. J Fluids Eng 131:051105-1–7
Blanchard D, Ligrani P (2006) Comparisons of different viscous pumps based on physical flow behavior. Sens Actuators, A 126:83–92
Challis VJ, Guest JK (2009) Level set topology optimization of fluids in Stokes flow. Int Numer Meth Eng 79:1284–1308
Chen H, Su J, Li K, Wang S (2014) A characteristic projection method for incompressible thermal flow. Numer Heat Tr B-Fund 65:554–590
Choi H-I, Lee Y, Choi D-H, Maeng J-S (2010) Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency. Struct Multidiscip O 40:537–548
da Silva AK, Kobayashi MH, Coimbra CFM (2007a) Optimal design of non-Newtonian, micro-scale viscous pumps for biomedical devices. Biotechnol Bioeng 96:37–47
da Silva AK, Kobayashi MH, Coimbra CFM (2007b) Optimal theoretical design of 2-D microscale viscous pumps for maximum mass flow rate and minimum power consumption. Int J Heat Fluid Flow 28:526–536
Decourtye D, Sen M, Gad-El-Hak M (1998) Analysis of viscous micropumps and microturbines. Int J Comput Fluid D 10:13–25
Deng Y, Liu Z, Zhang P, Liu Y, Wu Y (2011) Topology optimization of unsteady incompressible Navier–Stokes flows. J Comput Phys 230:6688–6708
Deng Y, Liu Z, Zhang P, Liu Y, Gao Q, Wu Y (2012) A flexible layout design method for passive micromixers. Biomed Microdevices 14:929–945
Deng Y, Liu Z, Wu J, Wu Y (2013a) Topology optimization of steady Navier–Stokes flow with body force. Comput Method Appl M 255:306–321
Deng Y, Liu Z, Wu Y (2013b) Topology optimization of steady and unsteady incompressible Navier–Stokes flows driven by body forces. Struct Multidiscip O 47:555–570
Ding X, Li P, Lin S-CS, Stratton ZS, Nama N, Guo F, Slotcavage D, Mao X, Shi J, Costanzo F (2013) Surface acoustic wave microfluidics. Lab Chip 13:3626–3649
Duan XB, Ma YC, Zhang R (2008a) Optimal shape control of fluid flow using variational level set method. Phys Lett A 372:1374–1379
Duan XB, Ma YC, Zhang R (2008b) Shape-topology optimization for Navier–Stokes problem using variational level set method. J Comput Appl Math 222:487–499
Duan XB, Ma YC, Zhang R (2008c) Shape-topology optimization of stokes flow via variational level set method. Appl Math Comput 202:200–209
Ejlebjerg Jensen K, Szabo P, Okkels F (2012) Topology optimization of viscoelastic rectifiers. Appl Phys Lett 100:234102-234102-234103
Hyun J, Wang S, Yang S (2014) Topology optimization of the shear thinning non-Newtonian fluidic systems for minimizing wall shear stress. Comput Math Appl 67:1154–1170
Iverson BD, Garimella SV (2008) Recent advances in microscale pumping technologies: a review and evaluation. Microfluid Nanofluid 5:145–174
Kreissl S, Maute K (2012) Levelset based fluid topology optimization using the extended finite element method. Struct Multidiscip O 46:311–326
Kreissl S, Pingen G, Evgrafov A, Maute K (2010) Topology optimization of flexible micro-fluidic devices. Struct Multidiscip O 42:495–516
Laser DJ, Santiago JG (2004) A review of micropumps. J Micromech Microeng 14:R35–R64
Maatoug H (2006) Shape optimization for the Stokes equations using topological sensitivity analysis. ARIMA 5:216–229
Nabavi M (2009) Steady and unsteady flow analysis in microdiffusers and micropumps: a critical review. Microfluid Nanofluid 7:599–619
Nguyen NT, Huang XY, Chuan TK (2002) MEMS-micropumps: A review. J Fluids Eng 124:384–392
Okkels F, Bruus H (2007) Scaling behavior of optimally structured catalytic microfluidic reactors. Phys Rev E 75:016301
Osher S, Fedkiw R (2003) Level set methods and dynamic implicit surfaces. Springer
Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12–49
Peng D, Merriman B, Osher S, Zhao H, Kang M (1999) A PDE-based fast local level set method. J Comput Phys 155:410–438
Pingen G, Maute K (2010) Optimal design for non-Newtonian flows using a topology optimization approach. Comput Math Appl 59:2340–2350
Reyes DR, Iossifidis D, Auroux PA, Manz A (2002) Micro total analysis systems. 1. introduction, theory, and technology. Anal Chem 74:2623–2636
Romero J, Silva E (2014) A topology optimization approach applied to laminar flow machine rotor design. Comput Method Appl M 279:268–300
Sen M, Wajerski D, GadelHak M (1996) A novel pump for MEMS applications. J Fluids Eng 118:624–627
Sethian JA (1999) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge University Press
Sharatchandra MC, Sen M, GadelHak M (1997) Navier–Stokes simulations of a novel viscous pump. J Fluids Eng 119:372–382
Sharatchandra MC, Sen M, Gad-el-Hak M (1998a) New approach to constrained shape optimization using genetic algorithms. AIAA J 36:51–61
Sharatchandra MC, Sen M, Gad-el-Hak M (1998b) Thermal aspects of a novel viscous pump. J Heat Transfer 120:99–107
Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114:146–159
Walburn FJ, Schneck DJ (1976) A constitutive equation for whole human blood. Biorheology 13:201–210
Wang MY (2005) Shape optimization with level set method incorporating topological derivatives. in: Sixth Congresses of Struc Multidisc Optim
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Method Appl M 192:227–246
Zhang B, Liu X (2015) Topology optimization study of arterial bypass configurations using the level set method. Struct Multidiscip O 51:773–798
Zhang B, Liu XM, Sun JJ (2013) Topology optimization for Stokes problem under multiple flow cases using an improved level set method. Proceedings of the ASME FEDSM2013, Paper FEDSM2013-16155, Nevada, USA
Zhou S, Li Q (2008) A variational level set method for the topology optimization of steady-state Navier–Stokes flow. J Comput Phys 227:10178–10195
Ziaie B, Baldi A, Lei M, Gu Y, Siegel RA (2004) Hard and soft micromachining for BioMEMS: review of techniques and examples of applications in microfluidics and drug delivery. Adv Drug Del Rev 56:145–172
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Grant No. 11272251).
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Zhang, B., Liu, X. & Sun, J. Topology optimization design of non-Newtonian roller-type viscous micropumps. Struct Multidisc Optim 53, 409–424 (2016). https://doi.org/10.1007/s00158-015-1346-5
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DOI: https://doi.org/10.1007/s00158-015-1346-5