Skip to main content
SpringerLink
Log in

A level set-based topology optimization method for optimal manifold designs with flow uniformity in plate-type microchannel reactors

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper proposes an optimal design method for plate-type microchannel reactor manifolds, using a level set-based topology optimization method that targets flow uniformity among the microchannels. For plate-type microchannel reactors, manifold designs must consider both the uniformity of flow among the microchannels and minimization of pressure drop in the device. To address these design requirements, the pressure drop in the device is defined as the objective functional to be minimized under a flow rate inequality constraint, defined as the deviation in flow rate among the microchannels during the optimization. In addition, we propose a comparably simple and stable augmented Lagrangian method using an exponential function, to determine the Lagrange multiplier that acts to satisfy the flow rate inequality constraint. To demonstrate the utility of our proposed method, two-dimensional Z-type and U-type manifold design problems are presented in the numerical examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  • Aage N, Poulsen TH, Gersborg-Hansen A, Sigmund O (2008) Topology optimization of large scale Stokes flow problems. Struct Multidisc Optim 35(2):175–180

    Article  MathSciNet  MATH  Google Scholar 

  • Allaire G, Jouve F, Toader A (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393

    Article  MathSciNet  MATH  Google Scholar 

  • Allaire G, Gournay F, Jouve F, Toader AM (2005) Structural optimization using topological and shape sensitivity via a level set method. Control Cybern 34(1):59–81

    MathSciNet  MATH  Google Scholar 

  • Bajura RA (1971) A model for flow distribution in manifolds. J Eng Power Trans ASME 93(1):7–12

    Article  Google Scholar 

  • Bajura RA, Jones EH (1976) Flow distribution manifolds. J Fluids Eng Trans ASME 98(1):654–666

    Article  Google Scholar 

  • Bassiouny MK, Martin H (1984a) Flow distribution and pressure drop in plate heat exchangers-I U-type arrangement. Chem Eng Sci 39(3):693–700

  • Bassiouny MK, Martin H (1984b) Flow distribution and pressure drop in plate heat exchangers-II Z-type arrangement. Chem Eng Sci 39(3):701–704

  • Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224

    Article  MathSciNet  MATH  Google Scholar 

  • Bendsøe MP, Sigmund O (1997) Optimization of Structural Topology, Shape and Material. Springer, Berlin

    MATH  Google Scholar 

  • Borrvall T, Petersson J (2003) Topology optimization of fluids in Stokes flow. Int J Numer Methods Fluids 41(1):77–107

    Article  MathSciNet  MATH  Google Scholar 

  • Bruns TE (2007) Topology optimization of convection-dominated, steady-state heat transfer problems. Int J Heat Mass Transfer 50(15–16):2859–2873

    Article  MATH  Google Scholar 

  • Challis VJ, Guest JK (2009) Level set topology optimization of fluids in Stokes flow. Int J Numer Methods Eng 79(10):1284–1308

    Article  MathSciNet  MATH  Google Scholar 

  • Deng Y, Liu Z, Zhang P, Liu Y, Wu Y (2011) Topology optimization of unsteady incompressible Navier-Stokes flows. J Comput Phys 230(17):6688–6708

    Article  MathSciNet  MATH  Google Scholar 

  • Deng Y, Liu Z, Wu J, Wu Y (2013) Topology optimization of steady Navier-Stokes flow with body force. Comput Methods Appl Mech Eng 255:306–321

    Article  MathSciNet  MATH  Google Scholar 

  • Diaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35(7):1487–1502

    Article  MathSciNet  MATH  Google Scholar 

  • Duan XB, Ma YC, Zhang R (2008) Shape-topology optimization for Navier-Stokes problem using variational level set method. J Comput Appl Math 222(2):487–499

    Article  MathSciNet  MATH  Google Scholar 

  • Eschenauer HA, Kobelev V, Schumacher A (1994) Bubble method for topology and shape optimization of structures. Struct Optim 8(1):42–51

    Article  Google Scholar 

  • Gersborg-Hansen A, Sigmund O, Haber RB (2005) Topology optimization of channel flow problems. Struct Multidisc Optim 30(3):181–192

    Article  MathSciNet  MATH  Google Scholar 

  • Gersborg-Hansen A, Berggren M, Dammann B (2006) Topology optimization of mass distribution problems in Stokes flow. Springer, Netherlands, pp 356–374

    Google Scholar 

  • Hassan JM, Mohammed WS, Mohamed TA, Alawee WH (2014) Review on Single-Phase Fluid Flow Distribution in Manifold. Int J Sci Res 3(1):325–330

    Google Scholar 

  • Hestenes MR (1969) Multiplier and gradient methods. J Optim Theory Appl 4(5):303–320

    Article  MathSciNet  MATH  Google Scholar 

  • Liu Z, Gao Q, Zhang P, Xuan M, Wu Y (2011) Topology optimization of fluid channels with flow rate equality constraints. Struct Multidisc Optim 44(1):31–37

    Article  MathSciNet  MATH  Google Scholar 

  • Ma ZD, Kikuchi N, Cheng HC (1995) Topological design for vibrating structures. Comput Methods Appl Mech Eng 121(1–4):259–280

    Article  MathSciNet  MATH  Google Scholar 

  • Matsumori T, Kondoh T, Kawamoto A, Nomura T (2013) Topology optimization for fluid-thermal interaction problems under constant input power. Struct Multidisc Optim 47(4):571–581

    Article  MATH  Google Scholar 

  • Mohammadi M, Jovanovic GN, Sharp KV (2013) Numerical study of flow uniformity and pressure characteristics within a microchannel array with triangular manifolds. Comput Chem Eng 52:134–144

    Article  Google Scholar 

  • Nishiwaki S, Frecker MI, Min S, Kikuchi N (1998) Topology optimization of compliant mechanisms using the homogenization method. Int J Numer Methods Eng 42(3):535–559

    Article  MathSciNet  MATH  Google Scholar 

  • Olesen LH, Okkels F, Bruus H (2006) A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow. Int J Numer Methods Eng 65(7):975–1001

    Article  MathSciNet  MATH  Google Scholar 

  • Osher S, Sethian JA (1988) Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 78(1):12–49

    Article  MathSciNet  MATH  Google Scholar 

  • Otomori M, Yamada T, Izui K, Nishiwaki S (2015) Matlab code for a level set-based topology optimization method using a reaction diffusion equation. Struct Multidisc Optim 51(5):1159– 1172

    Article  MathSciNet  Google Scholar 

  • Pan M, Tang Y, Pan L, Lu L (2008) Optimal design of complex manifold geometries for uniform flow distribution between microchannels. Chem Eng J 137(2):339–346

    Article  Google Scholar 

  • Rockafellar RT (1973) A dual approach to solving nonlinear programming problems by unconstrained optimization. Math Program 5(1):354–373

    Article  MathSciNet  MATH  Google Scholar 

  • Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Based Des Struct Mach 25(4):493–524

    Article  Google Scholar 

  • Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization 16:68–75

    Article  Google Scholar 

  • Sokolowski J, Zochowski A (1999) On the Topological Derivative in Shape Optimization. SIAM J Control Optim 37(4):1251–1272

    Article  MathSciNet  MATH  Google Scholar 

  • Suzuki K, Kikuchi N (1991) A homogenization method for shape and topology optimization. Comput Methods Appl Mech Eng 93(3):291–318

    Article  MATH  Google Scholar 

  • Tonkovich A, Kuhlmann D, Rogers A, McDaniel J, Fitzgerald S, Arora R, Yuschak T (2005) Microchannel technology scale-up to commercial capacity. Chem Eng Res Des 83(A6):634–639

    Article  Google Scholar 

  • Tonomura O, Tanaka S, Noda M, Kano M, Hasebe S, Hashimoto I (2004) CFD-based optimal design of manifold in plate-fin microdevices. Chem Eng J 101(1–3):397–402

    Article  Google Scholar 

  • Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246

    Article  MathSciNet  MATH  Google Scholar 

  • Yaji K, Yamada T, Yoshino M, Matsumoto T, Izui K, Nishiwaki S (2014) Topology optimization using the lattice Boltzmann method incorporating level set boundary expressions. J Comput Phys 274:158–181

    Article  MathSciNet  MATH  Google Scholar 

  • Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a fictitious interface energy. Comput Methods Appl Mech Eng 199(45–48):2876–2891

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou S, Li Q (2008) A variational level set method for the topology optimization of steady-state Navier-Stokes flow. J Comput Phys 227(24):10,178–10,195

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IHI Corporation, Yokohama, Kanagawa, 235-8501, Japan

    Seiji Kubo

  2. Department of Mechanical Engineering and Science, Kyoto University, Kyotodaigaku-katsura, Nishikyo-Ku, Kyoto, 615-8540, Japan

    Kentaro Yaji, Takayuki Yamada, Kazuhiro Izui & Shinji Nishiwaki

Authors
  1. Seiji Kubo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kentaro Yaji
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Takayuki Yamada
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kazuhiro Izui
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shinji Nishiwaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seiji Kubo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kubo, S., Yaji, K., Yamada, T. et al. A level set-based topology optimization method for optimal manifold designs with flow uniformity in plate-type microchannel reactors. Struct Multidisc Optim 55, 1311–1327 (2017). https://doi.org/10.1007/s00158-016-1577-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-016-1577-0

Keywords

Search

Navigation