Topology optimization of two fluid heat exchangers

Abstract A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for each of the fluids. A single design variable is used to describe the physical fields. The solid interface and the fluid domains are generated using an erosion-dilation based identification technique, which guarantees well-separated fluids, as well as a minimum wall thickness between them. Under the assumption of laminar steady flow, the two fluids are modelled separately, but in the entire computational domain using the Brinkman penalization technique for ensuring negligible velocities outside of the respective fluid subdomains. The heat transfer is modelled using the convection-diffusion equation, where the convection is driven by both fluid flows. A stabilized finite element discretization is used to solve the governing equations. Results are presented for two different problems: a two-dimensional case illustrating and verifying the methodology; and a three-dimensional case inspired by shell-and-tube heat exchangers. The optimized designs for both cases show an improved heat transfer compared to the baseline designs. For the shell-and-tube case, the full freedom topology optimization approach is shown to yield performance improvements of up to 113% under the same pressure drop.

[1]  James K. Guest,et al.  Level set topology optimization of fluids in Stokes flow , 2009 .

[2]  Cetin Batur Dilgen,et al.  Density based topology optimization of turbulent flow heat transfer systems , 2018 .

[3]  A. A. Bhuiyan,et al.  Heat and mass transfer for compact heat exchanger (CHXs) design: A state-of-the-art review , 2018, International Journal of Heat and Mass Transfer.

[4]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[5]  Gregory Nellis,et al.  A fully developed flow thermofluid model for topology optimization of 3D-printed air-cooled heat exchangers , 2017 .

[6]  A. Evgrafov.  The Limits of Porous Materials in the Topology Optimization of Stokes Flows , 2005 .

[7]  Reza Mahmoudi,et al.  Design and validation of topology optimized heat exchangers , 2019 .

[8]  Hiroki Kobayashi,et al.  Topology design of two-fluid heat exchange , 2020, ArXiv.

[9]  A. Evgrafov.  State space Newton’s method for topology optimization , 2014 .

[10]  Shutian Liu,et al.  Topology optimization of shell–infill structures using an erosion-based interface identification method , 2019, Computer Methods in Applied Mechanics and Engineering.

[11]  Nasir Hayat,et al.  CFD applications in various heat exchangers design: A review , 2012 .

[12]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[13]  Kurt Maute,et al.  CutFEM topology optimization of 3D laminar incompressible flow problems , 2017, ArXiv.

[14]  Yoshihiro Kanno,et al.  Topology optimization method for interior flow based on transient information of the lattice Boltzmann method with a level-set function , 2017 .

[15]  Ole Sigmund,et al.  Topology optimization of large scale stokes flow problems , 2008 .

[16]  Joe Alexandersen,et al.  A Review of Topology Optimisation for Fluid-Based Problems , 2020, Fluids.

[17]  Boyan Stefanov Lazarov,et al.  Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework , 2015 .

[18]  Ole Sigmund,et al.  Topology Optimisation for Coupled Convection Problems , 2013 .

[19]  Ilker Tari,et al.  Shell side CFD analysis of a small shell-and-tube heat exchanger , 2010 .

[20]  Kikuo Fujita,et al.  Large-scale topology optimization incorporating local-in-time adjoint-based method for unsteady thermal-fluid problem , 2018 .

[21]  Francesco Montomoli,et al.  Three-dimensional fluid topology optimization for heat transfer , 2018, Structural and Multidisciplinary Optimization.

[22]  Kikuo Fujita,et al.  Freeform winglet design of fin-and-tube heat exchangers guided by topology optimization , 2019, Applied Thermal Engineering.

[23]  O. Sigmund,et al.  Topology optimization of coated structures and material interface problems , 2015 .

[24]  O. Sigmund,et al.  Topology optimization of a pseudo 3D thermofluid heat sink model , 2018, International Journal of Heat and Mass Transfer.

[25]  P. Papazoglou.  Topology Optimization of Heat Exchangers , 2015 .

[26]  Ole Sigmund,et al.  On projection methods, convergence and robust formulations in topology optimization , 2011, Structural and Multidisciplinary Optimization.

[27]  Jacek Rokicki,et al.  Adjoint Lattice Boltzmann for topology optimization on multi-GPU architecture , 2015, Comput. Math. Appl..

[28]  Takayuki Yamada,et al.  Local-in-time adjoint-based topology optimization of unsteady fluid flows using the lattice Boltzmann method , 2017 .

[29]  E. Schlunder.  Heat exchanger design handbook , 1983 .

[30]  O. Sigmund,et al.  Design of passive coolers for light-emitting diode lamps using topology optimisation , 2018, International Journal of Heat and Mass Transfer.

[31]  K. Svanberg,et al.  An alternative interpolation scheme for minimum compliance topology optimization , 2001 .

[32]  Frank P. Incropera,et al.  Foundations of heat transfer , 2013 .

[33]  Chuan Sun,et al.  Thermal enhancement of fin and tube heat exchanger with guiding channels and topology optimisation , 2018, International Journal of Heat and Mass Transfer.

[34]  L. H. Olesen,et al.  A high‐level programming‐language implementation of topology optimization applied to steady‐state Navier–Stokes flow , 2004, physics/0410086.

[35]  Cetin Batur Dilgen,et al.  Topology Optimization of Turbulent Flows , 2018 .

[36]  Ole Sigmund,et al.  Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection , 2015, ArXiv.

[37]  James K. Guest,et al.  Eliminating beta-continuation from Heaviside projection and density filter algorithms , 2011 .

[38]  O. Sigmund,et al.  Topology optimization of channel flow problems , 2005 .

[39]  O. Sigmund,et al.  Topology optimisation for natural convection problems , 2014, 1408.2102.

[40]  M. Nemer,et al.  Topology optimization of heat and mass transfer problems in two fluids—one solid domains , 2019, Numerical Heat Transfer, Part B: Fundamentals.

[41]  Boyan S. Lazarov,et al.  Robust topology optimisation of microstructural details without length scale separation - using a spectral coarse basis preconditioner , 2014, ArXiv.

[42]  Jan Hendrik Klaas Haertel,et al.  Design of Thermal Systems Using Topology Optimization , 2018 .

[43]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[44]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[45]  Ole Sigmund,et al.  Topology optimization of 3D shell structures with porous infill , 2017 .

[46]  J. Petersson,et al.  Topology optimization of fluids in Stokes flow , 2003 .

[47]  O. Sigmund,et al.  Filters in topology optimization based on Helmholtz‐type differential equations , 2011 .