Topology optimization based on a two-dimensional swirl flow model of Tesla-type pump devices

Abstract Tesla pumps are composed of rotating disks (without blades) and are based on the boundary layer effect (i.e., viscous friction forces acting on the fluid and Coandă effect). The Tesla pump has various applications, however, the efficiency of its operation is quite low, which makes room for the optimization of its design. This way, novel configurations of devices based on this working principle can be developed. Thus, in this work, a Topology Optimization formulation is proposed to optimize the rotor of a Tesla-type pump device by using a 2D swirl flow model, which is a specific model that presents an axisymmetric flow with (or without) flow rotation around the axisymmetric axis. The 2D swirl laminar fluid flow modeling is solved by using the finite element method. A traditional material model is adopted by considering nodal design variables, and is extended to take into account the fact that the optimization is performed in a rotating reference frame and the relative tangential velocity behaves differently than the other velocity components (since the 2D swirl flow model is axisymmetric). A multi-objective function is defined in order to minimize energy dissipation and vorticity. An extra term is proposed to the vorticity function to reduce the generation of grayscale results. An interior point optimization algorithm (IPOPT) is applied to solve the optimization problem. Numerical results taking into account different aspects of the design of the rotor of a Tesla-type device are presented.

[1]  Richard B. Medvitz,et al.  A Passively Suspended Tesla Pump Left Ventricular Assist Device , 2009, ASAIO journal.

[2]  S. H. Hasinger,et al.  Investigation of a Shear-Force Pump , 1963 .

[3]  Joshua Kiddy K. Asamoah,et al.  Fractal–fractional age-structure study of omicron SARS-CoV-2 variant transmission dynamics , 2022, Partial Differential Equations in Applied Mathematics.

[4]  J. S. Romero,et al.  Non-newtonian laminar flow machine rotor design by using topology optimization , 2017 .

[5]  Qing Li,et al.  A variational level set method for the topology optimization of steady-state Navier-Stokes flow , 2008, J. Comput. Phys..

[6]  Patrick Amestoy,et al.  A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..

[7]  Kurt Maute,et al.  Optimal design for non-Newtonian flows using a topology optimization approach , 2010, Comput. Math. Appl..

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

[9]  M. Foster.  The potential of a Tesla type device as a non pulsatile blood pump , 2006 .

[10]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[11]  A. Evgrafov.  Topology optimization of slightly compressible fluids , 2006 .

[12]  Jan Sokolowski,et al.  On the Topological Derivative in Shape Optimization , 1999 .

[13]  Xianmin Zhang,et al.  A multi-objective method of hinge-free compliant mechanism optimization , 2014 .

[14]  Anders Logg,et al.  Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book , 2012 .

[15]  Richard Edwin Sonntag,et al.  Fundamentals of Thermodynamics , 1998 .

[16]  A. Klarbring,et al.  Topology optimization of regions of Darcy and Stokes flow , 2007 .

[17]  Xianbao Duan,et al.  Topology optimization of incompressible Navier-Stokes problem by level set based adaptive mesh method , 2016, Comput. Math. Appl..

[18]  Glaucio H. Paulino,et al.  Layout and material gradation in topology optimization of functionally graded structures: a global–local approach , 2010 .

[19]  Gil Ho Yoon,et al.  Topology optimization for turbulent flow with Spalart-Allmaras model , 2016 .

[20]  Şevki Çeşmeci,et al.  Design, testing and two-dimensional flow modeling of a multiple-disk fan , 2009 .

[21]  Laura Dodsworth.  Operational Parametric Study of a Prototype Tesla Pump , 2016 .

[22]  Anton Evgrafov,et al.  Topology Optimization of Navier-Stokes Equations , 2004 .

[23]  Mehdi Behbahani,et al.  A review of computational fluid dynamics analysis of blood pumps , 2009, European Journal of Applied Mathematics.

[24]  David Rubin,et al.  Introduction to Continuum Mechanics , 2009 .

[25]  Fridolin Okkels,et al.  Topology optimization of viscoelastic rectifiers , 2012 .

[26]  Richard B. Medvitz,et al.  Computational fluid dynamics design and analysis of a passively suspended Tesla pump left ventricular assist device. , 2011, Artificial organs.

[27]  O. Horikawa,et al.  Topology optimization applied to the development of small scale pump , 2018 .

[28]  L. F. N. Sá,et al.  Topology optimization applied to the design of 2D swirl flow devices , 2018, Structural and Multidisciplinary Optimization.

[29]  James K. Guest,et al.  Topology optimization of creeping fluid flows using a Darcy–Stokes finite element , 2006 .

[30]  Mark C. Breiter,et al.  Laminar Flow Between Two Parallel Rotating Disks , 1962 .

[31]  Emílio Carlos Nelli Silva,et al.  A topology optimization approach applied to laminar flow machine rotor design , 2014 .

[32]  S. Fatikow,et al.  Structural topology and shape optimization using a level set method with distance-suppression scheme , 2015 .

[33]  David A. Ham,et al.  Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs , 2013, SIAM J. Sci. Comput..

[34]  G. Rozvany.  Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics , 2001 .

[35]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[36]  K. Vafai.  Handbook of porous media , 2015 .

[37]  Ole Sigmund,et al.  Topology optimization of microfluidic mixers , 2009 .

[38]  E. C. N. Silva,et al.  Topological derivatives applied to fluid flow channel design optimization problems , 2016 .

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

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

[41]  Lin Wang,et al.  Multidisciplinary optimization of a butterfly valve. , 2009, ISA transactions.

[42]  M. Zhou,et al.  Generalized shape optimization without homogenization , 1992 .