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Topology optimization applied to the development of small scale pump

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Abstract

Flow machines are very important to industry, being widely used on various processes. Performance improvements are relevant factors and can be achieved by using optimization methods, such as topology optimization. Thus, this work aims to perform the complete development cycle of a small scale pump designed by using topology optimization method. For the pump modelling the finite element method is applied to solve the Navier-Stokes equations on a rotating reference frame. In the optimization phase, it is defined a multi-objective function that aims to minimize the viscous energy dissipation and vorticity. The optimized results obtained by using topology optimization are post-processed and manufactured by using a 3D printer, and prototypes with an electric motor are built. An experimental characterization is performed by measuring fluid flow and pressure head given by the pumps. Experimental and computational results are compared and the improvement is verified.

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Acknowledgements

This research was partly supported by CNPq (Brazilian Research Council) and FAPESP (Sao Paulo Research Foundation). The authors thank the supporting institutions. The first author thanks the financial support of FAPESP under grants 2016/19261-7, 2013/24434-0, and 2014/50279-4. The fourth author thanks the financial support of CNPq (National Council for Research and Development) under grant 304121/2013-4. Authors thank the NDF laboratory at Mechanical Engineering Department for sharing the ANSYS license.

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Authors and Affiliations

  1. Department of Mechatronics and Mechanical Systems Engineering of Escola Politecnica, University of Sao Paulo, Av. Prof. Mello Moraes, 2231 - 05508-030, Sao Paulo, Brazil

    L. F. N. Sá, O. Horikawa & E. C. N. Silva

  2. Department of Mechanical Engineering, Federal University of Espirito Santo, Espirito Santo, Brazil

    J. S. Romero

Authors
  1. L. F. N. Sá
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  2. J. S. Romero
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  3. O. Horikawa
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  4. E. C. N. Silva
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Correspondence to E. C. N. Silva.

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Appendix A: Mesh convergence analysis

Appendix A: Mesh convergence analysis

A mesh convergence analysis is performed for each rotor presented in Section 7.2.1. All meshes have a inflation refinement at the wall considering the first layer with 0.1[mm] and 10 layers with 5% growth rate. The convergence analysis is performed by changing the max element size and evaluating the desired variable. In pumps, usually, the convergence analysis is performed by considering the pressure convergence, however, in this case we are interested in the energy dissipation and vorticity. Thus these variables are also considered. The convergence analysis for all cases is done by considering the operation point of 2500[rpm] and the highest mass flow, i.e., 3.67[l/min] for the straight blade, 3.3[l/min] for the rotor optimized for energy dissipation and 3.61[l/min] for the rotor optimized for energy dissipation and vorticity.

The convergence analysis is performed for each variable. The pressure values are shown in Fig. 20. As we can see the convergence occurs even with a low number of elements in the pressure variable. However, the final mesh needs to be converged for the interest variable.

Fig. 20
figure 20

Pressure values for mesh convergence analysis

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Figure 21 shows the energy dissipation variation with the number of elements for each rotor. The last mesh analyzed has around 12,5 million of elements and the convergence is still not achieved. This is the limit of our computer power and takes a long time to calculate. Despite this, the overall tendency is that the optimized rotors present lower values of energy dissipation.

Fig. 21
figure 21

Energy dissipation values for mesh convergence analysis

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Figure 22 shows the vorticity variation with the number of elements for each model. Again, the expected convergence is not achieved with our computer power, nevertheless the conclusion of the straight blade rotor having a worse vorticity value still is preserved, even for low discretization meshes.

Fig. 22
figure 22

Vorticity values for mesh convergence analysis

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Thus, the results presented in Section 7.2.1 are obtained with an intermediary mesh consisting of around 5.5 million of elements and the conclusions are expected to be valid even for a mesh with higher discretization.

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Sá, L.F.N., Romero, J.S., Horikawa, O. et al. Topology optimization applied to the development of small scale pump. Struct Multidisc Optim 57, 2045–2059 (2018). https://doi.org/10.1007/s00158-018-1966-7

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  • DOI: https://doi.org/10.1007/s00158-018-1966-7

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