Computational Methods: For the numerical analysis ofthe heat transfer, solutions are found for the governingconservation equation of energy. The general objectivefunction in this optimization problem is equivalent tominimizing the total variation of the temperature in thedesign domain during a constant heat generation [1].Since an active cooling with air is intended, a limit on thesolid fraction is introduced to allow the fluid to pass by.The material distribution method (with the designvariable 𝜌𝑑𝑒𝑠) is used for the topology optimization. Thethermal conductivity is defined as a function of 𝜌𝑑𝑒𝑠 byapplying the SIMP rule [2]:

Numerical Optimization of Active Heat Sinks Considering Restrictions of Selective Laser Melting

F. Lange1, C. Hein1, G. Li1, C. Emmelmann1,2

1. Fraunhofer Research Institution for Additive Manufacturing Technologies IAPT, Hamburg, HH, Germany 2. Institute of Laser and System Technologies, Hamburg University of Technology, Hamburg, HH, Germany

Introduction: Additive manufacturing methods likeSelective Laser Melting are used for manufacturing ofcomplex topology optimized structures because of thegreat design freedom provided by a tool-free, layer-wiseproduction. This design freedom also allows for compactdesigns of thermal components with good adaptation togeometrical boundary conditions, while manufacturingrestrictions can be directly integrated into topologyoptimization simulations.In this work a parametric optimization and a topologyoptimization approach for an active heat sink arecompared, regarding the thermal performance, asshown in Figure 1.

CON PA TO TOF

m in kg 0.550 0.170 0.134 0.140

Rth in K W-1 0.360 0.462 0.376 0.373

R*th in K kg W-

10.198 0.079 0.050 0.053

Results & Conclusions: The best weight relatedthermal resistance is achieved by the topologicaloptimum without forced edging (TO), which is aroundfive times better than the conventional component(CON) and thus ideally suited for lightweightconstruction applications. The topological optimumwith forced edging (TOF) has a lower thermalresistance, but since it is a little bit heavier, theweighted thermal resistance is higher compared toTO.

References:1. E. M. Dede. Multiphysics topology optimization of heat transfer and fluid flow

systems. COMSOL Users Conference, (2009)2. M. P. Bendsøe, O. Sigmund. Topology Optimization: Theory, Methods and

Applications. (2003)

Figure 2. Used parameters (number offins not included), mesh and boundaryconditions for the parametricoptimization.

Figure 5. Simulation results and prototypes. Left: parametric optimum:top – simulation, bottom: printed and post-processed part. Right:topological optimum: upper left – simulation, upper right – printed andpost-processed TO, bottom – printed and post-processed TOF

Figure 4. Laser paths and laser dia-meter in comparison to the mathe-matical optimal surface.

Table 1. Mass (m), thermal resis-tance (Rth), and weight relatedthermal resistance (R*th) of theinvestigated Prototypes.Figure 1. Definition of the problem.

Figure 3. The boundary conditionsand design space the topologicaloptimization.

𝑓 = Ω

𝑞 ⋅ 𝑘 𝛻𝑇 2 + 1 − 𝑞h0hmaxA

𝛻𝜌𝑑𝑒𝑠 𝑥2 dΩ,

0 ≤ Ω

𝜌𝑑𝑒𝑠dΩ ≤ 𝛾

Furthermore, the total variation of the designvariable is used to define a penalty term as a wallthickness restriction. The final objective function hasthe form:

𝑘 = 𝑘𝑚𝑖𝑛 + 𝑘𝑚𝑎𝑥 − 𝑘𝑚𝑖𝑛 ⋅ 𝜌𝑑𝑒𝑠𝑝

Excerpt from the Proceedings of the 2018 COMSOL Conference in Lausanne