Concurrent shape and topology optimization for unsteady conjugate heat transfer
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RESEARCH PAPER
Concurrent shape and topology optimization for unsteady conjugate heat transfer David S. Makhija 1
&
Philip S. Beran 2
Received: 17 May 2019 / Revised: 18 November 2019 / Accepted: 20 February 2020 # This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2020
Abstract This work explores topology optimization under unsteady conditions on a fundamental design problem to gain design insights between steady and unsteady regimes. A previously studied steady conjugate heat transfer problem at a Reynolds number of 20 is extended to unsteady conditions at a Reynolds number of 100 exhibiting vortex shedding. Interesting non-intuitive optimized shapes and internal topologies for a heated body are computed that do not qualitatively match optimized designs generated with a Reynolds number of 20. Shape optimization under unsteady conditions with a solid interior relies on vortex shedding to improve heat transfer while shape optimization under steady conditions increased the exposed surface area near cool fluid. Concurrent shape and topology optimization with two shape parameter spaces are considered and show that the higher parameter space leverages a higher frequency of vortex shedding to improve cooling. The internal optimized topologies with concurrent shape and topology optimization prioritize heat transfer near the flow separation point biased towards the leading or trailing edge of the body, dependent on the location of most efficient convection. Computing reasonably converged time-averaged objectives and constraints for the presented unsteady case requires 4000 time steps while the steady case requires one time step, leading to a large marginal computational cost increase. Keywords Topology optimization . Shape optimization . Heat transfer . Fluid optimization . Conjugate heat transfer . Transient adjoint
1 Introduction High-fidelity physical modeling frequently predicts physical responses with time dependence or a lack of a steady state. Optimization under unsteady conditions is often avoided because of the expense of analysis and the higher implementation complexity of sensitivity analysis. This work contributes to the relatively sparse literature in optimization considering problems with unsteady physics. This work explores a fundamental design problem that exhibits unsteadiness as the flow speed is increased.
Responsible Editor: Somanath Nagendra Cleared for public release, 88ABW-2019-1080 * David S. Makhija [email protected] 1
Lateral Unbounded Software LLC, Co-located at AFRL/RQVC 2210 Eighth Street B146, WPAFB, OH 45433, USA
2
Air Force Research Laboratory RQVC, 2210 Eighth Street B146, WPAFB, OH 45433, USA
The selected application is conjugate heat transfer. Engineers have historically been concerned with design for thermal constraints, but the recent advances in electronics power density, extreme environment vehicles, and electrification of aircraft and automobiles have led to increased importance of design for ther
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