A new framework for design and validation of complex heat transfer surfaces based on adjoint optimization and rapid prototyping technologies

Abstract

In order to drastically accelerate the development processes of advanced heat exchangers, a new design framework integrating shape optimization, rapid prototyping and experimental validation is proposed. For the optimal design of heat transfer surfaces, a new adjoint-based shape optimization algorithm taking into account unsteady turbulent transport is developed. The present shape optimization algorithm is applied to two di ff erent conventional pin-fin arrays with circular cross sections so as to maximize the analogy factor, i.e., the ratio of heat transfer and pumping power for driving the fluid. The resultant optimal fin shapes are elongated in the streamwise direction and also characterized by bump-like structures formed on the upstream side of the pins. Investigation of numerical results reveals that the pressure drop of the optimal shape is significantly reduced by the suppression of vortex shedding behind the fin, whereas the heat transfer performance is maintained by the extended surface. The optimal shapes are fabricated by a resin-based additive manufacturing technique. A single-blow method allows to evaluate the heat transfer coe ffi cient of low-thermal conductivity materials by measuring the inlet and outlet air temperature only, while the pressure loss is estimated from the pressure measurements at the upstream and downstream of the text matrix by Pit ˆ ot-tubes. As a result, significant improvement of thermal hydraulic performance is experimentally confirmed for the optimal pin-fin arrays as predicted by numerical analyses. The governing equations are non-dimensionalized by a friction velocity based on mean pressure gradient, u (cid:3) (cid:28) , a friction temperature based on uniform heating source, (cid:18) (cid:3) (cid:28) and channel-half width (cid:14) (cid:3) , respectively. The friction-based Reynolds number is set to be Re (cid:28) = u (cid:3) (cid:28) (cid:14) (cid:3) =(cid:23) (cid:3) = 200 (Case 1), 300 (Case 2) which corresponds to an initial bulk Reynolds number of Re b = 500. The Prandtl number is set to Pr = 0 : 71. The fourth and fifth terms in the right-hand-side of Eq. (6) represent the driving force equivalent to a mean pressure gradient and an artificial body force for embedding a solid region in the Cartesian coordinate system by a volume penalization method (Goldstein et al., 1993; Schneider, 2005). Note that ϕ is non-zero only in the solid phase (see, Eq. (4)), so that the damping force acts only in the solid phase in order to eliminate the fluid velocity. Similarly, an isothermal condition on the solid surface is imposed via the last term on the right-hand-side of the energy equation. A periodic boundary condition is applied to the streamwise ( x (cid:0) ) and spanwise ( z (cid:0) ) directions, while the no-slip u = 0 and iso-thermal wall (cid:18) = 0 is applied on the two parallel walls. The grid spacings nondimensionalized by (cid:14) (cid:3) in the x (cid:0) , y (cid:0) , and z (cid:0) directions are ( ∆ x ; ∆ y ; ∆ z ) = (2 : 08 (cid:2) 10 (cid:0) 3 ; 2