Numerical Calculation of the Irreversible Entropy Production of Additively Manufacturable Off-Set Strip Fin Heat-Transferring Structures

Abstract

In this manuscript, off-set strip fin structures are presented which are adapted to the possibilities of additive manufacturing. For this purpose, the geometric parameters, including fin height, fin spacing, fin length, and fin longitudinal displacement, are varied, and the Colburn j-factor and the Fanning friction factor are numerically calculated in the Reynolds number range of 80–920. The structures are classified with respect to their entropy production number according to Bejan. This method is compared with the results from partial differential equations for the calculation of the irreversible entropy production rate due to shear stresses and heat conduction. This study reveals that the chosen temperature difference leads to deviation in terms of entropy production due to heat conduction, whereas the dissipation by shear stresses shows only small deviations of less than 2%. It is further shown that the variation in fin height and fin spacing has only a small influence on heat transfer and pressure drop, while a variation in fin length and fin longitudinal displacement shows a larger influence. With respect to the entropy production number, short and long fins, as well as large fin spacing and fin longitudinal displacement, are shown to be beneficial. A detailed examination of a single structure shows that the entropy production rate due to heat conduction is dominated by the entropy production rate in the wall, while the fluid has only a minor influence.

Shape Optimization of Heat Exchanger Fin Structures Using the Adjoint Method and Their Experimental Validation

“…The initial design for the optimizations presented in this paper is based on a parameter variation of different fin parameters (fin height, fin spacing, fin length and fin longitudinal displacement), which are presented in Fuchs et al [14]. The different fin parameters are evaluated on the basis of their entropy production number, and a parameter combination that has the lowest entropy generation is selected [15].…”

“…The correlations for calculating the j-and f-factors are power laws with adjustable parameters. The following approach is used for the j-factor: j = C j Re n j (14) and for the f-factor:…”

Experimental Investigation of Additively Manufactured High-Temperature Heat Exchangers

“…The development of the fin type "Reference" is based on geometrical parameter variations presented in Fuchs et al [19]. Based on the parameters presented there, an entropically optimal parameter combination giving the lowest entropy production rate in an average operating range is determined, which gives the fin type called "Reference".…”

“…The Nusselt-numbers can directly calculated by using the fluid and wall temperatures from the numerical calculations, using the definition of the logarithmic temperature difference for constant wall heat flux [29]. For more information on the numerical details of the fin type "Reference", such as validation against literature, determination of the Nusselt number, respectively j-and f-factors and mesh independence, please refer to Fuchs et al [19] and [30]. The fin types "FO" and "HTO" are based on the fin type "Reference", which is why the calculation mesh used there is used as a starting point and is refined using mesh independence analysis until a mesh-independent result is available.…”

“…The proper functioning of the optimization algorithm is validated in advance using numerical flow simulations for the "Reference" fin type. Based on the numerically determined fluid and wall temperatures given in Fuchs et al [19], the Nusselt numbers are determined for different Reynolds numbers and a correlation according to equation( 15) is derived. This is implemented in the design program and a calculation of different operating points (with and without axial heat conduction) with different mass flow rates and temperatures is performed.…”