C. Biserni

Evolution in the Design of V-Shaped Highly Conductive Pathways Embedded in a Heat-Generating Piece

This paper presents the evolution of architecture of high conductivity pathways embedded into a heat generating body on the basis of Constructal theory. The main objective is to introduce new geometries for the highly conductive pathways, precisely configurations shaped as V. Four types of V-shaped inserts, evolving from “V1” to “V4,” have been comparatively considered. Geometric optimization of design is conducted to minimize the peak temperature of the heat generating piece. Many ideas emerged from this work: first of all, the numerical results demonstrated that the V-shaped pathways remarkably surpass the performance of some basic configurations already mentioned in literature, i.e., “I and X-shaped” pathways. Furthermore, the evolution of configurations from V1 to V4 resulted in a gradual reduction of the hot spot temperature, according to the principle of “optimal distribution of imperfections” that characterizes the constructal law.

Constructal Design of Convective Y-Shaped Cavities by Means of Genetic Algorithm

In the present work constructal design is employed to optimize the geometry of a convective, Y-shaped cavity that intrudes into a solid conducting wall. The main purpose is to investigate the influence of the dimensionless heat transfer parameter a over the optimal geometries of the cavity, i.e., the ones that minimize the maximum excess of temperature (or reduce the thermal resistance of the solid domain). The search for the best geometry has been performed with the help of a genetic algorithm (GA). For square solids (H/L = 1.0) the results obtained with an exhaustive search (which is based on solution of all possible geometries) were adopted to validate the GA method, while for H/L ≠ 1.0 GA is used to find the best geometry for all degrees of freedom investigated here: H/L, t1/t0, L1/L0, and α (four times optimized). The results demonstrate that there is no universal optimal shape that minimizes the thermal field for all values of a investigated. Moreover, the temperature distribution along the solid domain becomes more homogeneous with an increase of a, until a limit where the configuration of “optimal distribution of imperfections” is achieved and the shape tends to remain fixed. Finally, it has been highlighted that the GA method proved to be very effective in the search for the best shapes with the number of required simulations much lower (8 times for the most difficult situation) than that necessary for exhaustive search.

Numerical Prediction of Flow Structure and Heat Transfer in Square Channels with Dimples Combined with Secondary Half-Size Dimples/Protrusions

The present study employs square cross-section dimpled channels with different arrangements of upstream secondary half-size dimples or protrusions to determine the optimal configurations for augmenting heat transfer rates with minimized pressure drop penalties. Five dimpled channels with and without upstream secondary dimples or protrusions are investigated (simple dimpled channel [case A]; dimpled channels with secondary dimples upstream each dimple [cases B1 and B2, respectively]; and dimpled channels with secondary protrusions upstream each dimple [cases C1 and C2, respectively]). All turbulent fluid flow and surface heat transfer results are obtained using computation fluid dynamics with a k-ϵ RNG turbulence model. Numerical results are qualified using grid-independent predictions of experimental data for one baseline dimple array arrangement. The channel inlet Reynolds number ranges from 8,000 to 24,000. From this study, secondary protrusions can bring forward flow separations and reduce the scope of recirculating flows in adjacent primary dimples and then greatly improve averaged local heat transfer of primary dimple surface. The result does not apply to secondary dimples which hinder flow reattachment in primary dimples and go against heat transfer enhancement. For averaged heat transfer on all the middle heated surfaces, heat transfer enhancement by secondary protrusions is not evident especially at high Reynolds numbers and the uniformity of roughness arrangements as dimples and protrusions makes a dominant role in the averaged heat transfer efficiency, while the dimple structure exhibits heat transfer advantage over protrusions at high Reynolds numbers. For the studied cases, case C1 obtains the best overall thermal performance at low Reynolds numbers, while case B2 is the best one at high Reynolds numbers. It is also recommend that case A can be effectively designed to exhibit the relatively good overall thermal performance with minimizing the blade weight and stress.

Computational fluid-dynamics-based analysis of a ball valve performance in the presence of cavitation

In this paper, the ball valve performance is numerically simulated using an unstructured CFD (Computational Fluid Dynamics) code based on the finite volume method. Navier-Stokes equations in addition to a transport equation for the vapor volume fraction were coupled in the RANS solver. Separation is modeled very well with a modification of turbulent viscosity. The results of CFD calculations of flow through a ball valve, based on the concept of experimental data, are described and analyzed. Comparison of the flow pattern at several opening angles is investigated. Pressure drop behind the ball valve and formation of the vortex flow downstream the valve section are also discussed. As the opening of the valve decreases, the vortices grow and cause higher pressure drop. In other words, more energy is lost due to these growing vortices. In general, the valve opening plays very important roles in the performance of a ball valve.

Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces

The purpose here is to investigate, by means of the constructal principle, the influence of the convective heat transfer flux at the cavity surfaces over the optimal geometry of a T-shaped cavity that intrudes into a solid conducting wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The convective heat flux is imposed as a boundary condition of the cavity surfaces and the geometric optimization is achieved for several values of parameter a = (2hA1/2/k)1/2. The structure of the T-shaped cavity has four degrees of freedom: L0/L1 (ratio between the lengths of the stem and bifurcated branches), H1/L1 (ratio between the thickness and length of the bifurcated branches), H0/L0 (ratio between the thickness and length of the stem), and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (φ). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for fixed values of H/L = 1.0 and φ = 0.1. Even for the first and second levels of optimization, (L1/L0)○○ and (H0/L0)○, the results revealed that there is no universal shape that optimizes the cavity geometry for every imposed value of a. The T-shaped cavity geometry adapts to the variation of the convective heat flux imposed at the cavity surfaces, i.e., the system flows and morphs with the imposed conditions so that its currents flow more and more easily. The three times optimal shape for lower ratios of a is achieved when the cavity has a higher penetration into the solid domain and for a thinner stem. As the magnitude of a increases, the bifurcated branch displaces toward the center of the solid domain and the number of highest temperature points also increases, i.e., the distribution of temperature field is improved according to the constructal principle of optimal distribution of imperfections.

Constructal design applied to the elastic buckling of thin plates with holes

Elastic buckling is an instability phenomenon that can occur if a slender and thin plate is subjected to axial compression. An important characteristic of the buckling is that the instability may occur at a stress level that is substantially lower than the material yield strength. Besides, the presence of holes in structural plate elements is common. However these perforations cause a redistribution in plate membrane stresses, significantly altering their stability. In this paper the Bejan’s Constructal Design was employed to optimize the geometry of simply supported, rectangular, thin perforated plates subjected to the elastic buckling. Three different centered hole shapes were considered: elliptical, rectangular and diamond. The objective function was to maximize the critical buckling load. The degree of freedom H/L (ratio between width and length of the plate) was kept constant, while H0/L0 (ratio between the characteristic dimensions of the holes) was optimized for several hole volume fractions (ϕ). A numerical model employing the Lanczos method and based on the finite element method was used. The results showed that, for lower values of ϕ the optimum geometry is the diamond hole. For intermediate and higher values of ϕ, the elliptical and rectangular hole, respectively, led to the best performance.

Geometric optimization of T-shaped constructs coupled with a heat generating basement: A numerical approach motivated by Bejan’s constructal theory

This work relies on constructal design to perform the geometric optimization of morphing T-shaped fins that remove a constant heat generation rate from a rectangular basement. The fins are bathed by a steady stream with constant ambient temperature and convective heat transfer. The body that serves as a basement for the T-shaped construct generates heat uniformly and it is perfectly insulated on the outer perimeter. It is shown numerically that the global dimensionless thermal resistance of the T-shaped construct can be minimized by geometric optimization subjected to constraints, namely, the basement area constraint, the T-shaped fins area fraction constraint and the auxiliary area fraction constraint, i.e., the ratio between the area that circumscribes the T-shaped fin and the basement area. The optimal design proved to be dependent on the degrees of freedom (L1/L0, t1/t0, H/L): first achieved results indicate that when the geometry is free to morph then the thermal performance is improved according to the constructal principle named by Bejan “optimal distribution of imperfections.”

Constructal Design of Thermal Systems

Constructal theory and design accounts for the universal phenomenon of generation and evolution of design [1, 2]. Constructal theory has been used to explain deterministically the generation of shape in flow structures of nature (river basins, lungs, atmospheric circulation, animal shapes, vascularized tissues, etc.) based on an evolutionary principle of flow access in time. That principle is the Constructal law: “for a flow system to persist in time “to survive,” it must evolve in such way that it provides easier and easier access to the currents that flow through it” [2]. This same principle is used to yield new designs for electronics, fuel cells, and tree networks for transport of people, goods, and information [3]. The applicability of this method/law to the physics of engineered flow systems has been widely discussed in recent literature [4–7].