Vascular structures for smart features: Self-cooling and self-healing

Here we show how smart features of self-cooling and self-healing can be gained to mechanical systems with embedded vascular structures. Vascular structures mimic the circulatory system of animals. Similar to blood distribution from heart to the animal body, vascular channels provide the distribution of coolant and/or healing agent from a point to the entire body of a mechanic system. Thus the mechanic system becomes capable of cooling itself under unpredictable heat attacks and capable of healing itself as cracks occur due to applied mechanical loads. These smart features are necessary for advanced devices, equipment and vehicles. The essential design parameter is vascularization in order to provide smart features. There are distinct configurations for vascularization such as radial, tree-shaped, grid and hybrids of these designs. In addition, several theories are available for the shape optimization of vascular structures such as fractal theory and constructal theory. Unlike fractal theory, constructal theory does not include constraints based on generic algorithms and dictated assumptions. Therefore, constructal theory approach is discussed in this paper. This paper shows how smart features can be gained to a mechanical system while its weight decreases and its mechanical strength increases simultaneously.Scientific and Technological Research Council of Turkey (TUBITAK 114M592

Constructal microdevice manifold design with uniform flow rate distribution by consideration of the tree-branching rule of Leonardo da Vinci and Hess-Murray rule

In this paper, we show how the design of a microdevice manifold should be tapered for uniform flow rate distribution. The designs based on the tree-branching rule of Leonardo da Vinci and the Hess-Murray rule were considered in addition to the constructal design. Both da Vinci and Hess-Murray designs are insensitive to the inlet velocity, and they provide better flow uniformity than the base (not tapered) design. However, the results of this paper uncover that not only pressure drop but also velocity distribution in the microdevice play an integral role in the flow uniformity. Therefore, an iterative approach was adopted with five degrees-of-freedom (inclined wall positions) and one constraint (constant distribution channel thickness) in order to uncover the constructal design which conforms the uniform flow rate distribution. In addition, the effect of slenderness of the microchannels (Svelteness) and inlet velocity on the flow rate distribution to the microchannels has been documented. This paper also uncovers that the design of a manifold should be designed with not only the consideration of pressure distribution but also dynamic pressure distribution especially for non-Svelte microdevices.The Scientific and Technological Research Council of Turkey (TUBITAK) under Grant No. 114M592

The effect of cooling on mechanical and thermal stresses in vascular structures

Here, we show how the vascular channel configuration and its shape affect the mechanical strength which is simultaneously subjected to heating and mechanical load. The material properties were defined as functions of temperature. The effect of channel cross-section on the coolant mass flow rate, peak temperature and peak stresses are documented. The results show that the resistances to flow of stresses and fluid is minimum with the circular channels while the resistance to the heat flow is the smallest with semi-circular channels. In addition, morphing the vascular design provides almost the smallest resistance to the heat flow with circular channels (0.3% difference in the peak temperature). This shows that even the convective resistances are the smallest with circular-cross section, overall thermal resistance is smaller in semi-circular design for the fixed fluid volume. The peak stress is smaller with hybrid design than the parallel designs for the entire pressure drop range. In addition, the effects of mechanical load, heating rate and reference temperature on the stress distribution are also documented. Furthermore, the thermal and mechanical stresses are also documented separately, and then compared with the coupled solution cases. The chief result of this paper is that for a coupled system minimizing only one of the resistance terms is not sufficient, all the resistances considered simultaneously in order to uncover the best performing design. In coupled solutions, we documented the simulation results with temperature dependent material properties and the resistances to the heat and fluid flow is affected by the mechanical deformations. In addition, the results show that the designs should be free to vary, the unexpected designs can be the best performing designs for the given parameters and constraints. Therefore, the design parameters based on the experience does not always yield the best performing designs as the objectives and constraints vary

Constructal vascularized structures

Smart features such as self-healing and selfcooling require bathing the entire volume with a coolant or/and healing agent. Bathing the entire volume is an example of point to area (or volume) flows. Point to area flows cover all the distributing and collecting kinds of flows, i.e. inhaling and exhaling, mining, river deltas, energy distribution, distribution of products on the landscape and so on. The flow resistances of a point to area flow can be decreased by changing the design with the guidance of the constructal law, which is the law of the design evolution in time. In this paper, how the flow resistances (heat, fluid and stress) can be decreased by using the constructal law is shown with examples. First, the validity of two assumptions is surveyed: using temperature independent Hess-Murray rule and using constant diameter ducts where the duct discharges fluid along its edge. Then, point to area types of flows are explained by illustrating the results of two examples: fluid networks and heating an area. Last, how the structures should be vascularized for cooling and mechanical strength is documented. This paper shows that flow resistances can be decreased by morphing the shape freely without any restrictions or generic algorithms

Inverted fins for cooling of a non-uniformly heated domain

This paper shows that the peak temperature of a nonuniformly heated region can be decreased by embedding highconductivity tree-shaped inserts which is in contact with a heat sink from its stem. The volume fraction of the high-conductivity material is fixed, and so is the volume of the solid region. The length scale of the solid domain is L. Inside there is a cubeshaped region with length scale of 0.1L and heat production 100 times greater than the rest of the domain. The location of this hot spot was varied to uncover how its location affects the peak temperature and the design of inverted fins, i.e. highconductivity tree-shaped inserts. The volume fraction of the high-conductivity tree was varied for number of bifurcation levels of 0, 1 and 2. This showed that increasing the number of the bifurcation levels decreases the peak temperature when the volume fraction decreases. The optimal diameter ratios and optimal bifurcation angles at the each junction level are also documented. Y-shaped trees promise smaller peak temperatures than T-shaped trees. The location of the vascular tree in the z direction also affects the peak temperature when the heat generation is non-uniform. In addition, the peak temperature is minimum when z = 0.65L even though the hot spot is located on z = 0.75

Constructal structures with and without high-conductivity inserts for self-cooling

Here we show how a heat generating domain can be gained self-cooling capability with embedded cooling channels and with and without high-conductivity fins. The volume of the heat generating domain is fixed, so is the overall volume of the cooling channels and high-conductivity inserts. Even though the coolant volume decreases with embedded high-conductivity fins, the peak temperature also decreases with high-conductivity inserts. The peak temperature is affected by the location, shape and complexity of the fins and the volume fraction. This paper documents how these degrees of freedoms should be changed in order to minimize peak temperature. This paper also discusses how the volume fraction affects each fin shape in order to minimize the peak temperature. This paper uncovers that the fins should be distributed non-equidistantly, and that high-conductivity material should be inserted as fins (bulks of high-conductivity materials) rather than uniform distribution in the domain. This paper concludes that the overall thermal conductance of a heat generating domain can be maximized by freely morphing the shape of the high-conductivity material. The optimal design exists for given conditions and assumptions, and this design should be morphed when conditions and assumptions change. This conclusion is in accord with the constructal law. Each optimal design for given conditions and assumptions is the constructal designTUBITAK (114M592

Constructal vascular structures with high-conductivity inserts for self-cooling

In this paper, we show how a heat-generating domain can be cooled with embedded cooling channels and high-conductivity inserts. The volume of cooling channels and high-conductivity inserts is fixed, so is the volume of the heat-generating domain. The maximum temperature in the domain decreases with high-conductivity inserts even though the coolant volume decreases. The locations and the shapes of high-conductivity inserts corresponding to the smallest peak temperatures for different number of inserts are documented,Scientific and Technological Research Council of Turkey (MAG-114M592

The effect of cavities and T-shaped assembly of fins on overall thermal resistances

In this study, authors show that maximum excess temperature on a heat generating cylindrical solid domain can be minimized with numerically optimized rectangular cavities and T-shaped fins. The effect of the cavities and the fins on overall thermal resistances were compared while their volume fraction in a unit volume element is fixed. Furthermore, the designs correspond to the minimum thermal resistance were uncovered for two types of flows; parallel and cross-flow. The governing equations of the heat transfer and the fluid flow were solved simultaneously in order to show the effects of design on the flow characteristics and the thermal performance. Two-dimensional solution domain was used to uncover the thermal performance in cross-flow case because the flow direction is perpendicular to the heat transfer surface area of the heat generating domain. However, three-dimensional domain was used in parallel flow case because the fluid flows along the outer surface of the heat generating domain. For the cross-flow case, the results show that T-shaped assembly of fins with longer stem and shorter tributaries correspond to the lower peak temperature. In addition, the results also show that there is an optimal cavity shape that minimizes the peak temperature. This optimal shape becomes thinner when the number of the cavities increase. In parallel flow case, fins with thicker and shorter stem and longer tributaries correspond to the minimum excess temperature. In addition, the longer and thinner cavities increase the thermal performance in parallel flow case

Constructal tree-shaped designs for self-cooling

In this paper, we show how a plate which is subjected to a heating load can be kept under an allowable temperature. Vascular channels in which coolant fluid flows have been embedded in the plate. Two types of vascular channel designs were compared: radial and tree-shaped. The effects of channel design on the thermal performance for different volume fractions (the fluid volume over the solid volume) are documented. Changing the design from radial to tree-shaped designs decreases the order of pressure drop. Hence increase in the order of the convection coefficient is achieved. However, treeshaped designs do not bath the entire domain. Therefore, we have inserted additional branches at the uncooled regions. Then, we have compared the peak temperatures of radial, traditional tree-shaped and improved tree-shaped designs. The effect of design on the maximum temperature shows that there should be an optimum design for a distinct set of boundary conditions, and this design should be varied as the boundary conditions change. This result is in accord with the constructal law, i.e. the shape should be varied in order to minimize resistances to the flows.TUBITAK 114M59

The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain

Here, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L0, where L0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change.Scientific and Technological Research Council of Turkey (114M592