Hybrid grid and tree structures for cooling and mechanical strength

Abstract

In this paper, we show how vascular design controls the cooling and mechanical performance of a solid square slab heated uniformly and loaded with uniform pressure. The vascular structure is a combination of one grid and several peripheral trees. The designs of trees with grid canopies provide greater robustness than purely dendritic designs. The coolant fluid enters the slab from the center or from the rim, cools the slab to an allowable temperature level, and then exits. Numerical simulations show the flow of the fluid, heat, and stresses. The results indicate that the lowest peak temperature and lowest flow resistance can be achieved with radial channels, and the lowest peak stress can be achieved with trees with canopies. The peak stresses are the lowest when the configuration is a hybrid grid and tree design. There is an optimal ratio of the grid length divided by the slab length for each specified fraction of the fluid volume occupied by the radial channels. When the heating is concentrated in a small area, the peak temperature is smaller when the heated spot is closer to the center of the slab.

Constructal vascularized structures

“…L, and embedded cooling channels, Figure 6a [9]. The plate is subjected to a uniformly distributed force acting from below, and it is heated uniformly.…”

“…In addition, the peak temperature and the maximum stress of a heated and mechanically loaded structure can be kept under an allowable limit as its weight decreases with vascularization [8,9]. Therefore, the penalty of moving the structure decreases which is crucial for avionics.…”

Vascularization for cooling and reduced thermal stresses

“…if the amount of solid material is fixed [8]. In addition, the peak temperature can be kept under an allowable limit by circulating coolant through the vascular channels [7][8][9][10]. In summary, the material should be placed where it is needed the most, i.e.…”

“…Smart capabilities can be built into a material by embedding vascular channels in it [1][2][3][4][5][6][7][8]. The vascular channels increase the mechanical strength if the material removed to make room for the channels is placed around the channels, i.e.…”

“…The design should be free to vary, in accord with the Constructal design method [1]. The current literature details the application of this method to smart structures [1][2][3][4][5][6][7][8][11][12][13] and thermofluid design [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In a few instances, mechanical strength was used as the design objective [29][30][31].…”