A convolution modeling method for pore plugging impact on transpiration cooling configurations perforated by straight holes

Transpiration cooling is one of the most efficient cooling technologies to protect hot section components such as turbine airfoils, missile heads and shells of rockets or space craft. This external cooling method has much higher efficiency than film cooling when consuming the same amount of coolant, due to the uniformity of coolant distribution. However, pore plugging, which frequently occurs during the operation of transpiration cooled components, has limited its long term stability and prevented its application in industrial components. Dust deposition is one of the main reasons causing plugging of pores for transpiration cooling. Although a lot of effort has been devoted into explaining dust deposition and erosion mechanisms of transpiration cooled components, reducing plugging impact remained difficult as the plugging caused by dusts was unpredictable for traditional porous media. Additive manufacturing, with capability to precisely construct structures in small scales, has emerged as considerable new tool to enhance the controllability of porous media, and furthermore, to achieve a good solution to minimize the plugging disadvantage. The present study selected a transpiration cooling configuration perforated by straight holes with an additive manufacturable diameter of 0.4 mm. Computational Fluid Dynamics (CFD) methods were employed to model the pore plugging and its effect on heat transfer. A scripting code in addition to the ANSYS CFX solver was utilized to simulate the random plugging conditions of the holes. Two hundred numerical cases with four different plugging probabilities were calculated and statistically evaluated to quantify the disadvantage of pore plugging on the cooling effectiveness. A theoretic model with convolution functions was developed to predict the local cooling effectiveness. Results obtained from the numerical analysis indicated that the overall plugging ratio was a dominating parameter for the cooling effectiveness but this single parameter was not adequate to scale the cooling effectiveness for all locations. On the contrary, the unique pair of discrete convolution parameters indexing all other transpiration holes in the array developed in this study had a significantly higher accuracy in predicting the cooling effectiveness than the overall plugging ratio. The present study was among one of the earliest to use convolution modeling method to predict transpiration cooling and related plugging disadvantages. This effort could provide a quantitative understanding of the random plugging on the specific transpiration cooling configuration, and could benefit further optimization effort to reduce the plugging disadvantage of transpiration cooling using additive manufacturing.