Uncertainty Quantification of the Effects of Small Manufacturing Deviations on Film Cooling: A Fan-Shaped Hole

• Main Authors: Wei Shi, Pingting Chen, Xueying Li, Jing Ren, Hongde Jiang
• Format: Article
• Language: English
• Published: MDPI AG 2019-04-01
• Series: Aerospace
• Subjects: manufacturing deviations; film cooling; uncertainty quantification; CFD
• Online Access: https://www.mdpi.com/2226-4310/6/4/46

The film cooling holes in the blade of modern gas turbines have commonly been manufactured by laser drilling, Electric Discharge Machining (EDM), and Additive Manufacturing (AM) in recent years. These manufacturing processes often result in small geometric deviations, such as conical angles, filleted edges, and diameter deviations of the hole, which can lead to deviations on the distribution of adiabatic cooling effectiveness (<i>&#951;</i>) values, the value of the discharge coefficient (<i>C_d</i>), and the characteristic of the in-hole flow field. The current study employed flat plate fan-shaped film cooling holes with length-to-diameter values (L/D) equal to 3.5 and six to investigate the effects of these manufacturing deviations on the distribution of <i>&#951;</i> values, the value of <i>C_d</i>, and the characteristic of in-hole flow field. An Uncertainty Quantification (UQ) analysis using the Polynomial Chaos Expansion (PCE) model was carried out to quantify the uncertainty in the values of <i>&#951;</i> and <i>C_d</i>. The statistical characteristics (mean values, standard deviation (Std) values, and Probability Density Function (PDF) values) of <i>&#951;</i> and <i>C_d</i> were also calculated. The results show that conical angle deviations exert no visible changes on the value of <i>&#951;</i>. However, the <i>C_d</i> value decreases by 6.2% when the conical angle changes from 0&#8211;0.5&#176;. The area averaged adiabatic cooling effectiveness (<inline-formula> <math display="inline"> <semantics> <mrow> <mover> <mi>&#951;</mi> <mo stretchy="false">=</mo> </mover> </mrow> </semantics> </math> </inline-formula>) decreases by 3.4%, while the <i>C_d</i> increases by 15.2% with the filleted edge deviation existing alone. However, the deviation value of <inline-formula> <math display="inline"> <semantics> <mrow> <mover> <mi>&#951;</mi> <mo stretchy="false">=</mo> </mover> </mrow> </semantics> </math> </inline-formula> is 7.6%, and that of <i>C_d</i> is 25.7% with the filleted edge deviation and the diameter deviation existing.