{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T13:37:30Z","timestamp":1790948250242,"version":"4.1.0"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,22]],"date-time":"2019-12-22T00:00:00Z","timestamp":1576972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Computational Fluid Dynamics (CFD) results are often presented in a deterministic way despite the uncertainties related to boundary conditions, numerical modelling, and discretization error. Uncertainty quantification is the field studying how these phenomena affect the numerical result. With these methods, the results obtained are directly comparable with the experimental ones, for which the uncertainty related to the measurement is always shown. This work presents an uncertainty quantification approach applied to CFD: the test case consists of an industrial prismatic gas turbine vane with standard film cooling shaped holes system on the suction side only. The vane was subject of a previous experimental test campaign which had the objective to evaluate the film cooling effectiveness through pressure-sensitive paint technique. CFD analyses are conducted coherently with the experiments: the analogy between heat and mass transfer is adopted to draw out the adiabatic film effectiveness, solving an additional transport equation to track the concentration of CO2 used as a coolant fluid. Both steady and unsteady simulations are carried out: the first one using a RANS approach with k-\u03c9 SST turbulence model the latter using a hybrid LES-RANS approach. Regarding uncertainty quantification, three geometrical input parameters are chosen: the hole dimension, the streamwise inclination angle of the holes, and the inlet fillet radius of the holes. Polynomial-chaos approach in conjunction with the probabilistic collocation method is used for the analysis: a first-order polynomial approximation was adopted which required eight evaluations only. RANS approach is used for the uncertainty quantification analysis in order to reduce the computational cost. Results show the confidence interval for the analysis as well as the probabilistic output. Moreover, a sensitivity analysis through Sobol\u2019s indices was carried out which prove how these input parameters contribute to the film cooling effectiveness, in particular, when dealing with the additive manufacturing process.<\/jats:p>","DOI":"10.3390\/e22010016","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:15:01Z","timestamp":1577070901000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Uncertainty Quantification of Film Cooling Performance of an Industrial Gas Turbine Vane"],"prefix":"10.3390","volume":"22","author":[{"given":"Andrea","family":"Gamannossi","sequence":"first","affiliation":[{"name":"Department of Engineering and Architecture, University of Parma, Via Universit\u00e0 12, 43121 Parma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alberto","family":"Amerini","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Florence, Via S. Marta 3, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lorenzo","family":"Mazzei","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Florence, Via S. Marta 3, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9890-3528","authenticated-orcid":false,"given":"Tommaso","family":"Bacci","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Florence, Via S. Marta 3, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matteo","family":"Poggiali","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Florence, Via S. Marta 3, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"Andreini","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Florence, Via S. Marta 3, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1016\/j.egypro.2017.08.253","article-title":"Experimental and CFD analyses of a high-loaded gas turbine blade","volume":"126","author":"Bacci","year":"2017","journal-title":"Energy Procedia"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bacci, T., Picchi, A., and Facchini, B. (2019). Flat Plate and Turbine Vane Film-Cooling Performance with Laid-Back Fan-Shaped Holes. Int. J. Turbomach. Propuls. Power, 4.","DOI":"10.3390\/ijtpp4020014"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bohn, D., Ren, J., and Kusterer, K. (2003, January 1). Conjugate Heat Transfer Analysis for Film Cooling Configurations. With Different Hole Geometries. Proceedings of the ASME Turbo Expo\u2013GT2003-38369, Atlanta, GA, USA.","DOI":"10.1115\/GT2003-38369"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.2514\/1.18034","article-title":"Gas turbine film cooling","volume":"2","author":"Bogard","year":"2006","journal-title":"ASME J. Propuls. Power"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Du, H., Mei, Z., Zou, J., Jiang, W., and Xie, D. (2019). Conjugate Heat Transfer Investigation on Swirl-Film Cooling at the Leading Edge of a Gas Turbine Vane. Entropy, 21.","DOI":"10.3390\/e21101007"},{"key":"ref_6","unstructured":"Aminossadati, S.M., and Mee, D.J. (October, January 29). Uncertainty Analysis for the Measurements of Aerodynamic Loss of Cooled Turbine Blades. Proceedings of the Fifth Biennial Engineering Mathematics and Applications Conference, Brisbane, Australia."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Farmer, J., Merino, Z., Gray, A., and Jacobs, D. (2019). Universal Sample Size Invariant Measures for Uncertainty Quantification in Density Estimation. Entropy, 21.","DOI":"10.3390\/e21111120"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"031014","DOI":"10.1115\/1.4007516","article-title":"Uncertainty Quantification and Conjugate Heat Transfer: A Stochastic Analysis","volume":"135","author":"Montomoli","year":"2013","journal-title":"ASME J. Turbomach."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Le Ma\u00eetre, O., and Knio, O. (2010). Spectral Methods for Uncertainty Quantification, Springer.","DOI":"10.1007\/978-90-481-3520-2"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"897","DOI":"10.2307\/2371268","article-title":"The Homogeneous Chaos","volume":"60","author":"Wiener","year":"1938","journal-title":"Am. J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Askey, R., and Wilson, J. (1985). Some Basic Hypergeometric Polynomials that Generalized Jacobi Polynomials, American Mathematical Society.","DOI":"10.1090\/memo\/0319"},{"key":"ref_12","unstructured":"Karniadakis, G., Xiu, D., Su, C.H., and Lucor, D. (2005). Generalized Polynomial Chaos Solution for Differential Equations with Random Inputs, Seminar f\u00fcr Angewandte Mathematik. Research report."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1007\/s00170-012-4605-2","article-title":"A review on 3D micro-additive manufacturing technologies","volume":"67","author":"Vaezi","year":"2013","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1007\/s00170-015-8289-2","article-title":"Data mining and statistical inference in selective laser melting","volume":"86","author":"Kamath","year":"2016","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"114502","DOI":"10.1115\/1.4034103","article-title":"Identifying uncertainty in laser powder bed fusion additive manufacturing models","volume":"138","author":"Lopez","year":"2016","journal-title":"J. Mech. Des."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Shi, W., Chen, P., Li, X., Ren, J., and Jiang, H. (2019). Uncertainty Quantification of the Effects of Small Manufacturing Deviations on Film Cooling: A Fan-Shaped Hole. Aerospace, 6.","DOI":"10.3390\/aerospace6040046"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.expthermflusci.2013.02.015","article-title":"Comparison between PSP and TLC steady state techniques for adiabatic effectiveness measurement on a multiperforated plate","volume":"48","author":"Caciolli","year":"2013","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_18","unstructured":"Frank, T., and Menter, F. (2017, January 3\u20135). Validation of URANS SST and SBES in ANSYS CFD for the Turbulent Mixing of Two Parallel Planar Water Jets Impinging on a Stationary Pool. Proceedings of the ASME 2017 Verification and Validation Symposium, Las Vegas, NV, USA."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Lenzi, T., Palanti, L., Picchi, A., Bacci, T., Mazzei, L., Andreini, A., Facchini, B., and Vitale, I. (2019, January 17\u201321). Time-Resolved Flow Field Analysis of Effusion Cooling System with Representative Swirling Main Flow. Proceedings of the ASME TURBO EXPO 2019: Power for Land, Sea and Air, Phoenix, AZ, USA.","DOI":"10.1115\/GT2019-91446"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1175\/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2","article-title":"General Circulation Experiments with the Primitive Equations","volume":"91","author":"Smagorinsky","year":"1963","journal-title":"Mon. Weather Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1063\/1.857955","article-title":"A Dynamic Subgrid-Scale Eddy Viscosity Model","volume":"3","author":"Germano","year":"1991","journal-title":"Phys. Fluids"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1017\/S0022112092001733","article-title":"Turbulence: The Filtering Approach","volume":"238","author":"Germano","year":"1992","journal-title":"J. Fluid Mech."},{"key":"ref_23","unstructured":"Adams, B., Bauman, L., Bohnhoff, W., Dalbey, K., Ebeida, M., Eddy, J., Eldred, M., Hough, P., Hu, K., and Jakeman, J. (2019, November 29). DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.9 User\u2019s Manual 2009. Available online: https:\/\/pdfs.semanticscholar.org\/5e30\/66fd427b1ba4b2a743cc3e042a0dfe9a87f2.pdf."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Bunker, R. (2008, January 9\u201313). The effects of manufacturing tolerances on gas turbine cooling. Proceedings of the ASME Turbo Expo 2008: Power for Land, Sea, and Air, Berlin, Germany.","DOI":"10.1115\/GT2008-50124"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"011019","DOI":"10.1115\/1.4003287","article-title":"Geometrical Uncertainty and Film Cooling: Fillet Radii","volume":"134","author":"Montomoli","year":"2012","journal-title":"J. Turbomach."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:44:44Z","timestamp":1760190284000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,22]]},"references-count":25,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["e22010016"],"URL":"https:\/\/doi.org\/10.3390\/e22010016","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,22]]}}}