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Model order reduction for film-cooled applications under probabilistic conditions: sparse reconstruction of POD in combination with Kriging

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Abstract

In this paper, to reduce the computational cost of Proper Orthogonal Decomposition (POD) method in film-cooling problems, a new method based on the combination of POD method with Sparse Polynomial Chaos Expansion (PCE) and Kriging approaches is developed. In the present method, firstly, by combining compressed sensing and POD methods, the optimal basis functions are obtained via low-fidelity calculations. These basis functions are subsequently used in the trend part of the Kriging surrogate model. Then, the trend coefficients and the stochastic Gaussian part are estimated through a limited number of high-fidelity calculations. The performance of the proposed method is investigated on two challenging test cases: 1) film-cooling jet in cross-flow and 2) leading edge film cooling of a gas turbine blade with 7 and 10 uncertain variables, respectively. For the first test case, the new method reduces the computational cost by \(91\%\) and \(53.9\%\) with respect to the full PCE and POD methods. For the second test case, the computational cost reductions are \(81\%\) and \(37.9\%\) in comparison to the full PCE and POD methods, respectively. In general, the proposed method is better in terms of accuracy in comparison to combined POD and compressed sensing, especially in the cases with the lower number of low-fidelity samples.

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Acknowledgements

Part of the work was carried out under the Collaborative Research Project of the Institute of Fluid Science, Tohoku University.

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Authors and Affiliations

  1. Hydraulic Machinery Research Institute, School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, 11155-4563, Iran

    Akbar Mohammadi-Ahmar, Arash Mohammadi & Mehrdad Raisee

  2. Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Koji Shimoyama

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Mohammadi-Ahmar, A., Mohammadi, A., Raisee, M. et al. Model order reduction for film-cooled applications under probabilistic conditions: sparse reconstruction of POD in combination with Kriging. Struct Multidisc Optim 65, 283 (2022). https://doi.org/10.1007/s00158-022-03384-w

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