A data assimilation pressure field measurement method for linear turbine cascades based on compressed sensing

Abstract

One of the most dominant measuring techniques for linear turbine cascades is to obtain the high spatial resolution pressure field by a discrete point array. In this work, a compressed sensing (CS) based data assimilation methodology is proposed, by which a set of optimal sparse measuring points can be derived through an optimization procedure. Combined with numerical simulations and the data-driven modal decomposition, the high spatial resolution pressure distribution can be reconstructed accurately with sparse random sampling. To this end, detailed comparative research is conducted. First, the impacts of different sparse bases, including the discrete Fourier transform (DFT), the discrete cosine transform (DCT), and the proper orthogonal decomposition (POD) matrices, and the compression ratio on the reconstruction performance are compared and analyzed systematically under different incidence angles and cascade exit isentropic Mach numbers. Results reveal that a CS approach on POD subspace (CS-POD) performs remarkably better than the CS-DFT and CS-DCT in capturing the spatially continuous pressure distribution, even with a small number of measuring points. Furthermore, effects of the order of truncated POD modes and the number of training dataset required to conduct POD on the error are also investigated that exhibits a downward trend with the rise in these two elements. To overcome the deficiency of randomly selected sparse observation sites with this methodology and the resulting high measuring cost under different conditions, a vectorized CS-POD (Vec-CS-POD) model is constructed to obtain one set of measuring distribution that could satisfy the multi-conditional measurements simultaneously, and its reliability and robustness are validated through cascade experiments. With the aid of the Vec-CS-POD based data fusion framework, spatially resolved end wall pressure fields can be acquired by only a few measuring ports, the number of which can be reduced by 77% compared to the conventional uniform arrangement. The generalization ability of the proposed framework is also validated and evaluated; thus, it exhibits broad potential in other flow field measurements.