From sparse data to high-resolution fields: ensemble particle modes as a basis for high-resolution flow characterization

In this work, we present an approach to reconstruct high-resolution flow velocity or scalar fields from sparse particle-based measurements such as particle tracking velocimetry, thermographic phosphors or pressure-sensitive particles. The proposed approach can be applied to any of those fields; without leading its generality, it is hereby assessed for flow velocity measurements. Particles allow probing physical quantities at multiple time instants in randomly located points in the investigated region. In previous works, it has been shown that high-resolution time-averaged fields can be estimated by an ensemble average of the particles contained into spatial bins whose size can be reduced almost ad libitum. In this work, high-resolution ensemble particle modes are estimated from the ensemble average of particles, weighted with Proper Orthogonal Decomposition time coefficients which are estimated from low-resolution spatially-averaged fields. These modes represent a self-tunable compressed-sensing library for the reconstruction of high-resolution fields. High-resolution instantaneous fields are then obtained from a linear combination of these modes times their respective time coefficients. This data-enhanced particle approach is assessed employing two DNS datasets: the wake of a cylinder and a fluidic pinball. It is shown here that it is possible to reconstruct phenomena whose characteristic wavelength is smaller than the mean particle spacing whenever such events are correlated with any other flow phenomenon with a wavelength large enough to be sampled. The proposed approach is also applied to experimental wind-tunnel data, again showing excellent performances in presence of realistic measurement-noise conditions.