Time-Volume Estimation of Velocity Fields From Non-Synchronous Planar Measurements Using Linear Stochastic Estimation

Abstract

Abstract With increasing complexity of aerodynamic devices such as gas turbine fuel swirl nozzles (FSN) and combustors, the need for time-resolved full volume flow characterisation is becoming greater. Even with modern advancements in both numerical and experimental methods, this remains a challenging area. The work presented in this paper combines multiple non-synchronous planar measurements to reconstruct an estimate of a synchronous, instantaneous flow field of the whole measurement set. Temporal information is retained through the linear stochastic estimation (LSE) technique. The technique is described, applied and validated with a simplified combustor and FSN geometry flow for which 3-component, 3-dimensional (3C3D) flow information is known from published tomographic PIV[1]. Using the tomographic PIV data set, multiple virtual ‘planes’ may be extracted to emulate single planar PIV measurements and produce the correlations required for LSE. In this example, multiple parallel planes are synchronised with a single perpendicular plane that intersects each of them. As the underlying data set is volumetric, the measured velocity is known a priori and therefore can be directly compared to the estimated velocity field for validation purposes. The work shows that when the input time-resolved planar velocity measurements are first POD (proper orthogonal decomposition) filtered, high correlation between the estimations and the validation velocity volumes are possible. This results in estimated full volume velocity distributions which are available at the same time instance as the input field — i.e. a time resolved velocity estimation at the frequency of the single input plane. While 3C3D information is used in the presented work, this is necessary only for validation; in true application planar technique would be used. The study concludes that provided the number of sensors used for input LSE exceeds the number of POD modes used for pre-filtering, it is possible to achieve correlation greater than 99%.