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

The work presented in this paper combines multiple nonsynchronous 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 fuel swirl nozzles (FSN) geometry flow for which three-component, three-dimensional (3C3D) flow information is available. Using the 3C3D dataset, multiple virtual “planes” may be extracted to emulate single planar particle image velocimetry (PIV) measurements and produce the correlations required for LSE. In this example, multiple parallel planes are synchronized with a single perpendicular plane that intersects each of them. As the underlying dataset is known, it 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 proper orthogonal decomposition (POD) 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 prefiltering, it is possible to achieve correlation greater than 99%.

Spurious PIV Vector Correction Using Linear Stochastic Estimation

Techniques for the experimental determination of velocity fields such as particle image velocimetry (PIV) can often be hampered by spurious vectors or sparse regions of measurement which may occur due to a number of reasons. Commonly used methods for detecting and replacing erroneous values are often based on statistical measures of the surrounding vectors and may be influenced by further poor data quality in the region. A new method is presented in this paper using Linear Stochastic Estimation for vector replacement (LSEVR) which allows for increased flexibility in situations with regions of spurious vectors. LSEVR is applied to PIV dataset to demonstrate and assess its performance relative to commonly used bilinear and bicubic interpolation methods. For replacement of a single vector, all methods performed well, with LSEVR having an average error of 11% in comparison to 14% and 18% for bilinear and bicubic interpolation respectively. A more significant difference was found in replacement of clusters of vectors which showed average vector angle errors of 10°, 9° and 6° for bilinear, bicubic and LSEVR respectively. Error in magnitude was 3% for both interpolation techniques and 1% for LSEVR showing a clear benefit to using LSEVR for conditions that require multiple clustered vectors to be replaced.

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

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%.

Linear stochastic estimation of the coherent structures in internal combustion engine flow

A methodology for estimating the in-cylinder flow of an internal combustion engine from a number of point velocity measurements (sensors) is presented. Particle image velocimetry is used to provide reference velocity fields for the linear stochastic estimation technique to investigate the number of point measurements required to provide a representative estimation of the flow field. A systematic iterative approach is taken, with sensor locations randomly generated in each iteration to negate sensor location effects. It was found that an overall velocity distribution accuracy of at least 75% may be achieved with 7 sensors and 95% with 35 sensors, with the potential for fewer if sensor locations are optimised. The accuracy of vortex centre location predictions is typically within 2–3 mm, suggesting that the presented technique could characterise individual cycle flow fields by indicating vortex locations, swirl magnitude or tumble, for example. With this information on the current cycle, a control system may be enabled to activate in-cycle adjustment of injection and/or ignition timing, for example, to minimise emissions.

Estimation of turbulent channel flow at based on the wall measurement using a simple sequential approach

The unsteady flow estimation problem of wall-bounded turbulence, numerically benchmarked by Chevalier et al. (J. Fluid Mech., vol. 552, 2006, pp. 167–187), is re-tackled with simple approaches. A turbulent channel flow at $Re_{\unicode[STIX]{x1D70F}}=100$ with periodic boundary conditions is reconstructed with linear stochastic estimation only based on the wall measurement, i.e. the wall shear stress in the streamwise and spanwise directions as well as the wall pressure over the entire wavenumber space. The results reveal that instantaneous information on the wall governs the success of the estimation in the vicinity of the wall ($y^{+}\lesssim 20$). The degrees of agreement are equivalent to those reported by Chevalier et al. using the extended Kalman filter as well as the ensemble Kalman filter performed in this study. This suggests that the instantaneous information on the wall dictates the reconstruction rather than the prediction step in these state observers solving the dynamical system. Subsequently, we feed the velocity components given by the linear stochastic estimation via the body-force term into the Navier–Stokes system: such an observer slightly improves the estimation in the log layer, indicating a small benefit of involving a dynamical system but over-suppression of turbulent motions beyond the viscous sublayer due to their low correlation with the wall measurement. Errors in the estimation grow in the buffer layer and prevent further reconstruction toward the centreline even if we relax the feedback forcing and let the flow evolve nonlinearly through the observer. We also discuss the flow components truly reconstructible from the wall measurement, which has limited degrees of freedom and poor correlation across wavenumbers.