Flow enhancement of tomographic particle image velocimetry measurements using sequential data assimilation

Abstract

Sequential data assimilation (DA) was performed on three-dimensional flow fields of a circular jet measured by tomography particle image velocimetry (tomo-PIV). The work focused on an in-depth analysis of the flow enhancement and the pressure determination from volumetric flow measurement data. The jet was issued from a circular nozzle with an inner diameter of [Formula: see text] 20 mm. A split-screen configuration including two high-speed cameras was used to capture the particle images from four different views for a tomography reconstruction of the voxels in the tomo-PIV measurement. Planar PIV was also performed to obtain the benchmark two-dimensional velocity fields for validation. The adjoint-based sequential DA scheme was used with the measurement uncertainty implanted using a threshold function to recover the flow fields with high fidelity and fewer measurement errors. The pressure was determined by either the direct mode, with implementation directly in the DA solver, or by the separate mode, which included solving the Poisson equation on the DA-recovered flow fields. Sequential DA recovered high signal-to-noise flow fields that had piecewise-smooth temporal variations due to the intermittent constraints of the observations, while only the temporal sequence of the fields at the observational instances was selected as the DA output. Errors were significantly reduced, and DA improved the divergence condition of the three-dimensional flow fields. DA also enhanced the dynamical features of the vortical structures, and the pressure determined by both modes successfully captured the downstream convection signatures of the vortex rings.

Four-dimensional variational data assimilation of a turbulent jet for super-temporal-resolution reconstruction

“…It is noted that this segregated DA strategy is necessary for the present application with time-sparse observations, as simultaneous assimilation of all the quantities would result in an indeterminacy problem in which the residual evaluated at the terminal step is insensitive to the initial and boundary conditions. The present 4D-Var algorithm is indeed different from the sequential DA scheme in our previous work (He et al 2020(He et al , 2022, where the backward integration was eliminated by limiting the DA window to one computational time step. Sequential DA solves the adjoint equations only at the instants that the observations exist and induces discontinuous variation of the flow quantities at the observational time.…”

“…Four virtual cameras with a resolution of 1000 × 2000 pixels are installed azimuthally with an included angle of approximately 20° around the jet using the layout adopted by He et al. (2022). The virtual measurement domain has fixed dimensions of 0.106 m , 0.053 m and 0.053 m in the x , y and z directions, respectively, and is placed 0.037 m downstream of the nozzle exit.…”

Machine learning for flow field measurements: a perspective

“…However, the spatial modes selected for reconstruction are sensitive to noise, as they are computed from the original noisy data. In this context, filtering processes directly imposed on the PIV algorithm or fusions of flow governing equations [120] are more promising alternatives to address random errors.…”

“…Cai et al [75] used PINNs to infer the full 3D velocity and pressure fields from snapshots of 3D temperature fields obtained by tomographic background-oriented schlieren imaging. The PINNs could integrate the governing equations and temperature data, similar to adjoint-based data assimilation methods [120]. Wang et al [132] used a PINN to reconstruct dense velocity fields with considerably lower noise levels than those of sparse tomography PIV data and to predict the pressure fields.…”

Approach to select optimal cross-correlation parameters for light field particle image velocimetry

“…In these processes, the flows are inherently 3D and unsteady, mostly highly turbulent on a large temporal-spatial dynamic scale. For an in-depth insight into these complex flow structures, it is necessary to develop an advanced flow diagnostic technique for instantaneous 3D flow velocity measurement [3][4][5][6][7]. In most industrial processes, the optical access to the measurement area of internal flows is limited due to the confined space, high temperature and pressure conditions.…”