Error reduction for time-resolved PIV data based on Navier–Stokes equations

Abstract

The post-processing of the measured velocity in particle image velocimetry (PIV) is a critical step in reducing error and predicting missing information of the flow field. In this work, time-resolved PIV data are incorporated with the incompressible Navier-Stokes (N-S) equations to reduce the measurement error and improve the accuracy. A pressure correction scheme (PCS) based on the projection method is adopted to solve the N-S equations, and an optimization algorithm is introduced to balance the fidelity between the PIV data and the numerical solutions. The PCS for PIV data, called PIV-PCS, cannot only reduce the errors in the velocity divergence and the curl of the pressure gradient but also ensure that the flow field satisfies the dynamic constraints imposed by the momentum equation. An important weight coefficient s that balances the level of the velocity modification with the residual of the governing equation is defined and numerically assessed. A method for optimizing the value of s is provided. The new approach is evaluated by two time-resolved PIV experiments: one on the 2D wake flow of a circular cylinder at low Reynolds number and one on tomographic PIV for the 3D wake flow of a hemisphere at high Reynolds number. All the numerical assessments and experimental applications are compared with the divergencefree smoothing (DFS) method. The results indicate that the presented PIV-PCS method is superior to the DFS method in terms of reducing the measurement error and recovering the real physical flow structures.

Assimilation of disparate data for enhanced reconstruction of turbulent mean flows

“…For example, the low fidelity methods such as Reynolds-averaged Navier-Stokes (RANS) simulation can provide fast but inaccurate prediction, while high fidelity simulations such as large eddy simulations and direct numerical simulations can make satisfactory predictions but at prohibitive computational costs [1,2]. On the other hand, the experimental measurements face the challenges of limited view domain, measurement noises, and insufficient resolution [3,4].…”

Fast 3D flow reconstructions from 2D cross-plane observations

“…An improvement to this technique was provided by Wang et al (2016) called the divergence-free smoothing (DFS) method which reduces divergence while also smoothing the velocity field to remove outliers and missing vectors. A more comprehensive approach would be to use the modified pressure correction scheme (PIV-PCS) of Wang et al (2018) where in the PIV data are combined with the incompressible Navier-Stokes equations to improve the data-set. The DCS and DFS family of methods provide an interesting approach towards obtaining divergence free flow fields.…”

Reconstructing the pressure field around a swimming fish using a physics-informed neural network

“…These results stress the need to have a pressure reconstruction algorithm that: 1) provides the user with the flexibility to alter the applied boundary conditions and 2) incorporates the kinematics of the undulating body into the pressure reconstruction. In recent years, new types of pressure reconstruction algorithms have been developed (Wang et al, 2017; Jeon et al, 2018; Huhn et al, 2016; Cai et al, 2020; Wang et al, 2018; He et al, 2020); although these methods have made significant progress in other aspects of pressure reconstruction from velocity measurements, they do not correct the highlighted limitations of Queen 2.0. Furthermore, their applicability to flow fields involving actively deforming bodies remains relatively untested.…”