Description
The instantaneous pressure distribution in a turbulent flow field can be measured non-intrusively by integrating the material acceleration based on particle image velocimetry (PIV). However, due to the finite spatial resolution of the PIV measurement, the pressure reconstructed from PIV is subjected to the effect of spatial filtering. Consequently, the reconstructed pressure is effectively imbedded with the contribution of the sub-grid scale (SGS) stress, a term appearing in the filtered Navier-Stokes equation. To quantify the effect of the SGS stress on pressure measurements, we use box filtering to filter three-dimensional velocity components in both the isotropic turbulence and the turbulent channel flow fields available to public from the John Hopkins University Turbulence Database (JHTDB). Then we reconstruct the pressure based on the filtered velocity data and compare to the filtered DNS pressure, thus gauging the error due to the measurement resolution effect. A 17×17×17 box filter as well as a 5×5×5 filter for comparison in parallel are used as a first level filtering to bring the DNS data resolution down to the PIV resolution level. Then a 3×3×3 box filter is applied to the already filtered velocity data to obtain modeled SGS stress based on similarity SGS stress modeling. Comparison of the reconstructed pressure with the filtered pressure shows that neglecting the SGS stress results in a significant random error, indicating that the SGS term must be accounted for in PIV pressure measurement. Results also show that correction using similarity SGS modeling reduces the random error due to omission of SGS stress, confirming the benefit of the error compensation method. The influence of the SGS stress and the effectiveness of the modeling-based correction method in the wave number space were also investigated by comparing the power spectra of the reconstructed pressures. Results show that filtering affects mostly the high wave number range, causing abatement of fluctuation energy there. With the increase of the filter size, the range of influence extends to the lower wave number range. The model-based correction is more effective in the low wave number space in reducing the error caused by the omission of the SGS stress.
