Effect of bubble on the pressure spectra of oscillating grid turbulent flow at low Taylor-Reynolds number

Abstract

For many engineering applications, measurements of velocity and pressure distributions in the system are of fundamental importance to provide insights into the flow characteristics. In the present study, the experiments were carried out in an oscillating grid system in absence and presence of two different bubble diameters (Db = 2.70 and 3.52 mm) rise using the non-intrusive two-dimensional (2D) particle image velocimetry (PIV) at the low Taylor-Reynolds number (Reλ) ranging from 12 to 60. Using the measured PIV velocity data, the instantaneous pressure fluctuations were estimated by integrating the full viscous form of the Navier-Stokes (N-S) equation. The obtained pressure field was compared with three dimensional (3D) computational fluid dynamics (CFD) simulation which was found to be in good agreement. The pressure spectra of single and two phase flow cases were evaluated by taking Fast Fourier transformation (FFT) of the computed pressure fluctuations. A spectral slope of −7/3 was found in the inertial subrange of the single-phase pressure spectrum. In contrast, the two-phase pressure spectrum exhibited a slope less steep than −7/3 in the inertial subrange because of the extra production of turbulence in the presence of bubble. For single-phase flow, the ratio of pressure integral length scale to the velocity integral length scale (Lp/L) was found to be ∼0.67, and the pressure Taylor microscale (λp) was approximately 0.79 ± 0.03 of the velocity Taylor microscale (λ) within the Taylor-Reynolds number range studied. The scaling ratios based on the single-phase experimental results were compared with existing theory and DNS results and found to accord well; however, these ratios deviate from the theoretical values for two-phase flow. Also, the energy dissipation rate was evaluated based on the pressure spectrum and found to be over-predicted (∼32%) compared those calculated from the velocity spectrum.