Energy dissipation estimates in oscillating grid setup: LDV and PIV measurements

Abstract

The dissipation of turbulent kinetic energy has been increasingly used as a scaling parameter to integrate microbiological accrual and metabolic rates with fluid-flow motion in natural and engineered aquatic ecosystems. The estimation of turbulent kinetic energy under field conditions and the generation of energy dissipation rates under controlled laboratory conditions with microbiological organisms are necessities required to integrate environmental/ecological laboratory protocols with a moving fluid in the environment. Turbulent fluid-flow conditions were generated in an oscillating grid setup, and turbulence variables were quantified using laser-Doppler velocimetry (LDV) and particle image velocimetry (PIV) measuring techniques. The rate of dissipation of the turbulent kinetic energy in the setup ranged from 10⁻⁹ to 10⁻⁴ m²/s³ and was similar to the levels of energy dissipation commonly reported in engineered and natural aquatic ecosystems. Time-averaged velocities were close to zero with the root-mean-square velocity ratios about 1, indicating nearly isotropic fluid-flow conditions in the setup. The velocity spectra, obtained by stationary LDV measurements for the vertical and horizontal velocity components across the setup revealed the existence of inertial subrange with the frequency power scaling law of “ω ^−5/3.” The estimated Eulerian frequency spectrum followed the theoretical functional relation and confirmed the applicability of inertial dissipation method for the estimation of turbulent kinetic energy dissipation rates. PIV was used for a direct estimation of dissipation by evaluating spatially distributed velocity gradients. The direct dissipation estimate in conjunction with the estimated Eulerian frequency spectrum provided evaluation of a “universal” constant, α, commonly used for the estimation of an energy dissipation rate over the inertial subrange of the Eulerian spectrum. The results demonstrated a range of values, rather than a universal constant, of α with a lognormal probability distribution for vertical and horizontal velocity components. In order to encompass a 0.955 probability range under the lognormal distribution ${({\frac{{\bar {\alpha}}}{{\sigma }^{2}} > {\alpha } > {\bar{\alpha}\sigma }^{2})}}$ the universal constant, α, should be in the range 2.91 ≥ α _u ≥ 0.43 and 4.44 ≥ α _w ≥ 0.42 for horizontal and vertical velocity components, respectively.