The decay power law in grid-generated turbulence

TLDR

Grid‑generated turbulence experiments span Reynolds numbers 6000–68000, mesh sizes 2.54–5.08 cm, and solidities 0.34–0.44. The study investigates how initial conditions affect the decay exponent, coefficient, and virtual origin of turbulence downstream of biplane grids, and develops criteria to isolate the nearly homogeneous, isotropic region. The authors analyze data from their own experiments and prior work, applying criteria based on low velocity skewness, constant derivative skewness, and turbulent kinetic energy balance to delineate the homogeneous, isotropic flow region. They find that selecting the virtual origin and excluding non‑homogeneous data significantly affects decay parameters; the exponent (≈1.30) and origin are independent of initial conditions, while the coefficient varies, confirming universal self‑similar decay of turbulent velocity variance.

Abstract

The effect of initial conditions on the decay exponent and coefficient and virtual origin in the decay power-law form for the variation of the variance of the turbulent velocity downstream of biplane grids constructed of rods of both round and square cross-section is determined. This effect is determined for data obtained as part of the present study as well as from previous studies. These studies cover a Reynolds number range from 6000 to 68000, mesh sizes of 2.54 and 5.08 cm, and solidities of 0.34 and 0.44. It is shown that the choice of the virtual origin and the use of data in the non-homogeneous portion of the flow can have a significant influence on the value of the parameters in the decay power-law. Criteria are developed to identify the nearly homogeneous and isotropic portion of the flow. These criteria include low values of the velocity skewness, constancy of the skewness of the velocity derivative and balance of the turbulent kinetic energy equation. Results based on data selected by means of these criteria show that the decay exponent and virtual origin are independent of initial conditions such as Reynolds number, mesh size, solidity, and rod shape and surface roughness with values of respectively 1.30 and 0. In contrast and as expected, the decay coefficient is found to be a function of these initial conditions. Thus, the downstream variation of the variance of the turbulent velocity is universally self-similar.