Estimation of the dissipation rate of turbulent kinetic energy: A review

Three-dimensional turbulence generated homogeneously by magnetic particles

“…Dimensional arguments estimate the dissipation rate from the velocity fluctuations as ǫ = cσ 3 u /L i [34,35] involving the integral scale L i , and c a constant of the order of unity [36,37]. Here, one finds c = 1.1 close to the values found with a boundary forcing (grid turbulence) [35,38]. These estimations of ǫ by five different methods are hardly obtained experimentally [39] and are found here to be all consistent as a consequence of the stationary, homogeneous and isotropic turbulence generated by this forcing in volume.…”

Statistical Treatment, Fourier and Modal Decomposition

“…The statistical treatment of turbulence is a vast subject, far beyond the scope of this lecture. The reader is referred to Pope (2000); Tennekes (1972); Davidson (2004); Mcdonough (2004) for an comprehensive introduction on the topic and to Saarenrinne and Piirto (2000); Lavoie et al (2007); Segalini et al (2014); Scharnowski et al (2018); Ayegba and Edomwonyi-Otu (2020); Wang et al (2021) for a discussion on the impact of measurement resolution on the main turbulence variables. This section recalls the definitions that are required to solve the provided exercises.…”

“…In its complete 3D form, this is defined as ε = ν ∂ x i u j (∂ x j u i + ∂ x i u j ) , with ν the kinematic viscosity, having used the indices i, j = 1, 2, 3 to index the velocity components and axes and having implied summation. The full expression counts 12 terms and it is of difficult evaluation in a 2D measurement because of the missing information in the direction normal to the measurement plane (see Saarenrinne and Piirto (2000); Wang et al (2021) for an interesting discussion). This quantity measures the rate at which turbulence energy is converted into thermal energy by viscous dissipation and is essential in the modeling of turbulent flows.…”

Simulation Study on Active Air Flow Distribution Characteristics of Closed Heat Pump Drying System with Waste Heat Recovery

“…The standard κ − model is chosen as the turbulence model, which is composed of turbulent kinetic energy equation and turbulent dissipation rate equation [28,29].…”