Analyzing the spectral energy cascade in turbulent channel flow

Abstract

An analysis of the spectral turbulent kinetic energy budget in a fully developed turbulent plane channel flow is performed. Direct numerical simulation data are evaluated at friction Reynolds numbers Re τ of 180 and 1000. The analysis is focused on the influence of the Reynolds number on the spectral cascade of energy and the corresponding energy cascade in physical space in the presence of inhomogeneity and anisotropy. The turbulent kinetic energy distribution is compared for both Reynolds numbers, and the relevant characteristics of the energy transfer process in a wall-bounded turbulent flow are described. Differences in energy cascade are noted between the Reynolds number at both low and high wavenumbers. The results of the analysis are further assessed with a comparison to an earlier study of spectral energy transfer at Re τ = 180.

Effect of the Reynolds number on turbulence kinetic energy exchanges in flows with highly variable fluid properties

“…Using direct numerical simulations, the energy exchanges associated with turbulence kinetic energy have been investigated in channel flows for various friction Reynolds number: 180 [33,46,1,25,64,38], 395 [46,1], 550-640 [46,16,1,25], 950-1000 [25,38], 2000 [24,25] and 5200 [38]. The spectral turbulence kinetic energy budget has been studied for the friction Reynolds numbers 170-210 [18,7,43,54,2], 500-615 [43,37,54], 900-1000 [43,37,2] and 5200 [37]. Andrade et al [2] showed that the spectral range of energy exchanges is broader at higher Reynolds number due to an increase in the low wavenumber scales.…”

“…The spectral turbulence kinetic energy budget has been studied for the friction Reynolds numbers 170-210 [18,7,43,54,2], 500-615 [43,37,54], 900-1000 [43,37,2] and 5200 [37]. Andrade et al [2] showed that the spectral range of energy exchanges is broader at higher Reynolds number due to an increase in the low wavenumber scales. Studies of energy exchanges have also been carried out in more complex wall-bounded geometries [6,54,44].…”

Análise spectral da cascata de energia turbulenta e desenvolvimento de um novo modelo submalha não linear para simulação das grandes escalas.

“…The form of the velocity field is altered and the flow field becomes more complex. Due to this complexity added to the velocity field, the flow presents inhomogeneity and anisotropy that are responsible for the generation of an energy transfer in the physical space, where the energy sources will behave differently depending on the distance from the wall [102,44,17,28,27,114,4].…”

“…More details about these behavior can be found in Sec. 2.3 and Andrade et al [4]. The hypothesis of alignment between τ and filtered rate-of-strain tensor ( S) is only possible to estimate a correctly general mean drain of energy from the resolved scales if the grid is sufficiently fine to resolve the SGS anisotropy.…”

“…Vreman and Kuerten 1. 4. Direct numerical simulation 15 [162] compared DNS databases to assess the accuracy and reproducibility of turbulence statistics of incompressible plane channel flow, they used relative deviations of mean profile of different cases in relation to the case that has probably a much lower statistical error, according to them.…”