Direct numerical simulation of turbulent channel flow up to Reτ ≈ 5200

Direct numerical simulation of turbulent channel flow up to Reτ ≈ 5200

Under consideration for publication | Myoungkyu Lee and Robert D. Moser
A direct numerical simulation (DNS) of incompressible channel flow at $ Re_{\tau} = 5186 $ has been conducted, revealing characteristics of high Reynolds number wall-bounded turbulence. The flow exhibits a logarithmic mean velocity profile with a von Kármán constant $ \kappa = 0.384 \pm 0.004 $, and the variance of the spanwise velocity component shows logarithmic dependence. A distinct separation of scales exists between large outer-layer structures and small inner-layer structures. The one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $ k^{-1} $ dependence over a short range in $ k $. When these spectra are multiplied by $ k $, they have a bi-modal structure with local peaks on either side of the $ k^{-1} $ range. The simulation, conducted at $ Re_{\tau} \approx 5200 $, is compared with previous simulations at lower Reynolds numbers and experimental data. The mean velocity profile shows a logarithmic layer with a flat $ \beta $ function, indicating a log-law region. The values of $ \kappa $ and $ B $ in the log-law equation are determined by fitting the mean velocity data, yielding $ \kappa = 0.384 \pm 0.004 $ and $ B = 4.27 $. The Reynolds stress tensor components show discrepancies between simulations at different Reynolds numbers, with the highest Reynolds number simulation (LM5200) showing better agreement with experimental data. The variance of the streamwise velocity fluctuation shows a logarithmic variation in the spanwise direction but not in the streamwise direction. The variance of the spanwise velocity fluctuation also shows a logarithmic variation in the outer region. The energy spectral density of the streamwise velocity fluctuations shows a plateau in the $ k^{-1} $ region, consistent with experimental data. The simulation also reveals a bi-modal structure in the premultiplied spectrum, with peaks on either side of the $ k^{-1} $ range. The simulation is statistically stationary, with small statistical uncertainties and good agreement with experimental data. The simulation provides valuable data on high Reynolds number wall-bounded turbulence, with resolution consistent with accepted standards and statistical uncertainties generally small. The flow is statistically stationary to high accuracy, and the simulation exhibits many characteristics of high Reynolds number wall-bounded turbulence, making it a good resource for the study of such flows.A direct numerical simulation (DNS) of incompressible channel flow at $ Re_{\tau} = 5186 $ has been conducted, revealing characteristics of high Reynolds number wall-bounded turbulence. The flow exhibits a logarithmic mean velocity profile with a von Kármán constant $ \kappa = 0.384 \pm 0.004 $, and the variance of the spanwise velocity component shows logarithmic dependence. A distinct separation of scales exists between large outer-layer structures and small inner-layer structures. The one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $ k^{-1} $ dependence over a short range in $ k $. When these spectra are multiplied by $ k $, they have a bi-modal structure with local peaks on either side of the $ k^{-1} $ range. The simulation, conducted at $ Re_{\tau} \approx 5200 $, is compared with previous simulations at lower Reynolds numbers and experimental data. The mean velocity profile shows a logarithmic layer with a flat $ \beta $ function, indicating a log-law region. The values of $ \kappa $ and $ B $ in the log-law equation are determined by fitting the mean velocity data, yielding $ \kappa = 0.384 \pm 0.004 $ and $ B = 4.27 $. The Reynolds stress tensor components show discrepancies between simulations at different Reynolds numbers, with the highest Reynolds number simulation (LM5200) showing better agreement with experimental data. The variance of the streamwise velocity fluctuation shows a logarithmic variation in the spanwise direction but not in the streamwise direction. The variance of the spanwise velocity fluctuation also shows a logarithmic variation in the outer region. The energy spectral density of the streamwise velocity fluctuations shows a plateau in the $ k^{-1} $ region, consistent with experimental data. The simulation also reveals a bi-modal structure in the premultiplied spectrum, with peaks on either side of the $ k^{-1} $ range. The simulation is statistically stationary, with small statistical uncertainties and good agreement with experimental data. The simulation provides valuable data on high Reynolds number wall-bounded turbulence, with resolution consistent with accepted standards and statistical uncertainties generally small. The flow is statistically stationary to high accuracy, and the simulation exhibits many characteristics of high Reynolds number wall-bounded turbulence, making it a good resource for the study of such flows.
Reach us at info@study.space
[slides] Direct numerical simulation of turbulent channel flow up to %24%5Cmathit%7BRe%7D %7B%7B%5Cit%5Ctau%7D%7D%5Capprox 5200%24 | StudySpace