TY - JOUR
T1 - Second Log-Wake Law from Pipe Symmetry and its Applications in Symmetric and Antisymmetric Channel Flows
AU - Guo, Junke
N1 - Publisher Copyright:
© 2020 American Society of Civil Engineers.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - The velocity distribution of turbulent pipe flow is often described by the Coles log-wake law that is a superposition of the law of the wall due to the wall shear stress and the law of the wake due to the free turbulence at the centerline. Yet, the log-wake law does not meet the pipe symmetry principle because it includes only the effects of the wall-induced turbulence at the invert (the log law) and the free turbulence at the pipe centerline (the wake law), it misses the effect of the wall-induced turbulence at the obvert. This research then adds an additional log term due to the pipe obvert to the Coles log-wake law and innovates a second log-wake law. The slight modification of the Coles log-wake law results in a significant change in the eddy viscosity law that leads to an accurate antisymmetric velocity distribution law (including a sine integral wake law) for turbulent Couette channel flow. These laws agree with data from pipes, symmetric channel flow, and antisymmetric channel flow. Furthermore, this research can lead to a new path to solving open channel flow, which is discussed in a separate paper.
AB - The velocity distribution of turbulent pipe flow is often described by the Coles log-wake law that is a superposition of the law of the wall due to the wall shear stress and the law of the wake due to the free turbulence at the centerline. Yet, the log-wake law does not meet the pipe symmetry principle because it includes only the effects of the wall-induced turbulence at the invert (the log law) and the free turbulence at the pipe centerline (the wake law), it misses the effect of the wall-induced turbulence at the obvert. This research then adds an additional log term due to the pipe obvert to the Coles log-wake law and innovates a second log-wake law. The slight modification of the Coles log-wake law results in a significant change in the eddy viscosity law that leads to an accurate antisymmetric velocity distribution law (including a sine integral wake law) for turbulent Couette channel flow. These laws agree with data from pipes, symmetric channel flow, and antisymmetric channel flow. Furthermore, this research can lead to a new path to solving open channel flow, which is discussed in a separate paper.
KW - Couette flow
KW - Eddy viscosity
KW - Log law
KW - Pipe flow
KW - Velocity distribution
KW - Wall-bounded flow
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U2 - 10.1061/(ASCE)HY.1943-7900.0001813
DO - 10.1061/(ASCE)HY.1943-7900.0001813
M3 - Article
AN - SCOPUS:85093122973
VL - 146
JO - American Society of Civil Engineers, Journal of the Hydraulics Division
JF - American Society of Civil Engineers, Journal of the Hydraulics Division
SN - 0733-9429
IS - 11
M1 - 06020014
ER -