DissipationfunctioninturbulentplanePoiseuilleandCo
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Key words dissipation function, spanwise rotation, plane Poiseuille flow (PPF), plane Couette flow (PCF)
Chinese Library Classification O35 2010 Mathematics Classification 76E07, 76F65
Appl. Math. Mech. -Engl. Ed., 40(2), 185–192 (2019)
Applied Mathematics and Mechanics (English Edition)
https:///10.1007/s10483-019-2422-6
Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations∗
∗ Citation: XIA, Z. H., SHI, Y. P., CAI, Q. D., and GAI, J. Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations. Applied Mathematics and Mechanics (English Edition), 40(2), 185–192 (2019) https:///10.1007/s10483-019-2422-6
Zhenhua XIA1,†, Yipeng SHI2, Qingdong CAI2, Jie GAI3
1. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China; 2. State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, China; 3. CRRC Changchun Railway Vehicles Co., Ltd., Changchun 130062, China (Received Sept. 4, 2018 / Revised Oct. 8, 2018)
1 Introduction
Due to the ubiquity and importance in turbomachinery, the wall-bounded turbulent flow in a rotating reference frame has received a great deal of attention. Ever since the experimental investigations of a spanwise rotating plane Poiseuille flow (RPPF) conducted by Johnston et al.[1], it has been well accepted that the existence of the Coriolis force due to the system rotation will alter both the mean flow and the turbulent fluctuations[2]. In order to unravel the physics of turbulence in rotating wall-bounded flows, many studies were conducted on some typical flow categories with simple flow geometries, among which RPPFs and spanwise rotating plane Couette flows (RPCFs) are two canonical prototypes[3]. In an RPPF, since the mean vorticity changes its sign across the channel, the Coriolis force destabilizes the flow in
Abstract The dissipation function in turbulent plane Poiseuille flows (PPFs) and plane Couette flows (PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs. However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations, when the rotation number increases, the dissipation function first decreases and then increases.
Chinese Library Classification O35 2010 Mathematics Classification 76E07, 76F65
Appl. Math. Mech. -Engl. Ed., 40(2), 185–192 (2019)
Applied Mathematics and Mechanics (English Edition)
https:///10.1007/s10483-019-2422-6
Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations∗
∗ Citation: XIA, Z. H., SHI, Y. P., CAI, Q. D., and GAI, J. Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations. Applied Mathematics and Mechanics (English Edition), 40(2), 185–192 (2019) https:///10.1007/s10483-019-2422-6
Zhenhua XIA1,†, Yipeng SHI2, Qingdong CAI2, Jie GAI3
1. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China; 2. State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, China; 3. CRRC Changchun Railway Vehicles Co., Ltd., Changchun 130062, China (Received Sept. 4, 2018 / Revised Oct. 8, 2018)
1 Introduction
Due to the ubiquity and importance in turbomachinery, the wall-bounded turbulent flow in a rotating reference frame has received a great deal of attention. Ever since the experimental investigations of a spanwise rotating plane Poiseuille flow (RPPF) conducted by Johnston et al.[1], it has been well accepted that the existence of the Coriolis force due to the system rotation will alter both the mean flow and the turbulent fluctuations[2]. In order to unravel the physics of turbulence in rotating wall-bounded flows, many studies were conducted on some typical flow categories with simple flow geometries, among which RPPFs and spanwise rotating plane Couette flows (RPCFs) are two canonical prototypes[3]. In an RPPF, since the mean vorticity changes its sign across the channel, the Coriolis force destabilizes the flow in
Abstract The dissipation function in turbulent plane Poiseuille flows (PPFs) and plane Couette flows (PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs. However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations, when the rotation number increases, the dissipation function first decreases and then increases.