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- Title
Relationship between the energy dissipation function and the skin friction law in a turbulent channel flow.
- Authors
Hiroyuki Abe; Antonia, Robert Anthony
- Abstract
Integrals of the mean and turbulent energy dissipation rates are examined using direct numerical simulation (DNS) databases in a turbulent channel flow. Four values of the Kármán number (h+ =180, 395, 640 and 1020; h is the channel half-width) are used. Particular attention is given to the functional h+ dependence by comparing existing DNS and experimental data up to h+ = 104. The logarithmic h+ dependence of the integrated turbulent energy dissipation rate is established for 300 ≤ h+ ≤ 104, and is intimately linked to the logarithmic skin friction law, viz. U+b = 2:54 ln.h+/ + 2:41 (Ub is the bulk mean velocity). This latter relationship is established on the basis of energy balances for both the mean and turbulent kinetic energy. When h+ is smaller than 300, viscosity affects the integrals of both the mean and turbulent energy dissipation rates significantly due to the lack of distinct separation between inner and outer regions. The logarithmic h+ dependence of U+b is clarified through the scaling behaviour of the turbulent energy dissipation rate ε¯ in different parts of the flow. The overlap between inner and outer regions is readily established in the region 30=h+ ≤ y/h ≤ 0:2 for h+ ≤ 300. At large h+ (≤5000) when the finite Reynolds number effect disappears, the magnitude of ε¯y/U3τ approaches 2.54 near the lower bound of the overlap region. This value is identical between the channel, pipe and boundary layer as a result of similarity in the constant stress region. As h+ becomes large, the overlap region tends to contribute exclusively to the 2:54 ln.h+/ dependence of the integrated turbulent energy dissipation rate. The present logarithmic h+ dependence of U+b is essentially linked to the overlap region, even at small h+.
- Subjects
ENERGY dissipation; FORCE &; energy; HEAD loss (Fluid mechanics); SKIN friction (Aerodynamics); AIR resistance; DRAG (Aerodynamics)
- Publication
Journal of Fluid Mechanics, 2016, Vol 798, p140
- ISSN
0022-1120
- Publication type
Article
- DOI
10.1017/jfm.2016.299