- Title
- Mean temperature calculations in a turbulent channel flow for air and mercury
- Creator
- Abe, Hiroyuki; Antonia, Robert Anthony
- Relation
- International Journal of Heat and Mass Transfer Vol. 132, Issue April 2019, p. 1152-1165
- Publisher Link
- http://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.11.100
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2019
- Description
- Direct numerical simulations (DNSs) in a turbulent channel flow are used to examine the behavior of the turbulent Prandtl number Prt for air (Pr = 0.71) and mercury (Pr = 0.025), with a view to calculating the mean temperature. Constant time-averaged (surface) heat flux (CHF) is used as a thermal boundary condition. For each Pr, four values of the Kármán number (h+ = 180, 395, 640, 1020) are used. Datasets for the constant heating source (CHS) are also examined. For Pr = 0.71, Prt is approximately 1.1 at the wall, varies between 0.9 and 1.1 in the region y+ <100, and is approximated by 0.9–0.3(y/h)2 for y/h > 0.2. The latter relation, with a low Re correction term (i.e. 25/h+), yields an excellent prediction for the mean temperature up to h+ = 2000, whereas a calculation based on Prt = 0.85 underestimates the mean temperature. The calculated maximum wall-normal turbulent heat flux and Nusselt number also agree well with the empirical relations over a wide range of h+. For Pr = 0.025, Prt departs significantly from unity inside the inner region (y/h < 0.2) owing to the strong conductive effect, whilst the magnitude in the outer region (y/h > 0.2) tends to approach that corresponding to Pr = 0.71 as h+ increases due to the increase in the Peclet number. The h+ dependence of Prt in the logarithmic and outer regions is represented adequately by the turbulent Peclet number, i.e.Pet≡Pr(vt/V. The resulting Prt relation, which is an extension of the expression established by Kays (1994), leads to a correct calculation of the mean temperature not only for mercury (Pr = 0.025) but also for liquid sodium (Pr = 0.01). The mean temperature defect profile exhibits an outer-layer similarity when Pe(≡RebPr) ≥ 2000; the Nusselt number is represented by reasonably well.
- Subject
- turbulent channel flow; mean temperature; Nusselt number; outer-layer
- Identifier
- http://hdl.handle.net/1959.13/1466624
- Identifier
- uon:47608
- Identifier
- ISSN:0017-9310
- Language
- eng
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