# zbMATH — the first resource for mathematics

Direct numerical simulation of turbulent forced convection in a pipe. (English) Zbl 1078.76038
Summary: Direct numerical simulations (DNS) are carried out to study fully developed turbulent pipe flow and heat transfer at Reynolds number $$Re_m \approx 5300$$ based on bulk velocity and pipe diameter. This paper provides detailed information on the mean properties and turbulence statistics up to fourth order, the budget and the wavenumber spectra of the temperature fluctuations, for three different wall boundary conditions. To investigate the differences between fully developed turbulent heat transfer in axisymmetric pipe and plane channel geometry, the present DNS results are compared to those obtained from channel flow simulations. The differences between channel and pipe flow statistics are modest and reveal that the temperature fluctuations in the pipe are slightly more intense. The present results show that the mean temperature profile does not conform to the accepted law of the wall. The boundary conditions affect the turbulence statistics both in the near-wall and core regions; this observation complements previous studies concerning different flow and heat transfer configurations.

##### MSC:
 76F65 Direct numerical and large eddy simulation of turbulence 76F35 Convective turbulence 76R05 Forced convection 76F55 Statistical turbulence modeling 80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text:
##### References:
 [1] Kim, Turbulent Shear Flows VI pp 85– (1989) · doi:10.1007/978-3-642-73948-4_9 [2] Kasagi, Journal of Heat Transfer 114 pp 598– (1992) [3] Tiselj, Physics of Fluids 13 pp 1028– (2001) [4] Kong, Physics of Fluids 12 pp 2555– (2000) [5] Piller, Journal of Fluid Mechanics 458 pp 419– (2002) [6] , . DNS of turbulent heat transfer in a channel flow with different thermal boundary conditions. Proceedings of the 6th ASME-JSME Thermal Engineering Joint Conference, Hawaii, U.S.A., 2003. [7] Heat Transfer. Wiley: New York, 1958. [8] Sommer, Transactions of ASME, sez. C: Journal of Heat Transfer 116 pp 855– (1994) [9] Patankar, Journal of Heat Transfer 99 pp 180– (1977) · doi:10.1115/1.3450666 [10] Griffin, Journal of Computational Physics 30 pp 352– (1979) [11] Akselvoll, Journal of Computational Physics 125 pp 454– (1996) · Zbl 0847.76043 [12] . Computational Methods for Fluid Dynamics. Springer: New York, 1999. · Zbl 0943.76001 · doi:10.1007/978-3-642-98037-4 [13] Gresho, International Journal for Numerical Methods in Fluids 11 pp 587– (1990) [14] Grötzbach, Journal of Computational Physics 49 pp 241– (1983) [15] Fukagata, Journal of Computational Physics 181 pp 478– (2002) [16] Eggels, Journal of Fluid Mechanics 268 pp 175– (1994) [17] , . Handbook of Single-Phase Convective Heat Transfer. Wiley: New York, 1987. [18] Subramanian, International Journal of Heat and Mass Transfer 24 pp 1833– (1981) [19] Johnk, Chemical Engineering Science 17 pp 867– (1962) [20] Na, International Journal of Heat and Fluid Flow 20 pp 187– (1999) [21] Kawamura, International Journal of Heat and Fluid Flow 20 pp 196– (1999) [22] , . Direct numerical simulation data base for turbulent channel flow with heat transfer. Turbulent poiseuille flow. Re$$\tau$$ = 180, Pr = 0.71, fourth-order finite-difference scheme with 256 $$\times$$ 128 $$\times$$ 256, 2003. [23] . A study of turbulence thermal structure in a channel flow through dns up to Re$$\tau$$ = 640 with Pr = 0.025 and 0.71. In Proceedings of 9th European Turbulence Conference, Castro I, Hancock P, Thomas T (eds), 2002; 399-402. [24] Chen, Journal of Fluid Mechanics 89 pp 1– (1978) [25] Elena, International Journal of Heat and Mass Transfer 20 pp 935– (1977) [26] . Intermittent structures in turbulent boundary layers. Proceedings of Meeting Agard, London, 1971.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.