Expression of turbulent heat flux in the Earth’s core in terms of a second moment closure model

2001 ◽  
Vol 128 (1-4) ◽  
pp. 137-148 ◽  
Author(s):  
Masaki Matsushima
Author(s):  
S. Jakirlic´ ◽  
R. Jester-Zu¨rker

Different flow configurations subjected to increasingly enhanced wall heating were selected to be computationally investigated by means of a differential, near-wall second-moment closure model based on the solution of transport equations for second moments of the fluctuating velocities and temperature, ui″uj″͠ and ui″θ͠ respectively. Both Reynolds stress model and heat flux model represent wall-topography free formulations with quadratic pressure-strain term and pressure-temperature-gradient correlation. The transport equations for the turbulent stress tensor and the turbulent heat flux are solved in conjunction with the equation governing a new scale supplying variable, so-called “homogeneous” dissipation rate, Jakirlic and Hanjalic (2002). Such an approach offers a number of important advantages: proper near-wall shape of the dissipation rate profile was obtained without introducing any additional term and the correct asymptotic behaviour of the stress dissipation components by approaching the solid wall is fulfilled automatically without necessity for any wall geometry-related parameter. The configurations considered include fully-developed and developing flows in channel (without and with a sudden expansion) and pipe in conjunction with the scalar transport under conditions of variable fluid properties for which an extensive experimental and numerical (DNS and LES) reference database exists.


1999 ◽  
Author(s):  
Hamn-Ching Chen ◽  
Gengsheng Wei ◽  
Je-Chin Han

Abstract A multiblock Favre-Averaged Navier-Stokes (FANS) method has been developed in conjunction with a chimera domain decomposition technique for investigation of flat surface, discrete-hole film cooling performance. The finite-analytic method solves the FANS equations in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model and a two-layer k-ε model. Comparisons of flow fields and turbulence quantities with experimental data clearly demonstrate the capability of the near-wall second-moment closure model for accurate resolution of the complex flow interaction bewteen the coolant jet and the mainstream. The near-wall second-moment anisotropic model provides better agreement in adiabatic film effectiveness prediction than the two-layer k-ε model.


2001 ◽  
Vol 123 (3) ◽  
pp. 563-575 ◽  
Author(s):  
Yong-Jun Jang ◽  
Hamn-Ching Chen ◽  
Je-Chin Han

Numerical predictions of three-dimensional flow and heat transfer are presented for a two-pass square channel with and without 60 deg angled parallel ribs. Square sectioned ribs were employed along one side surface. The rib height-to-hydraulic diameter ratio e/Dh is 0.125 and the rib pitch-to-height ratio (P/e) is 10. The computation results were compared with the experimental data of Ekkad and Han [1] at a Reynolds number (Re) of 30,000. A multi-block numerical method was used with a chimera domain decomposition technique. The finite analytic method solved the Reynolds-Averaged Navier Stokes equation in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model, and a two-layer k-ε isotropic eddy viscosity model. Comparing the second-moment and two-layer calculations with the experimental data clearly demonstrated that the angled rib turbulators and the 180 deg sharp turn of the channel produced strong non-isotropic turbulence and heat fluxes, which significantly affected the flow fields and heat transfer coefficients. The near-wall second-moment closure model provides an improved heat transfer prediction in comparison with the k-ε model.


2011 ◽  
Vol 12 ◽  
pp. N49 ◽  
Author(s):  
John D. Schwarzkopf ◽  
Daniel Livescu ◽  
Robert A. Gore ◽  
Rick M. Rauenzahn ◽  
J. Raymond Ristorcelli

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