Convective Heat Transfer in Wall-Bounded Flows Affected by Severe Fluid Properties Variation: A Second-Moment Closure Study

2010 ◽  
Author(s):  
S. Jakirlic´ ◽  
R. Jester-Zu¨rker
Keyword(s):  
Heat Flux ◽  
Dissipation Rate ◽  
Transport Equations ◽  
Moment Closure ◽  
Reference Database ◽  
Turbulent Heat ◽  
Second Moment ◽  
Fluid Properties ◽  
Second Moment Closure ◽  
Near Wall

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.

A DNS-based thermal second-moment closure for buoyant convection at vertical walls

1999 ◽  
Vol 391 ◽  
pp. 211-247 ◽  
Author(s):  
H. S. DOL ◽  
K. HANJALIĆ ◽  
T. A. M. VERSTEEGH
Keyword(s):  
A Priori ◽  
Vertical Channel ◽  
Turbulent Heat Flux ◽  
Transport Equations ◽  
Computational Effort ◽  
Moment Closure ◽  
Wall Region ◽  
Turbulent Heat ◽  
Second Moment ◽  
Near Wall

Direct numerical simulations (DNS) of natural convection in a vertical channel by Versteegh & Nieuwstadt (1998) are used for assessing the budget of the turbulent heat flux θui and the temperature variance θ2, and for modelling the transport equations governing these two properties. The analysis is confined to a simple fully developed situation in which the gravitational vector, as the sole driving force, is perpendicular to the only non-zero component of the mean temperature gradient. Despite its simplicity, the flow displays many interesting features and represents a generic case of the interaction of buoyancy-driven turbulent temperature and velocity fields. The paper discusses the near-wall variation of the second moments and their budgets, as well as possible scaling of θui and θ 2 both in the near-wall region and away from the wall. Various proposals for the Reynolds-averaged modelling are analysed and new models are proposed for these two transport equations using the term-by- term approach. An a priori test (using the DNS data for properties other than θui and θ 2) reproduced very well all terms in the transport equations, as well as their near-wall behaviours and wall limits, without the use of any wall-topology-dependent parameters. The computational effort is still comparable to that for the ‘basic model’. The new term-by-term model of the θui and θ 2 equations was then used for a full simulation in conjunction with a low-Reynolds-number second-moment velocity closure, which was earlier found to reproduce satisfactorily a variety of isothermal wall flows. Despite excellent term-by-term reproduction of thermal turbulence, the predictions with the full model show less satisfactory agreement with the DNS data than a priori validation, indicating a further need for improvement of the modelling of buoyancy effects on mechanical turbulence.

Computation of Discrete-Hole Film Cooling by a Near-Wall Second-Moment Turbulence Closure

1999 ◽  
Author(s):  
Hamn-Ching Chen ◽  
Gengsheng Wei ◽  
Je-Chin Han
Keyword(s):  
Film Cooling ◽  
Moment Closure ◽  
Navier Stokes ◽  
Closure Model ◽  
Complex Flow ◽  
Second Moment ◽  
Finite Analytic Method ◽  
Second Moment Closure ◽  
Effectiveness Prediction ◽  
Near Wall

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.

Second-moment closure for the near-wall sublayer - Development and application

AIAA Journal ◽  
1989 ◽  
Vol 27 (10) ◽  
pp. 1319-1325 ◽  
Author(s):  
B. E. Launder ◽  
N. Shima
Keyword(s):  
Moment Closure ◽  
Second Moment ◽  
Second Moment Closure ◽  
Near Wall

Computation of Flow and Heat Transfer in Two-Pass Channels With 60 deg Ribs

2001 ◽  
Vol 123 (3) ◽  
pp. 563-575 ◽  
Author(s):  
Yong-Jun Jang ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Moment Closure ◽  
Closure Model ◽  
Second Moment ◽  
Flow And Heat Transfer ◽  
Numerical Predictions ◽  
Sharp Turn ◽  
Second Moment Closure ◽  
Near Wall

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.

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