Direct Numerical Simulation and RANS Modeling of Turbulent Natural Convection for Low Prandtl Number Fluids

2004 ◽  
Author(s):  
I. Otic´ ◽  
G. Gro¨tzbach
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Kinetic Energy ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Temperature Variance ◽  
Flux Model ◽  
Heat Flux Model

Results of direct numerical simulation (DNS) of turbulent Rayleigh-Be´nard convection for a Prandtl number Pr = 0.025 and a Rayleigh number Ra = 105 are used to evaluate the turbulent heat flux and the temperature variance. The DNS evaluated turbulent heat flux is compared with the DNS based results of a standard gradient diffusion turbulent heat flux model and with the DNS based results of a standard algebraic turbulent heat flux model. The influence of the turbulence time scales on the predictions by the standard algebraic heat flux model at these Rayleigh- and Prandtl numbers is investigated. A four equation algebraic turbulent heat flux model based on the transport equations for the turbulent kinetic energy k, for the dissipation of the turbulent kinetic energy ε, for the temperature variance θ2, and for the temperature variance dissipation rate εθ is proposed. This model should be applicable to a wide range of low Prandtl number flows.

Direct Numerical Simulation of Turbulent Channel Flow With Heat Transfer for Low Prandtl and High Reynolds and Comparison With Algebraic Heat Flux Model

2015 ◽  
Author(s):  
Haomin Yuan ◽  
Elia Merzari
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Flux ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Liquid Metals ◽  
Turbulent Channel Flow ◽  
Flux Model ◽  
Heat Flux Model

The flow characteristic of fluid at low Prandtl number is of continued interest in the nuclear industry because liquid metals are to be used in the next-generation nuclear power reactors. In this work we performed direct numerical simulation (DNS) for turbulent channel flow with fluid of low Prandtl number. The Prandtl number was set to 0.025, which is representative of the behavior of liquid metals. Constant heat flux was imposed on the walls to study heat transfer behavior, with different boundary conditions for temperature fluctuation. The bulk Reynolds number was set as high as 50,000, with a corresponding friction Reynolds number of 1,200, which is closer to the situation in a reactor or a heat exchanger than used in normally available databases. Budgets for turbulent variables were computed and compared with predictions from several RANS turbulence models. In particular, the Algebraic Heat Flux Model (AHFM) has been the focus of this comparison with DNS data. The comparisons highlight some shortcomings of AHFM along with potential improvements.

Assessment and calibration of an algebraic turbulent heat flux model for low-Prandtl fluids

2014 ◽  
Vol 79 ◽  
pp. 589-601 ◽  
Author(s):  
A. Shams ◽  
F. Roelofs ◽  
E. Baglietto ◽  
S. Lardeau ◽  
S. Kenjeres
Keyword(s):  
Heat Flux ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Flux Model ◽  
Heat Flux Model

Algebraic Turbulent Heat Flux Model for Prediction of Thermal Stratification in Piping Systems

2013 ◽  
Vol 181 (1) ◽  
pp. 144-156
Author(s):  
M. Pellegrini ◽  
H. Endo ◽  
E. Merzari ◽  
H. Ninokata
Keyword(s):  
Heat Flux ◽  
Thermal Stratification ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Piping Systems ◽  
Flux Model ◽  
Heat Flux Model

An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows

2013 ◽  
Vol 723 ◽  
pp. 91-125 ◽  
Author(s):  
W. M. J. Lazeroms ◽  
G. Brethouwer ◽  
S. Wallin ◽  
A. V. Johansson
Keyword(s):  
Heat Flux ◽  
Kinetic Energy ◽  
Temperature Gradient ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Homogeneous Shear ◽  
Self Consistent ◽  
The Mean ◽  
Homogeneous Shear Flow

AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

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