A Two-Equation Model for Heat Transport in Wall Turbulent Shear Flows

1988 ◽  
Vol 110 (3) ◽  
pp. 583-589 ◽  
Author(s):  
Y. Nagano ◽  
C. Kim
Keyword(s):  
Prandtl Number ◽  
Turbulence Modeling ◽  
Plate Boundary ◽  
Eddy Diffusivity ◽  
Equation Model ◽  
Wall Turbulence ◽  
Turbulent Heat Transfer ◽  
Turbulent Shear ◽  
Turbulent Heat ◽  
Wide Range

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modeling. The eddy diffusivity concept is used in modeling. However, just as the eddy viscosity is determined from solutions of the k and ε equations, so the eddy diffusivity for heat is given as functions of temperature variance t2, and the dissipation rate of temperature fluctuations εt, together with k and ε. Thus, the proposed model does not require any questionable assumptions for the “turbulent Prandtl number.” Modeled forms of the t2 and εt equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat-plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with the experiment is generally very satisfactory.

DNS and Turbulence Modeling for Turbulent Boundary Layers With Various Thermal Stratifications

2007 ◽  
Author(s):  
H. Hattori ◽  
Y. Nagano
Keyword(s):  
Boundary Layers ◽  
Turbulence Model ◽  
Turbulence Modeling ◽  
Eddy Diffusivity ◽  
Turbulent Boundary Layers ◽  
Turbulent Heat Transfer ◽  
Transfer Model ◽  
Turbulent Heat ◽  
Turbulent Structures ◽  
Gradient Diffusion

Direct numerical simulations (DNS) of boundary layers with various thermal stratifications are carried out to investigate the turbulent structures of these flows. The present DNSs quantitatively provide the characteristics of thermally stratified turbulent boundary layers. In particular, the counter gradient diffusion phenomenon is found in a strong, stable stratified boundary layer. On the other hand, in order to adequately predict turbulent boundary layers with various thermal stratifications, an appropriate turbulence model should be employed in the calculation. Thus, using a database obtained by DNS, the strict assessment of turbulent heat transfer model is made so as to construct a reliable advanced turbulence model. The results of in-depth turbulent model evaluation are indicated, in which we have explored the prediction potential of the proposed nonlinear eddy diffusivity models for momentum and heat in both stable and unstable stratified boundary layers.

Coherent motions and heat transfer in a wall turbulent shear flow

1995 ◽  
Vol 305 ◽  
pp. 127-157 ◽  
Author(s):  
Y. Nagano ◽  
M. Tagawa
Keyword(s):  
Heat Transfer ◽  
Heat Transport ◽  
Phase Relationship ◽  
Transport Processes ◽  
Wall Turbulence ◽  
Ar Model ◽  
Turbulent Heat Transfer ◽  
Good Time ◽  
Turbulent Shear ◽  
Turbulent Heat

In wall turbulence, it is widely accepted that the coherent motions determine the essential features of turbulent transport phenomena. In the present study, we have refined a trajectory-based detection algorithm for coherent motions and have investigated the relationship between coherent motions and scalar (heat) transfer from a structural point of view, i. e. trajectory analysis of the VITA heat transfer events, extraction of key flow modules and the relevant heat transport, and the prediction of passive scalar transfer by means of an autoregressive (AR) model. As a result, it is shown that the phase relationship of fluctuating velocity components dominates the essential characteristics of the transport processes of heat and momentum in wall turbulence and there exist distinct differences in individual correspondence between the coherent motions and heat transport processes, neither of which can be revealed by the widely used VITA technique. Also, the AR model is shown to provide good time-series predictions for turbulent heat transfer associated with coherent structures near the wall.

Improved Form of the k-ε Model for Wall Turbulent Shear Flows

1987 ◽  
Vol 109 (2) ◽  
pp. 156-160 ◽  
Author(s):  
Y. Nagano ◽  
M. Hishida
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Plate Boundary ◽  
Wall Turbulence ◽  
Turbulent Shear ◽  
Committee Report ◽  
Low Reynolds Number Flows ◽  
Diffuser Flow ◽  
Wide Range ◽  
Predicted Values

An improved k-ε turbulence model for predicting wall turbulence is presented. The model was developed in conjunction with an accurate calculation of near-wall and low-Reynolds-number flows to meet the requirements of the Evaluation Committee report of the 1980–1981 Stanford Conference on Complex Turbulent Flows. The proposed model was tested by application to turbulent pipe and channel flows, a flat plate boundary layer, a relaminarizing flow, and a diffuser flow. In all cases, the predicted values of turbulent quantities agreed almost completely with measurements, which many previously proposed models failed to predict correctly, over a wide range of the Reynolds number.

Investigation of a Two-Equation Turbulent Heat Transfer Model Applied to Ducts

2003 ◽  
Vol 125 (1) ◽  
pp. 194-200 ◽  
Author(s):  
Masoud Rokni and ◽  
Bengt Sunde´n
Keyword(s):  
Heat Transfer ◽  
Eddy Diffusivity ◽  
Turbulent Heat Transfer ◽  
Transfer Model ◽  
Turbulent Heat ◽  
Scalar Flux ◽  
Eddy Viscosity Model ◽  
Wide Range ◽  
Flux Model ◽  
Prandtl Numbers

This investigation concerns numerical calculation of fully developed turbulent forced convective heat transfer and fluid flow in ducts over a wide range of Reynolds numbers. The low Reynolds number version of a non-linear eddy viscosity model is combined with a two-equation heat flux model with the eddy diffusivity concept. The model can theoretically be used for a range of Prandtl numbers or a range of different fluids. The computed results compare satisfactory with the available experiment. Based on existing DNS data and calculations in this work the ratio between the time-scales (temperature to velocity) is found to be approximately 0.7. In light of this assumption an algebraic scalar flux model with variable diffusivity is presented.

Turbulent Heat Transfer Between a Series of Parallel Plates With Surface-Mounted Discrete Heat Sources

1994 ◽  
Vol 116 (3) ◽  
pp. 577-587 ◽  
Author(s):  
S. H. Kim ◽  
N. K. Anand
Keyword(s):  
Heat Transfer ◽  
Thermal Resistance ◽  
Electronic Equipment ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Computational Domain ◽  
Heat Sources ◽  
Parallel Plates ◽  
Wide Range ◽  
Independent Parameters

Two-dimensional turbulent heat transfer between a series of parallel plates with surface mounted discrete block heat sources was studied numerically. The computational domain was subjected to periodic conditions in the streamwise direction and repeated conditions in the cross-stream direction (Double Cyclic). The second source term was included in the energy equation to facilitate the correct prediction of a periodically fully developed temperature field. These channels resemble cooling passages in electronic equipment. The k–ε model was used for turbulent closure and calculations were made for a wide range of independent parameters (Re, Ks/Kf, s/w, d/w, and h/w). The governing equations were solved by using a finite volume technique. The numerical procedure and implementation of the k–ε model was validated by comparing numerical predictions with published experimental data (Wirtz and Chen, 1991; Sparrow et al., 1982) for a single channel with several surface mounted blocks. Computations were performed for a wide range of Reynolds numbers (5 × 104–4 × 105) and geometric parameters and for Pr = 0.7. Substrate conduction was found to reduce the block temperature by redistributing the heat flux and to reduce the overall thermal resistance of the module. It was also found that the increase in the Reynolds number decreased the thermal resistance. The study showed that the substrate conduction can be an important parameter in the design and analysis of cooling channels of electronic equipment. Finally, correlations for the friction factor (f) and average thermal resistance (R) in terms of independent parameters were developed.

Control of Turbulent Transport: Less Friction and More Heat Transfer

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Nobuhide Kasagi ◽  
Yosuke Hasegawa ◽  
Koji Fukagata ◽  
Kaoru Iwamoto
Keyword(s):  
Heat Transfer ◽  
Heat Transport ◽  
Turbulent Transport ◽  
Scalar Fields ◽  
Wall Friction ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Control Input ◽  
Divergence Free Vector ◽  
Wide Range

Because of the importance of fundamental knowledge on turbulent heat transfer for further decreasing entropy production and improving efficiency in various thermofluid systems, we revisit a classical issue whether enhancing heat transfer is possible with skin friction reduced or at least not increased as much as heat transfer. The answer that numerous previous studies suggest is quite pessimistic because the analogy concept of momentum and heat transport holds well in a wide range of flows. Nevertheless, the recent progress in analyzing turbulence mechanics and designing turbulence control offers a chance to develop a scheme for dissimilar momentum and heat transport. By reexamining the governing equations and boundary conditions for convective heat transfer, the basic strategies for achieving dissimilar control in turbulent flow are generally classified into two groups, i.e., one for the averaged quantities and the other for the fluctuating turbulent components. As a result, two different approaches are discussed presently. First, under three typical heating conditions, the contribution of turbulent transport to wall friction and heat transfer is mathematically formulated, and it is shown that the difference in how the local turbulent transport of momentum and that of heat contribute to the friction and heat transfer coefficients is a key to answer whether the dissimilar control is feasible. Such control is likely to be achieved when the weight distributions for the stress and flux in the derived relationships are different. Second, we introduce a more general methodology, i.e., the optimal control theory. The Fréchet differentials obtained clearly show that the responses of velocity and scalar fields to a given control input are quite different due to the fact that the velocity is a divergence-free vector, while the temperature is a conservative scalar. By exploiting this inherent difference, the dissimilar control can be achieved even in flows where the averaged momentum and heat transport equations have the same form.

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