Relationship between the heat transfer law and the scalar dissipation function in a turbulent channel flow

2017 ◽  
Vol 830 ◽  
pp. 300-325 ◽  
Author(s):  
Hiroyuki Abe ◽  
Robert Anthony Antonia
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Mean Velocity ◽  
The Mean ◽  
Logarithmic Dependence

Integration across a fully developed turbulent channel flow of the transport equations for the mean and turbulent parts of the scalar dissipation rate yields relatively simple relations for the bulk mean scalar and wall heat transfer coefficient. These relations are tested using direct numerical simulation datasets obtained with two isothermal boundary conditions (constant heat flux and constant heating source) and a molecular Prandtl number Pr of 0.71. A logarithmic dependence on the Kármán number $h^{+}$ is established for the integrated mean scalar in the range $h^{+}\geqslant 400$ where the mean part of the total scalar dissipation exhibits near constancy, whilst the integral of the turbulent scalar dissipation rate $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$ increases logarithmically with $h^{+}$. This logarithmic dependence is similar to that established in a previous paper (Abe & Antonia, J. Fluid Mech., vol. 798, 2016, pp. 140–164) for the bulk mean velocity. However, the slope (2.18) for the integrated mean scalar is smaller than that (2.54) for the bulk mean velocity. The ratio of these two slopes is 0.85, which can be identified with the value of the turbulent Prandtl number in the overlap region. It is shown that the logarithmic $h^{+}$ increase of the integrated mean scalar is intrinsically associated with the overlap region of $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$, established for $h^{+}$ (${\geqslant}400$). The resulting heat transfer law also holds at a smaller $h^{+}$ (${\geqslant}200$) than that derived by assuming a log law for the mean temperature.

scholarly journals Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

2009 ◽  
Vol 627 ◽  
pp. 1-32 ◽  
Author(s):  
HIROYUKI ABE ◽  
ROBERT ANTHONY ANTONIA ◽  
HIROSHI KAWAMURA
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Compressive Strain ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Scalar Dissipation Rate

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

Heat transfer in a turbulent channel flow with square bars or circular rods on one wall

2015 ◽  
Vol 776 ◽  
pp. 512-530 ◽  
Author(s):  
S. Leonardi ◽  
P. Orlandi ◽  
L. Djenidi ◽  
R. A. Antonia
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Turbulent Heat ◽  
Turbulent Prandtl Number ◽  
Smooth Wall ◽  
Roughness Elements ◽  
Smooth Channel

Direct numerical simulations (DNS) are carried out to study the passive heat transport in a turbulent channel flow with either square bars or circular rods on one wall. Several values of the pitch (${\it\lambda}$) to height ($k$) ratio and two Reynolds numbers are considered. The roughness increases the heat transfer by inducing ejections at the leading edge of the roughness elements. The amounts of heat transfer and mixing depend on the separation between the roughness elements, an increase in heat transfer accompanying an increase in drag. The ratio of non-dimensional heat flux to the non-dimensional wall shear stress is higher for circular rods than square bars irrespectively of the pitch to height ratio. The turbulent heat flux varies within the cavities and is larger near the roughness elements. Both momentum and thermal eddy diffusivities increase relative to the smooth wall. For square cavities (${\it\lambda}/k=2$) the turbulent Prandtl number is smaller than for a smooth channel near the wall. As ${\it\lambda}/k$ increases, the turbulent Prandtl number increases up to a maximum of 2.5 at the crests plane of the square bars (${\it\lambda}/k=7.5$). With increasing distance from the wall, the differences with respect to the smooth wall vanish and at three roughness heights above the crests plane, the turbulent Prandtl number is essentially the same for smooth and rough walls.

scholarly journals Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

2013 ◽  
Vol 721 ◽  
pp. 627-668 ◽  
Author(s):  
Rémi Zamansky ◽  
Ivana Vinkovic ◽  
Mikhael Gorokhovski
Keyword(s):  
Stochastic Model ◽  
Channel Flow ◽  
Scaling Law ◽  
Stochastic Modelling ◽  
Turbulent Channel Flow ◽  
Mean Value ◽  
Mean Velocity ◽  
Wall Distance ◽  
Eddy Simulation ◽  
The Mean

AbstractThis paper focuses on the characterization and the stochastic modelling of the fluid acceleration in turbulent channel flow. In the first part, the acceleration is studied by direct numerical simulation (DNS) at three Reynolds numbers (${\mathit{Re}}_{\ast } = {u}_{\ast } h/ \nu = 180$, 590 and 1000). It is observed that whatever the wall distance is, the norm of acceleration is log-normally distributed and that the variance of the norm is very close to its mean value. It is also observed that from the wall to the centreline of the channel, the orientation of acceleration relaxes statistically towards isotropy. On the basis of dimensional analysis, a universal scaling law for the acceleration norm is proposed. In the second part, in the framework of the norm/orientation decomposition, a stochastic model of the acceleration is introduced. The stochastic model for the norm is based on fragmentation process which evolves across the channel with the wall distance. Simultaneously the orientation is simulated by a random walk on the surface of a unit sphere. The process is generated in such a way that the mean components of the orientation vector are equal to zero, whereas with increasing wall distance, all directions become equally probable. In the third part, the models are assessed in the framework of large-eddy simulation with stochastic subgrid acceleration model (LES–SSAM), introduced recently by Sabel’nikov, Chtab-Desportes & Gorokhovski (Euro. Phys. J. B, vol. 80, 2011, p. 177–187), and designed to account for the intermittency at subgrid scales. Computations by LES–SSAM and its assessment using DNS data show that the prediction of important statistics to characterize the flow, such as the mean velocity, the energy spectra at small scales, the viscous and turbulent stresses, the distribution of the acceleration can be considerably improved in comparison with standard LES. In the last part of this paper, the advantage of LES–SSAM in accounting for the subgrid flow structure is demonstrated in simulation of particle-laden turbulent channel flows. Compared to standard LES, it is shown that for different Stokes numbers, the particle dynamics and the turbophoresis effect can be predicted significantly better when LES–SSAM is applied.

Stability of turbulent channel flow, with application to Malkus's theory

1967 ◽  
Vol 27 (2) ◽  
pp. 253-272 ◽  
Author(s):  
W. C. Reynolds ◽  
W. G. Tiederman
Keyword(s):  
Velocity Profile ◽  
Channel Flow ◽  
Stability Problem ◽  
Turbulent Channel Flow ◽  
Velocity Profiles ◽  
Neutral Stability ◽  
Mean Velocity ◽  
The Mean ◽  
Two Parameter ◽  
Good Agreement

The Orr-Sommerfeld stability problem has been studied for velocity profiles appropriate to turbulent channel flow. The intent was to provide an evaluation of Malkus's theory that the flow assumes a state of maximum dissipation, subject to certain constraints, one of which is that the mean velocity profile is marginally stable. Dissipation rates and neutral stability curves were obtained for a representative two-parameter family of velocity profiles. Those in agreement with experimental profiles were found to be stable; the marginally stable profile of greatest dissipation was not in good agreement with experiments. An explanation for the apparent success of Malkus's theory is offered.

scholarly journals Simulation of Rotating Channel Flow With Heat Transfer: Evaluation of Closure Models

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Alan S. Hsieh ◽  
Sedat Biringen ◽  
Alec Kucala
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Stress ◽  
Channel Flow ◽  
Turbulence Models ◽  
Turbulent Channel Flow ◽  
Turbulent Heat ◽  
Stress Distributions ◽  
Mean Velocity ◽  
Closure Models

A direct numerical simulation (DNS) of spanwise-rotating turbulent channel flow was conducted for four rotation numbers: Rob=0, 0.2, 0.5, and 0.9 at a Reynolds number of 8000 based on laminar centerline mean velocity and Prandtl number 0.71. The results obtained from these DNS simulations were utilized to evaluate several turbulence closure models for momentum and heat transfer transport in rotating turbulent channel flow. Four nonlinear eddy viscosity turbulence models were tested and among these, explicit algebraic Reynolds stress models (EARSM) obtained the Reynolds stress distributions in best agreement with DNS data for rotational flows. The modeled pressure–strain functions of EARSM were shown to have strong influence on the Reynolds stress distributions near the wall. Turbulent heat flux distributions obtained from two explicit algebraic heat flux models (EAHFM) consistently displayed increasing disagreement with DNS data with increasing rotation rate.

Analysis and modelling of anisotropies in the dissipation rate of turbulence

1997 ◽  
Vol 344 ◽  
pp. 155-180 ◽  
Author(s):  
CHARLES G. SPEZIALE ◽  
THOMAS B. GATSKI
Keyword(s):  
Transport Equation ◽  
Dissipation Rate ◽  
Algebraic Model ◽  
Scalar Dissipation ◽  
Mean Velocity ◽  
Production Term ◽  
New Model ◽  
Symmetry Properties ◽  
The Mean ◽  
The Relationship

The modelling of anisotropies in the dissipation rate of turbulence is considered based on an analysis of the exact transport equation for the dissipation rate tensor. An algebraic model is systematically derived using integrity bases methods and tensor symmetry properties. The new model differs notably from all previously proposed models in that it depends nonlinearly on the mean velocity gradients. This gives rise to a transport equation for the scalar dissipation rate that is of the same general form as the commonly used model with one major exception: the coefficient of the production term is dependent on the invariants of both the rotational and irrotational strain rates. The relationship between the new model and other recently proposed models is examined in detail. Some basic tests and applications of the model are also provided along with a discussion of the implications for turbulence modelling.

Hybrid RANS-LES Simulation of Turbulent Heat Transfer in a Channel Flow With Imposed Spanwise and Streamwise Mean Temperature Gradient

2019 ◽  
Author(s):  
Olalekan O. Shobayo ◽  
D. Keith Walters
Keyword(s):  
Heat Transfer ◽  
Temperature Gradient ◽  
Channel Flow ◽  
Plane Channel ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Mean Temperature ◽  
The Mean

Abstract Computational fluid dynamics (CFD) results for turbulent flow and heat transfer in a plane channel are presented. This study presents an idealized fully-developed planar channel flow case for which the mean velocity gradient is non-zero only in the wall-normal direction, and the mean temperature gradient is imposed to be uniform and non-zero in the streamwise or spanwise direction. Previous studies have documented direct numerical simulation results for periodic channel flow with mean temperature gradient in both the streamwise and wall-normal directions, but limited investigations exist documenting the effect of imposed spanwise gradient. The objective of this study is to evaluate turbulent heat flux predictions for three different classes of modeling approach: Reynolds-averaged Navier-Stokes (RANS), large-eddy simulation (LES), and hybrid RANS-LES. Results are compared to available DNS data at Prandtl number of 0.71 and Reynolds number of 180 based on friction velocity and channel half-width. Specific models evaluated include the k-ω SST RANS model, monotonically integrated LES (MILES), improved delayed detached eddy simulation (IDDES), and dynamic hybrid RANS-LES (DHRL). The DHRL model includes both the standard formulation that has been previously documented in the literature as well as a modified version developed specifically to improve predictive capability for flows in which the primary mean velocity and mean temperature gradients are not closely aligned. The modification consists of using separate RANS-to-LES blending parameters in the momentum and energy equations. Results are interrogated to evaluate the performance of the three different model types and specifically to evaluate the performance of the new modified DHRL variant compared with the baseline version.

Passive Scalar Turbulent Channel Flow at Pr=25: DNS-LES Approach

2007 ◽  
Author(s):  
Iztok Tiselj ◽  
Luka Sˇtrubelj
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Buffer Layer ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Temperature Profiles ◽  
Temperature Scales ◽  
Mean Temperature ◽  
The Mean

DNS-LES numerical simulations of a passive scalar field in the turbulent channel flow were performed at friction Reynolds number Re_Tau = 180 and Prandtl number Pr = 25. Direct numerical simulation is used for description of the velocity field. Temperature field is described with LES-like approach with the smallest resolved temperature scales equal to the smallest scales of the velocity field. The consistency of the applied physical modelling and pseudo-spectral scheme is tested with the grid refinement study (grid refine ∼3 times in each direction) and with comparison of the results with the existing DNS simulations of Schwertfirm and Manhart (2006) at the same conditions. The comparison shows that the proposed approach produces very accurate mean temperature profiles, heat transfer coefficients and other low-order moments of the turbulent thermal field. It is shown that the mean temperature profiles near the wall can be accurately predicted even when the temperature scales between the Batchelor and Kolmogorov scale are not resolved. The key to the success of the proposed approach lies in the fact that the large-scale structures govern the turbulent heat transfer at high Prandtl numbers, while the role of the sub-Kolmogorov temperature scales in the diffusive sublayer and the thermal buffer layer (y+<5) is practically negligible. The contribution of the sub-Kolmogorov thermal scales becomes relevant above the thermal buffer layer (y+>5), where the unresolved temperature scales affect spectra and RMS temperature fluctuations, but not the log-law shape of the mean temperature profile and the mean heat transfer coefficient.

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