DNS of fully developed turbulent heat transfer of a viscoelastic drag-reducing flow

A direct numerical simulation (DNS) of turbulent heat transfer in a channel flow with a Giesekus model was carried out to investigate turbulent heat transfer mechanism of a viscoelastic drag-reducing flow by additives. The configuration was a fully-developed turbulent channel flow with uniform heat flux imposed on both the walls. The temperature was considered as a passive scalar with the effect of buoyancy force neglected. The Reynolds number based on the friction velocity and half the channel height was 150. Statistical quantities such as root-mean-square temperature fluctuations, turbulent heat fluxes and turbulent Prandtl number were obtained and compared with those of a Newtonian fluid flow. Budget terms of the temperature variance and turbulent heat fluxes were also presented.     

Turbulent open channel flow with heat transfer subjected to the control of a spanwise travelling wave

Turbulent open channel flows with heat transfer subjected to the control of a spanwise travelling wave have been investigated by means of direct numerical simulation (DNS). The three-dimensional Navier–Stokes and energy equations are numerically solved using a fractional-step method. The spanwise travelling wave is induced by a body force that is confined within the viscous layer with its maximum at the bottom wall and decaying exponentially away from it. The objective of this study is to reveal the near-wall turbulence behaviours, the turbulent heat transfer, and thermal structures under the control of the spanwise travelling wave. Three typical frequencies of the spanwise travelling wave, i.e., high-, middle- and low-frequency, corresponding to the exciting periods at T⁺ = 25, 50 and 100, are investigated to reveal the dynamics of turbulent motions and heat transfer. The Prandtl number (Pr) varies from 1 up to 100. To elucidate the behaviours of turbulence statistics and heat transfer, some typical quantities, including the mean velocity, velocity and vorticity fluctuations, temperature and its fluctuation, turbulent heat fluxes, and the structures of the temperature fluctuation, are exhibited and analyzed.     

Radiation effects on mixed turbulent natural and forced convection in a horizontal channel using direct numerical simulation

The purpose of this study is to clarify the radiation effects on mixed turbulent convection in a horizontal channel. The present study provides turbulence statistics using direct numerical simulation (DNS) in an optically thin medium. When the radiation effect is considered, the flow structure and the temperature distribution in the channel change with an increase in the optical thickness of the fluid. The radiation effect changes the distributions of the temperature fluctuation intensity and the turbulent heat flux. These radiation effects on mixed convection can be clearly explained by the turbulence statistics obtained from the DNS results.     

New scaling of turbulence statistics for incompressible thermal channel flow with different total heat flux gradients

The scaling of turbulence statistics for wall-bounded thermal turbulent flow with different total heat flux gradients was investigated using direct numerical simulation (DNS) of an incompressible turbulent channel flow with passive scalar transport at the friction Reynolds number of 300 and the Prandtl number of 0.72. DNSs for four cases were performed, where the non-dimensional total heat flux gradients were −1, −0.5, 0 and +0.5. It was revealed that temperature variance and turbulent heat flux were well scaled by the local friction temperature. In addition, using the linear stress-heat flux model, it was shown that the appearance of the logarithmic temperature profile was attributed to the distribution of the turbulent Prandtl number.     

A spatially advancing turbulent flow and heat transfer in a curved channel

Direct numerical simulation was performed for a spatially advancing turbulent flow and heat transfer in a two‐dimensional curved channel, where one wall was heated to a constant temperature and the other wall was cooled to a different constant temperature. In the simulation, fully developed flow and temperature from the straight‐channel driver was passed through the inlet of the curved‐channel domain. The frictional Reynolds number was assigned 150, and the Prandtl number was given 0.71. Since the flow field was examined in the previous paper, the thermal features are mainly targeted in this paper. The turbulent heat flux showed trends consistent with a growing process of large‐scale vortices. In the curved part, the wall‐normal component of the turbulent heat flux was twice as large as the counterpart in the straight part, suggesting active heat transport of large‐scale vortices. In the inner side of the same section, temperature fluctuation was abnormally large compared with the modest fluctuation of the wall‐normal velocity. This was caused by the combined effect of the large‐scale motion of the vortices and the wide variation of the mean temperature; in such a temperature distribution, large‐scale ejection of the hot fluid near the outer wall, which is transported into the near inner‐wall region, should have a large impact on the thermal boundary layer near the inner wall. Wave number decomposition was conducted for various statistics, which showed that the contribution of the large‐scale vortex to the total turbulent heat flux normal to the wall reached roughly 80% inside the channel 135^° downstream from the curved‐channel inlet. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20275     

Direct numerical simulation of turbulent channel flow under stable density stratification

Direct numerical simulations are performed for a fully developed horizontal turbulent channel flow under stable density stratification. The skin-friction and the Nusselt number agree well with the experimental results. Internal gravity waves (IGW) are found to be built up in the core region, where the turbulent heat flux is suppressed drastically and the steep mean velocity and temperature gradients result. In the central region of the channel, the stable density stratification works as the virtual wall to block turbulent heat transfer. It is also found that the energy of IGW is transferred from the shear-induced turbulence through the pressure diffusion. With an increase in the stratification, the flow on one wall starts to become laminar, although it is still turbulent on the other.     

Scaling heat transfer in fully developed turbulent channel flow

An analysis is given for fully developed thermal transport through a wall-bounded turbulent fluid flow with constant heat flux supplied at the boundary. The analysis proceeds from the averaged heat equation and utilizes, as principal tools, various scaling considerations. The paper first provides an accounting of the relative dominance of the three terms in that averaged equation, based on existing DNS data. The results show a clear decomposition of the turbulent layer into zones, each with its characteristic transport mechanisms. There follows a theoretical treatment based on the concept of a scaling patch that justifies and greatly extends these empirical results. The primary hypothesis in this development is the monotone and limiting Peclet number dependence (at fixed Reynolds number) of the difference between the specially scaled centerline and wall temperatures. This fact is well corroborated by DNS data. A fairly complete qualitative and order-of-magnitude quantitative picture emerges for a complete range in Peclet numbers. It agrees with known empirical information. In a manner similar to previous analyses of turbulent fluid flow in a channel, conditions for the existence or nonexistence of logarithmic-like mean temperature profiles are established. Throughout the paper, the classical arguments based on an assumed overlapping of regions where the inner and outer scalings are valid are avoided.     

Superficial heat transfer by forced convection and radiation in a horizontal channel

This paper presents a numerical investigation of turbulent forced convective flow in a horizontal channel. An exchanger isothermal test plate is embedded in the lower wall, in the fully developed region of the flow close to the exit of the channel. Above this isothermal plate, on the upper surface, a black coated isothermally heating resistance facing downwards is installed. This absorbing surface provides a controlled radiative heat flux on the lower test plate. In this study, custom-built tangential gradient fluxmeters (TGFM) are used to provide local measurements of convective heat transfer so as to validate the numerical predictions. Then, parametric studies are carried out. The profiles for the heat flux are presented for different Reynolds numbers in the flow direction along the cold isothermal lower plate. Then, the influence of the presence of an obstacle, located on the lower surface, on the heat flux is also investigated. All numerical predictions are carried out with Fluent, previously calibrated against benchmark problems and experimental measurements. In the paper, special emphasis is given in the systematic comparison between experimental and numerical results.     

Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall

The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10¹². The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k–ε, k–ω, k–ω–SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 (2003) 3551–3572]. The k–ω–SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10⁹–10¹².     

Near-Wall Determination of the Turbulent Prandtl Number Based on Experiments,Numerical Simulation and Analytical Models

Abstract

The Reynolds-averaged computation of turbulent flow with heat transfer most commonly models the turbulent heat flux as directly related to the turbulent flux of momentum through the turbulent Prandtl number. Its significant deviation from a uniform bulk flow value for high molecular Prandtl numbers needs to be adequately described to predict accurately the heat transfer. The present study derives a model for the near-wall variation of this important parameter, used as input into an analytical solution of heated turbulent pipe flow. The basic functional form of the profile of the turbulent Prandtl number is determined from direct numerical simulations (DNS), and experimental data are used for model calibration. The analytically predicted Nusselt numbers agree very well with experimental measurements, proving the reliability of the proposed model for the turbulent Prandtl number also for Reynolds numbers well beyond the scope of DNS. The validation against experiments further highlights the significant effect of the temperature-dependent material properties of the considered high Prandtl number liquids. Numerical simulations often discard this aspect to reduce the computational effort. The present combination of DNS, analytical solution, and experiments appears as a convenient approach for modeling turbulent key quantities such as the turbulent Prandtl number, which is well applicable to other convective flow conditions and Prandtl number regimes, as well.     

Turbulent heat transfer in a channel flow with arbitrary directional system rotation

Arbitrary directional system rotation of a channel flow can be decomposed into simultaneous componential rotations in the three orthogonal directions. In order to study its effect on turbulent heat transfer, three typical cases, i.e., combined spanwise and streamwise (Case I), streamwise and wall-normal (Case II), and wall-normal and spanwise rotations (Case III), are simulated with two of the three coordinate-axial rotations imposed on the system. In Case I, the effect of spanwise rotation dominates the heat transfer mechanism when the two componential rotation rates are comparable. However, if the streamwise rotation is much stronger than the spanwise rotation, the turbulent heat transfer can be enhanced on the two walls, but more strikingly on the suction side. In Case II, even though no explicit spanwise rotation is imposed on the system, the combined rotations also bring the enhancement/reduction of turbulent heat transfer on the pressure/suction side, respectively, which is similar to that in a spanwise rotating channel flow. In Case III, the spanwise rotation effect is still obvious, however, its effect is reduced somewhat due to the redirection of the mean flow by the wall-normal rotation.     

Large-eddy simulation of turbulent heat convection in a spanwise rotating channel flow

In this paper, we investigate the effects of the Coriolis force in a heated plane channel flow subjected to spanwise rotation using the method of large-eddy simulation. We present both the general and simplified transport equations for the resolved turbulent stresses, which are essential for understanding the unique pattern of turbulent kinetic energy production in a rotating system. Numerical simulations are performed using primarily two dynamic subgrid-scale stress models and one dynamic subgrid-scale heat flux model; namely, the conventional dynamic model (DM) and a novel dynamic nonlinear model (DNM) for closure of the filtered momentum equation, and an advanced dynamic full linear tensor thermal diffusivity model (DFLTDM) for closure of the filtered thermal energy equation. The turbulent flow field studied herein is characterized by a Reynolds number Re_τ = 150 and various rotation numbers Ro_τ ranging from 0 to 7.5. In order to validate the LES approach, turbulent statistics obtained from the simulations are thoroughly compared with the available experimental results and direct numerical simulation (DNS) data. A detailed comparative study has been conducted in order to evaluate the performance of the DM and DNM in terms of their prediction of characteristic features of the velocity and temperature fields and their capability of reflecting both forward and backward scatter of kinetic energy between the filtered and subgrid scales.     

On a subgrid-scale heat flux model for large eddy simulation of turbulent thermal flow

A non-linear subgrid-scale (SGS) heat flux model is introduced in large eddy simulation for turbulent thermal flows. Unlike the linear isotropic eddy diffusivity model, the proposed model accounts for the SGS heat flux in terms of the large-scale strain-rate tensor and the temperature gradients. This is equivalent to using a tensor diffusivity. The model is to some extent similar to a scale-similarity model subjected to a Taylor expansion for the filtering operation. The formulation leading to the present proposal is discussed. The model is examined in LES for a buoyant flow in an infinite vertical channel with two differentially heated side walls. It is shown that the proposed model reproduces reasonable results as compared with the isotropic SGS diffusivity model and DNS data.     

DNS of turbulent heat transfer in a channel flow with a varying streamwise thermal boundary condition

Direct numerical simulation (DNS) was performed for the turbulent heat transfer in a channel flow. In the present study, the effect of the thermal boundary condition was examined. DNS was carried out for varying streamwise thermal boundary conditions (Re_τ = 180) with Pr = 0.71 to obtain statistical mean temperatures, temperature variances, budget terms, and time scale ratios. The results obtained indicate that the time scale ratio varies along the stream direction. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(4): 265–278, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20114     

非均匀热流下水平管内混合对流大涡模拟研究

针对以槽式太阳能集热器为背景的高密度、高度非均匀热流下水平管内的混合对流换热问题,采用大涡模拟方法,研究了热流密度非均匀性对水平管内混合对流瞬态涡结构、脉动强度、湍流热通量及局部平均壁温的影响;揭示了非均匀热流下自然对流对管内湍流特性的影响规律;提出了适用于不同热边界条件下管内混合对流换热的强化措施。结果表明:均匀热流时,自然对流会抑制管顶部的湍流脉动,使流动层流化,造成传热能力局部恶化;非均匀热流时,随着自然对流的增强,近壁面速度脉动强度先减小后增大,二次流逐渐增强,换热能力逐渐提高,故管内换热能力受湍流脉动与二次流协同影响;在自然对流影响下,均匀加热时管顶部可采用针对层流的强化换热措施,非均匀加热时需着重提高管底部高热流区域的湍流脉动与涡强度。     

Turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

Turbulent natural convection in a vertical parallel plate channel has been investigated both experimentally and numerically. The experimental channel is formed of a uniform temperature heater wall and an opposing glass wall. A fibre flow laser doppler anemometer (LDA) is used to measure velocity profiles along the channel. Simultaneous velocity and temperature profile measurements are made at the channel outlet. A commercial computational fluid dynamics (CFD) code is used to simulate heat transfer and fluid flow in the channel numerically. The code is customised building in some low Reynolds number (LRN) k–ε turbulence models. The numerical method used in this study is found to predict heat transfer and flow rate fairly accurately. It is also capable of capturing velocity and temperature profiles with some accuracy. Experimental and numerical data are presented comparatively in the form of velocity, temperature, and turbulent kinetic energy profiles along the channel for a case. Correlating equations are obtained from the numerical results for heat transfer and induced flow rate and, are presented graphically comparing with other studies available in the literature.     

Turbulent transport from continuous sources at the wall of a channel

Dispersion from a continuous line source located at the wall of a turbulent channel and transport over a step change in wall heat flux are studied for fluids with Prandtl numbers between 0.1 and 2400. Direct Numerical Simulation is used to develop the velocity flow field, which is then coupled with a particle tracking algorithm to describe the behavior of heat or mass markers released from instantaneous sources on the wall. The positions in time and space of these markers, which have been available as a database created by Papavassiliou and Hanratty [Int. J. Heat Mass Transfer 40 (6) (1997) 1303], are used as the building block for the study of passive scalar transport from the wall of the channel. Qualitative and quantitative results are obtained with particular emphasis on transport parameters from the wall.     

Assessment of mean and fluctuating velocity and temperature of CuO/water nanofluid in a horizontal channel: Large eddy simulation

Abstract

A comprehensive investigation applying the large eddy simulation approach to turbulent forced convection of CuO/water nanofluid flowing through a horizontal channel is carried out. Dealing with the sub-grid scale stress tensor and heat flux vector, the wall-adopting local eddy-viscosity model is employed. The periodic boundary condition is imposed to the streamwise and spanwise directions, while the no-slip and constant heat flux are applied to the walls. The results indicate that adding nanoparticles into the base fluid increases the dimensionless mean velocity and fluctuations of velocity and temperature. This increment is more evident for turbulent Reynolds stress and turbulent heat flux in the streamwise direction than the other directions. Therefore, higher energy is transferred between nanofluid layers which results in a higher amount of heat transfer than the pure water. It is also observed that the nanoparticles enhance the turbulence energy at all frequencies, and the decay in the fluctuations occurs at the higher wavenumbers.     

Numerical Analysis of Thermal and Dynamic Behavior of a Roof Solar Collector

In some regions with a specific climate, summer comfort in the rooms located below the roof becomes critical if the roof system is not well designed. In order to analyze the efficiency of this system a numerical model was developed. This model is based on the study of the natural convection coupled with radiative heat transfer in an inclined air channel. The configuration studied is an inclined channel formed by two parallel plates. The upper and lower plates were maintained at fixed temperatures. The air flow in the channel which is due to the buoyancy forces is fully turbulent and the turbulence was modeled by using the k‐ε model. Some numerical results obtained were validated using the experimental works of Khedari and colleagues and those of Nouanégué and colleagues. The effect of physical and geometrical parameters and the radiative heat transfer on the channel behavior is shown. Correlations for Nusselt numbers and air flow rate were obtained as functions of the geometric parameters and the Rayleigh number. These correlations can be used in other models that represent this system.     

Conjugate heat transfer measurements with single-phase and water flow boiling in a single-side heated monoblock flow channel

Optimized and robust designs of one-side heated plasma-facing components and other heat flux removal components are dependent on conjugate heat transfer. In the present case, the conjugate heat transfer involved measuring the local distributions of the inside wall temperature and heat flux in a single-side heated monoblock flow channel with: (1) peripheral (radial and circumferential) heat transfer; and, (2) coupled internal turbulent, forced convective single-phase flow and flow boiling. For the first time, multi-dimensional boiling curves have been measured for a single-side heated monoblock flow channel. Using a thermal hydraulic diameter as the characteristic dimension in select correlations for the highest mass velocity (3.2 Mg/m² s), good agreement was obtained. At lower mass velocities, only the single-phase correlations agreed better with the data for the averaged net incident heat flux vs the inside channel wall temperature. Hence, additional correlation development and adaptation are needed for single-side heated monoblocks with peripheral heat transfer.