Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

A numerical study of turbulent flow and conjugate heat transfer in concentric annuli with moving inner rod

A numerical study is conducted to investigate turbulent flow and conjugate heat transfer in a concentric annulus with a heated inner cylinder moving in the streamwise direction. A modified two-equation k-ε model with low Reynolds number treatment near wall is employed to model the Reynolds stress and turbulent thermal field which are based on Boussinesq’s approximation. The governing equations are numerically resolved by means of a hybrid finite analysis method. A uniform inlet flow and thermal conditions are specified to consider the effects of entrance of both solid and fluid regions. For a constant Prandtl number of 6.99 of water flow, calculating results of the time-averaged streamwise velocity, turbulent viscosity and temperature field are obtained for the Reynolds numbers from 1.0 × 10⁴ to 5.0 × 10⁵, rod velocity ratio between 0 and 1.0, and the radius ratio ranging from 0.286 to 0.750. The parametric studies show that the bigger rod speed ratio or the radius ratio is, the temperature is higher within solid rod. For a certain absolute rod speed, temperature profile diminishes at both sides of solid rod and fluid as Reynolds number grows. Numerical results also show that compared with the case of β=0 where solid rod is stationary, for large rod speed ratio the averaged axial velocity and turbulent viscosity profiles have substantial deformations, that is, the gradient of averaged axial velocity and turbulent viscosity near rod surface greatly reduced by the axial movement of solid rod.     

The prediction of turbulent swirling jet flow

A space marching integration procedure is used to solve the Reynolds equations governing the axisymmetric incompressible turbulent swirling jet flow. Turbulence is modelled by the k−ε model with an isotropic turbulent viscosity. Besides mean velocity field, turbulent properties—such as Reynolds stresses, turbulent kinetic energy and dissipation rate—are obtained and the results are compared with experimental data. Agreement is quite encouraging and shows that the assumption of isotropic turbulent viscosity seems plausible.     

岛屿地貌单元的湍流能耗物理模型试验

岛屿地貌单元是珠江三角洲发育演变过程中的沉积核心,研究其消能机制,对理解河口动力过程及三角洲发育演变有重要意义。通过建立岛屿地貌单元的湍流能耗特性概化物理模型,基于16 MHz ADV采集高频流速数据,统计了时均及湍流特征量,并利用惯性耗散法分析了岛屿地貌单元的湍流动能耗率。结果表明,相同控制条件下岛屿地貌单元的形态阻力致使尾流中紊动强度量值为明渠的2~3倍,湍流剪切应力及湍流动能较明渠水流的大近1个数量级,湍流动能耗散率比明渠水流湍流动能耗散率大1~2个数量级。岛屿地貌单元的局部形态阻力导致尾流时均流速的空间梯度、切应力增大是湍流能耗率增大的原因。岛屿地貌单元的汇流作用增加了下游尾流区的水流掺混,并在尾流区域形成大量微尺度涡,导致区域湍流能耗作用增强,有利于岛屿沉积核心发育。研究成果有助于理解河口动力及三角洲的发育演变过程。     

On temperature prediction at low Re turbulent flows using the Churchill turbulent heat flux correlation

The present work investigates the prediction of mean temperature profiles in turbulent channel flow using the fraction of the heat flux due to turbulence. According to this new model, suggested by Churchill and co-workers, fully developed flow and convection can be expressed as local fractions of the shear stress and the heat flux density due to turbulent fluctuations, respectively. The fully developed temperature profile can be predicted if the velocity field and the turbulent Prandtl number are known. Temperature profiles for Pr between 0.01 and 50,000 have been obtained theoretically and with simulations through the use of Lagrangian methods for both plane Poiseuille flow and plane Couette flow. The half channel height for all simulations was h = 150 in wall units. The theoretical predictions have been found to agree with the data quite well for a range of Pr, but there are deviations at very high Pr.     

Mixed convection flow in an inclined enclosure under magnetic field with thermal radiation and heat generation

The influence of thermal radiation and heat generation on an unsteady two-dimensional natural convection flow in an inclined enclosure heated from one side and cooled from the adjacent side under the influence of a magnetic field using staggered grid finite-difference technique has been studied. The governing equations have been solved numerically for streamlines, isotherms, local Nusselt numbers and the average Nusselt number for various values of thermal radiation and heat generation parameters by considering three different inclination angles and magnetic field directions, keeping the aspect ratio fixed. The results indicate that the flow pattern and temperature fields are significantly dependent on the above mentioned parameters. It is found that magnetic field suppresses the convection flow and its direction influences the flow pattern which results in the appearance of inner loop and multiple eddies.     

The role of low temperature fuel chemistry on turbulent flame propagation

A new high temperature, high Reynolds number, Reactor Assisted Turbulent Slot (RATS) burner has been developed to investigate turbulent flame regimes and burning rates for large hydrocarbon transportation fuels, which exhibit strong low temperature chemistry behavior. The turbulent flow characteristics are quantified using hot wire anemometry. The turbulent flame structures and burning velocities of n-heptane/air mixtures are measured by using planar laser induced fluorescence of OH and CH₂O with reactant temperatures spanning from 400 K to 700 K. It is found for the first time that for n-heptane/air mixtures there are four unique turbulent flame regimes, a conventional chemically-frozen-flow regime, a low-temperature-ignition regime, a transitional regime between the low- to high-temperature-ignition regimes, and a high-temperature-ignition regime, depending on the initial reactant temperature and heated flow residence time prior to the flame. The turbulent burning velocities have been measured for the first two regimes, chemically-frozen-flow and low-temperature-ignition regimes, in order to quantitatively address the role of low temperature ignition on the turbulent burning velocity. In the latter case, large amount of CH₂O formation has been observed in the pre-flame zone, signaling a significant change in the reactant composition and chemistry. At a given reactant temperature and turbulent intensity, the normalized turbulent burning velocities can be varied depending on the extent of low temperature fuel oxidation by varying the heated flow residence time and reactant temperature. The present results suggest that contrary to the previous studies, the turbulent flame regimes and burning velocities for fuels with low temperature chemistry may not be uniquely defined at elevated temperatures.     

Four-equation turbulence model for prediction of the turbulent boundary layer affected by buoyancy force over a flat plate

Turbulent convective heat transfer with appreciable buoyancy effect over a heated or cooled horizontal flat plate is numerically analyzed by solving four equations for mean square temperature variance , its rate of destruction _θ, turbulent kinetic energy κ and the rate of kinetic energy dissipation . Turbulent time-scale ratio R of temperature fluctuations relative to velocity fluctuations defined by is found to vary widely across the boundary layer. For both highly stable and highly unstable conditions, the ‘four-equation’ model yields better results for mean temperature profile and surface heat flux than the two-equation model. It is also found that the magnitude of thermal von Karman constant κ_θ is not a universal constant but it depends on the thermal stratification of the boundary layer.     

Forced turbulent heat convection in a square duct with non-uniform wall temperature

In the present work, the numerical simulation to calculate the problem of the turbulent convection with non-uniform wall temperature in a square cross-section duct was adopted. To solve this problem some assumptions for the flow, such as: the condition of fully developed turbulence and incompressible flow have been assumed. The methodology of the dimensionless energy equation was used to calculate the fluid temperature field in the square cross-section in function of the non-uniform wall temperatures prescribed. Numerical simulations were done using two different turbulent models to resolve the momentum equations and two more models to resolve the energy equation. The models of turbulence k-ε Nonlinear Eddy Viscosity Model (NLEVM) and the Reynolds Stress Model (RSM) were used to determine the turbulent intensities as well as the profiles of axial and secondary mean velocities. The turbulence model RSM was simulated using a commercial software. The thermal field was determined from other two models: Simple Eddy Diffusivity (SED), based in the hypothesis of the constant turbulent Prandtl number; and Generalized Gradient Diffusion Hypothesis (GGDH). In this last model, as the turbulent heat transfer depends on the shear tensions, the anisotropy is considered. These two last equation models of the energy equation of the fluid have been implemented in FORTRAN, a code of programming. The performances of the models were evaluated by validating them based in the experimental and numerical results published in the literature. Two important parameters of great interest in engineering are presented: the friction factor and the Nusselt number. The results of this investigation allow the evaluation of the behavior of the turbulent flow and convective heat fluxes for different square cross-sectional sections throughout the direction of the main flow, which is mainly influenced by the temperature distribution in the wall.     

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.     

Prevision numérique de la convection forcée turbulente dans une cavité bidimensionnelle entrainée

Turbulent flow and associated heat transfer in confined geometry (driven closed cavity flow in two dimensions) has been studied using a finite-difference numerical method in primitive variables. Turbulence modelling is based on one point closures derived from the classicalk-ε model. Calculated mean velocity and turbulent kinetic energy are compared with available experimental data. In spite of its limitations, the k-ε model proved to be a useful tool for prediction of global quantities. The case of forced heat convection with fixed wall temperature is considered. Mean temperature field and overall thermal properties of the cavity flow are studied. Correlations giving Nusselt numbers at each face of the cavity versus Reynolds number are deduced from numerical results, they sum up mean transfer properties of such a flow configuration.     

Computational prediction of a slightly heated turbulent rectangular jet discharged into a narrow channel crossflow using two different turbulence models

A computational investigation of three-dimensional mean flow field resulting due to the interaction of a rectangular heated jet issuing into a narrow channel crossflow has been reported in the present paper. The jet discharge slot spans more than 55% of the crossflow channel bed, leaving a small clearance between the jet edge and sidewalls. Such flow configurations are encountered in several industrial processes such as mixing product streams, drying product streams, etc. The objective of the present work was to carry out a detailed investigation of the mean flow field and flow structure, which could not be obtained in a similar two-dimensional experimental work reported in the literature. The commercial code FLUENT 6.2.16 based on the finite volume method was used to predict the mean flow and temperature fields for the jet to crossflow velocity ratio (R) = 6. Two different turbulence models, namely, Reynolds-stress transport model (RSTM) and the standard k–ε model, were used for the computations. Different terms of the Reynolds-stress transport equation were modeled based on the proposals in the literature that are appropriate for the important flow features of the present configuration. Important flow features predicted by the two models, such as the formation of different vortical structures and their effects on the flow field are discussed. Some predicted results are compared with the available experimental data reported in the literature. The predicted mean and turbulent flow properties are shown to be in good agreement with the experimental data. However, the performance of RSTM is found to be better than that of the standard k–ε model.     

Production of hot air with quasi uniform temperature using concentrated solar radiation

The design of a hot air solar generator for different uses has been simulated while investigating the flow induced by a hot disc placed at the entrance of the open ended vertical cylinder. Ambient air (Pr = 0.7) enters the bottom of the cylinder with constant velocity and temperature, and flows up through the cylinder as a result of natural convection. The cylindrical wall is heated by thermal radiation emitted by the disc. The pressure drop due to acceleration of the flow to the cylinder-inlet causes the appearance of thermosyphon effect around the thermal plume. At the top part of the cylinder, the flow exploration shows the full development of the turbulence and the uniformity of thermal and hydrodynamic fields. The study of the thermal spectral density indicates that the turbulent structures seem to be sufficiently small not to be sensitive to viscosity, but large enough to be sensitive to Archimedes effects.     

Reduced-order modeling of turbulent forced convection with parametric conditions

Accurate reduced-order models of turbulent flows have been traditionally constructed with the proper orthogonal decomposition (POD), however the method has been limited to prototypical flows over a narrow parameter range. An orthogonal complement subspace method is developed here to treat inhomogeneous boundary conditions while implicitly coupling the velocity and temperature fields of turbulent convection. A new flux matching procedure is formulated as a state space residual series expansion to efficiently model parameter dependent convection, greatly extending the utility of the reduced-order modeling framework. An illustrative test case of turbulent channel flow over heated blocks shows flow and thermal models with 95% accuracy over the domain can be produced, while simultaneously reducing the number of degrees of freedom by a factor of 10³. Error bounds are formulated and provide a posteriori error estimates for the reduced-order model.     

DNS of turbulent thermal boundary layers up to Reθ = 2300

A technique, based on the Lund et al. (1998) [1] approach, is introduced in order to numerically prescribe time-dependent turbulent inflow conditions in spatially-developing thermal boundary layers. A major difference with Lund’s approach is that the new multi-scale approach considers different scaling laws for the inner and outer parts of the boundary layer. Direct numerical simulations (DNS) are performed for incompressible zero (ZPG) and adverse (APG) pressure gradient flows. To the best of our knowledge, the present DNS in ZPG flows at a momentum thickness Reynolds numbers (Re_θ) of 2300 represents the evolving thermal boundary layer simulations at the highest Re_θ in the turbulence community. The temperature is treated as a passive scalar with isothermal walls as a boundary condition and a molecular Prandtl number of 0.71. The predicted Stanton number shows fairly good agreement with empirical correlations, and experimental and numerical data from the literature. Moreover, the influences of the Reynolds number and the APG strength on thermal parameters are also examined. Furthermore, the budget of the temperature variance shows a significant increase of production, turbulent diffusion, and dissipation in the buffer layer at higher Reynolds numbers. The main effects of adverse pressure gradients on the temperature field are manifested by a decreasing trend of thermal fluctuations but an increasing trend of the wall-normal turbulent heat fluxes when normalized by wall units as the APG strength is augmented.     

Single-phase hybrid micro-channel/micro-jet impingement cooling

A new hybrid cooling scheme is proposed for high-flux thermal management of electronic and power devices. This scheme combines the cooling benefits of micro-channel flow and micro-jet impingement with those of indirect refrigeration cooling. Experiments were performed to assess single-phase cooling performance using HFE 7100 as working fluid. Excellent predictions were achieved using the standard k–ε model. The proposed cooling scheme is shown to involve complex interactions of impinging jets with micro-channel flow. Increasing jet velocity allows jets to penetrate the micro-channel flow toward the heated surface, especially in shallow micro-channels, greatly decreasing wall temperature. Despite the relatively poor thermophysical properties of HFE 7100, the proposed cooling scheme facilitated the dissipation of 304.9 W/cm² without phase change; further improvement is possible by increasing jet velocity and/or decreasing coolant temperature. In addition to the numerical predictions, a superpositioning technique is introduced that partitions the heat transfer surface into zones that are each dominated by a different heat transfer mechanism, and assigning a different heat transfer coefficient value to each zone. Using this technique, a new correlation is developed that fits the data with a mean absolute error of 6.04%.     

Numerical simulation of transient 3-D turbulent heated jet into crossflow in a thick-wall T-junction pipe

The present work is to investigate the transient three-dimensional heated turbulent jet into crossflow in a thickwall T-junction pipe using CFD package.Two cases with the jet-to-crossflow velocity ratio of 0.05 and 0.5 are computed,with a finite-volume method utilizing k-ε turbulent model.Comparison of the steady-state computations with measured data shows good qualitative agreement.Transient process of injection is simulated to examine the thermal shock on the T-junction component.Temporal temperature of the component is acquired by thermal coupling with the fluid.Via analysis of the flow and thermal characteristics,factors causing the thermal shock are studied.Optimal flow rates are discussed to reduce the thermal shock.     

Production of hydrogen by simple impingement of a turbulent jet of steam upon a high temperature zirconia surface

The present paper describes the first results of experiments for the production of hydrogen by simple impingement of a turbulent jet of steam on a zirconia surface heated at the focus of an image furnace. Experiments were made by varying the target temperature (2200–2500 K), the steam flow rate and the nozzle to target distance. The reaction is likely to occur in a thin thermal boundary layer close to the surface or by a partially heterogeneous wall dissociation. The results compare favorably with those of other methods using secondary cold turbulent jets of gas for quenching: less steam is wasted (no quenching device) and the available energy for heating the reactants is better used (thermal boundary layer concept).     

Depth-averaged turbulent heat and fluid flow in a vegetated porous medium

In this article, the latest developments of porous media science are used in order to simulate heat and fluid flow in a non-flexible vegetated porous media. Vegetation porosity and density at the domain interior are redefined. The same strategy is then applied in order to define the boundary porosity near the bed and water surface. Regarding the vegetation arrangement in natural streams and flumes, three different models are suggested for calculating the porosity near other boundaries. The microscopic time-mean secondary force in momentum equations is modified for a vegetated porous media and its macroscopic form is derived. A dissipation source term is derived and, it is added to vorticity equation in order to take account of vegetation damping effect on secondary flows. The effect of this dissipation source term on the absolute magnitude of vorticity and velocity field is then investigated. Application of a high Reynolds number turbulence model to turbulent flow in partially vegetated open channels is numerically examined. A model is suggested for taking account of vegetation material on heat flux through walls in a vegetated porous media. The thermal diffusion due to the porosity gradient is modeled and, the contribution of this porosity-induced heat flux on temperature field is investigated. The effect of laminar thermal dispersion on temperature field is also investigated at low stem Reynolds number.