Numerical analysis of heat transfer in pulsating turbulent flow in a pipe

Convection heat transfer in pulsating turbulent flow with large velocity oscillating amplitudes in a pipe at constant wall temperature is numerically studied. A low-Reynolds-number (LRN) k–ε turbulent model is used in the turbulence modeling. The model analysis indicates that Womersley number is a very important parameter in the study of pulsating flow and heat transfer. Flow and heat transfer in a wide range of process parameters are investigated to reveal the velocity and temperature characteristics of the flow. The numerical calculation results show that in a pulsating turbulent flow there is an optimum Womersley number at which heat transfer is maximally enhanced. Both larger amplitude of velocity oscillation and flow reversal in the pulsating turbulent flow also greatly promote the heat transfer enhancement.     

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.     

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。     

The effect of surface renewal due to largescale eddies on jet impingement heat transfer

The mechanism for the enhancement of stagnation-point heat transfer was explored analyzing the large-scale turbulent structures of an impinging round jet by a statistical technique with conditional sampling. It has been found that large-scale eddies impinging on the heat transfer surfaces produce a turbulent surface-renewal effect dominant for the enhancement of the jet impingement heat transfer. The effect of heat transfer enhancement can be described in terms of the turbulent Reynolds and Strouhal numbers based on the characteristic turbulence intensity and frequency of the large-scale eddies impinging on the stagnation-point boundary layer.     

Effects of free stream turbulence on turbulent boundary layer on a flat plate with zero pressure gradient (part V: The calculation of heat transfer)

The effects of free stream turbulence on turbulent heat transfer were calculated by using a two-equation model for heat transfer. The calculations were performed with respect to turbulent boundary layers along a flat plate with a uniform wall heat flux. From the measured values of near-wall thermal turbulence, an improvement on turbulence model function has been made in the turbulent heat flux equation. The results for the heat transfer rate, logarithmic temperature profile distribution, the eddy diffusivity of heat, and the turbulent Prandtl number agreed comparatively well with the experimental values. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 97–106, 1997     

Heat transfer from immersed vertical tube in a fluidized bed of group A particles near the transition to the turbulent fluidization flow regime

Experiments were performed in a 0.29 m ID fluidization column to investigate heat transfer from a vertical tube immersed in a bed of 70 μm FCC particles in the range of superficial velocities close to the transition to the turbulent fluidization regime. The results show that the transition is a gradual process and that the changing hydrodynamics affect the heat transfer. The highest heat transfer coefficients were found in the range of superficial gas velocities where the transition to turbulent regime occurred. Radial profiles of heat transfer coefficient were almost flat in the turbulent fluidization regime and changed very little with increasing superficial gas velocity.     

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.     

Heat transfer and hydraulic resistance of supercritical-pressure coolants. Part I: Specifics of thermophysical properties of supercritical pressure fluids and turbulent heat transfer under heating conditions in round tubes (state of the art)

The specifics of the thermophysical properties of single-phase supercritical pressure (SCP) coolants and the typical ranges of their thermodynamic state that determine the peculiarities of their turbulent heat transfer are considered. An assessment of the effect that dissolved gases with low critical parameters have on water and carbon dioxide properties is given. A brief analysis is presented of experimental studies on heat transfer of turbulent flows of SCP fluids in tubes when heating. Specific features of typical heat transfer modes (normal, deteriorated, and improved) are pointed out. The existing concepts concerning the nature of heat transfer deterioration are discussed. A simple classification of heat transfer regimes under high heat loads is proposed, which makes it possible to determine the reasons for and assess the degree of danger of heat transfer deterioration     

Deteriorated turbulent heat transfer (DTHT) of gas up-flow in a circular tube: Heat transfer correlations

This paper presents comparisons of recent experimental data, presented in a companion paper, to the existing correlations for heat transfer in various gas flow regimes and development of more accurate new correlations. The existing correlation of Celeta et al. showed the best agreement with the data in the turbulent heat transfer regime, while most of the existing correlations for laminar heat transfer showed unsuccessful predictions. Three new sets of correlations, each covering the mixed convection laminar, normal turbulent and deteriorated turbulent heat transfer (DTHT) regimes for heated gas up-flow, have been developed to agree better with the data in each regime.     

On the role of inserts in forced convection heat transfer augmentation

The role of inserts in internal forced convection has been widely acknowledged as a passive device in the heat transfer enhancement. The present study is aimed to empirically investigate the heat transfer enhancement in a tube fitted with a square-cut circular ring insert in the transitional and the fully turbulent flow regimes. By performing an in-depth analysis on the experimental data, the role of insert has been quantified by deriving a new non-dimensional group. This new non-dimensional group is proposed to characterize the effect of inserts on the heat transfer enhancement. While the findings show the incorporation of insert in the flow passage enhances the heat transfer rate, the characteristics of the flow in the transitional and the fully turbulent flow regimes induced by the effect of insert are distinct. The new non-dimensional group provides interesting insights into the role played by the insert. The physical significance of the non-dimensional number which provides a measure of the change of enthalpy relative to the change of flow energy in the flow direction can be used to explain the decrease of heat transfer augmentation in the turbulent flow regime relative to the transitional flow regime. Based on the analysis of the non-dimensional group, it can be deduced that the contribution of the axial pressure drop in the heat transfer augmentation is marginal albeit not negligible compared to the temperature rise in the characterization of the heat transfer augmentation with the incorporation of insert. The evaluation of heat transfer augmentation efficiency based on the rate of change of internal energy shows that the performance efficiency of an insert would be identical in different flow regimes, contradictory to the widely held axiom that the effect induced by the insert on the heat transfer augmentation diminishes in the turbulent flow regime.     

Turbulent heat transfer in a horizontal helically coiled tube

An experiment has been conducted in detail to study the turbulent heat transfer in horizontal helically coiled tubes over a wide range of experimental parameters. We found that the enhancement of heat transfer in the coils results from the effects of turbulent and secondary flows. With Reynolds number increasing to a high level, the contribution of the secondary flow becomes less to enhance heat transfer, and the average heat transfer coefficient of the coil is closer to that in straight tubes under the same conditions. The local heat transfer coefficients are not evenly distributed along both the tube axis and the periphery on the cross section. The local heat transfer coefficients on the outside are three or four times those on the inside, which is half of the average heat transfer. A correlation is proposed to describe the distribution of the heat transfer coefficients at a cross section. The average cross-section heat transfer coefficients are distributed along the tube axis. The average value at the outlet section should not be taken as the average heat transfer coefficient. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 395–403, 1999     

Numerical investigation on supercritical turbulent heat transfer of copper/n-decane nanofluid inside a miniature tube

To evaluate the potential benefits of kerosene-based nanofluids as coolants for regenerative cooling system, a detailed numerical study of the turbulent heat transfer of copper/n-decane nanofluid flowing inside a miniature cooling tube at supercritical pressures has been conducted. Numerical results reveal that copper nanoparticles can significantly improve heat transfer performance in the entire cooling tube. This can be explained by the fundamental mechanism that within the near-wall turbulent flow region, the reduction of nanofluid kinematic viscosity leads to increased turbulent thermal conductivity and consequently causes heat transfer enhancement. Moreover, heat transfer deterioration phenomenon is delayed or weakened by nanoparticles, and the overall heat transfer performance of the base fluid has been improved. Results indicate potential advantages of kerosene nanofluids as coolants for regenerative engine cooling applications.     

Study of Variable Turbulent Prandtl Number Model for Heat Transfer to Supercritical Fluids in Vertical Tubes

In order to improve the prediction performance of the numerical simulations for heat transfer of supercritical pressure fluids, a variable turbulent Prandtl number (Pr_t) model for vertical upward flow at supercritical pressures was developed in this study. The effects of Pr_t on the numerical simulation were analyzed, especially for the heat transfer deterioration conditions. Based on the analyses, the turbulent Prandtl number was modeled as a function of the turbulent viscosity ratio and molecular Prandtl number. The model was evaluated using experimental heat transfer data of CO₂, water and Freon. The wall temperatures, including the heat transfer deterioration cases, were more accurately predicted by this model than by traditional numerical calculations with a constant Pr_t. By analyzing the predicted results with and without the variable Pr_t model, it was found that the predicted velocity distribution and turbulent mixing characteristics with the variable Pr_t model are quite different from that predicted by a constant Pr_t. When heat transfer deterioration occurs, the radial velocity profile deviates from the log-law profile and the restrained turbulent mixing then leads to the deteriorated heat transfer.     

Heat Transfer Characteristics of Printed Circuit Heat Exchanger with Supercritical Carbon Dioxide and Molten Salt

Molten salt and supercritical carbon dioxide (S-CO_2) are important high temperature heat transfer media,but molten salt/S-CO_2 heat exchanger has been seldom reported.In present paper,heat transfer in printed circuit heat exchanger (PCHE) with molten salt and S-CO_2 is simulated and analyzed.Since S-CO_2 can be drove along passage wall by strong buoyancy force with large density difference,its heat transfer is enhanced by natural convection.In inlet region,natural convection weakens along flow direction with decreasing Richardson number,and the thermal boundary layer becomes thicker,so local heat transfer coefficient of S-CO_2 significantly decreases.In outlet region,turbulent kinetic energy gradually increases,and then heat transfer coefficient increases for turbulent heat transfer enhancement.Compared with transcritical CO_2 with lower inlet temperature,local heat transfer coefficient of S-CO_2 near inlet is lower for smaller Richardson number,while it will be higher for larger turbulent kinetic energy near outlet.Performance of PCHE is mainly determined by the pressure drop in molten salt passage and the heat transfer resistance in S-CO_2 passage.When molten salt passage width increases,molten salt pressure drop significantly decreases,and overall heat transfer coefficient slightly changes,so the comprehensive performance of PCHE is improved.As a result,PCHE unit with three semicircular passages and one semi-elliptic passage has better performance.     

Large eddy simulation of turbulent flow and heat transfer in outward transverse and helically corrugated tubes

Turbulent flow and heat transfer in outward transverse and helically corrugated tubes are performed with large eddy simulation by the ANSYS Fluent software. The prediction accuracy is validated by comparison with experimental data and empirical correlations for a wavy surface wall and smooth tube, respectively. The turbulent flow patterns, local heat transfer, and friction factor are discussed. The results show that the secondary and turbulent eddies are inhibited by the spiral flow. Otherwise, the flow impact of the wall is the key factor for heat transfer enhancement, and the spiral flow has of small effect on heat transfer performance, however it can decrease the flow resistance significantly. The overall heat transfer performance for the helical corrugated tube is 1.23, which is superior to the value of 1.18 for the transverse corrugated tube.     

Heat transfer enhancement of turbulent duct flow by vortex generators attached to a large eddy break-up manipulator

An experimental study was conducted to investigate the characteristics of wall heat transfer and momentum loss for turbulent duct flow disturbed by insertion of a complicated body composed of a Large Eddy Break-Up (LEBU) plate and winglet-type vortex generators. It was found that the LEBU plate reduces the wall heat transfer in the region downstream of the insertion position and that this suppression of heat transfer could be recovered by attaching vortex generators to the LEBU plate, i.e., conspicuous heat transfer enhancement was achieved over a large streamwise distance. The spatial distribution of the heat transfer coefficient obtained shows the same features as that observed in a previous study of a flat plate turbulent boundary layer. Therefore, the flow and thermal field structure of the turbulent duct flow downstream of the inserted body should be basically the same as those in the same region of the turbulent boundary layer. The effect of a notch, open in the LEBU plate behind the vortex generator, on heat transfer and pressure drop was also examined. The notch simulates the hole of the LEBU plate to be produced in a practical application when a vortex generator is produced by punching from the original plain LEBU plate. It was found that a vortex generator with an open notch works best in augmenting the wall heat transfer and also in suppressing the increase of momentum loss. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 189–200, 1999     

套管换热器对流换热的数值模拟研究

本文建立了一种复杂的数学模型用于预测套管式换热器内流体的流动及传热特性。数学模型包括计算流体力学模型和计算传热学模型。其中,计算传热学模型中的湍流扩散系数是利用温度方差t2和温度方差耗散率εt来求解,而不是利用通常采用的Pr数假设值或实验测定值来求解。为验证新建立模型预测结果的准确性,本文将数值模拟结果与文献中的实验结果进行了比较,结果吻合较好。     

Roughness enhanced mechanism for turbulent convective heat transfer

The mechanism of turbulent convective heat transfer enhancement was experimentally investigated by measuring the heat transfer in two dimensional roughness tubes with different roughness heights at various Reynolds numbers. The results show that there is a maximum Nusselt number ratio (Nu/Nu₀) for a fixed roughness height with increasing Reynolds numbers. For water as working fluid, heat transfer can hardly be increased when the roughness height is lower than the thickness of the viscous sublayer, and both heat transfer and flow friction begin to increase when the roughness height is higher than the viscous sublayer. When the roughness height is more than five times of the viscous sublayer thickness, the flow friction begins to increase sharply but heat transfer is slowly enhanced. So the best heat transfer enhancement for a given pumping power is reached when the roughness height is about three times of the viscous sublayer thickness. The Prandtl number influences to the turbulent heat transfer enhancement by roughness were also analyzed.     

Application of a k-ε Model to Heat Transfer in Impinging Flows

Local heat transfer is predicted in turbulent axisymmetric jets, impinging onto a flat plate. A non-linear k-e model is used, in which both the constitutive law for the turbulent stresses and the transport equation for the turbulent dissipation rate e have an important contribution in the improved heat transfer predictions. The shape of the Nusselt number profiles, expressing dimensionless heat transfer, as well as the stagnation point value, are well predicted for different distances between the nozzle exit and the plate. Accurate flow field predictions are the basis for good heat transfer predictions. For a fixed Reynolds number, the influence of the nozzle-plate distance is well captured. For a fixed distance, the influence of the Reynolds number is correctly reproduced. Comparisons are made to a low-Reynolds standard k-e model and the v2-f model. A thorough discussion is found in [4]. Only a summary of those results is discussed here, while some new results are also presented.     

Approximate solution to the natural convection heat transfer from a vertical plate

A new model for laminar natural convection heat transfer between an isothermal vertical plate to a power-law fluid is proposed. The difficulty caused by the fact that the momentum and energy equations are coupled is avoided by introducing an approximation based on the partial similarity between the velocity fields for forced and natural convections. The model proposed in this work agrees well with the available experimental data and correlations. Further, we have extended the analysis to turbulent natural convection heat transfer. The predicted turbulent heat transfer rates are in satisfactory agreement with the data and the correlations published in the literature.