Reynolds averaged simulation of flow and heat transfer in ribbed ducts

The accuracy of modern eddy-viscosity type turbulence models in predicting turbulent flows and heat transfer in complex passages is investigated. The particular geometries of interest here are those related to turbine blade cooling systems. This paper presents numerical data from the calculation of the turbulent flow field and heat transfer in two-dimensional (2D) cavities and three-dimensional (3D) ribbed ducts. It is found that heat transfer predictions obtained using the v²–f turbulence model for the 2D cavity are in good agreement with experimental data. However, there is only fair agreement with experimental data for the 3D ribbed duct. On the wall of the duct where ribs exist, predicted heat transfer agrees well with experimental data for all configurations (different streamwise rib spacing and the cavity depth) considered in this paper. But heat transfer predictions on the smooth-side wall do not concur with the experimental data. Evidence is provided that this is mainly due to the presence of strong secondary flow structures which might not be properly simulated with turbulence models based on eddy viscosity.     

An analytical wall-function for recirculating and impinging turbulent heat transfer

The performance of the analytical wall-function (AWF) of Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002, Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160.] is improved for predicting turbulent heat transfer in recirculating and impinging flows. Since constant parameters of the eddy viscosity formula were used to derive the AWF, the prediction accuracy of the original AWF tends to deteriorate in complex flows where those parameters need changing according to the local turbulence. To overcome such shortcomings, the present study introduces a functional behaviour on the strain parameter into the coefficient of the eddy viscosity of the AWF. The presently modified version of the AWF is validated in turbulent heat transfer of pipe flows, channel flows, back-step flows, pipe flows with abrupt expansion and plane impinging slot jets. The results confirm that the present modification successfully improves the performance of the original AWF for all the flows and heat transfer tested.     

Turbulent flow and convective heat transfer in a wavy wall channel

This paper reports the numerical modeling of turbulent flow and convective heat transfer over a wavy wall using a two equations eddy viscosity turbulence model. The wall boundary conditions were applied by using a new zonal modeling strategy based on DNS data and combining the standard k– turbulence model in the outer core flow with a one equation model to resolve the near-wall region.It was found that the two-layer model is successful in capturing most of the important physical features of a turbulent flow over a wavy wall with reasonable amount of memory storage and computer time. The predicted results show the shortcomings of the standard law of the wall for predicting such type of flows and consequently suggest that direct integrations to the wall must be used instead. Moreover, Comparison of the predicted results of a wavy wall with that of a straight channel, indicates that the averaged Nusselt number increases until a critical value is reached where the amplitude wave is increased. However, this heat transfer enhancement is accompanied by an increase in the pressure drop.     

Factors influencing heat transfer to the pressure surfaces of gas turbine blades

It is suggested that heat transfer through the laminar boundary layer flowing over the concave pressure surface of a turbine blade is strongly influenced by the presence of Taylor-Goertler vortices, as well as by mainstream turbulence. Transition occurs when these factors in concert outweigh the tendency of the boundary layer to remain laminar in the favourable pressure gradients characteristic of flow over pressure surfaces.     

The effect of the low Reynolds number k-e turbulence models on simulation of the enhanced and deteriorated convective heat transfer to the supercritical fluid flows

One of the most important challenges in mathematical modeling of convective heat transfer to the turbulent flow of a supercritical fluid is the turbulence modeling. The turbulence modeling, like other aspects of the supercritical fluid flows, seems to be high affected by the large variations of the fluid properties which needs to be further investigated. A two dimensional CFD code has been developed and used in this study to examine a number of the low Reynolds number k-e turbulence models. Both flow conditions corresponding to the heat transfer enhancement and deterioration have been studied. The results appear to be quite sensitive to the choice of the turbulence model, especially in the deteriorated regime of heat transfer. The turbulence model assisting the two-dimensional numerical model of the present study to best fit the experiments has been determined for both cases of the enhanced and deteriorated heat transfer. That is while the jump in the wall temperature occurring in the deteriorated regime of heat transfer is over- predicted by the present numerical code regardless of the turbulence model used.     

Assessment of Uncertainties in Modeling of Laminar to Turbulent Transition for Transonic Flows

The effect of physical variability and uncertainty in model correlations on laminar-turbulent transition in transonic flows is computed using two different Stochastic Collocation methods. Physical variability in the boundary conditions is first investigated for a flow over a flat plate with and without pressure gradient to quantify the uncertainties on the skin friction distribution along the plate surface. Since the laboratory conditions for the flat plate test cases are well defined and the applied transition model has been tuned for these cases, good agreement with experiments is achieved and the variability in the output is low. The second investigated cases exhibit boundary layer transition on the surface of a highly loaded turbine guide vane under transonic flow conditions. Comparisons between the predicted and measured wall heat transfer are used to quantify uncertainties in the free stream turbulence and the model correlations that accounts for compressibility effects on the onset and extension of the bypass transition. The computational results show that the uncertainties have a significant impact on the transition location for the turbine guide vane simulations and, consequently, on the reliability of the predictions for compressible flows. The output uncertainty accounts to a large extent for the difference between the deterministic simulation and the experiments. The results from the Simplex Stochastic Collocation method are computationally more efficient than those of the Stochastic Collocation based on Clenshaw–Curtis quadrature.     

Higher-order and length-scale statistics of velocity and temperature fluctuations in turbulent boundary layer along a heated vertical flat plate

Time-developing direct numerical simulation (DNS) was performed to clarify the higher-order turbulent behaviors in the thermally-driven boundary layers both in air and water along a heated vertical flat plate. The predicted statistics of the heat transfer rates and the higher-order turbulent behaviors such as skewness factors, flatness factors and spatial correlation coefficients of the velocity and temperature fluctuations in the natural-convection boundary layer correspond well with those obtained from experiments for space-developing flows. The numerical results reveal that the turbulent structures of the buoyancy-driven boundary layers are mainly controlled by the fluid motions in the outer region of the boundary layer, and these large-scale structures are strongly connected with the generation of turbulence in the thermally-driven boundary layers, in accordance with the actual observations for space-developing flows. Moreover, to specify the turbulence structures of the boundary layers, the cross-correlation coefficients and the characteristic length scales are examined for the velocity and thermal fields. Consequently, it is found that with a slight increase in freestream velocity, the cross-correlation coefficient for the Reynolds shear stress and turbulent heat flux increases for opposing flow and decreases for aiding flow, and the integral scales for the velocity and temperature fields become larger for opposing flow and smaller for aiding flow compared with those for the pure natural-convection boundary layer.     

Simulation of the Effect of the Freestream Turbulence Parameters on the Boundary Layer of a Curvilinear Airfoil

Modified variants of differential turbulence models which make it possible continuously to calculate both the entire flow region with laminar, transition and turbulent regimes and local low Reynolds number zones are proposed for investigating the flow and heat transfer in the boundary layers developing in compressible gas flow past curvilinear airfoils. The effect of the intensity and scale of free-stream turbulence and their variability along the outer boundary layer edge, as well as the combined action of the turbulence intensity and the streamwise pressure gradient in flow past blade profiles, on the heat transfer and near-wall turbulence characteristics is analyzed. The numerical results are compared with experimental and theoretical data.     

Turbulent boundary-layer analysis using finite elements

The use of finite element methods for turbulent boundary-layer flow is relatively recent and of limited extent.¹ In the present study, we extend the group variable approach of Fletcher and Fleer^2,3 to treat turbulent boundary layer flows with heat transfer using a two-equation turbulence model. The main concepts in the formulations include a Dorodnitsyn-type transformation which uses a velocity component as the transverse variable, a ‘variational’ formulation for the transformed equations using special test functions and development of a two-equation turbulence model in terms of the turbulent kinetic energy and turbulence dissipation rate as additional field variables. Several numerical test cases have been examined comparing the results with finite difference calculations and comparing the two-equation turbulence model with an algebraic turbulence model.     

湍流冲击射流流动与传热的数值研究进展

湍流冲击射流由于其冲击表面时具有很高的局部传热率和冲击力,被广泛应用于如表面的加热、电子元件的冷却、纸张的干燥和材料的切割等工程应用和工业过程中.由于其流动的复杂性,也常被作为一种理想的测试实例来评价湍流模型的性能.此外,湍升力射流与地面之间的空气动力作用对V/STOL (垂直或短距离起落)飞机的性能具有很大的影响.长期以来,人们从理论分析、实验测量和数值模拟方面对冲击射流进行了广泛而系统的研究,积累了丰富的资料.本文在分析了湍流冲击射流的数值研究现状的基础上,对近年来有关湍流冲击射流流动与传热的数值研究方面的文献有选择地进行了综述,重点评述了不同湍流模型对冲击射流流动与传热的预测能力,讨论了存在的问题并对该领域今后的研究方向进行了展望.      

Simulation of the Effect of the Freestream Turbulence Parameters on Heat Transfer in an Unsteady Boundary Layer

A variant of the two-parameter turbulence model which makes it possible continuously to calculate a flow region with laminar, transition and turbulent regimes is proposed for investigating the flow under conditions of high freestream turbulence intensity. It is shown that the properties of the thermal transition can be theoretically described using the quasi-steady turbulence model in the case of periodic freestream velocity distribution. The numerical results are compared with theoretical and experimental data. The approach proposed is developed for determining the combined effect of the parameters of harmonic fluctuations of the external velocity and freestream turbulence on the heat transfer characteristics on a flat plate with different boundary conditions for the enthalpy.     

Characteristics of turbulence transport for momentum and heat in particle-laden turbulent vertical channel flows

The dynamic and thermal performance of particle-laden turbulent flow is investigated via direction numerical simulation combined with the Lagrangian point-particle tracking under the condition of two-way coupling, with a focus on the contributions of particle feedback effect to momentum and heat transfer of turbulence. We take into account the effects of particles on flow drag and Nusselt number and explore the possibility of drag reduction in con-junction with heat transfer enhancement in particle-laden turbulent flows.The effects of particles on momentum and heat transfer are analyzed,and the possibility of drag reduc-tion in conjunction with heat transfer enhancement for the prototypical case of particle-laden turbulent channel flows is addressed.We present results of turbulence modification and heat transfer in turbulent particle-laden channel flow,which shows the heat transfer reduction when large inertial parti-cles with low specific heat capacity are added to the flow. However,we also found an enhancement of the heat transfer and a small reduction of the flow drag when particles with high specific heat capacity are involved.The present results show that particles,which are active agents,interact not only with the velocity field,but also the temperature field and can cause a dissimilarity in momentum and heat transport.This demonstrates that the possibility to increase heat transfer and suppress friction drag can be achieved with addition of par-ticles with different thermal properties.     

A turbulent near-wall model on convective heat transfer from an abrupt expansion tube

Turbulent heat transfer from a sudden expansion pipe subjected to an externally convective boundary condition is studied numerically using the proposed modified turbulence model. Both HYBRID and QUICK schemes are employed for comparison purposes. The calculated velocity distribution and turbulent kinetic energy show a significant improvement over the existing model solutions. The present results of center-line velocity, temperature distribution and Nusselt number under a limiting condition compare well with the available experimental data.     

Comparative Study of DNS,LES and Hybrid LES/RANS of Turbulent Boundary Layer with Heat Transfer Over 2d Hill

This paper first presents the turbulent heat transfer phenomenon of the boundary layer over a 2-dimensional hill using the direct numerical simulation (DNS). DNS results reveal turbulent heat transfer phenomena in the boundary layer over a 2-dimensional hill affected by the flow acceleration and the concave wall at the foreface of a hill, the convex wall at the top of the hill, and the flow deceleration, separation, and reattachment and the concave wall at the back of the hill. The prediction of turbulent heat transfer, the turbulence models of LES and HLR should be assessed in such heat transfer because these models have seldom been evaluated in the complex turbulent heat transfer. Therefore, this paper also presents evaluations of predictions of LES and HLR in the complicated turbulent heat transfer which is the boundary layer with heat transfer over a 2-dimensional hill. Consequently, this paper obviously shows the detailed turbulent heat transfer phenomena of a boundary layer over a 2-dimensional hill via DNS, and the evaluation results of prediction accuracy of LES and HLR for the heat transfer. LES and HLR give good prediction in comparison with DNS results, but the predicted reattachment and separation points are slightly different from DNS.     

环形通道内湍流旋流流动的数值模拟

本文应用一种考虑湍流－旋流相互作用及湍流脉动各向异性的新的代数Ｒｅｙｎｏｌｄｓ应力模型,对环形通道内的湍流旋流流动进行了数值模拟,研究了改主为旋流流数,进口轴向速度及半径比等参数对环形通道内湍流流动的影响,以及对强化环形通道内传热的作用。     

Investigation on convective heat transfer over a rotating disk with discrete pins

A three-dimensional numerical study on the flow and heat transfer characteristics over a rotating disk surface with discrete pins was conducted by the use of RNG k–ε turbulent model. And some experiments were also made for validation. The effects of rotating angular speed and pin configuration on the temperature maps and convective heat transfer characteristics on the rotating surface were analyzed. As the increase of rotating velocity, the impingement of pumping jet on the centre of rotating disk becomes stronger and the transition from laminar to turbulent occurs at the outer radius of rotating disk, which resulting in heat transfer enhancement. The pins on the disk make the pumping action of a rotating disk weaker. Simultaneously, they also act as perturbing elements to the cyclone flow near the rotating disk surface, making the overall heat transfer to be enhanced. The needle pins have higher convective heat transfer capacity than the discrete ring pins with the same extend pin areas.     

Modelling turbulent heat flux accounting for Turbulence-Radiation Interactions

The present work investigates the modeling of turbulent heat transfer in flows where radiative and convective heat transfer are coupled. In high temperature radiatively participating flows, radiation is the most relevant heat transfer mechanism and, due to its non-locality, it causes counter intuitive interactions with the turbulent temperature field. These so-called Turbulence-Radiation Interactions (TRI) largely affect the temperature field, modifying substantially the turbulent heat transfer. Therefore, in the context of modeling (RANS/LES), these interactions require a closure model. This work provides the inclusion of TRI in the modeling of the turbulent heat transfer by adopting a unique approach which consists in approximating the fluctuations of the radiative field with temperature fluctuations only. Based on this approximation, coefficients of proportionality are employed in order to close the unknown terms in the relevant model equations. A closed form of all radiation-temperature-velocity correlation is explicitly derived depending on the chosen turbulent heat transfer model. This model is applied to a standard two-equation turbulent heat transfer closure and used to reproduce results obtained with high-fidelity DNS simulations. While a standard approach (i.e., neglecting TRI) is not able to correctly predict the DNS data, the new model’s results shows exceptional agreement with the high-fidelity data. This clearly proves the validity (and the necessity) of the proposed model in non-reactive, radiative turbulent flows.     

Turbulent liquid metal flow in rectangular shaped contraction nozzles for target applications

Owing to the high beam power densities envisaged in advanced nuclear targets, liquid metal-operated free surface targets are conceived as one feasible option. There, the free surface is formed by an adequately shaped upstream located nozzle. Target boundary conditions necessitate a detailed knowledge on the turbulent flow in contraction nozzles in order to identify turbulence models accurately predicting experimental findings within the velocity range of interest for nuclear target and hence can then act as design optimisation tools. In this context, a combined experimental and numerical study is conducted on the basis of the turbulent flow in the contraction nozzle of the Super-FRS target. Two aspects determining the turbulent flow in the nozzle have been investigated. The first is a potential relaminarisation of the boundary layer caused by the acceleration within the contraction and the second is a development of the secondary flows due to the pressure gradient in the rectangular shaped ducts cross-section. Regarding the three different turbulence models investigated here only the V2F model exhibited the capability to predict the relaminarisation of the turbulent boundary layer both qualitatively and quantitatively. All turbulence models are able to predict the development of secondary flows induced by pressure gradients in transverse direction with an acceptable accuracy.     

An experimental investigation of heat transfer characteristics for turbulent flow over staggered ribs in a square duct

An experimental study of developing and fully developed turbulent air flow in a square duct with two opposite rib-roughened walls in which the ribs are attached in a staggered fashion was conducted to determine the heat transfer characteristics. The rib height-to-hydraulic diameter ratio (e/D_H) was 0.19, the rib pitch-to-height ratio (p/e) was 5.31. The streamwise temperature distribution was measured, and a law of the wall for the thermal boundary layer at each free-stream turbulence level was obtained. The effects of free-stream turbulence intensity with variations of 4–11% on heat transfer coefficients were also examined. Finally, the relationship between Nusselt number and Reynolds number was correlated. The results might be used in the design of turbine blade cooling channels.