Two-phase flow modelling: the closure issue for a two-layer flow

The fully-developed, laminar flow of two fluid layers in a horizontal channel is studied by means of the height-averaged balance equations. The closure issue is addressed and the closure relations for the wall and interfacial shear stresses are given for some particular cases.     

Second-moment closure for modelling the near-wall turbulence in 3D mean flows

A second-moment closure for the near-wall turbulence is proposed. The limiting behaviour of this closure near a wall is consistent with that of the exact Reynolds-stress transport equations, and it converts asymptotically into a high-Reynolds-number closure remote from the wall. The closure is applied to a pressure-driven 3D transient channel flow. The predicted results are in fair agreement with the DNS data. The project supported by the National Natural Science Foundation of China     

On the interfacial roughness scale in turbulent stratified two-phase flow: 3D lattice Boltzmann numerical simulations with forced turbulence and surfactant

Numerical 3D simulations of turbulent, stratified two-phase shear flow with a surfactant laden interface were used to test and develop a phenomenological interfacial roughness scale model where the energy required to deform the interface (buoyancy, interfacial tension, and viscous work) is proportional to the turbulent kinetic energy adjacent to the interface.The turbulence was forced in the upper and lower liquids in the simulations, to emulate the interfacial dynamics without requiring (prohibitively) large simulation domains and Reynolds numbers. The addition of surfactant lead to an increased roughness scale (for the same turbulent kinetic energy) due to the introduction of interfacial dilatational elasticity that suppressed horizontal motion parallel to the interface, and enhanced the vertical motion.The phenomenological roughness scale model was not fully developed for dilatational elasticity in this work, but we proposed a source term that represents surfactant induced pressure fluctuations near the interface. This source term should be developed further to account for the relation between surfactant density fluctuations and turbulence adjacent to the interface. We foresee that the roughness scale model can be used as a basis for more general interfacial closure relations in Reynolds averaged turbulence models, where also mobile surfactant is accounted for.     

基于CFD技术的垂直轴风力机动态尾流特性研究

利用CFD软件对麦克马斯特大学垂直轴风力机进行不同叶尖速比下的数值模拟,计算结果与风洞试验数据吻合良好。近场尾流中,与单叶片的风力机模拟结果比较,上游叶片产生并向下游延伸的旋涡影响下游运行轨道上叶片的升阻力特性,不仅使叶片扭矩输出峰值降低,而且峰值产生的时间延迟。对垂直轴风力机叶片叶梢进行修改,模拟结果显示,叶片扭矩输出峰值不变,但是谷值有所降低,修改后风力机沿风向推力幅值降低明显;远场尾流中,采用风速轮廓线原理,以瑞典的法尔肯贝里市200kW垂直轴风力机为原型,按照真实的空间排布进行数值模拟。模拟结果显示,上游风力机上下两端处产生较为集中的远场尾流,影响下游风力机叶片下半段的气动性能,下游风力机功率输出降低明显。     

Predictions of Axial and Transverse Injection into Supersonic Flow

CFD calculations are performed on a swept ramp injecting fuelaxially, and on a two-hole transverse fuel injection downstream of abackward-facing step, both into a supersonic turbulent flow. Theresulting complex flowfields are predicted using a cubick–ε turbulence closure. Comparisons with experimental data show very good agreement. A discussion of the main flow features is presented. The fast computational convergence demonstrates the readiness of the method for the design cycle. This revised version was published online in July 2006 with corrections to the Cover Date.     

Closure of the governing equations for immiscible,two-phase flow: A research comment

The derivation of the governing equations for immiscible, two-phase flow through porous media by Whitaker (Transport in Porous Media 1, 105–125 (1986)) contains an error which is corrected in the present work. The modified equations contain terms not present in the original equations, but their presence does not cause any fundamental changes from the conclusions reached in the original work. However, these extra terms may be important in computations associated with the closure problem.     

Prediction of Turbulence-Generated Secondary Mean Flow in a Square Duct

Near-wall second-moment closures have revealed a tendency to severely underpredict the strength of the turbulence-generated secondary flow in noncircular ducts. The aim of this study has been to elucidate the reasons for this failure that seems to be present at both high and low Reynolds numbers. Fully developed three-componential turbulent flow inside a straight square duct has been computed with the quasi-linear SSG second-moment closure and near-wall effects were modeled by elliptic relaxation. The results compared favourably with the reference DNS data, except that the strength of the turbulence-induced secondary flows is significantly underpredicted. A close examination of the generation mechanisms of the mean streamwise vorticity revealed that this discrepancy can be attributed to the secondary shear-stress component, the importance of which is generally overlooked. The normal-stress anisotropy was, however, adequately returned by the model and so was the variation of the friction velocity with Reynolds number over a wide Reynolds-number range. The present study supports the view that the wall-function approach should be abandoned in order to retain a physical appealing representation of the generation mechanisms of mean streamwise vorticity along internal corners. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling of inhomogeneous turbulence in the absence of mean velocity gradients

In this paper we propose a new rational model for turbulent transport of Reynolds stresses and dissipation. For this purpose we first analyse some properties of diffused turbulence i.e. turbulence where dissipation is balanced by turbulent diffusion arising from inhomogeneity. Then we use some of these results to deduce some mathematical requirements that must be satisfied by any rational model and we show that they are not verified by available models. Consequently we derive a more general model taking into account the various properties of diffused turbulence.     

Expressions for pressure-velocity-gradient correlations

The term for pressure-velocity-gradient correlation was initiated by Rott’srewriting the correlation between the pressure fluctuation gradient and velocity fluctuation.However,it is very difficult to consider the effect of this term.Since Rotta’s work,Launderet al.has made some estimates of this term.In this paper according to the equations forvelocity fluctuation,the pressure fluctuation is solved so that the average value of theproduct of the pressure fluctuation and the velocity fluctuation gradient is obtained.Thus,the whole expressions for the pressure-velocity-gradient correlation are derived.The resultexplains that the limited expressions by Rotta and Launder are reasonable to a certaindegree.The whole expressions in this paper are discussed respectively in two situations:oneis without a separate consideration of large and small vortexes;the other is with a separateconsideration of three kinds of vortexes.Therefore,the paper gives the whole expressions forpressure-velocity-gradient correlation     

应用脉冲热线技术测量含回流的高湍流流动

阐述脉冲热线测量原理、探针结构与数据处理方法；在实验雷诺数Ｒｅｃ＝６．６７×１０＾５时，用脉冲热线技术定量测量了 由楔形体模型产生的含回流的高湍流流动，得到了壁面切应力、流向时均速度、回流因子、脉动速度、偏斜因子和平坦因子等重要参数，提示了分离泡流动结构与特征。     

Turbulent heat transfer in a flat plate boundary layer disturbed by a cylinder

Augmentation of heat transfer from a flat plate using a turbulence promoter has been studied. A circular cylinder 8 mm in diameter was placed in the turbulent boundary layer detached from the flat plate. It was located parallel to the plate and perpendicular to the flow direction. Clearance, c, between the cylinder and the flat plate was varied in nine steps: c=0, 1, 2, 3, 4, 6, 11, 20 and 29.5 mm. Measurements were made of the local heat transfer coefficients, mean velocity profiles, turbulence intensity profiles, static pressure and skin friction. Experimental results showed that the heat transfer deterioration which occurs just downstream of the cylinder at c=0 mm can be removed by displacing the cylinder a small distance from the wall. The improvement in heat transfer is mainly due to the unsteadiness of the recirculating flow on the plate and the effect of intense turbulence arriving at the near wall region from the lower shear layer of the cylinder wake. Heat transfer augmentation is most effective when c=4 mm and becomes less effective when c is increased more than 6 mm. The enhancement disappears far downstream from the cylinder.     

Homogeneous turbulence subjected to rotation-dominated plane distortion

A new configuration of distorted homogeneous turbulence is investigated in the domain of rotation-dominated elliptical flows. The experimental results are compared with exact numerical solutions obtained in Fourier space for the linear part of the problem. The inherently periodic character of the flow results in typical oscillatory variations of the anisotropy and the pressure-strain correlations. A new two-point closure approach of the EDQNM type is proposed for the nonlinear problem; it is based on a representation of the spectral tensor by scalar functions expanded in terms of spherical harmonics.     

Transition Modelling for General Purpose CFD Codes

The paper addresses modelling concepts based on the RANS equations for laminar-turbulent transition prediction in general-purpose CFD codes. Available models are reviewed, with emphasis on their compatibility with modern CFD methods. Requirements for engineering transition models suitable for industrial CFD codes are specified. A new concept for transition modeling is introduced. It is based on the combination of experimental correlations with locally formulated transport equations. The concept is termed LCTM – Local Correlation-based Transition Model. An LCTM model, which satisfies most of the specified requirements is described, including results for a variety of different complex applications. An incremental approach was used to validate the model, first on 2D flat plates and airfoils and then on to progressively more complicated test cases such as a three-element flap, a 3D transonic wing and a full helicopter configuration. In all cases good agreement with the available experimental data was observed. The authors believe that the current formulation is a significant step forward in engineering transition modeling, as it allows the combination of transition correlations with general purpose CFD codes. There is a strong potential that the model will allow the 1st order effects of transition to be included in everyday industrial CFD simulations.     

Recent progress in the development of the Elliptic Blending Reynolds-stress model

The Elliptic Blending Reynolds Stress Model (EB-RSM), originally proposed by Manceau and Hanjalić (2002) to extend standard, weakly inhomogeneous Reynolds stress models to the near-wall region, has been subject to various modifications by several authors during the last decade, mainly for numerical robustness reasons. The present work revisits all these modifications from the theoretical standpoint and investigates in detail their influence on the reproduction of the physical mechanisms at the origin of the influence of the wall on turbulence. The analysis exploits recent DNS databases for high-Reynolds number channel flows, spanwise rotating channel flows with strong rotation rates, up to complete laminarization, and the separated flow after a sudden expansion without and with system rotation. Theoretical arguments and comparison with DNS results lead to the selection of a recommended formulation for the EB-RSM model. This formulation shows satisfactory predictions for the configurations described above, in particular as regards the modification of the mean flow and turbulent anisotropy on the anticyclonic or pressure side.     

A numerical study of turbulent flow over a two‐dimensional hill

Calculations of mean velocities and Reynolds stresses are reported for the recirculating flow established in the wake of two‐dimensional polynomial‐shaped obstacles that are symmetrical about a vertical axis and mounted in the water channel downstream of a fully developed channel flow for Re=6×10⁴. The study involves calculations of mean and fluctuating flow properties in the streamwise and spanwise directions and include comparisons with experimental data [Almeida GP, Durão DFG, Heitor MV. Wake flows behind two‐dimensional model hills. Experimental Thermal and Fluid Science 1993; 7: 87–101] for flow around a single obstacle with data resulting from the interaction of consecutive obstacles, using two versions of the low‐Reynolds number differential second‐moment (DSM) closure model. The results include analysis of the turbulent stresses in local flow co‐ordinates and reveal flow structure qualitatively similar to that found in other turbulent flows with a reattachment zone. It is found that the standard isotropization of production model (IPM), based on that proposed by Gibson and Launder [Ground effects on pressure fluctuations in the atmospheric boundary layer. Journal of Fluid Mechanics 1978; 86(3): 191–511], with the incorporation of the wall reflection model of Craft and Launder [New wall‐reflection model applied to the turbulent impinging jet. AIAA Journal 1992; 32(12): 2970–2972] predicts the mean velocities quite well, but underestimates the size of the recirculation region and turbulent quantities in the shear layer. These inadequacies are circumvented by adopting a new cubic Reynolds stress closure scheme based on that more recently developed by Craft and Launder [A Reynolds stress closure designed for complex geometries. International Journal of Heat and Fluid Flow 1996; 17: 245–254] which satisfies the two component limit (TCL) of turbulence. In this model the geometry‐specific quantities, such as the wall‐normal vector or wall distance, are replaced by invariant dimensionless gradient indicators. Also, the model captures the diverse behaviour of the different components of the stress dissipation, ε_ij, near the wall and uses a novel decomposition for the fluctuating pressure terms. Copyright © 2001 John Wiley & Sons, Ltd.     

Benchmark PIV database for the validation of CFD simulations in a transitional cavity flow

We present an experimental benchmark database for the transitional cavity flow. The database is obtained by planar Particle Image Velocimetry measurements at the median plane of the cavity model, for Reynolds numbers between 6300 and 19,000 based on the cavity height. A detailed uncertainty analysis of the experimental results is performed via the correlation statistics method for PIV uncertainty quantification and linear error propagation.The experimental results are compared to two-dimensional Reynolds-Averaged Navier Stokes (RANS) numerical simulations with different turbulence models. It is shown that, when the standard k-ω turbulence model is employed, the discrepancy between numerical simulations and experimental results exceeds the uncertainty of the latter. Conversely, RANS simulations with the SST k-ω turbulence model agree well with the experimental data in terms of time-averaged flow properties; however, the turbulent kinetic energy results present significant discrepancies at all considered Reynolds numbers. The data presented in this paper is made available for open-access download via the 4TU.ResearchData repository with DOI: https://doi.org/10.4121/14061233.     

On the closure problem of turbulence model theory

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Application of a reflection-free DSM to turbulent flow and heat transfer in a square-sectioned U-bend

The paper reports the outcome of applying two differential second-moment (DSM) closures to resolve the complex three-dimensional motion that arises in turbulent flow in a square-sectioned duct passing around a 180°C bend. The initial results showed (in accord with a number of recent studies) that, with the same underlying closure hypotheses, a DSM scheme produces better agreement with experiment than does the corresponding algebraic second-moment (ASM) treatment, although the differences were acceptably small. Thereafter, applications are reported for a new type of DSM that employs no wall-reflection terms. This leads to markedly better predictions of the turbulence field and thus of the wall heat transfer than the conventionally adopted version.