Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM

Understanding transition and turbulence in the flow of shear-thinning non-Newtonian fluids remains substantially unresolved and additional research is required to develop better computational methods for wall-bounded turbulent flows of these fluids. Previous DNS studies of shear-thinning fluids mainly use purpose-built codes and simple geometries such as pipes and channels. However in practical application, the geometry of mixing vessels, pumps and other process equipment is far more complex, and more flexible computational methods are required. In this paper a general-purpose DNS approach for shear-thinning fluids is undertaken using the OpenFOAM CFD library. DNS of turbulent Newtonian and non-Newtonian flow in a pipe flow are conducted and the accuracy and efficiency of OpenFOAM are assessed against a validated high-order spectral element-Fourier DNS code – Semtex. The results show that OpenFOAM predicts the flow of shear-thinning fluids to be a little more transitional than the predictions from Semtex, with lower radial and azimuthal turbulence intensities and higher axial intensity. Despite this, the first and second order turbulence statistics differ by at most 16%, and usually much less. An assessment of the parallel scaling of OpenFOAM indicates that OpenFOAM scales very well for the CPUs from 8 to 512, but the intranode scalability is poor for less than 8CPUs. The present work shows that OpenFOAM can be used for DNS of shear-thinning fluids in the simple case of pipe flow, and suggests that more complex flows, where flow separation is often important, are likely to be simulated with accuracies that are acceptably good for engineering application.     

Cavity flow simulation of Carreau–Yasuda non-Newtonian fluids using PIM meshfree method

Lid-driven cavity flow of a purely-viscous non-Newtonian fluid obeying Carreau–Yasuda rheological model is studied numerically using the PIM meshfree method combined with the Characteristic-Based Split-A algorithm. Results are reported for the velocity and pressure profiles at Reynolds numbers as high as 1000 for a non-Newtonian fluid obeying Carreau–Yasuda rheological model. For Newtonian fluids, results obtained from our PIM–CBS-A method show good agreement with benchmark results published in the literature and obtained using finite difference and/or Finite Element Methods. Our numerical results are also consistent with recent published results obtained using another meshfree method called LSM with the advantage that PIM needs less “points” to achieve the same degree of accuracy. Results obtained for the Carreau–Yasuda model reveals the strong effect of the shear-thinning behavior of a fluid on its flow kinematics within the cavity.     

Pulsatile flow of Herschel–Bulkley fluid through catheterized arteries – A mathematical model

The pulsatile flow of blood through catheterized artery has been studied in this paper by modeling blood as Herschel–Bulkley fluid and the catheter and artery as rigid coaxial circular cylinders. The Herschel–Bulkley fluid has two parameters, the yield stress θ and the power index n. Perturbation method is used to solve the resulting quasi-steady nonlinear coupled implicit system of differential equations. The effects of catheterization and non-Newtonian nature of blood on yield plane locations, velocity, flow rate, wall shear stress and longitudinal impedance of the artery are discussed. The existence of two yield plane locations is investigated and their dependence on yield stress θ, amplitude A, and time t are analyzed. The width of the plug core region increases with increasing value of yield stress at any time. The velocity and flow rate decrease, whereas wall shear stress and longitudinal impedance increase for increasing value of yield stress with other parameters held fixed. On the other hand, the velocity, flow rate and wall shear stress decrease but resistance to flow increases as the catheter radius ratio (ratio of catheter radius to vessel radius) increases with other parameters fixed. The results for power law fluid, Newtonian fluid and Bingham fluid are obtained as special cases from this model.     

宾汉流体稠密两相湍流流动中的二阶矩模型

建立的Bingham流体稠密两相流动的二阶矩-颗粒动力论湍流模型（USM-theta模型）既体现了两相的作用,又体现了屈服应力所引起的附加项,并提出了USM-theta模型下考虑浓度修正值影响的两相湍流流动的算法．利用该模型对圆管内Bingham流体的单相湍流流动、稠密液固两相的湍流流动进行了计算,并和五方程湍流模型进行了比较,结果表明该模型的预测效果更好．利用USM-theta模型对含颗粒的Bingham流体的两相湍流流动进行了模拟,随着屈服应力的增加,Bingham流体相与颗粒相在管道中心附近的主流速度减小．液固两相湍流和Bingham流体两相湍流的计算结果表明屈服应力引起的附加项对流动有很重要的影响．     

Direct numerical simulation of compressible isotropic turbulence

Direct numerical simulation (DNS) of decaying compressible isotropic turbulence at turbulence Mach numbers of M_t = 0.2-0.7 and Taylor Reynolds numbers of 72 and 153 is performed by using the 7th order upwind-biased difference and 8th order center difference schemes. Results show that proper upwind-biased difference schemes can release the limit of“start-up” problem to Mach numbers. Compressibility effects on the statistics of turbulent flow as well as the mechanics of shocklets in compressible turbulence are also studied, and the conclusion is drawn that high Mach number leads to more dissipation. Scaling laws in compressible turbulence are also analyzed. Evidence is obtained that scaling laws and extended self similarity (ESS) hold in the compressible turbulent flow in spite of the presence of shocklets, and compressibility has little effect on scaling exponents.     

180°弯曲方管牛顿流体及一种非牛顿流体湍性流动的数值模拟

运用湍流k-ε模式及实测壁面函数分别模拟牛顿流体(清水)及一种非牛顿流体(聚合物稀薄减阻溶液)流经180°弯曲方管的湍性流动,取得与实测速度分布吻合较好的结果.对于湍流模式对存在大涡的复杂流动的适应性,根据计算和试验结果进行了分析和讨论.     

A non-Newtonian fluid flow model for blood flow through a catheterized artery—Steady flow

In this paper the effects catheterization and non-Newtonian nature of blood in small arteries of diameter less than 100 μm, on velocity, flow resistance and wall shear stress are analyzed mathematically by modeling blood as a Herschel–Bulkley fluid with parameters n and θ and the artery and catheter by coaxial rigid circular cylinders. The influence of the catheter radius and the yield stress of the fluid on the yield plane locations, velocity distributions, flow rate, wall shear stress and frictional resistance are investigated assuming the flow to be steady. It is shown that the velocity decreases as the yield stress increases for given values of other parameters. The frictional resistance as well as the wall shear stress increases with increasing yield stress, whereas the frictional resistance increases and the wall shear stress decreases with increasing catheter radius ratio k (catheter radius to vessel radius). For the range of catheter radius ratio 0.3–0.6, in smaller arteries where blood is modeled by Herschel–Bulkley fluid with yield stress θ = 0.1, the resistance increases by a factor 3.98–21.12 for n = 0.95 and by a factor 4.35–25.09 for n = 1.05. When θ = 0.3, these factors are 7.47–124.6 when n = 0.95 and 8.97–247.76 when n = 1.05.     

Numerical investigation of the effect of helix angle and leaf margin on the flow pattern and the performance of the axial flow cyclone separator

A two-stage turbulence model based on the RNG κ–ε model combined with the Reynolds stress model is developed in this paper to analyze the gas flow in an axial flow cyclone separator. Five representative simulation cases are obtained by changing the helix angle and leaf margins of the cyclone. The pressure field and velocity field of the five cases are simulated, and then the effects of helix angle and leaf margins on the internal flow field of the cyclone are analyzed. When the continuum fluid (air) flow is relatively convergent, the discrete particle phase is added into the continuous phase and the gas-solid two-phase flow is simulated. One-way coupling method is used to solve the two-phase flow and a stochastic trajectory model is implemented for simulation of the particle phase. Finally, the pressure drop and separation efficiency of one case are measured and compare quantitatively well with the numerical results, which validates the reliability and accuracy of the simulation method based on the two-stage turbulence model.     

Assessment of turbulence modeling for gas flow in two-dimensional convergent–divergent rocket nozzle

In the present study, the turbulent gas flow dynamics in a two-dimensional convergent–divergent rocket nozzle is numerically predicted and the associated physical phenomena are investigated for various operating conditions. The nozzle is assumed to have impermeable and adiabatic walls with a flow straightener in the upstream side and is connected to a plenum surrounding the nozzle geometry and extended in the downstream direction. In this integrated component model, the inlet flow is assumed a two-dimensional, steady, compressible, turbulent and subsonic. The physics based mathematical model of the considered flow consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The system of the governing equations with turbulent effects is solved numerically using different turbulence models to demonstrate their numerical accuracy in predicting the characteristics of turbulent gas flow in such complex geometry. The performance of the different turbulence models adopted has been assessed by comparing the obtained results of the static wall pressure and the shock position with the available experimental and numerical data. The dimensionless shear stress at the nozzle wall and the separation point are also computed and the flow field is illustrated. The various implemented turbulence models have shown different behavior of the turbulent characteristics. However, the shear-stress transport (SST) k–ω model exhibits the best overall agreement with the experimental measurements. In general, the proposed numerical procedure applied in the present paper shows good capability in predicting the physical phenomena and the flow characteristics encountered in such kinds of complex turbulent flow.     

Numerical simulation of UV disinfection reactors: Evaluation of alternative turbulence models

Six turbulence models, including standard k–ε, k–ε RNG, k–ω (88), revised k–ω (98), Reynolds stress transport model (RSTM), and two-fluid model (TFM), were applied to the simulation of a closed conduit polychromatic UV reactor. Predicted flow field and turbulent kinetic energy were compared with the experimental data from a digital particle image velocimetry (DPIV). All of the predicted flow fields were combined with a multiple segment source summation (MSSS) fluence rate model and three different microbial response kinetic models to simulate the disinfection process at two UV lamp power conditions. Microbial transport was simulated using the Lagrangian particle tracking method. The results show that the fluence distributions and the effluent inactivation levels were sensitive to the turbulence model selection. The level of sensitivity was a function of the operating conditions and the UV response kinetics of the microorganisms. Simulations with operating conditions that produced higher log inactivation or utilized microorganisms with higher UV sensitivity showed greater sensitivity to the turbulence model selection. In addition, a broader fluence distribution was found with turbulence models that predicted a larger wake region behind the lamps.     

Performance of turbulence models for flows through rough pipes

The Reynolds-averaged Navier–Stokes (RANS) equations were solved along with turbulence models, namely k–ε, k–ω, Reynolds stress models (RSM), and filtered Navier–Stokes equations along with Large Eddy Simulation (LES) to study the fully-developed turbulent flows in circular pipes roughened by repeated square ribs with various spacings. Solutions of these flows were obtained using the commercial computational fluid dynamics (CFD) software Fluent. The numerical results were validated against experimental measurements and other numerical data published in literature. The performance of the turbulence models was compared and discussed. All the RANS models and LES model were observed to perform equally well in predicting the time-averaged flow statistics. However no instantaneous information can be obtained from the RANS results. Therefore, when a rough overview of the flow process in a pipe roughened by repeated ribs is needed, any one of the RANS models can be of value. On the other hand, the instantaneous as well as time-averaged flows could be studied with more insight using LES, albeit at a cost of CPU effort at least one order higher.     

A Free Boundary Problem Governed by Nonlinear Degenerate Equations of Parabolic Type

We consider a free boundary problem connected with non-Newtonian fluid motion, i.e. the flow of power law fluids with the yield stress. We obtain the solution of the relevant approximation problem by means of a parabolic quasi-variational inequality, and then obtain the weak solution of the original problem after a passage to the limit. Finally, we study the regularity of the weak solution.     

环空套管内粘弹性流体

本文用Ｈａｎｋｅｌ积分变换的方法分别给出了，二阶流体和Ｍａｘｗｅｌｌ流体在环形套管内不定常旋转运动方程的解析解，据此可以分析旋转速度和切应力分布的变化特征，为占井工程设计提供理论依据。     

Micromorphic theory of turbulence

Based on the theory of micromorphic fluid dynamics (MMF), a new theory of turbulence is introduced. The law of conservation of microinertia of MMF is replaced by a balance law of microinertia, with all other laws remaining unchanged, the theory is called, “extended micromorphic fluid dynamics”. The present theory of turbulence is founded on the extended theory. Thus, a new theory of turbulence, is founded on the first principles, not using any a priori closure assumptions or semi-empirical hypothesis. Field equations are solved for the two-dimensional steady channel flow. The mean velocity turbulent shear stress and all turbulent velocities are in remarkably good agreement with the experimentally observed turbulent velocities.     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.     

Numerical Studies of Viscoelastic Flow Using the Software OpenFOAM

Viscoelastic fluids are a special class of non-Newtonian fluids. There are several types of viscoelastic fluid models, and all of them have a complex rheological response in comparison to Newtonian fluids. This response can be viewed as a combination of viscous and elastic effects and non-linear phenomena. This complex physics makes a numerical simulation a rather challenging task, even in simple test-cases. Studies presented in this paper are numerical studies of the viscoelastic fluid flow in several test cases. These studies have been done in OpenFOAM, an open-source CFD package. Implementation of viscoelastic models and a solver is only available in a community driven version of software (OpenFOAM-ext). One of the goals of research in this paper was to test the solver and models on some simple test cases. We considered start-up and pulsating flows of viscoelastic fluid in a channel and a circular pipe. The important thing is that an analytical solution can be found in these cases, making in possible to test all aspects of numerical simulation in OpenFOAM. Obtained results showed an excellent agreement with the analytical solution for both velocity and stress components. These results encouraged authors' motivation and a choice to use OpenFOAM for simulation of viscoelastic flows. We hope that our research will make a contribution to the OpenFOAM community. Our plan for the further research is a simulation of blood flow in arteries with the viscoelastic solver. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A rheological model for fluid flows with arbitrary Reynolds numbers

An approach to constructing a phenomenological model of motion for a viscous fluid alternative to the Prandtl mixing-length hypothesis is suggested. The approach makes it possible to describe the motion of a fluid independently of the regime realized in a given region of the flow. On the basis of this approach, a differential one-parameter model for the flow of a viscous fluid applicable to any regimes of motion, called a uniform laminar-turbulent model, is constructed. For this purpose, the field of a scalar turbulence measure is introduced, which equals the ratio of the Reynolds stress to the total stress in the case of a simple shear flow. This makes it possible to write new expressions for turbulent viscosity. The influence of the turbulence measure field on the flow is taken into account by using an additional transport differential equation. The model is applicable to both compressible and incompressible fluids and makes it possible to obtain solutions in quadratures for steady simple shear flows. Various forms of the system of equations of motion and boundary conditions are given. Original Russian Text ￠ V.A. Pavlovskii, D.V. Nikushchenko, 2009, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2009, No. 1, pp. 104–112.     

基于多GPU的格子Boltzmann法对槽道湍流的直接数值模拟

采用多GPU并行的格子Boltzmann方法（lattice Boltzmann method, LBM）对充分发展的槽道湍流进行了直接数值模拟．GPU(graphic processing unit)的数据并行单指令多线程（single-instruction multiple-thread, SIMT)特征与LBM完美的并行性相匹配,使得LBM求解器在GPU上运行获得了极高的性能,亦使得大规模DNS(direct numerical simulation)在桌面级计算机上进行成为可能．采用8个GPU,网格数目达到6.7×107,全场网格尺寸Δ+=1.41．模拟3×106个时间步长,用时仅24 h．另外,直接模拟结果无论是在平均流速或湍流统计量上均与Moser等的结果吻合得很好,这也证实了二阶精度的格子Boltzmann法直接模拟湍流的能力与有效性     

Analytical and numerical solutions of a generalized hyperbolic non-Newtonian fluid flow

Generalized hyperbolic non-Newtonian fluid model first proposed by Al-Zahrani [1] is considered. The model was successfully applied to some drilling fluids with better performance in relating shear stress and velocity gradient compared to power-law and Hershel-Bulkley model. Special flow geometries namely pipe flow, parallel plate flow and flow between two rotating cylinders are treated. For the first two cases, analytical solutions of velocity profiles in the form of integrals are presented. For the flow between two rotating cylinders, the differential equation is solved by Runge-Kutta method combined with shooting. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of modeling of velocity fluctuations on prediction of collection efficiency of cyclone separators

The effect of modeling of velocity fluctuations on the prediction of collection efficiency of cyclone separators has been numerically investigated using the Reynolds stress turbulence model (RSTM) and large eddy simulation (LES). The Eulerian–Lagrangian modeling approach of CFD code Fluent 6.3.26 has been employed to simulate the three dimensional, unsteady turbulent gas–solid flows in a Stairmand high efficiency cyclone. The simulated results have been compared with experimental observations available in the literature. The analysis of results shows that the RSTM and the LES have adequately predicted the mean flow field. Results of the present study demonstrate that the LES has good performance on prediction of fluctuating flow field and collection efficiency for each and every particle size. However, the performance of the RSTM is found poor in terms of prediction of velocity fluctuations and collection efficiency, especially for small particles. This relates to the precessing of the vortex core phenomenon, which is resolved more accurately by LES as compared to the RSTM simulation. The results suggest that the prediction of collection efficiency, especially for small particles is greatly influenced by the simulation of velocity fluctuations in cyclones.