Computational analysis of supersonic turbulent boundary layers over rough surfaces using the k–ω and the stress–ω models

The influence of surface roughness in the prediction of the mean flow and turbulent properties of a high-speed supersonic (M = 2.7, Re/m = 2 × 10⁷) turbulent boundary layer flow over a flat plate is numerically investigated. In particular, the performance of the k–ω and stress–ω turbulence models is evaluated against the available experimental data. Even though the performance of these models have been proven satisfactory in the computation of incompressible boundary layer flow over rough surfaces, their validity for high-speed compressible has not been investigated yet. It is observed from this study that, for smooth surface, both k–ω and stress–ω models perform very well in predicting the mean flow and turbulence quantities in supersonic flow. For rough surfaces, both models matched the experimental data fairly well for lower roughness heights but performed unsatisfactorily for higher roughness conditions. Overall the performance of the k–ω model is better than the stress–ω model. The stress–ω model does not show any strong advantages to make up for the extra computational cost associated with it. The predictions indicate that the ω boundary conditions at the wall in both models, especially the stress–ω model, need to be refined and reconsidered to include the geometric factor for supersonic flow over surfaces with large roughness values.     

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.     

Model Equations for Turbulent Shear Flow

A set of model equations for the calculation of turbulent shear flows is presented. It is shown how the equations can be modified to allow for the inclusion of viscosity, compressibility and density variations. Some results of numerical computations are given. The constant in the law of the wall is predicted to within 10% for flow over a perfectly smooth wall, and a dependence on wall roughness is obtained. The empirical law of the wall for compressible flow is also shown to be a consequence of the equations.     

Numerical modeling of the pressure coefficient of the circular cylinder

The article examines the possibilities of numerical solution of chimney load from the effect of wind. The shear-stress transport (SST) k-ω turbulence model in ANSYS Fluent software is used to evaluate the task of the flow around the circumference of the rough cylinder. Calculations are performed on two different meshes that lead to the solution using wall function and near wall modeling. These two solution approaches in terms of defining wall roughness are presented in the paper by evaluating of the time dependence of the mean pressure coefficient distribution at the circumference, drag coefficient, and lift coefficient. The accuracy of the calculations is verified with parameters determined according to valid standards.     

From single obstacles to wall roughness: some fundamental investigations based on DNS results for turbulent channel flow

Turbulent flow through a plane channel with only one smooth wall is analyzed based on DNS results for three Reynolds numbers. The opposite wall has 2D bars of size k ×  k attached with the distance to each other as the crucial parameter. When they are close together they act as a wall roughness whereas they are single obstacles in character when they are far apart. These two extreme cases show very different coherent structures in the vicinity of the wall attached bars. The categories single obstacles and wall roughness are introduced as an alternative to the often used categorization in terms of k- and d-type roughness. Visualization of the coherent structures is achieved by introducing constant local entropy generation as a parameter. Finally it is discussed whether results gained in a channel with one rough wall can be transferred to the more realistic case when both walls are rough.     

Dynamical structure of the turbulent boundary layer on rough surface

The experiments on structure of turbulent boundary layer on the plane rough wall without pressure gradient are presented. Sand roughness of the wall is considered. Measurements are carried out using Time-Resolved PIV technique in planes parallel and perpendicular to the wall. The results on rough wall are compared with the base case of boundary layer on smooth wall. Hairpin vortices have been detected. Topology and typical size of those structures substantially differ in the cases in question. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

反映强流动曲率效应的非线性湍流模型

首先定性地分析了流线曲率效应对流场湍流结构的影响,然后以U型槽道流为典型算例,对多种湍流模型进行了评估．评估的模型包括:线性涡粘性模型,二阶和三阶非线性涡粘性模型,二阶显式代数应力模型和Reynolds应力模型．评估结果表明,性能良好的三阶非线性涡粘性模型,如黄于宁等人发展的HM模型以及CLS模型,可以较好地描述流线的曲率效应对湍流结构的影响,如凸曲率作用下内壁附近湍流强度的衰减和凹曲率作用下外壁附近湍流的增强,并且较好地确定了管道下游的分离点位置和分离泡长度,其预测的结果和实验符合较好,与Reynolds力模型的结果十分接近,因此可以较好地应用于具有曲率效应的工程湍流的计算．     

An Experimental/Numerical Investigation on Drag Reduction by Dimples

The paper is concerned with experimental and numerical investigations of the turbulent flow over dimpled surfaces. Shallow dimples distributed regularly over the wall of a plane channel with large aspect ratio are used to study their effect on the skin-friction drag. The resulting pressure drop in the channel was measured for smooth and dimpled walls. In addition to these investigations on internal flows, an external flow study was performed and boundary-layer profiles were measured using a Pitot-tube rake. Complementary to the measurements, direct numerical simulations for the internal flow configuration with and without dimples were carried out for two different grid resolutions and analyzed in detail. The objective was to clarify whether or not dimples cause reduction of the skin-friction drag. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

In this paper, we study the asymptotic behavior of the thermomicropolar fluid flow through a thin channel with rough boundary. The flow is governed by the prescribed pressure drop between the channel's ends and the heat exchange through the rough wall is allowed. Depending on the limit of the ratio between channel's thickness and the wavelength of the roughness, we rigorously derive different asymptotic models clearly showing the roughness-induced effects on the average velocity and microrotation. To accomplish that, we employ the adaptation of the unfolding method to a thin-domain setting.     

湍动尺度的模糊聚类分析

湍流运动可看成是大小不同尺度的涡体运动的叠加.定量地确定湍动尺度的分类,对于更好地描述不同尺度的涡体运动,探讨不同尺度涡体之间的相互作用,建立较好的湍流模式都具有重要的意义. 对事物按一定要求进行分类的数学方法,叫做聚类分析.由于湍动尺度的分类具有一定程度的模糊性,因而本文采用模糊聚类的方法,对壁面光滑及租糙两种边界条件下的湍动尺度进行了分类,并对各类结构的特性及其相互作用进行了探讨.     

Wall laws for fluid flows at a boundary with random roughness

The general concern of this paper is the effect of rough boundaries on fluids. We consider a stationary flow, governed by incompressible Navier‐Stokes equations, in an infinite domain bounded by two horizontal rough plates. The roughness is modeled by a spatially homogeneous random field, with characteristic size ε. A mathematical analysis of the flow for small ε is performed. The Navier's wall law is rigorously deduced from this analysis. This substantially extends former results obtained in the case of periodic roughness, notably in [16, 17]. © 2007 Wiley Periodicals, Inc.     

A Lagrangian simulation of particle deposition in a turbulent boundary layer in the presence of thermophoresis

Knowledge of particle deposition in turbulent flows is often required in engineering situations. Examples include fouling of turbine blades, plate-out in nuclear reactors and soot deposition. Thus it is important for numerical simulations to be able to predict particle deposition. Particle deposition is often principally determined by the forces acting on the particles in the boundary layer. The particle tracking facility in the CFD code uses the eddy lifetime model to simulate turbulent particle dispersion, no specific boundary layer being modelled. The particle tracking code has been modified to include a boundary layer. The non-dimensional yplus, y⁺, distance of the particle from the wall is determined and then values for the fluid velocity, fluctuating fluid velocity and eddy lifetime appropriate for a turbulent boundary layer used. Predictions including the boundary layer have been compared against experimental data for particle deposition in turbulent pipe flow. The results giving much better agreement. Many engineering problems also involve heat transfer and hence temperature gradients. Thermophoresis is a phenomena by which small particles experience a force in the opposite direction to the temperature gradient. Thus particles will tend to deposit on cold walls and be repulsed by hot walls. The effect of thermophoresis on the deposition of particles can be significant. The modifications of the particle tracking facility have been extended to include the effect of thermophoresis. A preliminary test case involving the deposition of particles in a heated pipe has been simulated. Comparison with experimental data from an extensive experimental programme undertaken at ISPRA, known as STORM (Simplified Tests on Resuspension Mechanisms), has been made.     

High-order approximations for an incompressible viscous flow on a rough boundary

In this paper, we propose approximations of fluid flow that could be used for obtaining wall laws of higher order. We consider the two-dimensional laminar fluid flow, modeled by the incompressible Stokes system in a straight channel with a rough side. The roughness is periodic and the ratio of the amplitude of the rough part and the size of the flow domain is denoted by ?, being a small number. We impose periodic boundary conditions on the flow. We generalize the boundary layers needed for the construction of flow approximations of higher order with respect to ?. The existence of the layers and their features are discussed. Finally we give the error estimates for the approximations and establish an explicit wall law.     

Asymptotic study of turbulent Poiseuille flow with wall transpiration

An incompressible, pressure–driven, fully developed turbulent flow between two parallel walls, with an extra constant transverse velocity component, is considered. A closure condition is formulated, which relates the shear stress to the first and second derivatives of the longitudinal mean velocity. The closure condition is derived without invoking any special hypotheses on the nature of turbulent motion, only taking advantage of the fact that the flow depends on a finite number of governing parameters. By virtue of the closure condition, the momentum equation is reduced to the boundary–value problem for a second–order differential equation, which is solved by the method of matched asymptotic expansions at high values of the logarithm of the Reynolds number based on the friction velocity. A limiting transpiration velocity is obtained, such that the shear stress at the injection wall vanishes, while the maximum point on the velocity profile approaches the suction wall. In this case, a sublayer near the suction wall appears where the mean velocity is proportional to the square root of the distance from the wall. A friction law for Poiseuille flow with transpiration is found, which makes it possible to describe the relation between the wall shear stress, the Reynolds number, and the transpiration velocity by a function of one variable. A velocity defect law, which generalizes the classical law for the core region in a channel with impermeable walls to the case of transpiration, is also established. In similarity variables, the mean velocity profiles across the whole channel width outside viscous sublayers can be described by a one–parameter family of curves. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation and analysis of turbulent MHD channel flow with a streamwise magnetic field

We perform large-eddy simulations of turbulent MHD channel flow with a streamwise magnetic field using a pseudo spectral method. The streamwise magnetic field leads to turbulent drag reduction due to the selective Joule damping of certain flow structures. Near the walls, the turbulent mean velocity profile retains the logarithmic layer but the von Karman constant decreases with increasing magnetic field strength. In the outer region, the flow is characterized by persistent streaky structures of large streamwise extent, which lead to a rather flat mean velocity profile. In addition, the streamwise velocity fluctuations develop a pronounced second peak upon increasing the magnetic induction as well as a second logarithmic layer that increases in steepness. We find that Prandtl's classical mixing-length model with a variable Kármán constant can describe the modified logarithmic layer reasonably accurately in a wide range of Reynolds and Hartmann numbers. However, the flow modification near the center of the channel is not properly captured by this approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

湍流相干结构的机理研究(Ⅱ)─粗糙壁边界层相干结构的物理模型*

本文主要分析了粗糙壁面相干结构的特性以及与光滑壁面相干结构的区别,讨论了从光滑壁到粗糙壁过渡的问题,在此基础上建立了粗糙壁面相干结构的物理模型,从理论上得到了慢条宽度、猝发时间等物理量与动量厚度雷诺数的关系,其结果与实验结果是相符合的.     

A mixing-length model for magnetohydrodynamic flows in channels and ducts with wall-parallel magnetic field

A spanwise magnetic field leads to turbulent drag reduction in channel flow of a conducting liquid due to the selective Joule damping of certain flow structures. This effect can be captured by a simple modification of Prandtl's classical mixing-length idea. The mixing length over which a turbulent fluctuation loses its momentum is not only constrained geometrically but also by magnetic damping. We therefore introduce a magnetic damping length that is proportional to friction velocity and the Joule damping time. The limitation of mixing length is implemented by using the harmonic mean between wall distance and this damping length. By combining this ansatz with the van-Driest model for turbulent stresses in channel flow we obtain a satisfactory prediction for the mean velocity distribution in magnetohydrodynamic channel flow with spanwise field for different Reynolds and Hartmann numbers. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical Considerations about Near-Wall Turbulence and Resulting Flow Control Schemes

Based on analytical considerations about how near-wall turbulence needs to be modified in order to reduce the momentum loss towards solid walls and to yield lower energy losses, a mechanism of turbulent drag reduction is proposed. This mechanism suggests that drag reducing flow control at high Reynolds numbers should be designed to minimize the turbulent dissipation rate. A previously published approach on how a reduction of the turbulent dissipation in the near-wall region can be achieved is analyzed further. The obtained results provide some new insight on the parameters that need to be considered when designing flow control schemes for skin friction drag reduction. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prandtl's Mixing Length Model - Revisited

The paper is concerned with a modification of Prandtl's mixing length model of Reynolds stresses in fully developed turbulent channel flows. Here it is a well established fact that Prandtl's model falls short to describe the Reynolds stresses correctly very close to the wall. Furthermore, the resulting solution of the time averaged velocity fails to describe the channel flow correctly from the wall to its center. To overcome these shortcomings, the only characteristic mixing length in Prandtl's model is replaced by separate mixing lengths for velocity fluctuations parallel to the wall and normal to the wall, respectively. The modified model describes the mean velocity, all Reynolds stresses, and the functional dependence between Reynolds number based on the mean velocity and the one based on the friction velocity. For all Reynolds numbers these results - and corresponding results for the production terms of Reynolds stresses and the energy balance of the mean flow - agree quantitatively with experimental data and with data obtained by numerical simulations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hybrid LES-RANS Modeling of Complex Turbulent Flows

The paper describes a state-of-the-art hybrid LES-URANS method for the simulation of complex internal and external turbulent flows. Relying on a unified LES-URANS approach with a soft interface the methodology is designed for wall-bounded non-equilibrium flows. The unsteady Reynolds-averaged Navier-Stokes (URANS) mode within the hybrid approach is taken into account by an explicit algebraic Reynolds stress model (EARSM), which guarantees an appropriate representation of the anisotropic near-wall turbulence. All non-closed terms in the transport equation of the turbulent kinetic energy are modeled by enhanced formulations using the EARSM (production and diffusion term) and the splitting of the dissipation rate into a homogeneous and an inhomogeneous contribution. The former is expressed analytically by a Taylor series expansion of the homogeneous lateral Taylor microscale in the vicinity of the wall guaranteeing the correct asymptotic behavior. The latter is incorporated into the diffusion term. The interface location between the large-eddy simulation (LES) mode and the URANS mode is determined automatically on-the-fly based on the modeled turbulent kinetic energy and the distance to the wall. For transitional (external) flows an additional dynamic transition criterion is applied which determines the laminar and the turbulent flow regimes and is combined with the existing interface criterion. An internal flow over a periodic arrangement of hills and an external flow past a SD7003 airfoil with a laminar separation bubble are taken into account for a detailed evaluation of the method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)