Direct numerical simulation of stably and unstably stratified turbulent open channel flows

Summary Direct numerical simulation of stably and unstably stratified turbulent open channel flow is performed. The three-dimensional Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method based on high-order accurate spatial schemes. The objective of this study is to reveal the effects of thermally stable and unstable stratification on the characteristics of turbulent flow and heat transfer and on turbulence structures near the free surface of open channel flow. Here, fully developed weakly stratified turbulent open channel flows are calculated for the Richardson number ranging from 20 (stably stratified flow) to 0 (unstratified flow) and to −10 (unstably stratified flow), the Reynolds number 180 based on the wall friction velocity and the channel depth, and the Prandtl number 1. To elucidate the turbulent flow and heat transfer behaviors, typical quantities including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of velocity and temperature fluctuations are analyzed.     

A coupled boundary/finite element method for the computation of magnetically and electrostatically levitated droplet shapes

A coupled finite element and boundary element method is developed to predict the magnetic vector and scalar potential distributions in the droplets levitated in an alternating magnetic or electrostatic field. The computational algorithm entails the application of boundary elements in the region of free space and finite elements in the droplet region, the two being coupled along the droplet–air interface. The coupled boundary and finite element scheme is further integrated with a WRM‐based algorithm to predict the free surface deformation of magnetically and electrostatically levitated droplets. Several corner treatments for the boundary and finite element coupling and their implications to free surface calculations are discussed. Detailed formulation and numerical implementation are given. Numerical results are compared with available analytical solutions whenever available. A selection of computed results is presented for mag‐ netically or electrostatically levitated droplets under both terrestrial and microgravity conditions. Copyright © 1999 John Wiley & Sons, Ltd.     

Premixed combustion study: Turbulence in the nozzle behind grids and spheres

The experimental investigation of turbulence in the nozzle behind grids and spheres as the instrumentation for turbulent combustion of premixed flows by means of PIV and thermoanemometry was carried out. These methods were compared and applied in turbulent flows behind grids and spheres. Flows with relatively low turbulence intensities of the mean flow velocity (~1%), corresponding to the laminar flow in the case of absence of obstacles at low flow rates were investigated. Numerical simulation of the flow in a channel with changing geometry was carried out. A good agreement between laboratory experiments and numerical simulations was obtained. The developed experimental device is recommended for use in turbulent combustion of premixed flows.     

Surface Oscillations of an Electromagnetically Levitated Droplet

The natural oscillation frequency of freely suspended liquid droplets can be related to the surface tension of the material, and the decay of oscillations to the liquid viscosity. However, the fluid flow inside the droplet must be laminar to measure viscosity with existing correlations; otherwise the damping of the oscillations is dominated by turbulent dissipation. Because no experimental method has yet been developed to visualize flow in electromagnetically levitated oscillating metal droplets, mathematical modeling can assist in predicting whether or not turbulence occurs, and under what processing conditions. In this paper, three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k−ɛ turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem when the interior flow is turbulent. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to available experimental results.     

Droplet Deformation and 2-D/3-D Marangoni Flow Phenomena in Droplets Levitated by Electric Fields

An integrated numerical model is presented for free surface phenomena and Marangoni fluid flows in electrically levitated droplets under both terrestrial and microgravity conditions. The model development is based on the boundary element solution of the Maxwell equations simplified for electrostatic levitation applications and the free surface deformation that is primarily caused from the surface Maxwell stresses resulting from the applied electric fields. The electric and free surface model is further integrated with a finite element model for the surface-tension-induced fluid flows in the levitated droplets. Both 2-D and 3-D fluid flow structures may be developed in the electrically levitated droplets depending on the applied laser heating sources. The integrated model is applied to study the electric field distribution, free surface deformation, and 2-D and 3-D internal fluid flow structures in normal and microgravity for single, symmetric two-beam, four-beam, and six-beam laser heating arrangements. Among these arrangements, the six-beam arrangement with equal heating intensity gives the smallest temperature difference and the smallest maximum velocity.     

PARTICLE DISPERSION IN ANISOTROPIC HOMOGENEOUS TURBULENCE

A numerical study of particle dispersion in anisotropic homogeneous turbulent flows is reported. The stochastic turbulent field is represented by a set of random numbers with a pre-set covariance simulating the Reynolds stress in a turbulent flow. The effects of turbulence intensity, aerodynamic response time and Reynolds stress on the particle dispersion are presented.     

Interfacial stability and internal flow of a levitated droplet

Under the microgravity environment, production of new and high quality material is expected. Large droplet is preferable for such a containerless processing in microgravity environment. There are a lot of previous studies for droplet levitation [1]. However, effect of surface instability and internal flow appear remarkable when the droplet becomes large. Elucidation of effect of surface instability and internal flow of the levitated droplet is required for the quality improvement of new material. The objective of present study is to clarify critical conditions of the occurrence of the internal flow and the surface instability. At first, the condition between the stable region and the unstable region of the droplet levitation was evaluated by using the existing critical Weber number theory. The experimental result agreed well with the theory. It was suggested that the stability of droplet can be evaluated by using the theory for the interfacial instability. Finally, two-dimensional visual measurement was conducted to investigate the internal flow structure in a levitated droplet. The effect of physical properties on the internal flow structure of the droplet is investigated by Particle Image Velocimetry (PIV) technique. As the result, it is indicated that the internal flow structure is affected by the physical property such as viscosity.     

On the behaviour of organised disturbances in a turbulent boundary-layer

This paper is in continuation of our earlier work on the role of hydrodynamic stability theory in understanding wall-bounded turbulent flows. Work in this area was pioneered by Malkus, followed by Reynolds, Tiederman and Hussain. Numerical results showed that the linear instability modes are damped, a result also confirmed by our earlier work for the boundary layer flow case. This led to waning of interest in this approach. In the present work the problem is reformulated using an improved nonisotropic model for the stress tensor based on the model of Pope. This improved model does yield unstable wall modes. A wide range of unstable wavenumbers is observed and these unstable modes mimic some of the key features of wall-bounded turbulent flows. Comparisons with experimental data are also presented. The present work keeps alive the question of relevance of stability theory to wall-bounded turbulent flows. This project was funded by the Council of Scientific and Industrial Research, New Delhi on grant nos. 22(229) SP/92 EMR-II and 22(254)/96 EMR-II.     

PARTICLE DISPERSION IN ANISOTROPIC HOMOGENEOUS TURBULENCE

ABSTRACT

A numerical study of particle dispersion in anisotropic homogeneous turbulent flows is reported. The stochastic turbulent field is represented by a set of random numbers with a pre-set covariance simulating the Reynolds stress in a turbulent flow. The effects of turbulence intensity, aerodynamic response time and Reynolds stress on the particle dispersion are presented.     

Experimental and theoretical progress in pipe flow transition

There have been many investigations of the stability of Hagen-Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition to turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays from turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.     

压电喷墨液滴撞击光滑壁面铺展行为的数值研究

目的 研究典型流体相关无量纲参数对墨滴在光滑承印物表面铺展行为的影响,确定各无量纲参数对铺展直径、铺展因子和稳定铺展时间的影响规律。方法 利用Ansys软件,建立墨滴撞击光滑壁面的数值计算模型,采用VOF模型追踪液滴形状,采用PISO算法计算压力速度耦合。引入韦伯数、雷诺数、奥内佐格数来分析墨滴撞击光滑承印物表面的铺展行为。结果 计算获得不同韦伯数、雷诺数、奥内佐格数下墨滴的最大铺展直径、最终平衡铺展直径、最大铺展因子和最终铺展时间。结论 韦伯数和雷诺数对墨滴最大铺展直径的影响较大,对最终平衡直径的影响较小。韦伯数或雷诺数越小,回缩阶段越短,越快达到平衡。韦伯数、雷诺数与最大铺展因子呈明显正相关。奥内佐格数对墨滴的最大铺展直径、最终平衡直径的影响都较小。奥内佐格数越小,回缩阶段越短,越快达到平衡,奥内佐格数与液滴最大铺展因子呈不明显的正相关性。     

High-performance computing in computational fluid dynamics: progress and challenges

Computational fluid dynamics (CFD) is by far the largest user of high-performance computing (HPC) in engineering. The main scientific challenge is the need to gain a greater understanding of turbulence and its consequences for the transfer of momentum, heat and mass in engineering applications, including aerodynamics, industrial flows and combustion systems. Availability of HPC has led to significant advances in direct numerical simulation (DNS) of turbulence and turbulent combustion, and has encouraged the development of large-eddy simulation (LES) for engineering flows. The statistical data generated by DNS have provided valuable insight into the physics of many turbulent flows and have led to rapid improvements in turbulence and combustion modelling for industry. Nevertheless, major challenges remain and the computational requirements for turbulence research, driven by well-established physical scaling laws, are likely to remain at the limit of the available HPC provision for some time to come.     

On the linear stability of Stokes layers

Oscillatory flows occur naturally, with applications ranging across many disciplines from engineering to physiology. Transition to turbulence in such flows is a topic of practical interest and this article discusses some recent work that has furthered our understanding of the stability of a class of time-periodic fluid motions. Our study starts with an examination of the linear stability of a classical flat Stokes layer. Although experiments conducted over many years have demonstrated conclusively that this layer is unstable at a sufficiently large Reynolds number, it has only been relatively recently that rigorous theoretical confirmation of this behaviour has been obtained. The analysis and numerical calculations for the planar Stokes layer were subsequently extended to flows in channels and pipes and for the flow within a torsionally oscillating circular cylinder. We discuss why our predictions for the onset of instability in these geometries are in disappointingly poor agreement with experimental results. Finally, some suggestions for future experimental work are given and some areas for future theoretical analysis outlined.     

Numerical simulation of turbulent cascade flows involving high turning angles

Numerical simulations of three dimensional turbulent incompressible flows through linear cascades of turbine rotor blades with high turning angles have been performed using a generalized k−ɛ model which is a high Reynolds number form and derived by RNG (renormalized group) method to account for the variation of the rate of strain. The convective terms are approximated by using a second order upwind scheme to suppress numerical diffusion. Boundary-fitted coordinates are adopted to represent the complex cascade geometry accurately. For the case without tip clearance, secondary flows and flow losses are shown to be in good agreement with previous experimental results. For the case with tip clearance, the effects of the passage vortex and tip clearance flow on the total pressure loss as well as their interactions are discussed. The flow within the tip clearance has been analyzed to illustrate the existences of the tip clearance vortex and vena contracta.     

不同压力差下微通道尺寸和表面粗糙度对摩擦系数的影响

该文数值模拟液体在圆形和梯形截面微通道内的流动,分析了层流和湍流下液体在微圆管内的流动状态。着重研究不同压力差、微通道尺寸和表面粗糙度下,液体在微通道内的流动摩擦系数,并通过摩擦系数随雷诺数的变化曲线推断微通道流动转捩的雷诺数范围。研究表明:微通道中流动的摩擦系数随雷诺数的增大逐渐减小;通道截面的当量直径会改变过渡状态存在的雷诺数范围;粗糙度会影响湍流状态下流动的摩擦系数,相同雷诺数下,粗糙度越大,摩擦系数越大。     

Hybrid LES — Review and assessment

In the late eighties and up to the beginning of nineties computation of turbulent flows is mostly dominated by RANS (Reynolds Averaged Navier-Stokes Simulation) type modelling. During the last few years URANS (Unsteady RANS) and LES (Large Eddy Simulation) type of approaches have been attempted with some success. Yet, there have been many difficulties when LES is applied to practical engineering problems and to high Reynolds number flows as energy dissipating eddies become really small and mesh resolution required for a reasonably resolved LES approaches that of DNS (Direct Numerical Simulation). An alternative solution suggested was to combine RANS and LES, which in general referred to as Hybrid LES. There have been many proposals for combining RANS and LES in different ways. In this article, some of the issues involved in performing hybrid LES reported in the recent literature is briefly reviewed.     

Numerical simulation of the separated fluid flows at large Reynolds numbers

The variety of flow regimes (steady separated, periodically separated-‘Karman vortex street’, unsteady turbulent) and their characteristic peculiarities (separation and reattachment points, secondary separation, boundary layer, instability of the shear mixing layer, etc.) require the construction of effective numerical methods, which will be able to simulate adequately the considered flows. MERANGE ? SMIF–a splitting method for physical factors of incompressible fluids¹-is used for calculations of the steady and unsteady fluid flows past a circular cylinder in a wide range of Reynolds numbers (10° < Re < lo6). The finite-difference scheme for this method is of second order accuracy in the space variables, has minimal numerical viscosity and is also monotonic. Use of the Navier-Stokes equations with the corresponding transformation of Cartesian co-ordinates allows the calculations to be made by one algorithm both in a boundary layer and out of it. The method allows calculations at Re = ∞ cc and simulation of d‘Alembert’s paradox. Some results on the classical problem of the flow around a circular cylinder for a wide range of Reynolds numbers are discussed. The crisis of the total drag coefficient and the sharp rise of the Strouhal number are simulated numerically (without any turbulence models) for the critical Reynolds numbers (Re ≈ 4 × 10⁵), and are in a good agreement with experimental data.     

Two-phase bubbly flows in microgravity: Some open questions

Several studies on gas-liquid pipe flows in micro gravity have been performed. They were motivated by the technical problems arising in the design of the thermohydraulic loops for the space applications. Most of the studies were focused on the determination of the flow pattern, wall shear stress, heat transfer and phase fraction and provided many empirical correlations. Unfortunately some basic mechanism are not yet well understood in micro gravity. For example the transition from bubbly to slug flow is well predicted by a critical value of the void fraction depending on an Ohnesorge number, but the criteria of transition cannot take into account the pipe length and the bubble size at the pipe inlet. To improve this criteria, a physical model of bubble coalescence in turbulent flow is used to predict the bubble size evolution along the pipe in micro gravity, but it is still limited to bubble smaller than the pipe diameter and should be extended to larger bubbles to predict the transition to slug flow. Another example concerns the radial distribution of the bubbles in pipe flow, which control the wall heat and momentum transfers. This distribution is very sensitive to gravity. On earth it is mainly controlled by the action of the lift force due to the bubble drift velocity. In micro gravity in absence of bubble drift, the bubbles are dispersed by the turbulence of the liquid and the classical model fails in the prediction of the bubble distribution. The first results of experiments and numerical simulations on isolated bubbles in normal and micro gravity conditions are presented. They should allow in the future improving the modelling of the turbulent bubbly flow in micro gravity but also on earth.     

Hybrid solution of the averaged Navier-Stokes equations for turbulent flow

The Generalized Integral Transform Technique (GITT) is utilized in the hybrid numerical-analytical solution of the Reynolds averaged Navier-Stokes equations, for developing turbulent flow inside a parallel-plates channel. An algebraic turbulence model is employed in modelling the turbulent diffusivity. The automatic global error control feature inherent to this approach, permits the determination of fully converged reference results for the validation of purely numerical methods. Therefore, numerical results for different values of Reynolds number are obtained, both for illustrating the convergence characteristics of the integral transform approach, and for critical comparisons with previously reported results through different models and numerical schemes.     

Comparative analysis of turbulence models

A comparative analysis is performed for a complete locally anisotropic turbulence model of the second order and existing turbulence models. The comparison draws on experimental data, data of a direct numerical simulation of the nonstationary Navier-Stokes equations for a developed channel flow and a uniform channel flow with a constant velocity shift, and results for turbulence damping behind a grid. The K-ɛ model and the quasi-isotropic turbulence model are shown to have marked disadvantages, especially in describing turbulent flows with a high degree of anisotropy of pulsatory motion. Use of a locally anisotropic turbulence model improves the accuracy of determining Reynolds stresses. Consideration is given to the advantages and disadvantages of the turbulence models discussed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 328–339, March—April, 2000.