A differential-pressure probe for velocity measurements in swirling air flows

For measuring air velocities in swirling flows a differential pressure probe of small axial length was developed. The determination of the velocity is based on measuring the difference between the stagnation pressure and the base pressure of a circular disk whose surface is perpendicular to the main flow direction.     

On the numerical solution of the turbulence energy equations for wave and tidal flows

This paper deals with the numerical solution, using finite difference methods, of the hydrodynamic and turbulence energy equations which describe wind wave and tidally induced flow. Calculations are performed using staggered and non-staggered finite difference grids in the vertical, with various time discretizations of the production and dissipation terms in the turbulence energy equations. It is shown that the time discretization of these terms can significantly influence the stability of the solution. The effect of time filtering on the numerical stability of the solution is also considered. The form of the mixing length is shown to significantly influence the bed stress in wind wave problems. A no-slip condition is applied at the sea bed, and the associated high-shear bottom boundary layer is resolved by transforming the equations onto a logarithmic or log-linear co-ordinate system before applying the finite difference scheme. A computationally economic method is developed which remains stable even when a very fine vertical grid (over 200 points) is used with a time step of up to 30 min.     

气体运动论数值算法在微槽道流中的应用研究

简要介绍基于Boltzmann模型方程的气体运动论数值算法基本思想及其对二维微槽道流动问题数值计算的推广,并阐述适用于微尺度流动问题的气体运动论边界条件数值处理方法。通过对压力驱动的二维微槽道流动问题进行数值模拟,将不同Knudsen数下的微槽道流计算结果分别与有关DSMC模拟值和经滑移流理论修正的N—S方程解进行比较分析,表明基于Boltzmann模型方程的气体运动论数值算法对微槽道气体流动问题具有很好的模拟能力。     

气体动理学格式与多尺度流动模拟

介绍了气体动理学格式(GKS)的基本构造原理及其在两种典型多尺度流动模拟中的应用。GKS利用介观BGK方程的跨尺度演化解来构造网格界面上的数值通量,从而发展出能随计算网格尺度变化自动切换物理模型的多尺度方法。对湍流这种宏观多尺度流动,发展了高精度GKS方法并成功用于低雷诺数湍流的直接数值模拟;为实现对高雷诺数湍流的高效精细模拟,基于拓展BGK方程和已有的RANS,LES模型建立了新型多尺度模拟框架。对跨流域稀薄流动,发展了适合大规模并行的三维统一气体动理学格式(UGKS),并建立了适合轴对称稀薄流动的UGKS。研究表明,GKS在多尺度流动高效模拟中的优异性能,具有很好的发展前景。     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Computation of strongly swirling confined flows with cubic eddy‐viscosity turbulence models

An investigation on the predictive performance of four cubic eddy‐viscosity turbulence models for two strongly swirling confined flows is presented. Comparisons of the prediction with the experiments show clearly the superiority of cubic models over the linear k–εmodel. The linear k–εmodel does not contain any mechanism to describe the stabilizing effects of swirling motion and as a consequence it performs poorly. Cubic models return a lower level of Reynolds stresses and the combined forced‐free vortex profiles of tangential velocity close to the measurements in response to the interaction between swirl‐induced curvature and stresses. However, a fully developed rotating pipe flow is too simple to contain enough flow physics, so the calibration of cubic terms is still a topic of investigation. It is shown that explicit algebraic stress models require fewer calibrations and contain more flow physics. Copyright © 2003 John Wiley & Sons, Ltd.     

On basic equations of turbulent swirling gas-solid flows and their application in cyclones

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model. These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.     

On numerical errors and turbulence modeling in tip vortex flow prediction

The accuracy of tip vortex flow prediction in the near‐field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a ‘numerical diffusion’ that artificially smears the vortex core. Low‐order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near‐wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three‐dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three‐dimensional, incompressible Navier–Stokes equations. Two one‐equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.     

Development and stability of swirling flows

The purpose of this research is to investigate steady axisymmetric swirling flows in channels and free vortices and also to establish the role of hydrodynamic instability in the formation of the sharp changes in flow structure associated with an increased rate of rotation. On the basis of numerical solutions of the complete Navier-Stokes equations obtained by a finite-difference method swirling flows in pipes with impermeable and permeable walls and in a free vortex are investigated. The stability of the swirling axisymmetric flows is considered on the assumption of local parallelism: the problem of the normal modes developing against the background of the axisymmetric flow determined by the velocity profiles in local cross sections of the flow is solved. Attention is mainly concentrated on free vortex flows with reverse current zones, their structure and stability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–11, July–August, 1988.     

Numerical prediction of particle slip velocity in turbulence by CFD-DEM simulation

Turbulent environment improves the flotation recovery of fine particles by promoting the particle–bubble collision rate, which directly depends on the particle slip velocity. However, the existing slip velocity models are not applicable to fine particles in turbulence. The mechanism of turbulence characteristics and particle properties on the slip velocity of fine particles in turbulence was unclear. In this study, a coupled ANSYS FLUENT and EDEM based on computational fluid dynamics (CFD) and discrete element method (DEM) were used to simulate the slip velocity of fine particles in the approximately homogenous isotropic turbulence, which was excited by the grid. The reliability of the used CFD-DEM simulation method was validated against the slip velocity measured by the particle image velocimetry (PIV) experiments. In particular, the effects of the particle shapes, particle densities, and turbulence intensities on the slip velocity have been investigated with this numerical method. Numerical results show that particle shapes have no significant effect on fine particles between 37 and 225 μm. The slip velocity of the spherical particles increases with the turbulence intensity and particle density. Based on the simulated data, a model which has a correlation coefficient of 0.95 is built by using nonlinear fitting.     

Dynamics of swirling jet flows

Experimental investigations of near-field structure of coaxial flows are presented for four different configurations: coaxial jets without rotation (reference case), outer flow rotating only (OFRO), inner-jet rotating only (IJRO) and corotating jets (CRJ). The investigations are performed in a cylindrical water tunnel, with an independent rotation of two coaxial flows. Laser tomography is used to document the flow field, and photographs are shown for different configurations. Time mean velocity profiles obtained by PIV, with and without swirl, are also presented. The dynamics of the swirling jets in the initial region (i.e. near the exit of the jets) is described. The effects of azimuthal velocity and axial velocity ratio variations on flow dynamics are examined. The appearance and growth of the first instabilities are presented and compared with some theoretical results, as is the influence of the rotation (inner or outer) on the dominating structures.     

Calculation of two-phase swirling flows

The results of calculating the diffusion of a dispersed admixture in turbulent swirling jet flows using the model of momentum transfer in a turbulent gas—dispersion flow proposed by the authors are presented. These results are compared with experimental data and with calculations based on various mathematical models. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 71–78, January–February, 1994.     

Cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density

An investigation on the predictive performance of cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density is presented. Comparisons of the prediction with the experiments show some improvements of cubic models over the linear k–ε model. The linear k–ε model does not contain any mechanism to represent the interaction of swirl and density variation and as a consequence it performs poorly. With appropriate modelling, two‐equation cubic turbulence models can capture the subcritical nature of the flow, represent the azimuthal velocity profiles of combined forced‐free vortex motion, and predict the combined effects of swirl and density variation fairly well. However, the calibration of model coefficients is still a topic of investigation. Further amendments are also needed for the equations of k and ε to take into account the effects of swirl and density gradients correctly. Copyright © 2004 John Wiley & Sons, Ltd.     

Large-eddy structures of turbulent swirling flows and methane-air swirling diffusion combustion

Turbulent swirling flows and methane-air swirling diffusion combustion are studied by large-eddy simulation (LES) using a Smagorinsky-Lilly subgrid scale turbulence model and a second-order moment (SOM) SGS combustion model, and also by RANS modeling using the Reynolds Stress equation model with the IPCM+wall and IPCM pressure-strain models and SOM combustion model. The LES statistical results for swirling flows give good agreement with the experimental results, indicating that the adopted subgrid-scale turbulence model is suitable for swirling flows. The LES instantaneous results show the complex vortex shedding pattern in swirling flows. The initially formed large vortex structures soon break up in swirling flows. The LES statistical results of combustion modeling are near the experimental results and are as good as the RANS-SOM modeling results. The LES results show that the size and range of large vortex structures in swirling combustion are different from those of isothermal swirling flows, and the chemical reaction is intensified by the large-eddy vortex structures. The project supported by the Special Funds for Major State Basic Research (G-1999-0222-07). The English text was polished by Keren Wang.     

Use of the turbulence energy equation in the theory of jet flows

In this study some of the assumptions introduced in [1] in developing a closed system of equations for a turbulent boundary layer will be simplified. With the aid of the system of equations of [1], a theoretical solution is found for the problem of a jet in an accompanying flow, it being assumed that the structure of the jet turbulence depends solely on local conditions. Experiment has shown that the turbulence in such a jet does depend also on the prehistory of the flow. At large distances from the source, the theoretical characteristics of the jet agree well with the experimentally determined characteristics of the wake beyond a body. Also examined is the problem of the boundary layer between two homogeneous flows, flowing with different velocities.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 75–81, March–April, 1973.     

Rotationally symmetric spontaneous swirling in MHD flows

The stability of steady axisymmetricMHD flows of an inviscid, incompressible, perfectly conducting fluid with respect to swirling—perturbations of the azimuthal components of the velocity field—is studied in a linear approximation. It is shown that for flows similar to a magnetohydrodynamic Hill-Shafranov vortex, the problem reduces to a one-dimensional problem on a closed streamline of the unperturbed flow (the arc length of the streamline is the spatial coordinate). A spectral boundary-value eigenvalue problem is formulated for a system of two ordinary differential equations with periodic coefficients and periodic boundary conditions. Sufficient conditions under which swirling is impossible are obtained. Numerical solution of the characteristic equation shows that, under certain conditions, for each streamline there is a real eigenvalue that yields monotonic exponential growth of the initial perturbations. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 120–129, September–October, 2000.     

Nonlinear acoustic oscillations in swirling gas flows

A class of exact solution of the gasdynamics equations with the linear dependence of the velocity components on the coordinates and a functional arbitrariness in the density (entropy) distribution is constructed. Using this class the characteristics of acoustic oscillations occurring, when a swirling gas flow deviates from the steady cyclostrophic equilibrium regime, that is, the equilibrium between the pressure gradient and the centrifugal force, are studied. An expression for the fundamental oscillation frequency agreeing with the measurements is derived.