Analysis of Flow Structure and Calculation of Drag Coefficient for Concurrent-up Gas-Solid Flow

This study investigates the heterogeneous structure and its influence on drag coefficient for concurrent up gas-solid flow.The energy-minimization multi-scale (EMMS) model is modified to simulate the variation of structure parameters with solids concentration,showing the tendency for particles to aggregated to form clusters and for fluid to pass around clusters.The global drag coefficient is resolved into that for the dense phase,for the dilutephase and for the so-called inter-phase,all of which can be obtained from their respective phase-specific structure parameters.The computational results show that the drag coefficients of the different phases are quite different,and the global drag coefficient calculated from the EMMS approach is much lower than that from the correlation of Wen and Yu.The simulation results demonstrate that the EMMS approach can well describe the heterogeneous flow structure,and is very promising for incorporation into the two-fluid model or the discrete particle model as the closure law for drag coefficient.

Parametric study on smoothed particle hydrodynamics for accurate determination of drag coefficient for a circular cylinder

Simulations of two-dimensional(2D) flow past a circular cylinder with the smoothed particle hydrodynamics(SPH) method were conducted in order to accurately determine the drag coefficient. The fluid was modeled as a viscous liquid with weak compressibility. Boundary conditions,such as a no-slip solid wall, inflow and outflow, and periodic boundaries, were employed to resemble the physical problem. A sensitivity analysis, which has been rarely addressed in previous studies, was conducted on several SPH parameters. Hence, the effects of distinct parameters, such as the kernel choices and the domain dimensions, were investigated with the goal of obtaining highly accurate results. A range of Reynolds numbers(1-500) was simulated, and the results were compared with existing experimental data. It was observed that the domain dimensions and the resolution of SPH particles, in comparison to the obstacle size, affected the obtained drag coefficient significantly. Other parameters, such as the background pressure, influenced the transient condition, but did not influence the steady state at which the drag coefficient was determined.

Numerical Study on the Drag Coefficients of Sphere and Double Spheres

Winds on the earth are commonly strong enough to erode transport and deposit sediment. The modes of sand transport by the wind are greatly different from those by water flow. On the other hand wind-blown sands are of a material circulation process of the earth surface. They affect wind-sand transport flux and sand ejection of a flux, the damage of grains formed cannot be neglected in engineering. Because of the complexity of windblown sand flux system, the understanding of its basic mechanics is not yet clear. The key forces in sand salutation mainly includes： the valid gravity, air drag force ＇Magnus force＇ Saffman force ＇Basset force＇ additional quality force and scatter force among grains. The most important force in sand salutation is the air drag force. Computation of the single sphere drag coefficient and double spheres drag coefficient is presented for the distance between two spheres being smaller than twelve times of the sphere diameter and the spheres being at different angular positions. The flow interference of two spheres was investigated for the distance s = 0.08 d to 12d, angular position 0 = 0 to 360 and Reynolds number 15≤Re≤1000.

Instability analysis and drag coefficient prediction on a swept RAE2822 wing with constant lift coefficient

Swept wing is widely used in civil aircraft,whose airfoil is chosen,designed and optimized to increase the cruise speed and decrease the drag coefficient.The parameters of swept wing,such as sweep angle and angle of attack,are determined according to the cruise lift coefficient requirement,and the drag coefficient is expected to be predicted accurately,which involves the instability characteristics and transition position of the flow.The pressure coefficient of the RAE2822 wing with given constant lift coefficient is obtained by solving the three-dimensional Navier-Stokes equation numerically,and then the mean flow is calculated by solving the boundary layer（BL） equation with spectral method.The cross-flow instability characteristic of boundary layer of swept wing in the windward and leeward is analyzed by linear stability theory（LST）,and the transition position is predicted by eNmethod.The drag coefficient is numerically predicted by introducing a laminar/turbulent indicator.A simple approach to calculate the lift coefficient of swept wing is proposed.It is found that there is a quantitative relationship between the angle of attack and sweep angle when the lift coefficient keeps constant;when the angle of attack is small,the flow on the leeward of the wing is stable.when the angle of attack is larger than 3°,the flow becomes unstable quickly;with the increase of sweep angle or angle of attack the disturbance on the windward becomes more unstable,leading to the moving forward of the transition position to the leading edge of the wing;the drag coefficient has two significant jumping growth due to the successive occurrence of transition in the windward and the leeward;the optimal range of sweep angle for civil aircraft is suggested.

Drag Reduction and Secondary-Flow Occurrence by Square Biplane Grid

In this paper, the characteristics of the three-dimensional flow field around the circular cylinder members forming a square biplane grid were experimentally investigated by using a wind tunnel and a water tunnel. In the wind tunnel testing, the span wise and circumference pressure distributions of surface on the circular cylinder were measured on the center mesh members formed by biplane grid in detail. Local drag coefficient was calculated from the surface pressure distributions. In addition, the flow visualization was performed in the water tunnel. As a result, it was suggested that the flow penetrating the contact region produced secondary-flow behind the biplane grid. Accordingly, the drag reduction would be caused by the presence of the secondary-flow.

基于PowerFlow的某重型牵引车外流场数值分析

在整车开发过程中,为更好地用车外流场的CFD分析为汽车气动外形进行设计和优化,文章针对某重型牵引车,利用基于LBM方法的大型商用CFD软件PowerFlow,建立了整车三维计算模型,并进行了外流场数值模拟,计算得到该重型牵引车的阻力系数为0.621,通过分析车身的压力分布及车身周围的速度分布等情况,提出了基于CFD分析结果的改进措施:在货箱前端和后端各加一个导流装置。结果表明:改进后整车风阻系数为0.589,较原来降低5.15%,效果较显著。该方法为整车气动性能设计提供了理论依据。

Basic Laws in Mechanics of Turbulent Flows

Turbulent flow is a basic form of fluid motion widely observed in nature. In hydraulic engineering, especially in the study of sediment movement, turbulence is a key problem. In this paper, based on the stochastic theory of wall turbulence developed by the author and the results by other investigators, fluc-tuation and mean structures and drag coefficient for Newtonian and drag reduction flows in all states (laminar, transitional, turbulent) and in all regions (smooth, transitional, rough) are theoretically discussed in detail. General laws for laminar and turbulent flows obtained by the author are verified by the experimental results obtained by others, and there is good agreement between them.

LARGE EDDY SIMULATION AND SPECTRUM ANALYSIS OF FLOW AROUND TWO SQUARE CYLINDERS ARRANGED SIDE BY SIDE

Large eddy simulation cooperated with the second order full extension ETG(Euler-Taylor-Galerkin) finite element method was applied to simulate the flow around two square cylinders arranged side by side at a spacing ratio of (1.5.) The second order full extension ETG finite element method was developed by Wang and He. By means of Taylor expansion of terms containing time derivative, time derivative is replaced by space derivative. The function of it is equal to introducing an artificial viscosity term. The streamlines of the flow at different moments were obtained. The time history of drag coefficient, lift coefficient and the streamwise velocity on the symmetrical points were presented. Furthermore, the symmetrical problem of the frequency spectrum of flow around two square cylinders arranged side by side were studied by using the spectral analysis technology. The data obtained at the initial stage are excluded in order to avoid the influence of initial condition on the results. The power spectrums of drag coefficient, lift coefficient, the streamwise velocity on the symmetrical points were analyzed respectively. The results show that although the time domain process of dynamic parameters is non-symmetrical, the frequency domain process of them is symmetrical under the symmetrical boundary conditions.

Two-Dimensional Numerical Simulation of Flow Around Three-Stranded Rope

Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-ε model and Shear-Stress Transport κ-ω(SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3–1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.

Calculation of terminal velocity in transitional flow for spherical particle

The terminal velocity has been widely used in extensive fields,but the complexity of drag coefficient expression leads to the calculation of terminal velocity in transitional flow e1 < Re 6 1000 T with much more difficulty than those in laminar flow eRe 6 1T and turbulent flow eRe P 1000 T.This paper summarized and compared 24 drag coefficient correlations,and developed an expression for calculating the terminal velocity in transitional flow,and also analyzed the effects of particle density and size,fluid density and viscosity on terminal velocity.The results show that 19 of 24 previously published correlations for drag coefficient have good prediction performance and can be used for calculating the terminal velocity in the entire transitional flow with higher accuracy.Adapting two dimensionless parameters(w*,d*),a proposed explicit correlation,w*=-25:68654 exp(-d*/77:02069)+24:89826,is attained in transitional flow with good performance,which is helpful in calculating the terminal velocity.

Drag Coefficients of Golf Balls

Drag across a golf ball can affect distance traveled when hitting a ball. An average golf ball will have a drag coefficient of, 0.24 CD ReD 35 m/s. This research found that a significantly deeper dimple pattern will greatly affect the boundary layer, thus changing the drag coefficient and boundary layer.

Numerical Analysis of Cavity-Based Control of Base Pressure Variations at Supersonic Mach Numbers

In the present study,the base pressure variations induced by the presence of a cavity,known to have a strong influence of the behaviour of supersonic projectiles,are investigated through numerical solution of the balance equations for mass,momentum,and energy.An area ratio of four is considered and numerical simulations are carried out at Mach M=1.2,1.4,1.6,and 1.8 assuming no cavity or cavity locations 0.5D,1D,1.5D,and 2D.The inlet pressure of the nozzle is considered as a flow variable.The Taguchi method is also used,and the considered cases are then analyzed using a full factorial experimental design.The results show that the cavity is effective in increasing the base pressure for the conditions examined.For other nozzle pressure ratios,cavities do not lead to passive control due the change in the reattachment length.The distribution of wall pressure reveals that,in general,a cavity used to implement passive control of the base pressure does not adversely influence the flow pattern in the domain.

壁面约束下椭球颗粒曳力特性研究

颗粒两相流系统广泛存在于自然界和工程应用中,实际颗粒往往并非球形且受其附近壁面的影响。基于欧拉-拉格朗日方法的颗粒两相流数值模拟已成为非球形颗粒两相流系统设计的重要工具,然而其准确性受限于非球形颗粒曳力模型。因此,深入研究壁面约束下非球形颗粒曳力特性并发展近壁修正预测模型具有重要意义。本文采用直接数值模拟方法对有限雷诺数(0.5≤Re≤10)下,不同颗粒长轴取向与来流之间的夹角以及颗粒-壁面间距的单椭球颗粒曳力特性开展详细数值研究,分析比较不同工况下曳力系数的变化,探明雷诺数、攻角以及壁面间距对椭球颗粒曳力系数的影响规律,并评估现有自由流中椭球颗粒曳力关系式的适用性,最后发展了考虑近壁修正的椭球颗粒曳力预测模型,为优化非球形颗粒两相流数值模拟工具提供重要支撑。

Influence of Cavity Leakage flow on Corner Separation in a Shrouded Stator Cascade

The impacts of the cavity leakage flow on the shrouded stator aerodynamic performance were investigated by modelling the annular cascade mainstream with the seal cavity flow path based on the validated numerical method.Meanwhile,the interactions between the cavity leakage and the mainstream were also determined in the current study.The development of hub corner separation under the action of leakage was discussed and the total pressure loss coefficient as well as the entropy-based loss coefficient was employed to evaluate the performance changes at different seal clearances and cavity rotational speeds.The results show that the cavity leakage flow induces a new vortex near the blade leading edge and plays an important role in the development of passage vortex and the size of concentrated shedding vortex.By increasing the seal clearance with more cavity leakage flow rate,an increase in the pitchwise extent of the separation region under 15%span is significant and the total pressure loss in the separation core increases.In addition,with the increase of cavity rotating speed,the starting point of corner separation moves backward,reducing the size and depth of the hub corner separation.The mainstream loss reduction in combination with the entropy increase in the seal cavity causes the entropy-based loss coefficient to perform a trend of decreasing first and then increasing with the cavity speed.

Influences of cavity leakage on the design of low flow coefficient centrifugal impeller

The low flow coefficient centrifugal impeller(LFCCI)gives a relatively low efficiency and a special treatment is required for the design of this kind of impeller.This paper investigates the influences of cavity leakage on the performance prediction and design of LFCCI based on Computational Fluid Dynamics(CFD)techniques.The results show that,the reduction in the effi-ciency of impeller due to the introduction of cavity leakage varies with the blade shape of impeller in a wide range since there is a strong and complex interaction of main flow and leakage flow in the LFCCI.To get a credible optimization result,the backside and foreside cavities should be considered in the CFD-based design of LFCCI.

切向射流对垂直管旋流载料输送的影响特性

为了提高非球形颗粒垂直液压输送系统的效率和安全性,采用一种新型带切向射流入口的管道输送系统。基于计算流体力学-离散元法(CFD-DEM)耦合方法,采用改进的非球形曳力系数模型对液固两相流动特性进行分析。研究不同切向流动比例对不同形状颗粒浓度和曳力的影响。根据颗粒的浓度来衡量输送效率,依据颗粒的曳力来评估输送安全性。结果表明:在旋流作用下,不同形状颗粒之间的浓度间隙和轴向阻力间隙减小,颗粒浓度增大,各组分颗粒混合输送均匀。

Precise drag prediction of airfoil flows by a new algebraic model

We report the results of accurate prediction of lift(C L)and drag(C D)coefficients of two typical airfoil flows(NACA0012 and RAE2822)by a new algebraic turbulence model,in which the eddy viscosity is specified by a stress length(SL)function predicted by structural ensemble dynamics(SED)theory.Unprecedented accuracy of the prediction of C D with error of a few counts(one count is 10−4)and of C L with error under 1%-2%are uniformly obtained for varying angles of attack(AoA),indicating an order of magnitude improvement of drag prediction accuracy compared to currently used models(typically around 20 to 30 counts).More interestingly,the SED-SL model is distinguished with fewer parameters of clear physical meaning,which quantify underlying turbulent boundary layer(TBL)with a universal multi-layer structure,and is thus promising to be more easily generalizable to complex TBL.The use of the new model for the calibration of flow condition in experiment and the extraction of flow physics from numerical simulation data of aeronautic flows are discussed.

计算域尺寸对风力机翼型数值模拟的影响

计算域尺寸的选取对风力机翼型数值模拟至关重要,文章通过建立13种不同尺寸的计算域模型,采用雷诺时均N-S方程和SST k-ω湍流模型,在雷诺数为3×10^(6)的条件下,分析不同计算域尺寸对NACA63-418翼型升力系数、阻力系数、压强系数和流场分布规律的影响。计算结果与实验结果的对比表明,风力机翼型数值模拟的计算域最小尺寸推荐为距离翼型前缘14倍弦长,距离翼型后缘27倍弦长,距离两侧边界15倍弦长。

基于幂律液固曳力模型流化床内湿颗粒流动特性的研究

采用欧拉-欧拉双流体模型(TFM)结合颗粒动理学理论(KTGF)方法,对三维幂律流化床中的液固两相流动行为进行了模拟。基于幂律流体的流变方程以及压降方程,提出了两种幂律液固曳力模型,引入了考虑液膜效应的湿颗粒动态恢复系数模型,计算幂律流体与湿颗粒之间的作用力。将预测固含率分别与文献中测得的实验数据进行比较,结果表明结合动态恢复系数模型的相对误差介于0.45%~1.59%,与实验结果吻合较好。探究了稠度系数K以及流性指数n对颗粒流动特性的影响,结果表明随着流变参数的增大,床层内的颗粒平均浓度降低,湿颗粒表面液膜逐渐变厚,法向恢复系数降低;颗粒拟温度随n的升高先增大后减小,随K的上升而增大;曳力系数、颗粒压力以及颗粒黏度均随流变参数的增大而逐渐减小。颗粒在壁面处的浓度明显高于中心处附近的浓度,且颗粒在中心处向上运动,在壁面处附近回落,在流化床中形成环-核结构。

模拟草被覆盖下坡面水流阻力特性试验研究

探究植被覆盖下的坡面流阻力特性对土壤侵蚀模型的建立有着重要意义。通过3个坡度、7个流量和10个草被覆盖度下的定床冲刷实验,系统分析坡面薄层水流的流型流态与阻力特性。实验结果表明,坡面水流流态受到草被覆盖度与坡度的综合影响,主要分布在层流区及过渡流区。通过等效粗糙度和坡面水流流动阻力规律,推导出等效阻力系数f_(e)的计算公式,公式表明草被覆盖度是影响水流阻力的重要因素,f_(e)值随覆盖度增加而整体增大,实验结果显示当覆盖度在0%~37.68%的范围内时,等效阻力系数始终小于1.5;而当覆盖度在56.52%~94.2%的范围内时,f_(e)由0.697~3.042增长至2.440~14.393。淹没度及雷诺数对等效阻力系数的影响与覆盖度密切相关,覆盖度低于18.84%时,等效阻力系数随淹没度与雷诺数的增加而呈减小趋势;而当覆盖度高于65.94%时,等效阻力系数随淹没度与雷诺数的增加而以较大的速率上升。研究结果以期为水土流失综合治理提供理论支撑。