New formula for drag coefficient of cylindrical particles

The drag force on a cylindrical particle is calculated using lattice Boltzmann method.The results show that the drag coefficient of a particle with different orientation angles decreases with increasing Reynolds number.When the principal axis of the particle is parallel to flow,the drag coefficient is much larger than that of others and decreases fastest with increasing Reynolds number,which becomes more obvious with increasing particle aspect ratio.When the principal axis of the particle is inclined to flo...     

The effects of freestream turbulence on the drag coefficient of a sphere

The effects of freestream turbulence intensity and integral length scale as freestream turbulent parameters on the drag coefficient of a sphere were experimentally investigated in a closed circuit wind tunnel. The Reynolds number, Re = Ud/ν, was varied from 2.2 × 10⁴ to 8 × 10⁴ by using spheres with diameter d of 20, 51 and 102 mm in addition to altering the freestream velocity, U. The freestream turbulence intensity Tu and flow integral length scale Λ were manipulated by the utilization of orifice perforated plates. The proper combination of orifice perforated plate hole diameter, sphere size, and sphere location along the center line of the wind tunnel enabled the independent alterations of turbulence intensity and relative integral length scale (Λ/d) from 1.8% to 10.7% and from 0.1 to 2.6, respectively, at each studied Reynolds number. Results show that over the range of conditions studied, the drag always decreases with increasing Tu and, the critical Reynolds number at which the drag coefficient is dramatically reduced is decreased by increasing Tu. Most interestingly, the drag at any particular Re and Tu may be significantly lowered by reducing Λ/d; this is particularly the case at high Re and Tu.     

The importance of turbulence macroscale in determining the drag coefficient of spheres

Turbulence macroscale, from evidence provided, is at least as important as its intensity in determining the drag coefficient of spheres, particularly when macroscale and sphere diameter are comparable. Particular combinations of scale, intensity and Reynolds number can produce sudden and repeatable marked changes in flow conditions which are as important as the well known change in boundary layer conditions at critical Reynolds number. More detailed analysis suggests that other researchers' results appear sometimes to be mutually incompatible simply because they were dealing with differnt areas of the complicated relationship between drag coefficient. Reynolds number, turbulence intensity and macroscale.     

Theoretical-experimental method of determining the drag coefficient of a harmonically oscillating thin plate

A method for determining the drag coefficient of a thin plate harmonically oscillating in a viscous incompressible fluid is proposed. The method is based on measuring the amplitude of deflections of cantilever-fixed thin plates exhibiting damping flexural oscillations with a frequency corresponding to the first mode and on solving an inverse problem of calculating the drag coefficient on the basis of the experimentally found logarithmic decrement of beam oscillations.     

Shock tube spherical particle accelerating study for drag coefficient determination

An original particle accelerating technique has been developed for a shock tube. The trajectories of calibrated spherical particles and in diameter have been measured by the multiple exposure shadowgraph technique coupled with a high speed drum camera. Both particle velocity and acceleration, deduced from the experimental trajectories, allow the determination of the drag coefficients for different, subsonic and supersonic, flow regimes for the particle Reynolds numbers from to and the particle Mach numbers from 0.6 to 1.2. The drag coefficient values have been compared with different correlations found in the literature. Received 8 April 2002/ Accepted 17 June 2002 Published online 19 December 2002 Correspondence to: L. Houas (e-mail: Lazhar.Houas@polytech.univ-mrs.fr)     

An analytic approximation of the drag coefficient for the viscous flow past a sphere

We give an analytic solution at the 10th order of approximation for the steady-state laminar viscous flows past a sphere in a uniform stream governed by the exact, fully non-linear Navier-Stokes equations. A new kind of analytic technique, namely the homotopy analysis method, is applied, by means of which Whitehead's paradox can be easily avoided and reasonably explained. Different from all previous perturbation approximations, our analytic approximations are valid in the whole field of flow, because we use the same approximations to express the flows near and far from the sphere. Our drag coefficient formula at the 10th order of approximation agrees better with experimental data in a region of Reynolds number R_d<30, which is considerably larger than that (R_d<5) of all previous theoretical ones.     

Reynolds number dependence of the drag coefficient for laminar flow through electrically-heated photoetched screens

Experiments are performed to measure the drag coefficient of electrically-heated screens. Square-pattern 80 mesh and 100 mesh screens of 50.8 m-wide wires photoetched from 50.8 m thick Inconel sheets are examined. Ambient air is passed through these screens at upstream velocities yielding wire-width Reynolds numbers from 2 to 35, and electrical current is passed through the screens to generate heat fluxes from o to 0.17 MW/m², based on the total screen area. The dependence of the drag coefficient on Reynolds number and heat flux is determined for these two screens by measuring pressure drops across the screens for a variety of conditions in these ranges. In all cases, heating is found to increase the drag coefficient above the unheated value. A correlation relating the heated drag coefficient to the unheated drag coefficient is developed based on the idea that the main effect of heating at these levels is to modify the Reynolds number through modifying the viscosity. This correlation is seen to reproduce the experimental results closely.List of Symbols A total screen cross sectional area - C fitting coefficient, near unity - c _D heated drag coefficient - c _{D, 0} unheated drag coefficient - C _p air specific heat at constant pressure - D photoetched wire width, sheet thickness - h _s stagnation point heat-transfer coefficient - k air thermal conductivity - M distance between adjacent wires - O open area fraction - p air pressure - p air pressure drop across screen - Pr Prandtl number for air, c _p/k - Q total electrical power to screen - R radius of curvature at stagnation point - Re _D wire width Reynolds number, UD/ - T air temperature - U air speed upstream of screen - air specific heat ratio - air density - air viscosity - exponent in temperature power law for viscosity - () quantity () evaluated at heated screen temperature The authors thank John Lewin and Bob Meyer for their assistance in the design and fabrication of the heated screen test facility and Tom Grasser for his help in performing the experiments. This work was performed at Sandia National laboratories, supported by the U.S. Department of Energy under contract number DE-AC04-94AL85000.     

融合稀疏八叉树与卷积神经网络的汽车风阻系数预测

针对汽车风阻系数预测研究中参数化方法难以准确表征汽车外造型的难题,提出融合稀疏八叉树与卷积神经网络的汽车风阻系数预测方法。将汽车外造型按照八叉树结构离散,使用平均法向量对离散的复杂曲面进行简化,利用卷积神经网络对八叉树形式的汽车外造型进行特征提取,进而对汽车风阻系数进行快速预测。通过改变卷积层数与全连接层数,研究了不同卷积神经网络结构对风阻系数预测精度的影响。与参数化方法相比,本文提出的外造型表示方法能更好地描述模型细节,构建的卷积神经网络结构对风阻系数预测的最小相对误差为1.453%,且计算速度是CFD仿真的1620倍,具有较高的精度及计算效率。     

Reynolds number dependence of the drag coefficient for laminar flow through fine-scale photoetched screens

The laminar steady flow downstream of fine-mesh screens is studied. Instead of woven-wire screens, high-uniformity screens are fabricated by photoetching holes into 50.8 m thick Inconel sheets. The resulting screens have minimum wire widths of 50.8 m and inter-wire separations of 254 m and 318 m for the two screens examined. A flow facility has been constructed for experiments with these screens. Air is passed through the screens at upstream velocities yielding wire width Reynolds numbers from 2 to 35. To determine the drag coefficient, pressure drops across the screens are measured using pressure transducers and manometers. Threedimensional flow simulations are also performed. The computational drag coefficients consistently overpredict the experimental values. However, the computational results exhibit sensitivity to the assumed wire cross section, indicating that detailed knowledge of the wire cross section is essential for unambiguous interpretation of experiments using photoetched screens. Standard semi-empirical drag correlations for woven-wire screens do not predict the present experimental results with consistent accuracy.List of symbols A ₁, A ₂ screen aspect ratios - c _d screen drag coefficient - d woven-wire diameter - D photoetched minimum wire width (spanwise) - f woven-wire screen drag function - M distance between adjacent wires - N spectral-element order - o woven-wire open area fraction - O photoetched open area fraction - _p pressure drop across screen - Re _d woven-wire diameter Reynolds number - Re _D photoetched wire width Reynolds number - U fluid velocity upstream of screen - W photoetched sheet thickness (streamwise) - x, y, z spatial coordinates - fluid density - fluid viscosity     

Approximate solutions for drag coefficient of bubbles moving in shear-thinning elastic fluids

The drag coefficient for bubbles with mobile or immobile interface rising in shear-thinning elastic fluids described by an Ellis or a Carreau model is discussed. Approximate solutions based on linearization of the equations of motion are presented for the highly elastic region of flow. These solutions are in reasonably good agreement with the theoretical predictions based on variational principles and with published experimental data. C _D Drag coefficient - E ^* Differential operator [E ^{* 2} = ²/² + (sin/ ²)/(1/sin /)] - El Ellis number - F _D Drag force - K Consistency index in the power-law model for non-Newtonian fluid - n Flow behaviour index in the Carreau and power-law models - P Dimensionless pressure [=(p – p ₀)/₀ (U /R)] - p Pressure - R Bubble radius - Re ₀ Reynolds number [= 2R U /₀] - Re Reynolds number defined for the power-law fluid [= (2R) ⁿ U ^2–n /K] - r Spherical coordinate - t Time - U Terminal velocity of a bubble - u Velocity - Wi Weissenberg number - Ellis model parameter - Rate of deformation - Apparent viscosity - ₀ Zero shear rate viscosity - Infinite shear rate viscosity - Spherical coordinate - Parameter in the Carreau model - ^* Dimensionless time [=/(U /R)] - Dimensionless length [=r/R] - Second invariant of rate of deformation tensors - ^* Dimensionless second invariant of rate of deformation tensors [=/(U /R)²] - Second invariant of stress tensors - ^* Dimensionless second invariant of second invariant of stress tensor [= / ₀ ² (U /R)²] - Fluid density - Shear stress - ^* Dimensionless shear stress [=/ ₀ (U /R)] - _1/2 Ellis model parameter - ₁ ^2/* Dimensionless Ellis model parameter [= _1/2/ ₀(U /R)] - Stream function - ^* Dimensionless stream function [=/U R ²]     

Comparison of the drag coefficients of bodies moving in liquids with various stratification profiles

For bodies moving in liquids with various stratification profiles, the relation between the drag coefficients considered as functions of the Froude number is investigated. The problems of stratified liquid dynamics have not previously been studied from this viewpoint, either experimentally or theoretically. On the range of the Froude numbers F₁-1, the drag force coefficients obtained from bench measurements of the towing resistance to the uniform horizontal motion of models in two-layer and continuously stratified liquids are compared. The experimental data obtained in a thermocline are then compared with the results of [1,2] for linearly stratified and two-layer liquids.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 4–11, July–August, 1996.     

Measurement of pressure coefficient of melt viscosity: drag flow versus capillary flow

The pressure coefficient of viscosity of poly(α-methylstyrene-co-acrylonitrile) was measured using a high-pressure sliding plate rheometer (HPSPR) and two types of capillary rheometer: a piston-driven device with a throttle at the exit [piston capillary rheometer with throttle (PCRWT)] operated at a fixed flow rate, and a counter-pressure nitrogen capillary rheometer (CPNCR) operated at a fixed pressure drop. In the HPSPR, the pressure, shear rate, density, and viscosity are all uniform throughout the sample, while the analysis of capillary data is complicated by the axial pressure gradient and the radial shear rate gradient. The polymer was found to be piezorheologically simple, and the HPSPR data indicated that the pressure coefficient of viscosity β ≡ dln(a _P)/dP decreased slightly with increasing pressure at high pressure. While β from PCRWT data from different laboratories and instruments agreed fairly well, the β values were on average about 2/3 of that from the HPSPR. The CPNCR yields β about 18% lower than that of the HPSPR.     

Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 m and on the order of 10¹² particles/m³, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.     

A drag coefficient model for Lagrangian particle dynamics relevant to high-speed flows

A blended drag coefficient model is constructed using a series of empirical relations based on Reynolds number, Mach number, and Knudsen number. When validated against experiments, the drag coefficient model produces matching values with a standard deviation error of 2.84% and a maximum error of 11.87%. The model is used in a Lagrangian code which is coupled to a hypersonic aerothermodynamic CFD code, and the particle velocity and trajectory are validated against experimental results. The comparative results agree well and show that the new blended drag coefficient model is capable of predicting the particle motion accurately over a range of Reynolds number, Mach number, and Knudsen number.     

三角形格构式塔身体型系数及屏蔽特性研究Study on shape coefficient and shielding effects of triangular latticed tower body

为满足高压／特高压输电铁塔风致倒塌问题对铁塔体型系数的精准度需求,研究了完全结构化多块网格对格构式三角形输电塔塔身流场的模拟能力,探讨了不同规范体型系数对某铁塔的适用性,并分析了塔身杆件复杂流动干扰作用下的屏蔽特性。结果表明,数值模拟与风洞试验的体型系数吻合很好;完全结构化网格能高保真、高度正交地对铁塔塔身这类复杂空间桁架流场进行离散;《英国杆塔荷载规范》的规定结果虽偏于保守,但其趋势最为接近真实值;在塔身桁架结构各个杆件之间流动干扰作用下,角钢弯折角朝向来流比背向来流的屏蔽作用更强;斜材弯折角背向气流和竖向辅助材弯折角朝向气流的组合之间的流动干扰,使得其对气流的屏蔽作用最强。     

CFD-DEM simulation of Small-Scale Challenge Problem 1 with EMMS bubble-based structure-dependent drag coefficient

In this study,the energy minimization multi-scale(EMMS)/Bubbling model is coupled with the computational fluid dynamics/discrete element method(CFD-DEM)model via a structure-dependent drag coefficient to simulate the National Energy Technology Laboratory(NETL)small-scale challenge problem using the open-source multiphase flow code MFIX.The numerical predictions are compared against particle velocity measurements obtained from high-speed particle image velocimetry(HSPIV)and differential pressure measurements.The drag-reduction effect of the EMMS bubble-based drag coefficient is observed to significantly improve predictions of the horizontal particle velocity and granular temperature when compared to several other drag coefficients tested;however,the vertical particle velocity and pressure fluctuation characteristic predictions are degraded.The drag-reduction effect is characterized by a reduction in the sizes of slugs or voids,as identified through spectral decomposition of the pressure fluctuations.Overall,this study shows great promise in employing drag coefficients,developed via multi-scale approaches(such as the EMMS paradigm),in CFD-DEM models.     

静水中气泡上升运动及阻力系数研究

采用模型计算法与实验法结合的方式对静水中气泡上升运动行为进行研究。通过牛顿运动定律,基于不同物理模型,建立气泡在水中运动的微分方程;假设气泡在运动过程中的关键参数取值,推导小气泡在水中浮升过程中的气泡行为预测公式;针对不同流态下的气泡上升关键参数进行适应性分析和算例计算。通过设计气泡上升运动实验,对气泡上升运动公式进行适应性分析,修正关键参数的取值。据此提出一种小气泡上升运动规律的计算方法以及关键参数取值方式及参考区间。