共查询到20条相似文献,搜索用时 15 毫秒
1.
G. I. Kelbaliyev 《Theoretical Foundations of Chemical Engineering》2011,45(3):248-266
This article, which is largely a review, deals with the drag force and drag coefficient for rigid spherical and deformable
particles in ordinary and non-Newtonian fluids. The most important theoretical formulas for small Reynolds numbers of Re ≪
1 and semiempirical formulas for the drag coefficient in a wide Re range up to 106 are presented. The deformation of drops and bubbles and its effect on the drag coefficient are considered. 相似文献
2.
Comparison of formulas for drag coefficient and settling velocity of spherical particles 总被引:1,自引:0,他引:1
Nian-Sheng Cheng 《Powder Technology》2009,189(3):395-1451
Two formulas are proposed for explicitly evaluating drag coefficient and settling velocity of spherical particles, respectively, in the entire subcritical region. Comparisons with fourteen previously-developed formulas show that the present study gives the best representation of a complete set of historical data reported in the literature for Reynolds numbers up to 2 × 105. 相似文献
3.
S. Bhattacharyya 《Chemical engineering science》2006,61(13):4451-4461
The flow-field and solute transport through and around a porous cylinder is investigated numerically. The range of Reynolds number (based on the cylinder diameter and the uniform sinking rate of the cylinder) considered here is between 1 and 40 with Darcy number (Da) in the range 10-6?Da?1.5 and porosity in the range 0.629?ε?0.999. The motivation of the present study is the application of flow through porous cylinder extensively applied in nuclear biological chemical filters as well as reduction of carbon fines in filtered water. The influence of Da on the drag coefficient, separation angle, recirculation length, streamline and vorticity pattern are investigated. The drag ratio, defined as the ratio of drag coefficient of porous cylinder to that of solid cylinder, is found to approach zero from unity as Da is increased from 10-6 to 1.5. The separation point shifts towards the rear stagnation point as Da is increased. The time evolution of the solutal field at different Reynolds number and Darcy number is presented. A long slender concentration plume is found to evolve from the cylinder with decreasing concentration at the outer edge. 相似文献
4.
The rising behavior of single bubbles has been investigated in six systems with different viscosity and Morton number(Mo) from 3.21×10-11 to 163. Bubbles with maximum equivalent diameter of up to 16 mm were investigated. The bubble Reynolds number(Re) ranged from 0.02 to 1200 covering 3 regimes in which two func-tions are obtained relating the drag coefficient,CD,with Re and Mo. It has been found that in the high Reynolds number regime the drag coefficient increases until the Reynolds number of about 1200. The classic expression of Jamialahmadi(1994) is improved and extended to high viscosity liquids. A new relationship for the aspect ratio of deformed bubbles in terms of Re,the Etvs number and Mo,applicable to a wide range of system properties,espe-cially in high viscosity liquids,is also suggested. 相似文献
5.
A simple correlation formula for the standard drag coefficient (i.e. a single stationary particle in a uniform flow) of arbitrary shaped particles is established using a large number of experimental data from the literature and a comprehensive numerical study [A. Hölzer, M. Sommerfeld, IUTAM Symposium on Computational Approaches to Multiphase Flow, Springer, 2006]. This new correlation formula accounts for the particle orientation over the entire range of Reynolds numbers up to the critical Reynolds number. Such a correlation may be easily used in the frame of Lagrangian computations where also the particle orientation along the trajectory is computed. 相似文献
6.
A general drag coefficient has been used in the equation of motion for solid spherical particles. The time constants, stopping times, and settling velocities in a still atmosphere are computed for a wide range of Reynolds numbers. The settling times are compared with the times calculated when a particle is falling in a fluctuating atmosphere. It is found that such particles will get significantly longer settling times owing to an enhancement in the drag coefficient caused by an increase of the relative velocity between the particle and the fluid. Surprisingly, this enhancement is present for a horizontal wind field due to a coupling between particle motion in different directions, but it is also present for a vertical field. The effect is most pronounced in the intermediate Reynolds number region, slightly above the Stokes range, where the increase in settling time can be more than 10% for certain fluctuation frequencies and amplitudes. This indicates that such particles must be carefully treated when they are falling in a nonstationary medium 相似文献
7.
Gudret Kelbaliyev 《Chemical Engineering Communications》2013,200(12):1623-1637
Some new correlations are derived to estimate the drag coefficient, the shape deformation, and the rising velocity of particles moving in an infinite liquid medium. The correlations are derived in terms of the dimensionless groups such as Reynolds number (Re), Morton number (Mo), and Weber number (We). The derivations are based on the experimental data or some other correlations given in the literature. A single statement is proposed to estimate the drag coefficient for the spherical solid particles that may be applicable in the range of 0.5 < Re < 105. Similarly, some other equations are also derived to estimate the drag coefficient, the shape deformation, or the rising velocity for gas bubbles or liquid drops. The drag equation is applicable in the range of 0.5 < Re < 100 and 9 × 10?7 ≤ Mo ≤ 7; the shape deformation equation is applicable in the range of 0.5 < Re < 100 and 1.1 × 10?5 ≤ Mo ≤ 7; and the rising velocity equation is applicable in the range of 0.1 < Re < 100 and 9 × 10?7 ≤ Mo ≤ 80. The model predictions are compared with the experimental data and with the other correlations given in the literature. The results indicated that the model predictions are in a good agreement with the literature data. 相似文献
8.
Results of experimental investigations on the influence of turbulence intensity and pitch-to-diameter ratio on heat transfer and pressure drop in single rows of plain tubes are presented. Vertically arranged tubes with 16 different pitch-to-diameter ratios between 1.26 and 5.73 were heated by saturated steam, condensing inside, and cooled outside by air in cross-flow. The turbulence intensity in the entrance cross-section was enhanced by means of different biplanar grids installed in the test section of a wind tunnel upstream of the single rows. The mean streamwise turbulence intensity behind the grids, measured with a constant temperature hot-wire anemometer, varied between 0.8% and 38.8%. Reynolds numbers ranged from 4 × 103 to 2 × 105. For single rows, the measurements show that the Nusselt number for a given turbulence intensity increases with increasing Reynolds number. In the investigated range of Reynolds numbers, the drag coefficient is only slightly influenced by the inlet turbulence intensity. The use of turbulence grids thus leads to higher efficiencies of heat exchangers. 相似文献
9.
Bo Ouyang Li-Tao Zhu Zhao-Quan Wen Xizhong Chen Zheng-Hong Luo 《American Institute of Chemical Engineers》2023,69(9):e18170
The drag force model is vital for capturing gas–solid flow dynamics in many simulation approaches. Most of the homogeneous drag models in the literature are expressed as a function of phase fraction (ε) and particle Reynolds number (Res). In this work, we use a “big data” approach to analyze ~108 data points for drag coefficient (Fd) for Geldart Group A particles at atmospheric pressure and find that the contribution of Res on Fd is much less than ε based on the Maximal information coefficient analysis. Thus, these drag models are separately reduced to machine learning and conventional expressions only related to ε. The reduced models achieve almost the same predictive performance as the originals in bubbling, turbulent, and jet fluidizations. Moreover, the reduced models provide better numerical stability for coarse grid simulations. These findings provide new insights into the drag coefficient for Geldart Group A particles under full fluidization conditions. 相似文献
10.
In a recently published paper(1), it has been demonstrated that the drag coefficient—Reynolds number relationship for a single spherical solid particle may be applied to multi-particle systems as well, provided that modified definitions of the drag coefficient and Reynolds number incorporating suitable functions of the particles volume fraction are used. This generalised approach is now extended to include the case of a fluid dispersed phase. This done by incorporating a function of the ratio of the phase viscosities, based on theoretical derivations due to Hadamard—Rybczinski and Taylor in the modified definition of Reynolds number. All available experimental data (88 points from 3 sources, on 12 different liquid-liquid systems) were recalculated and correlated on this basis. 相似文献
11.
P. Sivakumar 《Chemical engineering science》2006,61(18):6035-6046
The conditions for the formation of a wake and for the onset of wake instability for the flow of power-law fluids over an unconfined circular cylinder are investigated numerically by solving the continuity and momentum equations using FLUENT (version 6.2). The effect of power-law index on the critical Reynolds numbers, Strouhal number and drag coefficient has been presented over a wide range of power-law index (0.3?n?1.8) thereby establishing the limits of the flow without separation and the steady symmetric flow regimes, respectively. While both the shear-thinning (n<1) and the shear-thickening (n>1) seem to lower the value of the critical Reynolds number denoting the onset of wake instability as compared to that for Newtonian fluids, the effect is seen to be more prominent for shear-thickening fluids than that for shear-thinning fluids. The corresponding values of the critical Strouhal number (Stc) and drag coefficient have also been presented for the critical values of the Reynolds number. Included here are also a series of streamline plots showing the onset of asymmetry and of the time-dependent flow regime. 相似文献
12.
The Joule-Thomson effect is known to be important in arctic gas pipelines. The Joule-Thomson effects on forced convective heat transfer in the thermal entrance region of pipes with uniform wall temperature are studied for steady fully developed turbulent gas flows by the Graetz method. Thermal entrance heat transfer results are presented for Prandtl number 0.72, Reynolds number 105 and Brinkman number ± 0.1, ± 1.0 with Joule-Thomson parameter Jμ ranging from 0 to 1.0 to cover the possible range in practical applications. Bulk temperatures and Nusselt numbers are also presented for fully developed flow with Reynolds numbers from 5 × 103 to 106. For given Prandtl and Reynolds numbers, the asymptotic Nusselt number is found to be dependent on the Joule-Thomson parameter only and is independent of Brinkman number. The fully developed bulk temperature is a linear function of Brinkman number and a linear relationship exists between the bulk temperature parameter (-θbf/Br) and the Joule-Thomson parameter Jμ for given Prandtl and Reynolds numbers. 相似文献
13.
Measurements are reported for air drag on fine filaments whose axes are oriented at oblique and normal angles to the air velocity. In terms of the drag coefficient CDN the data are fit well by the following relation: CDN = 6.96(ReDN)?0.440(d/d0)0.404, where ReDN is the Reynolds number based on flow normal to the fiber axis, and d/d0 is a dimensionless fiber diameter. A wide range of conditions were tested: filament diameters ranged from 13 to 390 microns, gas velocities ranged from 22 to 83 m/s, and fiber Reynolds numbers ranged from 29 to 2120. 相似文献
14.
采用格子Boltzmann方法(LBM)研究了单颗粒绕流流动过程。通过使用LBM中的LBGK(lattice Bhatnagar-Gross-Krook)模型和二阶精度的曲线边界条件处理方法,实现了对单颗粒绕流问题的定常及非定常流动过程中涡结构的模拟。采用动量交换法分别计算了Reynolds数在0.1~200范围内27个不同Reynolds数时的曳力系数,并将计算结果拟合得到基于LBM数值模拟的曳力曲线。计算结果表明,LBM在气固两相流的模拟计算中具有精确、可靠的优点,使用LBM模拟计算曳力曲线的方法经济、易行,并且可以克服由传统实验方法获得曳力曲线的局限性。 相似文献
15.
Pilot scale experiments have been performed to study the effect of a heterogeneous surfactant into the drag and heat transfer coefficient in crude oil pipelines. The effects of surfactant concentration, pipe diameter, Reynolds number and temperature were studied in this research program.
An extensive set of data was obtained for heat transfer and friction coefficients for a heterogeneous surfactant known as MDR-2000. A wide range of Reynolds numbers were covered and experiments were conducted for many different Prandtl numbers. All drag and heat transfer reduction experiments were performed in the same installation using the same measurement techniques which facilitates the assessment of the trends caused by the various parameters studied.
Typical results showed that the friction coefficient was reduced by half at the optimum concentration. While, the heat transfer coefficient was reduced even more dramatically. 相似文献
An extensive set of data was obtained for heat transfer and friction coefficients for a heterogeneous surfactant known as MDR-2000. A wide range of Reynolds numbers were covered and experiments were conducted for many different Prandtl numbers. All drag and heat transfer reduction experiments were performed in the same installation using the same measurement techniques which facilitates the assessment of the trends caused by the various parameters studied.
Typical results showed that the friction coefficient was reduced by half at the optimum concentration. While, the heat transfer coefficient was reduced even more dramatically. 相似文献
16.
C. Shin 《Chemical engineering science》2006,61(8):2324-2329
In this paper, the numerical model for separation efficiency and transport in periodic porous media is studied. Finite element method was used to simulate the development of a predictive model of behavior of porous media during injection of particles. This paper describes the effects of injected particle size, Reynolds number and particle drag coefficient. The numerical results show that the separation efficiency increased with injected particle size increase. The separation efficiency is found to increase with increasing Reynolds number. For the effect of drag force, CD, in porous media, numerical results show that for CD<10 and CD>100, the separation efficiency is not affected by drag coefficient in the range of drag coefficient from 10 to 100, and the separation efficiency significantly depends on the Reynolds number. 相似文献
17.
The free surface and zero vorticity cell models have been combined with the equations of motion to investigate numerically the steady flow of incompressible power‐law (shear‐thinning and shear‐thickening) fluids across banks of long cylinders. The equations of motion in the stream function/vorticity formulation have been solved numerically using a second order accurate finite difference method to obtain extensive information on the behaviour of the drag coefficient, surface vorticity distribution, streamlines and iso‐vorticity patterns, for high Reynolds numbers (Re = 50 500) and using a wide range of power‐law index (0.3 ≤ n ≤ 2.0), and porosity (0.4 ≤ e ≤0.9) values. The behaviour of the aforementioned parameters at low Reynolds numbers has also been investigated and validated using theoretical and numerical work from the literature. The results reported here enable extension of the limits of creeping flow behaviour up to Re = 50 for fluids with highly shear‐thickening characteristics under low porosity conditions. 相似文献
18.
The problem of steady-state freezing of liquids in turbulent flow inside a tube with its walls kept at a uniform temperature lower than the freezing temperature of the liquid is solved for a wide range of Reynolds and Prandtl numbers, 104 ≤ Re ≤ 104 and 0 ≤ Pr ≤ 103. The effects of Prandtl and Reynolds number on the location of the solid-liquid interface and on the heat transfer rate as a function of position along the tube are established. 相似文献
19.
Pressure drop and homogenization efficiency of a motionless mixer of helical type have been studied experimentally. For evaluation of the drag coefficient the equation has been proposed which is valid within the range of Reynolds number from 10?2 to 104 The efficiency of the motionless mixer for mixing of two Newtonian liquids has been investigated by using a decolourization method. For the operating conditions studied in this work it appears that there is the worse performance of the mixer about the Reynolds number of 50. No influence of volume flow rate ratios (from 1 to 10) upon the performance of the mixer has been observed. A higher number of mixing elements must be applied for homogemzation of liquids with viscosity ratios above 100 as compared with that for viscosity ratio 1. 相似文献
20.
Newton's second law of motion has been applied here to a vaporizing drop being depleted according to the ‘d2-relation’ in order to determine the velocity histories of drops injected vertically into stagnant gas. In the evaluation of the drag forces, three possible values of drag coefficient, namely Stokes value based on instantaneous velocity and diameter, Stokes value based on average velocity and initial diameter, and a constant value of 1.0 independent of Reynolds number (for which there is experimental justification at Reynolds numbers not too small), have been employed. The second and third cases result in non-linear differential equations for the velocity histories, and have been solved using the Runge-Kutta-Nyström method. The effects on the histories of the initial velocity with which the drops are injected into the ambient gas, either vertically down or up, have been investigated for all three drag values. The results have been plotted in terms of normalized coordinates which (unlike others in the literature) are shown to have physical significance. The concept of a terminal velocity does not apply for a particle whose size is decreasing with time. The velocity histories for the two Stokes drag coefficients are quite similar, despite the considerably different manner in which the Reynolds number is defined in the two cases; this vindicates the common practice of calculating and correlating experimental values of (Re) and CD on the basis of initial diameter and average velocity for the sake of convenience and practicality. For large downward injection velocities, the gravitational and buoyancy forces can be neglected, especially for the two cases of Stokes CD; but the errors for all three cases of upward injection are too significant to be neglected. 相似文献