The flow fields in and around a droplet moving axially within a tube

1970 ◽  
Vol 41 (4) ◽  
pp. 689-705 ◽  
Author(s):  
G. Hetsroni ◽  
S. Haber ◽  
E. Wacholder
Keyword(s):  
Flow Field ◽  
Viscous Fluid ◽  
Velocity Distribution ◽  
General Equation ◽  
Iterative Procedure ◽  
Settling Velocity ◽  
Circular Tube ◽  
Higher Order ◽  
Spherical Droplet ◽  
Special Cases

A solution is presented for the flow field in and around a single spherical droplet or bubble moving axially at an arbitrary radial location, within a long circular tube. In the tube there is viscous fluid flowing with a constant Poiseuillian velocity distribution far from the droplet.The settling velocity of the droplet or bubble is \begin{eqnarray*} U = \frac{2(\rho_i-\rho_e)ga^2}{9\mu_e}\frac{1+\alpha}{\frac{2}{3}+\alpha}\left[1-\frac{2+3\alpha}{3(1+\alpha)}\left(\frac{a}{R_0}\right)f\left(\frac{b}{R_0}\right)\right]+U_0\left[1-\left(\frac{b}{R_0}\right)^2\right.\\ \left. - \frac{2\alpha}{2+3\alpha}\left(\frac{a}{R_0}\right)^2\right] + O\left(\frac{a}{R_0}\right)^3. \end{eqnarray*} This is a general equation and it contains as special cases the familiar solutions of Stokes, Hadamard-Rybczynski, Brenner & Happel, Greenstein & Happel and Haberman & Sayre.The function describing the deviation of the interface from sphericity is solved and an iterative procedure is suggested for obtaining higher order solutions.

THE GAS-ASSISTED FLUID FLOW EXPELLED IN FRONT OF A LONG BUBBLE IN A CIRCULAR TUBE

2006 ◽  
Vol 30 (1) ◽  
pp. 7-17
Author(s):  
Cheng-Hsing Hsu ◽  
Kuang-Yuan Kung ◽  
Po-Chuang Chen ◽  
Sam-Dih Huang
Keyword(s):  
Fluid Flow ◽  
Flow Field ◽  
Viscous Fluid ◽  
Transient Flow ◽  
Circular Tube ◽  
Bypass Flow ◽  
Steady State Flow ◽  
Recirculation Flow ◽  
Successive Over Relaxation ◽  
Viscous Flow Field

This study investigates the steady-state flow field in a circular tube filled with a viscous fluid expelled by a long gas bubble. We use a finite difference method with successive over-relaxation in the computation of the viscous flow field. An empirical bubble profile is employed to simplify the computation of the interface shape between the gas and the viscous fluid. By varying the ratio of the bubble width to the diameter of the circular tube (λ), the numerical simulation shows three fluid flow patterns: the complete bypass flow, the recirculation flow and the transient flow. The transient flow is only observed in a limited λ range of √1/2 < λ < 0.7143 and isn’t clearly discussed in the previous studies. The variation of vorticity also is observed by the various sizes of λ.

Methodology of Calculation the Terminal Settling Velocity Distribution of Irregular Particles for High Values of the Reynold’s Number/Metodologia Wyliczania Rozkładu Granicznej Prędkości Opadania Ziaren Nieregularnych Dla Wysokich Wartości Liczb Reynoldsa

2014 ◽  
Vol 59 (2) ◽  
pp. 553-562 ◽  
Author(s):  
Agnieszka Surowiak ◽  
Marian Brożek
Keyword(s):  
Velocity Distribution ◽  
Settling Velocity ◽  
Random Variables ◽  
Independent Random Variables ◽  
Calculation Algorithm ◽  
Shape Coefficient ◽  
Geometrical Properties ◽  
Size And Shape ◽  
Physical Density ◽  
Settling Velocity Distribution

Abstract Settling velocity of particles, which is the main parameter of jig separation, is affected by physical (density) and the geometrical properties (size and shape) of particles. The authors worked out a calculation algorithm of particles settling velocity distribution for irregular particles assuming that the density of particles, their size and shape constitute independent random variables of fixed distributions. Applying theorems of probability, concerning distributions function of random variables, the authors present general formula of probability density function of settling velocity irregular particles for the turbulent motion. The distributions of settling velocity of irregular particles were calculated utilizing industrial sample. The measurements were executed and the histograms of distributions of volume and dynamic shape coefficient, were drawn. The separation accuracy was measured by the change of process imperfection of irregular particles in relation to spherical ones, resulting from the distribution of particles settling velocity.

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

Line Contact Deformation: A Cylinder Between Two Flat Plates

1981 ◽  
Vol 103 (1) ◽  
pp. 21-25 ◽  
Author(s):  
M. R. Hoeprich ◽  
H. Zantopulos
Keyword(s):  
Plane Strain ◽  
General Equation ◽  
Roller Bearing ◽  
Experimental Results ◽  
Line Contact ◽  
Contact Deformation ◽  
Flat Plates ◽  
Special Cases ◽  
Analytical Work

Various line contact deformation equations used in roller bearing technology are analyzed. Many of these deformation equations, primarily involving plane strain, are shown to be special cases of a general equation derived in this paper. Experimental results are also presented to support the results of the analytical work.

Numerical Simulation of Condenser Throat Combining with Low-Pressure Exhaust Hood for 600MW Thermal Power Unit

2012 ◽  
Vol 614-615 ◽  
pp. 77-82
Author(s):  
Jian Li ◽  
Li Zhang ◽  
Si Ping Wang
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Velocity Distribution ◽  
Calculation Result ◽  
Thermal Power ◽  
Low Pressure ◽  
Exhaust Hood ◽  
Combined Model ◽  
Real Condition ◽  
Reasonable Result

In order to obtain the more real condition of the flow field at condenser throat the flow field of condenser throat is numerical simulated by the FLUENT commercial software, alone or coupling with the low-pressure exhaust hood. The results show that the flow field of condenser throat is strongly influenced by low-pressure exhaust hood, the frustum’s diffuse-angle, the low-pressure heater and the injection of the exhaust steam from the small turbine. The velocity distribution at the outlet of the throat isn’t uniform. The calculation result of combined model is also different from the single calculation result of condenser throat. Combined numerical simulation obtains more reasonable result.

scholarly journals Numerical Simulation and Experimental Study on Flow Field in a Swirl Nozzle

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yicheng Sun ◽  
Yufan Fu ◽  
Baohui Chen ◽  
Jiaxing Lu ◽  
Wanquan Deng
Keyword(s):  
Flow Field ◽  
Velocity Distribution ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Low Pressure ◽  
External Flow ◽  
Droplet Velocity ◽  
Inlet Pressure ◽  
Outlet Section ◽  
Local Pressure

In order to study the internal flow characteristics and external droplet velocity distribution characteristics of the swirl nozzle, the following methods were used: numerical simulations were used to study the internal flow characteristics of a swirl nozzle and phase Doppler particle velocimetry was used to determine the corresponding external droplet velocity distribution under medium and low pressure conditions. The distributions of pressure and water velocity inside the nozzle were obtained. Meanwhile, the velocities of droplets outside the nozzle in different sections were discussed. The results show that the flow rate in the swirl nozzle increases with the increase in inlet pressure, and the local pressure in the region decreases because of the excessive velocity at the internal outlet section of the swirl nozzle, resulting in cavitation. The experimental results show that under an external flow field, the minimum droplet velocity occurs in the axial direction; starting from the axis, the velocity first increases and then decreases along the radial direction. Swirling motion inside the nozzle and velocity variations in the external flow field occur under medium and low pressure conditions. The relationship between the inlet pressure and the distributions of water droplets’ velocities was established, which provides a reference for the research and development of the swirl nozzle.

Numerical Simulation of Impacts of Different Types of Air Duct Outlets on Ventilation Efficiency

2013 ◽  
Vol 438-439 ◽  
pp. 1098-1103
Author(s):  
Chun Zi Nan ◽  
Ji Ming Ma ◽  
Luo Zhao
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Velocity Distribution ◽  
Flow Velocity ◽  
Numerical Method ◽  
Concentration Effect ◽  
Mixing Zone ◽  
Mixing Effect ◽  
Ventilation Efficiency ◽  
Different Types

To enhance the exhaust efficiency during ventilation, three types of air duct outlets were imported. According to the characteristics of velocity distribution simulated by numerical method, the flow field is divided into the mixing zone and the exhaust zone. The gradual contracted air duct outlet can enhance the mixing effect between fresh air and smoke. In the exhaust zone, however, the flow velocity on the upper section of the tunnel is weakened, which is unfavorable for smoke exhaust. Gradual expanded air duct outlet, on the contrary, may weaken the concentration effect of the airflow. The flow velocity on the upper section of the tunnel is increased in the exhaust zone, thus the flow field is more homogenized, which is in favor of smoke exhaust.

Investigation on Laminar Flow Field Performances in a Dual-Impeller Stirred Tank

2012 ◽  
Vol 550-553 ◽  
pp. 2964-2967
Author(s):  
De Yu Luan ◽  
Shen Jie Zhou ◽  
Song Ying Chen
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Velocity Distribution ◽  
Radial Velocity ◽  
Velocity Vector ◽  
Equations Of Motion ◽  
Stirred Tank ◽  
Field Pattern ◽  
3D Flow ◽  
Multiple Reference

Abstract: The 3D flow field generated by a dual-impeller in the agitation of glycerin fluid was simulated using the commercial CFD package. The flow was modeled as laminar and a multiple reference frame (MRF) approach was used to solve the discretized equations of motion. The velocity profiles with a dual-impeller rotating at constant speed of 200r/min and at different layer clearances were obtained. By analysis to their axial and radial velocity vector plots and velocity distribution curves, it is found that the velocity distributions of the dual 6-bladed radial disc turbines (2-6DT) are better when the clearance is bigger or equal to the T/2, accompanied with the flow field pattern of parallel flow. Moreover，when the clearance is smaller or equal to the T/3, there are more advantages for 6-bladed radial disc turbines + pitch 4-bladed turbines (6DT+PTB) than other combinations，followed by the flow field pattern of connected flow.

Iterative combinations for Srivastava–Gupta operators

2020 ◽  
pp. 2150108
Author(s):  
Prerna Maheshwari Sharma
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Positive Operators ◽  
Integral Type ◽  
Linear Positive Operators ◽  
General Family ◽  
Special Cases

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.

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