Drag Coefficients of Viscous Drops

2000 ◽  
Author(s):  
Zhigang Feng ◽  
Efstathios E. Michaelides
Keyword(s):  
Drag Coefficient ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Computational Technique ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Viscous Drops

Abstract We have used a finite-difference scheme to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, we obtained the hydrodynamic forces and the steady-state drag coefficient of the spheres. The computational technique we have used enables us to extend the results to Reynolds numbers between 0 and 1,000. The viscosity ratio of the computations ranges between 0 (inviscid bubble) and infinity (solid particle). The method presented here makes use of a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [O(Re−1/2)] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The computations yield the friction and the form drag of the sphere. It is observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. If all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.

Drag Coefficients of Viscous Spheres at Intermediate and High Reynolds Numbers

2001 ◽  
Vol 123 (4) ◽  
pp. 841-849 ◽  
Author(s):  
Zhi-Gang Feng ◽  
Efstathios E. Michaelides
Keyword(s):  
Drag Coefficient ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Computational Domain ◽  
High Reynolds

A finite-difference scheme is used to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, the hydrodynamic force and the steady-state drag coefficient of the spheres are obtained. The Reynolds numbers of the computations range between 0.5 and 1000 and the viscosity ratio ranges between 0 (inviscid bubble) and infinity (solid particle). Unlike the numerical schemes previously implemented in similar studies (uniform grid in a stretched coordinate system) the present method introduces a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [ORe−1/2] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The need for such a double-layered domain arises from the observation that at intermediate and large Reynolds numbers a very thin boundary layer appears at the fluid-fluid interface. The computations yield the friction and the form drag of the sphere. It is found that with the present scheme, one is able to obtain results for the drag coefficient up to 1000 with relatively low computational power. It is also observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. The results show that, if all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.

scholarly journals A Dynamic Model of Drag Force for Catalytic Micromotors Based on Navier–Stokes Equations

Micromachines ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 459 ◽  
Author(s):  
Zhen Wang ◽  
Qingjia Chi ◽  
Tao Bai ◽  
Qiang Wang ◽  
Lisheng Liu
Keyword(s):  
Drag Coefficient ◽  
Drag Force ◽  
Environmental Remediation ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Cone Angle ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Support

In past decades, considerable advances have been achieved in micro and nanomotors. Particular attention has been given to self-propelled catalytic micromotors, which have been widely used in cell separation, drug delivery, microsurgery, lithography and environmental remediation. Fast moving, long life micromotors appear regularly, however it seems there are no solutions yet that thoroughly clarify the hydrodynamic behavior of catalytic micromotors moving in fluid. Dynamic behavior of this kind of micromotors is mainly determined by the driving force and drag force acting on the micromotors. Based on the hydromechanics theory, a hydrodynamic model is established to predict the drag force for a conical micromotor immersed in the flow field. By using the computational fluid dynamics software Fluent 18.0 (ANSYS), the drag force and the drag coefficient of different conical micromotors are calculated. A mathematical model was proposed to describe the relationship among Reynolds numbers Re, the ratio λ, the semi-cone angle δ and the drag coefficient Cd of the micromotors. This work provides theoretical support and reference for optimizing the design and development of conical micromotors.

scholarly journals Numerical investigation of the aerodynamic breakup of diesel droplets under various gas pressures

2017 ◽  
Author(s):  
Dionisis Stefanitsis ◽  
Ilias Malgarinos ◽  
George Strotos ◽  
Nikolaos Nikolopoulos ◽  
Emmanouil Kakaras ◽  
...  
Keyword(s):  
Drag Coefficient ◽  
Internal Combustion Engines ◽  
Stokes Equations ◽  
Ambient Pressure ◽  
Density Ratio ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Local Grid ◽  
Density Ratios

The present study investigates numerically the aerodynamic breakup of Diesel droplets for a wide range of ambient pressures encountered in engineering applications relevant to oil burners and internal combustion engines. The numerical model solves the Navier-Stokes equations coupled with the Volume of Fluid (VOF) methodology utilized for capturing the interface between the liquid and the surrounding gas. An adaptive local grid refinement technique is used to increase the accuracy of the numerical results around the interface. The Weber (We) numbers examined are in the range of 14 to 279 which correspond to bag, multimode and sheet-thinning breakup regimes. Model results are initially compared against published experimental data and show a good agreement in predicting the drop deformation and the different breakup modes. The predicted breakup initiation times for all cases lie within the theoretical limits given by empirical correlations based on the We number. Following the model validation, the effect of density ratio on the breakup process is examined by varying the gas density (or equivalently the ambient pressure), while the We number is kept almost constant equal to 270; ambient gas pressure varies from 1 up to 146bar and the corresponding density ratios (ε) range from 700 down to 5. Results indicate that the predicted breakup mode of sheet-thinning remains unchanged for changing the density ratio. Useful information about the instantaneous drag coefficient (Cd) and surface area as functions of the selected non-dimensional time is given. It is shown that the density ratio is affecting the drag coefficient, in agreement with previous numerical studies.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4690

scholarly journals NUMERICAL SOLUTION OF FLUID-STRUCTURE INTERACTION PROBLEMS WITH CONSIDERING OF CONTACTS

2021 ◽  
Vol 61 (SI) ◽  
pp. 155-162
Author(s):  
Petr Sváček
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Computational Mesh ◽  
Arbitrary Lagrangian Eulerian Method ◽  
High Reynolds

This paper is interested in the mathematical modelling of the voice production process. The main attention is on the possible closure of the glottis, which is included in the model with the concept of a fictitious porous media and using the Hertz impact force The time dependent computational domain is treated with the aid of the Arbitrary Lagrangian-Eulerian method and the fluid motion is described by the incompressible Navier-Stokes equations coupled to structural dynamics. In order to overcome the instability caused by the dominating convection due to high Reynolds numbers, stabilization procedures are applied and numerically analyzed for a simplified problem. The possible distortion of the computational mesh is considered. Numerical results are shown.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Reynolds Numbers ◽  
Drop Impact ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Viscous Drop

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.

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