Experimental Determination and Prediction of Drag
Coefficient of Newtonian Fluids Flowing Over Solid
and Hollow Objects

Abstract

Drag offered by fluid medium on submerged object is subject of intense research as needed in multiple process and solid handling applications. In spite of this, the literature remains silent on some critical problems. Catering the issues and limitations in literature is the main motivation of this work. Movement of sphere along inclined plane is involved in numerous applications. Nevertheless, a few published articles are available to deal with this for a limited scope of diameter ratio and angle of inclinations, θ. In the prospective of extending this work for broader
range of diameter ratio and tube inclinations, this study encompasses diameter ratio 0.09 to 0.37 and channel inclination 10o-90o. The terminal velocity shows an increasing trend (reverse of the available experimental data) with d/D ratio. It also increases with θ due to increase in downward force. The drag coefficient, CD, is reported as a function of Re, d/D and θ. CD also shows the reverse trend with d/D ratio. The dependency of CDRe on fluid viscosity and θ are expressed in terms of the developed correlations. The variation of CD with the inverse of Re is studied graphically to find out the flow regimes of the experimental data which are at laminar or early state of transition flow. The experimental CD values are validated with numerically calculated data using Ansys Fluent v15.0 for both vertical and inclined channels. The close agreement with experimental results confirms the applicability of the used numerical approximation.

Like, solid object, hollow objects are also involved in numerous industrial processes but, no single research article is available in literature to explain the fluid dynamic interaction for hollow particle. Hence, here the fluid dynamic behavior of flow over hollow frustum and
cylinder are studied in terms of terminal velocity and drag coefficient in both vertical and inclined channel. Like sphere, the predictive equations are also developed for each tube inclination for the hollow objects. The numerical prediction using Ansys Fluent is employed to predict the drag coefficient for above mentioned hollow objects and an excellent agreement is observed while comparing with experimental drag coefficients.

In spite of having the experimental results for conical shaped particle, the numerical study still untouched in open sources. In view of this, the effect of blockage ratio i.e. diameter ratio of cone, d, and flow channel, D on the drag coefficients of Newtonian fluid flow over cone is studied numerically by solving the CFD equations in Ansys FLUENT. The drag coefficients (CD) as a function of Reynolds number (Re) and d/D are reported for the range of Re: 0.01-30000 and d/D: 0.0015-0.9. The CD values are obtained higher for confined flow (high d/D) than unconfined flow. The variations of angle of separation and its effect on the drag coefficients are examined and justified. The comparative studies among the drag coefficients of sphere, cylinder and cone, are carried out in terms of wall effect, re-circulation length and slope of axial velocity profile. The observations revealed the following order of CD : cylinder>cone>sphere. The hydrodynamic interactions between wall and fluid medium are presented with the help of velocity contour plots. The simulated results presented herein for unconfined flow are in good agreement with the literature data. Furthermore, the variation of drag coefficient due to change of shape the particle from cone to cylinder are also studied to enrich the literature and for industrial applications.