0
Forced Convection

Heat and Fluid Flow Around a Sphere With Cylindrical Bore

[+] Author and Article Information
Andreas Richter, Petr A. Nikrityuk

CIC VIRTUHCON,  Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germanya.richter@vtc.tu-freiberg.de

J. Heat Transfer 134(7), 071704 (May 22, 2012) (13 pages) doi:10.1115/1.4006114 History: Received June 29, 2011; Revised January 04, 2012; Published May 22, 2012; Online May 22, 2012

This work is devoted to the numerical investigation of heat and fluid flow past a sphere with a centric, cylindrical bore. Such spherical rings are of interest in many technological processes. In chemical reactors, for example, spherical rings are used as a catalyst with an increased reacting surface. Motivated by this fact, we considered spherical rings with different bores and different orientations in flow regimes corresponding to Reynolds numbers from 10 up to 300. The results show a significant influence of the bore diameter on the symmetry and hence the steadiness of the flow field. The Nusselt number can be increased, which leads to a moderate rise in the drag coefficient. Thereby, the effect of the borehole depends on the Reynolds number, the bore diameter, and the angle of attack. For that reason, drag forces and total heat transfers do not simply follow the heat exchanging surface area. Based on the presented results, new correlations are given for both the drag coefficient and the Nusselt number; correlations which incorporate the bore geometry and the bore orientation in the flow field.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 23

Numerical grid along the xy plane containing a sliding surface. γ = 30 deg.

Grahic Jump Location
Figure 24

Streamtraces and magnitude of the velocity |u→| predicted for different angles of attack. The velocity field is displayed along the xy plane. Re = 200.

Grahic Jump Location
Figure 25

Change in drag coefficient as a function of γ. Drag coefficient is related to cd for γ = 0 deg. For 90 deg < γ < 180 deg, the curve is mirror-symmetrical.

Grahic Jump Location
Figure 26

Change in Nusselt number depending on angle of attack. Nusselt number Nu is related to Nusselt number at γ = 0 deg.

Grahic Jump Location
Figure 28

Relative drag coefficient as a function of γ. The drag coefficient is related to cd,n for γ = 0 deg. Empty symbols: numerical results, filled symbols: regression formula (see Eq. (18)).

Grahic Jump Location
Figure 29

Nusselt number as a function of γ. Nu is related to the Nusselt number at γ = 0 deg. Empty symbols: numerical results, filled symbols: regression formula following Eq. 20.

Grahic Jump Location
Figure 14

Relative Nusselt number as a function of sphericity

Grahic Jump Location
Figure 15

Change in modified Nusselt number depending on bore diameter. The Nusselt number Nun incorporates the surface area of the reference sphere (without bore).

Grahic Jump Location
Figure 16

Absolute Nusselt number as a function of Re. Symbols: numerical results, solid lines: regression curves.

Grahic Jump Location
Figure 17

Magnitude of the velocity |u→|=ux2+uy2+uz2. Velocity field is displayed along the xy plane. Re = 200.

Grahic Jump Location
Figure 18

Drag coefficient as a function of Re. Squares: smooth sphere, circles: crosswise-orientated borehole. The drag coefficient incorporates the surface area of a smooth sphere (cd,n=F/qA⊥,sphere).

Grahic Jump Location
Figure 19

Influence of a crosswise-orientated borehole on the flow field. Streamlines predicted for Re = 250.

Grahic Jump Location
Figure 20

Nondimensional temperature with and without a crosswise-orientated bore. Re = 200.

Grahic Jump Location
Figure 21

Nusselt number depending on the Reynolds number estimated for the smooth sphere (squares) and for the sphere with a borehole orientated crosswise (circles)

Grahic Jump Location
Figure 22

Definition of the angle of attack γ and the polar angle δ = 90 deg. The surrounding gas flow is orientated parallel to the x axis (compare Fig. 1).

Grahic Jump Location
Figure 27

Change in normalized Nusselt number Nun as a function of γ. The Nusselt number Nun is related to the Nusselt number for a sphere without a bore.

Grahic Jump Location
Figure 1

Computational domain and numerical setup

Grahic Jump Location
Figure 2

Nondimensional temperature profile in forward stagnation point for different Reynolds numbers

Grahic Jump Location
Figure 3

Numerical grid along the xy plane. Bore ratio r/R = 0.5.

Grahic Jump Location
Figure 4

Drag coefficients from the literature and present study for the flow around a sphere (without bores) as a function of the Reynolds number

Grahic Jump Location
Figure 5

Particles surface ratio for different bore diameters. Solid line: total surface area, dashed line: outer surface area of the remaining sphere, dotted–dashed line: surface area of the inner bore.

Grahic Jump Location
Figure 6

Streamlines for Re = 250 and different bore radii

Grahic Jump Location
Figure 7

Flow around a sphere with cylindrical bore. Flow patterns (isosurfaces of λ2  =  − 100) for Reynolds number 250.

Grahic Jump Location
Figure 8

Variation of drag coefficient as a function of Reynolds number and bore diameter. Drag coefficient cd=F/qA⊥ is based on effective projected area.

Grahic Jump Location
Figure 9

Variation of drag coefficient for different surface area ratios and Reynolds numbers. Drag coefficient cd=F/qA⊥ is based on effective projected area.

Grahic Jump Location
Figure 10

Change in normalized drag coefficient depending on bore diameter. Contrary to Fig. 8, the drag coefficient incorporates the surface area of the ideal sphere (cd,n=F/qA⊥,sphere).

Grahic Jump Location
Figure 11

Drag coefficient as a function of Re. Symbols correspond to numerical results, solid lines refer to regression curves.

Grahic Jump Location
Figure 12

Nondimensional temperature field for Re = 250 and different inner radii. The point of view is changed to illustrate the middle plane for which the flow field exhibits its asymmetry.

Grahic Jump Location
Figure 13

Relative change in Nusselt number for different bore diameters and Reynolds numbers

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In