Research Papers: Multiphase Flows

Application of a Three-Dimensional Immersed Boundary Method for Free Convection From Single Spheres and Aggregates

[+] Author and Article Information
Samuel G. Musong

Mechanical Engineering,
The University of Texas at San Antonio,
San Antonio, TX 78249
e-mail: sam_musong@yahoo.com

Zhi-Gang Feng

Mechanical Engineering,
The University of Texas at San Antonio,
San Antonio, TX 78249
e-mail: Zhigang.Feng@utsa.edu

Efstathios E. Michaelides

Fellow ASME
Department of Engineering,
Fort Worth, TX 76129
e-mail: E.Michaelides@tcu.edu

Shaolin Mao

Mechanical Engineering,
The University of Texas at El Paso,
El Paso, TX 79968
e-mail: smao@utep.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 16, 2014; final manuscript received August 24, 2015; published online December 8, 2015. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 138(4), 041304 (Dec 08, 2015) (10 pages) Paper No: FE-14-1757; doi: 10.1115/1.4031688 History: Received December 16, 2014; Revised August 24, 2015

A three-dimensional immersed boundary method (IBM) is applied for the solution of the thermal interactions between spherical particles in a viscous Newtonian fluid. At first, the free convection of an isolated isothermal sphere immersed in a viscous fluid is analyzed as a function of the Grashof number. A new correlation for the heat transfer rate from a single sphere is obtained, which is valid in the ranges 0.5 ≤ Pr ≤ 200 and 0 ≤ Gr ≤ 500. Second, the free convection heat transfer rate from pairs of spheres (bispheres) and from small spherical clusters immersed in air (Pr = 0.72) is investigated using this numerical technique. For bispheres, their orientation and the thermal plume interactions within a range of interparticle distances may cause the enhancement of the heat transfer rate above the values observed for two isolated spheres. For the simple triangular particle clusters, where the particles are in contact, it was observed that the average heat transfer rate per sphere decreases with the increased number of spheres in the cluster.

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Grahic Jump Location
Fig. 2

An isothermal sphere of radius a and temperature Tp immersed in a viscous fluid of ambient temperature Tf0

Grahic Jump Location
Fig. 3

The evolution of the overall Nusselt number in time. Analytical solution and numerical results for Gr = 0.

Grahic Jump Location
Fig. 4

Temperature distribution at various times for unsteady conduction

Grahic Jump Location
Fig. 1

Conceptual model of three circular particles suspended in a fluid

Grahic Jump Location
Fig. 5

(a) Nusselt numbers at different Grashof numbers of time, for Pr = 0.72 and (b) temperature fields at steady-state for Gr = 50, 100, and 200

Grahic Jump Location
Fig. 6

(a) Nu for different Gr as functions of time for Pr = 7 and (b) temperature fields at Gr = 10, 50, and 200 for Pr = 7

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Fig. 13

Average Nu for spherical clusters in contact

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Fig. 10

Effect of interparticle distance and orientation on the average Nu for bispheres aligned side-by-side and in tandem for Pr = 0.72 and Gr = 100

Grahic Jump Location
Fig. 11

Side-by-side bisphere for l/a = 5, Gr = 100, and for Pr = 0.72 (left side) and Gr = 100, Pr = 7 (right side). Upper: temperature contours; middle: velocity vector map; and lower: isothermal contours (Θ  = 0.6).

Grahic Jump Location
Fig. 12

Free convection from an isolated sphere, bispheres in contact, and triangular cluster for Pr = 0.72 and Gr = 100: (a) temperature contours at time 3 s and (b) isovorticity lines at time 1.5 s

Grahic Jump Location
Fig. 7

Characteristics of thermal plumes for (a) Pr = 0.72 and (b) Pr = 7 at t = 2.5 s and Gr = 100. Left: temperature field; middle: velocity vector field; and right: isothermal contours Θ  = 0.6.

Grahic Jump Location
Fig. 8

Nusselt number for Gr = 100 and different Prandtl numbers

Grahic Jump Location
Fig. 9

Comparison of results from Eq. (19) for (a) Pr = 0.72 and (b) Pr = 7




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