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5.1  PASS: Potential flow around a sphere

Author
Stéphane Popinet
Command
sh axi.sh axi.gfs
Version
1.3.0
Required files
axi.gfs (view) (download)
axi.sh error.ref order.ref isolines.gfv
Running time
36 seconds

The axisymmetric potential flow around a sphere is computed (Figure 52) and compared to the theoretical solution [15]. A large domain is used together with variable spatial resolution to minimise the influence of the finite domain size.

Figure 53 and 54 illustrate the convergence of the solution for the horizontal component of velocity with increased resolution.


Figure 52: Isolines of the velocity components (x in red, y in blue).


Figure 53: Evolution of the error as a function of resolution.


Figure 54: Corresponding convergence order.

5.1.1  PASS: Viscous flow past a sphere

Author
Stéphane Popinet
Command
sh viscous.sh
Version
1.3.0
Required files
viscous.gfs (view) (download)
viscous.sh cp-12-200 fadlun fadlun-cp-100 fadlun-cp-200 Re-12 zhang blanco-1995 masliyah-1970 isolines.gfv fornberg
Running time
25 minutes 2 seconds

When viscosity is added, a recirculation region develops behind the sphere (Figure 55).


Figure 55: Viscous flow around a sphere at Reynolds 100. Isolines of the velocity components (x in red, y in blue). The recirculation region is indicated by the green isoline where the value of the horizontal velocity component vanishes.

The length of the recirculation depends on the Reynolds number. Figure 56 plots the results obtained with Gerris as well as previously published results. Published results agree with Gerris for Reynolds numbers smaller than 100. The mismatch for results at Reynolds 200 can be attributed to the coarse mesh used to resolve the wake in the studies of Fornberg [10] and Fadlun et al [9].


Figure 56: Relative length of the recirculation region as a function of the Reynolds number. The results of Gerris are compared with the results of Masliyah & Epstein [19], Fornberg [10], Blanco & Magnaudet [4], Fadlun et al [9] and Zhang & Zheng [35].

The pressure profiles are also in good agreement with those reported by Fadlun et al (which also agree with those of Fornberg) (Figure 57).


Figure 57: Pressure coefficient over the sphere surface at Reynolds numbers 100 and 200.


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