Convective shielding mechanisms in melting of double circular ice bodies

doi:10.1007/s10483-026-3365-7

Abstract

Abstract:

Global climate change has intensified research on glacier melting. Direct numerical simulations employing the phase-field method are conducted to investigate the influence of arrangement angle α (ranging from 0° to 90°) on the melting dynamics of two-dimensional double circular ice bodies under uniform flow at Re = 400 and Pr = 7, aiming to elucidate the interactions within ice clusters. As α varies, the melting process can be divided into three distinct regimes characterized by different flow structures: individual, collective, and shielding regimes. In the individual regime, the melting rates of the two ice bodies exhibit negligible differences. In the collective regime, the downstream ice body melts faster than the upstream one. In the shielding regime, the shielding effect markedly impedes the melting of the downstream ice body, resulting in its slower melting rate relative to the upstream counterpart. Notably, at α = 90°, the downstream ice body becomes fully enveloped by the low-temperature wake, inducing a profound shift in its melting scaling law from the convection-dominated classical form A(t) = A₀(1 – t/t_f)^4/3 to a conduction-dominated form A(t) = A₀(1 – t/t_f).

Key words: double circular ice bodies, shielding effect, melting scaling law

2010 MSC Number:

Minghao GENG, Kaileong CHONG, Yuan MA. Convective shielding mechanisms in melting of double circular ice bodies. Applied Mathematics and Mechanics (English Edition), 2026, 47(4): 927-940.

TrendMD

Figures/Tables 9

Fig. 1

Table 1

Parameter settings for different cases of double circular ice melting"

Case	α	$L c$	$N y × N z$	$d t$
1	0	1.2	$690 × 1 152$	$1 × 10 − 4$
2	11.25	1.2	$690 × 1 152$	$1 × 10 − 4$
3	22.5	1.2	$690 × 1 152$	$1 × 10 − 4$
4	33.75	1.2	$690 × 1 152$	$1 × 10 − 4$
5	45	1.2	$690 × 1 152$	$1 × 10 − 4$
6	56.25	1.2	$690 × 1 152$	$1 × 10 − 4$
7	67.5	1.2	$690 × 1 152$	$1 × 10 − 4$
8	78.75	1.2	$690 × 1 152$	$1 × 10 − 4$
9	90	1.2	$690 × 1 152$	$1 × 10 − 4$

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

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