Ambiguous temperature difference in aerodynamic levitation process: Modelling, solving and application

doi:10.1016/j.jmst.2019.03.024

Abstract

Abstract:

The aerodynamic levitation provides an efficient technique for the research on thermophysical properties and solidification behavior of refractory materials. However, there is a nonnegligible temperature differences across sample, causing unexpected uncertainty of measurement, such as, thermal expansivity and undercooling limit. We establish thermal filed model with properly simplified boundary condition, and derive quantitative expressions of this ambiguous temperature difference. Here we show that the temperature difference not only related to the average temperature, relative size and thermal conductivity of sample, but significantly influenced by the rotation pattern of sample. A huge temperature differences is almost inevitable when the sample with low thermal conductivity and high melting point is smelted in stationary suspension pattern, however, a drastically reduction of temperature difference can be fulfilled by simply making the sample rotation in up to down pattern. The thermal filed simulation was used to confirm the validity of these theoretical expressions. This work shed light on temperature difference in aerodynamic levitation. Based on this work, one can simply estimate the extent of temperature difference across the sample, and regulated that conveniently if needed, which benefit for novel material preparation and solidification mechanism study based on this technique.

Key words: Solidification, Levitation, Modelling, Temperature difference

Xuan Ge, Xiaowei Xu, Qiaodan Hu, Wenquan Lu, Liang Yang, Sheng Cao, Mingxu Xia, Jianguo Li. Ambiguous temperature difference in aerodynamic levitation process: Modelling, solving and application[J]. J. Mater. Sci. Technol., 2019, 35(8): 1636-1643.

Figures/Tables 10

Fig. 1. (a) Schematic diagram of ADL devices; (b) an illustration of heat transfer process between the droplet and surrounding environment.

Fig. 2. Calculated temperature differences within the sample with two different types of rotation motion. (a) Relationship between temperature differences and average temperature when sample with a radius at 1 mm. (b) Influence of relative laser exposure area on the temperature differences with a constant average temperature at 2373 K. The insert graph is an enlargement of (b) in the range of temperature differences ΔT from 0 to 900 K.

Table 1 Physical quantities used in the temperature differences calculation of alumina melt at temperature close to its melting point.

Property	Sample [unit]	Value
Atmosphere temperature	T₀ [K]	298
Dynamic viscosity of oxygen	η [m²/s]	0.0000308 [28]
Density of oxygen	ρ₀ [g/L]	1.292
Specific heat of oxygen	C_p [J/(kg*K)]	0.921 [28]
Thermal conductivity of oxygen	λ_o [W/(m·K)]	0.0399
Radius of sample	R [m]	0.001
Density of sample	ρ_s [g/mL]	3.7455 [29]
Heat capacity of the sample	C_p [kJ/(kg*K)]	1.443 [29]
Thermal conductivity of sample	λ_s [W/(m·K)]	33 and 6
The average temperature of sample	T [K]	2327
The hemispherical total emissivity	ε	0.6 [29]
The diameter of the laser spot	d [m]	0.0014
Stefan-Boltzmann constant	σ [W/(m² ·K⁴)]	5.67 × 10^-8
Mean speed of Oxygen surrounding sample	υ [m/s]	12.23
Reynolds number	Re	1428
Planck number	Pr	0.715
Heat-transfer coefficient	h [W/(m²·K)]	272.6

Fig. 3. Schematic diagram of (a) right to left rotation, and (d) up to down rotation. (b)-(c) and (c)-(f) the temperature distribution in YOZ profile simulated with two thermal conductivities in two type of rotation motions.

Table 2 Comparison between calculated and simulated temperature differences.

	Right to left		up to down
	33 W/(m K)	6 W/(m K)	33 W/(m K)	6 W/(m K)
Calculation	308.18	1561.10	43.54	227.77
Simulation	337.85	1400.41	65.10	298.03

Fig. 4. (a) Temperature-time profiles for BT2 with different reduced laser power rates of two types of rotation. (b) Relationship between cooling rates and the pre-recalescence temperature in two types of rotation.

Fig. 5. SEM morphology of samples after solidification with laser power decreasing step of 0.5 W/s: (a) the nucleation sites under the bottom of right to left rotation sample. (b) The nucleation regions under the bottom of up to down rotation sample. (c) The enlarged initial sites of divergent crystal growth, marked with the magenta dashed box in (b).

Fig. 6. Temperature-time profile of BT2 with different cooling rates, and the insert showing the critical cooling rate profile of BT2 glass transition.

Fig. 7. XRD spectra after crystallization with different cooling rates.

Fig. 8. (a) Continuous cooling transformation diagram (CCT) of BT2. (b) DSC result of BT2 glass heating process.

References

[1]	J.J. Wall, R. Weber, J. Kim, P.K. Liaw, H. Choo, Mater. Sci. Eng. A 445 (2007) 219-222.
[2]	M. Kaneko, J.D. Yu, A. Masuno, H. Inoue, M.S. Vijaya Kumar, O. Odawara, S. Yoda, J. Am. Ceram. Soc. 95 (2012) 79-81.
[3]	D. Langstaff, M. Gunn, G.N. Greaves, A. Marsing, F. Kargl, Rev. Sci. Instrum. 84 (2013), 573-22.
[4]	Y. Ohishi, F. Kargl, F. Nakamori, H. Muta, K. Kurosaki, S. Yamanaka, J. Nuclear Mater. 487 (2017) 121-127.
[5]	J.K.R. Weber, C.J. Benmore, L.B. Skinner, J. Neuefeind, S.K. Tumber, G. Jennings, L.J. Santodonato, D. Jin, J. Du, J.B. Parise, J. Non-Crystalline Solids 383 (2014) 49-51.
[6]	L.B. Skinner, C.J. Benmore, J.K.R. Weber, M.A. Williamson, A. Tamalonis, A. Hebden, T. Wiencek, O.L.G. Alderman, M. Guthrie, L. Leibowitz, Science 346 (2014), p. 984.
[7]	C.J. Benmore, J.K.R. Weber, Adv. Phys.: X 2 (2017) 717-736.
[8]	S.J. McCormack, J.K.R. Weber, W.M. Kriven, Acta Mater. 161 (2018) 127-137.
[9]	A. Pack, K. Kremer, N. Albrecht, K. Simon, A. Kronz, Geochem. Trans. 11 (2010) 1-16.
[10]	H.P. Wang, C.H. Zheng, P.F. Zou, S.J. Yang, L. Hu, B. Wei, J. Mater. Sci. Technol. 34 (2018) 436-439.
[11]	H.P. Wang, M.X. Li, P.F. Zou, X. Cai, L. Hu, B. Wei, Phys. Rev. E (2018), 063106.
[12]	S. Yoda, W.S. Cho, R. Imai, Rev. Sci. Instrum. 68 (2015) 2127.
[13]	S.V. Ushakov, A. Navrotsky, J. Am. Ceram. Soc. 95 (2012) 1463-1482.
[14]	Y. Arai, T. Aoyama, S. Yoda, Rev. Sci. Instrum. 75 (2004) 2262-2265.
[15]	X.G. Ma, J.Q. Li, Z.J. Peng, B.Q. Ma, X.Y. Li, W. Pan, L.H. Qi, Crystal Growth Des. 15 (2015) 5652-5655.
[16]	M.Q. Xu, L. Wang, W.Q. Lu, L. Zeng, H.B. Nadendla, Y. Wang, J. Li, Q.D. Hu, M.X. Xia, J.G. Li, Metall. Mater. Trans. A 49 (2018) 1-8.
[17]	M.J. Li, K. Kuribayashi, J. Appl. Phys. 95 (2004) 2342-2347.
[18]	M.J. Li, K. Kuribayashi, Acta Mater. 52 (2004) 3639-3647.
[19]	Q. Ren, H.J. Su, J. Zhang, W.D. Ma, B. Yao, L. Liu, H.Z. Fu, Scripta Mater. 125 (2016) 39-43.
[20]	K. Nagashio, K. Kuribayashi, Y. Takamura, Acta Mater. 48 (2000) 3049-3057.
[21]	S.V. Ushakov, A. Shvarev, T. Alexeev, D. Kapush, A. Navrotsky, J. Am. Ceram. Soc. 100 (2017) 754-760.
[22]	J. Schroers, S. Bossuyt, W.K. Rhim, J.Z. Li, Z.H. Zhou, W.L. Johnson, Rev. Sci. Instrum. 75 (2004) 4523-4527.
[23]	H. Katsui, K. Shiga, R. Tu, T. Goto, J. Crystal Growth 384 (2013) 66-70.
[24]	X. Ge, Q. Hu, W. Lu, S. Cao, L. Yang, M. Xu, F. Cao, M. Xia, J. Li: Polymorphic transition and nucleation pathway study of barium dititanate (BaTi2O5) in crystallization from undercooled liquid,(submitted).
[25]	J.D. Yu, Y. Arai, T. Masaki, T. Ishikawa, S. Yoda, S. Kohara, H. Taniguchi, M. Itoh, Y. Kuroiwa, Chem. Mater. 18 (2006) 2169-2173.
[26]	A. Masuno, Y. Watanabe, H. Inoue, Y. Arai, J.D. Yu, M. Kaneko, Phys. Status Solidi C 9 (2012) 2424-2427.
[27]	S. Whitaker, AIChE J. 18 (1972) 361-371.
[28]	K. Nagashio, K. Kuribayashi, Acta Mater. 50 (2002) 1973-1981.
[29]	T. Ishikawa, J. Appl. Phys. 43 (2004) 1496.
[30]	K. Horai, J. Geophys. Res. 76 (1971) 1278-1308.
[31]	K. Nagashio, J. Sasaki, K. Kuribayashi, Mater. Trans. 45 (2004) 2723-2727.
[32]	K. Nagashio, K. Kuribayashi, Acta Mater. 49 (2001) 1947-1955.
[33]	S. Polosan, J. Non-Crystalline Solids 472 (2017) 55-60.
[34]	N.V.D. Brande, G.V. Assche, B.V. Mele, Crystal Growth Des. 15 (2015) 5614-5623.