SELF-SIMILARITY OF VERTICAL BUBBLY JETS

Lima Neto, I. E.

doi:10.1590/0104-6632.20150322s00003371

I. E. Lima Neto* To whom correspondence should be addressed

Assistant Professor, Dept. of Hydraulic and Environmental Engineering, Federal University of Ceará, Fortaleza - CE, Brazil. E-mail: iran@deha.ufc.br

* To whom correspondence should be addressed

Thumbnail

Figure 1
Schematic of a vertical bubbly jet, assuming Gaussian type self-similarity of liquid velocity, bubble velocity and void fraction along the axial direction.

Thumbnail

Figure 2
Comparison between model predictions and experimental data of mean liquid velocity given by Lima Neto et al. (2008b)Lima Neto, I. E., Zhu, D. Z. and Rajaratnam, N., Bubbly jets in stagnant water. Int. J. Multiphase Flow, 34(12), 1130-1141 (2008b).. The numbers (1) to (15) correspond to the experimental conditions shown in . The normalized radial profiles of u/uo cover a range of z/d from about 30 to 120.

Thumbnail

Figure 3
Comparison between model predictions and experimental data of void fraction given by Lima Neto et al. (2008b)Lima Neto, I. E., Zhu, D. Z. and Rajaratnam, N., Bubbly jets in stagnant water. Int. J. Multiphase Flow, 34(12), 1130-1141 (2008b).. The numbers (1) to (15) correspond to the experimental conditions shown in Table 1. The normalized radial profiles of C/C_o cover a range of z/d from about 30 to 120.

Thumbnail

Figure 4
Comparison between model predictions and experimental data of bubble velocity given by Lima Neto et al. (2008b)Lima Neto, I. E., Zhu, D. Z. and Rajaratnam, N., Bubbly jets in stagnant water. Int. J. Multiphase Flow, 34(12), 1130-1141 (2008b).. The numbers (1) to (15) correspond to the experimental conditions shown in . The normalized radial profiles of w/uo cover a range of z/d from about 30 to 120. Dashed lines indicate model simulations using the correlations of Clift et al. (1978)Clift, R., Grace, J. R. and Weber, M. E., Bubbles, drops and particles. Academic Press, New York (1978). to estimate the terminal velocity for individual bubbles [instead of ].

Thumbnail

Figure 5
Comparison between model predictions and experimental data of liquid velocity given by Sun and Faeth (1986a)Sun, T. Y. and Faeth, G. M., Structure of turbulent bubbly jets - I. Methods and centerline properties. Int. J. Multiphase Flow, 12(1), 99-114 (1986a).. The numbers (16) to (18) correspond to the experimental conditions shown in .

Thumbnail

Figure 6
Comparison between model predictions and experimental data of bubble velocity given by Sun and Faeth (1986a)Sun, T. Y. and Faeth, G. M., Structure of turbulent bubbly jets - I. Methods and centerline properties. Int. J. Multiphase Flow, 12(1), 99-114 (1986a).. The numbers (16) to (18) correspond to the experimental conditions shown in . Dashed lines indicate model simulations using the correlations of Clift et al. (1978)Clift, R., Grace, J. R. and Weber, M. E., Bubbles, drops and particles. Academic Press, New York (1978). to estimate the terminal velocity for individual bubbles [instead of ].

Thumbnail

Figure 7
Comparison between model predictions and experimental data of liquid velocity given by Iguchi et al. (1997)Iguchi, M., Okita, K., Nakatani, T. and Kasai, N., Structure of turbulent round bubbling jet generated by premixed gas and liquid injection. Int. J. Multiphase Flow, 23(2), 249-262 (1997).. The numbers (19) to (21) correspond to the experimental conditions shown in .

Thumbnail

Figure 8
Simulations using the present model (bubbly jet), analytical solutions reported by Zhang et al. (2011)Zhang, W. M., Rajaratnam, N. and Zhu, D. Z., Transport with Jets and Plumes of Chemicals in the Environment. Encyclopedia of Sustainability Science and Technology, Robert A. Meyers (Ed.), Springer, New York (2011). (single-phase buoyant jet), and empirical correlations given by Iguchi et al. (1997)Iguchi, M., Okita, K., Nakatani, T. and Kasai, N., Structure of turbulent round bubbling jet generated by premixed gas and liquid injection. Int. J. Multiphase Flow, 23(2), 249-262 (1997). (confined bubbly jet): (a) normalized centerline liquid velocity, (b) normalized radius, and (c) normalized centerline void fraction (or concentration, in the case of the single-phase buoyant jet).

Thumbnail

Figure 9
Simulations using the present model (bubbly jet) and empirical correlations given by Zhang et al. (2011)Zhang, W. M., Rajaratnam, N. and Zhu, D. Z., Transport with Jets and Plumes of Chemicals in the Environment. Encyclopedia of Sustainability Science and Technology, Robert A. Meyers (Ed.), Springer, New York (2011). (slurry jet): (a) normalized centerline bubble (or sand) velocity, (b) normalized radius, and (c) normalized centerline void fraction (or concentration, in the case of the slurry jet).

Thumbnail

Table 1
Experimental conditions of vertical bubbly jets used for comparison with the present model simulations.

Thumbnail

Table 2
Impact of different combinations of the entrainment coefficient (α), momentum amplification factor (γ), and spreading ratio of the bubble core (λ) on the standard deviations between model predictions and experimental data of mean liquid velocity (u) and void fraction. (C).

Thumbnail

Expt.	Reference	H	L	d	Qgo	Qlo	Co	Re	Fr
		(m)	(m)^* * L is the width (or diameter) of the tank	(mm)	(l/min)	(l/min)	(%)
1				13.5	3.00	7.00	30.0	11003	5.4
2				9.0	5.00	3.50	58.8	8252	7.1
3				9.0	2.00	5.00	28.6	11789	10.7
4				6.0	3.00	3.00	50.0	10610	16.6
5				6.0	5.00	3.00	62.5	10610	16.7
6				6.0	5.00	4.00	55.6	14147	22.3
7				6.0	5.00	5.00	50.0	17684	27.7
8	*Lima Neto et al.* (2008b)**Lima Neto, I. E., Zhu, D. Z. and Rajaratnam, N., Bubbly jets in stagnant water. Int. J. Multiphase Flow, 34(12), 1130-1141 (2008b).	0.8	1.2	6.0	4.00	5.00	44.4	17684	27.8
9				9.0	0.40	7.00	5.4	16505	27.8
10				6.0	3.00	5.00	37.5	17684	28.1
11				4.0	5.00	2.00	71.4	10610	28.7
12				6.0	2.00	5.00	28.6	17684	29.4
13				4.0	1.00	2.00	33.3	10610	31.5
14				6.0	1.00	5.00	16.7	17684	34.4
15				6.0	0.40	5.00	7.4	17684	47.5
16				5.1	0.20	2.00	9.1	8355	26.4
17	Sun and Faeth (1986aSun, T. Y. and Faeth, G. M., Structure of turbulent bubbly jets - I. Methods and centerline properties. Int. J. Multiphase Flow, 12(1), 99-114 (1986a).,b)Sun, T. Y. and Faeth, G. M., Structure of turbulent bubbly jets - II. Phase properties profiles. Int. J. Multiphase Flow, 12(1), 115-126 (1986b).	0.9	0.4	5.1	0.10	2.00	4.8	8355	34.8
18				5.1	0.05	2.00	2.4	8355	47.4
19				5.0	2.40	2.50	49.0	10610	22.1
20	*Iguchi et al.* (1997)**Iguchi, M., Okita, K., Nakatani, T. and Kasai, N., Structure of turbulent round bubbling jet generated by premixed gas and liquid injection. Int. J. Multiphase Flow, 23(2), 249-262 (1997).	0.4	0.2	5.0	1.20	2.50	32.4	10610	22.8
21				5.0	0.60	5.00	10.7	21221	63.7

Interaction	α	γ	λ	STD of	STD of	Average
Interaction	α	γ	λ	u	C	STD
1	0.040	1.0	0.4	39%	73%	56%
2	0.120	3.0	1.0	29%	64%	47%
3	0.040	2.0	0.7	37%	47%	42%
4	0.120	2.0	0.7	28%	50%	39%
5	0.080	2.0	1.0	13%	50%	32%
6	0.080	2.0	0.4	15%	44%	30%
7	0.080	3.0	0.7	16%	30%	23%
8	0.080	2.0	0.7	14%	29%	22%
9	0.080	1.0	0.7	10%	28%	19%
10	0.077	1.0	0.6	10%	18%	14%

[1] * To whom correspondence should be addressed

Brasil

Brasil

SELF-SIMILARITY OF VERTICAL BUBBLY JETS

Abstract