Experimental Study on the Critical Characteristics of Liquid

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Experimental Study on Critical Characteristics of Liquid Atomization by Spinning Disk Hao Peng, Na Wang, Dongxiang Wang, and Xiang Ling Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b00401 • Publication Date (Web): 09 May 2016 Downloaded from http://pubs.acs.org on May 16, 2016

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Industrial & Engineering Chemistry Research

Experimental Study on Critical Characteristics of Liquid Atomization by Spinning Disk Hao Penga, *, Na Wanga, Dongxiang Wanga, b, Xiang Linga, * a

Jiangsu Key Laboratory of Process Enhancement and New Energy Equipment Technology, School of Mechanical and

Power Engineering, Nanjing Tech University, No. 30 Pu Zhu South Road, Nanjing 211816, P. R. China b

School of Mechanical Engineering, Jiangnan University, No. 1800 Li Hu Road, Wuxi 214122, China

Abstract The centrifugal atomization process of liquid by spinning disk has been investigated by visualized experiments. Firstly, the non-dimensional critical equations are derived theoretically and obtained from the experimental data. Accordingly, a transition map is proposed to analyze the effects of operating conditions (liquid flow rate Q, angular speed ω and disk diameter D) and liquid properties (fluid density ρ, fluid viscosity μ, surface tension σ) on transition characteristics of spinning disk atomization. The results indicated that the transition from direct drop-ligament mode and ligament-sheet mode are promoted with the increase of Q, ω, ρ and μ. For the transition from direct drop-ligament mode, the critical volume flow rate will not always rise with increasing the D. By contrast, the reduction in critical volume flow rate can be attributed to the incomplete wetting of the disk surface. In fully-ligament breakup stage, the increased Q creates a longer ligaments length and a wider ligaments diameter, while the number of ligaments remains constant. Key Words: Centrifugal atomization; direct drop mode; ligament mode; sheet mode; transition characteristics 1

Introduction Spinning disk/cup atomizers have successful applications in the chemical,1, 2 metallurgical,3, 4 and food5

industries. Especially in the field of chemical industry, it can be used for many chemical reactions like organic syntheses6, 7 or catalyzed8 reactions. The most attractive advantage of such atomizer is their ability to be fully applicable to low viscous liquid, high viscous liquid, emulsions and suspensions 9, 10. In spinning atomization, liquid is fed to the center of a rotating disk/cup, then centrifugal force cause the liquid to spread out. Due to instability, three breakup modes of liquid film may take place around the rim: direct drop mode, ligament mode and sheet mode. Transition from one mode to another occurs by changing

*

Corresponding author Tel: 86-25-83587570

Fax: 86-25-83600956

Email address: [email protected] (H. Peng) Email address: [email protected] (X. Ling)

ACS Paragon Plus Environment


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the operating parameters and geometrical configurations. Generally, in various chemical engineering processes, it is important to identify the breakup mode prevailing at a given set of operating conditions, and even more important to characterize the droplet generated11, 12. Most studies are concerning the transition characteristics of spinning cup atomization. Liu et al.13, 14, Hinze and Milborn 15, Fraser et al 16, Dombrowski and Lloyd

17

, Champagne and Angers

18

carried out a great number of experiments and developed various

transition criteria correlations for spinning cup. In particular, Ahmed and Youssef

19

reported that, even at

relatively high angular speeds, spinning disks can save energy and secure more stability comparing with other complex shapes of spinning cups. However, only few correlations have been reported in the literature for the transition characteristics by spinning disk. Matsumoto et al. 20 proposed a correlation for the transition from direct drop to ligament mode, while Kamiya and Kayano 21 developed a criterion for the transition from ligament to sheet mode. Frost

22

reported the criterion for the transition of direct drop, ligament and sheet

mode in spinning disk and developed an expression for the prediction of droplet size, which is perhaps the most comprehensive criterion. These investigations concluded that the transition from direct drop to ligament mode, and from ligament to sheet mode were produced by increasing flow rate, angular speed, liquid density, and viscosity, or by decreasing disk diameter, and liquid surface tension. Some of these correlations for spinning cup or disk are listed in Table.1. Despite the above investigative effort, the following aspects about transition characteristics of spinning disk are still lacking or insufficient. (1) These reported correlations have shown obvious discrepancies. The reason is probably due to the different operating conditions and disk configurations. Frost

22

reported that three breakup modes occurred in their

range of operating conditions. However, Matsumoto et al.

20

reported that direct drop and ligament regimes

were observed, while Kamiya and Kayano 21 reported that ligament and sheet regimes were observed in their experimental works. So, different breakup modes associated with each correlation are obtained. (2) The variables used in some of the correlations are dimensional, making it problematic to extrapolate beyond the applicable range. Therefore, it is inconvenient to utilize these correlations in dimensional form for atomization system design. (3) The mechanism of transition characteristics in spinning disk atomization has not been clearly explored. Accordingly, as a useful complement for the previous fruitful works, an experimental study is performed to obtain the non-dimensional critical transition correlations between different breakup modes. The correlations are related to operating conditions, liquid properties, and disk geometries, which can be expressed in terms of Reynolds number (Re) and Weber number (We). Also the effects of operating


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conditions and liquid properties on transition characteristics are analyzed. The present work provides correlations for a wider range of operating conditions, which should contribute to the designing and optimizing of centrifugal atomization using spinning disk atomizer. Table.1 Critical transition correlations for spinning disk and cup atomization Authors

Atomizer

Correlations

RCA

[

 Q 2  2 D3 0.6  2 0.167 ][ ] [ ]  1.77   D  D3

Ligament-Sheet

RCA

[

 2 D3 Q 34  D 0.19 ][ ] [ ]  0.363   D3  Q

Ligament-Sheet

[

Q 0.6  0.17  0.71 ][ ]  0.07 D0.68  0.88

Direct Drop-Ligament

[

Q 0.6  0.17  0.71 ][ ]  1.33 D0.68  0.88

Ligament-Sheet

Hinze &Milborn15 Fraser et al.16

Champagne &

Breakup Range

RCA Angers 18

Liu et al.13

Q  2 R3 1.161  2 0.0705  6.5[ ] [ ]   R  R3

Direct Drop-Ligament

Q  2 R3 0.789  2 0.036  5.13[ ] [ ]   R  R3

Ligament-Sheet

SDA

Q2  2 0.45  2 R3 0.85  0.0333[ ] [ ] 3  D  R

Ligament-Sheet

SDA

Q  24.16[

RCA

Matsumoto et al. 20 Kamiya & Kayano 21

QVcos(θ), radial distance of liquid sheet a tends to zero gradually, then sheet breakup mode transfers into ligament breakup mode, Equation (3) can be expressed as

Q 4 ( D 2) Q b  K0 ( ) 2 Rh Q D

(4)

Where h is the film thickness at the disk rim and can be calculated by Burns et al. 23, 24.

h(

3K1Q 13 ) 2 R 2 2

(5)

Finally, Equation (4) can be expressed as


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(

1 Q 34  2 D3  D b  13 ) ( ) =3.061K0 K13 3 8 Q D

(6)

In order to generalize the model and the corresponding results, the non-dimensional critical volume flow rate Q*, Weber number We, Reynolds number Re and Constant K* are defined as:

Q*  Q  D3

(7)

We=  2 D3 8

(8)

Re  Q  D

(9)

K * =2.314K03 4 K11 4

(10)

Substituting Equations (7)~(10) to Equation (6), yields -

3

3b 1  4

Q* =K *We 4 Re 4

(11)

* * -3 4 3b 4 1 4 When Q μ40% Glycerol> μwater), especially in lower angular speed. However, the viscosity has a slight influence on critical volume flow rates from droplet to ligament mode for a higher angular speed. Figure 7 shows the effect of disk diameter on critical volume flow for transition from direct drop to


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ligament breakup mode. As shown in this figure, the value of critical volume flow rate will not always rise with increasing the disk diameter for the transition from drop to ligament breakup mode. By contrast, it maybe reduces due to the incomplete wetting of the disk surface, in accordance with phenomenon observed by the visual experiments (Figure 5). The aforementioned Equation (12) shows the transition criteria from one mode to another. In this section, using non-linear regression, the value of K*, m and n for the drop-ligament transition regression formation can be determined, as expressed in Equation (16).

Q* =0.308We-0.994 Re0.201

(16)

Equation (16) is developed for the following ranges of operating variables: Q*=1.17×10-6 ~ 9.81×10-4, We=0.815×103 ~ 2.0×105, Re=0.18 ~ 95. The mean squared error (MSE) for Q* calculated by Equation (16) is 1.72×10-5, with the correlation coefficient (R2) of 0.9830. Figure 8 shows a graph of the experimental data and the transition curve according to Equation (16). It is observed that the Equation (16) fits well with the experimental data with the average relative error (RE) limit of +13.87% and -15.50%. The area below and above the curve indicate the regions where the direct drop and ligament are produced. It is evident that Q* increases with decreasing Weber number (We) or rising Reynolds number (Re). In our case, We was predominantly affected by changing angular speed as the surface tension was nearly the same for all liquids used. Therefore, if the spinning disk is rotating at a low angular speed (low We), the direct drop mode can occur at a high flow rate. As the angular speed is further increased (high We), transition from direct drop mode to ligament mode occurs.

Figure 6. Critical volume flow rate for the transition from direct drop to ligament breakup mode

Figure 7. Effect of disk diameter on critical volume flow rate for transition from direct drop to ligament mode

Figure 8. Transition curve from direct drop mode to ligament mode 3.3 Characteristics of fully-ligament breakup mode Figure 9 illustrated the influence of liquid (60% Glycerol solution) volume flow rate on the breakup process of fully-ligament mode at angular speed of 94.2 rad/s and disk diameter of 0.05m. It can be seen that, when the liquid flow rate ranges from 4.76 ml/s to 11.84 ml/s, fully-ligament mode appears and clearly ligaments are formed at the lip of the disk with stable trajectory. Because the surface of spinning disk is fully wetted at this stage and the tangential velocity of liquid film at disk rim is much higher than the radial



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velocity, the trajectories of ligaments are presented as an involute profile. Interestingly, the number of ligaments remains constant (KL=35) with the increase in liquid volume flow rate15, 22. It is well known that the thin liquid film at the disk rim disintegration in ligament mode occurs due to the Rayleigh-Taylor (RT) instabilities that developed on the liquid film driven by centrifugal forces. Due to RT instability, a quantity of ligament streams attaches on the disk rim. The breakup of the liquid film at the disk rim results from the wave with the fastest growth rate, the wave number that determines the number of ligaments is controlled by the liquid physical properties, disk parameters and angular speed together (Kamiya & Kayano 21; Wang et al. 25

; Liu et al.

13

; Taylor

26

). Therefore in the full-ligament mode, the number of ligaments reaches the

maximum and remains constant (as shown in Figure 9). In other word, the flow rate has little influence on the ligaments number for a given rotational speed. Instead, a longer ligaments length and a wider ligaments diameter are observed as the flow rate increased. Figure 10 shows the critical volume flow rates against the angular speed for different working fluids. The trend of these curves is very similar to the previous transition characteristics from direct drop to ligament mode. The critical volume flow rate is decreasing with the increase of fluid viscosity in a certain angular speed. The influence of disk diameter on critical flow rate is shown in Figure 11. The value of critical volume flow rate rises with the increase in the disk diameter. Take ω=157.1 rad/s for example, the critical volume flow rate of 40% Glycerol is increasing from 4.4ml/s to 6.6 ml/s with the increase of disk diameter from 0.05m to 0.1m. The regression equation for transition characteristics from ligament to fully-ligament breakup mode can be expressed by Equation (17). Figure 12 illustrates the corresponding transition curve with the average relative error (RE) bonds of +5.74% and -12.83%.

Q* =0.126We-0.779 Re0.118

(17)

Equation (17) is developed for the following ranges of operating variables: Q*=1.01×10-5 ~ 1.23×10-3, We=0.815×103 ~ 2.0×105, Re=1.82 ~ 156. The mean squared error (MSE) for Q* calculated by Equation (17) is 2.99×10-5, with the correlation coefficient (R2) of 0.9627.

Figure 9. Effect of volume flow rate on fully-ligament breakup mode (a) Q=4.76ml/s, (b) Q=8.43ml/s, (c) Q=11.84ml/s

Figure 10. Critical volume flow rate for fully-ligament breakup mode


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Figure 11. Effect of disk diameter on critical volume flow rate for fully-ligament breakup mode

Figure 12. Transition curve from ligament to fully-ligament mode 3.4 Transition characteristics from fully-ligament to sheet mode The transition processes from fully-ligament to sheet breakup mode by camera are displayed in Figure 13. The working fluid is 60% Glycerol solution, the angular speed is 157.1 rad/s and the disk diameter is 0.05 m. As mentioned before, the number of ligaments remains constant with the increase of liquid volume flow rate in fully-ligament breakup mode. However, as the flow rate increased, the stable trajectory of ligaments shows fluctuation. It is noted that the first merging of two adjacent ligaments is formed at the periphery of the spinning disk (Figure 13a). When the liquid flow rate further increases to 14.18ml/s, a continuous liquid torus with enlarged outer diameter expanded to the most part of disk rim (Figure 13b). Finally, a thin and wide liquid sheet, instead of partial torus, was formed at the lip of the spinning disk and then the sheet mode subsequently developed. In addition, compared with the atomization process in direct droplet and ligament mode, the droplets produced by sheet mode appear in quite irregular shape (spherical and strip), as shown in Figure 13c. The relationship between critical volume flow rate and angular speed, at which transition from fully-ligament to sheet breakup mode occurs is illustrated in Figure 14. From this figure, the effects of angular speed, liquid viscosity and disk diameter on the critical volume flow rate can be observed. Because the tendency is similar to the previous phenomena and the detailed reasons has been explained in section 4.2 and 4.3, so that won't be covered again here. According to nonlinear regression with the experimental data, Equation (18) is obtained as the critical condition for transition from fully-ligament to sheet breakup mode. The corresponding transition curve according to the Equation (18) is shown in Figure 15, with +9.02% and -9.75% average relative error bonds, respectively.

Q* =0.257We-0.75 Re0.133

(18)

Equation (18) is developed for the following ranges of operating variables: Q*=3.61×10-5 ~ 3.89×10-3, We = 0.815×103 ~ 2.0×105, Re = 7.92 ~ 542. The mean squared error (MSE) for Q* calculated by Equation (18) is 7.31×10-5, with the correlation coefficient (R2) of 0.9957.



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Figure 13. Transition image from ligament breakup to sheet breakup (a) Q=12.25ml/s, (b) Q=14.18ml/s, (c) Q=16.40ml/s

Figure 14. Critical volume flow rate for the transition from ligament to sheet breakup mode

Figure 15. Transition curve from ligament breakup to sheet breakup mode 3.5 Further analysis of critical transition characteristics To sum-up, the correlations for the transition criteria from one mode to another are listed in Table 3, which are applicable in a wide range of operating variables. And the corresponding transition map is shown in Figure 16. In fact, the centrifugal atomization of liquid on a disk is an exceedingly complex process. In Figure 16, the synthetical effects of operating conditions (liquid flow rate Q, angular speed ω and disk diameter D) and liquid properties (fluid density ρ, fluid viscosity μ, surface tension σ) on transition characteristics of spinning disk atomization can be further determined. Firstly, as mentioned above, the transition from direct drop to ligament mode, and ligament to sheet mode are promoted with the increase of liquid flow rate Q and angular speed ω. However, the effect of disk diameter D is found to be more complicated. It is well known that increasing the D can contribute to a higher We number, while the non-dimensional liquid flow rate Q* is decreasing on the contrary. As a result of the opposite effect between the two actions, the breakup mode may not change. Take the case of disk diameter D=0.05 m, ω at 219.9 rad/s, Q at 1.8ml/s for 60% Glycerol for example (Point P1 in Fig. 16), the breakup mode is in ligament type range captured from our visible experiments. When the disk diameter D increases from 0.05 m to 0.1 m (Point P2 in Fig. 16), there is no change in the breakup mode (remained ligament mode) from the experimental data. It is obvious that the increased D enhances the effect of centrifugal force, while the surface tension force at the film edge is also reinforced. Both the two aspects are counteracted each other, the force balance may be well maintained, resulting in the unchanged breakup mode. Secondly, for a given operating conditions, the increase of the liquid fluid density ρ created an enhanced centrifugal force, which resulted in the liquid film extended outwards and formed the sheet breakup mode. The effect of liquid viscosity μ on the transition between different breakup modes is almost identical to the effect of Q, while the transition from direct drop-ligament and ligament-sheet appeared by increasing the liquid viscosity μ. However, the effect of μ is less obvious (∞μ0.201) than that of the effect of Q, as illustrated in Equation (16). In addition, the increased surface tension σ causes the rising of the contraction velocity Vc at the liquid sheet edge (shown in Figure 1), and the liquid sheet edge tends to be toward to the disk rim. As a


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result, the breakup mode of liquid film at the disk rim is probably maintained in direct drop or ligament mode even under a relative high Q or ω. Table 3 Correlation of the critical transition condition Breakup Transition

Correlation

Operation variables Q*=1.17×10-6 ~ 9.81×10-4, We=0.815×103 ~ 2.0×105,

Direct drop to Ligament

*

Q =0.308We

-0.994

Re

0.201

Re=0.18 ~ 95 Q*=1.01×10-5 ~ 1.23×10-3, We=0.815×103 ~ 2.0×105,

Ligament to *

Q =0.126We

-0.779

Re

0.118

Fully-ligament

Re=1.82 ~ 156 Q*=3.61×10-5 ~ 3.89×10-3, We=0.815×103 ~ 2.0×105, *

Q =0.257We

Fully ligament to Sheet

-0.75

Re

0.133

Re=7.92 ~ 542

Figure 16. Transition map for different breakup modes 4

Conclusions The centrifugal atomization of liquid by spinning disk has been investigated experimentally. The

transition equations between different breakup modes were obtained and the effects of operating conditions and liquid properties on transition characteristics were analyzed. Key findings of this study were: (1) The non-dimensional correlations Equations (16~18) with high-accuracy (Average RE0.95) were developed from the experimental data, which are applicable for predicting the transition criteria from direct drop to ligament, ligament to fully-ligament, and fully-ligament to sheet mode in a wide ranges of operating variables (Q*, We and Re). (2) For the transition from direct drop to ligament mode, the value of critical volume flow rate will not always rise with increasing the disk diameter D. By contrast, the reduction in critical volume flow rate can be attributed to the incomplete wetting of the disk surface. In fully-ligament breakup stage, the increased volume flow rate creates a longer ligaments length and a wider ligaments diameter, while the number of ligaments remains constant. (3) The transition map for different breakup modes is drawn. In general, the transition from direct drop to ligament mode, and ligament to sheet mode are promoted with the increase of liquid flow rate Q, angular speed ω, fluid density ρ, and viscosity μ. However, the influences of disk diameter D and liquid surface tension σ on transition characteristics need comprehensive estimate through the transition map according to the real operating conditions.



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Acknowledgements The authors acknowledge the financial support provided by National Natural Science Foundation of China (Grant No. 51406078), Major Collegiate Project of Natural Science Foundation of Jiangsu Province (Grant No. 15KJA480001) and Natural Science Foundation of Jiangsu Province (Grant No. BK20151539).

Nomenclature a

Radial extension distance of liquid sheet [m]

D

Disk diameter [m]

h

Liquid film thickness [m]

K0

Constant value

K1

Constant value

*

K

Constant value

KL

Number of liquid column

MSE

Mean squared error

m

Constant value

n

Constant value

Q

Volume flow rate [ml/s]

Q

*

Dimensionless critical volume flow rate

R

Disk radius [m]

RE

Relative error

Re

Reynolds number

R2

correlation coefficient

V

Liquid sheet edge velocity [m/s]

Vc

Contraction velocity [m/s]

We

Weber number

Acronyms RCA

Rotary Cup Atomizer

SDA

Spinning Disk Atomizer

Greek symbols ω

Angular speed [rad/s]


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ρ

Density [kg/m3]

σ

Surface tension [N/m]

θ

Angle between V and Vc [º]

μ

Dynamic viscosity [Pa  s]

ν

Kinematic viscosity [m2/s]

Subscripts c

Contraction

Upper scripts e

experimental

p

predicted

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10. Ahmed, M.; Youssef, M. S., Characteristics of Mean Droplet Size Produced by Spinning Disk Atomizers. J. Fluid Eng. 2012, 134, 1-9. 11. Zhao, H.; Liu, H. F.; Xu, J. L.; Li, W. F., Experimental Study of Drop Size Distribution in the Bag Breakup Regime. Ind. Eng. Chem. Res. 2011, 50, 9767-9773. 12. Wegener, M.; Muhmood, L.; Sun, S.; Deev, A. V., Novel High-Temperature Experimental Setup to Study Dynamic Surface Tension Phenomena in Oxide Melts. Ind. Eng. Chem. Res. 2013, 52, 16444-16456. 13. Liu, J.; Yu, Q.; Guo, Q., Experimental investigation of liquid disintegration by rotary cups. Chem. Eng. Sci. 2012, 73, 44-50. 14. Liu, J.; Yu, Q.; Duan, W.; Qin, Q., Experimental investigation on ligament formation for molten slag granulation. Appl. Therm. Eng. 2014, 73, 888-893. 15. Hinze, J.; Milborn, H., Atomization of liquid by means of a rotating cup. J. Appl. Mech-T ASME 1950, 17, 145-153. 16. Fraser, R. P.; Dombrowski, N.; Routley, J. H., The filming of liquids by spinning cups. Chem. Eng. Sci. 1963, 18, 323-337. 17. Dombrowski, N.; Lloyd, T. L., Atomisation of Liquids by Spinning Cups. Chem. Eng. J. 1974, 8, 63-81. 18. Champagne, B.; Angers, R., Rep Atomization Mechanisms. Int. J. Powder Metall 1984, 16, 125-128. 19. Ahmed, M.; Youssef, M. S., Influence of spinning cup and disk atomizer configurations on droplet size and velocity characteristics. Chem. Eng. Sci. 2014, 107, 149-157. 20. Matsumoto, S.; Saito, K.; Takashima. Y., Phenomenal Transition of Liquid Atomization from Disk. J. Chem.Eng. Jpn.1974, 7, 13-19. 21. Kamiya, T.; Kayano, A., Film-type disintegration by rotating disk. J. Chem.Eng. Jpn. 1972, 5, 174-182. 22. Frost, A. R., Rotary Atomization in the Ligament Formation Mode. J. Agr. Eng. Res. 1981, 26, 63-78. 23. Burns, J. R.; Ramshaw, C.; Jachuck, R. J., Measurement of liquid film thickness and the determination of spin-up radius on a rotating disc using an electrical resistance technique. Chem. Eng. Sci. 2003, 58, 2245-2253. 24. Burns, J. R.; Jachuck, R. J. J., Determination of liquid–solid mass transfer coefficients for a spinning


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disc reactor using a limiting current technique. In. J. Heat Mass Tran. 2005, 48, 2540-2547. 25. Wang, D.; Ling, X.; Peng, H., Simulation of ligament mode breakup of molten slag by spinning disk in the dry granulation process. Appl. Therm. Eng. 2015, 84, 437-447. 26. Taylor, G. I., The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Soc. London. 1950, 201, 192-196.



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List of Figures Figure 1 Velocity vectors at the free edge of a liquid sheet Figure 2 Schematic of experimental system process Figure 3 Photograph of the experimental setup Figure 4. Breakup mode of liquid film for 60% Glycerol solution with different volume flow rates (a) Q=0.82ml/s, (b) Q=1.44ml/s, (c) Q=1.94ml/s, (d) Q=3.24ml/s, (e) Q=12.25ml/s, (f) Q=16.40ml/s. Figure 5. Spinning disk surface with incomplete wetting for 60% Glycerol solution (a) D=0.1m, Q=0.82ml/s, ω=94rad/s, (b) D=0.1m, Q=1.57ml/s, ω=157rad/s Figure 6 Critical volume flow rate for the transition from direct drop to ligament breakup mode Figure 7 Effect of disk diameter on critical volume flow rate for transition from direct drop to ligament mode Figure 8 Transition curve from direct drop mode to ligament mode Figure 9. Effect of volume flow rate on fully-ligament breakup mode (a) Q=4.76ml/s, (b) Q=8.43ml/s, (c) Q=11.84ml/s Figure 10 Critical volume flow rate for fully-ligament breakup mode Figure 11 Effect of disk diameter on critical volume flow rate for fully-ligament breakup mode Figure 12 Transition curve from ligament to fully-ligament mode Figure 13. Transition image from ligament breakup to sheet breakup (a) Q=12.25ml/s, (b) Q=14.18ml/s, (c) Q=16.40ml/s Figure 14 Critical volume flow rate for the transition from ligament to sheet breakup mode Figure 15 Transition curve from ligament breakup to sheet breakup mode Figure 16 Transition map for different breakup modes


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Figure 1. Velocity vectors at the free edge of a liquid sheet

Figure 2. Schematic of experimental system process



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High-speed camera

Pouring tube

Electromagnetic Flowmeter

Spinning disk

Flow control valve Motor shaft Motor case

Collecting tank Storage tank Transducer Thermostatic water tank

Figure 3. Photograph of the experimental setup


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(a) 0.82 ml/s

(b) 1.44 ml/s

Incomplete wetting

Incomplete wetting Direct drop-Ligament

Direct drop formation (d) 3.24 ml/s

(c) 1.94 ml/s

Ligament (e) 12.25 ml/s

Fully-Ligament (f) 16.40 ml/s

Film appearance

Fully-Sheet

Figure 4. Breakup mode of liquid film for 60% Glycerol solution with different volume flow rates (a) Q=0.82ml/s, (b) Q=1.44ml/s, (c) Q=1.94ml/s, (d) Q=3.24ml/s, (e) Q=12.25ml/s, (f) Q=16.40ml/s.

Figure 5. Spinning disk surface with incomplete wetting for 60% Glycerol solution (a) D=0.1m, Q=0.82ml/s, ω=94rad/s, (b) D=0.1m, Q=1.57ml/s, ω=157rad/s



Volume flow rate/ ml/s

8 D=0.05 m Water 40% Glycerine 60% Glycerine

6

4

2

0 50

100

150 200 250 Angular speed/ rad/s

300

350

8


D=0.1 m Water 40% Glycerine 60% Glycerine

6

4

2

0 50

100


300

350

Figure 6. Critical volume flow rate for the transition from direct drop to ligament breakup mode

5 40% Glycerine D=0.05 m D=0.1 m

4 Volume flow rate/ ml/s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3 2 1 0 50

100


300

350

Figure 7. Effect of disk diameter on critical volume flow rate for transition from direct drop to ligament mode


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+13.78%

‐4

‐0.201

10

Ligament mode

-15.50%

Q*Re

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

‐5

Predicted data D=0.05 m Water 40% Glycerine 60% Glycerine D=0.1 m Water 40% Glycerine 60% Glycerine

Direct drop mode

10

‐6

10

3

10

4

We

10

5

Figure 8. Transition curve from direct drop mode to ligament mode

Figure 9. Effect of volume flow rate on fully-ligament breakup mode (a) Q=4.76ml/s, (b) Q=8.43ml/s, (c) Q=11.84ml/s





10 8 6 4 2 50

100


300

350



12 10 8 6 4 2 50

100


300

350

Figure 10. Critical volume flow rate for fully-ligament breakup mode 12 40% Glycerine D=0.05 m D=0.1 m


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8 6 4 2 50

100


300

350

Figure 11. Effect of disk diameter on critical volume flow rate for fully-ligament breakup mode


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Fully‐Ligament mode

‐0.118

+5.47%

10

-12.83%

‐4

Q*Re

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Ligament mode 10

‐5

10

3

10

4

We

10

5

Figure 12. Transition curve from ligament to fully-ligament mode (a)

(b)

(c)

Figure 13. Transition image from ligament breakup to sheet breakup (a) Q=12.25ml/s, (b) Q=14.18ml/s, (c) Q=16.40ml/s



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30 24 18 12 6 50

100


300

350


50 D=0.1m Water 40% Glycerine 60% Glycerine

40

30

20

10 50

100


300

350

Figure 14. Critical volume flow rate for the transition from ligament to sheet breakup mode

‐3

+9.02%

‐0.133

10

Sheet mode

Q*Re

-9.79%

10


‐4

Fully‐Ligament mode

10

3

10

4

We

10

5

Figure 15. Transition curve from ligament breakup to sheet breakup mode


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10

Ligament‐Sheet

‐3

Fully‐Ligament Q(



m

10

‐4

Q*Re

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




P1 Q *  K *W ea R eb

10

10

‐5

D-L

F-L



D

L-S

K*

0.308

0.126

0.257

a

-0.994

-0.779

-0.75

b

0.201

0.118

0.133

P2 Direct drop‐Ligament

‐6

10

3

10

4

10

5

We Figure 16. Transition map for different breakup modes



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TOC Image 80x47mm (300 x 300 DPI)


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Experimental Study on the Critical Characteristics of Liquid

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