ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Regular Article
Controlled Disintegration of Multiple Jets of Molten Slag
Mirco WegenerTill KuhlmeyerLuckman MuhmoodShouyi SunAlexandre Vladimirovich Deev
Author information

2014 Volume 54 Issue 12 Pages 2761-2766


The capillary breakup of multiple molten oxide jets was investigated. A graphite nozzle head allowed producing an array of laminar slag jets which disintegrate into droplets due to the growth of instabilities. A high temperature furnace with optical access and a pressurized crucible was used to generate the coherent circular jets which were recorded using a high-speed camera. External perturbations by means of a pneumatic vibrator were applied to investigate the impact of the vibration frequency on the length of each jet strand, the drop formation rate, the spacing between consecutive droplets and the drop size distribution. Results show excellent consistency in droplet formation when external vibration is applied and very good agreement with theoretical predictions. The findings may be used to facilitate the design of a droplet heat exchanger in which the latent heat of a molten slag can be transferred to a counter-current gas in a predictable manner.

1. Introduction

Molten slag contains a large amount of latent heat which is not easy to recover. Consequently, slag is usually either cooled slowly in open pits or slag dumps after tapping or, especially in the case of blast furnace slags, rapidly water quenched to obtain amorphous granules that can be used in cement manufacturing.1) Although there are technologies being developed to recover heat from molten slags (amongst others see e.g. Jahanshahi and Xie,2) McDonald3)), there is currently - on an industrial level - no facility installed and/or commercialized yet.

The challenging conditions at temperatures around 1500°C are certainly one major issue which posts significant obstacles to the successful transition of promising recovery processes from pilot to industrial scale. As heat recovery in the wet granulation process is usually not feasible, the dry granulation technique has been identified to be one of the most promising. Consequently, this technique is the most developed and is close to reaching industrial scale application. A comprehensive review was recently published by Barati et al.1) summarizing and evaluating the different available approaches.

Slag can also be viewed as a thermally stable fluid which may be used in solar thermal power plants as a heat transfer medium4,5) to increase the efficiency of the process. Currently, molten salts are used as the heat transfer medium, preferably with low melting point. Usually, these fluids are not thermally stable which limits the upper temperature to around 560°C. The company Halotechnics recently released a molten salt with a maximum temperature of 700°C. It is desirable to operate at even higher temperatures using a combinatorial approach to find suitable compositions of stable oxides which increase the operation window further (1200°C), as presented by Halotechnics.6) In the early 80’s Bruckner4) proposed to use oxide melts which can operate at 1500°C and above without deterioration. The relatively high melting point becomes an issue here and has to be kept in mind. He proposed to install a Liquid Droplet Heat Exchanger (LDHX) in which the slag passes through a nozzle plate by forming vertical jets which will disintegrate into strings of - in the ideal case monodispersed - droplets due to capillary forces. There were some first laboratory tests to investigate the nature of slag jet disintegration,7) but those were quantitatively useful to a limited extent only.

However, no matter which fluid will be used and no matter if the fluid is granulated by rotational devices or by disintegrating vertical jets, efficient heat recovery is only possible if the transfer liquid is granulated into droplets in a controlled manner, exhibiting a narrow drop (or particle) size distribution. This size distribution should be unimodal, hence no satellite droplet formation, which would facilitate better controlled heat transfer. At the same time, the droplets should be large enough to avoid entrainment by the flowing gas, and small enough to avoid agglomeration and to obtain optimum heat transfer characteristics (the residence time is limited; hence larger droplets may still contain a significant amount of sensible heat when they exit the apparatus).

The disintegration of liquid filaments, threads or jets into droplets is governed by interplay of viscous, inertia, gravity and surface forces. Instabilities on the jet surface grow in time and space until their amplitude equals the radius of the jet which ultimately leads to the formation of a droplet. In recent studies we have investigated at high temporal resolution the controlled breakup of jets of molten oxides at high temperatures by means of optical measurement techniques.5,8,9,10) In the mentioned references, only one nozzle was used, and hence the disintegration phenomena occurring at one jet have been investigated. In future LDHX applications, arrays of nozzles and jets are required. Consequently, we designed a new multiple nozzle head as a further development towards the design of a LDHX. This paper reports the experimental measurements of the disintegration of an array of three vertical laminar jets of molten slag at high temperature (above 1700°C) into droplets using a purposely designed graphite nozzle head. The drop formation rate, the drop size distribution, and the jet length of each strand were measured in a quantitative manner in response to a distinct external vibrational perturbation. The main goal is to control and predict the droplet formation from jets of high temperature oxide melts.

2. Material and Methods

The basic experimental device used in this study was the same long hot zone furnace with horizontal optical access described in earlier papers.8,9,10) Figure 1 gives a schematic view of the relevant and most important components. The furnace (1) was designed to provide a relatively large heated zone (approx. 700 mm) with three arrays of MoSi2 elements, and to facilitate optical measurements by means of a high-speed camera (2) in order to observe and quantify processes at small time scales at high temperatures. Optical access was made possible by a special reaction tube design, with two alumina tubes to form a cross (3). The vertical tube (3a) was circular and housed the graphite crucible assembly (4), while the non-circular horizontal tube (3b) provided optical access through a glass window (5) which was kept in one of the four water cooled flanges. The opposite flange was equipped with an oxygen probe (6) in conjunction with an internal R-type thermocouple to measure the oxygen partial pressure and the temperature close to the alumina tube junction. The horizontal tube had two circular 38 mm holes in its center position to allow the slag droplets and jets to fall through. The slag was caught by a stainless steel cup (7) at the bottom of the furnace which rested on a graphite stand (8) secured on a precision balance (9).

Fig. 1.

Schematic of the high-temperature furnace and auxiliaries. 1: Heating chamber, 2: High-speed camera and computer, 3a: Vertical alumina tube, 3b: Horizontal alumina tube, 4: Graphite crucible multiple jet/droplet generation device, 5: Quartz window, 6: Oxygen probe with R-type thermocouple, 7: Stainless steel cup for droplet collection, 8: Graphite stand, 9: Balance chamber, 10: Precision linear actuator, 11: Graphite crucible water cooled end cap, 12: Precision pressure regulator, 13: Differential pressure transducer, 14: Pneumatic turbine vibrator. Other parts not mentioned in the text: 15: Gas rotameter, 16: Gas bubbler and exhaust alumina tube unit, 17: Safety relief valve, 18: Needle valve, 19: Gas bubbler and exhaust graphite crucible unit. Qw: flow rate cooling water, Qg: flow rate purging gas.

The graphite crucible (4) consisted of three main parts: the main body in which the slag was melted with the multiple nozzle head at its bottom (capacity approx. 500 g of slag), a cylindrical hollow shank, and a hollow stopper with a ball shaped end to close the entry to the nozzle chamber. The stopper also housed a type-B thermocouple to monitor the melt temperature. It was attached to a linear actuator (10) which allowed to initiate and to interrupt the flow of molten slag into the nozzle head. The graphite assembly was suspended from three steel rods which were connected to the water cooled end cap (11) which also provided the gas delivery and exhaust when in pressurizing mode. The crucible was pressurized using ultra high purity argon. The pressure was controlled by a precision pressure regulator (12) and monitored by a differential pressure transducer (13).

In the present study, the same pneumatic turbine vibrator (14) as recently reported by Wegener et al.11) was used in order to impose a controlled periodic excitation on the jet. It was mounted on one of the steel rods mentioned above, which fixed the graphite crucible end cap. A precision pressure regulator ensured a steady rotation speed and hence vibration frequency. Prior to experiments at high temperatures, a calibration was conducted at room temperature using a piezoelectric accelerometer connected to the bottom of the graphite crucible. The calibration procedure linked the input pressure of the pneumatic vibrator with the vibration frequency of the crucible bottom. It is possible that the frequency response may slightly change when the crucible is hot and loaded with molten slag, however, the difference was found to be small.10)

2.1. Multiple Nozzle Head

The nozzle head was made of graphite; see Fig. 2(a), which allowed the creation of three jets at the same time and under the same conditions. Figure 2(b) shows the schematics of the assembly. The three nozzle head (1) was screwed into the tapered bottom piece (2) of the graphite crucible (3). A design was chosen in which the molten slag filled a cylindrical chamber (4) first from where it flowed through the three in-line capillaries. The chamber facilitated a homogeneous distribution of the slag across the chamber to fill all capillaries equally. The inner capillary diameter was nominally 1 mm (at room temperature) with a length of 15 mm each. The three holes were drilled on the centerline to position the jets in the focal plane of the camera lens. The central capillary was positioned at the center of the bottom disk. The distance between the capillaries was 7 mm which is enough to prevent coalescing phenomena while in dripping mode. The tips of the capillaries were shaped in a 45° angle to reduce wetting issues.

Fig. 2.

Three nozzle head as used in the experiments. a: rendered CAD-image (courtesy of S. Kerr, Mersen Oceania). b: schematic showing the nozzle head with the three capillaries (1), the tapered crucible base (2), the crucible (3), the intermediate chamber (4), the ball-headed graphite stopper (5), the thermocouple sheath (6), and the interface between slag and argon (7).

The slag flow was controlled by a graphite stopper (5). In contrast to previous studies, we used a ball shaped stopper tip. A B-type thermocouple was enclosed in an alumina sheath (6) inserted in the graphite stopper. The thermocouple measured the temperature of the slag bath.

2.2. Experimental Procedure

For the experiments, the graphite crucible was lowered inside the vertical alumina furnace tube until the tips of the three capillaries could be seen through the glass window. As in the previous studies, a calcia-alumina slag close to eutectic composition was used. The density was measured by the dripping method: single slag droplets were weighed by the precision balance. Then, the drop volume was evaluated from recorded images of the droplet silhouette using the slice method.11) The density was found to be in very close agreement with that published by Sikora and Zielinski12) for nearly the same slag composition and was approximated with a linear equation ρ = –1.3378ϑ + 5013.3 (with [ρ] = kgm–3 and [ϑ] = °C). The viscosity was obtained as reported previously by Wegener et al.10) and could be approximated with the Urbain model. A power law function was used to evaluate the values: μ = 2.5881·1027ϑ–8.7071 (with [μ] = Pas and [ϑ] = °C). The surface tension was measured using the drop weight and the oscillating jet method. The surface tension was found to be in reasonable agreement with the values obtained by Mukai and Ishikawa.13) A linear relationship was found: σ = –9.25·10–5ϑ + 0.776 (with [σ] = Nm–1). Table 1 summarizes working temperature and physical properties of the slag used in the present study. Note that the jet diameter was larger than the nominal capillary diameter at ambient temperature. The jet diameter was measured at experimental temperature by image analysis and is used from here on for all subsequent calculations. The low Bond number suggests a relatively small influence of gravity on the jets.14)

Table 1. Jet diameter and physical properties of calcia-alumina slags at experimental temperature.
ϑ [°C]ρ [kgm–3]μ [Pas]σ [mNm–1]djet [mm]Oh [–]Bo [–]

Table 2 shows a summary of the three experiments; all trials were at 1725°C and 1 bar pressure above ambient in the crucible. The balance measured the total weight gain per unit time, hence for all three capillaries combined. This method did not allow calculating the individual jet velocity; instead it gave the average jet velocity based on the cross-section of the jet at the capillary exit. Reynolds and Weber numbers were around 22 and 7, respectively. The frame rate was set to 5000 fps in all runs. The vibration frequency of the pneumatic vibrator was changed from 0 to above 200 Hz. One should keep in mind that the frequency values given in Table 2 are values based on the calibration performed at room temperature (with no liquid slag in the crucible) and do not necessarily reflect the real frequency imposed on the capillaries at the working temperature. The perturbation frequency f, the jet velocity νjet and the wavelength of the instabilities λ are connected via the equation νjet = λf. The wavelength which corresponds to the maximum instability growth rate can be expressed by15)   

λ max =2π R jet 2+3 2 O h R (1)
for viscous jets. In this case, the jet radius Rjet is the characteristic length in the Ohnesorge number OhR = μ(ρσRjet)–1/2. Equation (1) yields λ = 5.95 mm. The average jet velocity at capillary exit in Table 2 is 1.2 ms–1 and gives f = 203 Hz. However, once the jets issued from the capillaries, they accelerate and reach higher velocities. With the current setup, it was possible to measure the wave velocity of the jet which was obtained one wavelength before breakup. The obtained values, as can be seen in Table 2, reflect the acceleration. These values lead to frequencies between 230 and 260 Hz. Hence, it was decided to set the vibrator frequency on the higher side rather than on the lower side.
Table 2. Overview of performed experiments.
Exp. no.ϑ [°C]Δp [bar]fvib [Hz] M ˙ tot [gs–1] v ¯ jet [ms–1] v ¯ wave [ms–1]Re [–]We [–]Frame rate [fps]

3. Results and Discussion

Figure 3 shows some images of the jets issuing simultaneously from the three nozzle graphite head. No external vibration was applied; hence natural breakup mode is observed which normally leads to unequal jet lengths and drop sizes as can be seen in Figs. 3(a)–3(d). Figure 3(a) gives an example of satellite droplet formation. After primary breakup of jet no. 2, two satellites have been formed by secondary breakup. Jet no. 1 in Fig. 3(b) gives an example how droplets of larger size are formed. In contrast to the ideal case that the volume contained in one wavelength of an instability will form one droplet,16) the volume of several wavelengths will flow into one droplet until it separates as an entity from the jet. In Fig. 3(c), jet no. 1 breaks up earlier upstream due to an instability with larger amplitude. The jet length reduces dramatically, and the detached thread decomposes into several droplets of different size. One can clearly see one filament which is retracting symmetrically due to surface tension. A similar scenario was observed in jet no. 2 in Fig. 3(d).

Fig. 3.

Snapshots of multiple slag jets issuing from graphite nozzles. Natural breakup mode, ϑ = 1725°C. The jet length varies due to non-linear phenomena. a) Satellite formation in jet no. 2. b) Multiple waves form one droplet in jets no. 1 and 3. c) Breakup of longer piece of material. Retraction of elongated threads in jet no. 1. d) Breakup of longer thread in jet no. 2 with consecutive satellite formation.

With external vibration, the appearance of the jet changes quite substantially (see Figs. 4(a)–4(d)). The jet length is reduced, the drop size distribution is narrower, and the effect of non-linearities is suppressed to a great extent. However, every now and then, an externally disturbed jet may break early at the upper part which leads to an interval in which no droplets can be observed, see for instance jet no. 1 in Fig. 4(a). Also, the droplet size increases as the volume contained in several instability waves will form new droplets until the jet recovers and the droplet production becomes ‘normal’ again. Very rarely, satellite droplets were observed, as in jet no. 1 in Fig. 4(b). Figs. 4(c) and 4(d) show the regular case in which no satellites are formed and the spacing between the formed droplets is relatively equal. The small droplets which can be seen at the breakup point quickly coalesce with the next droplet being produced and hence will not exist as an entity.

Fig. 4.

Snapshots of multiple slag jets issuing from graphite nozzles. External perturbation mode (a and b: 280 Hz, c and d: 235 Hz assumed frequency, ϑ = 1725°C. In general, the jet length is shorter and drop sizes more equal compared to natural breakup. Rarely, non-linear phenomena occur from time to time. a) Gap in jet no. 1 after intermediate breakup. b) Formation of a satellite in jet no. 1. c) Formation of a short-term satellite in jets no. 1 and 2. They merge with the next droplet. d) Example of steady-state breakup mode, no satellites, equal spacing and drop size.

A comparison of the jet length distribution between natural and perturbation mode is displayed in Fig. 5 for all three capillaries named C1,2,3. The normalized frequency of the jet length is plotted as a function of the jet length class. For that purpose, the length of each jet was measured on each image of a sequence using an automated image analysis procedure. For each set of experimental data, a Gaussian distribution is plotted as well to demonstrate that the jet length is fairly well normally distributed. The results show that the jet length is significantly decreased around 40% in external perturbation mode. This is due to the larger initial disturbance amplitude imposed by the vibrator which causes the jet to break up earlier. The peak of the jet length distribution is not equal for the three capillaries in natural mode and varies between 53 mm (C3) and 63 mm (C1). Interestingly, for C3, the peak nearly coincides with the jet length prediction by Grant and Middleman17)   

L b d jet =( 2.66 ln( Oh ) +7.68 ) [ W e jet +3 W e jet R e jet ] (2)
which is given as a vertical dash-dotted line in each Figure. The reason for the different jet lengths may probably be due to the fact that the nozzles may not be completely identical, for instance in cross-section. The latter could explain slightly different jet velocities for the same driving pressure. The differences in jet length slightly reduce in external perturbation mode (Ljet,C1,2 ≈ 37 mm, Ljet,C3 ≈ 32 mm), but still the jet issuing from C3 produces the shortest jets. The jet length distribution is narrower producing a higher peak in the frequency in perturbation mode.
Fig. 5.

Distribution of the jet length as a function of diameter class for the three capillaries C1, C2, and C3. In each Figure, the case without vibration and those with vibration are displayed. The vertical dash-dotted line represents the prediction according to Eq. (2) based on the exit velocity of the undisturbed jet.

The two different vibration frequencies produce a slightly different output. The jets perturbed with the lower frequency are longer in all cases than the jets excited by the higher frequency. The absolute difference of the maximum values is around 2–4 mm. The differences will be even more apparent when a Fast Fourier Transform is applied to the jet length. The result is shown in Fig. 6 in which each color (red, black, blue) represents one of the three jets. In Fig. 6(a), the case without vibration is displayed. There is no distinct peak visible, and it seems that there is a broad frequency spectrum. The impact of vibration becomes apparent in Figs. 6(b) and 6(c). Distinct peaks emerge from the background noise. The peaks are located at the same frequency for all capillaries. For the assumed frequency of 280 Hz, the main peak is at 235 Hz, and a smaller one at 205 Hz. As shown in a recent paper,10) the main peak represents the droplet formation frequency which in turn represents the external perturbation frequency, which is also the case here. The measured droplet formation rate was exactly 235 Hz. The main peak for the assumed frequency of 235 Hz is at 220 Hz, again confirmed by image analysis of the droplet detachment rate. One conclusion here is that the Fast Fourier Transform of the jet length signal gives a much better value to determine the ‘real’ perturbation frequency compared to the rough calibration under ambient conditions. Second, all capillaries yield the same result in terms of droplet formation rate. This result shows that one external vibration source applied to a head with several nozzles is a suitable way to induce instabilities in all three jets, eventually leading to similar jet breakup behavior.

Fig. 6.

Fast Fourier Transform of jet lengths for the different cases. a: no vibration, b: assumed perturbation frequency 280 Hz, c: assumed perturbation frequency 235 Hz. In all Figures, three curves are given in different colors, representing the three capillaries.

The drop size distribution is displayed in Fig. 7. Figure 7(a) shows the results for Experiment no. 2 (assumed perturbation frequency 280 Hz), Fig. 7(b) results for Experiment no. 3 (assumed perturbation frequency 235 Hz). In both Figures, the individual drop size distribution for each capillary is given. The normalized distributions are based on approx. 300 droplets per jet. For both vibration frequencies, the drop size distribution is very narrow and does not exhibit considerably smaller or larger droplets. Those satellites formed, as e.g. displayed in Fig. 4(b) coalesce during their fall and therefore could not be counted during image analysis as the area of interest of the analysis was in the lower section of the image. Another interesting result is that the peak droplet size of capillary C3 is shifted towards smaller droplets for the 280 Hz case and nearly coincides with the prediction by Tyler16)   

d P d jet =1.89 (3)
plotted as a dashed-dotted line in Fig. 7. Equation (3) assumes that the volume of one wavelength forms one droplet, and the droplet diameter only depends on the jet diameter. The other two capillaries produce droplets of a slightly larger diameter. Their value coincides with the classical equation by Weber18) who took viscosity into account:   
d P d jet = ( 1+3Oh ) 1/6 [ 3π 2 ] 1/3 (4)
Fig. 7.

Measured drop size distribution from disintegrating slag jets. a: assumed frequency 280 Hz, b: assumed frequency 235 Hz, c: comparison of droplets produced by jet issued from capillary C3. In all three Figures, the drop size distribution is based on around 300 droplets per jet.

Equation (4) yields 2.26 mm for the present configuration whereas Eq. (3) predicts 2.15 mm. The drop size distribution exhibits a more consistent behavior for the 235 Hz case. Here, all jets disintegrate into a distribution with the peak value at equal diameters which is a better result if monodispersity is important. All peaks nearly coincide with the Weber equation and with capillaries 1 and 2 from the ‘280’ Hz case.

Figure 7(c) compares the drop size distributions of capillary C3 for the three vibration modes. Without vibration, the distribution is relatively wide and exhibits a small peak at around 0.9 mm. With vibration, the distribution becomes narrower and satellite droplet formation is suppressed. Obviously, the frequency does have a small effect on the droplet production from jets issuing from capillary C3. This result confirms that if one finds the ‘correct’ frequency which matches the inherent resonance frequency of the jet, one can hope to get a consistent and repeatable jet disintegration behavior which is highly beneficial for the design of granulation devices based on surface tension induced breakup.

4. Summary and Conclusion

The breakup of jets of molten calcia-alumina slag at high temperatures was observed and investigated in a quantitative manner at high temporal resolution. A new nozzle head was presented equipped with three graphite capillaries, hence three jets of molten slag were produced simultaneously. High-speed images were obtained which show in detail the jet disintegration into strings of single droplets. Automated image analysis was used to determine the jet length and the drop size distribution. The impact of an external vibration imposed by a pneumatic turbine on jet length and droplet formation rate compared to natural breakup (no additional external vibration) was studied in detail.

In natural breakup mode, non-linear phenomena led to formation of satellite droplets and irregular jet breakup. An imposed perturbation reduced the jet length about 40% and produced a highly repetitive drop formation mechanism for all capillaries. The drop size distribution is extremely narrow which is not the case in natural breakup mode. The peak value of the drop size distribution can be predicted reasonably accurate by Weber’s classical Eq. (4). The present work shows that high-temperature liquids can be dispersed into droplets of defined size in a controlled and predictable manner. Simultaneous jet formation was achieved which can now be extended to an array of jets aiming for the development of a Liquid Droplet Heat Exchanger.


The authors thank the Division of Process Science and Engineering and the Minerals Down Under Flagship of the Commonwealth Scientific and Industrial Research Organisation (CSIRO) for funding the research fellowships for M. Wegener, T. Kuhlmeyer and L. Muhmood.


Latin letters

djet jet diameter, m

dP droplet diameter, m

f frequency, s–1

g gravity, m2s–1

ID inner diameter, m

k wavenumber, m–1

L length, m

Lb jet breakup length, m

M ˙  mass flow rate, kgs–1

p pressure, Pa

Rjet jet radius, m

R0 initial jet radius at the capillary tip, m

t time, s

UHP ultra high purity

ν velocity, ms–1

V volume, m3

Greek letters

Δp pressure difference, Pa

ϑ temperature, °C

λ wavelength, m

μ dynamic viscosity, Pa s

ρ density, kgm–3

σ surface tension, Nm–1


0 initial, at t = 0

b breakup

cap capillary

g gas

jet jet

max maximum

P droplet

tot total

vib vibration

w water

wave instability wave

Dimensionless numbers

Bo Bond number, Bo=ρg R jet 2 σ -1

Oh Ohnesorge number, Oh= We R e -1 =μ ( ρσ d jet ) -1/2

Re Reynolds number, Re=ρv d jet μ -1

We Weber number, We=ρ v 2 d jet σ -1

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