Relationship between Orifice Parameters of Slinger and Atomization Performance

Wenlong Tan

(Chinese Flight Test Establishment, Xi’an 710089, China)

Abstract: Slinger is a rotary atomizer whose atomization performance is affected by the parameters of orifice. 8 kinds of orifices with different structure parameters were investigated, and an optimal diameter exists for the round orifice with that the spray SMD is the smallest and the uniformity is the best. Increases in the axial length of slot orifice decrease the spray SMD and improve the spray uniformity, but increases in the width of the slot orifice are invalid for liquid spray SMD, and the spray uniformity becomes even worse. In most cases, the spray SMD of slot orifice is smaller than that of round orifice with the same perimeter, and the spray uniformity is better likewise. Increases in radial length of orifice cause the spray SMD to be larger, but the spray uniformity become obviously better. The spray SMD become larger with decreases in liquid surface tension. The spray uniformity became better nevertheless.

Keywords: rotary atomization; slinger; orifice parameters; spray uniformity; SMD

0 Introduction

Slinger is a kind of rotary atomizer that accelerates the liquid to a high relative speed to the air by mechanical rotation and produces a fine liquid spray. It is usually used in the combustion chamber of small aircraft engines. The shape of the orifice on a slinger is usually round or slot, and the geometric parameters of the orifice play an important role in the slinger atomization.

Dahm investigated the slinger with various orifices. The geometric parameters of the orifices are shown in Table 1[1-3]. The liquid leaves the slinger orifice in two regimes: film mode and stream mode. The film mode indicates the liquid leaves the orifice along its circumference and forms a liquid film, while the stream mode indicates the liquid leaves the orifice on the side of the orifice that is opposite to the slinger rotation direction and forms a liquid column. The film mode performs in two breakup ways: subcritical breakup and supercritical breakup. After leaving the orifice, the liquid film first aggregates into a liquid column and then breaks into droplets, which is termed subcritical breakup; if the liquid film breaks into droplets directly after leaving the orifice, it is termed supercritical breakup. The breakup modes of the film are related to the Weber numberWehwith the liquid film thicknesshas the characteristic length. The smaller theWeh, the more likely the liquid film performs subcritical breakup. The slinger’s liquid spray SMD is related toWet, withtas the characteristic length.tis determined by the liquid regimes when it leaves the orifice. When the liquid leaves the orifice in film-supercritical regime,tis equivalent to the thickness of the liquid film; when the liquid performs film-subcritical regime,tis equivalent to the diameter of the liquid column that is aggregated by the liquid film; when the liquid performs stream mode,tis equivalent to the diameter of the orifice.

Table 1 Geometric parameters of test orifices[1-2]

Carmen found the liquid breakup distance after leaving the orifice to increase with the increases in the liquid flowrate, and decrease with the increases in the slinger rotary speed[4-7]. The distribution range of the diameter of the droplets in the liquid spray increases with the increases in the liquid flowrate, and decreases with the increases in the slinger rotary speed. The liquid breakup distance and the spray SMD decrease with the increases in the diameter of the orifice.

Choi found the liquid in the slinger performs irregular breakup when the rotary speed is low or the liquid flowrate is high, which will produce large droplets and deteriorate the atomization performance[8-11]. The spatial distribution of the liquid spray depends on the diameter of the orifice. The orifice with a larger diameter can produce a more uniform and wider distributed liquid spray. If the slinger works in a lateral airflow, whose flow direction is parallel to the axis of the slinger, the velocity of the airflow will affect the atomization of the slinger. When the velocity of the lateral airflow is less than 50 m/s, the liquid spray SMD decreases with the increases in the slinger rotary speed. However, if the velocity of the lateral airflow is more than 100 m/s, the spray SMD will not change significantly with the change of slinger rotary speed.

Ye[12]presented a three-dimensional numerical simulation to study the liquid regimes near the orifice of the slinger. He found the liquid flowrates of each orifices are different in a short time and the total liquid flowrate of the slinger varies with time as well. Chakraborty[13]found the Coriolis force cannot be ignored when the slinger’s rotary speed is high, and the liquid will leave the orifice from the orifice side that is opposite to the rotary direction. Based on Dahm’s research[1-3], Rezayat[14]found when the rotary speed of slinger is up to 4000 r/min, and the liquid performs subcritical breakup; when the rotary speed is more than 5000 r/min, a phenomenon of liquid jet bifurcation is observed; when the rotary speed is up to 10000 r/min, the liquid performs supercritical breakup.

The existing researches on how the parameters of the orifice affect the atomization of the slinger are mainly qualitative results obtained from theoretical analysis or experimental research. This paper will present quantitative research and explore how the geometric parameters of the orifice affect the atomization of the slinger.

1 Test Apparatus

Fig.1 is a diagram of the test rig. A motor drives the slinger with a rotary speed range of 0-24 kr/min and the minimum adjustment unit is 6 r/min.

Fig.1 Diagram of the test rig

A transparent shield surrounds the slinger and is used to collect the liquid thrown out from the test slinger and return it to the liquid tank. The liquid in the tank is driven by a pump. It passes through the filter, pump, valve, and mass flowmeter, and then is ejected from the inject tube and finally hits on the wall of the test slinger to start a new liquid recycle. The minimum measuring unit of the mass flowmeter is 0.1 g/s, and the measuring range corresponds to 0-40 g/s.

The measurement equipment includes a high-speed camera and aphase of doppler particle analyzer (PDPA). The high-speed camera is used to capture the liquid regime near the slinger, and the maximum shooting frequency corresponds to 2500 fps. The PDPA is used to measure the diameter of the droplets in the liquid spray, from which SMD and the RR (Rosin-Rammler) distribution indexncan be calculated. The spray SMD is used to evaluate the size of the droplets. The smaller the SMD, the smaller the droplets.nis used to evaluate the uniformity of the liquid spray. The larger then, the more uniform the liquid spray. The minimum measuring unit corresponds to the laser wavelength of the PDPA and is about 0.5 mm. The measuring error of the PDPA is related to the types of the measurement particles when measuring liquid spray. The relative error for measuring the diameter of the droplet is 0.5%, while that for the quantity of the droplets is 1%[15].

Water is used as the main test liquid. Adding sulfonic acid in the water will change its surface tension, which can be used to explore the effect of the liquid surface tension on the atomization performance. The property of liquid solutions is shown in Table 2.

Table 2 Property of liquid solutions

The structure of the test slinger is shown in Fig.2. The radiusRof the slinger is 50 mm. The serial number and the shape parameters of the test orifices are shown in Fig.3. The radial lengthlof orificeA-Fis 3 mm, the shape of orificeA-Cis round, and orificeD-Eis a slot. The perimeters of orificeBandDare the same, and orificeC,E, andFhave the same perimeter likewise. Besides, two orificeBlandDlwith the same shape parameters as orificeBandDrespectively are added, and their the radial lengthlare 6 mm.

Fig.2 Schematic diagram of the slinger

Fig.3 Chart of orifices shape and size(Unit:mm)

2 Theoretical Analysis

High-speed photography found three liquid regimes exist near the orifice. Except for film mode and stream mode found by Dahm[1-3], the full mode will be formed when the liquid fills the orifice. The three liquid regimes are shown in Fig.4.

Fig.4 Liquid regimes in the orifice

Weber numberWetis the most important parameter to predict the liquid atomization, and the characteristic lengthtofWetis different when the liquid leaves the orifice in various regimes. However, it was found through experiments that when the rotary speed of the slinger is larger than 3 kr/min, the three liquid regimes all perform turbulent breakup. That means the liquid film or stream is severely torn by the air to form multiple fragments with a diameter approximating to the thicknesshof the liquid film in the orifice. According to Dahm’s research[1-3], there is

(1)

whereμLdenotes dynamic viscosity of the liquid and is 0.001 Pa·s,mdenotes mass flowrate of the liquid,ρLdenotes the density of the liquid and is 1000 kg/m3,ωdenotes the rotary speed of the liquid, andddenotes the diameter of the orifice. When the orifice is a slot, there is

d=P/π

(2)

wherePdenotes the perimeter of the orifice.

In most cases, the liquid regimes perform turbulent breakup as shown in Fig.5. ThereforeWehwithhas the characteristic length has the highest correlation coefficient with the liquid spray, and that was proved by the experiment results.

Weh=ρGu2h/σ

(3)

Fig.5 Regimes of turbulent breakup

whereρGis the density of gas and is 1.29 kg/m3, anduis the velocity at the edge of the slinger. The following equation is obtained:

u=ωR

(4)

Substituting Eqs.(1),(4) and the values of other parameters into Eq.(3):

(5)

3 Results

The radial position of the point where the liquid is thrown from the slinger completely broke into droplets corresponding to the working condition of the slinger. That means the radial position where the spray SMD is the minimum changes with the slinger working condition. In previous researches, the parameters of the liquid spray are usually measured at a fixed point and the effect of the changes in the minimun SMD position cannot be considered. In the experiment of this paper, the liquid spray parameters at a series of radial positions were firstly measured, then the parameters where the liquid SMD was the minimum were selected and analyzed, hence the effect of the change in the minimum SMD position was eliminated.

Liquid spray SMD and distribution indexnare the two main parameters to evaluate the atomization performance. Fig.6 shows the liquid spray SMD from various orifices versusWeh.The test data are discretely distributed corresponding toWeh, thus it is impossible to compare SMD quantitatively. First, the fitting formulas between SMD andWehof each orifice were calculated, then the fitting formulas were compared with each other, and the quantitative comparisons can be achieved.

(a)Orifice A/B/C

Exponential, linearity, logarithmic, power, and polynomial functions were used to fit the relationship between SMD/nandWeh.The formula with the highest relative coefficient was selected as the fitting formula and used to represent the atomization performance of the orifice. Table 3 is the table of fitting formula about SMD andWeh, and Table 4 is the table of fitting formula aboutnandWeh.The relative coefficients of the SMD fitting formulas are higher than those ofn, which means the analysis of SMD is reliable, while the analysis ofnis only reliable to a certain extent.

Table 3 Fitting formulas of spray SMD

Table 4 Fitting formulas of n

4 Analysis and Discussion

4.1 Change Rules of SMD

4.1.1Effectofdiameterofroundorifice

Fig.7 Curves of the effect of round orifice diameter on SMD

Fig.8 Curves of the effect of shape parameters of slot orifice on SMD

4.1.2Effectofshapeparametersofslotorifice

OrificeDandEhave the same width but different axial lengths, orificeDandFhave the same axial length but different widths, and orificeEandFhave the same perimeter. As shown in Fig.8, in most cases, orificeEexhibits smaller SMD than orificeD, and only whenWeh>6.853, the SMD of orificeDis smaller. Compare orificeDwithF; whenWeh<4.184, the SMD of orificeFis smaller; whenWeh>4.184, orificeDexhibits smaller SMD. The SMD of orificeEis always smaller than that of orificeF.

Previous research shows that an increase in the axial length of a slot orifice can reduce the spray SMD within a large range ofWeh, but increases in the width of a slot orifice have little effect on spray SMD. When the perimeters of the slot orifices are the same, the one whose axial length is larger exhibits a smaller SMD. WhenWehis large enough, orificeDwith a smaller perimeter exhibits the smallest SMD. Therefore, lengthening the slot orifice is beneficial to atomization whenWehis not very large, but widening the slot orifice is not recommended.

4.1.3Effectofshapesoforifices

When the perimeters of the orifices are the same, thedin Eq.(1) of each orifice is the same likewise. Fig.9 shows the comparison curves of SMD between the orifices with the same perimeters. WhenWeh<2.620, the spray SMD of slot orificeDis larger than that of round orificeB; whenWeh>2.620, orificeDexhibits a smaller SMD than orificeB.Compare slot orificeE/Fwith round orificeC; the SMD ofE/Fis always smaller than that of orificeC.The results mean that whenWehis the same, the slot orifice performs smaller SMD than round orifice in most cases. Only when the perimeter andWehare both small, the round orifice’s SMD is smaller.

Fig.9 Curves of the effect of orifice shapes on SMD

4.1.4Effectofradiallengthoftheorifice

Fig.10 is the comparison curves of SMD between the orifices with different radial lengths but the same shape parameters. The radial length ofBlandDlis 6 mm, while that ofBandDis 3 mm. WhenWeh<5.748, the SMD of round orificeBlis larger than that of orificeB; whenWeh>5.748, the SMD of orificeBlis smaller than that of orificeB, but the values of SMD of both orifices are very close. In slot orifices, whenWeh<0.769, orificeDlexhibits a smaller SMD than orificeD; whenWeh>0.769, the SMD of orificeDlis larger than that of orificeD.WhenWehis the same, the SMD of orificeDlis larger than that of orificeDby about 5 μm. Consequently, increases in the radial length of an orifice will cause an increase in SMD in most cases, especially in slot orifice.

Fig.10 Curves of the effect of radial length l of the orifice on SMD

4.1.5Effectofsurfacetension

Fig.11 shows curves of the relationship between SMD andWehwhen the surface tension is different, and the values of the test solutions’ surface tension are shown in Table 2. WhenWehis the same, the SMD of Solution I is the minimum, while those of Solution II and III are nearly the same. From Fig.12, it is found the SMD of Solution II is smaller than Solution III. Consequently, whenWehkeeps the same, SMD increases with decreases in surface tension. It is found from Eq.(5) thatWeh～σ-1.IfWehkeeps the same whenσdecreases, other parameters such as rotary speed or flowrate should decrease too, and the spray SMD may increase.

Fig.11 Curves of the effect of surface tension on SMD (orifice C)

Fig.12 Comparison curve between Solution II and Solution III (orifice C)

4.2 Change Rules of n

4.2.1Effectofthediameterofroundorifice

As shown in Fig.13, in most cases,nincreases with increases in diameter of round orifice. Only when 1.16

Fig.13 Curves of the effect of diameter of the round orifice on n

4.2.2Effectofshapeparametersofslotorifice

As shown in Fig.14, orificeEexhibits the maximumn, andnof orificeDis larger than that of orificeF.Only whenWeh<0.59,nof orificeDis larger than that of orificeE; whenWeh<0.63,nof orificeFis larger than that of orificeE; whenWeh<0.85,nof orificeFis larger than orificeD.Consequently, lengthening the slot orifice is beneficial to increase the uniformity of the spray, but widening the slot orifice will cause a less uniform spray.

Fig.14 Curves of the effect of shape parameters of slot orifice on n

4.2.3Effectofshapesoforifices

Fig.15 is the spray distribution index comparison curves between the round orifice and the slot orifice with the same perimeter. If the perimeter of the orifice is 2π(orificeBandD), whenWeh<3.51,nof the round orifice is larger; whenWeh>3.51,nof slot orifice is larger, but the difference between the values ofnof both orifices are less than 0.1. If the perimeter of the orifice is 3π(orificeC/E/F),nof orificeEis larger than that of orificeC, and only whenWeh<0.91, orificeCperforms a largern.nof orificeFis always smaller than that of orificeC.

Fig.15 Curves of the effect of orifice shape on n

The projection length of the orificeDin the axis direction of slinger is longer than that of orificeB, and that of orificeEis longer than that of orificeC, but the axis projection length of orificeFis shorter than that of orificeC.Consequently, it can be considered that when the perimeters of the orifices are the same, the orifice with a longer axis projection length performs a more uniform spray. Only whenWehis very small, the round orifice performs a more uniform spray.

4.2.4Effectofradiallengthoftheorifice

Fig.16 shows spray distribution index comparison curves between orifices with different radial lengths but the same shape parameters. In most cases,nof the orifice with a longer radial length is larger, especially in slot orifices. Only whenWeh<0.33,nof orificeBis larger than that of orificeBl; whenWeh<0.34,nof orificeDis larger than that of orificeDl.Consequently, with the orifice in the radial direction lengthened, the uniformity of the spray becomes obviously better, especially in slot orifices.

Fig.16 Curves of the effect of orifice radial length on n

4.2.5Effectofsurfacetension

As shown in Fig.17, when the liquid surface tension decreases,nincreases at the sameWeh.Only whenWeh<1.97,nof Solution III is smaller than that of Solution I; whenWeh<2.32,nof Solution II is smaller than that of Solution I; whenWeh<0.33,nof Solution III is smaller than that of Solution II. Consequently, whenWehkeeps the same, the uniformity of the spray becomes better as the liquid surface tension decreases. Only whenWehis small, the uniformity of the spray does not optimize as the surface tension decreases.

Fig.17 Curves of the effect of surface tension on n (orifice C)

5 Summary and Discussion

In a certain range ofWeh, an optimal diameter exists when the round orifice produces the smallest liquid spray. Under the sameWeh, increases in the axial length of a slot orifice decrease the spray SMD. In most cases, the spray SMD of slot orifice is smaller than that of the round orifice; increases in the radial length of orifice cause the spray SMD to be larger, especially in slot orifice; when the liquid surface tension decreases, the spray SMD increases.

Under the sameWeh, enlarging the round orifice will improve the uniformity of spray in most cases. Increases in the axial length of the orifice will improve the uniformity of the spray likewise, but if the axial length is too long, the spray uniformity becomes worse. When the equivalent diameters of the orifices are the same, the orifice with a longer axial projection length will produce a more uniform spray. Increasing the radial length of the orifice improves the spray uniformity significantly; the bigger the liquid surface tension, the worse the spray uniformity.

In conclusion, the parameters of the orifice should be determined according to the range ofWehof the slinger's actual work condition. Usually, the slot orifice performs a better spray than round orifice with the same perimeter. Increases in the radial length of the orifice cause the spray SMD to be larger, but the spray uniformity becomes better at the same time. To a certain extent, increases in the axial length of slot orifice improve the liquid spray, but if the axial length is too large, the uniformity of the spray will become worse.