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Liquid jet formation during a suspended liquid suction process
Journal Pre-proofs Liquid Jet Formation during a Suspended liquid Suction Process Liang Hu, Hanghang Xu, Mingbo Li, Weiting Liu, Wenyu Chen, Haibo Xie, Xin Fu PII: DOI: Reference:
S0894-1777(19)30586-2 https://doi.org/10.1016/j.expthermflusci.2019.109952 ETF 109952
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
12 April 2019 7 October 2019 12 October 2019
Please cite this article as: L. Hu, H. Xu, M. Li, W. Liu, W. Chen, H. Xie, X. Fu, Liquid Jet Formation during a Suspended liquid Suction Process, Experimental Thermal and Fluid Science (2019), doi: https://doi.org/10.1016/ j.expthermflusci.2019.109952
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© 2019 Published by Elsevier Inc.
Liquid Jet Formation during a Suspended liquid Suction Process Liang Hu, Hanghang Xu, Mingbo Li, Weiting Liu, Wenyu Chen, Haibo Xie and Xin Fu* The State Key Laboratory of Fluid Power & Mechatronic Systems, Zhejiang University, Hangzhou 310027, China.
Abstract: In the tubular co-flowing gas-liquid jet, liquid is sucked through a nozzle suspended above the flat gas-liquid interface. The liquid hump can be induced by the sudden pressure change just beneath the nozzle entrance. At a sufficiently fast initial gas superficial velocity, the interface undergoes a transition and liquid starts to be sucked. The suction flow is in the form of an axisymmetric liquid jet surrounded by an upwards coaxial gas flow. In the present study, we discuss the evolution and characteristics of the suspended liquid suction flow. The jet dynamics include the interface deformation and development (the hump stage), the tubular co-flowing jet (the spout state) and the destabilization of the liquid jet (the jet state). Tube inner diameter, suspension height, and initial gas superficial velocity are three important parameters that influence the suction flow. Due to the inward gas flow, a relatively large amount of pressure gradients is imparted to a small mass of liquid near a free surface, which leads to interface deformation. The lateral boundary of the liquid hump circumferentially shrinks and the top liquid gradually rises following the shrinkage. There is a comparatively stable axisymmetric liquid jet surrounded by an upwards coaxial gas flow inside the tube. Surprisingly, no evidence is shown the dependence of jet spout with initial gas axisymmetric superficial velocity below the nozzle through plenty of experiment figures and statistical analysis. On the other hand, the velocity difference between the fast light fast gas flow and the slow dense liquid is critical to the destabilization of the liquid jet.
Keywords: Non-contact liquid sucking; Two-phase coaxial jet; Forming conditions; Quasi-static liquid spout.
* Corresponding author. E-mail addresses: [email protected] (Xin Fu).
1. Introduction Many important and complex physical processes rely on morphological transitions of a fluid interface which changes easily in response to stress. In this paper, we will concentrate on both the mechanism that produces the particularly absorbing ‘a tubular co-flowing gas-liquid jet’ and its characteristics. The tubular co-flowing gas-liquid jet can be observed in a simple experiment. The upward liquid jet occurs because of a sudden pressure drop inside a vertical tube suspend above a container of liquid (see Fig. 1). In our laboratory, the gasliquid two-phase flow that happened in the immersion lithography machine is being studied. During the liquid collection, not only the recycled immersion liquid but also the air around it is also inhaled into the micro collection holes. So that, we generated interest in it during making a simplified experiment of immersion liquid recovery in immersion lithography. Similar deformation examples include the fluid entrainment by selective withdrawal, that fluid is withdrawn from a container holding stratified layers of immiscible fluids through a tube placed near their interface. It has widespread application in the in many industrial and physical processes of both large and small length scales, including but not limited water pollution control, coating of microparticles, steady microscopic liquid thread, fabrication of thin glass fibers, etc. [1-4] Experimental and numerical studies dealt with well-controlled two immiscible fluids systems [5]. A morphology change occurred when shear stresses cause the initially smooth interface to erupt into a spout between two immiscible fluids. Typically, stresses determine the fluid flows near the transition. Cohen and Nagel examined an analogous transition by using flow in an upper layer of shear oil to entrain water from a lower layer [6]. And their results were supplemented by extending to systems with different viscosity ratios [7]. The investigations of the influence of flow rate and the geometric setup (such as tube heights, tube diameters, and so on) were done with experiments and simulations as well [5][8]. In general, the flow behaviors may be classified into two regimes, selective withdrawal regime and shear entrainment regime. In the selective withdrawal regime, the interface forms a steady hump directly under the tube with a stagnation point at the hump tip and only the upper fluid is withdrawn through the tube. With increasing suction flow rate, the interface deformed more and eventually changes into the shear entrainment regime, and the lower fluid is withdrawn together in a thin spout form along with the upper fluid. There is another classification: subcritical regime, supercritical regime, and critical regime. The first two correspond to the selective withdrawal regime and the left belongs to the entrainment regime respectively [10]. And in between, the critical regime is the threshold for the uptake of the interface, but few with gas-liquid systems. Selective withdrawal not only refers to the suction flow in the neighborhood of a liquid-liquid interface but also the flow in the neighborhood of a gas-liquid interface. In a gas-liquid system, whether the suction tube sits in the gas or the liquid strongly influences the appearance of the shear entrainment regime. If the tube is in the liquid, the air-liquid surface of a container draining form a hole in the bottom. The free surface always attains a smooth steady-state morphology. A
sharp tip is formed when a shear fluid is withdrawn from the neighborhood interfacing with ambient air. No gas can be drawn into the tube no matter what the flow rate, except when the tip is inside the orifice [11-12]. On the other hand, if the tube is in the gas, a liquid jet can be formed similar to the liquid-liquid system. It was widely applied to the field of material synthesis for creating uniform microparticles, especially on the generation of droplets in microfluidic networks [13]. A continuous gas flow to produce uniform liquid sprays was first proposed and demonstrated by placing a capillary tube behind a round orifice plate [3]. Inspired by this method, scholars recently performed an analysis of a liquid jet and coflowing gas stream surrounding the jet into an open environment [14-16]. Basically, this flow is characterized by the formation of a steady microscopic liquid jet in the core of a highly accelerating (extensional) laminar gas stream and the steady thin liquid jet emitted from the cusp-like drop. And by controlling the pressure of the focused and shear flows, the size distribution of the microdroplets becomes uniform. The pressure-driven jetting phenomena that are also closely related to the annular tubular jet created by focusing momentum into a small mass of liquid so as to make it jetting. An example is a tubular flow first reported by Lorenceau et al. [17]. Jet could be observed to emerge from the central surface of the rising liquid column while a sudden release of the pressure in the tube. The driving and focusing mechanisms for this jet were presented by R. Bergmann et al. through highspeed imaging, particle image velocimetry, and numerical simulations [18]. The tubular jet was found to be created by the convergence of the flow as it entered the tube. A second example was a tube filled with a perfectly wetting liquid falling axially under its own weight [19]. In its gravity-free reference frame, the liquid interface was deformed by surface tension into a hemispherical shape. While the falling tube impacted on a rigid floor, a sudden change of tube velocity induced a pressure gradient, which in turn led to a sudden change of liquid velocity inside the tube. As a result, the interface curvature reversed violently and finally formed a concentrated jet. A third example is the high-speed liquid jet generated when a small air bubble bursts from an equilibrium position at an air-water interface. In this case, the surface tension stresses focused on the base of an unstable cavity at the surface, just like jetting in a glass of champagne in our daily life [20]. There are many other similar phenomena, not limited to the above. The tubular co-flowing gas-liquid jet is a little different from the flow examples discussed above. The liquid entering into the tube is confined by the gas flow, and the tube wall obstructs the gas flow partly. Generally, its main characters are the formation of a liquid spout in the core of an axisymmetric high-speed gas flow, which is an unsteady gas-liquid jet. In this paper, we focus on the characterization of the morphological transitions of this special gas-liquid jet inside the tube and discussion on the nature of the morphology change. A rich set of two-phase flow regimes are observed in a millisecond. A liquid hump is induced by the sudden pressure change as soon as the air in the tube is sucked. Following some complex 3
motions, the hump gradually deformed into an axisymmetric spout and a liquid jet can be seen to emerge from the central liquid surface just beneath the nozzle. Besides, because of the coaxial gas flow disturbing, it is also observed surface instability and intricate drop breakup inside the tube. This paper reports our experimental study of the tubular co-flowing gas-liquid jet produced by the suspended liquid suction due to a negative pressure. Once the liquid is suction converging, it is replenished from around. This paper is organized as follows, the experimental methods and the designed apparatus are introduced firstly. And then, the suction process is identified to three different stages. In addition, the experimental data on the occurrence of observed flow stages under different parameters are discussed. Through the analysis of the above experiment results, the criterion of tubular coflowing gas-liquid jet formation is found directly determined by the initial gas superficial velocity. Thus, the correspondence relationship between them is summarized. Finally, the characteristics of the onset of tubular co-flowing jet and the jet column are both discussed.
2. Experimental apparatus and methods
Fig. 1. Schematic of experimental apparatus A schematic drawing of the suspended liquid suction and a diagram of the experimental apparatus are shown respectively in Fig. 1. A transparent Perspex container (dimensions 100mm×100mm×150mm) is filled to a depth of H’ with purified water. And a vertical, cylindrical tube with inner diameter D is held at a distance H’+H from the container bottom. The depth of the water H’ is measured by taking the known tube diameter as a reference in the observation window of a high-speed camera. The container walls and the water are sufficiently distant and thick so as not to affect the suction flow. Considering the error of observation in the observation window, it is more reasonable to consider observation accuracy as 0.1mm. The values of related experimental parameters, nozzle diameter D, suspension height H, and differential pressure ∆P, 4
are listed in Table I. The nozzle diameter D is variable by changing different tubes. In experiments, the suspension height H vertically from the nozzle to the flat liquid surface is adjusted by a lifting platform with a maximum scale of 20 mm and an accuracy of 0.1 mm. In the suspended liquid suction process, the suspension height H remains essentially constant at the hump state and increases very slowly at the subsequent flow states. In reduce the influence of height change in drawing some qualitative conclusions, we pay attention to the co-flowing gas-liquid jet before the obvious surface decline. The characteristics of suspended suction flow discussed in this paper are the premise with the suspension height H without considering its subtle variability. Table Ⅰ. Experiment parameters Inner diameter, D (mm)
Suspension height, H (mm)
Differential pressure, ∆𝐏 (mbar)
4.0
2.0
200
5.0
3.0
300
6.0
4.0
400
Experiments are carried out at the temperature of 25 ± 1 ◦C and the environment pressure of 101.3 kPa. Gas-liquid mixtures are sucked through a tube using a vacuum pump (Vacuubrand MD 12 NT VARIO) with a variable speed motor. The downstream side of the tube is connected with a control valve (VHK2-08F-06F, the distance between the valve and the tube L=500.0mm and the cross-sectional area S1 = 9 × 10 ―6m2). The control valve is a mechanical valve that only permits two-phase flow in one direction. The valve is closed in advance in order to let system pressure gradually decrease to a preset pressure. It is hypothesized that a steady-state gas flow will be formed immediately as long as the valve opened even at the initial opening. The initial gas superficial velocity U is thus acquired corresponding to the instant of opening the valve. According to Bernoulli's principle, the relation between differential pressure ∆P and gas velocity U1 in the valve entrance satisfies the equation as follows: ∆P ― Ploss ρg
U21
(1)
= 2g
In the direction of flow, due to friction caused by the viscosity of the fluid, we have Ploss the drag losses. It consists of line losses and local losses. The cross-sectional areas of the tube and valve are of the same order of magnitude, the local losses are considered to raise by the sudden expansion of the valve to the tube. So that the drag losses satisfy: Ploss ρg
L U2
U2
(2)
= λD2g + KL2g S 2
in which U is the gas velocities in the tube, ρ = 1.205 kg/m3 is the gas density and KL = (1 ― S1) 5
is the entrance loss
coefficient for the sudden expansion of the cross-sectional area. Since the relative roughness of the tube is small, λ is calculated by the Blasius function λ = 0.3164Re ―1/4. Reynolds number Re = Ud/ν and ν = 1.83 × 10 ―5 Pa ∙ s is the kinetic viscosity of air. The relationship of U1 and U is S1U1 = SU, in which S =
πD2 4
the cross-sectional area of the tube.
Before the mixtures reached the pump, the liquid will be separated in an airtight separation tank, which also serves as a pressure stabilizer. Outside the tank, a high-speed camera (Phantom 120S) was set up approximately level with the bottom of the tube, perpendicular to the glass sidewall of the container. The time-evolution of the complex shape of the free surface and the flow around the cylindrical tube were recorded by the camera with a rate of 1000 frames/s and an exposure time of 60 microseconds. Backlighting of the tube was achieved by a lamp placed at the opposite side of the tank to obtain typical images like those of Fig. 2. All of the recorded images were saved in digital shadowgraph format, which can be easily processed and analyzed in MATlab.
3. Results and discussion 3.1 Overview of the jet dynamics During the suspended suck process, complex interactions between the gas and liquid phases as well as the tube wall occur in a millisecond. Different images of interface profiles of the intact suspended liquid suction process are presented in Fig. 2(a). The main jet dynamics include the interface deformation (the hump state), the tubular co-flowing jet (the spout state) and the destabilization of the liquid jet (the jet state).
Fig. 2. (a) Evolution of the free surface during a typical suspended suck, including the liquid hump in t=0,13ms, the jet 6
spout in t=14,15ms and the jet in t=35ms (D=4.0mm, H=3.0mm, U=95.9m/s), (b) the changing surface profiles of liquid hump just beneath the tube with time, (c) the height trend of the liquid hump for the same data shown in (b), (d) schematically shows the parts of the changing surface profiles of jet spout interface at the jet state at different times. As soon as the surrounding air is sucked into the tube and a radially inward gas flow upon the interface will be formed. In the meanwhile, the pressure inside the tube drops instantaneously. Subsequently, the liquid under the nozzle entrance converges inwards radially and extends axially. As we can see, the surface deformation changes slowly at first and gradually accelerates. The curved upper surface of liquid hump becomes asymptotically flat is a relatively special phenomenon as shown in the middle picture in Fig. 2(a). The changing surface profiles of liquid hump just beneath the tube with time is shown in Fig. 2(b). The interface curvature is constantly changing as time goes on. Interface deformation modifies the air suction flow and results in a relative high-pressure area in the middle of the tube nozzle. The mean curvature is proportional 2γ
to the additional pressure difference across a fluid surface, as seen in the equation rH = ∆P, where the mean curvature 1
κ = rH. This explains why the interface curvature of the liquid hump becomes smaller. The changing profiles are pulled in the axial direction and can be closely approximated by a parabolic segment. The height of the liquid hump indicated by a red line segment in Fig. 2(a) can be utilized to evaluate the instantaneous hump size. The height trend of the liquid hump for the same data shown in (b) is shown in Fig. 2(c). The liquid extends axially and diameter decreases with increasing hump height. A jet spout starts to emerge from the center of the rising liquid hump. During the suction process, the radial component of the shear force continually squeezed the liquid hump, benefitting its inwards radial convergence and axial stretch. The upwards coaxial gas flow squeezed the smaller mass of liquid more easily. It is an interactive process. Liquid in the container entered the tube through the nozzle forming a comparatively stable axisymmetric liquid jet surrounded by an upwards coaxial gas flow. The fifth picture in Fig. 2(a) shows that the liquid jet suffers a Kelvin–Helmholtz instability and even forming corrugations ligaments along the downstream. Once the liquid is sucked converging, it is replenished from around. The suspension height naturally increases after a while. The parts of the changing surface profiles of jet spout interface at the jet state at different times are shown in Fig. 2(d). The surface profiles of jet spout interface becomes thinner significantly from t=15ms to 890ms, while it changes not obviously from t=890ms to 1490ms. Besides, in the gas suction flow, the ligaments are stretched and their diameters decrease until they break into drops. The disordered liquid collides with the tube wall, eventually entering the separation tank.
3.2 Forming conditions 7
While many of the parameters mentioned influencing the flows, our understanding can be conveyed by focusing on tube inner diameter, suspension height, and initial gas superficial velocity. The onset characteristics of tubular co-flowing jet influenced by those parameters mentioned above are discussed in detail in this section. This phenomenon is best described as a pressure-driven geometrical flow focusing. The sudden change of the motion of the boundaries generates large pressure gradients which in turn produce a sudden change in the velocity at every point of the liquid [21]. In selective withdrawal, researchers put forward a simplicity assumption which the axisymmetric withdrawal would form a point sink located within the upper of two semi-infinite layers of viscous fluid [5][22]. CFD simulation is shown that the air pressure just above the liquid surface under the nozzle entrance decreases in the flow direction. Interface deformation occurs when a relatively large amount of pressure gradients is imparted to a small mass of liquid near a free surface.
Fig. 3. Comparison of different hump deformations (a: D=6.0mm, H=4.0mm, U=49.7m/s; b: D=6.0mm, H=4.0mm, U=63.2m/s). Fig. 3 compares hump deformations with different initial gas superficial velocities. Solid lines indicate the initial flat liquid surface and dotted lines indicate the deformed liquid surface. Pressure gradients exerted by the inward gas flow are strongly influenced by the flow domain beneath the tube. The pressure gradients reverse the initial liquid surface in the axial direction violently, while both liquid gravity and surface tension resist the deformation. Balancing the combined force is a necessary condition for the formation of tubular co-flowing gas-liquid jet. Fig. 3(a1)-(a3) illustrates that the slower initial gas superficial velocity brings difficult in liquid suction flow. The liquid surface fluctuates up and down slightly and h/H is about less than 1/5 under these conditions. Fig. 3(b1)-(b3) illustrates that the faster initial gas superficial velocity intensifies the interface deformation. As a conclusion, when the initial gas superficial velocity is slow, a hump forms just above the liquid surface under the nozzle entrance merely. When the initial gas superficial velocity of inward gas flow exceeds a threshold value Uc, the hump translates into a spout.
8
Fig. 4. Phase diagram of critical initial gas superficial velocity versus suspension height, (a) d versus H for three tube inner diameters, (b) Uc versus D/H for the same data shown in (a). The critical initial gas superficial velocity versus suspension height for different values of tube inner diameter is shown in Fig. 4(a). The relationship between Uc and H is got by polynomial fit. The higher the suspension height is, the higher the Uc the flow needs. A higher height will create more pressure reduction that should be compensated by increasing the gas velocity. In Fig. 4(b), a curve is drawn with D/H as abscissa and critical initial gas superficial velocity as ordinate. It shows that Uc and D/H scale as an exponential relationship, Uc = 214.8e ―1.385D/H +25.63e ―0.1099D/H. And we defined a dimensionless flow rate Ca = πνρU/4γ [9]. Ca is plotted on the right side of Fig.4.
Fig. 5. A typical onset of the tubular co-flowing jet (D=4.0mm, H=4.0mm, U=86.9m/s). As mentioned above, the lateral boundary of the liquid hump will circumferentially shrink and the top liquid will gradually rise following the shrinkage. A liquid jet spout gradually stabilizes. Fig. 5 shows the deformations of hump and spout before the onset of the tubular co-flowing jet. The curved liquid hump becomes asymptotically flat, an omen of the liquid jet. The surface shape modifies the direction of gas flow in turn. Pressure near the nozzle changes once the liquid approaches the nozzle due to the ratio of gas and liquid. The stresses are continually induced by gas flow and liquid surface tension. Assuming that the gravity of this small part liquid and the surface shear force keeps constant in this short time, the differential pressure induced by gas flow in axial direction gradually decreases. It has influence over interfacial interaction, which is perpendicular to the surface. So that, the boundary of liquid profiles below the tube nozzle shows an arc-shaped gas-liquid surface. Because of the influence of a continuity gas flow, a gas stagnation area appears at the center of the liquid 9
level. A flat liquid surface becomes visible when the height of liquid hump is around 0.6H. It is a result of the local stress balance between the pressure difference and the stress arising from the interfacial curvature. There is no clearly definitely transition between the hump and the spout. When the liquid gradually approaches the nozzle, the passage of gas flow suddenly contracts and the gas flow velocity increases sharply. Interfacial interaction suddenly decreases, and the diameter of the liquid spout becomes a little larger but then thinner immediately. In the axial direction, the pressure on the upper portion of the liquid suddenly decreases, which causes the liquid jet emergence and growing upward.
Fig. 6. The changing heights of liquid hump under various jet parameters ((a): different suspension height H with the initial gas superficial velocity U=75.2m/s, the inner diameter D= 5.0mm, (b): different initial gas superficial velocity U with the suspension height H = 3.0mm, the inner diameter D= 5.0mm and (c): different inner diameter D with the suspension height H = 3.0mm, the initial gas superficial velocity U=75.2m/s.) Shortly after the valve opens, the circular hump forms and develops refer to Fig. 2(b). Changes of the hump height under various jet parameters are compared. Considering that the change of the initial liquid level is less obvious, the focus is on the moment before the liquid enters the tube, that is, the moment when the jet appears. Therefore, the moment 0 is set when the liquid column reaches the nozzle, and the height of the liquid hump tip before this moment is recorded. The ratios of hump height h to suspension height H recorded as a function of τ are plotted in Fig. 6(a)-(c), τ =
t ρLH3/σ
is the capillary
time. Here ρL and σ are the density and surface tension coefficient of liquid, respectively. Through these certain number of data points, the changing trend of liquid surface can be determined. As we can see, the deformation of the free surface is gradually accelerating. Fig. 6(a) compares the deformation at different H. Comparing the slopes of trends at τ = 0, it shows that the liquid surface rises faster at H=3.0mm ,4.0mm than H=2.0mm near the nozzle. Moreover, increasing the height retard movement of liquid inward convergence. Larger suspension height adds a larger duration of the hump stage. Similarly, comparing changing trends at different initial gas superficial velocity U from 60.9m/s to 87.3m/s in Fig. 6(b), we find out that a faster initial gas superficial velocity can produce the same effect law as the smaller height. Besides, we also changed the tube 10
inner diameter from 4.0mm, 5.0mm to 6.0mm as shown in Fig. 6(c). A smaller the inner diameter links to a faster deformation of hump. So, in order to make the liquid suction flow more easily, we should fix a tube with a smaller inner diameter at a smaller suspension height and adjust the negative pressure as large as possible.
3.3 Characteristics of quasi-static liquid spout and liquid column
Fig. 7. Images of a tubular co-flowing gas-liquid jet under various jet parameters (different initial gas superficial velocity U with the suspension height H=3.0mm, the inner diameter D=4.0mm in the first column, different suspension height H with the initial gas superficial velocity U=75.2m/s, the inner diameter D=5.0mm in the second column and different inner diameter D with the suspension height H=4.0mm, the initial gas superficial velocity U=77.0m/s in the third column). At the spout state, the sucked liquid is in the form of a liquid column inside the tube continuously. The liquid column diameters of tubular co-flowing gas-liquid jet under various jet parameters are given in Fig. 7 and its change rules are discussed. The measuring position of the liquid column diameter is chosen slightly higher than the nozzle entrance. Referring to the lengths of white line segments shown in Fig. 7(a1)-(a3), it is obvious that the diameter of the jet liquid column is almost constant despite increasing the initial gas superficial velocity U but fixing the suspension height H=3.0mm, the inner diameter D=4.0mm. Besides, when fixing the initial gas superficial velocity U=75.2m/s, the inner diameter D=5.0 mm but increasing the suspension height H, the diameter is becoming smaller as shown in Fig. 7(b1)-(b3). Observed From Fig. 7 (c1)-(c3), as the inner diameter D rising from 4.0mm to 6.0mm with the suspension height H=4.0mm, the initial gas superficial velocity U=77.0m/s, it is found the liquid column diameter enlarged. And after counting, arranging and averaging the diameter of the liquid column under different jet parameters, three more figures with U as the abscissa are given in Fig. 8. 11
Fig. 8. Experimental results of the diameter of jet liquid column d as a function of initial gas superficial velocity U at different suspension height (the tube diameters from left to right are 4.0mm, 5.0mm, 6.0mm). For each set of data, d has little change with U increasing. It shows that different initial gas superficial velocities do not affect the diameter of the jet liquid column, essentially in agreement with Fig. 7(a1)-(a3). At a certain suspension height, a thicker liquid column links with a larger tube diameter, and vice versa. For the 4.0mm inner diameter as shown in Fig. 8 (a), the diameter of the liquid column increase from 1.3mm to 2.1mm when the suspension height increase from 2.0mm to 4.0mm. Moreover, comparing circular data dots in Fig. 8 (a)-(c) in which the suspension height is 3.0mm, it shows that the diameter increases from 1.58mm to 3.50mm at increasing tube diameter. That is to say, the diameter of the jet liquid column becomes larger as increasing the tube inner diameter or reducing the suspension height. The above phenomena can be explained from the aspect of energetic equilibrium. A smaller suspension height or a larger inner diameter costs less jetting energy. More liquids can be sucked and generate into a thicker liquid column. Through averaging the different diameters of the liquid column without considering different gas superficial velocities, Fig. 8 merges into Fig. 9(a). It can better represent the effect of suspension height and inner diameter on the diameter of the liquid column.
Fig. 9. Phase diagram of average diameter of jet liquid column versus the suspension height, (a) d versus H for three tube inner diameters, (b) d/(D-d) versus D/H for the same data shown in (a). It shows that the diameter of the liquid column decreases linearly with the increase of the suspension height. The proportion of gas is larger. After normalization of three sets of data, it turns out that d/(D-d) increases linearly with D/H as scaled out in Fig. 9(b), d/(D-d) = (D/H)0.93. 12
Fig. 10. The change of profiles of axisymmetric jet spout beneath the nozzle (D=4.0mm and H=4.0mm). The effect of the initial gas superficial velocity on the axisymmetric jet spout is also considered. A typical example profile of this phenomenon is drawn in Fig. 10. In this figure, ds/D represents the ratio of spout diameter to the diameter of the recovery tube and h(ds)/H represents the ratio of the liquid spout height to the suspension height. The radius of the surface profiles is changing on the different sections of the liquid spout. The quasi-static liquid spout becomes thin in the direction of gas flow. In addition, data points of different shapes indicate the positional relationship of the gas-liquid boundary distance axis at different gas superficial velocities. It seems that the close-up of the spout shape with a center of symmetry is constant despite the growing gas superficial velocities. Under both the same inner diameter and suspension height, different gas superficial velocities almost do not influence axisymmetric jet spout. The quasi-static liquid spout is the result of the equilibrium relationship in the mechanics of axisymmetric jet spout below the nozzle. The axisymmetric tubular co-flowing gas-liquid jet starts from a pressure excitation point located beneath the nozzle. Ignoring inertial force, the forces acting on the cross-section of liquid spout include four parts: the first part is the pressure force produced by meniscus and pump suck, the second part is the shear force generated by gas flow, the third part is the surface tension and the fourth part is the gravity force applied by upper liquid. The balance of these forces makes meniscus stable at different gas superficial velocities. Radial forces cancel each other out. While in the axial direction, an accurate formula for related force can hardly be determined for the lack of some physical quantity. We only scratch the surface of this problem here.
Fig. 11. Phase diagram of different diameters of the quasi-static liquid spout (ds). 13
As D and H varied, the profiles of axisymmetric jet spout change and their diameters are recorded in Fig. 11. The horizontal ordinate h(ds)/H changes from 0 to 1.0 means that the surface is gradually away from the nozzle entrance. For the same inner diameter, the larger suspension height is the faster diameter changes before the diameter of spout ds reaches tube diameter D. However, if ds is larger than D, the case is on the contrary. The turning point of h(ds)/H is a fixed value for an inner diameter. For D=4.0mm, h(ds)/H=0.5; for D=5.0mm, h(ds)/H=0.38; and for D=6.0mm, h(ds)/H=0.3. It is related to the distribution of pressure below the nozzle. Around the tube nozzle, complex interactions appear between the gas and liquid phases as well as the tube wall. The diameter of the liquid spout at the nozzle position influences the pressure distribution. The bigger ratio of liquid around the nozzle hinders the gas flow, which results in a larger pressure gradient near the interface. So that the turning point seems lower as D increases.
Fig. 12. The intact growth progress of destabilization of the liquid jet. Note the duration of the experiment and the length scale. (D=5.0mm, H=3.0mm, U=75.2m/s). At the root of the liquid column, the fast coaxial gas flow induces a destabilization of the jet as shown in Fig. 12. A
wavelike
destabilization
The
velocity
difference between the fast light fast gas flow and the slow dense liquid is indeed an essential ingredient of the destabilization of the liquid jet. The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) occurs when there is velocity shear in a single continuous fluid, or where there is a velocity difference across the surface between two fluids [24]. A necessary condition has been analyzed by A. Vujinovic through considering potential and kinetic energy [25]. Given an initial wavelike perturbation, mass conservation requires accelerated horizontal flow above the crests and below the troughs. They thought that mixing occurrence in the layer close to the interface with the height of ∆H. As heavier fluid (ρ2) with a velocity u2 on the bottom is raised and lighter fluid (ρ1) with velocity u1 at the top lowered so potential energy is increased. That movement is provided by a decrease in kinetic energy of the flow. The necessary condition for 14
mixing to occur is
g∆H(ρ2 ― ρ1) ρ(u1 ― u2)2
< 1, where ρ is the average density. Since ρ2 ≫ ρ1, u1 = U ≫ u2 and ∆H~(D ― d) in
these experiments, it is a condition always fulfilled. There is a more specific discussion of the characteristics of the instabilities below. The development of instabilities at the liquid surface here inside the tube is slightly different. The undulations transmit along the jet and grow in amplitude, and eventually degenerate in crown-forms of liquid impact instead of merely disperse droplets. The intact growth progress lasts around 5ms. Fig. 12 characterizes the progress of crown-forms of liquid impact. A tiny undulation first appears faintly at the root of a jet column and becomes observable. It moves upwards uniformly as the red line marked in the figure. The liquid crest is gathering velocity influenced by the co-flowing gas flow and instability waves. Once the amplitude of the undulations is high enough, aerodynamic drag comes into play and the crown-forms of liquid impact forms. After comparing the slopes of different color lines in Fig. 12, it seems that the impact accelerates the movement of waves. Meanwhile, the liquid is replenished from around and converges at the center of the tube. As a conclusion, both the velocities dispersion from crest to crest and the undulations transmitting along the downstream distance are two reasons that contribute to the destabilization of the liquid jet. Fig. 13 shows two forms of instabilities at the liquid surface.
Fig. 13. Two forms observed when a liquid jet flows in a faster coaxial gas flow, (a) at high suspension height, the liquid jet meanders in the gas stream, possibly forming bags (D=4.0mm, H=5.0mm, U=126.4m/s), (b) for lower suspension heights, the jet is peeled-off at its surface, disintegrating via a succession of surface instabilities (D=4.0mm, H=2.0mm, U=126.4m/s). Marmottant and Villermaux performed various experiments on the atomization of a liquid jet when a gas stream flows coaxially to its surface [26]. A configuration was designed to realize around liquid jet surrounded by a coaxial gas flow. The velocities of liquid flow and gas flow were adjustable. Their experimental findings suggest that a Kelvin-Helmholtz type instability triggers axisymmetric modulation on the liquid by shear between the slow liquid and the fast gas stream at first. When the gas velocity goes beyond a critical velocity, these axisymmetric waves undergo transverse azimuthal 15
modulations due to the Rayleigh-Taylor instability (instability of a surface between two fluids of different densities that occurs when the lighter fluid is pushing the heavier fluid). The undulations are no longer axisymmetric and display digitations. These digitations grow in amplitude and eventually degenerate in liquid ligaments which are further accelerated in the fast gas flow. Villermaux and Clanet have proposed that transient acceleration in the direction normal to the liquid at the rims triggers a Rayleigh-Taylor instability, which produces the azimuthal perturbation [27]. At azimuthal wave crests, liquid ligaments are produced, elongated by the gas stream, and finally broken into droplets. Comparing two forms observed when a liquid jet flows in a faster coaxial gas flow, it shows that at high suspension height, a liquid jet with smaller diameters wanders in the gas flow, inducing bags and rims. For lower suspension heights, the undulations transmitting along the downstream distance, and then the liquid jet is no longer deformed as a whole, but it is peeled at its surface forming ligaments. These ligaments are eventually broken into small liquid droplets. In addition, the diameters of developed undulations di before the crown-forms of liquid impact are given and discussed.
Fig. 14. Phase diagram of averaging diameter of developed undulations versus the suspension height, (a) di versus H for three tube inner diameters, (b) di/D versus D/H for the same data shown in (a). As we can see, the diameters of developed undulations decrease with larger suspension height. And for larger tube inner diameter, di is bigger. After normalization of three sets of data, it turns out that di/D increases linearly with D/H as scaled out in Fig. 14(b), di/D = (D/H)0.49.
4. Conclusions The deformation and development of tubular co-flowing gas-liquid jet in a vertical suspended suck tube with negative pressures are studied experimentally. We observe a complex process in a short time, including the interface deformation, the tubular co-flowing jet, and the destabilization of the liquid jet. In liquid hump regime, the surrounding air is sucked into the tube and forms a radially inward gas flow upon the interface. A relatively large amount of pressure gradients is imparted to a small mass of liquid near a free surface. Interface 16
deformation occurs and an axisymmetric liquid flow follows after. There is no clearly definitely transition exist between the hump and the spout. During the hump stage, the curved upper surface of liquid hump further deformed because of the force balance. In addition, surface deformation modifies the air suction flow in turn. In the spout stage, the liquid in the container enters into the tube in the form of a comparatively stable axisymmetric liquid jet surrounded by an upwards coaxial gas flow. Three parameters including tube inner diameter, suspension height and initial gas superficial velocity influence the tubular co-flowing jet a lot and critical gas superficial velocities at different cross-sectional areas are acquired. Tube inner diameter, suspension height, and initial gas superficial velocity are the three important parameters that influence the liquid jet. The pressure gradients induced by inwards gas suction flow in the axial direction violently reverse the initial interface curvature, while gravity and interfacial tension resist this deformation. Balancing the combined force is a necessary condition for the formation of a tubular co-flowing gas-liquid jet. Alternatively, a hump forms just above the liquid surface and fluctuates from the equilibrium position under the nozzle entrance merely. The typical onset of tubular co-flowing jet is described elaborately as well. The ratios of hump height to suspension height recorded as a function of τ appears associated with those three control parameters. Beneath the tube, the quasi-static liquid spout is upward thinner towards the direction of gas flow and the shear force influences the liquid column. Both experiment figures and statistical results confirm that the initial gas superficial velocity does not affect the diameter of the liquid column and the axisymmetric jet spout. Inside the tube, undulations transmit along the jet and grow in amplitude, and eventually degenerate in crown-forms of liquid impact instead of merely disperse droplets in some cases. The liquid jet instability is somewhat different at high suspension height and lower suspension height. The former, a liquid jet with smaller diameters wanders in the gas flow, inducing bags and rims. For lower suspension heights, the liquid jet is no longer deformed as a whole, but the crown-forms of liquid impact with each other and it is peeled at its surface forming ligaments. The liquid jet suffers a Kelvin-Helmholtz instability due to the velocity difference between the fast light fast gas flow and the slow dense liquid, and the liquid at the crests triggers a RayleighTaylor instability. Both the velocities dispersion from crest to crest and the undulations transmitting along the downstream distance are the reasons contribute to the destabilization of the liquid jet. The purpose of this paper is to show the tubular co-flowing gas-liquid jet in the tube during a suspended liquid suction process, which we believe exceeds others’ expectations. Therefore, in order to present the phenomenon clearly, we discuss this phenomenon, which commonly happens, in our daily life under different conditions. It is worth to pay attention to the normalized presentation of the results. The generation mechanism and critical parameters of this jet and the characteristics of the quasi-static liquid spout and the liquid column are sufficiently discussed. The former discussion may provide new 17
ideas for non-contact liquid sucking making use of a negative pressure directly but without complex structure to generate tornado flow. The latter may help to know more about the gas-liquid coaxial flow. Unfortunately, it is still difficult to express the deformation process and established relevant mathematic models accurately. We hope to study and discuss these problems through further more researches.
Acknowledgments The authors are grateful to supports of the National Natural Science Foundations of China (No. 51575476 and No. 51875506), the Science Funding for Creative Research Groups of the National Natural Science Foundation of China (No. 51521064) and the Fundamental Research Funds for the Central Universities (2016XZZX002-08). 51875506
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doi:10.1103/physrevlett.93.184502 [15] M. A. Herrada, A. M. Gañán-Calvo, A. Ojeda-Monge, et al., Liquid flow focused by a gas: jet, dripping, and recirculation, Phys. Rev. E 78.2(2008) 036323. doi:10.1103/PhysRevE.78.036323 [16] J. M. Gordillo, M. Perezsaborid, A.M. Ganancalvo, Linear stability of co-flowing liquid-gas jets, J. Fluid Mech. 448.448(2001) 23-51. doi:10.1017/S0022112001005729 [17] E. Lorenceau, D. Quere, J. Y. Ollitrault, et al., Gravitational oscillations of a liquid column in a pipe, Phys. Fluids 14.6(2002) 1985-1992. doi:10.1063/1.1476670 [18] R. Bergmann, E. De Jong, J.B. Choimet, et al., The origin of the tubular jet, J. Fluid Mech. 600.600(2008) 19-43. doi:10.1017/S0022112008000347 [19] A. Antkowiak, N. Bremond, S. Le Dizès, et al., Short-term dynamics of a density interface following an impact, J. Fluid Mech. 577.577(2007) 241-250. doi:10.1017/S0022112007005058 [20] J. M. BoultonStone, J. R. Blake, Gas bubbles bursting at a free surface, J. Fluid Mech. 254.9(1993) 437-466. doi:10.1017/S0022112093002216 [21] G. K. Batchelor, An introduction to fluid dynamics, Cambridge University Press, England, 2000. [22] J. R. Lister, Selective withdrawal from a viscous two-layer system, J. Fluid Mech. 198.198(2006) 231-254. doi:10.1017/S002211208900011X [23] B. Cushman-Roisin and J. M. Beckers, Introduction to geophysical fluid dynamics: physical and numerical aspects, Academic Press, 2009. [24] Kelvin–Helmholtz instability, Wikipedia, https://en.wikipedia.org/wiki/Kelvin-Helmholtz_instability. [25] A. Vujinovic, “Kelvin-Helmholtz Instability,” Univerza v Ljubljani Fakulteta za Matematiko in Fiziko, 2015. [26] P. H. Marmottant, E. Villermaux, On spray formation, J. Fluid Mech. 498.498(2004) 73-111. doi:10.1017/S0022112003006529 [27] E, Villermaux, C. Clanet, Life of a flapping liquid sheet. J. Fluid Mech. 462(2002) 341-363363. doi:10.1017/S0022112002008376
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A new gas-liquid interface jet was observed during a suspended liquid suck process. It was found that the jet is developed from a pressure-driven flow and then maintained by up-wards coaxial gas flow. It was pointed out that the gas superficial velocities almost do not influence the quasi-static axisymmetric jet spout below the nozzle. It was pointed out that the shear force produced by the gas-liquid interaction cause interface instabilities inside the tube.
20
S0894-1777(19)30586-2 https://doi.org/10.1016/j.expthermflusci.2019.109952 ETF 109952
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
12 April 2019 7 October 2019 12 October 2019
Please cite this article as: L. Hu, H. Xu, M. Li, W. Liu, W. Chen, H. Xie, X. Fu, Liquid Jet Formation during a Suspended liquid Suction Process, Experimental Thermal and Fluid Science (2019), doi: https://doi.org/10.1016/ j.expthermflusci.2019.109952
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© 2019 Published by Elsevier Inc.
Liquid Jet Formation during a Suspended liquid Suction Process Liang Hu, Hanghang Xu, Mingbo Li, Weiting Liu, Wenyu Chen, Haibo Xie and Xin Fu* The State Key Laboratory of Fluid Power & Mechatronic Systems, Zhejiang University, Hangzhou 310027, China.
Abstract: In the tubular co-flowing gas-liquid jet, liquid is sucked through a nozzle suspended above the flat gas-liquid interface. The liquid hump can be induced by the sudden pressure change just beneath the nozzle entrance. At a sufficiently fast initial gas superficial velocity, the interface undergoes a transition and liquid starts to be sucked. The suction flow is in the form of an axisymmetric liquid jet surrounded by an upwards coaxial gas flow. In the present study, we discuss the evolution and characteristics of the suspended liquid suction flow. The jet dynamics include the interface deformation and development (the hump stage), the tubular co-flowing jet (the spout state) and the destabilization of the liquid jet (the jet state). Tube inner diameter, suspension height, and initial gas superficial velocity are three important parameters that influence the suction flow. Due to the inward gas flow, a relatively large amount of pressure gradients is imparted to a small mass of liquid near a free surface, which leads to interface deformation. The lateral boundary of the liquid hump circumferentially shrinks and the top liquid gradually rises following the shrinkage. There is a comparatively stable axisymmetric liquid jet surrounded by an upwards coaxial gas flow inside the tube. Surprisingly, no evidence is shown the dependence of jet spout with initial gas axisymmetric superficial velocity below the nozzle through plenty of experiment figures and statistical analysis. On the other hand, the velocity difference between the fast light fast gas flow and the slow dense liquid is critical to the destabilization of the liquid jet.
Keywords: Non-contact liquid sucking; Two-phase coaxial jet; Forming conditions; Quasi-static liquid spout.
* Corresponding author. E-mail addresses: [email protected] (Xin Fu).
1. Introduction Many important and complex physical processes rely on morphological transitions of a fluid interface which changes easily in response to stress. In this paper, we will concentrate on both the mechanism that produces the particularly absorbing ‘a tubular co-flowing gas-liquid jet’ and its characteristics. The tubular co-flowing gas-liquid jet can be observed in a simple experiment. The upward liquid jet occurs because of a sudden pressure drop inside a vertical tube suspend above a container of liquid (see Fig. 1). In our laboratory, the gasliquid two-phase flow that happened in the immersion lithography machine is being studied. During the liquid collection, not only the recycled immersion liquid but also the air around it is also inhaled into the micro collection holes. So that, we generated interest in it during making a simplified experiment of immersion liquid recovery in immersion lithography. Similar deformation examples include the fluid entrainment by selective withdrawal, that fluid is withdrawn from a container holding stratified layers of immiscible fluids through a tube placed near their interface. It has widespread application in the in many industrial and physical processes of both large and small length scales, including but not limited water pollution control, coating of microparticles, steady microscopic liquid thread, fabrication of thin glass fibers, etc. [1-4] Experimental and numerical studies dealt with well-controlled two immiscible fluids systems [5]. A morphology change occurred when shear stresses cause the initially smooth interface to erupt into a spout between two immiscible fluids. Typically, stresses determine the fluid flows near the transition. Cohen and Nagel examined an analogous transition by using flow in an upper layer of shear oil to entrain water from a lower layer [6]. And their results were supplemented by extending to systems with different viscosity ratios [7]. The investigations of the influence of flow rate and the geometric setup (such as tube heights, tube diameters, and so on) were done with experiments and simulations as well [5][8]. In general, the flow behaviors may be classified into two regimes, selective withdrawal regime and shear entrainment regime. In the selective withdrawal regime, the interface forms a steady hump directly under the tube with a stagnation point at the hump tip and only the upper fluid is withdrawn through the tube. With increasing suction flow rate, the interface deformed more and eventually changes into the shear entrainment regime, and the lower fluid is withdrawn together in a thin spout form along with the upper fluid. There is another classification: subcritical regime, supercritical regime, and critical regime. The first two correspond to the selective withdrawal regime and the left belongs to the entrainment regime respectively [10]. And in between, the critical regime is the threshold for the uptake of the interface, but few with gas-liquid systems. Selective withdrawal not only refers to the suction flow in the neighborhood of a liquid-liquid interface but also the flow in the neighborhood of a gas-liquid interface. In a gas-liquid system, whether the suction tube sits in the gas or the liquid strongly influences the appearance of the shear entrainment regime. If the tube is in the liquid, the air-liquid surface of a container draining form a hole in the bottom. The free surface always attains a smooth steady-state morphology. A
sharp tip is formed when a shear fluid is withdrawn from the neighborhood interfacing with ambient air. No gas can be drawn into the tube no matter what the flow rate, except when the tip is inside the orifice [11-12]. On the other hand, if the tube is in the gas, a liquid jet can be formed similar to the liquid-liquid system. It was widely applied to the field of material synthesis for creating uniform microparticles, especially on the generation of droplets in microfluidic networks [13]. A continuous gas flow to produce uniform liquid sprays was first proposed and demonstrated by placing a capillary tube behind a round orifice plate [3]. Inspired by this method, scholars recently performed an analysis of a liquid jet and coflowing gas stream surrounding the jet into an open environment [14-16]. Basically, this flow is characterized by the formation of a steady microscopic liquid jet in the core of a highly accelerating (extensional) laminar gas stream and the steady thin liquid jet emitted from the cusp-like drop. And by controlling the pressure of the focused and shear flows, the size distribution of the microdroplets becomes uniform. The pressure-driven jetting phenomena that are also closely related to the annular tubular jet created by focusing momentum into a small mass of liquid so as to make it jetting. An example is a tubular flow first reported by Lorenceau et al. [17]. Jet could be observed to emerge from the central surface of the rising liquid column while a sudden release of the pressure in the tube. The driving and focusing mechanisms for this jet were presented by R. Bergmann et al. through highspeed imaging, particle image velocimetry, and numerical simulations [18]. The tubular jet was found to be created by the convergence of the flow as it entered the tube. A second example was a tube filled with a perfectly wetting liquid falling axially under its own weight [19]. In its gravity-free reference frame, the liquid interface was deformed by surface tension into a hemispherical shape. While the falling tube impacted on a rigid floor, a sudden change of tube velocity induced a pressure gradient, which in turn led to a sudden change of liquid velocity inside the tube. As a result, the interface curvature reversed violently and finally formed a concentrated jet. A third example is the high-speed liquid jet generated when a small air bubble bursts from an equilibrium position at an air-water interface. In this case, the surface tension stresses focused on the base of an unstable cavity at the surface, just like jetting in a glass of champagne in our daily life [20]. There are many other similar phenomena, not limited to the above. The tubular co-flowing gas-liquid jet is a little different from the flow examples discussed above. The liquid entering into the tube is confined by the gas flow, and the tube wall obstructs the gas flow partly. Generally, its main characters are the formation of a liquid spout in the core of an axisymmetric high-speed gas flow, which is an unsteady gas-liquid jet. In this paper, we focus on the characterization of the morphological transitions of this special gas-liquid jet inside the tube and discussion on the nature of the morphology change. A rich set of two-phase flow regimes are observed in a millisecond. A liquid hump is induced by the sudden pressure change as soon as the air in the tube is sucked. Following some complex 3
motions, the hump gradually deformed into an axisymmetric spout and a liquid jet can be seen to emerge from the central liquid surface just beneath the nozzle. Besides, because of the coaxial gas flow disturbing, it is also observed surface instability and intricate drop breakup inside the tube. This paper reports our experimental study of the tubular co-flowing gas-liquid jet produced by the suspended liquid suction due to a negative pressure. Once the liquid is suction converging, it is replenished from around. This paper is organized as follows, the experimental methods and the designed apparatus are introduced firstly. And then, the suction process is identified to three different stages. In addition, the experimental data on the occurrence of observed flow stages under different parameters are discussed. Through the analysis of the above experiment results, the criterion of tubular coflowing gas-liquid jet formation is found directly determined by the initial gas superficial velocity. Thus, the correspondence relationship between them is summarized. Finally, the characteristics of the onset of tubular co-flowing jet and the jet column are both discussed.
2. Experimental apparatus and methods
Fig. 1. Schematic of experimental apparatus A schematic drawing of the suspended liquid suction and a diagram of the experimental apparatus are shown respectively in Fig. 1. A transparent Perspex container (dimensions 100mm×100mm×150mm) is filled to a depth of H’ with purified water. And a vertical, cylindrical tube with inner diameter D is held at a distance H’+H from the container bottom. The depth of the water H’ is measured by taking the known tube diameter as a reference in the observation window of a high-speed camera. The container walls and the water are sufficiently distant and thick so as not to affect the suction flow. Considering the error of observation in the observation window, it is more reasonable to consider observation accuracy as 0.1mm. The values of related experimental parameters, nozzle diameter D, suspension height H, and differential pressure ∆P, 4
are listed in Table I. The nozzle diameter D is variable by changing different tubes. In experiments, the suspension height H vertically from the nozzle to the flat liquid surface is adjusted by a lifting platform with a maximum scale of 20 mm and an accuracy of 0.1 mm. In the suspended liquid suction process, the suspension height H remains essentially constant at the hump state and increases very slowly at the subsequent flow states. In reduce the influence of height change in drawing some qualitative conclusions, we pay attention to the co-flowing gas-liquid jet before the obvious surface decline. The characteristics of suspended suction flow discussed in this paper are the premise with the suspension height H without considering its subtle variability. Table Ⅰ. Experiment parameters Inner diameter, D (mm)
Suspension height, H (mm)
Differential pressure, ∆𝐏 (mbar)
4.0
2.0
200
5.0
3.0
300
6.0
4.0
400
Experiments are carried out at the temperature of 25 ± 1 ◦C and the environment pressure of 101.3 kPa. Gas-liquid mixtures are sucked through a tube using a vacuum pump (Vacuubrand MD 12 NT VARIO) with a variable speed motor. The downstream side of the tube is connected with a control valve (VHK2-08F-06F, the distance between the valve and the tube L=500.0mm and the cross-sectional area S1 = 9 × 10 ―6m2). The control valve is a mechanical valve that only permits two-phase flow in one direction. The valve is closed in advance in order to let system pressure gradually decrease to a preset pressure. It is hypothesized that a steady-state gas flow will be formed immediately as long as the valve opened even at the initial opening. The initial gas superficial velocity U is thus acquired corresponding to the instant of opening the valve. According to Bernoulli's principle, the relation between differential pressure ∆P and gas velocity U1 in the valve entrance satisfies the equation as follows: ∆P ― Ploss ρg
U21
(1)
= 2g
In the direction of flow, due to friction caused by the viscosity of the fluid, we have Ploss the drag losses. It consists of line losses and local losses. The cross-sectional areas of the tube and valve are of the same order of magnitude, the local losses are considered to raise by the sudden expansion of the valve to the tube. So that the drag losses satisfy: Ploss ρg
L U2
U2
(2)
= λD2g + KL2g S 2
in which U is the gas velocities in the tube, ρ = 1.205 kg/m3 is the gas density and KL = (1 ― S1) 5
is the entrance loss
coefficient for the sudden expansion of the cross-sectional area. Since the relative roughness of the tube is small, λ is calculated by the Blasius function λ = 0.3164Re ―1/4. Reynolds number Re = Ud/ν and ν = 1.83 × 10 ―5 Pa ∙ s is the kinetic viscosity of air. The relationship of U1 and U is S1U1 = SU, in which S =
πD2 4
the cross-sectional area of the tube.
Before the mixtures reached the pump, the liquid will be separated in an airtight separation tank, which also serves as a pressure stabilizer. Outside the tank, a high-speed camera (Phantom 120S) was set up approximately level with the bottom of the tube, perpendicular to the glass sidewall of the container. The time-evolution of the complex shape of the free surface and the flow around the cylindrical tube were recorded by the camera with a rate of 1000 frames/s and an exposure time of 60 microseconds. Backlighting of the tube was achieved by a lamp placed at the opposite side of the tank to obtain typical images like those of Fig. 2. All of the recorded images were saved in digital shadowgraph format, which can be easily processed and analyzed in MATlab.
3. Results and discussion 3.1 Overview of the jet dynamics During the suspended suck process, complex interactions between the gas and liquid phases as well as the tube wall occur in a millisecond. Different images of interface profiles of the intact suspended liquid suction process are presented in Fig. 2(a). The main jet dynamics include the interface deformation (the hump state), the tubular co-flowing jet (the spout state) and the destabilization of the liquid jet (the jet state).
Fig. 2. (a) Evolution of the free surface during a typical suspended suck, including the liquid hump in t=0,13ms, the jet 6
spout in t=14,15ms and the jet in t=35ms (D=4.0mm, H=3.0mm, U=95.9m/s), (b) the changing surface profiles of liquid hump just beneath the tube with time, (c) the height trend of the liquid hump for the same data shown in (b), (d) schematically shows the parts of the changing surface profiles of jet spout interface at the jet state at different times. As soon as the surrounding air is sucked into the tube and a radially inward gas flow upon the interface will be formed. In the meanwhile, the pressure inside the tube drops instantaneously. Subsequently, the liquid under the nozzle entrance converges inwards radially and extends axially. As we can see, the surface deformation changes slowly at first and gradually accelerates. The curved upper surface of liquid hump becomes asymptotically flat is a relatively special phenomenon as shown in the middle picture in Fig. 2(a). The changing surface profiles of liquid hump just beneath the tube with time is shown in Fig. 2(b). The interface curvature is constantly changing as time goes on. Interface deformation modifies the air suction flow and results in a relative high-pressure area in the middle of the tube nozzle. The mean curvature is proportional 2γ
to the additional pressure difference across a fluid surface, as seen in the equation rH = ∆P, where the mean curvature 1
κ = rH. This explains why the interface curvature of the liquid hump becomes smaller. The changing profiles are pulled in the axial direction and can be closely approximated by a parabolic segment. The height of the liquid hump indicated by a red line segment in Fig. 2(a) can be utilized to evaluate the instantaneous hump size. The height trend of the liquid hump for the same data shown in (b) is shown in Fig. 2(c). The liquid extends axially and diameter decreases with increasing hump height. A jet spout starts to emerge from the center of the rising liquid hump. During the suction process, the radial component of the shear force continually squeezed the liquid hump, benefitting its inwards radial convergence and axial stretch. The upwards coaxial gas flow squeezed the smaller mass of liquid more easily. It is an interactive process. Liquid in the container entered the tube through the nozzle forming a comparatively stable axisymmetric liquid jet surrounded by an upwards coaxial gas flow. The fifth picture in Fig. 2(a) shows that the liquid jet suffers a Kelvin–Helmholtz instability and even forming corrugations ligaments along the downstream. Once the liquid is sucked converging, it is replenished from around. The suspension height naturally increases after a while. The parts of the changing surface profiles of jet spout interface at the jet state at different times are shown in Fig. 2(d). The surface profiles of jet spout interface becomes thinner significantly from t=15ms to 890ms, while it changes not obviously from t=890ms to 1490ms. Besides, in the gas suction flow, the ligaments are stretched and their diameters decrease until they break into drops. The disordered liquid collides with the tube wall, eventually entering the separation tank.
3.2 Forming conditions 7
While many of the parameters mentioned influencing the flows, our understanding can be conveyed by focusing on tube inner diameter, suspension height, and initial gas superficial velocity. The onset characteristics of tubular co-flowing jet influenced by those parameters mentioned above are discussed in detail in this section. This phenomenon is best described as a pressure-driven geometrical flow focusing. The sudden change of the motion of the boundaries generates large pressure gradients which in turn produce a sudden change in the velocity at every point of the liquid [21]. In selective withdrawal, researchers put forward a simplicity assumption which the axisymmetric withdrawal would form a point sink located within the upper of two semi-infinite layers of viscous fluid [5][22]. CFD simulation is shown that the air pressure just above the liquid surface under the nozzle entrance decreases in the flow direction. Interface deformation occurs when a relatively large amount of pressure gradients is imparted to a small mass of liquid near a free surface.
Fig. 3. Comparison of different hump deformations (a: D=6.0mm, H=4.0mm, U=49.7m/s; b: D=6.0mm, H=4.0mm, U=63.2m/s). Fig. 3 compares hump deformations with different initial gas superficial velocities. Solid lines indicate the initial flat liquid surface and dotted lines indicate the deformed liquid surface. Pressure gradients exerted by the inward gas flow are strongly influenced by the flow domain beneath the tube. The pressure gradients reverse the initial liquid surface in the axial direction violently, while both liquid gravity and surface tension resist the deformation. Balancing the combined force is a necessary condition for the formation of tubular co-flowing gas-liquid jet. Fig. 3(a1)-(a3) illustrates that the slower initial gas superficial velocity brings difficult in liquid suction flow. The liquid surface fluctuates up and down slightly and h/H is about less than 1/5 under these conditions. Fig. 3(b1)-(b3) illustrates that the faster initial gas superficial velocity intensifies the interface deformation. As a conclusion, when the initial gas superficial velocity is slow, a hump forms just above the liquid surface under the nozzle entrance merely. When the initial gas superficial velocity of inward gas flow exceeds a threshold value Uc, the hump translates into a spout.
8
Fig. 4. Phase diagram of critical initial gas superficial velocity versus suspension height, (a) d versus H for three tube inner diameters, (b) Uc versus D/H for the same data shown in (a). The critical initial gas superficial velocity versus suspension height for different values of tube inner diameter is shown in Fig. 4(a). The relationship between Uc and H is got by polynomial fit. The higher the suspension height is, the higher the Uc the flow needs. A higher height will create more pressure reduction that should be compensated by increasing the gas velocity. In Fig. 4(b), a curve is drawn with D/H as abscissa and critical initial gas superficial velocity as ordinate. It shows that Uc and D/H scale as an exponential relationship, Uc = 214.8e ―1.385D/H +25.63e ―0.1099D/H. And we defined a dimensionless flow rate Ca = πνρU/4γ [9]. Ca is plotted on the right side of Fig.4.
Fig. 5. A typical onset of the tubular co-flowing jet (D=4.0mm, H=4.0mm, U=86.9m/s). As mentioned above, the lateral boundary of the liquid hump will circumferentially shrink and the top liquid will gradually rise following the shrinkage. A liquid jet spout gradually stabilizes. Fig. 5 shows the deformations of hump and spout before the onset of the tubular co-flowing jet. The curved liquid hump becomes asymptotically flat, an omen of the liquid jet. The surface shape modifies the direction of gas flow in turn. Pressure near the nozzle changes once the liquid approaches the nozzle due to the ratio of gas and liquid. The stresses are continually induced by gas flow and liquid surface tension. Assuming that the gravity of this small part liquid and the surface shear force keeps constant in this short time, the differential pressure induced by gas flow in axial direction gradually decreases. It has influence over interfacial interaction, which is perpendicular to the surface. So that, the boundary of liquid profiles below the tube nozzle shows an arc-shaped gas-liquid surface. Because of the influence of a continuity gas flow, a gas stagnation area appears at the center of the liquid 9
level. A flat liquid surface becomes visible when the height of liquid hump is around 0.6H. It is a result of the local stress balance between the pressure difference and the stress arising from the interfacial curvature. There is no clearly definitely transition between the hump and the spout. When the liquid gradually approaches the nozzle, the passage of gas flow suddenly contracts and the gas flow velocity increases sharply. Interfacial interaction suddenly decreases, and the diameter of the liquid spout becomes a little larger but then thinner immediately. In the axial direction, the pressure on the upper portion of the liquid suddenly decreases, which causes the liquid jet emergence and growing upward.
Fig. 6. The changing heights of liquid hump under various jet parameters ((a): different suspension height H with the initial gas superficial velocity U=75.2m/s, the inner diameter D= 5.0mm, (b): different initial gas superficial velocity U with the suspension height H = 3.0mm, the inner diameter D= 5.0mm and (c): different inner diameter D with the suspension height H = 3.0mm, the initial gas superficial velocity U=75.2m/s.) Shortly after the valve opens, the circular hump forms and develops refer to Fig. 2(b). Changes of the hump height under various jet parameters are compared. Considering that the change of the initial liquid level is less obvious, the focus is on the moment before the liquid enters the tube, that is, the moment when the jet appears. Therefore, the moment 0 is set when the liquid column reaches the nozzle, and the height of the liquid hump tip before this moment is recorded. The ratios of hump height h to suspension height H recorded as a function of τ are plotted in Fig. 6(a)-(c), τ =
t ρLH3/σ
is the capillary
time. Here ρL and σ are the density and surface tension coefficient of liquid, respectively. Through these certain number of data points, the changing trend of liquid surface can be determined. As we can see, the deformation of the free surface is gradually accelerating. Fig. 6(a) compares the deformation at different H. Comparing the slopes of trends at τ = 0, it shows that the liquid surface rises faster at H=3.0mm ,4.0mm than H=2.0mm near the nozzle. Moreover, increasing the height retard movement of liquid inward convergence. Larger suspension height adds a larger duration of the hump stage. Similarly, comparing changing trends at different initial gas superficial velocity U from 60.9m/s to 87.3m/s in Fig. 6(b), we find out that a faster initial gas superficial velocity can produce the same effect law as the smaller height. Besides, we also changed the tube 10
inner diameter from 4.0mm, 5.0mm to 6.0mm as shown in Fig. 6(c). A smaller the inner diameter links to a faster deformation of hump. So, in order to make the liquid suction flow more easily, we should fix a tube with a smaller inner diameter at a smaller suspension height and adjust the negative pressure as large as possible.
3.3 Characteristics of quasi-static liquid spout and liquid column
Fig. 7. Images of a tubular co-flowing gas-liquid jet under various jet parameters (different initial gas superficial velocity U with the suspension height H=3.0mm, the inner diameter D=4.0mm in the first column, different suspension height H with the initial gas superficial velocity U=75.2m/s, the inner diameter D=5.0mm in the second column and different inner diameter D with the suspension height H=4.0mm, the initial gas superficial velocity U=77.0m/s in the third column). At the spout state, the sucked liquid is in the form of a liquid column inside the tube continuously. The liquid column diameters of tubular co-flowing gas-liquid jet under various jet parameters are given in Fig. 7 and its change rules are discussed. The measuring position of the liquid column diameter is chosen slightly higher than the nozzle entrance. Referring to the lengths of white line segments shown in Fig. 7(a1)-(a3), it is obvious that the diameter of the jet liquid column is almost constant despite increasing the initial gas superficial velocity U but fixing the suspension height H=3.0mm, the inner diameter D=4.0mm. Besides, when fixing the initial gas superficial velocity U=75.2m/s, the inner diameter D=5.0 mm but increasing the suspension height H, the diameter is becoming smaller as shown in Fig. 7(b1)-(b3). Observed From Fig. 7 (c1)-(c3), as the inner diameter D rising from 4.0mm to 6.0mm with the suspension height H=4.0mm, the initial gas superficial velocity U=77.0m/s, it is found the liquid column diameter enlarged. And after counting, arranging and averaging the diameter of the liquid column under different jet parameters, three more figures with U as the abscissa are given in Fig. 8. 11
Fig. 8. Experimental results of the diameter of jet liquid column d as a function of initial gas superficial velocity U at different suspension height (the tube diameters from left to right are 4.0mm, 5.0mm, 6.0mm). For each set of data, d has little change with U increasing. It shows that different initial gas superficial velocities do not affect the diameter of the jet liquid column, essentially in agreement with Fig. 7(a1)-(a3). At a certain suspension height, a thicker liquid column links with a larger tube diameter, and vice versa. For the 4.0mm inner diameter as shown in Fig. 8 (a), the diameter of the liquid column increase from 1.3mm to 2.1mm when the suspension height increase from 2.0mm to 4.0mm. Moreover, comparing circular data dots in Fig. 8 (a)-(c) in which the suspension height is 3.0mm, it shows that the diameter increases from 1.58mm to 3.50mm at increasing tube diameter. That is to say, the diameter of the jet liquid column becomes larger as increasing the tube inner diameter or reducing the suspension height. The above phenomena can be explained from the aspect of energetic equilibrium. A smaller suspension height or a larger inner diameter costs less jetting energy. More liquids can be sucked and generate into a thicker liquid column. Through averaging the different diameters of the liquid column without considering different gas superficial velocities, Fig. 8 merges into Fig. 9(a). It can better represent the effect of suspension height and inner diameter on the diameter of the liquid column.
Fig. 9. Phase diagram of average diameter of jet liquid column versus the suspension height, (a) d versus H for three tube inner diameters, (b) d/(D-d) versus D/H for the same data shown in (a). It shows that the diameter of the liquid column decreases linearly with the increase of the suspension height. The proportion of gas is larger. After normalization of three sets of data, it turns out that d/(D-d) increases linearly with D/H as scaled out in Fig. 9(b), d/(D-d) = (D/H)0.93. 12
Fig. 10. The change of profiles of axisymmetric jet spout beneath the nozzle (D=4.0mm and H=4.0mm). The effect of the initial gas superficial velocity on the axisymmetric jet spout is also considered. A typical example profile of this phenomenon is drawn in Fig. 10. In this figure, ds/D represents the ratio of spout diameter to the diameter of the recovery tube and h(ds)/H represents the ratio of the liquid spout height to the suspension height. The radius of the surface profiles is changing on the different sections of the liquid spout. The quasi-static liquid spout becomes thin in the direction of gas flow. In addition, data points of different shapes indicate the positional relationship of the gas-liquid boundary distance axis at different gas superficial velocities. It seems that the close-up of the spout shape with a center of symmetry is constant despite the growing gas superficial velocities. Under both the same inner diameter and suspension height, different gas superficial velocities almost do not influence axisymmetric jet spout. The quasi-static liquid spout is the result of the equilibrium relationship in the mechanics of axisymmetric jet spout below the nozzle. The axisymmetric tubular co-flowing gas-liquid jet starts from a pressure excitation point located beneath the nozzle. Ignoring inertial force, the forces acting on the cross-section of liquid spout include four parts: the first part is the pressure force produced by meniscus and pump suck, the second part is the shear force generated by gas flow, the third part is the surface tension and the fourth part is the gravity force applied by upper liquid. The balance of these forces makes meniscus stable at different gas superficial velocities. Radial forces cancel each other out. While in the axial direction, an accurate formula for related force can hardly be determined for the lack of some physical quantity. We only scratch the surface of this problem here.
Fig. 11. Phase diagram of different diameters of the quasi-static liquid spout (ds). 13
As D and H varied, the profiles of axisymmetric jet spout change and their diameters are recorded in Fig. 11. The horizontal ordinate h(ds)/H changes from 0 to 1.0 means that the surface is gradually away from the nozzle entrance. For the same inner diameter, the larger suspension height is the faster diameter changes before the diameter of spout ds reaches tube diameter D. However, if ds is larger than D, the case is on the contrary. The turning point of h(ds)/H is a fixed value for an inner diameter. For D=4.0mm, h(ds)/H=0.5; for D=5.0mm, h(ds)/H=0.38; and for D=6.0mm, h(ds)/H=0.3. It is related to the distribution of pressure below the nozzle. Around the tube nozzle, complex interactions appear between the gas and liquid phases as well as the tube wall. The diameter of the liquid spout at the nozzle position influences the pressure distribution. The bigger ratio of liquid around the nozzle hinders the gas flow, which results in a larger pressure gradient near the interface. So that the turning point seems lower as D increases.
Fig. 12. The intact growth progress of destabilization of the liquid jet. Note the duration of the experiment and the length scale. (D=5.0mm, H=3.0mm, U=75.2m/s). At the root of the liquid column, the fast coaxial gas flow induces a destabilization of the jet as shown in Fig. 12. A
wavelike
destabilization
The
velocity
difference between the fast light fast gas flow and the slow dense liquid is indeed an essential ingredient of the destabilization of the liquid jet. The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) occurs when there is velocity shear in a single continuous fluid, or where there is a velocity difference across the surface between two fluids [24]. A necessary condition has been analyzed by A. Vujinovic through considering potential and kinetic energy [25]. Given an initial wavelike perturbation, mass conservation requires accelerated horizontal flow above the crests and below the troughs. They thought that mixing occurrence in the layer close to the interface with the height of ∆H. As heavier fluid (ρ2) with a velocity u2 on the bottom is raised and lighter fluid (ρ1) with velocity u1 at the top lowered so potential energy is increased. That movement is provided by a decrease in kinetic energy of the flow. The necessary condition for 14
mixing to occur is
g∆H(ρ2 ― ρ1) ρ(u1 ― u2)2
< 1, where ρ is the average density. Since ρ2 ≫ ρ1, u1 = U ≫ u2 and ∆H~(D ― d) in
these experiments, it is a condition always fulfilled. There is a more specific discussion of the characteristics of the instabilities below. The development of instabilities at the liquid surface here inside the tube is slightly different. The undulations transmit along the jet and grow in amplitude, and eventually degenerate in crown-forms of liquid impact instead of merely disperse droplets. The intact growth progress lasts around 5ms. Fig. 12 characterizes the progress of crown-forms of liquid impact. A tiny undulation first appears faintly at the root of a jet column and becomes observable. It moves upwards uniformly as the red line marked in the figure. The liquid crest is gathering velocity influenced by the co-flowing gas flow and instability waves. Once the amplitude of the undulations is high enough, aerodynamic drag comes into play and the crown-forms of liquid impact forms. After comparing the slopes of different color lines in Fig. 12, it seems that the impact accelerates the movement of waves. Meanwhile, the liquid is replenished from around and converges at the center of the tube. As a conclusion, both the velocities dispersion from crest to crest and the undulations transmitting along the downstream distance are two reasons that contribute to the destabilization of the liquid jet. Fig. 13 shows two forms of instabilities at the liquid surface.
Fig. 13. Two forms observed when a liquid jet flows in a faster coaxial gas flow, (a) at high suspension height, the liquid jet meanders in the gas stream, possibly forming bags (D=4.0mm, H=5.0mm, U=126.4m/s), (b) for lower suspension heights, the jet is peeled-off at its surface, disintegrating via a succession of surface instabilities (D=4.0mm, H=2.0mm, U=126.4m/s). Marmottant and Villermaux performed various experiments on the atomization of a liquid jet when a gas stream flows coaxially to its surface [26]. A configuration was designed to realize around liquid jet surrounded by a coaxial gas flow. The velocities of liquid flow and gas flow were adjustable. Their experimental findings suggest that a Kelvin-Helmholtz type instability triggers axisymmetric modulation on the liquid by shear between the slow liquid and the fast gas stream at first. When the gas velocity goes beyond a critical velocity, these axisymmetric waves undergo transverse azimuthal 15
modulations due to the Rayleigh-Taylor instability (instability of a surface between two fluids of different densities that occurs when the lighter fluid is pushing the heavier fluid). The undulations are no longer axisymmetric and display digitations. These digitations grow in amplitude and eventually degenerate in liquid ligaments which are further accelerated in the fast gas flow. Villermaux and Clanet have proposed that transient acceleration in the direction normal to the liquid at the rims triggers a Rayleigh-Taylor instability, which produces the azimuthal perturbation [27]. At azimuthal wave crests, liquid ligaments are produced, elongated by the gas stream, and finally broken into droplets. Comparing two forms observed when a liquid jet flows in a faster coaxial gas flow, it shows that at high suspension height, a liquid jet with smaller diameters wanders in the gas flow, inducing bags and rims. For lower suspension heights, the undulations transmitting along the downstream distance, and then the liquid jet is no longer deformed as a whole, but it is peeled at its surface forming ligaments. These ligaments are eventually broken into small liquid droplets. In addition, the diameters of developed undulations di before the crown-forms of liquid impact are given and discussed.
Fig. 14. Phase diagram of averaging diameter of developed undulations versus the suspension height, (a) di versus H for three tube inner diameters, (b) di/D versus D/H for the same data shown in (a). As we can see, the diameters of developed undulations decrease with larger suspension height. And for larger tube inner diameter, di is bigger. After normalization of three sets of data, it turns out that di/D increases linearly with D/H as scaled out in Fig. 14(b), di/D = (D/H)0.49.
4. Conclusions The deformation and development of tubular co-flowing gas-liquid jet in a vertical suspended suck tube with negative pressures are studied experimentally. We observe a complex process in a short time, including the interface deformation, the tubular co-flowing jet, and the destabilization of the liquid jet. In liquid hump regime, the surrounding air is sucked into the tube and forms a radially inward gas flow upon the interface. A relatively large amount of pressure gradients is imparted to a small mass of liquid near a free surface. Interface 16
deformation occurs and an axisymmetric liquid flow follows after. There is no clearly definitely transition exist between the hump and the spout. During the hump stage, the curved upper surface of liquid hump further deformed because of the force balance. In addition, surface deformation modifies the air suction flow in turn. In the spout stage, the liquid in the container enters into the tube in the form of a comparatively stable axisymmetric liquid jet surrounded by an upwards coaxial gas flow. Three parameters including tube inner diameter, suspension height and initial gas superficial velocity influence the tubular co-flowing jet a lot and critical gas superficial velocities at different cross-sectional areas are acquired. Tube inner diameter, suspension height, and initial gas superficial velocity are the three important parameters that influence the liquid jet. The pressure gradients induced by inwards gas suction flow in the axial direction violently reverse the initial interface curvature, while gravity and interfacial tension resist this deformation. Balancing the combined force is a necessary condition for the formation of a tubular co-flowing gas-liquid jet. Alternatively, a hump forms just above the liquid surface and fluctuates from the equilibrium position under the nozzle entrance merely. The typical onset of tubular co-flowing jet is described elaborately as well. The ratios of hump height to suspension height recorded as a function of τ appears associated with those three control parameters. Beneath the tube, the quasi-static liquid spout is upward thinner towards the direction of gas flow and the shear force influences the liquid column. Both experiment figures and statistical results confirm that the initial gas superficial velocity does not affect the diameter of the liquid column and the axisymmetric jet spout. Inside the tube, undulations transmit along the jet and grow in amplitude, and eventually degenerate in crown-forms of liquid impact instead of merely disperse droplets in some cases. The liquid jet instability is somewhat different at high suspension height and lower suspension height. The former, a liquid jet with smaller diameters wanders in the gas flow, inducing bags and rims. For lower suspension heights, the liquid jet is no longer deformed as a whole, but the crown-forms of liquid impact with each other and it is peeled at its surface forming ligaments. The liquid jet suffers a Kelvin-Helmholtz instability due to the velocity difference between the fast light fast gas flow and the slow dense liquid, and the liquid at the crests triggers a RayleighTaylor instability. Both the velocities dispersion from crest to crest and the undulations transmitting along the downstream distance are the reasons contribute to the destabilization of the liquid jet. The purpose of this paper is to show the tubular co-flowing gas-liquid jet in the tube during a suspended liquid suction process, which we believe exceeds others’ expectations. Therefore, in order to present the phenomenon clearly, we discuss this phenomenon, which commonly happens, in our daily life under different conditions. It is worth to pay attention to the normalized presentation of the results. The generation mechanism and critical parameters of this jet and the characteristics of the quasi-static liquid spout and the liquid column are sufficiently discussed. The former discussion may provide new 17
ideas for non-contact liquid sucking making use of a negative pressure directly but without complex structure to generate tornado flow. The latter may help to know more about the gas-liquid coaxial flow. Unfortunately, it is still difficult to express the deformation process and established relevant mathematic models accurately. We hope to study and discuss these problems through further more researches.
Acknowledgments The authors are grateful to supports of the National Natural Science Foundations of China (No. 51575476 and No. 51875506), the Science Funding for Creative Research Groups of the National Natural Science Foundation of China (No. 51521064) and the Fundamental Research Funds for the Central Universities (2016XZZX002-08). 51875506
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A new gas-liquid interface jet was observed during a suspended liquid suck process. It was found that the jet is developed from a pressure-driven flow and then maintained by up-wards coaxial gas flow. It was pointed out that the gas superficial velocities almost do not influence the quasi-static axisymmetric jet spout below the nozzle. It was pointed out that the shear force produced by the gas-liquid interaction cause interface instabilities inside the tube.
20