Experimental investigation of biofuel drop impact on stainless steel surface

Experimental Thermal and Fluid Science 54 (2014) 38–46

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Experimental investigation of biofuel drop impact on stainless steel surface S. Sen, V. Vaikuntanathan, D. Sivakumar ⇑ Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560 012, India

a r t i c l e

i n f o

Article history: Received 28 October 2013 Received in revised form 24 January 2014 Accepted 24 January 2014 Available online 3 February 2014 Keywords: Biofuel Camelina Drop impact Spreading

a b s t r a c t Blends of conventional fuels such as Jet-A1 (aviation kerosene) and diesel with bio-derived components, referred to as biofuels, are gradually replacing the conventional fuels in aircraft and automobile engines. There is a lack of understanding on the interaction of spray drops of such biofuels with solid surfaces. The present study is an experimental investigation on the impact of biofuel drops onto a smooth stainless steel surface. The biofuel is a mixture of 90% commercially available camelina-derived biofuel and 10% aromatics. Biofuel drops were generated using a syringe–hypodermic needle arrangement. On demand, the needle delivers an almost spherical drop with drop diameter in the range 2.05–2.15 mm. Static wetting experiments show that the biofuel drop completely wets the stainless steel surface and exhibits an equilibrium contact angle of 5.6°. High speed video camera was used to capture the impact dynamics of biofuel drops with Weber number ranging from 20 to 570. The spreading dynamics and maximum spreading diameter of impacting biofuel drops on the target surface were analyzed. For the impact of high Weber number biofuel drops, the spreading law suggests b  s0.5 where b is the spread factor and s, the nondimensionalized time. The experimentally observed trend of maximum spread factor, bmax of camelina biofuel drop on the target surface with We compares well with the theoretically predicted trend from Ukiwe–Kwok model. After reaching bmax, the impacting biofuel drop undergoes a prolonged sluggish spreading due to the high wetting nature of the camelina biofuel-stainless steel system. As a result, the final spread factor is found to be a little more than bmax. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Understanding the mechanisms of fuel spray–wall interaction process is of importance in the design of engine combustors. Often the interaction process results in an increase in unburned hydrocarbons, secondary atomization, wall-film formation, etc. Several single-drop impact studies have been devoted to understand the problem of spray–wall interaction [1–3]. Although any direct use of results arrived at from single-drop impact studies to spray impingement problems poses limitations [4], the studies of single-drop impact still provide valuable tools to the modeling of spray impingement phenomenon [5]. In addition to fuel spray impingement encountered in engine combustors, the single-drop impact on a solid surface has been studied in the context of numerous practical applications such as ink-jet printing [6], droplet-based manufacturing [7,8], and thermal spray coating [9]. On a solid surface, the dynamics of drop impact is primarily governed by the competition between liquid ⇑ Corresponding author. Tel.: +91 80 2293 3022. E-mail address: [email protected] (D. Sivakumar). http://dx.doi.org/10.1016/j.expthermflusci.2014.01.014 0894-1777/Ó 2014 Elsevier Inc. All rights reserved.

inertia (resulting from the droplet kinetic energy), surface (resulting from the fluid interfaces), and viscous (resulting from the dropsurface interaction) forces. An impacting liquid drop spreads on the surface axisymmetrically during the initial stages of drop impact process. This regime of drop spreading is dominated by the drop inertia. The drop reaches a maximum diameter at the end of inertia dominated spreading and then starts to recede. Often, depending on the characteristics of the solid surface and liquid properties, the drop liquid undergoes a series of post-spreading oscillations and reaches an equilibrium final drop diameter on the surface. Previous studies characterized the drop impact phenomenon in terms of Weber number, We, which compares the inertia to the capillary forces, Ohnesorge number, Oh, which compares the viscous to the capillary forces, and Reynolds number, Re, which compares the inertia to the viscous forces [3,10]. Rioboo et al. [11,12] studied the temporal evolution of drop impact phenomenon by altering several control parameters such as drop impact velocity, drop diameter, liquid viscosity, surface tension, surface wettability and mean surface roughness. The effect of control parameters on the phenomenon is seen mainly in the spreading and receding processes as well as the final outcome of

S. Sen et al. / Experimental Thermal and Fluid Science 54 (2014) 38–46

39

Nomenclature Re Oh We Es,o Es,i Wd Cf g k Dmax Do S Uo do H m Ra t tmax tf

Reynolds number Ohnesorge number Weber number surface energy of the drop at the tip of needle (J) surface energy of the drop just prior to impact (J) work done in overcoming resistance due to drag (J) drag co-efficient acceleration due to gravity (m/s2) constant maximum spreading diameter (mm) diameter of the drop before impact (mm) sphericity of the drop before impact drop impact velocity (m/s) outer diameter of the needle (mm) impact height (mm) mass of the drop (kg) mean surface roughness (lm) time elapsed from the start of the drop impact (ms) time taken to reach the maximum diameter (ms) time taken to reach final equilibrium of drop impactdriven processes (ms)

spr average spreading velocity (m/s)

impacting drops. The maximum spreading diameter, Dmax of an impacting drop increases with the increasing We and Re [13]. Several studies have analyzed the variation of Dmax with the control parameters theoretically using the energy balance approach [2,14–20]. These models predict Dmax reasonably well. For low viscosity drop impacts, Clanet et al. [21] found that Dmax = DoWe0.25 with a pre-factor of 0.9. A recent work by Bayer and Megaridis [22] on drop impact on different solid surfaces varying in their surface wettability proposed that Dmax = 0.72 Do(ReWe0.5)0.14. Ukiwe and Kwok [17] proposed a model for Dmax by incorporating the solid–liquid and solid–vapor interfacial energies in the surface energy term of the energy balance equation. The predictions of Dmax obtained from the new model agree very well with the experimental measurements of Dmax for the impact of moderate to high We water and formamide drops on well-prepared flat polymer surfaces. The effect of surface temperature on drop impact dynamics on heated surfaces, which is of relevance in practical applications such as spray cooling, has been studied by various research groups focusing on various aspects such as morphological dynamics – film boiling, nucleate boiling, and contact boiling – of liquid drop [2,23,24]; Leidenfrost phenomena and its characteristics such as drop contact time [25], restitution coefficient [26], as well as how it is affected by surface roughness, drop impact velocity, surface inclination, and oxidation layer thickness on surface [24,27–29]; and maximum drop spreading [24,25,28]. Numerical simulations of drop impact phenomenon by considering the fluid dynamics of the spreading lamella have been reported in the literature [18,30–35]. The comprehensive reviews of drop impact phenomenon by Rein [36], Yarin [37], and Marengo et al. [38] provide further details associated with the drop impact phenomenon. The drop impact dynamics of bio-derived fuel drops on solid surfaces at ambient room temperature is the topic of present investigation. Bio-derived alternative fuels, produced from biomass sources such as camelina, jatropha, and algae (referred as synthetic paraffinic kerosene, SPK), can significantly reduce engine-related emissions produced by the aviation industry. The American Society for Testing and Materials (ASTM) has already approved the use of a 50% blend of Jet A-1 (conventional aviation kerosene) and SPK in aircraft engines. Currently, camelina-derived

Greek symbols q density of biofuel (kg/m3) r surface tension of biofuel (N/m) l viscosity of biofuel (Pa s) hY Young’s contact angle of biofuel drop on solid surface he equilibrium contact angle of biofuel drop on solid surface qair density of air (kg/m3) cSV solid–vapor interfacial tension cSL solid–liquid interfacial tension a1 fraction of drop weight taking part in the drop detachment process b spread factor bmax maximum spread factor bf final spread factor s non-dimensionalised time smax non-dimensionalised time to reach the maximum diameter a slope of b versus s in log–log scale spr average normalized spreading velocity

biofuel is being considered as a future alternative fuel for airplanes [39] and several studies have been reported in recent years on the characteristics of camelina-derived biofuel in the context of aircraft engine technology [40–43]. Limited studies have been reported on the impact of hydrocarbon fuel drops [2,44]. It has been observed that the impact dynamics of such fuel drops exhibits no droplet receding owing to the reduced surface tension. The current development and rapid advancement on the use of bio-derived fuels in the engine combustors necessitates an in-depth analysis of such fuel behavior on several fundamental research topics including spray and drop impact phenomena. The present study investigates the normal impact of bio-derived camelina fuel drops released from a hypodermic needle on a smooth stainless steel surface at ambient room temperature. The impact velocity of drop was varied in the range 0.6–3.0 m/s. Quantitative experimental measurements on the diameter of drop released from the needle, drop spreading characteristics, maximum spreading diameter, and final drop diameter were obtained. The applicability of existing models for the estimation of some of the abovementioned quantities for impact of camelina fuel drops was explored.

2. Experimental details 2.1. Details of drop liquid (camelina biofuel) As mentioned earlier, camelina biofuel is being considered as an alternative aviation fuel. It is derived using hydroprocessing of camelina seed oil which go through the conventional refinery process to deoxygenate and remove undesirable materials including nitrogen, sulphur and residual metals and break down carbon chain lengths. It was procured from UOP (www.uop.com). Since camelina biofuel is free from any aromatic content, 10% aromatics was added with camelina biofuel obtained from UOP to meet ASTM D1655 aviation fuel specifications. The blending and characterization of fuel was carried out at Indian Oil Corporation Limited (IOCL) and Hindustan Petroleum Corporation Limited (HPCL). The physical properties of fuel such as density, dynamic viscosity, and surface tension are known to influence the dynamics of drop impact

40

S. Sen et al. / Experimental Thermal and Fluid Science 54 (2014) 38–46

process. The measured values of physical properties at 25 °C are: density, q = 771.9 kg/m3, dynamic viscosity, l = 1.26  103 Pa s, and surface tension, r = 0.0248 N/m.

2.15

2.2. Experimental setup for drop impact study

2.10

3.1. Drop formation process Fig. 1 shows an image sequence, obtained from high speed digital videos captured during experiments, highlighting the formation of a camelina fuel drop from the flat-tipped stainless steel hypodermic needle. The blue-dashed line shown in the images indicate the location of the needle tip. It is clear from the first three images that the biofuel issuing out of the needle tip spreads upwards along the outer surface of the needle owing to low surface tension of fuel and its high wetting on stainless steel. As more fuel flows from the needle tip, the mass of fuel attached to the outer surface of needle increases reaching a critical value required to overcome surface tension forces exerted on the drop. With time, the drop slides down along the needle’s outer surface, reaches the needle tip (4th to 6th images in Fig. 1), detaches from there

S α1 = 1.0 1.0

2.05

S Do

2.00 0

100

Experiments Experiments 200

300

S = 1.0 Eq. (1) 400

500

0.9 600

H (mm) Fig. 2. Experimentally measured drop size, Do and sphericity, S of camelina biofuel drop just prior to impact on target surface with the impact height, H. Theoretical predictions of Do for two different values of a are also shown by dotted green lines.

through a necking process (6th and 7th images in Fig. 1), and delivers a fuel drop as seen in Fig. 1. The diameter of biofuel drops released from the needle tip, kept at a height from the stainless steel target surface, was measured just above the target surface from high speed video images. A set of three images of drop were chosen for measurement. The variation of average drop diameter, Do with the impact height, H, defined as the distance between the hypodermic needle tip and the target surface, is shown in Fig. 2. The error bars represent the maximum deviation from the average drop diameter. Fig. 2 shows that the Do lies in the range 2.05–2.15 mm. The theoretical prediction of Do considering a balance between the surface tension force holding the drop onto the needle tip and the weight of fuel drop trying to detach it from the needle tip is expressed as [46]

 Do ¼

3. Results and discussion

1.1

Do (mm)

The experiments of camelina fuel drop on the target surface were carried out in an experimental setup comprising of a liquid drop delivery system, a target surface table, and a high-speed video acquisition system. A complete description of the experimental setup is given in Vaikuntanathan et al. [45]. Camelina fuel drops were generated using a flat-tipped hypodermic needle with internal and external diameters of 0.27 mm and 0.45 mm, respectively. The fuel drops were pinched-off by gravity from the hypodermic needle tip and allowed to fall freely onto the target solid surface kept at the ambient room temperature of around 25 °C. The target solid surface of size 50 mm  25 mm  5 mm was prepared using stainless steel material (SS-304 grade). The target surface underwent diamond paste polishing process to obtain mirror-polished smooth stainless steel surface. The measured mean surface roughness, Ra (obtained using Wyko NT9080 optical profiler system), of the target surface was in the range of 0.013–0.040 microns. The dynamics of an impacting drop was recorded using a high-speed video camera (Redlake Y4) at a frame rate of 6000 fps and exposure of 5 ls. The size of an impacting drop prior to impact, Do and the velocity of an impacting drop, Uo were measured using the images obtained from high-speed camera. From the captured high-speed motion pictures of drop impact, the temporal variations of the impacting drop parameters were obtained using image processing and analysis. The time, elapsed from the start of drop impact, t measured from the instant at which the impacting drop touches the top surface of the stainless steel surface was estimated from the camera frame rate. The experiments of drop impact were conducted for 15 different values of Uo in the range 0.6–3.0 m/s.

1.2

α1 = 0.9

6rdo a1 qg

13 ð1Þ

where do is the outer diameter of the needle, a1, the fraction of drop weight taking part in the drop detachment process, and g, the acceleration due to gravity. The predicted value of Do using Eq. (1) is shown in Fig. 2 as dashed lines for two different values of a1 (1.0 and 0.9). It is evident from Fig. 2 that the experimentally measured and theoretically predicted values of Do show a satisfactory match within the error limits of the experiment. Further, the experimentally measured Do with varying H lie within the theoretical predictions of Do obtained with a1 = 1.0 and a1 = 0.9. This suggests that only a small mass of liquid is left attached to the needle tip when the drop detachment occurs. Fig. 2 also shows the drop sphericity, S defined as the ratio of minimum of drop diameters measured along two orthogonal axes to their maximum, at different impact heights. S values greater than 0.95 in Fig. 2 indicate that the drops can be considered to be almost spherical.

Fig. 1. High speed image sequence showing the formation and detachment of camelina biofuel drop from hypodermic needle. The blue dotted horizontal line highlights the position of needle tip.

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S. Sen et al. / Experimental Thermal and Fluid Science 54 (2014) 38–46

3.5 3.0

Uo (m/s)

2.5

Needle tip with drop liquid spread over its surface

e

~ 5.6o

2.0 1.5 1.0 0.5

Equilibrium drop profile

Eq. (3) Eq. (4); Cf = 0.8

Experiments 0.0 0

100

200

Target surface (Smooth SS)

300

400

500

H (mm) Fig. 4. Variation of Uo with H and its comparison with theoretical equations without and with the effect of drag force.

2 mm Fig. 3. Equilibrium configuration of camelina biofuel drop on smooth stainless steel surface obtained from static wetting experiment using sessile drop method. The equilibrium contact angle, he is highlighted in the extracted drop profile.

overcome the resistance due to drag. By neglecting the deviation of drop shape from sphere due to shape oscillations (Es,o = Es,i) and the drag force acting on the drop (Wd = 0), Eq. (2) is expressed as

3.2. Wetting of target surface by camelina biofuel

Uo ¼

The equilibrium wetting of a 2.09 mm (diameter) biofuel drop on the smooth stainless steel surface was experimentally measured through sessile drop method [47]. The needle tip was placed vertically above and as close to the target surface as possible to enable gradual placement of the drop on the target surface without any significant impact velocity. As soon as the biofuel drop adopts equilibrium configuration on the target surface (<5 s), its image was captured using a high resolution video microscope (Keyence). This exercise was repeated 3–5 times to ensure repeatability of measurements. The captured images are further analyzed using image processing software, ImageJ to obtain the equilibrium contact angle, he of camelina biofuel drop on the smooth stainless steel surface. The average he of camelina biofuel drop on the smooth stainless steel surface obtained from repeated trials was 5.6° (±1.5°) which is indicative of the high wetting of biofuel drop on stainless steel surface. Fig. 3 shows the equilibrium configuration attained by a camelina biofuel drop on the target stainless steel surface.

The variation of Uo with H obtained using Eq. (3) is shown in Fig. 4 as the continuous line. Range and Feuillebois [48] expressed Uo without neglecting Wd as

3 qair C f ; 4 qDo

ð4Þ

where qair is the density of air and Cf, the drag coefficient. The variation of Uo with H obtained using Eq. (4) with qair = 1.225 kg/m3 and Cf = 0.8 [48] is shown in Fig. 4 as the blue dashed line. It can be seen from Fig. 4 that the experimental Uo closely follows the prediction using Eq. (3) at moderate velocities. At higher Uo, the experimental measurements start deviating from Eq. (3) and move closer to Eq. (4) since drag force becomes significant at these velocities. 3.4. Impact dynamics of camelina biofuel drop on solid surface The camelina biofuel drop delivered from the needle tip was made to impact on the smooth stainless steel surface. The drop impact conditions can be represented in the We–Oh regime map as shown by open circles in Fig. 5. Here, We and Oh are the drop Weber number and Ohnesorge number, respectively and defined as

1000

Impact driven Oh 2

100

1 0.1

III

W e=

I 10

ð2Þ

In the above equation, the LHS corresponds to the total energy of the drop in state o with the first term being the potential energy of the drop (with respect to a datum fixed at the centre of drop in state i) and the second term corresponding to the surface (liquid– vapor interfacial) energy of the drop. The first term on the RHS of Eq. (2) is the kinetic energy of drop and the second term corresponds to the surface (liquid–vapor interfacial) energy of the drop in state i. The third term is the work done by the falling drop to

A¼

Highly viscous

mgðH  Do Þ þ Es;o

1 ¼ mU 2o þ Es;i þ W d 2

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi g  ð1  e2AðHDo Þ Þ; A

We

The impact velocity of drop, Uo in the present study was varied by varying H. It was measured just prior to the impingement of drop on the target surface by tracking the drop position from images captured using the high speed camera. The variation of experimentally measured Uo with H is shown in Fig. 4. Considering an energy balance between two states of the drop – immediately after pinch-off from the needle (state o), and just prior to impacting the solid surface (state i) – gives the following.

ð3Þ

Almost inviscid

3.3. Measurements of drop impact velocity

Uo ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gðH  Do Þ:

IV

II

0.01 1E-3 1E-3

Capillary driven 0.01

0.1

1

10

100

1000

Oh Fig. 5. We–Oh regime map indicating the region where the current experimental conditions fall.

42

We ¼

S. Sen et al. / Experimental Thermal and Fluid Science 54 (2014) 38–46

qU 2o Do l and Oh ¼ pffiffiffiffiffiffiffiffiffiffiffiffi : r qrDo

5

ð5Þ

4

It is clear from Fig. 5 that all the present experimental drop impact conditions fall under the impact-driven and almost inviscid case. However, it should be noted that at different stages of drop impact dynamics corresponding to a particular impact condition, the dominance of various forces – inertia, viscous, capillary, and wettability – on the dynamics will vary [12]. Fig. 6 shows the impact of camelina biofuel drop on the smooth stainless surface at four different values of We. The images were captured with the camera positioned at an angle of 50° with respect to the target surface plane. The images presented in a row show the deformation of camelina biofuel drop of a given We during impact on the stainless steel surface. The time, elapsed from the start of drop impact, t is increasing from left to right. Among the rows, the images are so chosen that in each column the value of t, corresponding to an image, is kept the same. For a given We, it is observed from Fig. 6 that, as soon as the drop impacts on the smooth surface, the drop liquid spreads out radially from the impact point till a maximum drop spread is achieved on the surface. In this process, a central lamella is created by the spreading of the impacting drop mass (see 2nd and 3rd images in any row of Fig. 6). This lamella is bounded by a thicker rim at its periphery, the thickness of which is a function of the spreading rate of drop front (three phase contact line, TPCL), the spreading rate of inner edge of drop rim, and the mass flux from the thin lamella into the rim [33]. Upon reaching the maximum drop spread (4th image in the first row of Fig. 6), the inner edge of the outer rim starts to recoil towards the impact point whereas the outer edge of outer rim (TPCL) remains almost stationary. This results in an increase in the rim width as seen from 5th image onwards in the first row of Fig. 6. With further increase in t, the impacting drop gradually settles down to a final equilibrium drop configuration (9th image in the

t (ms) -0.043

1.867

3.028

6.013

β

3

2

We = 25.0 We = 117.1 We = 222.1 We = 429.3 We = 560.3

1

0 0

2

4

6

τ

8

10

12

Fig. 7. The temporal variation of spread factor for camelina biofuel drop impact on smooth stainless surface for five different values of We.

first row of Fig. 6). At higher We, splashing of the impacting drop, characterized by the circumferential ejection of secondary droplets from impacting drop, is observed (shown at the bottom of Fig. 6, with the help of images with their background subtracted, for We  560). The ejected secondary droplets fly radially away from the impact location. The dynamics of interaction between the impacting drop and the target surface can be quantitatively explained using the measurements of drop contact diameter on the surface, D (highlighted in the last row of Fig. 6). Often, D is normalized with respect to Do to obtain the spread factor, b. Fig. 7 shows the temporal variation of b for camelina biofuel drop impacting on the smooth stainless steel surface for the impact conditions presented in Fig. 6. The time, t in X-axis of Fig. 7 is normalized with respect to the inertial time scale Do/Uo as s = tUo/Do. The temporal variation of b can be sub-divided into three regions depending on the forces that dominate the

8.667

(a)

8.834

32.816

57.265

81.151

We = 25.0 Rim Lamella

(b)

We = 222.1

(c)

We = 429.3

D

(d)

We = 560.3

5 mm

Secondary droplets ejected from impacting drop Fig. 6. High speed image sequences showing the impact dynamics of camelina biofuel drop on smooth stainless steel surface for four different values of We. Each row of images corresponds to a particular We (indicated on the right of each row) and among the rows along a particular column the time, t elapsed from the start of impact process remains the same. t corresponding to each column is shown at the top of image. At We = 560.3, background subtracted images corresponding to early-time spreading of drop on stainless steel surface are shown highlighting the ejection of secondary droplets from impacting camelina biofuel drop. Two scales are shown at the bottom left corner since the camera was positioned at an angle of 50° to the plane of target surface.

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S. Sen et al. / Experimental Thermal and Fluid Science 54 (2014) 38–46

(a) 1.0

5.0 4.5 4.0

βmax

impact dynamics [12]: initial kinematic phase, spreading phase, and relaxation/equilibrium phase. The kinematic phase is defined as the one where lamella formation and drop spreading are not clearly observed during the very early stages of drop impact when impact waves are seen propagating vertically over the impacting drop surface [12]. This occurs at s < 0.1 [12]. The spreading phase corresponds to the formation and development of a thin lamella, around the central impacting drop liquid, surrounded by a thick rim (see 2nd and 3rd images of Fig. 6(b)). The temporal variation of b in this phase shows an increasing trend, however, with a decreasing slope as time increases. The dependence of b on s for each We was calculated by fitting the spreading phase curve (s > 0.1) in log–log scale, corresponding to each We, by a straight line giving a relation of the form b = ksa where k and a are constants. Fig. 8(a) shows the variation of the exponent a with We. The exponent decreases with increase in We tending to a value of 0.5 at higher We. This implies that the spreading law during spreading phase at high We is similar to that in kinematic phase at any We. Fig. 8(b) shows the variation of spreading velocity,

spr with We. The spreading velocity was obtained as an average of the time-varying spreading velocity by linearly fitting the temporal variation of spread factor in the spreading phase. It is clear that the average normalized spreading velocity, spr =

spr/Uo decreases with increase in We. This implies that the fraction of impact velocity utilized for spreading decreases with increase in We as more of the impact kinetic energy is lost in the form of viscous dissipation due to a larger extent of spreading on the target solid surface. It is also interesting to note that the average spreading velocity at low We is more than Uo. A power law fit of the experimental measurements of spreading velocity shows that spr varies as We0.19. When the spreading velocity becomes zero, the corresponding drop spread factor is the maximum spread factor, bmax. Fig. 9 shows the variation of bmax with We obtained for the impact of camelina biofuel drop on smooth stainless steel surface. It is clear that bmax increases with We due to the increase in impact kinetic energy of the drop. We attempt to compare the experimental measurements of bmax with that predicted by some of the well-known theoretical models. As mentioned earlier, Clanet et al. [21] proposed that bmax = We0.25 for drop impacts with the impact number, P = We/ Re4/5 < 1 (capillary regime observed at low Uo, low l, and high r) and bmax = Re0.2 for P > 1 (viscous regime); P values were less than 0.4 and greater than 4 in their study. The values of P are in the range 0.1–0.8 in the present study. However, as shown in Fig. 9,

3.5 3.0

Experiments 1.73We0.14 Ukiwe-Kwok Clanet et al.

2.5 2.0 0

100

200

300

  We 3ð1  cos hY Þ þ 4 pffiffiffiffiffiffi b3max  ðWe þ 12Þbmax þ 8 ¼ 0: Re

Here hY is the Young’s contact angle of drop in equilibrium on an ideal (smooth) solid surface of the same material as the target surface and is given by the Young’s equation as

cos hY ¼

cSV  cSL : r

ð7Þ

We approximate hY by he measured in static wetting experiments since the target surface is close to an ideal solid surface (Ra  40 nm). As shown in Fig. 9, the Ukiwe–Kwok model (Eq. (6)) is seen to predict the experimental maximum spread factor better than the Clanet et al.’s [21] scaling law. Also shown in Fig. 9 is the best fit power law curve for the experimental measurements of bmax which indicates a lower exponential dependence of bmax on We (0.14 as opposed to 0.2–0.5 reported

0.65

3

α

2

0.4

0.2

3

We = 25.0

β

spr =

spr /Uo

β = 1.97τ τ 1

0.6

1.2

β = 1.17τ + 0.78

1 0 0

0.9

100

200

300

We

400

500

600

1

τ

2

3

0.6

0.3

Experiments -0.19 2.15We

0.0

0.0 0

ð6Þ

2

β 1

600

the scaling law bmax = We0.25 does not predict the experimental measurements of bmax obtained in the present study accurately. The P values in the present study indicate a transitional regime where the effects of capillarity and viscosity have to be considered simultaneously as opposed to Clanet et al.’s scaling laws which consider these effects separately in two different regimes. Using energy balance approach, Ukiwe and Kwok [17] expressed bmax as

2

0.8

500

Fig. 9. The variation of bmax with We obtained for camelina drop impact on smooth stainless steel surface. Comparison of the experimental trend with theoretical models of Ukiwe and Kwok [17] and Clanet et al. [21] is also given along with the best fit curve of experimental data.

(b) 1.5

5 4 We = 25.0 3

400

We

0

100

200

300

400

500

600

We

Fig. 8. (a) The variation of exponent a (in b  sa) with We extracted from the temporal variation of spread factor by linearly fitting the spreading phase data for the corresponding We presented in log–log plot (for example, see insert), and (b) the variation of normalized spreading rate, extracted by linearly fitting the spreading phase data for each We (for example, see insert), with We. The error bars shown in the plot are standard deviation of fitted parameters.

44

S. Sen et al. / Experimental Thermal and Fluid Science 54 (2014) 38–46

in literature [49] for drop impact on smooth surfaces). The dependence of bmax on We as predicted by Ukiwe–Kwok model can be deduced from Eq. (6) as

Experiments 0.75We0.28

4

τmax

  We 3ð1  cos hY Þ þ 4 pffiffiffiffiffiffi b3max  ðWe þ 12Þbmax ) bmax Re " #0:5 We þ 12  ffiffiffiffi 3ð1  cos hY Þ þ 4 pWe

5

3

ð8Þ

Re

The above scaling of maximum spread is similar to that given by Pasandideh-Fard et al. who used the advancing contact angle instead of hY [30]. Applying the limit of hY ? 0 (which corresponds to low surface tension liquids on hydrophilic metallic surfaces as in the present study) and re-writing Re as We0.5/Oh, Eq. (8) yields bmax  We0.125. The exponent 0.125 corresponds closely to the exponent 0.14 of the best-fit curve in Fig. 9. We attempt to compare the dependence of bmax on Uo as observed in our experiments with that predicted by theoretical models as well as previously reported semi-empirical models obtained from experiments over a wide range of parameters (see Table 1). The theoretical model of Ukiwe and Kwok [17] captures the current experimental exponent of 0.28 more accurately. The exponent in semi-empirical model of Bayer and Megaridis [22], obtained from drop impact experiments on different surfaces varying in their surface wettability, shows an exact match with the current experimental data. Further, if the value of Oh in current experiments (0.0063) is included in the semiempirical model of Bayer and Megaridis [22], it gives a pre-factor of 1.46 which is comparable to 1.73 of our best fit curve. Other models show a higher dependence of bmax on Uo compared to that observed in our experiments. Fig. 10 shows the variation of the time taken for reaching maximum spreading diameter on the target surface, tmax with We. In the plot, tmax is normalized with the inertial time scale Do/Uo as smax = t maxUo/Do. smax increases with increase in We and in the range of We studied here smax > 1. This indicates that the time taken by the impacting camelina biofuel drop to reach Dmax on the stainless steel surface is greater than the inertial time scale Do/Uo. It should be noted here that, although smax increases with We, the time taken to reach Dmax, tmax decreases with increase in We since Uo increases with increase in We. The best fit curve shown

2

10

100

1000

We Fig. 10. The variation of non-dimensionalized time taken for camelina drop to attain maximum spread on smooth stainless steel surface with We. The best fit curve of experimental data is also shown.

in Fig. 10 indicates that smax varies as We0.28. This corresponds to an exponent of 0.56 for Uo which is comparable, within the fitting error, to the value of 0.5 obtained by Antonini et al. [49] for water drop impact on hydrophilic glass surface.

smax ¼ /

t max U o  Do We0:14 We0:19



Dmax < dD=dt>spr



Uo Do

 ¼

bmax < db=ds>spr

¼ We0:33

ð9Þ

Eq. (9) is comparable, within experimental error and standard deviation of fitting, to the exponent obtained through the best-fit curve in Fig. 10. This supports the scaling of tmax as Dmax/

spr. In the We range of 100–300, it is seen that smax remains almost constant with We. Similar observations can also be made from the works reported by other research groups [10,12,19,49]. More detailed studies involving different liquid drops and solid surfaces, which are beyond the aim and scope of the current study, are required to comment on this behavior. Subsequent to reaching the maximum spreading diameter on the target surface, it is seen that the drop liquid front (outer edge

Table 1 Comparison of the dependence of bmax on Uo observed in present experiments with that reported in literature. Range of physical parameters Ukiwe and Kwok [17]

Theoretical model

18 < We < 370

Equation h i ffiffiffiffi b3max  ðWe þ 12Þbmax þ 8 ¼ 0 3ð1  cos hY Þ þ 4 pWe Re

a** 0.25

1866 < Re < 9735 SCA*: [66.3°, 90.7°] Clanet et al. [21]

Theoretical model

2 < We < 900 10 < Re < 10,000 Surface: superhydrophobic surfaces, plastic

P = WeRe4/5 < 1: bmax = We0.25

0.50

Scheller and Bousfield [50]

Empirical model based on experiments

19 < Re < 16,400

bmax = 0.61(We/Oh)0.166

0.332

bmax = 0.72(ReWe0.5)0.14

0.28

bmax = 1.73(We0.14)

0.28

0.002 < Oh < 0.58 Surface: polystyrene film, glass (w/ or w/o hydrophobic surface treatment) Bayer and Megaridis [22]

Empirical model based on experiments

0.1 < We < 120 140 < Re < 2100 SCA: [20°,157°]

Present experimental data: power law best fit

Empirical model based on experiments

20 < We < 600 790 < Re < 3775 SCA: 5.6°

* **

Static contact angle. Exponent of Uo in bmax  (Uo)a.

S. Sen et al. / Experimental Thermal and Fluid Science 54 (2014) 38–46

5

45

predictions obtained using existing theoretical and semi-empirical models were obtained. A summary of the major findings from the present study is given below.

βmax, βf

4

3

βf βmax 2 0

100

200

300

400

500

600

We Fig. 11. Comparison of the trends of bf and bmax with We for camelina biofuel drop impact on smooth stainless steel surface.

of spreading drop) remains almost stationary as indicated by the ‘‘plateau-like’’ region in Fig. 7. No measurable receding of camelina biofuel drop front on the smooth stainless steel surface can be observed in the range of We studied here. This is characteristic of a completely wetting liquid–solid system (he close to zero) [12] as in the case of biofuel-stainless steel combination in the present study. However, the inner edge of outer rim of drop shows a retraction towards the drop impact point leading to an increase in drop rim thickness (in the radial direction). After the retraction of inner edge of drop rim ends, the impacting biofuel drop gradually attains a final equilibrium configuration on the stainless steel surface (corresponding to tf  300 ms). It should be mentioned here that, the term ‘‘equilibrium’’ is used with respect to the completion of processes related to drop impact dynamics; due to the volatility of biofuel, the drop may still undergo evaporation under ambient conditions. Fig. 11 shows the variation of the final spread factor, bf corresponding to the end of impact-related processes (tf  300 ms), with We. It is observed that bf increases with We. This may be due to the increase of maximum spread with We together with the absence of drop front retraction. This is in contrast to a partially wetting system (such as water drop impacting on smooth stainless steel surface) where the presence of a drop retraction process results in an almost negligible variation of bf with We, especially at low to moderate values of We [51]. Moreover, bf is more than bmax for all We studied here. This implies that the drop spreads out a little over the maximum spread in a prolonged period of time indicating a very slow spreading process. A simple linear fit analysis shows that rate of this spreading process  {(bf–bmax)/(sf–smax)}Uo is less than 0.006 Uo for all the We studied here indicating that it is not an impact-related event. This slow spreading process, however, could be a combined outcome of the high wetting nature [12] and evaporation process of biofuel drop on the stainless steel surface.

4. Conclusions The impact of camelina-derived biofuel drops, generated using a syringe–hypodermic needle arrangement, onto a smooth stainless steel surface was studied. High speed video camera was used to capture the impact dynamics of biofuel drops with Weber number (We) ranging from 20 to 570. The characteristics of biofuel drop before the start of impact such as formation of biofuel drop in the hypodermic needle, drop sphericity, drop size and velocity were analyzed. Various stages of biofuel drop impact dynamics on the stainless steel surface were analyzed using high speed video images captured during the experiments. Comparisons between the experimental measurements of biofuel drop impact and the

 Low surface tension of biofuel makes the drop liquid issuing from the hypodermic needle to spread over the outer surface of the needle. However, the size of pinched-off biofuel drops from the needle correlated well with the theory. During static wetting experiments, the camelina-based biofuel drop fully wets the surface and forms a thin circular arc-shaped profile with a low equilibrium contact angle of 5.6°.  For a given drop impact case, the impacting biofuel drop spreads out radially, reaches a maximum spreading diameter, and then undergoes a prolonged sluggish drop spreading. The absence of any significant drop receding during the impact process at these impact conditions is attributed to the high wetting of camelina biofuel on the target surface. For the impact of high We biofuel drops, the spreading law linking the spreading factor, b and nondimensionlized time, s tends to b  s0.5.  The experimentally observed trend of maximum spread factor, bmax of camelina biofuel drop impact on the target surface with We is compared well with the theoretically predicted trend from Ukiwe–Kwok model. The exponential dependence of bmax on drop impact velocity, Uo as observed from the best curve fit of current experimental measurements is found to be 0.28 which almost matches with the previous models reported in the literature. The time taken for achieving the maximum spreading diameter normalized with the inertial time scale, smax increases with increasing We. The exponential dependence of smax on We is found to be 0.28.  The final spread factor, bf measured long after the start of impact process (t  300 ms) increases with increasing We. This is in contrast to water drop impact on stainless steel surface where bf remains almost constant with We at moderate values of We. The final spread factor is little more than bmax due to a very slow spreading process driven by the high wetting nature of the camelina biofuel-stainless steel system.

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