Study on Dynamic Wetting Behavior in Microgravity Condition Targeted for Propellant Tank

Transcription

1 Int. J. Microgravity Sci. Appl., 34 (3) (2017) DOI: //jasma IIIII AMS2016 Proceedings IIIII (Original Paper) Study on Dynamic Wetting Beavior in Microgravity Condition Targeted for Propellant Tank Ryoji IMAI and Mori MICHIHARA Abstract Fluid beavior in microgravity (g) is different from in ground gravity since surface tension, viscous force, and wetting are dominant in g condition. In propellant tank for artificial satellite and future on-orbit spacecraft, slosing due to disturbance and settling beavior by cange of acceleration ave to be understood for design of propellant supply system and attitude control system. Tese fluid beaviors in g are affected by a dynamic wetting significantly, terefore it is important to understand dynamic wetting wic dominates fluid beavior. We observed fluid beaviors in cylindrical containers in microgravity conditions created by drop tower facility, and effect of viscosity and diameter of container on fluid beaviors were investigated. CFD analyses were conducted and tese results were compared wit experimental results. It was confirmed tat numerical model considering dependence of contact line velocity in dynamic contact angle by empirical and teoretical metods provided more reasonable results. Keyword(s): Microgravity, Propellant tank, Two pase flow, Surface tension, Dynamic wetting, Contact angle, CFD Received 30 May 2017, Accepted 20 July 2017, Publised 31 July Introduction Fluid wit free surface under microgravity (g) beaves differently from in ground gravity since surface tension, viscous force, and wetting are dominant in g condition. Propellant tanks on liquid propellant system, e.g. attitude control system in artificial satellite, 2nd stage rocket and future on-orbit spacecraft are under g condition, terefore special treatment is required for managing liquid propellant. For example, location of propellant in tank will be unstable because gravitational force is too small and its direction is indeterminate, terefore propellant management devices (PMDs) or liquid acquisition devices (LADs) are usually installed on tese tanks 1). As passive metods among tese devices, surface tension or capillary force is utilized to collect and acquire propellant on outlet of tank. Gallery PMDs are designed to make flow pat to outlet werever propellant is located 1). Sponge PMDs wic as some tin plates called Vanes are designed to acquire propellant on te outlet 1),2). In order to design tese PMDs, accurate estimation tecnology of liquid beaviors dominated by surface tension as to be establised. In te upper stages of current rocket system, operation in wic engine restarts after long coasting pases is considered in order tat upper stage carries te satellite near te targeted orbit so as to minimize propellant consumption for satellite trust system 3). Propellant tanks on upper stages during coasting pase are under microgravity condition, terefore retention trust system is installed in order to stabilize propellant location. In tis system, sufficient trust is exposed so as to settle propellant on te outlet and to keep free surface be flatten. However if retention trust could be reduced, propellant consumption and system weigt could be minimized. However propellant beavior will be dominated by surface tension in tis condition, terefore accurate estimation tecnology of propellant movement will provide great elp for system and operation design of retention truster. In above mentioned situation, fluid beavior were surface tension and viscous force are governed instead of gravitational force could be simulated relatively easily. On te oter and, simulation of wetting dominating flow as muc more difficulty because we ave to consider bot macroscopic fluid beavior and microscopic molecular penomena in te vicinity of contact line of free surface against solid wall. In fact, tere are large number of researces for dynamic wetting in ground gravity condition 4),5). However, dynamic wetting penomena ave not been fully understood since tere are difficulties in treating from micro to macroscopic pysics 4),5). In addition of tis, tese studies targeted to small scale objects suc as capillary tube and droplet, terefore tere are less studies treating relation between dynamic wetting and macroscopic fluid beavior under microgravity condition in wic dynamic wetting is dominant even in large scale object. Additionally influence of pase cange, tat is, evaporation and condensation on dynamic wetting are significant especially for cryogenic fluid suc as propellant and oxidizer for trust system of spacecraft. However, tis penomena is extremely complicated since we ave to treat microscopic termal and fluid beavior including pase cange. Our final target is to understand ow dynamic wetting affect macroscopic and large scale fluid beavior in closed container in Course of Aerospace Engineering, Muroran Institute of Tecnology, 27-1, Mizumoto-co, Muroran, Hokkaido , Japan ( r_imai@mmm.muroran-it.ac.jp) /2017/34(3)/340304(11) Te Jpn. Soc. Microgravity Appl ttp://

2 Study on Dynamic Wetting Beavior in Microgravity Condition Targeted for Propellant Tank Fig. 1 Experimental apparatus for sort duration microgravity condition (left) and time istory of acceleration (rigt). microgravity condition. Objective of present study is to investigate dynamic wetting witout pase cange as a first step. In tis paper, results of computational fluid dynamic (CFD) analyses wic investigate te effect of teoretical and empirical equations for dynamic contact angle on fluid beaviors in microgravity condition are described. Results by CFD were evaluated by experimental ones in microgravity condition obtained by free fall experimental apparatus and facility Sec Free Fall Experimental Facility Sort duration microgravity condition was created by free fall facility named by COSMOTORRE in Uematsu Electric Co., Ltd. General description of tis experimental apparatus is sown in Fig. 2. Test section was installed on cylindrical drop capsule prepared by Uematsu Electric Co., Ltd. Tis capsule is ung up 2. Metod of Microgravity Experiment We observed fluid beaviors, mainly movement of free surface in container after entering microgravity condition. Cylindrical containers wit different radius and eigts were selected as a test section, since symmetric two dimensional calculation domain is able to be applied. In tis study, two kinds of sort duration microgravity experiments were conducted. Microgravity durations were 0.4 sec and 2.5 sec obtained by 2.3 m and 45 m in free fall distance. In tese experiments, silicone oil (KF-96 series by Sin-Etsu Cemical Co. Ltd.) was used as a working fluid. KF-96L-1cs and KF-96-50cs were adopted as low and ig viscous fluid respectively Sec Free Fall Experimental Apparatus Sort duration microgravity condition was created by free fall apparatus sown in Fig. 1. Test section was installed on rectangular box, wic we called "capsule" and capsule was placed at 2.3 m ig place from ground level wit anging by a fising line. Capsule was fallen by cutting tis fising line calmly by scissors to suppress fluctuation of acceleration by structural vibration just after starting to fall. Rigt figure in Fig. 1 sows time istory of acceleration. We can see tat order of 0.01 G in gravity level and about 0.4 sec in microgravity duration was performed. Left: Experimental apparatus installed on drop capsule. Rigt: Test section and observation system. Test Section Test section: Material: acrylic resin Dia.: 30,45,60 mm Heigt: 60,90,120 mm Fig. 2 Experimental apparatus and test section

3 Ryoji IMAI and Mori MICHIHARA by crane and raised at about 50 m ig before dropping. Free fall distance of capsule is 45 m, and microgravity duration is obtained to be about 2.5 sec. Experimental rack wic installs experimental apparatus is being floated in te capsule during free falling, terefore ig quality microgravity condition is obtained. Microgravity level in our experiments was performed to be order of G. On upper side in Fig. 2, experimental apparatus in tis experiment is sown. Two sets of cylindrical containers as test section, video camera (GoPro Hero4), LED ligt source and battery were installed on wooden circular plate. Fluid beaviors in eac test section were observed from two direction, terefore four sets of video cameras were used. Test section is sown on te lower side of Fig. 2. Test section is made of transparent acrylic resin, and cylindrical sape is formed on te rectangular block, wic intends to minimize te effect of refraction in observing liquid beavior in container. Tree kinds of test section were prepared; 30, 45, and 60 mm in diameter and 60, 90, and 120 mm in eigt respectively. Te objective to prepare tese test sections are to clarify te effect of scale on unstable fluid beavior in sudden cange of gravitational force. Scale will be related to inertia force, capillary force, viscous force and gravitational force. However main subjects of tis paper are comparison between experimental and numerical results and treatment of dynamic contact angle. Terefore description of discussion about scale effect as well as results for 45 mm in diameter and 90 mm in eigt won t be described in tis paper. Tis experimental apparatus was installed on tird stage from bottom of experimental rack sown as Fig Metod of Numerical Calculation Fluid beaviors in cylindrical container under microgravity condition in consideration of dynamic wetting were analyzed by commercial CFD code of ANSYS FLUENT ver Calculation Domain Figure 3 sows calculation domain. Flow field was assumed to be two dimensional axisymmetric, terefore calculation domain was set to be rectangular region. In te microgravity experiments, it was confirmed tat free surface beaved twodimensionally by te observations from two direction. Terefore two dimensional calculation domain in tis study is reasonable. Ten, meses were set to be finer approacing to te solid wall. Number of cells in calculation domain is 3600 for domain corresponding to eac test section. Terefore averaged cell size increases wit domain size. Tis fact doesn t affect quality of numerical results since microscopic region in te vicinity of contact line is excluded from calculation domain by introducing treatment of dynamic wetting mentioned ereafter. VOF (Volume of Fluid) metod was employed to calculate two pase flow, and geometric reconstruction sceme 6) was applied as an interface reconstruction algoritm. Liquid and gas flow Table 1 Fluid Liquid pase Fig. 3 Calculation domain. Fluid substance and tese properties in present calculation. Dynamic Density Surface viscosity [kg/m 3 ] tension [mm 2 /s] [mn/m] KF-96L cs KF cs Gas pase Air N/A were assumed to be laminar. Surface tension was considered as a source term in momentum equations by CSF (Continuum Surface Force) metod 7). Diameter and eigt of calculation domain was 30,45,60 mm and 60,90,120 mm respectively corresponding to test section. As an initial condition, volume of liquid was given to be a alf of container volume. Table 1 sows fluids substance and tese properties in present calculation. 3.2 Treatment of Dynamic Wetting In te vicinity of contact line, tat is, intersection of free surface and solid wall, tin liquid film is formed. It is difficult to simulate flow field in tis region reasonably since molecular force is not able to be neglected. Additionally some treatments ave to be required to prevent numerical instability by applying extremely fine mes in tin liquid film region. To overcome tis difficulty, a metod of introducing dynamic contact angle and applying tis as a boundary condition on solid wall is generally taken. In present study, existing equations for dynamic contact angle wit dependence of contact line velocity was applied as a boundary condition on solid wall. As anoter metod, flow field in tin liquid film region was separately calculated, were effect of molecular force was considered, and dynamic contact angle wit dependency of contact line velocity was obtained as a numerical results. We call tis metod as tin liquid film teory

4 Study on Dynamic Wetting Beavior in Microgravity Condition Targeted for Propellant Tank A. Metod to use Existing Equations for Dynamic Contact angle Tere are many equations for dynamic contact angle wic as dependency of contact line velocity by teoretical and empirical approac. Cox s 8) and Kato s 9),10) equations were used to provide dynamic contact angle. Tese equations are sown as follows; Cox s equation d 3 1 / 3 9C Ca,C lnl / S (1) Kato s equation 31 cosd cos Ca tan were is static contact angle, d dynamic contact angle, L caracteristic lengt, S slip lengt, and te ratio of te surface area occupied by defects. Ca is a dimensionless parameter of Capillary number defined as; d (2) U Ca (3) were is viscosity, U contact line velocity, and surface tension. Cox tried to represent flow in te vicinity of contact line analytically, ten e found tat viscous stress on contact line ad singularity, tat is, integral of tis stress became infinite 8). Terefore e introduced slip lengt S, te area lengt from contact line in wic searing stress on solid wasn t considered. From te Brake s review 5) it is mentioned tat S as very wide value according to liquid substance and experimental conditions, terefore, tis as to be treated as adjustable parameter. In our calculation, C parameter was treated as adjustable parameter since S is included in te definition formula of C. In Kato s equation, is te ratio of te surface area occupied by defects. Here, defects means rougness or absorbed foreign molecules wit a macroscopic scale on te solid surface. Additionally, is treated as adjustable parameter 10). Contact line velocity was obtained by multiplying velocity vector on numerical cell neigbored on sidewall and unit gradient vector of volume fraction of liquid. B. Metod to Consider a Tin Liquid Film Flow Teory near Contact Line In order to consider a tin liquid film flow near contact line, disjoining pressure as well as surface tension were introduced to consider pressure difference troug free surface. Figure 4 sows tin liquid film flow and pressure difference troug free surface 11),12). Tickness of liquid film is expressed by x as a function of coordinate x along solid wall. We constructed governing equations for tin liquid film teory by combining metods by Standingford 11) and Wang 12). Pressure balance troug free surface is sow as follows; p g p p p (4) l c d y were pg is gas pase pressure, pl liquid pase pressure. pc capillary pressure difference, and pd disjoining pressure 12),13) is given as follows; p (5) c B p d (6) 4 were is curvature of free surface, B is coefficient for disjoining pressure expressed by following equation; xx (7) x were subscript x indicate differential of x respectively. Disjoining pressure is introduced to consider te effect of molecular force in te vicinity of contact line. Equation for disjoining pressure is derived by excanging molecular force obtained from Lenard-Jones potential to pressure, ten tis is sows as follows 14) ; A p d (8) 3 Te coefficient A is called as Hamaker constant 14). In numerical analysis of termal and fluid beavior for evaporating menisci, Pancamgam et. al. employed eq.(6) as disjoining pressure for relatively ticker liquid film. We tried bot equations, consequently it was confirmed tat reasonable results were obtained in eq.(6). Terefore, we applied eq.(6) as disjoining pressure ereafter. If we consider pg =0 as a base pressure, pl is replaced by p, B p pc pd (9) 4 From te lubrication teory 15), following equation is derived; u yy Fig. 4 Tin liquid film flow near contact line. px (10) were subscript y indicate differential of y respectively. From te continuous condition for volumetric flow rate and solution of eq.(10), we obtain; p x 3 U (11) 3 were is coating tickness sown in Fig. 4. From eq.(9) to eq.(11), following ordinary differential equation p g pl x

5 Ryoji IMAI and Mori MICHIHARA for tickness of liquid film x is derived; xxx 2 3 / 2 3x 2 4B U / 1 3 x 2 xx 5 x x x 1 (12) In order to solve tis differential equation, coating tickness as to be provided. Tis tickness is supposed to be corresponding to so-called precursor film wic is extremely difficult to be observed. In our study, tis tickness was treated as adjustable parameter, and was determined to be 4.0x10-8 m, in wic it was confirmed tat reasonable relationsip between contact line velocity and dynamic contact angle was obtained as a result of parametric study of. However more reasonable metod to determine as to be considered, tis is currently open problem. In tis numerical analysis, liquid beavior in microgravity condition created drop tower facility was targeted. Terefore consideration of coating film or precursor film is supposed to be reasonable in tis calculation since solid wall faced on gas pase will be wet due to swinging motion of experimental apparatus during preparation pase of microgravity experiment. It was sown tat curvature of liquid film surface obtained by eq.(12) approaced to constant value, were we defined dynamic contact angle from a gradient of tickness of liquid film. Relationsips between contact line velocity and dynamic contact angle was calculated, wic were inputted to CFD calculation model as boundary condition at side wall. 4.2 Results by 2.5 Sec Free Fall Experimental Facility Figure 6 sows dynamic liquid beavior in cylindrical container wit 30 mm in diameter and 60 mm in eigt, same size as one used in 0.4 sec free fall experimental apparatus. From tis figure, we can see tat fluid beavior just after entering microgravity condition was similar wit one by 0.4 sec free fall experimental apparatus. During microgravity condition obtained in tis free fall facility, movement of free surface almost ceased, Gas pase Free surface Liquid pase 0 sec 0.3 sec 0.7 sec 4. Results of Microgravity 4.1 Results by 0.4 Sec Fall Experimental Apparatus Figure 5 sows dynamic liquid beavior in cylindrical container wit 30 mm in diameter and 60 mm in eigt. Here dynamic viscosity of liquid was 1 mm 2 /s. From tis figure, we can see tat contact line of free surface against solid wall was raised by surface tension and tat free surface on center axis went down. Also we can see tat curvature of free surface on center line was larger just after entering microgravity condition, ten became smaller and free surface on center line went up. 1.5 sec 2.5 sec Fig. 6 Snapsot of liquid beavior. Diameter is mm and eigt is 60 mm. Dynamic viscosity is 1 mm 2 /s. Fig. 5 Dynamic beavior of liquid in container. 30 mm in diameter and 60 mm in eigt. Dynamic viscosity is 1mm 2 /s. Fig. 7 Time istory of position of free surface on center axis

6 Study on Dynamic Wetting Beavior in Microgravity Condition Targeted for Propellant Tank Gas pase Free surface Gas pase Free surface Liquid pase Liquid pase 0 sec 0.3 sec 0.7 sec 0 sec 0.3 sec 0.7 sec Fig sec 2.5 sec Snapsot of liquid beavior. Diameter is mm and eigt is 120 mm. Dynamic viscosity is 1 mm 2 /s. 1.5 sec 2.5 sec tat is, fluid beavior reaced almost stable. We can see tat curvature of free surface was almost uniform, terefore, sape of free surface was similar wit part of spere. Figure 7 sows te time istory of position of free surface on center axis obtained by 0.4 sec free fall apparatus and 2.5 sec free fall facility. We can see tat coordinate of free surface on center axis went down to negative coordinate just after entering microgravity condition and went up after reacing minimum coordinate. It is found tat tis minimum value was smaller in experiment by 2.5 sec free fall facility, since microgravity level is lower tan by 0.4 sec free fall apparatus, terefore contact line of free surface was raised larger. Figures 8 and 9 sow dynamic liquid beavior of 1 mm 2 /s and 50 mm 2 /s in dynamic viscosity for 60 mm in diameter and 120 mm in eigt. In Fig. 8, we can see flatten sape at 0.3 sec and larger curvature at 0.7 sec in free surface before reacing stable and uniform curvature. In Fig. 9, we can see tat free surface approaces to stable sape witout oversoot seen in case of low viscosity. 4.3 Measurement of dynamic contact angle In order to obtain te relation between contact line velocity and dynamic contact angle, we captured image were contact line was enlarged by digital video camera. Tese measurements were conducted in bot 0.4 sec free fall experiment and 2.5 sec free fall experiment respectively. As for 0.4 sec free fall experiment, measurement metod and results were described in previous Fig. 9 Snapsot of liquid beavior. Diameter is mm and eigt is 120 mm. Dynamic viscosity is 50 mm 2 /s. paper by autors 16), terefore detail description will be skipped. We compared our experimental results wit ones by Cox s formula, consequently, it was found tat dynamic contact angle wit range of 5 to 40 in C value can generally cover our experimental results. Measurements and adjustment in C value in 2.5 sec free fall experiment is described below in detail. Figure 10 sows te snapsot of liquid beavior in container of 60 mm in diameter. Location of contact line and contact angle were measured by use of image processing software named ImageJ. A contact line speed was calculated from time derivative of contact line coordinate. Figure 11 sows contact line velocity vs. dynamic contact angle obtained from experimental results sown in Fig. 10. In tis figure, advanced dynamic contact angle was indicated since contact line proceeded upward. Dynamic contact angle by Cox equation wit various coefficient C values was also sown in tis figure. We can see tat tere are some scattering in experimental data. Tere were some errors in detecting contact point due to insufficient resolution in image and due to lack of performance of video camera. We expect tis scattering will be reduced if we capture furter enlarged image of free surface near contact line. Anyway we can see tat dynamic contact angle by Cox s equation wit range of 1 to 5 in C value can generally cover our experimental results

7 Ryoji IMAI and Mori MICHIHARA Gas pase Tank wall Contact line Liquid pase 0 sec 0.15 sec 0.3 sec 0 sec 0.1 sec 0.17 sec 0.49 sec Fig. 12 Snapsot of liquid beavior. Dynamic contact angle is 4.0 deg. Red and blue portion indicates liquid and gas pase respectively. Diameter of container is mm and eigt is 60 mm. Dynamic viscosity is 1 mm 2 /s. 0.4 sec 0.6 sec Fig. 10 Snapsot of free surface sape near contact line. Diameter is mm and eigt is 120 mm. Dynamic viscosity is 1 mm 2 /s. Fig. 13 Contact line velocity vs. dynamic contact angle by Cox s and Kato s equation 5.1 Numerical results corresponding to experiment by 0.4sec free fall experimental apparatus Fig. 11 Contact line velocity vs. dynamic contact angle. 5. Results of numerical calculations We calculated unsteady fluid beavior in cylindrical container wen acceleration was imposed vertically downward canged from 1 G to 0.01 G and G in order to simulate microgravity condition by free fall experiment. Tese conditions correspond to results by 0.4 sec free fall experimental apparatus and 2.5 sec free fall experimental facility respectively. Figure 12 sows snapsot for contour of volume fraction in liquid pase were dynamic contact angle was given to be constant value of 4.0 deg wic was obtained from observation of static meniscus for 30 mm in diameter of container. Red and blue portion sows te area were volume fraction of liquid is unity and zero respectively. Tis means tat read and blue portion indicate liquid and gas pase respectively. From tese figures, we can see tat free surface was raised by surface tension on te side wall, and concave sape in free surface is formed between side wall and center axis and convex sape on center axis just after entering to microgravity condition. Ten tis concave sape disappeared by free surface on te center axis starting to go down. After tis, contact line on side wall repeated downward and upward movement, and free surface on center axis repeated opposite direction movement simultaneously. Tis repeatedly movement would damp by viscous stress. We calculated liquid beaviors were Cox s and Kato s equation was applied as dynamic contact angle. Prior to conduct tis calculation, we obtained relation between contact line velocity and dynamic contact angle sown as Fig. 13. Here, C in

8 Study on Dynamic Wetting Beavior in Microgravity Condition Targeted for Propellant Tank 0sec 0.1sec 0.17sec 0.49sec Fig. 14 Snapsot of liquid beavior. Dynamic contact angle was given by Cox s equation. Coefficient C is Red and blue portion indicates liquid and gas pase respectively. Dynamic viscosity is 1 mm 2 /s. Fig. 16 Contact line velocity vs. dynamic contact angle considering tin liquid film teory. (a) Tickness of liquid film Fig. 17 Snapsot of liquid beavior Dynamic contact angle was applied according to tin liquid film teory. Red and blue portion indicates liquid and gas pase respectively. Dynamic viscosity is 1 mm 2 /s. Cox formula is 29.8, and in Kato s formula is 0.021, tese value were same as ones used in Kato s experiment 10). We can see tat results by Cox s and Kato s equation agree wit eac oter. (b) Curvature of liquid film Fig. 15 Tickness and curvature of liquid film. Figure 14 sows snapsot of liquid beavior were Cox s equation was applied as dynamic contact angle wit dependence of contact line speed. Tere are a less difference in istory of free surface sape compared to constant dynamic contact angle of d = 4 deg. Also we confirmed tat effect of C on istory of free surface sape was very small wit range of 5 to 40 in C. In addition of tis, we investigated dynamic liquid beavior by using Kato s equation as dynamic contact angle. We confirmed tat tis results were consistent wit ones by giving constant value and variable value according to Cox s equation in dynamic contact angle. Next we will sow calculated results wic considered flow in te vicinity of contact line. As a first step, we obtained relationsip between contact line speed and dynamic contact angle. Figure 15 sows (x); distribution of liquid film and curvature of free surface obtained as solution of eq.(10). Here, coefficient for disjoining pressure was set to be B= -1.2x10-27 used by Pancamgam et al. 13) Te effect of contact line speed U was also sown in tese figures. We can see tat curvature converged as distance from contact point x increased. Dynamic contact angle was obtained from te gradient of liquid film tickness at wic curvature converged. Figure 16 sows relationsip between contact line velocity and dynamic contact angle obtained by solving eq. (10). In tis figure, results using Cox s and Kato s equation were also sown. We can find tat dynamic contact angle by tin liquid film teory was muc larger tan by oter equations. We made a polynomial equation for contact line velocity vs. dynamic contact angle. Tis equation for dynamic contact angle was applied as boundary condition on side wall in te numerical calculations

9 Ryoji IMAI and Mori MICHIHARA Figure 17 sows snapsot of liquid beavior wen dynamic contact angle wit dependence of contact line velocity. We can see tat rising distance of contact line is smaller compared wit results in constant value of 4 deg and Cox s equation in contact angle sown in Figs. 12 and Fig Numerical Results Corresponding to Experiment by 2.5 Sec Free Fall Experimental Facility Figures 18 and 19 sow snapsot of volume fraction of liquid pase in case tat dynamic contact angle was given to be constant 0 sec 0.3 sec 0.7 sec 2.5 sec 1mm 2 /s 0 sec 0.3 sec 0.7 sec 2.5 sec 50 mm 2 /s Fig.18 Snapsot of liquid beavior. Dynamic contact angle is 4.0 deg. Red and blue portion indicates liquid and gas pase respectively. Diameter is mm and eigt is 120 mm. 0 sec 0.08 sec 0.17 sec 2.5 sec 1 mm 2 /s value wic was obtained from observation of static meniscus for 60 mm and 30 mm in diameter of container. In low viscosity case, liquid beavior is similar wit one obtained in te condition for 0.4 sec free fall experimental apparatus. In ig viscous liquid, we can t see convex sape and going down movement for free surface on center axis, and we can see tat displacement of free surface is muc smaller tan for low viscous liquid. In low viscosity case for 30 and 60 mm in diameter, we can see concave sape in free surface on center axis, and it takes longer time in φ60 mm case to obtain tat sape from entering micro gravity condition. Tis means liquid moves slower in larger diameter of container. We calculated fluid beaviors in case tat dynamic contact angle was given by Cox s formula and tin liquid films teory for 60 mm and 30 mm in diameter of container respectively. We confirmed tat liquid beaviors were quite similar wit ones in constant dynamic contact angle, terefore we skip snapsot of liquid beavior in tese cases. 5. Discussion 5.1 Comparison between Experimental and Numerical results for 0.4 Sec Free Fall Experimental Apparatus Time istory of center position was compared between numerical and experimental results. Figure 20 sows comparison between experimental and numerical results were Cox s equation was applied as dynamic contact angle. We can see tat center position on center line went down just after microgravity condition started, ten went up. Also we can see tat te dependency of coefficient C is very small in numerical results. It was found tat agreement between experimental and numerical results was not so good especially after about 0.2 sec. In Fig. 20 we can see some fluctuations in numerical results. Tese penomena were also seen in oter low viscous fluid cases mentioned ereafter, owever, tese were not obtained in experimental results. We supposed tat tese fluctuations were caused by numerical error, wic was expected be reduced by appropriate surface capturing algorism. Tis is currently open problem. 0 sec 0.3 sec 0.7 sec 2.5 sec 50 mm 2 /s Fig. 19 Snapsot of liquid beavior. Dynamic contact angle is 4.0 deg. Red and blue portion indicates liquid and gas pase respectively. Diameter is mm and eigt is 60 mm. Fig. 20 Time istory of center position of free surface (Comparison wit Cox s equation)

10 Study on Dynamic Wetting Beavior in Microgravity Condition Targeted for Propellant Tank On side wall Fig. 21 Time istory of center position of free surface (Comparison wit tin liquid film teory). On center axis Figure 21 sows comparison between experimental and numerical results were dynamic contact angle was obtained by tin liquid film teory. It was found tat numerical results agreed wit experimental one very well. 5.2 Comparison between Experimental and Numerical Results for 2.5 Sec Free Fall Experimental Facility Figures 22 and 23 sows te istory of center position and contact point against solid wall in free surface, and comparison between experimental and numerical results were constant value, Cox s equation, and tin liquid film teory were applied as dynamic contact angle in 60 mm container, and low and ig viscous case respectively. We can see experimental results sows tat center position on center axis went down just after microgravity condition started, ten went up. However in case of low viscous liquid in 60 mm container, numerical results sow tat cange in position of free surface on center axis is very small just after entering microgravity condition, terefore tere is disagreement between experimental and numerical results. On te oter and, we can t see tis disagreement in oter cases sown in Fig 23. Tis disagreement results from te fact tat concave sape of free surface on te center axis couldn t be detected due to measurement metod in te experiments. We can see tat numerical results concerning position of free surface on side wall wit constant contact angle don t agree wit experimental ones in low viscous liquid, tat is, contact position by numerical results decreased faster after about 1.5 sec. On te oter and, it is found tat numerical results by Cox formula and tin liquid film teory agree wit experimental ones favorably. Figure 24 sows experimental and numerical results in case of low viscous liquid in 0 mm container. We can see tat agreements between experimental and numerical results were favorable in te istory of free surface position on center axis. And it is found tat numerical results concerning position of free surface on side wall wit constant contact angle don t agree wit experimental ones in low viscous liquid. On te oter and, we can see tat numerical results by Cox formula and tin liquid film teory agrees wit experimental ones very well. Fig. 22 Fig. 23 Fig. 24 Contact line velocity vs. dynamic contact angle. Dia.:60 mm, eigt:120 mm, low viscous liquid case (KF-96L-1cs). Contact line velocity vs. dynamic contact angle. Dia.:60 mm, eigt:120 mm, ig viscosity liquid case (KF-96L-50cs). Contact line velocity vs. dynamic contact angle. Dia.:30 mm, eigt:60 mm, low viscosity liquid case (KF-96L-1cs). 6. Conclusion On side wall On center axis On side wall On center axis Numerical calculation for dynamic wetting beavior in cylindrical container was conducted, and tese results were evaluated by sort duration microgravity experiments using 0.4 sec free fall experimental apparatus and 2.5 sec free fall

11 Ryoji IMAI and Mori MICHIHARA experimental facility. In numerical calculations, dynamic contact angle wit dependency of contact line velocity was adapted as te boundary condition on side wall. Relation between contact line velocity and dynamic contact angle was obtained in advance by two kinds of metod; Cox s equation and tin liquid film teory. Dynamic liquid beaviors after entering to microgravity condition were investigated in detail. Dynamic wetting beaviors in microgravity conditions were observed by using sort duration free fall apparatus. Evaluation of numerical results were made by comparing wit experimental results. In case of microgravity condition by 0.4 sec free fall experimental apparatus, it was sown tat numerical result were dynamic contact angle was calculated by tin liquid film teory agreed wit experimental ones using better tan by Cox s formula and by given as constant value. In case of microgravity condition by 2.5 sec free fall experimental facility, we found tat numerical results by Cox s formula and tin liquid film teory agreed wit experimental ones very well. Finally, we ave to evaluate numerical model by more experimental data in microgravity condition. As a final target, we are going to construct te numerical calculation model considering microscopic wetting penomena, macroscopic fluid beavior, and teir interrelationsip. Also dynamic wetting wit pase cange troug free surface as to be investigated targeted to cryogenic propellant management system for future on-orbit transfer veicle. References 1) F.T. Dodge: Te New Dynamic Beavior of Liquids in Moving Containers ftp://apollo.ssl.berkeley.edu/pub/me_arcives/government%20a nd%20industry%20standards/nasa%20documents/swri_fuel _Slos_Update.pdf (2014). 2) R. Imai, Y. Takano, K. Yamada, K. Hama and S. Nakamura: Proceedings of te Twenty-Fift International Symposium on Space Tecnology and Science selected papers Kanazawa, ISTS 2006-a-02, 25 (2006) 1. 3) M. Niitsu, M. Yasui, K. Simura, J. Yabana, Y. Tanabe and K. Isikawa: Mitsubisi Heavy Industries Tecnical Review, 51 (2014) 26. 4) D. Bonn, J. Eggers, J. Indekeu, J. Meunier and E. Rolleyonn: Review of modern pysics, 81 (2009) ) T.D. Blake: J. of Colloid and Interface Science, 299 (2006) 1. 6) D.L. Youngs: Numerical Metods for Fluid Dynamics, Academic Press (1982). 7) J.U. Brackbill, D.B. Kote and C., Zemac: J. of Computational Pysics, 100 (1992) ) R. Cox: J. of Fluid Mecanics, 168, (1986)169. 9) K. Kato, T. Wakimoto and S. Nitta: J. Jap. Soc. Exp. Mec. 10, s62-s66 (2010). 10) L. Kato, T. Wakimoto, Y. Yamamoto and T. Ito: Experimental Termal and Fluid Science, 60 (2015) ) D.W.F. Standingford and L.W. Scwartz: AIAA, (1999). 12) H. Wang, J.Y. Murty, and S.V. Garimella: Int. J. of Heat and Mass Transfer, 51 (2008) ) S.S. Pancamgam, S.J. Gokale, J.L. Plawsky, S. DasGupta and P.C. Wayner, Jr.: Trans ASME, J. of Heat Transfer, 127 (2005) ) S. Batzdorf: Tecnisce Universit Darmstadt P D Tesis, ) F.P. Breterton: J. of Fluid Mecanics, p. 166 (1960). 16) R. Imai, Y. Amanom and S. Goto: proceeding of AJCPP2016, (2016)