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Flow Dynamics in the Melt Puddle during Planar Flow Melt Spinning Process
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 4 (2017) 3728–3735
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Flow Dynamics in the Melt Puddle during Planar Flow Melt Spinning Process Sowjanya M.a, * and Kishen Kumar Reddy T.b a
Muffakham Jah College of Engineerng and Technology, Hyderabad,500034, India Jawaharlal Nehru Technological University Hyderabad, Hyerabad, 500085, India
b
Abstract Quality of amorphous ribbons obtained during planar flow melt spinning process depends highly on the dynamics of the melt puddle. The present study investigates the flow dynamics using pressure profiles, path lines and stream function. Pressure profiles help in predicting the melt blow-out. Transformation of planar flow melt spinning to free jet melt spinning can be observed using path lines in the puddle. Oscillations in the puddle can be traced by the stream function at the melt wheel contact. The analysis helps the experimentalists to carefully select the ejection pressure, wheel speed and nozzle-wheel gap to obtain a quality ribbon. ©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:Planar Flow Melt spinning; Puddle dynamics; Path lines; Stream Function; Melt Puddle.
1. Introduction Amorphous ribbons are produced directly from molten alloy by the rapid solidification technique called 'Planar flow melt spinning process (PFMS)' Fig. 1a schematically shows the formation of ribbon upon ejection of melt on a cooling wheel in the PFMS process. Fig. 1b shows the puddle formation with upstream (USM) and downstream meniscus (DSM) between the nozzle-wheel gap. Gong et al. [1] reported that the quality of amorphous ribbon by PFMS process depends on the shape and stability of the melt puddle formed between the nozzle and the rotating
* Corresponding author. Tel.: +91-9492932682; fax: +91-40-24342010. E-mail address:[email protected] 2214-7853©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
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copper wheel. Wang et al. [2] revealed that the fluid dynamics (heat and mass transfer) controls the stability of the puddle which in turn dictates the PFMS process. Experimental investigation of the melt puddle during the process is difficult due to high operating speeds. However, numerical simulations can be employed to observe the flow dynamics in the melt puddle at very small time steps of few micro-seconds. Liu et al. [3] presented a numerical model to simulate the initial puddle formation for a successful set of process parameters. Upadhya and Stefanescu [4] considered flat wheel surface and predicted the shape of the puddle to be parabolic and observed the crystallization at lower wheel speeds for Fe-3wt%B alloy. Wu et al. [5] developed a 2D model and suggested that a low negative pressure at the rear side of the puddle (upstream meniscus) is developed which reduces the non contact area at the melt substrate interface. Bussmann et al.[6] and Liu et al.[3] reported that the stability of the melt puddle was attained by 10 ms in the numerical simulation. Present authors (Majumdar et al. [7]) used a 2D, time dependent numerical model to simulate the puddle formation at various ejection pressures, nozzle wheel gap and validated with experimental results obtained by Srinivas et al. [8]. The present work is an extended numerical investigation of the flow dynamics of the corresponding melt puddles. Nomenclature F P Ud T Tg Cp ρ
volume fraction pressure wheel speed temperature glass transition temperature specific heat density
[-] [kPa.] [m/s] [K] [K] [J/kgK] [Kg/m3]
µ k g σ w G
dynamic viscosity thermal conductivity gravitational acceleration surface tension slit width Nozzle-wheel gap
[Pa.s] w/mK [m/s2] [N/m] mm mm
2. Numerical Model Fig. 1(b) shows the domain considered for the simulations between the flat bottom of nozzle (BE) and wheel surface (GH). Fig. 1c shows the quad mesh created in the domain. BC and DE are nozzle walls and CD represents nozzle slit opening. Regions AB, EF, AG & FH represent surrounding atmospheric air conditions. Volume of fluid technique along with conservation equations are solved to simulate the puddle formation. Assumptions and Boundary conditions All the wall surfaces employ the no slip boundary condition to impose the boundary layer flow. Wheel surface is at constant temperature of 300 K and smooth. Nozzle walls are made of quartz and hence no heat flux. Latent heat is neglected due to the formation of amorphous phase in the ribbon. Radiation heat loss is less and hence neglected. All the properties are constant with temperature. Melt viscosity is calculated using equation (1). Melt enters the domain with specified pressure and temperature through CD (inlet boundary). Wall GH is at constant temperature of 300 K and moving with the given speed. Nozzle walls BC and DE are stationary wall boundaries with no heat flux. AB, EF and AG are the pressure inlet boundaries to simulate the presence of surrounding air. Domain outlet FH is the pressure outlet boundary. Table 1 gives the amorphous material properties used for the present model and eqn.(1) gives the temperature dependent viscosity equation (Liu et al. [3]) is used for the melt.
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Fig. 1 Schematic diagram of a) planar flow melt spinning process and b) melt puddle formation c) Two dimensional mesh of air domain (AFHGA) between nozzle and wheel, (G=0.3 mm, w=0.3 mm) .
µ(T) = -0.1(exp (3.6528 + 734.1/ (T - 674))).
(1)
Table1. Properties of molten alloy (Fe-Si-B) used in the model. Designation ρ Cp K μ σ
Parameters Density Specific heat Thermal conductivity Viscosity Surface Tension
Values 7180 kgm-3 544 Jkg-1K-1 8.99 W/mK μ(T) 1.2 N/m
3. Results and Discussions Fig 2 shows a study puddle at 10 ms by simulating the puddle at the same set of process parameters at which high speed image is presented [8]. In the present study simulation time is extended up to 30 milliseconds but observed that the steady puddle is attained by 10 ms for the selected range of process conditions. Distance 'XY' from USM to DSM at the nozzle wall and corresponding length in the high speed image are nearly same and equal to 2 mm [7]. Simulations are carried out for the experimental process conditions mentioned by Srinivas et al. [8] to study the flow dynamics by varying the process parameters such as ejection pressure (P), nozzle wheel gap (G) and wheel speed (V).
Fig.2. VOF contour of the melt puddle at P=9.8kPa, w: 0.5 mm, V: 17 m/s, G: 0.2 mm, (CD= Nozzle Slit).
3.1 Pressure distribution in the puddle at various ejection pressures Fig. 3(a) to (c) shows the pressure contours superimposed with USM and DSM of the puddle simulated for different ejection pressures of P=9.8 kPa, P=29.42 kPa and P=68 kPa respectively, other process parameters were kept constant at w: 0.5 mm, V: 17 m/s and G: 0.2 mm. Points 1, 2, 3 shown are the position of pressure contours outside, at and inside of the USM, respectively. Point 4 is the position of maximum pressure on the wheel. Points 5, 6, 7 are the position of pressure contours inside, at and outside of the DSM, respectively. The pressure values obtained from simulation at points 1 – 7 are given in table 2.
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Fig.3. Outline of the melt puddles superimposed with pressure contours at ejection pressures; (a) P=9.8kPa. (b) P=29.4 kPa, (c) P=68 kPa (d) Enlarged view of pressure contours for 68 kPa, superimposed with path lines and velocity vectors colored by phase. Other process parameters are ; w: 0.5 mm, V: 17 m/s, G: 0.2 mm. Table 2: Pressure distribution in the puddle
P (kPa)
P1 (kPa)
P2 (kPa)
P3 (kPa)
9.8
0.7
2 .1
3 .6
29.42
0.7
2.1
3.6
68
0.7
2 .1
3 .6
P4 (kPa) 56.4 60 90
P5 (kPa)
P6 (kPa)
P7 (kPa)
-3.6
-2.1
-0.7
-3.6
-2.1
-0.7
-3.5
-2.1
-0.7
P1 to P7 are the pressures at points 1 to 7 respectively. It is interesting to note that the pressures at points 1, 2 and 3 and at 5, 6 and 7 are equal for ejection pressures, selected for the present investigation. This is because of the stability attained by the puddle within 30 ms. Pressure at point 4 (Table 2) increases with ejection pressure and leads to increase in spread of melt on the wheel. It is interesting to observe that the pressure at points 1 and 7, 2 and 6, and 3 and 5 are equal in magnitude, irrespective of the ejection pressure. Positive and negative pressures in the puddle represent rise and drop in pressure respectively, as in the case of a plain Couette flow condition. As the wheel is rotating in the clockwise direction, it imparts acceleration on the melt to the right of point 4 and deceleration on the melt to the left of point 4. Deceleration causes increase in pressure and acceleration causes decrease in pressure. Hence, positive and negative pressures with equal magnitude are observed at upstream and downstream meniscus respectively. Fig. 4(a - c) shows the pressure profile at the melt wheel contact for the contours shown in Fig.3(a - c) respectively. Bigger puddle is observed to form with increase in ejection pressure due to increase in reaction pressure at the melt wheel contact. With increase in puddle size more amount of melt is accumulated in the puddle which acts as a reservoir for the ribbon formation. This results in obtaining thicker ribbons and affects the amorphous phase formation. Fig. 4(a) shows the path lines and velocity vectors super imposed on the pressure contours. Another pressure concentration is observed in the puddle near the USM, where the flow reversal is observed due to wheel rotation. With increase in ejection pressure, higher reaction pressure at point 4 may lead to blow out of melt at USM for few cases. This melt blow out at USM has been observed by Srinivas et al.[7] with further increase in ejection pressure to 68.6 kPa keeping other process conditions constant. Fig. 4 (b) shows similar melt blow out condition when the simulation is performed at the same process conditions.
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(b) Fig. 4 (a) Enlarged view of pressure contours for 68 kPa, superimposed with path lines and velocity vectors coloured by phase (b) Simulated puddle at 68.6 kPa showing melt blow-out towards USM.
3.2 Path lines in the puddle for various Nozzle-Wheel gaps Path lines of the melt and air in the entire domain are presented, varying the nozzle wheel gap from 0.2 mm to 1 mm. To distinguish between the air and melt phases, the outlines of upstream meniscus (USM) and downstream meniscus (DSM) of melt puddle are superimposed on the path lines. Path lines clearly show the recirculation in the melt puddle and air on both sides of the nozzle slit.
Fig.5. Series of melt puddles simulated up to a time interval of 30 ms superimposed with path lines in the air domain by varying the nozzle wheel gap G as (a) 0.2 mm (b) 0.3 mm (c ) 0.5 mm (d) 0.6 mm (e) 1 mm. Other process parameters are: P=9.8 kPa, T=1500 K, V=17 m/s, w=0.5 mm.
It is observed from Fig. 5(a-c) that the melt spreads more towards the right of nozzle slit up to the gap 0.5 mm, which is equal to the slit width. The recirculation towards DSM increases with gap up to 0.5 mm. With the increase of nozzle wheel gap to 0.6 mm, the recirculation increases towards USM, whereas it decreases towards DSM. The DSM recedes towards nozzle slit and USM moves away as shown in Fig. 5(d). Further increase of gap to 1 mm, the DSM almost starts from the slit boundary with no recirculation zone and the flow becomes normal to the wheel surface. The situation resembles Free Jet Melt Spinning (FJMS) process where the puddle is not guided by the nozzle-wheel gap. Thomas J. Praisner et al. [9] has experimentally found that in case of Pb-Sn alloy, the transition from PFMS to FJMS occurs when the nozzle wheel gap is above 1mm for a 1.43mm slit width of nozzle. FJMS process is suitable only when flaky ribbons are required, as continuous ribbons with high dimensional tolerance cannot be achieved.
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3.3 Puddle formation and instantaneous mass flow rate at various wheel speeds Fig. 6a & 6b shows the formation of puddles simulated for a wheel speeds (V) of 34 m/s and 51 m/s respectively. Other process parameters for these cases are kept constant at: w: 0.5 mm, P: 9.8 kPa G: 0.2 mm, T: 1500 K. Fig. 2a shows the puddle formed for a wheel speed of 17 m/s keeping other process parameters as constant. Severe oscillation of the downstream meniscus were reported to be noticed [8] during processing at the wheel speed of 51 m/s. The slope of the boundary lines (melt and air) from both sides of the puddle increases with wheel speed resulting in the formation of stiffer upstream and downstream meniscus. Fig. 7a, b and c depict the corresponding difference in stream function distribution of the melt along the wheel surface at 30 ms, when the wheel velocity is at 17 m/s, 34 m/s and 51 m/s respectively. Fig. 7 (a) shows increase in flow rate from 1.5 to 2.1 kg/s and further increase to 3.3 kg/s gradually. For a wheel speed of 34 m/s, a sharp rise in the flow rate from 2.7 kg/s to 4 kg/s on the wheel surface can be observed .
Fig.6. The melt puddles simulated by varying the wheel velocity; (a)V= 34m/s, (b) V=51 m/s. Other process parameters are P=9.8 k Pa, T=1373 K, w: 0.5 mm, G: 0.2 mm.
This is followed by a gradual increase in its value from 4 kg/s to 4.66 kg/s and then remains constant as shown in Fig. 7b. For higher wheel speeds of 51 m/s, a steep rise from 2.4 kg/s to 4.5 kg/s is observed below the nozzle slit, followed by oscillations in the stream function as shown in Fig. 7c. It is observed from the stream function ( instantaneous mass flow rate) graphs that melt removal rate from the puddle increases with increase in wheel speed. This, eventually, results in less amount of melt in the puddle and discontinuous ribbons. Further increase in wheel speed leads to the oscillation of DSM which is observed during experiments and ribbons so obtained are of streak topography (Srinivas et al., [8]) which are not suitable for transformer core applications. Also the present authors [10] have observed that the air entrainment at higher wheel speeds lead to ribbons of streak pattern.
Fig.7. Difference of stream function distribution (instantaneous mass flow rate) of the melt along the wheel surface corresponding to wheel speeds at (a) 17 m/s ,(b) 34 m/s and (c) 51 m/s , at 30 ms .
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4. Conclusions A two dimensional numerical model is used to study the flow dynamics in the puddle during planar flow melt spinning (PFMS) process at different conditions and correlated with the experimental observations. The following inferences are drawn from the analysis which helps the experimentalists to understand the flow dynamics in the puddle thereby carefully select the ejection pressure, nozzle wheel gap and wheel speed for a successful cast. • • •
Pressure profiles show that the melt blows out at higher ejection pressures. Hence, lower operating pressures are preferred for a successful cast. Path lines show that with increase in nozzle-wheel gap more than slit-width, planar flow melt spinning (PFMS) process is transformed to free jet melt spinning (FJMS) process resulting in flaky ribbons. The operable limit of the nozzle-wheel gap selected is to be less than the slit-width. Sharp rise in the difference of stream function at higher wheel speeds shows higher melt removal rate resulting in smaller puddle and oscillations. Moderate wheel speeds are to be selected to avoid ribbons of streak pattern and obtain a stable puddle thereby a good quality ribbon.
Acknowledgements Authors thank the organizations DMRL Hyderabad, JNTUH Hyderabad for the collaboration to carry out the research under DRDO Proj. No. ERIP /ER/1103966/M/01/1455. One of the author1 sincerely thank Dr. S.V. Kamat, Sc. ‘H’, Director, DMRL for his support during the research work and Dr Bhaskar Majumdar Sc. ‘F’ for sparing his time for the technical discussions. Appendix: Equations used in the Model Properties in the control volume cell are calculated as below: ρ = ρmF+ρa (1 - F) μ = μmF+ μa(1 - F) Cp = Cp, m F+ Cp, a (1 - F) k = k mF+ k a(1 - F)
(2)
Where the suffix ‘a’ denotes air and ‘m’ denotes melt and F is the volume fraction of the melt in the cell. F= 1 for melt and F= 0 for air. Governing equations: Continuity equation: ∂ρ/∂t + ∂(ρui)/∂xi=0
------
(3)
-----
(4)
Momentum equation: ∂ (ρui)/∂t+ ∂ (ρuiuj)/ ∂xj = -∂p/∂xi+ (∂/∂xj) [ [µ[∂ui/∂xj +∂uj/∂xi)] +ρgi + f
Where f is the volume force term in the momentum equation resulting from surface tension, given by f = (ρk∇F) / [(1/2) (ρa+ρm)] and k is the curvature and given by k = - ∇[ ∇F/|∇F| ]
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Energy conservation equation: ∂ (ρCpT)/∂t +∂ (ρCpuiT)/ ∂xi= (∂/∂xi )(K(∂T/∂xi))
------------
(5)
-------------
(6)
Volume fraction equation: (∂F/∂t) + ui (∂F/∂xi )= 0 References [1] Gong, Z., Wilde P., Matthys E.F., Int. J Rapid Soldf. 6 (1991) 1-28. [2] Wang, G.X., Matthys, E.F., Mater. Sci. Eng., 10 (2002) 35-55. [3] Heping Liu, Wenzhi Chen, Shengtao Qui and Guodong Liu, Metall. Mater. Trans.B, 40 (2009) 411-429. [4] Upadhya, G., Stefanescu, D.M., Mater. Sci. Eng. A, 158(1992) 215 – 226. [5] Wu. S.L, Chen. C.W, Hwang. W.S and Yang. C.C, Appl. Math. Modell. 16(1992) 394-403. [6] Bussmann. M, J. Mostaghimi a, D.W. Kirk b, J.W. Graydon bM.Haddas-S, Int. J Heat Mass Trans., 45(2002) 3997–4010. [7] Majumdar. B, Sowjanya. M, Srinivas. M, D.A.Babu, T.Kishen Kumar Reddy, Trans. Indian Inst. Met., 65(2012) 841-847. [8] M. Srinivas, B. Majumdar, G. Phanikumar, and D. Akhtar, Metall. Mater. Trans. B, 42(2011) 370-379. [9] Thomas J. Praisner, Jim s.-J. Chen and Ampere A. Tseng, Metall. Mater. Trans. B, 26(1995) 1995-1199. [10] Sowjanya M., Kishen Kumar Reddy T., Srivathsa B., and Majumdar B. , Appl. Mech. Mater. 446-447(2014) 352-355.
ScienceDirect Materials Today: Proceedings 4 (2017) 3728–3735
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Flow Dynamics in the Melt Puddle during Planar Flow Melt Spinning Process Sowjanya M.a, * and Kishen Kumar Reddy T.b a
Muffakham Jah College of Engineerng and Technology, Hyderabad,500034, India Jawaharlal Nehru Technological University Hyderabad, Hyerabad, 500085, India
b
Abstract Quality of amorphous ribbons obtained during planar flow melt spinning process depends highly on the dynamics of the melt puddle. The present study investigates the flow dynamics using pressure profiles, path lines and stream function. Pressure profiles help in predicting the melt blow-out. Transformation of planar flow melt spinning to free jet melt spinning can be observed using path lines in the puddle. Oscillations in the puddle can be traced by the stream function at the melt wheel contact. The analysis helps the experimentalists to carefully select the ejection pressure, wheel speed and nozzle-wheel gap to obtain a quality ribbon. ©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:Planar Flow Melt spinning; Puddle dynamics; Path lines; Stream Function; Melt Puddle.
1. Introduction Amorphous ribbons are produced directly from molten alloy by the rapid solidification technique called 'Planar flow melt spinning process (PFMS)' Fig. 1a schematically shows the formation of ribbon upon ejection of melt on a cooling wheel in the PFMS process. Fig. 1b shows the puddle formation with upstream (USM) and downstream meniscus (DSM) between the nozzle-wheel gap. Gong et al. [1] reported that the quality of amorphous ribbon by PFMS process depends on the shape and stability of the melt puddle formed between the nozzle and the rotating
* Corresponding author. Tel.: +91-9492932682; fax: +91-40-24342010. E-mail address:[email protected] 2214-7853©2017 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
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copper wheel. Wang et al. [2] revealed that the fluid dynamics (heat and mass transfer) controls the stability of the puddle which in turn dictates the PFMS process. Experimental investigation of the melt puddle during the process is difficult due to high operating speeds. However, numerical simulations can be employed to observe the flow dynamics in the melt puddle at very small time steps of few micro-seconds. Liu et al. [3] presented a numerical model to simulate the initial puddle formation for a successful set of process parameters. Upadhya and Stefanescu [4] considered flat wheel surface and predicted the shape of the puddle to be parabolic and observed the crystallization at lower wheel speeds for Fe-3wt%B alloy. Wu et al. [5] developed a 2D model and suggested that a low negative pressure at the rear side of the puddle (upstream meniscus) is developed which reduces the non contact area at the melt substrate interface. Bussmann et al.[6] and Liu et al.[3] reported that the stability of the melt puddle was attained by 10 ms in the numerical simulation. Present authors (Majumdar et al. [7]) used a 2D, time dependent numerical model to simulate the puddle formation at various ejection pressures, nozzle wheel gap and validated with experimental results obtained by Srinivas et al. [8]. The present work is an extended numerical investigation of the flow dynamics of the corresponding melt puddles. Nomenclature F P Ud T Tg Cp ρ
volume fraction pressure wheel speed temperature glass transition temperature specific heat density
[-] [kPa.] [m/s] [K] [K] [J/kgK] [Kg/m3]
µ k g σ w G
dynamic viscosity thermal conductivity gravitational acceleration surface tension slit width Nozzle-wheel gap
[Pa.s] w/mK [m/s2] [N/m] mm mm
2. Numerical Model Fig. 1(b) shows the domain considered for the simulations between the flat bottom of nozzle (BE) and wheel surface (GH). Fig. 1c shows the quad mesh created in the domain. BC and DE are nozzle walls and CD represents nozzle slit opening. Regions AB, EF, AG & FH represent surrounding atmospheric air conditions. Volume of fluid technique along with conservation equations are solved to simulate the puddle formation. Assumptions and Boundary conditions All the wall surfaces employ the no slip boundary condition to impose the boundary layer flow. Wheel surface is at constant temperature of 300 K and smooth. Nozzle walls are made of quartz and hence no heat flux. Latent heat is neglected due to the formation of amorphous phase in the ribbon. Radiation heat loss is less and hence neglected. All the properties are constant with temperature. Melt viscosity is calculated using equation (1). Melt enters the domain with specified pressure and temperature through CD (inlet boundary). Wall GH is at constant temperature of 300 K and moving with the given speed. Nozzle walls BC and DE are stationary wall boundaries with no heat flux. AB, EF and AG are the pressure inlet boundaries to simulate the presence of surrounding air. Domain outlet FH is the pressure outlet boundary. Table 1 gives the amorphous material properties used for the present model and eqn.(1) gives the temperature dependent viscosity equation (Liu et al. [3]) is used for the melt.
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Fig. 1 Schematic diagram of a) planar flow melt spinning process and b) melt puddle formation c) Two dimensional mesh of air domain (AFHGA) between nozzle and wheel, (G=0.3 mm, w=0.3 mm) .
µ(T) = -0.1(exp (3.6528 + 734.1/ (T - 674))).
(1)
Table1. Properties of molten alloy (Fe-Si-B) used in the model. Designation ρ Cp K μ σ
Parameters Density Specific heat Thermal conductivity Viscosity Surface Tension
Values 7180 kgm-3 544 Jkg-1K-1 8.99 W/mK μ(T) 1.2 N/m
3. Results and Discussions Fig 2 shows a study puddle at 10 ms by simulating the puddle at the same set of process parameters at which high speed image is presented [8]. In the present study simulation time is extended up to 30 milliseconds but observed that the steady puddle is attained by 10 ms for the selected range of process conditions. Distance 'XY' from USM to DSM at the nozzle wall and corresponding length in the high speed image are nearly same and equal to 2 mm [7]. Simulations are carried out for the experimental process conditions mentioned by Srinivas et al. [8] to study the flow dynamics by varying the process parameters such as ejection pressure (P), nozzle wheel gap (G) and wheel speed (V).
Fig.2. VOF contour of the melt puddle at P=9.8kPa, w: 0.5 mm, V: 17 m/s, G: 0.2 mm, (CD= Nozzle Slit).
3.1 Pressure distribution in the puddle at various ejection pressures Fig. 3(a) to (c) shows the pressure contours superimposed with USM and DSM of the puddle simulated for different ejection pressures of P=9.8 kPa, P=29.42 kPa and P=68 kPa respectively, other process parameters were kept constant at w: 0.5 mm, V: 17 m/s and G: 0.2 mm. Points 1, 2, 3 shown are the position of pressure contours outside, at and inside of the USM, respectively. Point 4 is the position of maximum pressure on the wheel. Points 5, 6, 7 are the position of pressure contours inside, at and outside of the DSM, respectively. The pressure values obtained from simulation at points 1 – 7 are given in table 2.
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Fig.3. Outline of the melt puddles superimposed with pressure contours at ejection pressures; (a) P=9.8kPa. (b) P=29.4 kPa, (c) P=68 kPa (d) Enlarged view of pressure contours for 68 kPa, superimposed with path lines and velocity vectors colored by phase. Other process parameters are ; w: 0.5 mm, V: 17 m/s, G: 0.2 mm. Table 2: Pressure distribution in the puddle
P (kPa)
P1 (kPa)
P2 (kPa)
P3 (kPa)
9.8
0.7
2 .1
3 .6
29.42
0.7
2.1
3.6
68
0.7
2 .1
3 .6
P4 (kPa) 56.4 60 90
P5 (kPa)
P6 (kPa)
P7 (kPa)
-3.6
-2.1
-0.7
-3.6
-2.1
-0.7
-3.5
-2.1
-0.7
P1 to P7 are the pressures at points 1 to 7 respectively. It is interesting to note that the pressures at points 1, 2 and 3 and at 5, 6 and 7 are equal for ejection pressures, selected for the present investigation. This is because of the stability attained by the puddle within 30 ms. Pressure at point 4 (Table 2) increases with ejection pressure and leads to increase in spread of melt on the wheel. It is interesting to observe that the pressure at points 1 and 7, 2 and 6, and 3 and 5 are equal in magnitude, irrespective of the ejection pressure. Positive and negative pressures in the puddle represent rise and drop in pressure respectively, as in the case of a plain Couette flow condition. As the wheel is rotating in the clockwise direction, it imparts acceleration on the melt to the right of point 4 and deceleration on the melt to the left of point 4. Deceleration causes increase in pressure and acceleration causes decrease in pressure. Hence, positive and negative pressures with equal magnitude are observed at upstream and downstream meniscus respectively. Fig. 4(a - c) shows the pressure profile at the melt wheel contact for the contours shown in Fig.3(a - c) respectively. Bigger puddle is observed to form with increase in ejection pressure due to increase in reaction pressure at the melt wheel contact. With increase in puddle size more amount of melt is accumulated in the puddle which acts as a reservoir for the ribbon formation. This results in obtaining thicker ribbons and affects the amorphous phase formation. Fig. 4(a) shows the path lines and velocity vectors super imposed on the pressure contours. Another pressure concentration is observed in the puddle near the USM, where the flow reversal is observed due to wheel rotation. With increase in ejection pressure, higher reaction pressure at point 4 may lead to blow out of melt at USM for few cases. This melt blow out at USM has been observed by Srinivas et al.[7] with further increase in ejection pressure to 68.6 kPa keeping other process conditions constant. Fig. 4 (b) shows similar melt blow out condition when the simulation is performed at the same process conditions.
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(b) Fig. 4 (a) Enlarged view of pressure contours for 68 kPa, superimposed with path lines and velocity vectors coloured by phase (b) Simulated puddle at 68.6 kPa showing melt blow-out towards USM.
3.2 Path lines in the puddle for various Nozzle-Wheel gaps Path lines of the melt and air in the entire domain are presented, varying the nozzle wheel gap from 0.2 mm to 1 mm. To distinguish between the air and melt phases, the outlines of upstream meniscus (USM) and downstream meniscus (DSM) of melt puddle are superimposed on the path lines. Path lines clearly show the recirculation in the melt puddle and air on both sides of the nozzle slit.
Fig.5. Series of melt puddles simulated up to a time interval of 30 ms superimposed with path lines in the air domain by varying the nozzle wheel gap G as (a) 0.2 mm (b) 0.3 mm (c ) 0.5 mm (d) 0.6 mm (e) 1 mm. Other process parameters are: P=9.8 kPa, T=1500 K, V=17 m/s, w=0.5 mm.
It is observed from Fig. 5(a-c) that the melt spreads more towards the right of nozzle slit up to the gap 0.5 mm, which is equal to the slit width. The recirculation towards DSM increases with gap up to 0.5 mm. With the increase of nozzle wheel gap to 0.6 mm, the recirculation increases towards USM, whereas it decreases towards DSM. The DSM recedes towards nozzle slit and USM moves away as shown in Fig. 5(d). Further increase of gap to 1 mm, the DSM almost starts from the slit boundary with no recirculation zone and the flow becomes normal to the wheel surface. The situation resembles Free Jet Melt Spinning (FJMS) process where the puddle is not guided by the nozzle-wheel gap. Thomas J. Praisner et al. [9] has experimentally found that in case of Pb-Sn alloy, the transition from PFMS to FJMS occurs when the nozzle wheel gap is above 1mm for a 1.43mm slit width of nozzle. FJMS process is suitable only when flaky ribbons are required, as continuous ribbons with high dimensional tolerance cannot be achieved.
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3.3 Puddle formation and instantaneous mass flow rate at various wheel speeds Fig. 6a & 6b shows the formation of puddles simulated for a wheel speeds (V) of 34 m/s and 51 m/s respectively. Other process parameters for these cases are kept constant at: w: 0.5 mm, P: 9.8 kPa G: 0.2 mm, T: 1500 K. Fig. 2a shows the puddle formed for a wheel speed of 17 m/s keeping other process parameters as constant. Severe oscillation of the downstream meniscus were reported to be noticed [8] during processing at the wheel speed of 51 m/s. The slope of the boundary lines (melt and air) from both sides of the puddle increases with wheel speed resulting in the formation of stiffer upstream and downstream meniscus. Fig. 7a, b and c depict the corresponding difference in stream function distribution of the melt along the wheel surface at 30 ms, when the wheel velocity is at 17 m/s, 34 m/s and 51 m/s respectively. Fig. 7 (a) shows increase in flow rate from 1.5 to 2.1 kg/s and further increase to 3.3 kg/s gradually. For a wheel speed of 34 m/s, a sharp rise in the flow rate from 2.7 kg/s to 4 kg/s on the wheel surface can be observed .
Fig.6. The melt puddles simulated by varying the wheel velocity; (a)V= 34m/s, (b) V=51 m/s. Other process parameters are P=9.8 k Pa, T=1373 K, w: 0.5 mm, G: 0.2 mm.
This is followed by a gradual increase in its value from 4 kg/s to 4.66 kg/s and then remains constant as shown in Fig. 7b. For higher wheel speeds of 51 m/s, a steep rise from 2.4 kg/s to 4.5 kg/s is observed below the nozzle slit, followed by oscillations in the stream function as shown in Fig. 7c. It is observed from the stream function ( instantaneous mass flow rate) graphs that melt removal rate from the puddle increases with increase in wheel speed. This, eventually, results in less amount of melt in the puddle and discontinuous ribbons. Further increase in wheel speed leads to the oscillation of DSM which is observed during experiments and ribbons so obtained are of streak topography (Srinivas et al., [8]) which are not suitable for transformer core applications. Also the present authors [10] have observed that the air entrainment at higher wheel speeds lead to ribbons of streak pattern.
Fig.7. Difference of stream function distribution (instantaneous mass flow rate) of the melt along the wheel surface corresponding to wheel speeds at (a) 17 m/s ,(b) 34 m/s and (c) 51 m/s , at 30 ms .
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4. Conclusions A two dimensional numerical model is used to study the flow dynamics in the puddle during planar flow melt spinning (PFMS) process at different conditions and correlated with the experimental observations. The following inferences are drawn from the analysis which helps the experimentalists to understand the flow dynamics in the puddle thereby carefully select the ejection pressure, nozzle wheel gap and wheel speed for a successful cast. • • •
Pressure profiles show that the melt blows out at higher ejection pressures. Hence, lower operating pressures are preferred for a successful cast. Path lines show that with increase in nozzle-wheel gap more than slit-width, planar flow melt spinning (PFMS) process is transformed to free jet melt spinning (FJMS) process resulting in flaky ribbons. The operable limit of the nozzle-wheel gap selected is to be less than the slit-width. Sharp rise in the difference of stream function at higher wheel speeds shows higher melt removal rate resulting in smaller puddle and oscillations. Moderate wheel speeds are to be selected to avoid ribbons of streak pattern and obtain a stable puddle thereby a good quality ribbon.
Acknowledgements Authors thank the organizations DMRL Hyderabad, JNTUH Hyderabad for the collaboration to carry out the research under DRDO Proj. No. ERIP /ER/1103966/M/01/1455. One of the author1 sincerely thank Dr. S.V. Kamat, Sc. ‘H’, Director, DMRL for his support during the research work and Dr Bhaskar Majumdar Sc. ‘F’ for sparing his time for the technical discussions. Appendix: Equations used in the Model Properties in the control volume cell are calculated as below: ρ = ρmF+ρa (1 - F) μ = μmF+ μa(1 - F) Cp = Cp, m F+ Cp, a (1 - F) k = k mF+ k a(1 - F)
(2)
Where the suffix ‘a’ denotes air and ‘m’ denotes melt and F is the volume fraction of the melt in the cell. F= 1 for melt and F= 0 for air. Governing equations: Continuity equation: ∂ρ/∂t + ∂(ρui)/∂xi=0
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(3)
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(4)
Momentum equation: ∂ (ρui)/∂t+ ∂ (ρuiuj)/ ∂xj = -∂p/∂xi+ (∂/∂xj) [ [µ[∂ui/∂xj +∂uj/∂xi)] +ρgi + f
Where f is the volume force term in the momentum equation resulting from surface tension, given by f = (ρk∇F) / [(1/2) (ρa+ρm)] and k is the curvature and given by k = - ∇[ ∇F/|∇F| ]
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Energy conservation equation: ∂ (ρCpT)/∂t +∂ (ρCpuiT)/ ∂xi= (∂/∂xi )(K(∂T/∂xi))
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(5)
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(6)
Volume fraction equation: (∂F/∂t) + ui (∂F/∂xi )= 0 References [1] Gong, Z., Wilde P., Matthys E.F., Int. J Rapid Soldf. 6 (1991) 1-28. [2] Wang, G.X., Matthys, E.F., Mater. Sci. Eng., 10 (2002) 35-55. [3] Heping Liu, Wenzhi Chen, Shengtao Qui and Guodong Liu, Metall. Mater. Trans.B, 40 (2009) 411-429. [4] Upadhya, G., Stefanescu, D.M., Mater. Sci. Eng. A, 158(1992) 215 – 226. [5] Wu. S.L, Chen. C.W, Hwang. W.S and Yang. C.C, Appl. Math. Modell. 16(1992) 394-403. [6] Bussmann. M, J. Mostaghimi a, D.W. Kirk b, J.W. Graydon bM.Haddas-S, Int. J Heat Mass Trans., 45(2002) 3997–4010. [7] Majumdar. B, Sowjanya. M, Srinivas. M, D.A.Babu, T.Kishen Kumar Reddy, Trans. Indian Inst. Met., 65(2012) 841-847. [8] M. Srinivas, B. Majumdar, G. Phanikumar, and D. Akhtar, Metall. Mater. Trans. B, 42(2011) 370-379. [9] Thomas J. Praisner, Jim s.-J. Chen and Ampere A. Tseng, Metall. Mater. Trans. B, 26(1995) 1995-1199. [10] Sowjanya M., Kishen Kumar Reddy T., Srivathsa B., and Majumdar B. , Appl. Mech. Mater. 446-447(2014) 352-355.