128 Dental Materials Journal 10(2): , 1991

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1 128 Dental Materials Journal 10(2): , 1991 Molten Titanium Flow in a Mesh Cavity by the Flow Visualization Technique Kouichi WATANABE*, Seigo OKAWA*, Osamu MIYAKAWA*, Syuji NAKANO*, Nobuhiro SHIOKAWA*, Masayoshi KOBAYASHI** *Dental Materials and Technology, School of Dentistry, Niigata University **EMX Laboratory, Niigata University, 5274, Gakkoucho-dori 2, Niigata 951, Japan Received on July 31, 1991 Accepted on September 28, 1991 The tracer element molten (TEM) method, which provides titanium flow visualization in a mold cavity, was applied to investigate the flow in a mesh pattern. When a pressure casting machine was used, most of the mesh rods were composed of many solidification layers, which implied that the flow was laminar and almost steady. When a centrifugal casting machine was used, the flow was almost irregular and a stack of solidification layers was observed in only a few segments. These results indicate that the flow was turbulent. In a complicated cavity, such as a mesh pattern, pressure rather than centrifugal force acts as an effective casting force. Therefore, in such a cavity, favorable castability can be achieved with high pressure and laminar flow. Key words: Titanium casting, Flow visualization, Mesh cavity INTRODUCTION Pure titanium has excellent bio-compatibility but has serious weak points, such as its high melting temperature (1,670 Ž) and chemical reactivity at high temperatures1). Under conventional conditions of dental titanium casting, the mold temperature is much lower than the melting temperature. Therefore, the rapidity with which the molten titanium enters and spreads throughout the mold cavity is one of the most important requirements for successful casting. In previous studies2,3), we obtained several findings regarding titanium flow by using the tracer element molten (TEM) method. Typical results were: 1) The flow velocity obtained by centrifugal casting was much larger than that obtained by pressure casting. 2) In a mold cavity, molten titanium moved as a laminar flow with pressure casting and as a turbulent flow with centrifugal casting. In clinical dental applications, complicated castings, such as cast plate dentures, must be produced. However, there are very few reports4,5) on titanium casting for such a complicated cavity. The purpose of this investigation was to elucidate the flow characteristics in a mesh cavity by using the flow visualization technique. Special emphasis was placed on the difference in flow behavior, which should depend upon whether the casting method was one of pressure or centrifugal force.

2 MOLTEN TITANIUM FLOW IN MESH CAVITY 129 MATERIALS AND METHODS A square wax pattern, composed of 64 open squares and 81 segments, was prepared using a commercial mesh pattern*. Although each segment was not exactly circular in section, it could be taken as a rod of 0.9mm diameter. Sprue, 3.3mm in diameter, was attached to the mesh pattern according to the spruing conditions shown in Fig. 1. A gold wire 0.1 ~0.2mm2 in cross section and a palladium wire 0.2 ~0.2mm2 in section, were inserted into the sprue. Each prepared pattern was attached to a suitable crucible former according to the casting type and was invested with ethyl silicate#. For centrifugal casting, the sprue stood with its axis tilted to 20 from the casting ring axis, since the molten titanium from the sprue was deflected at 20 by both Coriolis' force and the force arising from increasing rotational speed. After the application of heat shock, by which surplus alcohol in the mold was eliminated, the mold was heated in a burn-out furnace to 900 Ž in 3h, maintained for 1 h. at 900 Ž, and cooled to room temperature in the furnace. Pure titanium was cast by either a titanium pressure casting machine or a centrifugal one&. Most conditions were in accordance with the manufacturer's instructions, other than the mold temperature for the pressure casting, and the investment material for the centrifugal casting. After sandblast was applied to the casting, it was chemically etched with cleaning solution at Ž for 90s. This etching can remove a surface layer 0.015mm in thickness, including the stained oxide layer. Each mesh casting was ground to half of its original diameter with emery papers and the emergent longitudinal sections were analyzed through an electron probe microanalyzer (EPMA)@ equipped with an H II mapping system. Step width was 0.048mm for the macroscopic observation, and some partial annalyses were also carried out under magnification. The tracer element molten method2), with is a flow visualization technique, is carried out through the following steps. Tracer element wires, gold and palladium wire, are inserted into a suitable portion of a wax sprue prior to the burn-out operation. When the molten titanium reaches the insert position, the wire is melted and the tracer is carried away by the titanium, as a result of which the tracer element is scattered in the casting. After solidification, the tracer concentration at each position is detected with an electron probe microanalyzer and thus the configuration of titanium flow is observable. The relationship between the tracer content and the time order of inflow is assumed to be as follows: The first part of the influx (first inflow) contains neither Au nor Pd because the flow front passes the inserted wires before they melt. The portion which contains only Au indicates the next influx (second inflow) because the melting point of Au (1,063 Ž) is much lower than that of Pd (1,550 Ž). The third part of the influx

3 130 K. WATANABE, S. OKAWA, O. MIYAKAWA, S. NAKANO, N. SHIOKAWA, M. KOBAYASHI (third inflow) contains Pd. The last part contain neither Au nor Pd, since the inserted wires are exhausted. RESULTS Figure 2 shows the flow configurations in the mesh casting (Type I) which was cast through the pressure casting machine. The sprue was attached at the center of this casting and is indicated as the white circle. Photos, A and B, are elemental mappings of Au and Pd, respectively. Microanalyses, C and D, are mappings at the portion, p, in photo A. Analyses under large magnification are shown in photos E and F, both of which are of the portion indicated by the arrow in photo A. Macroscopic analyses (photos A and B) show that the flow configurations as well as the casting itself possess an axis of symmetry that is four-fold with respect to the sprue direction. The first inflow has reached the farthest areas in each direction of the mesh casting. From photos C and D, early inflows have solidified in the outer layers of each mesh rod. Many well-ordered layers are observed in photos E and F. These facts indicate laminar and steady flow. Figure 3 shows the flow configurations in the mesh casting (Type I) which was cast through the centrifugal casting machine. The sprue was attached at the center of this casting and is indicated as the white circle. The rotational direction in this figure is from left to richt. Photos, A and B, are elemental mappings of Au and Pd, respectively. Microanalyses, C and D, are mappings at portions q and r, respectively, in photo A. Analyses with large magnification are shown in Photos E and F, which are the portions indicated by the arrows, X and Y, respectively, in photo C. Macroscopic analysis shows that the distributions of both tracer elements, as well as the casting itself, are irregular. That is, the first inflow has not necessarily reached thefarthest areas, but has solidified in random portions (dark areas in both photos). Fig. 1 Two types of spruing conditions, perpendicular to the mesh plane (Type I) and parallel to it (Type II). A gold and a palladium wire were inserted at the positions indicated by the arrows.

4 MOLTEN TITANIUM FLOW IN MESH CAVITY 131 Fig. 2 Distribution maps of tracer elements in mesh casting through the pressure type machine: Microanalyses, C and D, are the results at portion p in photo A. Photos, E and F, are the results of microanalysis of the portion indicated by the arrow in photo A. Magnifying power can be seen as a line gap at the left corner of the top in each photo.

5 132 K. WATANABE, Fig. 3 S. OKAWA, O. MIYAKAWA, S. NAKANO, N. SHIOKAWA, M. KOBAYASHI Distribution maps of tracer elements in mesh casting through the centrifugal type machine: Microanalyses, C and D, are the results at portions q and r respectively, in photo A. Photos E and F are the results of microanalysis of the portions indicated by the arrows, X and Y, respectively, in photo C.

MOLTEN TITANIUM FLOW IN MESH CAVITY 133 Fig. 4 Pd distribution maps of mesh casting: The castings in photos A and C were obtained by pressure casting and centrifugal casting, respectively.

6 MOLTEN TITANIUM FLOW IN MESH CAVITY 133 Fig. 4 Pd distribution maps of mesh casting: The castings in photos A and C were obtained by pressure casting and centrifugal casting, respectively. Photos B and D are the results of microanalysis of portion s in photo A and portion t in photo C, respectively. This is because the flow is, to a certain extent, random. In photos C and D, some concave portions are found on the surface of the casting rod; this was due to both low internal pressure and pressure fluctuation. As seen in photo D, the content level of the tracer element (Pd) is homogeneous in each area. This is directly attributable to the turbulent flow, in which mixing and large scale diffusion take place. Furthermore, the content level of each area is discontinuous at the boundary, in spite of liquid-to-liquid contact (photos D and F). This concentration gap is probably due to a solidified film or thin oxide layer on the surface of each liquid portion. As shown in photo E, there are a few areas which are composed of some layers. Figure 4 shows the flow configurations of Pd in the mesh castings (Type II). The Au distribution maps are omitted since they merely provide information similar to that for Pd. Photo A is of a cast through the pressure casting machine and photo C is of a

7 134 K. WATANABE, S. OKAWA, O. MIYAKAWA, S. NAKANO, N. SHIOKAWA, M. KOBAYASHI cast through the centrifugal one. Microanalyses, B and D, are mappings of the portions s in photo A and t in photo C, respectively. As indicated by the arrows, the sprue of each casting was attached at the center of the bottom segment and the direction of the sprue was parallel to the plane of the mesh. Photo A shows that, while the casting was almost symmetrical with respect to the sprue direction, the Pd distribution is somewhat asymmetric. This is probably due to the deviation of the inserted palladium wire from the center of the sprue. Analogous to Fig. 3 B, solidification areas of early inflows (dark portions) seen in photo C have been scattered at random in the mesh casting. The centrifugal force has acted from bottom to top in this photo, but the influence on flow configuration cannot be observed directly. Similarly to Fig. 3 D, the neighboring areas show a concentration gap in spite of the collision between the two streams. In contrast to this, Pd concentration changes smoothly in the region where the two streams are mixed in photo B. DISCUSSION Flow change at entrance zone to the mesh cavity The cross-section of each segment of the mesh pattern can be taken as a circle 0.9 mm in diameter, the area of which is less than one-tenth that of the sprue. When the molten titanium entered such a fine cavity, the flow velocity suddenly dropped and this was accompanied by a rise in pressure, depending on the kinetic energy change6), as shown in the schematic illustration in Fig. 5. With pressure casting, the ratio of the velocity (Up) drop is relatively low compared to that for centrifugal casting because of the smaller friction loss of the laminar flow8). The pressure (Pp) level, nevertheless, is significantly high, since high argon pressure is applied to the molten titanium as a casting pressure and is effectively transmitted throughout the fluid. With centrifugal casting, when the first inflows flow into the fine cavity, the velocity drops to a large extent, since the resistance factor is strongly dependent on the velocity9). Such a velocity drop causses a significant increase in pressure due to transformation of the momentum involved. The resulting pressure, however, did not reach very high levels since the original pressure, which arises only from the liquid pressure associated with both the density and the centrifugal force in the sprue, was lower. Flow behavior produced in the mesh cavity by pressure casting As seen in Fig. 5, pressure is effectively transmitted in the fluid, so that an appreciably high pressure is maintained even in the mesh cavity. As a result, the flow velocity does not drop so quickly because of continuous acceleration produced by such pressure. Consequently, the pressure casting machine permits the molten titanium to flow more widely than the centrifugal casting machine. Another important aspect of the nature of this flow behavior is its laminar flow, which implies less frictional loss of kinetic energy. In this case, each fluid part proceeds

8 MOLTEN TITANIUM FLOW IN MESH CAVITY 135 Fig. 5 Schematic illustration of changes in the velocity and pressure of the fluid in the early stage of casting: The abscissa indicates the distance from a mold crucible. The terminal portion of the sprue is regarded as a quasi stagnatiop area where the pressure is maximum. With the pressure casting, the velocity Up, as well as the pressure Pp, is maintained at a significantly high level even in the mesh cavity. With the centrifugal casting, although the velocity Uc (mean value) in the sprue is larger than Up, it decreases quickly because of the high rate of resistance losses. In addition, the pressure Pc level is insufficient to accelerate the movement of the fluid throughout the casting process. Note that the Bernoulli's equation is invalid around the entrance zone because the friction loss cannot be reasonably evaluated7), that the contribution of gravity is entirely negligible, that even the centrifugal force makes small contributions to accelerate the fluid movement in a mesh cavity, and that, in the later stages of casting, this illustration is inadequate to explain the flow behavior, since the velocity produced by centrifugal casting, even in the sprue, becomes very low. smoothly along a simple well-defined path10). Therefore in most areas, there are many solidification layers, which are clearly observed in Fig. 2 E and F. Flow behavior produced in the mesh cavity by centrifugal casting When the molten titanium enters the mesh cavity, the Reynolds number ought to be reduced appreceably11) because of the velocity drop and smaller dimension. Various small eddies of turbulence, however, could not be diminished so quickly, so that the flow

9 136 K. WATANABE, S. OKAWA, O. MIYAKAWA, S. NAKANO, N. SHIOKAWA, M. KOBAYASHI retained its random fluctuation. In such a state, the flow velocity (U) is generally divided into two parts12) as follows: U=U0+u where U0 is a mean velocity and u is a fluctuating velocity. If the u is zero, the flow is laminar. In a turbulent flow, u is significantly large and is the decisive factor in the flow characteristics, as follows: (1) The fluctuating part causes changes in the direction in which the flow is proceeding: If mean velocity becomes small, the fluctuation part u becomes relatively large and the flow direction even changes randomly. Consequently, the flow path was changed irregularly so that the early inflows solidified at random portions in the mesh casting (Figs. 3A and 4C). (2) The fluctuating part affects the shape of the solidification layer: Even near the entrance zone where the pressure is relatively high, the solidification layer is not uniform, but wavy (Fig. 3C). This is because the layer thickness depends on the local velocity, which changes randomly due to u. When the pressure becomes small, concave surfaces even developed (Fig. 3D). (3) The fluctuating part causes an increase in net viscosity and thermal conductivity: The net viscosity of the turbulent flow is the sum of the liquid viscosity of the molten titanium itself and the eddy viscosity, which originates from the Reynolds stress in fluctuating motion12). As a result, the total viscosity is significantly large when compared to that of the laminar flow. In addition, random eddy motion causes an increase in thermal conductivity13), so that the molten titanium in the mold is liable to solidify quickly. Both properties lead to a rapid drop of the flow velocity and, consequently, castability in the mesh cavity is rather disadvantageous. CONCLUSIONS To investigate titanium flow behavior in a mesh cavity, a flow visualization technique, using a tracer element molten method, was applied. Special emphasis was placed on the difference in the flow characteristics arising from different casting methods, namely, centrifugal casting and pressure casting. During the course of this investigation, the following conclusions were reached. 1) With pressure casting, not only the castings, but also the flow configurations, were almost symmetrical with respect to the sprue direction. In addition, each segment was composed of many solidification layers which involved early inflows in the outer part and later inflows around the center of the rod. The surfaces of the castings were convex everywhere. These facts indicate that the flow was laminar and that sufficient pressure was maintained in the fluid until the moment of solidification. 2) With centrifugal casting, the flow configurations, as well as the castings, were irregular. That is, early inflows were solidified at random portions in each mesh casting. There was a marked tendency for the content of the tracer element to be uniform in any

10 MOLTEN TITANIUM FLOW IN MESH CAVITY 137 portion. Some concave areas were found on the surface of the castings. These facts indicate that the flow was turbulent and that internal pressure was relatively low, and as a result the flow velocity dropped quickly although the velocity in the sprue was high in the early stage. 3) In a complicated cavity such as a mesh pattern, favorable castability can be achieved with high pressure and laminar flow. REFERENCES 1) Ida, K., Togaya, T., Tsutsumi, s. and Takiuchi, M.: Effect of Magnesia Investments in the Dental Casting of Pure Titanium or Titanium alloys, Dent Mater J 1(1): 8-21, ) Watanabe, K., Okawa, S., Miyakawa, O., Nakano, S., Shiokawa, N. and Kobayashi, M.: Determination of Titanium Flow by the Tracer Element Molten Method in the Dental Precision Casting, 1. The Principle of Flow Visualization and Application to Simple Castings, J J Dent Mater 9(4): , (in Japanese) 3) Watanabe, K., Okawa, S., Miyakawa, O., Nakano, S., Shiokawa, N. and Kobayashi, M.: Research on Titanium Flow by the Tracer Element Molten Method in the Dental Precision Casting, 2. Relationship between the Titanium Flow in Plate Molds and the Casting Defects, J J Dent Mater 10(1): 77-96, (in Japanese) 4) Yamauch, M., Sakai, M. and Kawano, J.: Clinical Application of Pure Titanium for Cast Plate Denture, Dent Mater J 7(1): 39-47, ) Takahashi, J., Kimura, H., Lautenschlager, E.P., Chernlin, J.H., Moser, J.B. and Greener, E.H.: Casting Pure Titanium into Commercial Phosphate-bonded SiO2 Investment Molds, J Dent Res 69 (12): , ) Prandtl, L. and Tietjens, O.G.: Applied Hydro- and Aeromechanics, Dover Publications, Inc., New York, 1934, pp ) White, F.M.: Fluid Mechanics, 2nd ed., McGraw-Hill, New York, 1986, pp ) Goldstein, S.: Modern Developments in Fluid Dynamics, Dover Publications, Inc., New York, 1965, pp ) Schlichting, H.: Boundary-Layer Theory, Sixth ed., McGraw-Hill, New York, 1968, pp ) Tritton, D.J.: Physical fluid Dynamics, 2nd ed., Oxford University Press, Oxford, 1989, pp ) Tritton, D.J.: Physical fluid Dynamics, 2nd ed., Oxford University Press, Oxford, 1989, pp ) Tritton, D.J.: Physical fluid Dynamics, 2nd ed., Oxford University Press, Oxford, 1989, pp ) Kreith, F.: Principles of Heat Transfer, 2nd ed., International Textbook Company, Pennsylvania, 1965, pp

232 流れ可視化の一方法である標識元素溶解法を用いて, 層の重なりも僅かな部分でしか認められず,乱流であるメッシュパターン内のチタン溶湯の流れを検討したそことが分かったまた,メッシュパターンのような複雑の結果,差圧鋳造の場合,鋳造体のほとんどの部位で, な空洞

12 232 流れ可視化の一方法である標識元素溶解法を用いて, 層の重なりも僅かな部分でしか認められず,乱流であるメッシュパターン内のチタン溶湯の流れを検討したそことが分かったまた,メッシュパターンのような複雑の結果,差圧鋳造の場合,鋳造体のほとんどの部位で, な空洞では,鋳造力として,遠心力よりも圧力の方が有多くの凝固層の積み重なりが観察され,これは層流で効に作用していることが推定されるそのため,層流とあって,しかも流れが定常状態に近いことを示していして流れ,しかも高い圧力の時に鋳造性が良くなることた遠心鋳造の場合は,流れに殆ど規則性がなく,凝固が結論された

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