Numerical Simulation of the Investment Casting Process - American ...

Paper 05-160(04).pdf, Page 1 of 11 AFS Transactions 2005 © American Foundry Society, Schaumburg, IL USA

Numerical Simulation of the Investment Casting Process A. S. Sabau Oak Ridge National Laboratory, Oak Ridge, Tennessee Copyright 2005 American Foundry Society ABSTRACT Determining alloy shrinkage factors is very important for the investment casting process. Casting dimensions can be obtained from numerical simulations of heat transfer and deformation phenomena. The accuracy of the dimensional results depends on heat transfer results. In order to validate heat transfer models, temperature data were obtained during casting of aluminum alloy A356 in shell molds made of fused silica and a zircon prime coat. The airflow near mold surfaces was partially restricted by the geometrical features of the casting, sprue, gating, or support system. It was shown that values for heat transfer coefficients at air-mold interfaces must be determined based on natural convection regimes and critical length scales for each surface. Numerical simulations results for the temperature are in good agreement with experimental results. INTRODUCTION The investment casting process consists of making wax patterns by injecting wax into metal dies, building of ceramic shell molds around the wax patterns, dewaxing of ceramic shell molds, and casting of alloys into the shell molds. Dimensional changes between the pattern tooling and its corresponding cast part occur as a result of deformation of the wax, shell, and alloy materials during the processing. The difference between the die dimensions and corresponding casting dimensions are usually referred to as the tooling allowances for the pattern die. Tooling allowances are estimated from the part dimensions based on dimensional changes associated with the wax, shell, and alloy systems. Shrinkage of the alloy is one of the largest components of the overall dimensional change between the pattern tooling and its corresponding cast part. The alloy tooling allowances can be determined from a combined analysis of heat transfer and deformation during the casting process. The accuracy of the dimensional results depends on heat transfer results. In this paper, the numerical simulation of the investment casting process is discussed. The shell molds were thought of as a packed bed of sintered ceramic particles of different sizes and shapes. At high temperatures, the semi-transparent effects in the fused silica, which enhance the heat transfer, were considered in numerical simulations by a temperature-dependent thermal conductivity. For shell molds made of fused silica with a zircon prime coat, data on relevant properties were given in Sabau and Viswanathan (2004). In most studies on the investment casting process, such as in Roches and Chevrier (1988), Browne and Sayers (1995), Upadhya et al. (1995), Givler and Saylors (2000), and Gebelin and Jolly (2003), a constant Heat Transfer Coefficient (HTC) was used to describe the heat transfer losses from the shell mold to the ambient. Anderson et al. (1997) found that the use on one HTC for all mold surfaces was not appropriate. The major contribution of this study was to demonstrate that HTC at mold surfaces must be calculated based on firstprinciple theories of natural convection. The cooling conditions at mold surfaces were determined by the airflow pattern of natural convection. Some mold surfaces were fully open to natural convection, while others were partially open as the natural convection was affected by the proximity and geometrical configuration of other surfaces. Thus, the heat transfer conditions at each mold surface depended on the surface length scale and surface position in the casting tree. Shell emissivity was determined from experimental data. Shell temperature was measured using different thermocouple arrangements. Recommendations for thermocouple use in the investment casting were included. Numerical simulations were performed using constitutive equations for the heat transfer coefficients based on correlations developed for natural convection. Castings were poured at two independent foundries, Precision Casting of Tennessee, Inc. (PCT), and at Oak Ridge National Laboratory (ORNL), in order provide sufficient experimental data. Numerical simulation results agree well with experimental data, validating computer models for the investment casting process, such as ProCASTTM. Finally, recommendations for conducting numerical simulations of the investment casting process are presented.


THERMOPHYSICAL PROPERTIES For this study, a zircon and fused silica shell system with three coats was used (Sabau and Viswanathan, 2004). The fused o silica shells considered in this study were sintered for at least 45 min at 1000 oC (1,830 F), a process called shell prefiring. After prefiring, the shell molds were ready for metal pouring. Aluminum alloy A356 was poured in the shell molds after they were cooled to lower temperatures. At room temperature, the thermal diffusivity was measured for the shell mold to be approximately 1.3 times larger than that reported by Sabau and Viswanathan (2004). The thermal conductivity used in this 3 study, was given by k(T) = ak + bk T , where ak=0.85 and bk=6.25E-10. Shell emissivity was measured using an infrared camera Sabau and Dinwiddie (2005). The values obtained from infrared measurements are shown in Table 1. Table 1. Shell Emissivity From Infrared Measurements

Temperature [oC (oF)] 20 (68) 500 (930) 950 (1740)

Emissivity

Comments

0.62 0.72 0.83

extrapolated measured measured

CASTING EXPERIMENTS In this section, casting experiments were presented. The castings were designed such that there would be strong radiation effects among some mold surfaces. Three castings containing two plates were poured for this study. The plates were 25 mm (1 in.) thick. Castings were poured at two independent foundries, i.e., at a commercial foundry (CF) and a research laboratory (RL), in order provide sufficient experimental data for assessing the existent capabilities of the computer simulation software. Aluminum A356 was considered in this study. At the research laboratory foundry, two furnaces were used to preheat the shell molds. The first furnace was used to sinter the molds, while the second furnace was used to obtain a o uniform temperature distribution in the molds. The temperature of the second furnace was set to approximately 400 C (750 o F). After sintering, the shell molds were cooled in the second furnace until the desired mold temperature was reached, and the metal was poured. CASTING CONFIGURATION The casting configuration considered in this study contained a downsprue, runner, and two plate castings (Figure 1). The mold was cooled in the air. The natural convection of air around the shell mold, thermal radiation within the shell, and thermal radiation from shell surfaces were the dominant heat transfer mechanisms associated with the mold. Unlike in any other casting processes, the outer surface of the mold mimicked closely the shape of the casting, providing different levels of restriction to the airflow to mold surfaces. The natural convection and thermal radiation were furthermore affected by the final arrangement of many parts into a tree or cluster as some surfaces became close to other surfaces.

(a)

(b)

Figure 1. (a) Wax pattern assembly showing casting configuration and (b) pouring of aluminum A356 alloy. Mold was placed on a firebrick and supported by two firebricks on their sides.


In the casting experiments, the casting tree was supported on its sides by firebricks as shown in Figure 1 and in a representation shown in Figure 2. The two bricks reduced the air flow on the lower part of the plate, sprue, and runner. The space between plates was a closed channel, while the space between first plate and sprue was partially open on the sprue side, as the width of the sprue was less than that of the plate. Due to these geometrical differences, it was expected that cooling conditions for the first plate would have been different on the first plate than that of the second plate. These geometrical considerations have not been addressed in any study on investment casting and were considered in this study. Having discussed the specific casting configuration of this study, a short discussion is here presented for casting arrangements in general. In a casting tree, the path of airflow could be restricted by the new surface configurations, such as closed channels that were created by proximity of other parts (Figure 3). The end of the casting tree is fully open to airflow. At the other tree end, near by the riser/sprue, the airflow is obstructed by the sprue. The cooling of the casting surface near the sprue is less effective than the cooling of the surface at the end of the casting tree. Thus, different heat transfer coefficients must be assigned according to the proximity of other surfaces or the lack thereof.

(a)

(b)

Figure 2. Schematic of casting arrangement showing mold support (a) mold rests on a brick, is supported by two bricks on each side and end of casting tree is fully open to air flow; (b) sprue/riser is close to the first casting part.

Figure 3. Surfaces were hatched with different symbols according to the amount of air flow restriction, which affects their cooling:

surfaces in the cluster facing other surfaces; surface facing the riser; and

surface at the end of cluster; open surfaces.

TEMPERATURE MEASUREMENTS IN THE SHELL MOLD AND CASTING In this section, temperature measurements in shell molds and castings were presented. Thermocouples were inserted in the shell and the center of the plates as indicated in Figure 4 (b) and (c). Ungrounded stainless steel sheathed thermocouples, 0.032 in. (0.081cm) thick, were embedded in the shell during shell investment. The larger gauge wire was used in this study since the 0.01 in. (0.025cm) gauge thermocouple wires, which were used in previous study, were too fragile to survive the shell investment process. In order to minimize conduction losses from the thermocouple wires to the ambient, the thermocouples were embedded in the shell mold over a significant length (Fig. 4) and were insulated outside the mold using braided ceramic sheathing.


One casting from the commercial foundry and two castings from the research laboratory foundry were considered (see Table 2). Pictures were taken during pouring (see Fig. 1) to document the inlet area of the metal stream in the pouring cup and the metallostatic head of the metal, i.e., from the ladle to the pouring cup surface. The pouring area was initially estimated to be 1.3 x 1.3 cm (0.5 x 0.5 in.). For commercial foundry castings, there were two operators that used a larger ladle, keeping the metallostatic head and the pouring cup constant during filling. The filling velocity for the commercial foundry castings was estimated to be 12.7 cm/s (5 in/s). For research laboratory castings, the operator lowered the ladle during pouring, increasing the filling area. The inlet velocity based on the filling time, filling area, and casting volume was estimated to vary as follows: 10.1, 12.2, 13.7, and 20.3 cm/s (4, 4.8, 5.4, 8 in./s) at 0, 2, 2.5, and 5s. The pouring temperature was estimated from a thermocouple placed in the sprue. The filling time was estimated from videotape recordings of the casting process. The casting conditions were shown in Table 2. The shell thickness was measured for each of the molds after casting (Table 3). The shell mold was destroyed to identify the thermocouple location.

face coats intermediate coats backup coats seal coat Casting

Casting

Ambient

A

(a)

C1

S11

S12

S21

C2

(b)

(c)

(d)

Figure 4. Sketch showing thermocouple placement in (a) first plate and shell, and (b) in the second plate. (c) Sketch showing thermocouple embedded in the shell. (d) Picture showing one thermocouple S11. Table 2. Casting Conditions Case CF1

Pouring Temp. o C (oF) 680 (1255)

Prefiring Furnace o C (oF) 900 (1650)

Prefiring Time [min] 60

Shell Temp.* o C (oF) 450 (840)

Holding Time [min] 90

RL1 RL2

680 (1255) 670 (1240)

975 (1800) 975 (1800)

45 45

430 (800) 412 (770)

15 15

Holding Furnace oC (oF) 900 to 630 (1650-1165) 400 (750) 400 (750)

Shell in ambient [s]

Filling Time [s]

130

8

36 29

5 5

* average shell temperature at pouring Table 3. Measurement of Shell Thickness and Thermocouple Location Case CF1 RL1 RL2

Shell thickness [mm] Min 6.9 6.4 6.6

Max 8.2 8.2 7.7

Average 7.4 7.2 7.2

Bulge* 9.5 8.7 8.6

Thermocouple distance from casting interface [mm] S11 S12 S21 0.9 4.1 1.3 2.6 3.1 1.0 1.1 2.9 1.1

*bulge = shell thickness in regions where two thermocouples were embedded. HEAT TRANSFER COEFFICIENTS AT SHELL MOLD SURFACE The overall HTC between the ambient and shell mold, ha can be given as a function of the convection heat transfer coefficient, hma, and shell emissivity, as:

ha = hma + hR = hma + σε(T 2 + TA2 )(T + TA )

(1)

where hR is an effective radiation HTC, T is the temperature of the surface [K], and TA is ambient temperature [K]. There are different correlations for the HTC depending on the characteristic length of the surface and surface orientation, i.e., vertical and horizontal (Incropera and DeWitt, 1990). Most of correlations on natural convection are given in terms of the Nusselt number, NuL , and Rayeigh number, RaL :


NuL =

gβ (Ts − T∞ )L3 hma L and RaL = k vα

(2)

where g = gravitational acceleration, β is the thermal expansion coefficient, v is the kinematic viscosity of the fluid, L is the characteristic length scale, and α is the thermal diffusivity, Ts is the surface temperature, and T∞ is the ambient temperature. For air at ambient temperature, the thermal conductivity k=2.6E-2 W/mK and gβ vα = 9.07E+7 [1/m3K]. The characteristic length scale, L for a surface can be computed as the ratio between the surface area, A, and its perimeter, p, i.e., L=A/p. The HTC is determined from the Nusselt number, as:

hma =

k ⋅ NuL L

(3)

NATURAL CONVECTION CORRELATIONS FOR SURFACES FULLY OPEN TO AIR FLOW In order to determine the HTC, it was necessary to take into account the different airflow patterns that took place at mold surfaces as shown in previous Section. For surfaces that are fully open to airflow, NuL can be expressed in terms of the Rayeigh number, RaL , as (Bejan, 2004):

Nu L = 0.54 Ra L

1/ 4

(4)

1/ 4 L

Nu L = 0.27 Ra 1/ 4 NuL = 0.68 + 0.515 RaL

(5) (6)

Equations 4 and 5 describe the correlations for the cooling of a horizontal surface facing upward and downward, respectively. Equations 6 is for vertical surfaces. For inclined walls, correlation (6) can be used provided that RaL is evaluated considering the gravitational acceleration component that is parallel to the wall. In the literature, there are also correlations given for cylinders and other shapes. NATURAL CONVECTION CORRELATIONS FOR SURFACES PARTIALLY OPEN TO AIR FLOW Other types of mold surfaces encountered in investment casting are those between adjacent casting parts, i.e., surfaces facing other surfaces. In this case, the air flow is partially restricted, and we can use the correlations developed for the “two plate” configuration. The equations for the Nusselt number for a channel between two plates is: 3/4 ⎡ -35 L ⎤⎞ ⎛ S ⎞⎛ 1 Nus = Ras⎜ ⎟⎜1− exp⎢ ⎥⎟ ⎝ L ⎠⎝ 24 ⎣ Ras S ⎦⎠

(7)

where S is the distance between the two plates and Rayeigh number is computed based on S. The HTC are shown in Table 4 for the casting configuration considered. Table 4. Heat Transfer Coefficients Used in Numerical Simulations Symbol

Mold – air

Mold Region Direct contact between the mold and other supporting materials Sprue

o ca

Mold – air

Surfaces within the cluster

hcaop

Mold – air

Surfaces within the cluster facing other cluster surfaces

o hma

Mold – air

At the end of cluster

op hma

Mold – air

At the end of cluster

hms hsa

h

Interface Mold – support

Comments Where the casting rests or is supported, i.e., sand, side bricks. Surfaces fully open to air flow, i.e., narrow plate surfaces Surfaces partially open to air flow, i.e., between plates Plate surface at the end of cluster, which is fully open to air flow Plate surface facing the sprue, which is partially open to air flow


COMPUTATIONAL RESULTS Numerical simulations were conducted for conditions similar to those of the experiments. The casting parameters, material properties, and boundary conditions were computed based on equations from the previous sections. The mesh was created using the shelling feature in MeshCAST™, a module in available in the commercial casting software used. One mesh layer (0.026 in., 0.66 mm) was used for the zircon face coat, another layer (0.036 in., 0.9 mm) was used for the intermediate fused silica coat, and three layers (0.048 in., 1.2 mm each) were used for the fused silica backup coat. In order to account for the shell bulge in the center of the plates, where thermocouples were embedded, a patch of different shell thickness was created. Initially, the value for the HTC at the mold-metal interface, hmm, was based on recommendations made by Woodbury et al. (2003). Preliminary calculations were conducted to assess the effect of the hmm on the shell temperature and a value of 850 2 W/m K was found to be appropriate (Table 5). This value was close to that determined by Woodbury et al. (2003). Table 5. Heat Transfer Coefficients Held Constant iIn Numerical Simulations Symbol

Interface

Region

hmm

Metal - mold

-

hra

Metal – air

Value [W/m2 K] 850 30

Top of riser/sprue

COOLING OF SHELL MOLD BEFORE POURING After sintering, the shell molds were taken from the firing furnace and set for pouring. The molds have a nonuniform temperature distribution when they were held outside the firing furnace a relatively long time before metal pouring. For the o o CF, case the shell temperature at pouring varied from 400 to 470 C (750 to 880 F). The thermocouple S21 provided data for the surface of the second plate facing the ambient, while thermocouple S11 provided data for the similar surface of the first plate, surface that was facing the second plate. The S21 surface was fully open to airflow and radiated heat directly to the ambient. The S11 surface exchanged radiation heat with the second plate and it was less cooled by the airflow due to reduced natural convection between the two plates. Thus, as seen in Figure 5(a), surface S21 cools faster than surface S11. In most numerical simulations, shell mold is assumed to have a uniform temperature. This assumption may decrease the accuracy of simulation results in cases when the shell temperature exhibits large variations. For the CF casting experiments, the shell mold was held outside the furnace for about 130s such that its temperature would drop to the desired temperature. The shell temperature was obtained at pouring time by carrying out numerical simulations for the period of time in which the empty molds cool. The results are shown in Figure 5. For the sake of completion, the air temperature in the mold cavity was also shown in Figure 5(b). It was found that adequate shell temperatures were obtained by simply considering that the mold cavity was filled with hot air that cools with the shell. (1,200)

650

(1,200)

600

(1,110)

600

(1,110)

550

(1,020)

550

(1,020)

500

S11, exp S11, comp

400 350

(a)

(930)

450

0

20

40

S12, exp S12, comp

60 80 Time [s]

S21, exp S21, comp

100

120

(840) (750)

o

Temperature ( C)

Temperature (oC)

650

(660) (oF) (b)

500

(930)

450

(840)

400 350

0

20

P1, exp

C1, exp

C2, exp

P1, comp

C1, comp

C2, comp

40

60 80 Time [s]

100

120

(750) (660) (oF)

Figure 5. Comparison between experimental results obtained at commercial foundry (empty symbols) and computational results (solid symbols) as the mold cools outside the furnace: (a) temperature in the shell, and (b) temperature in the mold cavity. Time origin is the instant at which shell was taken out of the furnace.

HEAT TRANSFER COEFFICIENTS ON MOLD SUPPORT AND DOWNSPRUE In the remainder of this paper, the time origin for all figures is at the onset at metal pouring. The shell molds at the research laboratory foundry have a more uniform temperature than those at commercial foundry. In order to isolate the effect of the nonuniform shell mold temperature, the first series of simulations were conducted for the RL castings. During preliminary calculations, it was found that the heat transfer coefficient between shell mold and supporting materials, hms , was an important variable. As shown in Figure 6, the last region to solidify in the RL castings was shown to be influenced by the choice of hms . For a high value of hms , the last region to solidify was located in the upper regions of the plates, while for a


low value of hms , the last region to solidify was located in the lower regions of the plate. In order to identify which are the last regions to solidify, the castings were cut through their vertical symmetry plane. As evidenced by Figure 7, the last regions to solidify were located right in the center of the casting. This information was used in estimating the useful range of values for the hms .

(b)

(a)

Figure 6. Solid fraction profile for two cases: (a) (b)

hms =840 W/m2 K and

hms =8.40 W/m2 K, showing the last region to solidify in casting.

(a)

(b) Figure 7. Micrograph showing the concentration of porosity in the center of the plates from at a) commercial foundry and (b) research laboratory.

The correlations shown in previous Sections for natural convection were applied for the investment casting process. Equations 7-10 gave the HTC dependence on the surface dimensions. Preliminary calculations were performed using the same heat transfer coefficient of 17 W/m2 K on all shell surfaces. The results shown in Figure 8 indicated that the temperature in the sprue was not accurately predicted. When a HTC of 34 W/m2 K was used for the sprue surface, corresponding to its characteristic dimension (1 in or 2.54 cm), the accuracy of temperature predictions was greatly improved. The recommendation from the results shown in Figure 8 was to calculate the HTC values for each surface based on characteristic surface dimension. Further computational results showed that hsa =38 W/m2 K was found to yield the best results for the sprue temperature. Sprue Temperature ( oC)

700 Experimental

650

h

600

hsa=34

sa=17

(1,290) (1,200) (1,110)

550

(1,020)

500

(930)

450 35

92.14 149.3 206.4 263.6 320.7 377.9 435 Time [s]

(840) (oF)

Figure 8. Temperature at a location in the center of the sprue for research laboratory castings.


HEAT TRANSFER COEFFICIENT ON SURFACES PARTIALLY OPEN TO NATURAL CONVECTION For the two-plate configuration considered, the airflow pattern for the region between the plates should have been different than that for a plate fully open to air flow. Therefore, the HTC had to be adjusted accordingly. The parameters for the cases considered are shown in Table 6. In the RLS1 case, no distinction was made between cooling conditions on plate surfaces facing the sprue, between the plates, and facing the ambient (i.e., surface at the end of the casting tree). The results obtained for RLS1 are shown in Figure 9(a). The RLS1 results showed that there was no distinction between the cooling curves in the plate centers, unlike it was experimentally observed. In the RLS2 case, a HTC was computed using the formulas for the natural convection between two plates of length 3 in. (7.62cm) separated by an air gap of 2 in. (5cm). The results were similar to the RLS1 case, i.e., the center plate temperatures were almost the same. However, the predicted temperatures were closer to the C2 temperature. Table 6. Values of Heat Transfer Coefficients Used [W/m2 K] for Different Research Laboratory Simulations

hms

RLS1 RLS2 RLS3

21 21 21

hsa 38 38 38

hcao 38 38 38

Temperature (oC)

650

C1, exp C1, comp

C2, exp C2, comp

(1,020)

135

235

(a)

335 435 Time [s]

535

(o F)

Between the plates Include restrictive airflow effects of sprue

P1, exp P1, comp

650

C1, exp C1, comp

(1,290)

C2, exp C2, comp

(1,200)

600

(1,110)

550 500 35

735 (930)

635

12.5 12.5 4.2

700

(1,290)

(1,110)

550

Natural convection effects

op hma

12.5 12.5 12.5

(1,200)

600

500 35

o hma

12.5 17 17

700 P1, exp P1, comp

hcaop

Temperature (oC)

Case ID

(1,020)

135

235

(b)

335 435 Time [s]

535

735 (930)

635

(o F)

Figure 9. Temperature in the center of the plates for (a) RLS1 case and (b) RLS2 case. C1- center of plate close to the sprue.

For the two-plate configuration considered, the airflow pattern should had been different for the plate surface facing the sprue than for the plate surface at the end of cluster, which faced the ambient, since the sprue obstructed the flow of air. Thus, a more enhanced cooling was experienced by the surface of the second plate at the end of the cluster than the surface of the first plate facing the sprue. In case RLS3, a lower HTC was used on the plate surface facing the sprue. The agreement for casting temperatures was excellent (Figure 10). For the shell mold, the temperature also showed a good agreement.

650

C1, exp

C2, exp

P1, comp

C1, comp

C2, comp

600

(1,200) (1,110)

550 500 35

(a)

(1,290) P1, exp

(1,020)

135

235

335 435 Time [s]

535

635

735 (930) ( o F)

Temperature (oC)

Temperature (oC)

700

600

(1,110)

550

(1,020)

500

(930)

450

(840)

400 350

(b)

S11, exp S11, comp

0

100

200

S12, comp S12, comp

300 400 Time [s]

S21, exp S21, comp

500

600

700

(750) (660) (oF)

Figure 10. Temperature for RLS3 case (a) in the center of the plates, and (b) in the shell.

NUMERICAL SIMULATIONS FOR THE COMMERCIAL FOUNDRY CASTINGS The next series of simulations were conducted for the CF castings. The shell molds at commercial foundry had a more nonuniform temperature than those at research laboratory foundry due to their different temperature schedule before pouring. Unlike at RL, the shell molds at CF were held in the furnace after sintering, and the furnace was allowed to cool for a long time. It was thus expected that the amount of sintering during firing was different at the two foundries. In addition, the


following differences between the molds used at RL and CF were observed: the average shell thickness was slightly different and the shell bulge, where thermocouples were placed, was larger. For the sake of simplicity, the same mesh was used for the CF case. Thus, the same shell thickness, including in the region where thermocouple were embedded in the shell, was used for the CF simulations. Three cases were considered for the CF simulations (Table 7). In the CFS1 case, the same shell thermal conductivity was used and the HTC were varied until a good agreement with experimental results was reached (Figure 11). It can be observed that there was approximately the same ratio between the HTC used for the RL simulation and those for the CF simulation. This fact indicated that the shell mold has a different thermal conductivity. Thus, for the next case, CFS2, it was decided to adjust the thermal conductivity of the shell accordingly, while keeping the same HTC as for the RLS3 case since, the correlations for natural convection indicated that there had to be the same HTC at both foundries. The results for CFS2 case are presented in Figure 12. A good agreement between the computational and experimental results was obtained. However, the solidification time was slightly higher in the numerical results. In order to decrease the solidification time in the second o

plate, in the third numerical simulation case, CFS3, the HTC on the casting tree end, hma , had to be increased from 12.5 to 21 W/m2 K (Figure 13). Looking back at the experimental conditions at CF, it was noted that fans were used on the plant o

floor to enhance the cooling conditions. Thus, the enhanced cooling conditions at CF, supported the use of higher hma , which were found to be required for accurate temperature predictions. Table 7. Values of Heat Transfer Coefficients [W/m2 K] and Parameters for the Thermal Conductivity of Shell Used for Commercial Foundry Simulations

hms

CFS1 CFS2 CFS3

21 21 21

hsa 17 38 38

hcao 17 38 38

Temperature (oC)

700 P1, exp P1, comp

650

C1, exp C1, comp

C2, exp C2, comp

(1,020)

0

(a)

3.4 12.5 21

(1,290)

(1,110)

550

o hma

4.2 17 17

(1,200)

600

500

hcaop

100 200 300 400 500 600 700 800 (930) Time [s] (o F)

Temperature (oC)

Case ID

op hma

0.8 4.2 4.2

ak 0.85 0.39 0.39

bk 6.25E-10 2.9E-10 2.9E-10

600

(1,110)

550

(1,020)

500

(930)

450

(840) S11, exp S11, comp

400 350

0

(b)

S12, exp S12, comp

S21, exp S21, comp

100 200 300 400 500 600 700 800 Time [s]

(750) (660) (oF)

Figure 11. Temperature for CFS1 case (a) in the center of the plates, and (b) in the shell.

650

C1, exp C1, comp

C2, exp C2, comp

(1,290) (1,200)

600

(1,110)

550 500

(a)

P1, exp P1, comp

(1,020)

0

100 200 300 400 500 600 700 800 (930) Time [s] (o F)

Temperature (oC)

Temperature (oC)

700

600

(1,110)

550

(1,020)

500

(930)

450 400 350

(b)

S11, exp S11, comp

0

S12, exp S12, comp

S21, exp S21, comp

100 200 300 400 500 600 700 800 Time [s]


(840) (750) (660) (oF)


Temperature (oC)

650

(a)

C1, exp

C2, exp

P1, comp

C1, comp

C2, comp

(1,200) (1,110)

600 550 500

P1, exp

(1,020)

0

100 200 300 400 500 600 700 800 (930) Time [s] (o F)

Temperature (oC)

(1,290)

700

600

(1,110)

550

(1,020)

500

(930)

450 400 350

(b)

(840) S11, exp S11, comp

0

S12, exp S12, comp

S21, exp S21, comp

100 200 300 400 500 600 700 800 Time [s]

(750) (660) (oF)


CONCLUSIONS RECOMMENDATIONS FOR NUMERICAL SIMULATIONS Numerical simulations are an important tool for process analysis and increasingly used in the investment casting industry. In order to obtain data to a specific foundry, combined experimental and computational programs must take place. The experimental program should be concentrated on measuring material properties. The experimental program should be relatively small since it could be carried only once per each type of shell mold. The properties for alloy systems are much more available since they were likely to be measured for other material processing applications. For that shell system, the mold property data can be used for castings of any geometry. Based on the results presented in previous Sections, the following recommendations were made for the use of numerical simulation in the investment casting process: 1) Determine properties and dimensions for the shell mold: a. Measure shell emissivity using infrared techniques b. Measure thermal diffusivity of shell molds at room temperature using the laser flash technique. Account for thermal radiation within the shell mold using the following correlation for thermal conductivity: k(T) = ak + bk T3 c. Measure shell thickness. 2) Compute heat transfer coefficients using correlations for natural convection. a. The calculations will be conducted according to well know relationships for natural convection based on each surface dimensions and orientation with respect to the vertical direction. b. To date, there are correlations for casting surfaces fully open to ambient airflow and for surfaces within the casting tree, i.e., surfaces facing from one part facing surfaces from adjacent parts. c. For other surfaces partially open to airflow, the heat transfer coefficients need to be adjusted since no correlations are available for the actual geometrical configuration. 3) Use a heat transfer coefficient of approximately 800-2,800 W/m2K for the metal- mold interface (for shell molds with a zircon prime coat) 4) Mesh the shell using at least four or five-grid spacing across its thickness. 5) Determine the temperature distribution in the mold, in cases when shell is held out of the furnace for a long time before pouring. At the time of metal pouring, the mold has a nonuniform temperature as the shell mold cools after it has been taken out of the furnace. The degree of temperature nonuniformity increases with the amount of time the shell is held out of the furnace before pouring. The nonuniform temperature distribution of the mold can be obtained by performing numerical simulations of the heat transfer within the shell mold and hot air that fills it. The following recommendations were made for measuring the shell temperature for the investment casting process: 1) Use ungrounded gauge thermocouples 0.032 in. (0.081cm). These thermocouples can withstand the shell investment process, while providing a small time response of approximately 0.3s. The thermocouples must be embedded in the shell molds for at least 0.5-1 in (1.2-2.5 cm) in order to minimize conduction losses through the wires. 2) For the 0.01 in. (0.025cm) small gauge thermocouple wire, a high failure rate (50%) was recorded during shell investment and they should be used only when a very small time response of the thermocouple is required. The following recommendations were made with respect to computer software for the investment casting process. Significant amount of time was required to set up the heat transfer coefficients on different casting surfaces. The setup of numerical simulations could be easily simplified if surfaces can be automatically grouped according to their dimensions, orientations, and amount of obstruction to natural convection. Each surface group would then be assigned a heat transfer coefficient.


It was demonstrated in this study that accurate computational results were obtained when HTCs at mold surfaces were assigned based on first-principle theories of natural convection. The heat transfer conditions at each mold surface depended on the surface length scale and surface position in the casting tree. The assignment of the heat transfer conditions based on first-principles eliminated the guesswork in conducting numerical simulations, increased the accuracy of the results and reduced the operator time required to obtain process recommendations. ACKNOWLEDGMENTS This work was performed for the project on Predicting Pattern Tooling and Casting Dimensions for Investment Casting, conducted in collaboration with the 4L Investment Casting Committee of the American Foundry Society and the Cast Metals Coalition. We would like to thank J. Snow, D. Scott, and B. Sneider of Minco, Inc. for shell investment and for embedding thermocouples within the shell, E. Hatfield of Oak Ridge National Laboratory for casting assistance, T. A. Parham for assistance with thermocouples, Jim Gardner of J.E.M. Manufacturing, for casting design and injection of wax patterns, B. Schrey of Schrey & Sons Mold Co. for making the die mold for the sprue; Mike Payne and Allen Bransford of Precision Casting of Tennessee, Inc. for casting, Z. Wu, a University of Tennessee graduate student, for working on the figures using raw data files, G. Romanoski and T. Tiegs for reviewing the manuscript, and G. Carter for typing the manuscript. The research was sponsored by the U.S. Department of Energy, Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Industrial Technologies, Metal Casting Industries of the Future Program, under contract DE-AC05-00OR22725 with UT-Battelle, LLC. REFERENCES Anderson, J.T., Gethin, D.T., Lewis, R.W., “Experimental Investigation and Numerical Simulation in Investment Casting,” Int. J. Cast Metals Res., Vol. 9, pp. 285-293 (1997). Bejan, A., Convection Heat Transfer, 3rd ed., John Wiley and Sons, Inc., Hoboken, NJ (2004). Browne, D.J., Sayers, K., “Experimental Measurement of Investment Shell Properties and Use of the Data in Casting Simulation Software,” Proc. 7th Conference Model, Casting Welding Adv. Solid. Process, 1995. Gebelin, J., Jolly, M.R., “Modelling of the Investment Casting Process,” Journal of Materials Processing Technology, Vol. 135, pp. 291-300 (2003). Givler, R.C., Saylors, D.B., “Efficient Runner Networks for Investment Castings,” International Journal for Numerical Methods in Engineering, Vol. 48, pp. 1601-1614 (2000). Incropera, F.P., DeWitt, D.P., Fundamentals of Heat and Mass Transfer, 3rd ed., John Wiley & Sons, Inc., New York, NY (1990) Roches, L.V., Chevrier, J.C., “Radiation Heat Transfer Modelling in Precision Investment Casting Technology, Solidification Processing 1987, The Institute of Metals, London, pp. 522-524 (1988). Sabau, A.S., and Viswanathan, S., “Thermophysical Properties of Zircon and Fused Silica-based Shells used in the Investment Casting Process,” Transactions of the American Foundry Society, vol. 112, Paper No. 04-081, 2004. Woodbury, K A; Woolley, J W; Piwonka, T S, "Metal/Mold and mold/environment interfacial heat transfer,” Transactions of the American Foundry Society, Vol. 111 Paper No. 03-114, pp. 529-541, 2003. Upadhya, G.K., Das, S., Chandra, U., Paul, A.J., “Modelling the Investment Casting Process: A Novel Approach for View Factor Calculations and Defect Prediction,” Appl. Math. Modelling, Vol. 19, pp. 354-362 (1995). Sabau, A.S., and Dinwiddie, R.B., Unpublished report, ORNL (2004).