Comparison of theory with experiment in one-dimensional analytical modeling of directional solidification

Overfelt, Ruel A.; Matlock, C.A.; Wilcox, R.C.

doi:10.1016/0022-0248(94)00830-2

Cited by 9 publications

(8 citation statements)

References 7 publications

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“…This has been reported in other systems where simplified heatconduction theories fail at high velocities. [17] A longitudinal section from the beginning of growth of the 0.05 cm/s sample is shown in Figure 6. The sudden change in microstructure shown in Figure 6 is due to changing the growth velocity from 0 to 0.05 cm/s and not due to electrical current pulsing.…”

Section: A Mushy-zone Position and Velocity Transient Behaviormentioning

confidence: 99%

Microstructural and compositional transients during accelerated directional solidification of Al-4.5 wt pct Cu

Su¹,

Overfelt

Jemian

1998

Metall Mater Trans A

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The transient behavior of mushy-zone velocities, primary dendrite arm spacings, and microsegregation effects have been investigated for an Al-4.5 wt pct Cu alloy by instantaneous velocity changes in a standard Bridgman furnace. After suddenly imposed velocity changes, the mushy-zone velocities, dendrite arm spacings, and compositions exponentially adjust to new steady-state values. Good agreement was found between the transient mushy-zone positions and velocities and predictions from the theoretical model of Saitou and Hirata. The primary dendrite arm spacings appear to adjust to changed velocity conditions about as rapidly as the mushy-zone velocity adjusts. Steady-state arm spacings agree very well with corresponding steady-state data from the literature. However, the observed composition profiles in the dendrite core and the interdendritic liquid appear to adjust more slowly than the corresponding adjustment of the mushy-zone velocity and arm spacings. Our observation of the sluggish response of the compositional profiles is consistent with an estimated Lewis number of 9.4 ϫ 10 3 for the aluminum-copper system. The diffusivity of heat, thus, greatly k (Le ϭ ) c D p exceeds the diffusivity of solute in this system. These results indicate that testing for the steady state during directional solidification experiments by looking for constant primary dendrite arm spacings can lead to errors, since the microsegregation profiles adjust more slowly than the spacings. It is suggested that constancy of composition also be tested for critical experiments investigating steadystate microsegregation effects.

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Section: A Mushy-zone Position and Velocity Transient Behaviormentioning

confidence: 99%

Microstructural and compositional transients during accelerated directional solidification of Al-4.5 wt pct Cu

Su¹,

Overfelt

Jemian

1998

Metall Mater Trans A

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“…Properties for the remaining materials were based on data for the respective materials predefined in ProCAST, available in the literature, or derived from empirical assumptions and experimental evidence. [5,11,13,14,17,43,44,49,52,[58][59][60] While the parameters for heat transfer within or through each individual material and for radiation heat transfer, which are primarily dependent on material properties, were readily available, the heat-transfer coefficients for the interfaces between materials illustrated in Figure 3, which are primarily conduction or convection, are often not well characterized in the literature. As discussed in the following sections, each process model was particularly sensitive to different, but specific, heat-transfer steps in each process requiring numerous parametric revisions before agreement between experimental results and the model was achieved.…”

Section: Casting Process Modelsmentioning

confidence: 99%

“…More accurate and fully three-dimensional analyses will be very important in accounting for casting geometry and nonaxial heat extraction, which have been shown experimentally to have a significant impact on dendrite arm spacing and crystallographic growth orientation. [20,[49][50][51] As mentioned, solidification modeling of directional solidification with liquid-metal cooling has received only limited attention. [5,11,14] Prior modeling of the LMC process has been restricted to one-dimensional axisymmetric rod simulations [11] or has simplified the heat flux conditions at the mold:coolant interface.…”

Section: Introductionmentioning

confidence: 99%

Thermal Analysis of the Bridgman and Liquid-Metal-Cooled Directional Solidification Investment Casting Processes

Elliott¹,

Pollock

2007

Metall Mater Trans A

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Thermal profiles obtained during directional solidification of Ni-base superalloy castings by the Bridgman and liquid-metal-cooled (LMC) techniques have been used to develop and validate the finite-element models of these processes. Models of the directional solidification processes for the columnar-grain alloy GTD-444 are used to evaluate the various heat-transfer steps and heat extraction modes within each process. This analysis highlights the similarities and the fundamental differences in heat-transfer modes between the two solidification approaches. Ultimately, the unique limiting heat-transfer step of each process is identified. For the stepped plate configuration investigated, heat extraction is limited by radiation from the exterior mold surface in the Bridgman process. Heat transfer between the casting and the interior mold surface is the primary resistance in the LMC process, and heat extraction is enhanced by the lowering coolant temperatures in this process.

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“…Too high withdrawal rate would cause extremely concave solid-liquid (S/L) interface, which leads to declining grains, transverse grains or other defects, whereas too low withdrawal rate would bring coarsened grain, crack in the shell, or other defects and thus low productivity. Both numerical methods [7][8][9][10][11][12][13][14] and experimental methods [15][16][17][18] are used to learn more about the Bridgman process in the past few decades. Many kinds of numerical methods and models are proposed to simulate the process of Bridgman directional solidification process and microstructure of columnar grains in blade castings.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of microstructure evolution during directional solidification process in directional solidified (DS) turbine blades

Hang

Tang

et al. 2011

Sci. China Technol. Sci.

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Directional solidified (DS) turbine blades are widely used in advanced gas turbine engine. The size and orientation of columnar grains have great influence on the high temperature property and performance of the turbine blade. Numerical simulation of the directional solidification process is an effective way to investigate the grain's growth and morphology, and hence to optimize the process. In this paper, a mathematical model was presented to study the directional solidified microstructures at different withdrawal rates. Ray-tracing method was applied to calculate the temperature variation of the blade. By using a Modified Cellular Automation (MCA) method and a simple linear interpolation method, the mushy zone and the microstructure evolution were studied in detail. Experimental validations were carried out at different withdrawal rates. The calculated cooling curves and microstructure agreed well with those experimental. It is indicated that the withdrawal rate affects the temperature distribution and growth rate of the grain directly, which determines the final size and morphology of the columnar grain. A moderate withdrawal rate can lead to high quality DS turbine blades for industrial application. directional solidified (DS) turbine blade, Cellular Automation (CA), numerical modeling and simulation Citation: Zhang H, Xu Q Y, Tang N, et al. Numerical simulation of microstructure evolution during directional solidification process in directional solidified (DS) turbine blades.

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Comparison of theory with experiment in one-dimensional analytical modeling of directional solidification

Cited by 9 publications

References 7 publications

Microstructural and compositional transients during accelerated directional solidification of Al-4.5 wt pct Cu

Microstructural and compositional transients during accelerated directional solidification of Al-4.5 wt pct Cu

Thermal Analysis of the Bridgman and Liquid-Metal-Cooled Directional Solidification Investment Casting Processes

Numerical simulation of microstructure evolution during directional solidification process in directional solidified (DS) turbine blades

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