Measurement of magnitude and direction of velocity in high-temperature liquid metals. Part II: Experimental measurements
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I. MEASUREMENT OF THE MAGNITUDE OF THE VELOCITY
THE mathematical model developed in Part I of this twopart series provided valuable information regarding the melting dynamics of metallic spheres in baths of the same composition as the spheres. For a given metal system, for example, aluminum, the total melting time of a sphere will be a function of the diameter, bath superheat, and velocity. According to the results of the numerical model, the melting time for the spheres under forced convection has the form shown in Eq. [1]. MT
D3>2 SPH # u1>2
[1]
In order to obtain the velocity from the measurement of the melting time, the calculated velocity u will be u
D3 MT SPH2 2#
[2]
The proportionality constant will be a function of the thermophysical properties of the metal system in question. The error involved in the estimation of the properties of the material will not be considered, because it will be assumed that the method will be used prior to calibration in a material of similar thermophysical properties. Performing an uncertainty analysis on the system, with the velocity calculated from Eq. [2], Eq. [3] is obtained: a
USPH 2 Uu 2 UD 2 UMT 2 b 4a b b 9a b 4a u D MT SPH
II. EXPERIMENTAL MEASUREMENTS A. Revolving Liquid Metal Tank Construction
[3]
BLAS MELISSARI, Ph.D., formerly a Graduate Student with the Materials Science and Engineering Department, University of Toronto, Toronto, ON, Canada, is now an Engineer with HATCH and Associates, Mississauga, ON, Canada. STAVROS A. ARGYROPOULOS, Professor, is with the Materials Science and Engineering Department, University of Toronto, Toronto, ON, Canada M5S 3E4. Contact e-mail: [email protected] Manuscript submitted July 9, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
The weight of the spheres had a standard deviation lower than 1 pct based on ten spheres weighed at random. In order to obtain velocities with the least amount of uncertainty, experimental results with low relative uncertainty in the melting time and in the superheat are targeted. This means that considering an uncertainty of 1 °C in the temperature (either the measured or the melting point of the material), the superheat has to be at least 20 °C in order to reduce the relative uncertainty to 5 pct. Also, if the melting time measured is lower than 10 seconds, the relative uncertainty in the melting time will be higher that 10 pct. Considering the case of 10 pct uncertainty in the melting time and 5 pct uncertainty in the superheat, the uncertainty in the velocity will be around 20 pct. Using the results of the numerical model, a series of experiments were conducted. The spheres used were fabricated using commercially pure aluminum of 3, 5, and 7 cm in diameter. The velocities will range from 0 to 0.5 m/s and the superheat range will be set according to the diameter, in order to obtain melting times larger than 10 seconds. For the 3-cm sphere, the superheats considered will be of 20 °C to 40 °C; for the 7-cm sphere, the superheat range can be expanded to 100 °C. All of the
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