Physical modeling of the effects of thermal buoyancy driven flows in aluminum casters
- PDF / 1,511,924 Bytes
- 4 Pages / 612 x 792 pts (letter) Page_size
- 101 Downloads / 179 Views
ead Scientist, is with the Advanced Product Technology Center, Motorola, Ft. Lauderdale, FL 33322. D. XU, Senior Project Engineer, is with the Advent Process Engineering, Burlington, ON, Canada M9C 1G8. J.W. EVANS, Professor of Metallurgy, is with the Department of Materials Science and Engineering, University of California, Berkeley, CA 94720. Manuscript submitted April 10, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS B
elsewhere.[2,3] The focus will be on the variation in the flow generated by the addition of buoyancy driven flow. This should provide information regarding the importance of including buoyancy driven flows in physical and mathematical models of EM and DC aluminum casters. Only one significant piece of equipment, a water heater, has been added to the existing water model. It was determined that, by adding an inline water heater, instead of using a large reservoir of hot water, the temperature of the fluid entering the model could be precisely controlled. Therefore, a water heater (Advanced Tech Industries, Miami, FL, model S220) was inserted into the flow loop after the pump and before the flow meter (Figure 1). The heater consisted of three 1.5 kW resistance elements that operated in parallel. Due to the high power, it was important that combinations of elements could be disconnected, thus greatly increasing the range of superheats that could be modeled. The water was pumped from the reservoir; a portion was diverted through the heater and remixed before flowing through the flow meter. The amount diverted was based on the desired superheat of the water. A thermocouple was inserted into the side of the nozzle to measure the temperature of the flow upon exit. Furthermore, the reservoir temperature was measured and the difference in these two values was set as the superheat. The speed of the water at the nozzle was set at 41 cm/s. In order to arrive at a thermal similarity between the two systems, it has been proposed[4] that the tundish number for the systems should be equal. The tundish number is Tu ⫽
gL ⌬T Gr ⫽ Re2 U2
[1]
where g is gravity, L is a characteristic length of the system,  is the volumetric thermal expansion coefficient, ⌬T is the superheat, and U is a characteristic velocity. Since g and L are constant, they can be eliminated and a relation to determine the ⌬T in the water model can be developed, such that
w ⌬Tw al ⌬Tal ⫽ U 2w U 2al
[2]
where the subscripts w and al stand for water and aluminum, respectively. Due to a flow restriction in the heater, the maximum flow rate obtained in the water model was U 2w ⫽ 0.64U 2al
[3]
Therefore, Eq. [2] can be rewritten as ⌬Tw ⫽ 0.64
al ⌬T w al
[4]
Values of the volumetric thermal expansion coefficient[5,6] were taken as w ⫽ 3.21 ⫻ 10⫺4 K⫺1 (taken as a mean value of  for T between 25 ⬚C and 40 ⬚C) and al ⫽ 1.02 ⫻ 10⫺4 K⫺1. The value of al was chosen for pure liquid aluminum, and it is believed that the variation due to the alloying element should not change this value significantly. This gives a useful relationship between t
Data Loading...
