A computational assessment of viscosity measurement in rotating viscometers through detailed numerical simulation
- PDF / 527,530 Bytes
- 5 Pages / 612 x 786 pts Page_size
- 25 Downloads / 180 Views
07/08/2004
5:33 PM
Page 805
Communications A Computational Assessment of Viscosity Measurement in Rotating Viscometers through Detailed Numerical Simulation M. MADAN and D. MAZUMDAR The viscosity values of slags and metals constitute important kinetic data and, therefore, are of considerable importance to the modeling and controlling of various metallurgical processes. Naturally, therefore, significant efforts have been made by researchers to measure the viscosity of a diverse range of metallurgical melts.[1–8] In practically all of these investigations, a rotating viscometer, either with a rotating crucible[8] or a rotating cylinder/spindle,[1–7] has been applied. A typical measurement, for example, involves imparting a rotational motion to either the crucible or the spindle and recording the corresponding equilibrium torque experienced by the cylinder or the spindle, i.e., the entire submerged assembly, as in Figure 1. From the measuredtorque, melt viscosity is deduced following one of the two popular approaches: 1. a technique relying entirely on calibration,[1] in which a torque vs viscosity relationship established a priori from standard melts is applied to translate the measured torque into viscosity; and 2. a simplified one-dimensional momentum transfer analysis wherein wall shear stress inferred from the measured torque is equated against the corresponding shear strain rate and thereby melt viscosity is determined.[7] According to the simplified theory of flows in rotating viscometers,[7,9] the viscosity of the liquid or melt is obtained by dividing the shear stress with the corresponding shear strain rate, both evaluated at the spindle surface (Figure 1), e.g., t m c d u rrspindle
[1]
In Eq. [1], and are the shear strain rate and the shear stress at the cylinder/spindle surface and are, respectively, given by[7,9] 2 2p [2] u a bn° 60 2 1 RspindlenR2 crucible
and t
Q 2pR2spindle
Lspindle
[3]
M. MADAN, Graduate Student, and D. MAZUMDAR, Professor, are with the Department of Materials and Metallurgical Engineering, Indian Institute of Technology, Kanpur, India 208016. Contact e-mail:dipak@ iitk.ac.in Manuscript submitted February 19, 2003. METALLURGICAL AND MATERIALS TRANSACTIONS B
in which, n° is the rotational speed of the spindle and Q is the measured torque. It can be readily seen from these equations that the certainty with which melt viscosity is estimated from Eq. [1] depends in turn on the accuracy with which the measured torque is translated to a surface shear stress value via Eq. [3]. Since neither the torque–shear stress relationship nor the expression for shear strain rate given above is applicable to the viscometer geometry in a rigorous sense, consequently, a sufficiently accurate value of shear stress is unlikely to result from the unidimensional flow theory (viz., on the basis of Eqs. [1] through [3]) considering the surface area of the spindle alone (as in Eq. [3]). This is so the associated end effects as well as the additional resistance to the flow offered by the shaft
Data Loading...
