Metallurgical and Materials Transactions B

, Volume 32, Issue 6, pp 1185–1193 | Cite as

A new approach to the analysis of vessel residence time distribution curves

  • Sergio P. Ferro
  • R. Javier Principe
  • Marcela B. Goldschmit
Article

Abstract

Mathematical models for the evaluation of residence time distribution (RTD) curves on a large variety of vessels are presented. These models have been constructed by combination of different tanks or volumes. In order to obtain a good representation of RTD curves, a new volume (called convection diffusion volume) is introduced. The convection-diffusion volume allows the approximation of different experimental or numerical RTD curves with very simple models. An algorithm has been developed to calculate the parameters of the models for any given set of RTD curve experimental points. Validation of the models is carried out by comparison with experimental RTD curves taken from the literature and with a numerical RTD curve obtained by three-dimensional simulation of the flow inside a tundish.

List of Symbols

a(Pe)

area subtended by the origin and the peak of the curve in a RTD plot (dimensionless)

C

dimensionless concentration

C0

dimensionless concentration at the vessel entrance.

Cp

dimensionless concentration of the peak of the RTD curve

D

mean turbulent, diffusivity (mm2/s)

fVi

volume fraction (dimensionless)

KPe

kernel associated to the convection-diffusion volume (dimensionless)

\(\hat K_{Pe} \)

kernel developed by Levenspiel and Smith[6] (dimensionless)

L

length of the one-dimensional domain (mm)

Pe

Péclet number (dimensionless)

qi

relative flow rate (dimensionless)

Q

flow rate in the vessel (mm3/s)

v

mean velocity inside the one-dimensional domain (mm/s)

va

active volume fraction (dimensionless)

vd

dead volume fraction (dimensionless)

V

volume of the vessel (mm3)

x

dimensionless coordinate along the flow direction

θ

dimensionless time

θp

dimensionless time for the peak of the RTD curve

θav

average residence time (dimensionless)

τ

theoretical residence time (s)

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Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2001

Authors and Affiliations

  • Sergio P. Ferro
    • 1
  • R. Javier Principe
    • 1
  • Marcela B. Goldschmit
    • 1
  1. 1.Computational Mechanics Departmentthe Center for Industrial Research (CINI), FUDETECBuenos, AiresArgentina

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