Cristin-resultat-ID: 1750721
Sist endret: 21. november 2019 19:00
Resultat
Vitenskapelig foredrag
2019

Non-dimensional equations and toy models - Tools to improve the basic process understanding

Bidragsytere:
  • Svenn Anton Halvorsen
  • Manuel Sparta og
  • Mads Fromreide

Konferanse

Tittel: 1st Conference on Transfer between Mathematics & Industry [CTMI 2019]

Sted:

Santiago de Compostela
Spania
Utbredelsesområde: Internasjonalt
Årstall: 2019
Dato fra: 22. juli 2019
Dato til: 24. juli 2019

Arrangør:

ITMATI, math-in

Om resultatet

Vitenskapelig foredrag
Publiseringsår: 2019
Fagfellevurdert
Plenar

Klassifisering

Vitenskapsdisipliner

Anvendt matematikk

Emneord

Vekselstrøm • Matematisk modellering • Prosessmetallurgi

Finansiering

  • Norges forskningsråd
    Prosjektkode: 247791

Beskrivelse Beskrivelse

Tittel

Non-dimensional equations and toy models - Tools to improve the basic process understanding

Sammendrag

Fundamental insight can be acquired by studying very simple mathematical models, called toy models. Such models should include some fundamental properties but will often be simplified to a degree that precludes direct, realistic, predictions. We recommend that the models are non-dimensionalized as part of a model study. The non-dimensional equations will reveal which non-dimensional groups can be relevant, and how these groups will identify various model regimes. The methodology will be demonstrated for a 2D electric model for a smelting furnace running on alternating current (AC). The model includes electrodes, non-conductive lining and charge, slag or coke bed, and a metal layer. Assuming constant material properties, each region can be characterized by its electromagnetic penetration depth. Three different types of non-dimensional groups can be defined: - The squared ratio between two geometric lengths - The squared ratio between two penetration depths - The squared ratio between a geometric length and a penetration depth. Some of these groups define interesting model regimes, classified by whether the relevant non-dimensional group is very small, of order 1, or very large. Some examples will be discussed. Among others, the study has revealed conditions for when a direct current (DC) model can be appropriately applied to compute the furnace power distribution. Keywords: Toy model, Non-dimensional equation, Model regimes, Process understanding, Metallurgy, Alternating Current, AC

Bidragsytere

Svenn Anton Halvorsen

  • Tilknyttet:
    Forfatter
    ved NORCE Teknologi ved NORCE Norwegian Research Centre AS

Manuel Sparta

  • Tilknyttet:
    Forfatter
    ved NORCE Teknologi ved NORCE Norwegian Research Centre AS

Mads Fromreide

  • Tilknyttet:
    Forfatter
    ved NORCE Teknologi ved NORCE Norwegian Research Centre AS
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