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en:grundlagenhandbuch:aufschmelzberechnung:modifiziertes_disperses_aufschmelzen [2026/02/05 11:06] – [Influence of finite Channel Dimension] pkaen:grundlagenhandbuch:aufschmelzberechnung:modifiziertes_disperses_aufschmelzen [2026/02/05 11:10] (aktuell) – [Particles' Influence on the Flow] pka
Zeile 47: Zeile 47:
 The melting process can not be considered without taking into account the whole process. Interactions between single particles as well as the particle dimension have an influence on the viscosity of the melt-solid mixture. The melting process can not be considered without taking into account the whole process. Interactions between single particles as well as the particle dimension have an influence on the viscosity of the melt-solid mixture.
  
-According to Potente and Melisch [Meli98, Pote96] the interactions are considered by using an effective channel height and width which is dependent on the amount of solid. As shown in the illustration below the melt-solid mixture is considered independent of each component. In this way the flow can be modelled through the melt above the solid layer.+According to Potente and Melisch [[en:grundlagenhandbuch:aufschmelzberechnung:literatur|[Meli98, Pote96]]] the interactions are considered by using an effective channel height and width which is dependent on the amount of solid. As shown in the illustration below the melt-solid mixture is considered independent of each component. In this way the flow can be modelled through the melt above the solid layer.
  
 {{ :en:grundlagenhandbuch:aufschmelzberechnung:en_sigma150_dlg_grundlagenhandbuch_aufschmelzberechnung_012.svg?700%nolink |}} {{ :en:grundlagenhandbuch:aufschmelzberechnung:en_sigma150_dlg_grundlagenhandbuch_aufschmelzberechnung_012.svg?700%nolink |}}
  
-**Figure:** Consideration of the solid particle amount in the original disperse melting model [Thüm08]+**Figure:** Consideration of the solid particle amount in the original disperse melting model [[en:grundlagenhandbuch:aufschmelzberechnung:literatur|[Thüm08]]]
  
 In the modified melting model the flow in the melt-solid mixture is formed with the help of an adjustment of the viscosity. For this purpose the correction of the power law consistency with the factor $f_Φ$ is in introduced. In the modified melting model the flow in the melt-solid mixture is formed with the help of an adjustment of the viscosity. For this purpose the correction of the power law consistency with the factor $f_Φ$ is in introduced.
Zeile 67: Zeile 67:
 $$f_\phi = 1 + \frac{5}{2}\left(\frac{\phi_{M,s}}{\phi_{M,s} + \frac{\rho_s}{\rho_m}(1 - \phi_{M,s})}\right)\phi_{V,s} + \frac{141}{10}\left(\frac{\phi_{M,s}}{\phi_{M,s} + \frac{\rho_s}{\rho_m}(1 - \phi_{M,s})}\right)^2$$ $$f_\phi = 1 + \frac{5}{2}\left(\frac{\phi_{M,s}}{\phi_{M,s} + \frac{\rho_s}{\rho_m}(1 - \phi_{M,s})}\right)\phi_{V,s} + \frac{141}{10}\left(\frac{\phi_{M,s}}{\phi_{M,s} + \frac{\rho_s}{\rho_m}(1 - \phi_{M,s})}\right)^2$$
  
-If the $d_p/h$-ratio approaches 1 the particle diameter considered corresponds approximately to the channel height, and the influence of the particle size on the flow has to be considered. Following Pape [Pap06] another correction of the power law consistency is introduced.+If the $d_p/h$-ratio approaches 1 the particle diameter considered corresponds approximately to the channel height, and the influence of the particle size on the flow has to be considered. Following Pape [[en:grundlagenhandbuch:aufschmelzberechnung:literatur|[Pape06]]] another correction of the power law consistency is introduced.
  
 $$K_{sm} = K \cdot f_\phi \cdot f_{dh}$$ $$K_{sm} = K \cdot f_\phi \cdot f_{dh}$$