Trang 2019a - Revision history

Rimni at 09:59, 2 July 2021

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Rimni at 09:55, 2 July 2021

2021-07-02T09:55:01Z

Rimni: /* 5. Conclusions */

2021-07-02T09:54:44Z

‎5. Conclusions

Rimni at 09:48, 2 July 2021

2021-07-02T09:48:32Z

Rimni at 09:47, 2 July 2021

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Rimni at 09:46, 2 July 2021

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Rimni at 09:46, 2 July 2021

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Rimni at 09:45, 2 July 2021

2021-07-02T09:45:42Z

Rimni: /* 4. Results */

2021-07-02T09:45:20Z

‎4. Results

Rimni at 09:43, 2 July 2021

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 ==References==
 <div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
 <div id="cite-1"></div>

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 The problem of determining a thin film on a RD and the minimum film thickness are investigated using CFD for a partially-submerged rotating drum. The analytical solution is too simplified to determine the <math display="inline">\delta _{min} </math> and CFD is needed to understand the dynamics of liquid film. A no-slip boundary condition was considered on the RD wall and the meniscus free surface was predicted using VOF. CFD investigation shows that <math display="inline">\delta _{min} </math>  increases with, same as experimental dd analytical solution. Because plunging end of RD was avoided by using a wiper, convergence behavior was quite stable.
-All the 12 case of the simulations shown in this paper were for isothermal conditions &nbsp;<span id='citeF-41'></span>[[#cite-41|[41]]], a terms used for this is called 'cold modeling'. It is possible to extend the model developed for the non-isothermal condition were the physical properties would change as a function of temperature. It is possible to extend the model developed for non-isothermal conditions were the physical properties would change as a function of temperature. If crystallization does occur and vaporization takes place, an equivalent sink/source term to be added in the model equations to account the mass/momentum/energy transfer and it would be more complicated. For the higher rate crystallization, the back flow will be miminised. From CFD point of the view, viscous film hold up is less complicated to predict. For a partial crystallization of the film would between Eq.(6) and Eq.(7).
+All the 12 case of the simulations shown in this paper were for isothermal conditions &nbsp;<span id='citeF-41'></span>[[#cite-41|[41]]], a terms used for this is called 'cold modeling'. It is possible to extend the model developed for the non-isothermal condition were the physical properties would change as a function of temperature. It is possible to extend the model developed for non-isothermal conditions were the physical properties would change as a function of temperature. If crystallization does occur and vaporization takes place, an equivalent sink/source term to be added in the model equations to account the mass/momentum/energy transfer and it would be more complicated. For the higher rate crystallization, the back flow will be miminised. From CFD point of the view, viscous film hold up is less complicated to predict. For a partial crystallization of the film would between Eqs.(6) and (7).
 ==6 List of Symbols==

@@ Line 188: / Line 188: @@
 <div id='img-4'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto%;"
 |-
 |style="padding:10px;"|[[Image:Trang_2019a_8061_a3a99387-1efd-4226-b821-454a619753bb-ufig4.png|400px|A minimum liquid film thickness for hexyl alcohol as a function of rotating speed of the drum for αₒ= 58<sup>o</sup>]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding-bottom:10px;"| '''Figure 4'''. A minimum liquid film thickness for hexyl alcohol as a function of rotating speed of the drum for <math>\alpha _o= </math>58<math>^{o}</math>
+| colspan="1" style="padding:10px;"| '''Figure 4'''. A minimum liquid film thickness for hexyl alcohol as a function of rotating speed of the drum for <math>\alpha _o= </math>58<math>^{o}</math>
 |}

@@ Line 12: / Line 12: @@
 <div id='img-1'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 60%;max-width: 60%;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;"
 |-
 |style="padding:10px;"|[[Image:Trang_2019a_8813_d71ae35a-79e2-422f-856c-ab069574daa4-ufig1.png|350px|Schematic diagram of the thin film on a partially-submerged rotating drum.]]

@@ Line 14: / Line 14: @@
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 60%;max-width: 60%;"
 |-
-|style="padding:10px;"|[[Image:Trang_2019a_8813_d71ae35a-79e2-422f-856c-ab069574daa4-ufig1.png|400px|Schematic diagram of the thin film on a partially-submerged rotating drum.]]
+|style="padding:10px;"|[[Image:Trang_2019a_8813_d71ae35a-79e2-422f-856c-ab069574daa4-ufig1.png|350px|Schematic diagram of the thin film on a partially-submerged rotating drum.]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding-bottom:10px;" | '''Figure 1'''. Schematic diagram of the thin film on a partially-submerged rotating drum
+| colspan="1" style="padding:10px;" | '''Figure 1'''. Schematic diagram of the thin film on a partially-submerged rotating drum
 |}

@@ Line 174: / Line 174: @@
 |style="padding:10px;"|[[Image:Trang_2019a_6821_561b9b41-2c2a-458c-91a8-f336b8733dbd-ufig3.png|400px|A minimum film thickness for hexyl alcohol as a function of ''rpm'' of the drum for αₒ= 47<sup>o</sup>]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding-bottom:10px;"| '''Figure 3'''. A minimum film thickness for hexyl alcohol as a function of ''rpm'' of the drum for <math>\alpha _o= </math>47<math>^{o}</math>
+| colspan="1" style="padding:10px;"| '''Figure 3'''. A minimum film thickness for hexyl alcohol as a function of ''rpm'' of the drum for <math>\alpha _o= </math>47<math>^{o}</math>
 |}

@@ Line 167: / Line 167: @@
 ==4. Results==
-Figure&nbsp;[[#img-3|3]] shows the <math display="inline">\delta _{min} </math> as function of'' rpm'' for <math display="inline">\alpha _o </math> = 47<math>^{0}</math> from three different sources, e.g., analytical solution without the CF (Eq.(6)), analytical solution with CF (Eq.(7)) and CFD &nbsp;<span id='citeF-35'></span>[[#cite-35|[35]]] solution. Apparently, the analytical solution without the CF is very close to the CFD &nbsp;<span id='citeF-36'></span><span id='citeF-37'></span>[[#cite-36|[36,37]]] prediction. In all three lots, the trend is the same. From Eq.(6) and Eq.(7), the <math display="inline">\delta _{min} </math> varies with is relationship of'' rpm'' (<math display="inline">\delta _{min}\infty rpm^{0.50} </math> ), for the CFD results it varies as <math display="inline">\delta _{min}\infty rpm^{0.47} </math>  . The properties of the hexyl alcohol are the same for all three sources (<math display="inline">\sigma  </math> =0.00384 N/m, <math display="inline">\rho </math>=812 kg/m3, <math display="inline">\mu </math> =0.00392 kg/m/s). In the original paper of &nbsp;<span id='citeF-8'></span><span id='citeF-9'></span>[[#cite-8|[8,9]]], the precise properties of hexyl alcohol was not reported.
+[[#img-3|Figure 3]] shows the <math display="inline">\delta _{min} </math> as function of'' rpm'' for <math display="inline">\alpha _o </math> = 47<math>^{0}</math> from three different sources, e.g., analytical solution without the CF (Eq.(6)), analytical solution with CF (Eq.(7)) and CFD &nbsp;<span id='citeF-35'></span>[[#cite-35|[35]]] solution. Apparently, the analytical solution without the CF is very close to the CFD &nbsp;<span id='citeF-36'></span><span id='citeF-37'></span>[[#cite-36|[36,37]]] prediction. In all three lots, the trend is the same. From Eqs.(6) and (7), the <math display="inline">\delta _{min} </math> varies with is relationship of'' rpm'' (<math display="inline">\delta _{min}\infty rpm^{0.50} </math> ), for the CFD results it varies as <math display="inline">\delta _{min}\infty rpm^{0.47} </math>  . The properties of the hexyl alcohol are the same for all three sources (<math display="inline">\sigma  </math> =0.00384 N/m, <math display="inline">\rho </math>=812 kg/m3, <math display="inline">\mu </math> =0.00392 kg/m/s). In the original paper of &nbsp;<span id='citeF-8'></span><span id='citeF-9'></span>[[#cite-8|[8,9]]], the precise properties of hexyl alcohol was not reported.
 <div id='img-3'></div>
@@ Line 177: / Line 177: @@
 |}
-There are few important aspects to highlight here. Firstly, the loss of liquid at the pressure outlet BC (Figure&nbsp;[[#img-2|2]]) is compensated by the same amount of liquid injection at the pressure inlet BC which is far away from the RD so there is little impact on the film dynamics of the inflow on the RD. It was expected though for a laminar condition when the plunging &nbsp;<span id='citeF-38'></span><span id='citeF-39'></span><span id='citeF-40'></span>[[#cite-38|[38,39,40]]] the point is avoided (no drop passes the wiper and falls on the receiving tank), there would be a steady state solution which is found to be wrong. Secondly, because of the plunging point is avoided; there is less complicate in terms of numerical instability. Thirdly, as the 10 plunging point is avoided, there is no consequence of entrained air in the form of bubbles from the plunging point which would disturb the stability of the solution. Fourthly, in the real wiper (Figure&nbsp;[[#img-1|1]]), it would not cause the surface completely free from hexyl alcohol
+There are few important aspects to highlight here. Firstly, the loss of liquid at the pressure outlet BC ([[#img-2|Figure 2]]) is compensated by the same amount of liquid injection at the pressure inlet BC which is far away from the RD so there is little impact on the film dynamics of the inflow on the RD. It was expected though for a laminar condition when the plunging &nbsp;<span id='citeF-38'></span><span id='citeF-39'></span><span id='citeF-40'></span>[[#cite-38|[38,39,40]]] the point is avoided (no drop passes the wiper and falls on the receiving tank), there would be a steady state solution which is found to be wrong. Secondly, because of the plunging point is avoided; there is less complicate in terms of numerical instability. Thirdly, as the 10 plunging point is avoided, there is no consequence of entrained air in the form of bubbles from the plunging point which would disturb the stability of the solution. Fourthly, in the real wiper ([[#img-1|Figure 1]]), it would not cause the surface completely free from hexyl alcohol
 before plunging into the liquid bath and also the surface property would change because of the erosion and the friction between the RD and the wiper would cause heat (maybe negligible).
@@ Line 195: / Line 195: @@
 |}
-Again striking similarities have been found for <math display="inline">\alpha _o </math> = 58<math>^{0}</math> as shown in Figure&nbsp;[[#img-4|4]] . There are four plots in Figure 4, e.g., two analytical solutions (Eq.(6) and Eq.(7)), CFD solutions and experimental data. The trend of variation of <math display="inline">\delta _{min} </math> has been proved the same in CFD, experimental and analytical results. In CFD results, <math display="inline">\delta _{min} </math> varies with ''rpm'' by <math display="inline">\delta _{min}=rpm^{0.48} </math> . Surprisingly again, Eq.(6) and CFD results are close and away from the Eq.(7) and experimental data by a factor 1/CF. The proportionality constant in CFD prediction for this case is only 4% a way from the critical prediction.
+Again striking similarities have been found for <math display="inline">\alpha _o </math> = 58<math>^{0}</math> as shown in [[#img-4|Figure 4]]. There are four plots in [[#img-4|Figure 4]], e.g., two analytical solutions (Eqs.(6) and (7)), CFD solutions and experimental data. The trend of variation of <math display="inline">\delta _{min} </math> has been proved the same in CFD, experimental and analytical results. In CFD results, <math display="inline">\delta _{min} </math> varies with ''rpm'' by <math display="inline">\delta _{min}=rpm^{0.48} </math> . Surprisingly again, Eq.(6) and CFD results are close and away from the Eq.(7) and experimental data by a factor 1/CF. The proportionality constant in CFD prediction for this case is only 4% a way from the critical prediction.
 ==5. Conclusions==

@@ Line 26: / Line 26: @@
 ==2. Computation Domain==
-The computational domain of an RD rotating anti-clockwise on a free liquid surface is shown in Figure&nbsp;[[#img-2|2]]. Various boundary conditions are shown in Table&nbsp;[[#table-1|1]].
+The computational domain of an RD rotating anti-clockwise on a free liquid surface is shown in [[#img-2|Figure 2]]. Various boundary conditions are shown in [[#table-1|Table 1]].
 <div class="center" style="font-size: 75%;">
 '''Table 1'''. List of BC for the model </div>
+<div id='table-1'></div>
 {|  class="floating_tableSCP" style="text-align: left; margin: 1em auto;border-top: 2px solid;border-bottom: 2px solid;min-width:40%;font-size:85%;"
 |-