Butler et al 2010a - Revision history

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Cinmemj moved page Draft Samper 527002806 to Butler et al 2010a

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← Older revision		Revision as of 13:43, 26 February 2018
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−	~~<span id='_GoBack'></span>~~
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−	~~==Modeling thermoplastic melt spread over different flooring materials==~~
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−	~~'''K.M. Butler'''<sup>1</sup>, '''E. Oñate'''<sup>2</sup>, '''R. Rossi'''<sup>2</sup>, '''J. Marti'''<sup>2</sup>, '''S.R. Idelsohn'''<sup>2</sup>~~
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−	~~<sup>1</sup> National Institute of Standards and Technology (NIST), USA<br />~~
−	~~<sup>2</sup> International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain~~

	==ABSTRACT==		==ABSTRACT==

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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-'''Figure 4.'''  Temperature contour plots at t = 750 s for 12.7 mm thick oak, ceramic, and steel floors</div>
+'''Figure 4.'''  Temperature contour plots at t = 750 s for 12.7 mm thick oak, ceramic, and steel floors</div><br />
 The locations of the melt front to the left and right of the drip point are plotted in Figure 6.  As observed, the spread rate for the cooling melt is slower than for the heated melt.  It is also not as even over time, reflecting slight changes in flow rate from the sample that are smoothed out by the more uniform viscosity of the heated melt.  The spread rate over steel is faster than that over ceramic for both cooling and heated melts.  This can be explained by the high conductivity of steel, which causes the temperature to rise over the entire steel substrate, reducing the viscosity at the outer edges of the melt pool.  Figure 7 illustrates this factor more clearly by plotting the temperatures of the particles on the leading edges of the spreading melt as a function of height above the floor.  In each case the average values of temperature along the leading edge are higher for steel than for oak, resulting in lower viscosities for the melt spreading over steel.  Since the viscosity of the melt at the edges of the melt pool is higher than the viscosity at the center, the edge viscosities are expected to have the greatest control over the spread rate.

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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 4.  Temperature contour plots at t = 750 s for 12.7 mm thick oak, ceramic, and steel floors</div>
+'''Figure 4.'''  Temperature contour plots at t = 750 s for 12.7 mm thick oak, ceramic, and steel floors</div>
 The locations of the melt front to the left and right of the drip point are plotted in Figure 6.  As observed, the spread rate for the cooling melt is slower than for the heated melt.  It is also not as even over time, reflecting slight changes in flow rate from the sample that are smoothed out by the more uniform viscosity of the heated melt.  The spread rate over steel is faster than that over ceramic for both cooling and heated melts.  This can be explained by the high conductivity of steel, which causes the temperature to rise over the entire steel substrate, reducing the viscosity at the outer edges of the melt pool.  Figure 7 illustrates this factor more clearly by plotting the temperatures of the particles on the leading edges of the spreading melt as a function of height above the floor.  In each case the average values of temperature along the leading edge are higher for steel than for oak, resulting in lower viscosities for the melt spreading over steel.  Since the viscosity of the melt at the edges of the melt pool is higher than the viscosity at the center, the edge viscosities are expected to have the greatest control over the spread rate.
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 5.  Temperature contour plots at t = 750 s for 12.7 mm thick oak, ceramic, and steel floors with a heated melt pool.</div>
+'''Figure 5.'''  Temperature contour plots at t = 750 s for 12.7 mm thick oak, ceramic, and steel floors with a heated melt pool.</div><br />
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 6.  Locations of leading edges of melt pool for 12.7 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors with and without heat flux to the melt pool.</div>
+'''Figure 6.'''  Locations of leading edges of melt pool for 12.7 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors with and without heat flux to the melt pool.</div><br />
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 7.  Temperatures along left and right leading edges of melt pool at time t= 750 for 12.7 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors a) without and b) with heat flux to the melt pool.</div>
+'''Figure 7.'''  Temperatures along left and right leading edges of melt pool at time t= 750 for 12.7 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors a) without and b) with heat flux to the melt pool.</div><br />
 Figures 8-11 show the behavior of the melt flow over thin oak, ceramic, and steel floors.  For both cooling and heated melt pools, Figure 10 shows that the spread rate over steel is the fastest overall, although for earlier times the spread rate is somewhat slower.  This may be an indication of the effects of the high thermal inertia of steel noted by Sherratt and Drysdale<sup>1</sup>, in which the initial melt spread is slowed due to the rapid conduction of heat away from the melt pool.  Due to the statistic nature of the PFEM, early drips are somewhat scattered in space, so this effect is difficult to assess.  A larger number of particles, providing a higher resolution finite element mesh, will be necessary to accurately view this phenomenon.
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 8.  Temperature contour plots at t = 750 s for 3 mm thick oak, ceramic, and steel floors</div>
+'''Figure 8.'''  Temperature contour plots at t = 750 s for 3 mm thick oak, ceramic, and steel floors</div><br />
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 9.  Temperature contour plots at t = 750 s for 3 mm thick oak, ceramic, and steel floors with a heated melt pool.</div>
+'''Figure 9.'''  Temperature contour plots at t = 750 s for 3 mm thick oak, ceramic, and steel floors with a heated melt pool.</div><br />
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 10.  Locations of leading edges of melt pool for 3 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors with and without heat flux to the melt pool</div>
+'''Figure 10.'''  Locations of leading edges of melt pool for 3 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors with and without heat flux to the melt pool</div><br />
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Figure 11.  Temperatures along left and right leading edges of melt pool at time t= 750 for 3 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors a) without and b) with heat flux to the melt pool</div>
+'''Figure 11.'''  Temperatures along left and right leading edges of melt pool at time t= 750 for 3 mm thick oak (dashed line), ceramic (dotted line), and steel (solid line) floors a) without and b) with heat flux to the melt pool</div><br />
 ==CONCLUSIONS==

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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-'''Figure 3'''.  Viscosity vs. temperature for PP702N polypropylene in its initial undegraded form and after exposure to 30 kW/m<sup>2</sup> and 40 kW/m<sup>2</sup> heat fluxes.  The black curve follows the extrapolation of viscosity to high temperatures</div>
+'''Figure 3'''.  Viscosity vs. temperature for PP702N polypropylene in its initial undegraded form and after exposure to 30 kW/m<sup>2</sup> and 40 kW/m<sup>2</sup> heat fluxes.  The black curve follows the extrapolation of viscosity to high temperatures</div><br />
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-'''Table 1'''. Material properties for polymer melt and floor</div>
+<span style="text-align: center; font-size: 75%;">
 {| style="width: 100%;border-collapse: collapse;"

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 <span style="text-align: center; font-size: 75%;">
 [[Image:draft_Samper_527002806-image1.png|center|282px]]
 '''Figure 1'''. Alpha shape determination of domain boundaries</span></div><br />

← Older revision	Revision as of 13:45, 26 February 2018
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 <span style="text-align: center; font-size: 75%;">
 [[Image:draft_Samper_527002806-image2.png|center|600px]]
 '''Figure 2'''. Attachment of fluid to a solid surface in the PFEM.</span></div><br />

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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-'''Figure 1'''. Alpha shape determination of domain boundaries</div><br />
+<span style="text-align: center; font-size: 75%;">
 Of particular interest for the dripping problem is the process by which the particles falling off the thermoplastic object land on the catch plate.  Figure 2 illustrates the approach of a fluid mass toward a wall.  In this illustration, '''C''' denotes the cloud of particles, '''Γ''' the boundary of the fluid mass derived from the particle locations, and '''V '''the analysis domain for the fluid, with superscripts ''n'' and ''n+1'' denoting times ''t<sub>n</sub>'' and ''t<sub>n+1</sub>''.  The alpha-shape method detects when a particle approaches to a point h<sup>e</sup> within a critical distance h<sub>crit</sub> of the wall.  When this occurs, the incompressibility constraint prevents the particle from going through the wall and converts momentum toward the wall into momentum parallel to the wall.  The particle experiences two additional forces: a normal force proportional to the difference (h<sup>e</sup>-h<sub>crit</sub>) in the direction away from the wall and a tangential force proportional to viscosity times the normal force pointed in the same direction as the original tangential velocity.  This procedure puts a limitation on the time step for the dripping thermoplastic problem, since drops must be detected before they travel through the catch plate.
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-'''Figure 2'''. Attachment of fluid to a solid surface in the PFEM.</div><br />
+<span style="text-align: center; font-size: 75%;">
 ==MODEL GEOMETRY AND INPUT PARAMETERS==

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 '''K.M. Butler'''<sup>1</sup>, '''E. Oñate'''<sup>2</sup>, '''R. Rossi'''<sup>2</sup>, '''J. Marti'''<sup>2</sup>,  '''S.R. Idelsohn'''<sup>2</sup>
-<sup>1</sup>National Institute of Standards and Technology (NIST), USA<br />
+<sup>1</sup> National Institute of Standards and Technology (NIST), USA<br />
-<sup>2</sup>International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain
+<sup>2</sup> International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain
 ==ABSTRACT==