First Order Phase Transition Material - Revision history

Nairnj: /* History Variables */

2019-06-26T22:31:13Z

History Variables

← Older revision		Revision as of 22:31, 26 June 2019
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	== History Variables ==		== History Variables ==

	This material tracks two history variables:		This material tracks two history variables if ΔT>0 and three if ΔT<=0 (''i.e.'', when using a sharp transition):

	# The currently active phase with 0 for solid phase and 1 for liquid phase. When modeling a sharp transition, this value will range form 0 to 1 to indicate fraction liquid state.		# The currently active phase with 0 for solid phase and 1 for liquid phase. When modeling a sharp transition, this value will range form 0 to 1 to indicate fraction liquid state.
	# The melting point of the particle. It is constant throughout the analysis, but can be visualized as random variable if Tsigma>0.		# The melting point of the particle. It is constant throughout the analysis, but can be visualized as random variable if Tsigma>0.
	# Particle ΔV in time step during transition when modeled with a sharp transition (ΔT<0).		# Particle ΔV in time step during transition when modeled with a sharp transition (only when ΔT<=0).

	~~For history variable~~ n>~~2, the output is history variable~~ n~~-2 of~~ the solid ~~phase~~ material. ~~The~~ liquid ~~phase will start after~~ the ~~solid phase~~ variables.		History variables greater than ''n'' (where ''n''=2 for ΔT>0 and ''n''=3 for ΔT<=0) will be for the solid or the liquid material. If the solid material as ''s'' history variable and liquid has ''l'' variables, the variables are access by number using

			# Solid variables 1 to ''s'' are in history ''n''+1 to ''n+s''
			# Liquid variables 1 to ''l'' are in history variables ''n+s''+1 to ''n+s+l''

	== Examples ==		== Examples ==

Nairnj: /* Material Properties */

2019-06-26T22:20:15Z

Material Properties

← Older revision		Revision as of 22:20, 26 June 2019
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	\| Tsigma \|\| The standard deviation for the transition temperature (K). The temperature range will be limited to +/- three standard deviations \|\| K \|\| 0		\| Tsigma \|\| The standard deviation for the transition temperature (K). The temperature range will be limited to +/- three standard deviations \|\| K \|\| 0
	\|-		\|-
	\| DeltaT \|\| A transition width for application of increased heat capacity and increased thermal expansion. If K=0 ~~(only allowed in "transport only" compiled code)~~, the transition is sharp at the melting point. \|\| K \|\| 10		\| DeltaT \|\| A transition width for application of increased heat capacity and increased thermal expansion. If ΔT<=0, the transition is sharp at the melting point. \|\| K \|\| 10
	\|-		\|-
	\| PeakShape \|\| Peak style for transition region: 0=hat, 1=box, 2=sech<sup>2</sup>, 3=smooth step as described above \|\| none \|\| 3		\| PeakShape \|\| Peak style for transition region: 0=hat, 1=box, 2=sech<sup>2</sup>, 3=smooth step as described above \|\| none \|\| 3

Nairnj: /* History Variables */

2018-11-02T23:18:09Z

History Variables

← Older revision		Revision as of 23:18, 2 November 2018
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	# The currently active phase with 0 for solid phase and 1 for liquid phase. When modeling a sharp transition, this value will range form 0 to 1 to indicate fraction liquid state.		# The currently active phase with 0 for solid phase and 1 for liquid phase. When modeling a sharp transition, this value will range form 0 to 1 to indicate fraction liquid state.
	# The melting point of the particle. It is constant throughout the analysis, but can be visualized as random variable if Tsigma>0.		# The melting point of the particle. It is constant throughout the analysis, but can be visualized as random variable if Tsigma>0.
			# Particle ΔV in time step during transition when modeled with a sharp transition (ΔT<0).

	For history variable n>2, the output is history variable n-2 of the solid phase material. The liquid phase will start after the solid phase variables.		For history variable n>2, the output is history variable n-2 of the solid phase material. The liquid phase will start after the solid phase variables.

Nairnj: /* Examples */

2018-09-07T18:18:14Z

Examples

← Older revision		Revision as of 18:18, 7 September 2018
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	Cv 21.13		Cv 21.13
	Done		Done

	Material "liquid","Liquid Material","TaitLiquid"		Material "liquid","Liquid Material","TaitLiquid"
	K 2.5		K 2.5
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	alpha 70		alpha 70
	Done		Done

	Material "phases","Transition Material","PhaseTransition"		Material "phases","Transition Material","PhaseTransition"
	SolidPhase "solid"		SolidPhase "solid"

Nairnj: /* Examples */

2018-09-07T18:18:00Z

Examples

← Older revision		Revision as of 18:18, 7 September 2018
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	== Examples ==		== Examples ==

	Material "solid","Neohookean Material","Neohookean"		Material "solid","Neohookean Material","Neohookean"
	E ~~#Ebase~~		E 10
	nu ~~#nuBase~~		nu .33
	~~rho #~~rho		rho 1
	alpha ~~#aBase~~		alpha 40
	kCond 200		kCond 200
	Cv 21.13		Cv 21.13
	Done		Done

	Material "liquid","Liquid Material","TaitLiquid"		Material "liquid","Liquid Material","TaitLiquid"
	K ~~#Kbulk/4~~		K 2.5
	viscosity 50		viscosity 50
	rho 1		rho 1
	kCond 100		kCond 100
	Cv 41.13		Cv 41.13
	alpha 70		alpha 70
	Done		Done

	Material "phases","Transition Material","PhaseTransition"		Material "phases","Transition Material","PhaseTransition"
	SolidPhase "solid"		SolidPhase "solid"
	LiquidPhase "liquid"		LiquidPhase "liquid"
	Tmelt 310		Tmelt 310
	DeltaT 5		DeltaT 5
	Tsigma 3		Tsigma 3
	Hfusion 250		Hfusion 250
	Done		Done

Nairnj: /* Examples */

2018-09-07T18:15:20Z

Examples

← Older revision		Revision as of 18:15, 7 September 2018
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	== Examples ==		== Examples ==

			Material "solid","Neohookean Material","Neohookean"
			E #Ebase
			nu #nuBase
			rho #rho
			alpha #aBase
			kCond 200
			Cv 21.13
			Done

			Material "liquid","Liquid Material","TaitLiquid"
			K #Kbulk/4
			viscosity 50
			rho 1
			kCond 100
			Cv 41.13
			alpha 70
			Done

			Material "phases","Transition Material","PhaseTransition"
			SolidPhase "solid"
			LiquidPhase "liquid"
			Tmelt 310
			DeltaT 5
			Tsigma 3
			Hfusion 250
			Done

Nairnj: /* Modeling with a Finite Width Transition */

2018-09-07T18:07:40Z

Modeling with a Finite Width Transition

← Older revision		Revision as of 18:07, 7 September 2018
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	<math>f_L = \frac{1}{2}\left[1-\coth(k)\tanh\left(\frac{k(T-T_m)}{\Delta T}\right)\right]</math>		<math>f_L = \frac{1}{2}\left[1-\coth(k)\tanh\left(\frac{k(T-T_m)}{\Delta T}\right)\right]</math>
	<br><br>The resulting peak follows a sech<sup>2</sup> function with peak ΔC of k coth(k)ΔH<sub>f</sub>/(2ΔT) and Δα of k coth(k)ΔV<sub>f</sub>/(2ΔT) at T<sub>m</sub>. Here k is a parameter characterizing sharpness of the transition. As k approaches zero, this shape become a box shape. As k increases the peak gets sharper and approaches Dirac δ(T-T<sub>m</sub>) function for large k. Choosing very high k effectively makes the transition very stiff and simulations lose accuracy unless ~~any~~ transitions occur ~~vary~~ slowly. The default value is k = 3.		<br><br>The resulting peak follows a sech<sup>2</sup> function with peak ΔC of k coth(k)ΔH<sub>f</sub>/(2ΔT) and Δα of k coth(k)ΔV<sub>f</sub>/(2ΔT) at T<sub>m</sub>. Here k is a parameter characterizing sharpness of the transition. As k approaches zero, this shape become a box shape. As k increases the peak gets sharper and approaches Dirac δ(T-T<sub>m</sub>) function for large k. Choosing very high k effectively makes the transition very stiff and simulations lose accuracy unless transitions occur very slowly. The default value is k = 3.
	</li>		</li>
	<li>Smooth Step (shape 3): This option sets ''f<sub>L</sub>'' to a [https://en.wikipedia.org/wiki/Smoothstep fifth-order step function] from 0 to 1 such that peak shape has zero slopes at T<sub>melt</sub>-ΔT and T<sub>melt</sub>+ΔT and peak ΔC of 15ΔH<sub>f</sub>/(16ΔT) and peak Δα of 15ΔV<sub>f</sub>/(16ΔT) at T<sub>m</sub>		<li>Smooth Step (shape 3): This option sets ''f<sub>L</sub>'' to a [https://en.wikipedia.org/wiki/Smoothstep fifth-order step function] from 0 to 1 such that peak shape has zero slopes at T<sub>melt</sub>-ΔT and T<sub>melt</sub>+ΔT and peak ΔC of 15ΔH<sub>f</sub>/(16ΔT) and peak Δα of 15ΔV<sub>f</sub>/(16ΔT) at T<sub>m</sub>

Yaimene: /* Modeling with a Finite Width Transition */

2018-06-26T22:03:48Z

Modeling with a Finite Width Transition

← Older revision		Revision as of 22:03, 26 June 2018
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	<ul>		<ul>
	<li>Hat (shape 0): This option uses a piece-wise quadratic function for ''f<sub>L</sub>'' such that transition peak ia triangular "hat" function with peak ΔC of ΔH<sub>f</sub>/ΔT and peak Δα of ΔV<sub>f</sub>/ΔT at T<sub>m</sub>.</li>		<li>Hat (shape 0): This option uses a piece-wise quadratic function for ''f<sub>L</sub>'' such that transition peak is triangular "hat" function with peak ΔC of ΔH<sub>f</sub>/ΔT and peak Δα of ΔV<sub>f</sub>/ΔT at T<sub>m</sub>.</li>
	<li>Box (shape 1): This option sets ''f<sub>L</sub>'' to a linear function from 0 to 1 that results in constant ΔC = ΔH<sub>f</sub>/(2ΔT) and Δα = ΔV<sub>f</sub>/(2ΔT) within the transition.</li>		<li>Box (shape 1): This option sets ''f<sub>L</sub>'' to a linear function from 0 to 1 that results in constant ΔC = ΔH<sub>f</sub>/(2ΔT) and Δα = ΔV<sub>f</sub>/(2ΔT) within the transition.</li>
	<li>~~Sech^~~2 (shape 2): This option sets ''f<sub>L</sub>'' to a truncated and normalized exponential step function:		<li>sech<sup>2</sup> (shape 2): This option sets ''f<sub>L</sub>'' to a truncated and normalized exponential step function:
	<br><br>		<br><br>

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	The figure on the right plots the above shapes for ΔT = 10 degrees.		The figure on the right plots the above shapes for ΔT = 10 degrees.

	For numerical modeling, ~~the~~ you enter the total heat of fusion, ''f<sub>L</sub>'' shape style, transition width parameter ΔT, and peak shape factor (if needed, such as k for shape=2). The same transition function is used for Δα where ΔV<sub>f</sub> is found from density difference between solid and liquid phases. Because implementation of heat of fusion is done through heat capacity, all simulations with phase transition materials should activate [[Thermal_Calculations#Conduction\|coupled conduction calculations]] (conduction is also needed to see changes in temperature that can lead to phase changes). The values for ΔT and peak shape function may need to varied for numerical stability in specific problems.		For numerical modeling, you enter the total heat of fusion, ''f<sub>L</sub>'' shape style, transition width parameter ΔT, and peak shape factor (if needed, such as k for shape=2). The same transition function is used for Δα where ΔV<sub>f</sub> is found from density difference between solid and liquid phases. Because implementation of heat of fusion is done through heat capacity, all simulations with phase transition materials should activate [[Thermal_Calculations#Conduction\|coupled conduction calculations]] (conduction is also needed to see changes in temperature that can lead to phase changes). The values for ΔT and peak shape function may need to varied for numerical stability in specific problems.

	=== Modeling with a Sharp Transition ===		=== Modeling with a Sharp Transition ===

Nairnj: /* Modeling with a Finite Width Transition */

2018-03-01T00:13:07Z

Modeling with a Finite Width Transition

← Older revision		Revision as of 00:13, 1 March 2018
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	<br><br>The resulting peak follows a sech<sup>2</sup> function with peak ΔC of k coth(k)ΔH<sub>f</sub>/(2ΔT) and Δα of k coth(k)ΔV<sub>f</sub>/(2ΔT) at T<sub>m</sub>. Here k is a parameter characterizing sharpness of the transition. As k approaches zero, this shape become a box shape. As k increases the peak gets sharper and approaches Dirac δ(T-T<sub>m</sub>) function for large k. Choosing very high k effectively makes the transition very stiff and simulations lose accuracy unless any transitions occur vary slowly. The default value is k = 3.		<br><br>The resulting peak follows a sech<sup>2</sup> function with peak ΔC of k coth(k)ΔH<sub>f</sub>/(2ΔT) and Δα of k coth(k)ΔV<sub>f</sub>/(2ΔT) at T<sub>m</sub>. Here k is a parameter characterizing sharpness of the transition. As k approaches zero, this shape become a box shape. As k increases the peak gets sharper and approaches Dirac δ(T-T<sub>m</sub>) function for large k. Choosing very high k effectively makes the transition very stiff and simulations lose accuracy unless any transitions occur vary slowly. The default value is k = 3.
	</li>		</li>
	<li>Smooth Step (shape 3): This option sets ''f<sub>L</sub>'' to a [https://en.wikipedia.org/wiki/Smoothstep fifth-order step function] from 0 to 1 such that peak shape has zero slopes at T<sub>melt</sub>-ΔT and T<sub>melt</sub>+ΔT and peak ΔC of ~~16ΔH~~<sub>f</sub>/(16ΔT) and ~~peak~~ peak Δα of 15ΔV<sub>f</sub>/(16ΔT) at T<sub>m</sub>		<li>Smooth Step (shape 3): This option sets ''f<sub>L</sub>'' to a [https://en.wikipedia.org/wiki/Smoothstep fifth-order step function] from 0 to 1 such that peak shape has zero slopes at T<sub>melt</sub>-ΔT and T<sub>melt</sub>+ΔT and peak ΔC of 15ΔH<sub>f</sub>/(16ΔT) and peak Δα of 15ΔV<sub>f</sub>/(16ΔT) at T<sub>m</sub>
	</ul>		</ul>

Nairnj: /* Modeling with a Finite Width Transition */

2018-02-15T19:38:40Z

Modeling with a Finite Width Transition

← Older revision		Revision as of 19:38, 15 February 2018
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	This material can use several different ''f<sub>L</sub>'' functions:		This material can use several different ''f<sub>L</sub>'' functions:

	[[File:TransitionPeaks.png\|right]]		[[File:TransitionPeaks.png\|400px\|right]]

	<ul>		<ul>