FPROPS/Viscosity - Revision history

MarkJones: /* First correlation */ corrected some typos

2016-01-02T14:11:52Z

First correlation: corrected some typos

← Older revision		Revision as of 14:11, 2 January 2016
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	:<math>\mu_0 \left( T \right) = \frac{0.0266958 \sqrt{MT}}{\sigma^2 \Omega \left(T^{{}*{}}\right)}</math>		:<math>\mu_0 \left( T \right) = \frac{0.0266958 \sqrt{MT}}{\sigma^2 \Omega \left(T^{{}*{}}\right)}</math>

	Here, <math>\sigma</math> is referred to as the ''Lennard-Jones size parameter'', and is a length value specific to each fluid. <math>M</math>< is the molecular mass. The units of the value <math>0.0266958</math> need to be determined; Lemmon & Jacobsen state that the result as-written is returned in units of µPa·s. The expression <math>\Omega\left(T^{{}*{}}\right)</math> is referred to as the ''collision integral'' and is a series with fluid-specific coefficients <math>b_i</math> and exponents </math>i</math>, calculated as		Here, <math>\sigma</math> is referred to as the ''Lennard-Jones size parameter'', and is a length value specific to each fluid. <math>M</math> is the molecular mass. The units of the value <math>0.0266958</math> need to be determined; Lemmon & Jacobsen state that the result as-written is returned in units of µPa·s. The expression <math>\Omega\left(T^{{}*{}}\right)</math> is referred to as the ''collision integral'' and is a series with fluid-specific coefficients <math>b_i</math> and exponents <math>i</math>, calculated as

	:<math>\Omega \left( T^{{}{}} \right) = \exp \left(\sum_{i=0}^{n}{b_i {\left[\ln \left( T^{{}{}} \right) \right]} ^i} \right)</math>		:<math>\Omega \left( T^{{}{}} \right) = \exp \left(\sum_{i=0}^{n}{b_i {\left[\ln \left( T^{{}{}} \right) \right]} ^i} \right)</math>

Jpye at 05:08, 20 July 2014

2014-07-20T05:08:21Z

← Older revision		Revision as of 05:08, 20 July 2014
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	== First correlation ==		== First correlation ==

	Driven by the use-case of transport properties for supercritical carbon dioxide, the first required viscosity correlation follows this form<ref>A ~~Fengour~~, W A Wakeham and V Vesovic, 1998. "The Viscosity of Carbon Dioxide", ''J Phys Chem Ref Data'' '''27'''(1) ({{doi\|10.1063/1.556013}}, [http://web.mit.edu/ruddman/Public/Thermodynamics/co2%20viscosity.pdf pdf])</ref><ref>E W Lemmon and R T Jacobsen, 2004. "Viscosity and Thermal Conductivity Equations for Nitrogen, Oxgen, Argon and Air", ''International Journal of Thermophysics'' '''25'''(1) ({{doi\|10.1023/B:IJOT.0000022327.04529.f3}}, [http://www.boulder.nist.gov/div838/theory/refprop/NAO.PDF pdf])</ref>		Driven by the use-case of transport properties for supercritical carbon dioxide, the first required viscosity correlation follows this form<ref>A Fenghour, W A Wakeham and V Vesovic, 1998. "The Viscosity of Carbon Dioxide", ''J Phys Chem Ref Data'' '''27'''(1) ({{doi\|10.1063/1.556013}}, [http://web.mit.edu/ruddman/Public/Thermodynamics/co2%20viscosity.pdf pdf])</ref><ref>E W Lemmon and R T Jacobsen, 2004. "Viscosity and Thermal Conductivity Equations for Nitrogen, Oxgen, Argon and Air", ''International Journal of Thermophysics'' '''25'''(1) ({{doi\|10.1023/B:IJOT.0000022327.04529.f3}}, [http://www.boulder.nist.gov/div838/theory/refprop/NAO.PDF pdf])</ref>

	:<math>\mu = \mu_0 \left(T \right) + \mu_r \left(\tau,\delta \right) + \mu_c \left(\tau, \delta \right)</math>		:<math>\mu = \mu_0 \left(T \right) + \mu_r \left(\tau,\delta \right) + \mu_c \left(\tau, \delta \right)</math>

Jpye: /* First correlation */

2014-03-09T02:31:03Z

First correlation

← Older revision		Revision as of 02:31, 9 March 2014
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	:<math>\mu_r \left(\tau,\delta\right) = \sum_{i=1}^{n}{N_i \tau^{t_i} \delta^{d_i} \exp \left(-\gamma_i \delta^{l_i} \right)}</math>		:<math>\mu_r \left(\tau,\delta\right) = \sum_{i=1}^{n}{N_i \tau^{t_i} \delta^{d_i} \exp \left(-\gamma_i \delta^{l_i} \right)}</math>

	where <math>\tau = T_c / T</math>, <math>\delta = \rho / \rho_c</math<, and fluid-specific correlation data provides a table with n rows of values for <math>N_i</math>, <math>t_i</math>, <math>d_i</math> and <math>l_i</math>. The coefficient <math>\gamma_i</math> is defined as		where <math>\tau = T_c / T</math>, <math>\delta = \rho / \rho_c</math>, and fluid-specific correlation data provides a table with n rows of values for <math>N_i</math>, <math>t_i</math>, <math>d_i</math> and <math>l_i</math>. The coefficient <math>\gamma_i</math> is defined as

	:<math>\gamma_i = \begin{cases}		:<math>\gamma_i = \begin{cases}

Jpye: /* First correlation */

2014-03-09T02:30:45Z

First correlation

← Older revision		Revision as of 02:30, 9 March 2014
Line 21:		Line 21:
	:<math>\mu_r \left(\tau,\delta\right) = \sum_{i=1}^{n}{N_i \tau^{t_i} \delta^{d_i} \exp \left(-\gamma_i \delta^{l_i} \right)}</math>		:<math>\mu_r \left(\tau,\delta\right) = \sum_{i=1}^{n}{N_i \tau^{t_i} \delta^{d_i} \exp \left(-\gamma_i \delta^{l_i} \right)}</math>

	where a table with n rows of values for <math>N_i</math>, <math>t_i</math>, <math>d_i</math> and <math>l_i</math> ~~are part of the fluid-specific correlation data~~. The coefficient <math>\gamma_i</math> is defined as		where <math>\tau = T_c / T</math>, <math>\delta = \rho / \rho_c</math<, and fluid-specific correlation data provides a table with n rows of values for <math>N_i</math>, <math>t_i</math>, <math>d_i</math> and <math>l_i</math>. The coefficient <math>\gamma_i</math> is defined as

	:<math>\gamma_i = \begin{cases}		:<math>\gamma_i = \begin{cases}

Jpye at 00:19, 9 March 2014

2014-03-09T00:19:24Z

← Older revision		Revision as of 00:19, 9 March 2014
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	</math>		</math>

	The critical-point component, <math>\mu_c<\math> is not yet implemented.		The critical-point component, <math>\mu_c</math> is not yet implemented.

	== References ==		== References ==
	<references/>		<references/>

Jpye at 00:18, 9 March 2014

2014-03-09T00:18:44Z

← Older revision		Revision as of 00:18, 9 March 2014
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	The ideal part is calculated as		The ideal part is calculated as

	:<math>\mu_0 \left( T\right) = \frac{0.0266958 \sqrt{MT}}{\sigma^2 \Omega\left(T^{{}*{}}\right)</math>		:<math>\mu_0 \left( T \right) = \frac{0.0266958 \sqrt{MT}}{\sigma^2 \Omega \left(T^{{}*{}}\right)}</math>

	Here, <math>\sigma</math> is referred to as the ''Lennard-Jones size parameter'', a value ~~is provided for~~ each fluid. The expression <math>\Omega\left(\T^{{}*{}}\right) is referred to as the ''collision integral'' and is a series with fluid-specific coefficients and exponents calculated as		Here, <math>\sigma</math> is referred to as the ''Lennard-Jones size parameter'', and is a length value specific to each fluid. <math>M</math>< is the molecular mass. The units of the value <math>0.0266958</math> need to be determined; Lemmon & Jacobsen state that the result as-written is returned in units of µPa·s. The expression <math>\Omega\left(T^{{}*{}}\right)</math> is referred to as the ''collision integral'' and is a series with fluid-specific coefficients <math>b_i</math> and exponents </math>i</math>, calculated as

	:<math>\Omega \left( T^{{}{}} \right) = \exp left(\sum_{i=0}^{n}{b_i {\left[\ln \left( T^{{}{}} \right) \right]} ^i}</math>		:<math>\Omega \left( T^{{}{}} \right) = \exp \left(\sum_{i=0}^{n}{b_i {\left[\ln \left( T^{{}{}} \right) \right]} ^i} \right)</math>

			The residual part is calculated more simply, as

			:<math>\mu_r \left(\tau,\delta\right) = \sum_{i=1}^{n}{N_i \tau^{t_i} \delta^{d_i} \exp \left(-\gamma_i \delta^{l_i} \right)}</math>

			where a table with n rows of values for <math>N_i</math>, <math>t_i</math>, <math>d_i</math> and <math>l_i</math> are part of the fluid-specific correlation data. The coefficient <math>\gamma_i</math> is defined as

			:<math>\gamma_i = \begin{cases}
			0 & l_i = 0 \\
			1 & \mbox{otherwise}
			\end{cases}
			</math>

			The critical-point component, <math>\mu_c<\math> is not yet implemented.

	== References ==		== References ==
	<references/>		<references/>

Jpye at 23:37, 8 March 2014

2014-03-08T23:37:00Z

← Older revision		Revision as of 23:37, 8 March 2014
Line 11:		Line 11:
	The ideal part is calculated as		The ideal part is calculated as

	:<math>\mu_0 \left(T\right) = \frac{0.0266958 \sqrt{MT}}{\sigma^2 \Omega\left(T^{{}*{}}\right)</math>		:<math>\mu_0 \left( T\right) = \frac{0.0266958 \sqrt{MT}}{\sigma^2 \Omega\left(T^{{}*{}}\right)</math>

	Here, <math>\sigma</math> is referred to as the ''Lennard-Jones size parameter'', a value is provided for each fluid. The expression <math>\Omega\left(\T^{{}*{}}\right) is referred to as the ''collision integral'' and is a series with fluid-specific coefficients and exponents calculated as		Here, <math>\sigma</math> is referred to as the ''Lennard-Jones size parameter'', a value is provided for each fluid. The expression <math>\Omega\left(\T^{{}*{}}\right) is referred to as the ''collision integral'' and is a series with fluid-specific coefficients and exponents calculated as

	:<math>\Omega \left(T^{{}{}}\right) = \exp left(\sum_{i=0}^{n}{b_i \left(\ln \left(T^{{}{}}\right)\right]^i}</math>		:<math>\Omega \left( T^{{}{}} \right) = \exp left(\sum_{i=0}^{n}{b_i {\left[\ln \left( T^{{}{}} \right) \right]} ^i}</math>


	== References ==		== References ==
	<references/>		<references/>

Jpye at 23:35, 8 March 2014

2014-03-08T23:35:49Z

← Older revision		Revision as of 23:35, 8 March 2014
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	where dynamic viscosity <math>\mu</math> is the sum of an ideal (zero-pressure) component <math>\mu_0</math>, a residual component <math>\mu_r</math>, and optionally, a critical-region component <math>\mu_c</math>. Note that viscosity is said to increase to infinity in the vicinity of the critical point (which seems to suggest that it would make more sense to calculate in terms of something like an 'inviscidity' instead...?)		where dynamic viscosity <math>\mu</math> is the sum of an ideal (zero-pressure) component <math>\mu_0</math>, a residual component <math>\mu_r</math>, and optionally, a critical-region component <math>\mu_c</math>. Note that viscosity is said to increase to infinity in the vicinity of the critical point (which seems to suggest that it would make more sense to calculate in terms of something like an 'inviscidity' instead...?)

			The ideal part is calculated as

			:<math>\mu_0 \left(T\right) = \frac{0.0266958 \sqrt{MT}}{\sigma^2 \Omega\left(T^{{}*{}}\right)</math>

			Here, <math>\sigma</math> is referred to as the ''Lennard-Jones size parameter'', a value is provided for each fluid. The expression <math>\Omega\left(\T^{{}*{}}\right) is referred to as the ''collision integral'' and is a series with fluid-specific coefficients and exponents calculated as

			:<math>\Omega \left(T^{{}{}}\right) = \exp left(\sum_{i=0}^{n}{b_i \left(\ln \left(T^{{}{}}\right)\right]^i}</math>


	== References ==		== References ==
	<references/>		<references/>

Jpye: Created page with "Calculation of '''viscosity''' in FPROPS is currently in development. Ultimately, different publications provide different types of correlations (equations), so we impleme..."

2014-03-08T23:30:23Z

Created page with "Calculation of '''viscosity''' in FPROPS is currently in development. Ultimately, different publications provide different types of correlations (equations), so we impleme..."

New page

Calculation of '''viscosity''' in [[FPROPS]] is currently in development. Ultimately, different publications provide different types of correlations (equations), so we implement a system that permits alternative correlations to be selected.

== First correlation ==

Driven by the use-case of transport properties for supercritical carbon dioxide, the first required viscosity correlation follows this form<ref>A Fengour, W A Wakeham and V Vesovic, 1998. "The Viscosity of Carbon Dioxide", ''J Phys Chem Ref Data'' '''27'''(1) ({{doi|10.1063/1.556013}}, [http://web.mit.edu/ruddman/Public/Thermodynamics/co2%20viscosity.pdf pdf])</ref><ref>E W Lemmon and R T Jacobsen, 2004. "Viscosity and Thermal Conductivity Equations for Nitrogen, Oxgen, Argon and Air", ''International Journal of Thermophysics'' '''25'''(1) ({{doi|10.1023/B:IJOT.0000022327.04529.f3}}, [http://www.boulder.nist.gov/div838/theory/refprop/NAO.PDF pdf])</ref>

:<math>\mu = \mu_0 \left(T \right) + \mu_r \left(\tau,\delta \right) + \mu_c \left(\tau, \delta \right)</math>

where dynamic viscosity <math>\mu</math> is the sum of an ideal (zero-pressure) component <math>\mu_0</math>, a residual component <math>\mu_r</math>, and optionally, a critical-region component <math>\mu_c</math>. Note that viscosity is said to increase to infinity in the vicinity of the critical point (which seems to suggest that it would make more sense to calculate in terms of something like an 'inviscidity' instead...?)

== References ==
<references/>