Properties update: lbh15 linking

[fpepe-polito]

Up to now, coolant properties are computed and updated by means of linear interpolation of tabulated values (ex. file lead.csv in the data folder) or defined by the user in the input file. All the tables in the data folder are obtained by means of correlations [1], and properties are calculated at a few specific temperatures. The following concerns have been identified:

• Since the temperature difference between successive values in tables is large (50 K), linear interpolation (as the one performed in the code) is less accurate.
• Some of the properties are given at temperatures outside of the validity range suggested for that specific correlation in [1]. In Tables 1-3, DASSH properties' range is compared to the validity range provided by the [2] for each correlation. Please, consider that information provided by the SCK reference coincides with those provided by the OECD/NEA Handbook [2].
• In Figure 1c, DASSH viscosity shows a discontinuous behavior, due to the approximation to 1e-3. Approximation in the tabulated values of viscosity leads to large relative errors when compared to the value given by the SCK correlation, as plotted in Figure 2.
• The values for the conductivity of LBE are not in accordance with the correlation in the reference, as shown in Figure 1d and Figure 3.

Given the issues presented above, linking DASSH to the properties' library lbh15 [3] can be performed for lead, bismuth and LBE, in order to obtain more accurate values for properties, to correct uncertain values (conductivity for LBE) and to adhere to the correct validity ranges by providing a warning each time the evaluation of the properties is required outside them.

LEAD	DASSH range [K]	Correlation NEA	Validity range [K]
Density	600 - 2000	Sobolev 2008a	600.60 - 2021
Specific heat	600 - 2000	gurvich1991	600.60 - 2000
Viscosity	600 - 2000	Sobolev 2007b	600.60 - 1473
Conductivity	600 - 2000	Sobolev 2007b	600.60 - 1300

Table 1: DASSH range of temperatures vs SCK vality range for lead properties.

LBE	DASSH range [K]	Correlation NEA	Validity range [K]
Density	400 - 1800	OECD/NEA Handbook	398 - 1927
Specific heat	400 - 1800	Sobolev 2011	400 - 1927
Viscosity	400 - 1800	Sobolev 2007b	398 - 1300
Conductivity	400 - 1800	Sobolev 2011	398 - 1200

Table 2: DASSH range of temperatures vs actual vality range for LBE properties.

BISMUTH	DASSH range [K]	Correlation NEA	Validity range [K]
Density	500 - 1800	Imbeni 1998a	544.60 - 1831
Specific heat	500 - 1800	Imbeni 1998a	544.60 - 1831
Viscosity	500 - 1800	Lucas 1984b	544.60 - 1300
Conductivity	500 - 1800	Touloukian 1970b	544.60 - 1000

Table 3: DASSH range of temperatures vs actual vality range for bismuth properties.

Figure 1: properties: DASSH vs lbh15.

Figure 2: viscosity relative error: DASSH vs lbh15.

Figure 3: thermal conductivity for LBE relative error: DASSH vs lbh15.

[1] https://inis.iaea.org/collection/NCLCollectionStore/_Public/43/095/43095088.pdf
[2] C. Fazio et Al. Handbook on Lead-bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal-hydraulics and Technologies. Technical Report No. 7268, OECD/Nuclear Energy Agency (NEA), Paris, France, 2015. doi:10.1787/42dcd531-en.
[3] https://newcleo-dev-team.github.io/lbh15/

[lelaus]

New tests implemented in 69f62d2 work appropriately. Please, @fpepe-polito improve their structure to avoid hard-coded values and automatize the management of all the available materials. All such requests will be managed in issue #2.

[fpepe-polito]

Property tables for lead, lbe and bismuth have been updated in d246ebb. Main changes are:

• only values within the validity range have been considered;
• precision is improved by including more significant digits (expecially for viscosity);
• values for lbe thermal conductivity have been computed again using Sobolev 2011, and corrected.

[fpepe-polito]

Computational time of the update() call with lbh15 and with the linear interpolation from tables, originally used in dassh, has been evaluated. As it can be observed in the figures attached, the increase in computational cost is of almost two orders of magnitudes with lbh15 is used. The user should decide the best method for his aim, choosing to favor precision over computational time or the opposite. Thus, the lbh15 option should be added to the input file.

[lelaus]

All the requests about the link to lbh15 package have been managed. Tests have been modified accordingly.

[lelaus]

The link to lbh15 does not cover all the available features. In particular, DASSH should allow the user to select which correlations of lbh15 to use.