Viscosity Correlation for Aqueous Lithium Bromide Solution [original]

Vol.:(0123456789)

International Journal of Thermophysics (2023) 44:21

https://doi.org/10.1007/s10765-022-03122-w

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Viscosity Correlation forAqueous Lithium Bromide Solution

ChristianFleßner1 · FelixZiegler1

Received: 20 July 2022 / Accepted: 21 October 2022 / Published online: 2 December 2022

Abstract

A correlation for dynamic viscosity of aqueous lithium bromide solution is pro-

posed. The correlation is based on an empirical approach accounting for physical

limitations. The data are compiled from 11 sources over a temperature range from

− 20

◦

C to 110

◦

C and from pure water to salt mass fractions of 65%. The correla-

tion succeeds in predicting the solution’s viscosity over the chosen range of meas-

ured data. In most parts of its validity range the accuracy is significantly improved

compared to previous equations.

Keywords Aqueous solution· Correlation· Lithium bromide· Saline solution·

Viscosity

1 Introduction

The extension of the operation range of absorption heat pumps and chillers with

aqueous lithium bromide as working pair to evaporator temperatures below

0◦C

requires an additive in the refrigerant circuit to avoid freezing. Lithium Bromide

(LiBr) is an obvious choice for this purpose. Thus, the need to calculate thermody-

namic and transport processes as well as the need to evaluate measured data over an

extended range of mass fraction and temperature arises. This depends on reliable

and consistent property data.

The dynamic viscosity is an important measure for all calculations of heat and

mass transfer related to flow phenomena. Ideally, a single correlation should be usa-

ble to accurately calculate viscosity from very dilute conditions near to pure water

at temperatures below

0◦C

to concentrated solutions at high temperatures, to avoid

inconsistencies. No currently available empirical or theoretical equation is able to

provide this range.

* Christian Fleßner

[email protected]

Felix Ziegler

f[email protected]

1 Institut für Energietechnik, Technische Universität Berlin, Marchstr. 18, 10587Berlin, Germany

International Journal of Thermophysics (2023) 44:21

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Fleßner etal. [1] presented an approach for a correlation of low-temperature ther-

mophysical property data of dilute aqueous solutions of lithium bromide based on

the experimental data of Sawada etal. [2] normalized with pure water properties

calculated by IAPWS SR06-08 [3, 4]. The issue with the selected approach is its

limitation to the low concentration range of the data it is based on. The correlation

is not suitable for extrapolation to mass fractions higher than

𝜉=0.2

. Attempts to fit

data over a wider range with the same form of correlation failed to deliver satisfac-

tory results.

Simple theory-based approaches like the Falkenhagen [5] and Jones–Dole equa-

tions [6] are limited to very dilute solutions. Extensions like the semi-empirical

Kaminsky equation [7] suffer from difficulties for the determination of the tempera-

ture dependence of their higher order coefficients. More recent approaches for a the-

oretical derivation like from Jiang and Sandler [8] are computationally too demand-

ing for general purpose engineering calculations.

The often used correlation of Lee etal. [9] featured in the textbook by Herold

etal. [10] is primarily centered on the mass fraction and temperature range encoun-

tered in absorber and desorber of absorption heat pumps, claiming a validity of

𝜉=0.45

to 0.65 and

T=312.9 K

to 427.7 K. The correlation used in the second

edition of the same textbook [11] does not give any validity range at all. It is not

published and available only via the help files of the calculation software EES [12].

The correlation of Kim and Infante Ferreira [13,p. 32] is based on the experi-

mental data of Lee etal. [9] and unspecified data for pure water. A validity of

𝜉=0

to 65 and

0◦C

220 ◦C

is claimed. A commercial implementation for several com-

putational software suites [14] also exists.

To remedy the lack of an applicable equation ranging from below

0◦C

to high

desorber temperatures, a simple new correlation extended from the form of [1] to fit

the experimental data in a temperature range from

−20 ◦C

110 ◦C

and from pure

water to saline mass fractions of

𝜉=0.65

is proposed. The limits of the temperature

range are determined by the validity limits of the correlation chosen for the normali-

zation [3]. In the present article, the data considered for this equation are analyzed

first. In a next step the equation’s form is derived from the experimental data’s slope

and suitable parameters are fitted. Finally, the correlation is compared to the experi-

mental data with an additional comparison of existing correlations with the same set

of data.

2 Analysis ofData

The experimental data of [2, 9, 15–23] have been compiled. Only measured data are

used. Therefore, interpolated data like [24, 25] as well as the smoothed data reported

in [16] have been excluded from the compilation of data. The data of Valyashko’s

compilation [26] were not used, since apart from the data of Lee etal. [9] it contains

only data for temperatures outside the scope of this study (

446 K

and above). The

data were collected either by extracting them from diagrams with WebPlotDigitizer

[27] or by transcribing tabular data. Different units for salt content were converted

to mass fraction. Temperature and dynamic viscosity were converted to

and

Pa s

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International Journal of Thermophysics (2023) 44:21 Page 3 of 23 21

The data sources with their respective limits and number of overall and excluded

data points as well as the symbols used in Figs.1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are listed

in Table1.

The viscosity of pure water

𝜂W

used to determine the reduced viscosity (viscosity of

solution divided by viscosity of solvent —

𝜂sol∕𝜂W

) is calculated with IAPWS SR6-

08 [3, 4] since it provides an accurate and computationally efficient equation with

only temperature as the independent variable. Pressure dependence of thermophysi-

cal properties of aqueous solutions is not an issue at the moderate pressures encoun-

tered in absorption chillers and heat pumps (see the comparison in Appendix A).

This correlation is valid from

−20 ◦C

110 ◦C

, determining the limits of the pre-

sented correlation in terms of temperature. This range is sufficient for single-effect

absorption heat pumps and chillers. For a further extension of validity aiming at

multi effect chillers and heat pumps as well as heat transformers a different equation

for pure water has to be used.

The limits concerning mass fraction are derived from the desire for an extrapola-

tion to pure water on the one hand and from the highest mass fraction of measured

data available on the other hand.

The range of data considered is displayed in Fig.1. The dashed lines indicate

the selected temperature range. The other boundaries are given by the calculated

crystallization lines [28] and the overall selected mass fraction range. No significant

gaps in the considered range are visible. The measured values not included into the

fit are marked in a lighter shade of gray. It is visible that only data of Lee etal. [9]

are above the upper boundary. The only data below the selected temperature range

are from Mashovets etal. [19]. It is noticeable that some of the data are below the

calculated crystallization line. This includes the lowest temperature data of [19] as

well as single data points of [2, 23]. It cannot be discerned whether this is due to

uncertainties of the calculated crystallization line, due to uncertainties of the respec-

tive author’s mass fraction measurement or due to subcooled states in the exper-

imental investigations. Since these data are still plausible within the usual uncer-

tainty they were included into the correlation’s database. Apart from data outside the

desired validity range, further data points were excluded from the database before

fitting. The data for pure water from Cao etal. [15] and Löwer [17] were not used, to

avoid contradictions with the calculated pure water properties according to IAPWS

SR6-08 [3] in the fitting process. Data points with a viscosity lower than that of pure

water occurring in the datasets of Rohman etal. [21] and Sawada etal. [2] are also

excluded from the fit. Though such a behavior occurs in some saline solutions like

potassium bromide (see Jiang & Sandler [8]), all known experimental data or theo-

retical studies for lithium bromide apart from [21] and some data points of [2] show

a monotonic increase of reduced viscosity with increasing salt content. Therefore,

the respective data are discarded as unphysical.

Figure2 shows the viscosity of all selected data points over T and

𝜉

. Despite the

high density of data points basic outlines of isosteric and isothermal lines are visible

following the experimental conditions selected by their original authors. In Fig.2a

the viscosity of pure water is visualized with a dotted line with additional larger

dots. Otherwise only the respective data’s sources are distinguished with different

International Journal of Thermophysics (2023) 44:21

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Table 1 Overview on data sources

a Data outside the selected validity range are excluded from the correlation’s database and are not included in Figs.2, 3, 4, 5, 6, 7, 8, and 9

b The pure water data were not included into the correlation’s database, but are included in Figs.2, 3, 4, and 6

c The data below the viscosity of pure water were removed from the correlation’s database, see below. They are still included in Figs.2, 3, 4, and 6

Data source

Tmin

(K)

Tmax

(K)

𝜉min

𝜉max

ndata

nexcl

Symbol

Cao etal. [15]

303.15

343.15

0 0.5468 40 5b

Hasaba etal. [16]

273.15

363.15

0.1143 0.6068 61 0

◻

Lee etal. [9]

312.9

472.9

0.45 0.65 52 30a

♢

Löwer [17]

273.15

373.15

0 0.65 147 11b

◦

Lo Surdo etal. [18]

278.15

338.15

0.0799 0.4648 33 0

▿

Mashovets etal. [19]

213.15

363.15

0.0506 0.4988 54 9a

⊲

Raatschen [20]

293.15

333.15

0.3 0.55 9 0

⊳

Rohman etal. [21]

273.15

323.15

0.0105 0.5498 176 33c

Satoh etal. [22]

300.15

0.0502 0.3196 10 0

Sawada etal. [2]

264.57

298.69

0.05 0.2 74 7cX

Wimby etal. [23]

298.06

373.26

0.1531 0.5850 29 0

△

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International Journal of Thermophysics (2023) 44:21 Page 5 of 23 21

Fig. 1 Crystallization line and measured data used for correlation, Symbols for data sources in the legend

according to Table1

(a) (b)

Fig. 2 Viscosity over T (a) and

𝜉

(b), measured data, not filtered , Symbols for data sources in the legend

according to Table1

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