Energy losses of ice slurry in pipe sudden contractions
Introduction
Environmentally friendly refrigerants such as ammonia, carbon dioxide, hydrocarbons, or water (and solutions) are more and more frequently used nowadays. Ice slurry belongs to new ecological coolants applied in indirect cooling systems. It is a mixture of a basic liquid (which can even be water) and solid particles with the size of up to 0.5 mm. The coolant has a range of advantages, such as the fact that it causes no adverse environmental effects, has good thermal qualities (high thermal capacity – the heat transfer coefficient of the ice slurry is less dependent on the mass fraction of solid particles in the turbulent flow area, than in laminar range [1]). Ice slurry is mostly used as a secondary coolant (although not very frequently) in cooling systems.
Ice slurry is a non-Newtonian liquid, most frequently described in reference works as the rheologically stable liquid (with the exception of [2]). Such rheological models as the Bingham model [3], [4], [5], [6], Oswald-de Waele power model [7], [8], and Casson model [9] are the ones most often associated with this liquid [1]. In the literature, the first two models are associated with ice slurry produced on the basis of ethanol, with both constant (11%) and changeable (5%, 10%, 20%) initial concentration of ethanol.
This paper also deals with ice slurry produced on the basis of the ethanol with an initial concentration of 10.6%. The Bingham model was used to describe this phenomenon.
As presented in paper [6], when determining the resistance flow, one can expect lower flow resistance of the ice slurry with a high ice mass fraction (25–30%), than of the liquid without the ice fraction, at the same flow velocity (for Re around 3000). This phenomenon is connected with the difference in the rheological qualities of the ice slurry and the liquid without ice (different moment of transition from laminar to turbulent flow). Some researchers dealing with ice slurry flow suggest that the slurry can demonstrate some features of the Newtonian liquid for given ice contents in the mixture. As it is presented by the researchers in such works as [1], [10], the critical Reynolds number Recrit, determining the moment of the transition from laminar to turbulent flow, is not constant and depends among other things, on the content of solid ice particles in the slurry and on pipe diameter. In literature, Reynolds numbers are defined by authors in various way, and as a consequence, Reynolds numbers have various critical values. As started in other studies, in depending of the Hedström number (He) and the quotient of the diameter of the ice solid particles and the internal pipe diameter, the critical value of the Recrit can amount to 1900–2500 [1], [11], and more for He above 3500 [1], [12].
Section snippets
Mathematical flow modelling
In relevant works, one can find information on frictional losses of ice slurry in the straight sections of circular pipes, frictional losses in the slit pipes, or the local losses in the bends and elbows [6], [13]. There is still lack of studies on other parts of the fittings, such as ball and poppet valves, control valves, contractions, expansions, three-way pipes, distributors and others.
Despite the fact that there is lack of experimental studies on the loss coefficient during ice slurry flow
Experimental studies
The study presented in this paper focuses on the flow processes occurring in sudden pipe contractions with ice slurry flow. In the results of the experimental studies, specific qualities of the slurry were taken into consideration. Six different sudden pipe contractions with the contraction ratios shown in Table 2 were examined.
Experimentally determining the flow resistances in pipe contraction and of the local loss coefficient was performed by means of measuring the pressure in front of and
Results of experimental studies
While comparing the calculations and the experimental studies, the correlation from the papers [16], [17] was discarded as the loss coefficients calculated on its basis varied widely from the results presented in this paper.
Fig. 3, Fig. 4, Fig. 5 compare the results of the study on the loss coefficient of the ice slurry flowing through sudden pipe contractions with specific contraction ratios, with the calculations made in accordance to the formulas given by Turian et al. (Fig. 3), Fester et
Correlations for calculating the local loss coefficient of the ice slurry
On the basis of the results of experimental studies, the original form of the correlation (1) from paper [18] was chosen in order to develop the authors’ own correlations for all the examined sudden contractions and all mass fractions of ice. On the basis of the results obtained in experimental studies, the (C and m) parameters from correlation (1) were developed and presented in Table 5 for all the examined contractions.
In Table 5 the average absolute deviate is defined as [18]:
Conclusions
The local loss coefficient of ice slurry flow through sudden pipe contractions is insufficiently presented in the literature probably because of the painstaking process of calculation, in which one often has to take into consideration contradictory data from the various references works concerning for instance the qualities of ice slurry, the critical Reynolds number and kinetic energy correction factors.
In literature there are no theoretical relationships supported by experimental studies that
Acknowledgements
This Project has been financially supported from funds earmarked for science in Poland in the years 2008–2011.
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Flow and heat transfer characteristics of ice slurry in typical components of cooling systems: A review
2019, International Journal of Heat and Mass TransferCitation Excerpt :In addition, the overall efficiency was obviously higher for ice slurry than that for the pure carrier fluid with no ice. The pressure drops of ice slurry in the fittings such as the contractions, expansions, flow dividers, bends, elbows and poppet-type flow control valves were experimentally investigated [68–73]. The results showed that the local resistance coefficients of the fittings with ice slurry flow increased with the increasing ice fraction.
Application of the building block approach to characterize the pressure loss of water and fracturing fluid in contraction-expansion pipe
2019, Journal of Petroleum Science and EngineeringFlow visualizations and pressure drop measurements of isothermal ice slurry pipe flows
2018, Experimental Thermal and Fluid ScienceCitation Excerpt :One could cite also the experimental work of Kumano et al. [23], who investigated the rheological behavior of ice slurries in narrow tubes. Mika [24–26] carried out several experimental and analytical investigations on pressure drops through singularities: sudden contractions, sudden contractions and expansions and flow dividers. He also considered experimentally and numerically the ice slurry flows in a poppet-type flow control valve [27].
Numerical and analytical investigation of ice slurry isothermal flow through horizontal bends
2018, International Journal of RefrigerationCitation Excerpt :Nørgaard et al. (2005) designed a pipe ring composed of straight pipes and fittings, and the friction loss coefficient for the straight pipe and each fitting was tested and compared. Mike (2011, 2012, 2013) measured the friction loss coefficients of the sudden contraction, expansion and divider in an experimental transport system of ice slurry. Several semi-empirical formulas were proposed to estimate the pressure drop of ice slurry through different types of fittings.
Experimental determination of the energy optimum for the transport of floating particles in pipes
2015, Experimental Thermal and Fluid ScienceIce slurry flow in a poppet-type flow control valve
2013, Experimental Thermal and Fluid ScienceCitation Excerpt :Another factor which hinders a broader application of ice slurries is the behaviour of the cooling agent in particular pipeline elements, which has not yet been fully investigated, especially as regards fittings used to regulate the flow of the slurry. Various papers have been published focusing on the flow of ice slurry in straight pipe fragments with various cross-sections [1,2], and in various pipeline fittings, such as: contractions [3], expansions [4] and knees and elbows [4]. Publications focusing on the results of simulation calculations for ice slurry flow in some pipeline elements [5] are also available.