ARCHIVES
of
FOUNDRY ENGINEERING
Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences
ISSN (1897-3310)
Volume 10
Special Issue 3/2010
201 – 204
38/3
Resistance coefficient during ice slurry flow
through pipe sudden constriction
Ł. Mika
Zakład Chłodnictwa i Klimatyzacji, Politechnika Krakowska, al. Jana Pawła II 37, 31-864 Kraków
Corresponding author. E-mail address: [email protected]
Received 30.04.2010; accepted in revised form 30.05.2010
Summary
Due to the adverse environmental effects of some commonly-used refrigerants, efforts are still underway to find new cooling mediums
that would be safer to the ozone layer and would not increase the greenhouse effect. Ice slurry as a new ecological coolant suits the
processes requiring the preservation of constant and equal temperature in the cooling process of the full section of the cooled solid. Thanks
to that, ice slurry can find a wide potential application in such branches of industry, as heat treatment, materials engineering, or foundry. In
this paper, flow systems which are commonly used in fittings elements such as diameter’s reductions in ice slurry pipelines, are
experimentally investigated. In the study reported in this paper, the consideration was given to the specific features of the slurry flow in
which the flow qualities depend mainly on the volume fraction of solid particles. The results of the experimental studies on the flow
resistance, presented herein, enabled to determine the resistance coefficient during the ice slurry flow through the pipe sudden constriction.
The volume fraction of solid particles in the slurry ranged from 5 to 30%. The recommended and non-recommended range of the Reynolds
number for the ice slurry flow through the pipe sudden constriction were presented in this paper. The experimental studies were conducted
on a few variants of the most common reductions of copper pipes. Further studies on the determination of the resistance coefficient in the
remaining fittings elements of the pipeline were recommended in the paper as well as the further theoretical studies intended to determine
the theoretical relations to calculate the resistance coefficient in all the fittings elements in the pipeline (on the basis of the experimental
studies) and to elaborate the calculation pattern of the entire ice slurry system.
Keywords: environment protection, ice slurry, application of the ice slurry, studies on the flow resistance, resistance coefficient of the ice
slurry
1. Introduction
Due to the adverse environmental effects caused by some
refrigerants commonly used in the air-condition and cooling
industry, efforts are still underway to find new cooling fluids that
would be safer for the ozone layer and would not increase the
greenhouse effect. Proecological refrigerants such as ammonia,
carbon dioxide, hydrocarbons, or water (and solutions) are more
frequently used nowadays.
Ice slurry belongs to the group of new ecological refrigerants
applied in intermediate cooling systems. It is the mixture of the
basic liquid (which could even be water) and the solid particles
with the dimensions up to 0,5 mm. Due to such advantages of this
refrigerant as showing no adverse environmental effects, having
perfect thermal qualities (high thermal capacity, high coefficient
of a heat transfer, high heat capacity) ice slurry can be used as a
direct cooling medium or a medium in which cold is accumulated.
First ice slurry systems were built at the beginning of the eighties.
However, the commercial application of this technology can be
dated to the nineties (for instance in Germany, Switzerland,
Austria, Columbia and Singapore). At present this cooling
medium is frequently used to cool down the air conditioning
systems of office buildings and hotels as well as in the mine’s air
conditioning systems. The usage of this cooling medium can also
be noticed in supermarkets in refrigerators, refrigerated counters,
ARCHIVES of FOUNDRY ENGINEERING Volume 10, Special Issue 3/2010, 201-204
201
or food store cold rooms. It is also used in the petrochemical
industry, medical engineering, and fire-fighting engineering [1].
Other applications of the ice slurry are still not discovered. It is
known, that even due to the heat of the phase change, ice slurry
preserve the constant or nearly constant temperature during the
heat collecting (ice slurry made on the basis of water and
admixtures lowering the freezing point of water). Therefore it can
be used in indirect and direct systems (slurry collecting heat from
the primary coolant) to the processes requiring the preservation of
the constant and equal temperature during the cooling process of
the full section of the cooled solid. Thanks to that, ice slurry can
find a wide potential application in such branches of industry, as
for instance heat treatment, materials engineering, or foundry.
The qualities of slurry ice depend to large extent on the
volume fraction of solid particles [2]:
• with the content of solid particles up to 20% it is a fluid
showing the qualities of pure water,
• with the content of solid particles 20%-40% the mixture is
still fluid, yet of much higher viscosity than water,
• with the content of solid particles over 40% the mixture
looks like wet snow, and due to the transport difficulties it is
not used in refrigerating engineering,
• with the content of solid particles of about 90% the mixture
is treated as simple ice.
Favourable qualities of flow resistance are a great advantage
of slurry ice. The mixture can be considered so called Bingham
fluid, which in its classic form displays the characteristic
connected to the lack of laminar or turbulent flow. The motion of
this fluid can be called a piston flow, i.e. the velocity of the fluid
is constant nearly in the entire pipeline section. [3,4].
Apart from the advantages presented above, slurry ice has its
disadvantages. One of them is a tendency of ice agglomerating in
a tank, and what fallows, the necessity of taking care of the
homogenizing of the mixture. Such disadvantage can be
eliminated by assembling a special stirrer in the ice tank that
would provide the unification of the mixture ratio in each place of
the tank. It enables to supply the exchanger with the mixture of
the equal composition. The shape of the pipelines is of
significance. One cannot permit of resting the slurry ice in one
section of the pipeline for a long time, as it would result in the
stratification of ice solid particles in the liquid. The cause of such
phenomena is the significant difference of densities of the
solution and the ice solid particles. The difference arise from the
fact that only the water freezes; therefore the alteration of the
remaining liquid concentration ensues. Furthermore, due to the
physical properties, the volume of ice and the volume of the water
from the ice differ. Such situation follows from the fact that water
belongs to the group of substances which enlarge their volume
during the solidification. After a long period of time, the
stratification of the mixture can cause the flow blockage in the
pipeline. The same phenomena can proceed in the three-way pipes
which are vertical installed. Ice solid particles can accumulate in
the branching-out ducts and result in the flow blockage of this
duct. Therefore in such systems branches should be designed
horizontally or downwards.
In the subject literature one can find publications dealing with
the frictional resistance of ice slurry in the straight sections of the
pipeline of the circular cut, the frictional resistance in the slit
pipes, or the local resistances in the bends and elbows of a
circular cut [5]. There is still insufficiency of studies on the
remaining parts of the fittings, such as ball valves, poppet and
202
control valves, reductions, three-way pipes, and distributors. The
common usage of the ice slurry is conditioned by the knowledge
of the flow resistances in every element of the pipeline.
2. The effect of crossing the curves of
the carrying fluid resistance
The subject of the study, presented in this paper, are the flow
processes occurring in the commonly-used elements of the fittings
such as pipe sudden constrictions in the pipeline with the ice
slurry flow. In the results of the experimental studies, specific
qualities of the slurry, which can be treated as a pseudoplastic
non-Newtonian liquid with the qualities of the Bingham liquid,
were taken into consideration.
During the preliminary experimental studies [2], one can
observe the intrinsic growth of the volume stream of the slurry ice
flowing in the system. This effect occurs till the resistance curves’
of the carrying fluid are crossed by the curves of the ice slurry
resistance (with the content of solid particles over 20% and high
flow velocities). The verification of this phenomenon was
conducted in several various slurry ice distribution systems. It was
observed that the drop of the flow resistance in all the systems
commences below -6,0°C, i.e. with the content of solid particles
over 20%. The relative extremum (minimum) occurs at about 7,1°C. Despite the fact that such effect proceeds similarly in
various ice slurry systems, the scale of this phenomenon strongly
depends on the type of the elements of the fittings, such as
straight sections, reductions, three-way pipes, valves, dividers,
etc., which are used in a given system.
Fig. 1. The example relations of the slurry ice volume stream and
the volume fraction of ice solid particles in the slurry in the
temperature function
3. Methodology of experimental studies
Each change of the pipeline’s geometry which evokes the
local resistance is the cause of disturbance in the flow of the
slurry stream. It induces the loss of energy of the flowing liquid.
Local resistances in such element can be determined on the basis
of the following relations [6]:
ARCHIVES of FOUNDRY ENGINEERING Volume 10, Special Issue 3/2010, 201-204
Δp=
ζ ⋅ρ⋅v2
where:
2
(1)
ζ - local resistance coefficient [-],
ρ - density of the liquid [kg/m3],
v - velocity of the liquid [m/s].
Experimentally determining the flow resistances in pipe
constriction and the local resistance coefficient took place by the
measuring of the pressure drop in front of and behind the element.
The gauging sections should be placed in large distances so that
their velocity profiles are fully developed and the results of the
measurement are not disturbed by the transient phenomena in the
recirculation and stagnation sections. The distances of the pipeline
in front of and behind the obstacle which are required to obtain
the fully developed velocity can be found in the literature [7].
with the volume fraction of 5%, 10%, 15%) behaved in a different
way than the others. For such slurries it is characteristic to have
slightly higher local resistance than it could be assumed on the
basis of the theoretical calculations. The exception to the rule is
the 28/15mm reduction. For the sudden constriction all the
slurries in the range of 2400÷6300 of Reynolds number behave in
a similar way.
4. Experimental studies
Several most frequently used elements of the fittings were
experimentally tested in order to observe the effect in which the
resistance curves of the carrying fluid are crossed by the curves of
the ice slurry resistance. Such examination is also needed to make
a model of the ice slurry flow in the system. In the experimental
studies the diameters reduction of the copper pipeline of 28/22
mm, 28/18 mm, 28/15 mm, 22/18 mm, 22/15 mm and 18/15mm
were used. In the studies the volume fraction of ice solid particles
in particular slurries were: 5%, 10%, 15%, 20%, 25% and 30%.
Fig. 3. The relation of the resistance coefficient and the Reynolds
number for the ice slurry treated as Bingham fluid in the sudden
pipe constriction (28/15) [8]
Fig. 4. The relation of the resistance coefficient and the Reynolds
number for the ice slurry treated as Bingham fluid in the sudden
pipe constriction (28/18) [8]
Fig. 2. The example relations of the slurry ice flow resistance in
the pipeline’s diameter reduction (28/18) and the slurry velocity
for various volume fraction of the ice particles [2]
Figure 2 presents the example of relations of the slurry ice
flow resistance in the pipeline’s diameter reduction of 28/18mm
and the slurry velocity behind the reduction.
The results of the experimental studies of the ice slurry
resistance coefficient during its flow through the sudden pipe
constrictions of a different type were compared to the results of
the theoretical calculations of this coefficient. Such comparison is
presented in Figures 3-6. During the flow through the sudden pipe
constriction ice slurries of a lower ice volume fraction (slurries
For the Reynolds number below 2400, 5%, 10% and 15%
slurries behave in a similar way as traditionally used coolants
such as water. It should be noticed that in the theoretical
calculations the values of the resistance coefficient are slightly
overstated as compared to the actual resistance coefficients of the
water (up to a dozen or so percent [7]). Experimental
investigations of the slurry ice of over 15% ice fraction for the
Reynolds number 2000-6000 shows that local resistance are lower
(even 2 times, for Re about 4200) than it could be assumed on the
basis of the theoretical calculations. It is recommended range for
using the slurry ice. Ice slurry should not be used in the low flow
velocities meeting the range 0÷2000 of the Reynolds number.
In the experimental studies conducted to determine the
resistance coefficient, losses of friction were also determined for
the straight sections of the pipeline with the diameters of φ15mm,
φ18mm, φ22mm, and φ28mm.
ARCHIVES of FOUNDRY ENGINEERING Volume 10, Special Issue 3/2010, 201-204
203
Fig. 5. The relation of the resistance coefficient and the Reynolds
number for the ice slurry treated as Bingham fluid in the sudden
pipe constriction (28/22) [8]
4. Ice slurry flow through the sudden pipe section cannot be
easily described. This phenomenon is determined not only by
the geometry of the constriction and the content of ice solid
particles, but also by the Reynolds number.
5. The behaviour of a particular ice slurry during the flow
through the sudden constrictions can be generalized by
dividing the slurry into two groups. The slurries of 5%, 10%,
15% and 20%, 25%, 30% show a similar character of
resistance coefficient changes. The constriction 28/15 is one
exception in which all the slurries behave similarly.
6. The actual value of the resistance coefficient for the ice slurry
of 20%, 25%, 30% can much differ from the theoretical value.
It can be even several times higher for the Reynolds number
below 2000 (non-recommended range).
7. The slurries with the 20%, 25% i 30% content of the ice solid
particles in the 2000÷6000 range of Reynolds number show
lower actual values of the resistance coefficient than the
theoretical values (30% slurry even two times lower for the
Reynolds number between 3500÷4500).
8. Further studies on the determination of the resistance
coefficient in the remaining fittings elements of the pipeline
are necessary as well as the further theoretical studies intended
to determine the theoretical relations to calculate the local
resistance coefficient in all the fittings elements in the pipeline
(on the basis of the experimental studies) and to elaborate the
calculation pattern of the entire ice slurry system.
Scientific work financed from funds earmarked for science in
the years 2008-2011 under research project.
Fig. 6. The relation of the resistance coefficient and the Reynolds
number for the ice slurry treated as Bingham fluid in the sudden
pipe constriction (18/15) [8]
5. Conclusions
1. The application of the ice slurry as the intermediary agent
results in many benefits, such as for instance decreasing the
degradation of the atmosphere due to limiting the usage of the
harmful freon, increasing the heat penetration factor which
enables to reduce the heat exchange surface, the pump
capacities and pipeline diameters as compared to the brine
systems. It also reduces the agent flow resistance in the system.
Another important advantage is also the usability in the process
of cooling the products which need to be cooled quickly.
Thanks to the usage of this coolant the time in which the first
effects of cooling appear is reduced from one hour – in brine
systems – to a dozen or so minutes – in the slurry ice systems.
Due to this fact, higher quality of the products could be
obtained.
2. The results of the experimental studies on the flow resistance,
presented in this paper, enabled to determine the resistance
coefficient during the ice slurry flow through the pipe sudden
constriction. The volume fractions of ice solid particles in the
mixture ranged from 5 to 30%.
3. The recommended (Re about 4000) and non-recommended (Re
below 2000) ranges of the Reynolds number for the ice slurry
flow through the copper pipe sudden constrictions of 28/22
mm, 28/18 mm, 28/15 mm, 22/18 mm, 22/15 mm and
18/15mm were presented in this paper.
204
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