Abstract A problem of metal particles movement in a tube under action of a pulse gas flow was numerically and experimentally solved. Comparison of computational and experimental data was carried out. On the basis of researches the optimum characteristics of the work of pulse pneumatic transportation of metal radioactive waste materials are determined. Modeling was performed within the framework of model of non-stationary two-dimensional motion of ideal compressible media on the basis of laws of conservation of mass, pulse and energy in case of axial symmetry. The thermodynamic flow field has been computed both in gas and solid phases. Processes of particles mutual interactions, coalescence, fragmentation, interaction with a tube walls and motion have been investigated in detail. Interface borders have been considered as contact discontinuity surfaces, where a condition of a continuity of normal to the surface component of a flow velocity vector and the continuity of normal component of tension tensor were satisfied. Modeling was performed numerically on the basis of the method of individual particles. The comparison of the computational and experimental data confirms the reliability of numerical algorithm. The optimum pipeline parameters (optimum nozzle diameter is 37 mm, pressure of gas in receiver chamber is about 8 MPa) are determined, at which the effective pulse cleaning of pipelines from metal wastes with the least expenses is possible. It was found that series of pulses is more effective mode of transportation than a single pulse, having similar total power

Dmitriy V Voronin

Vyacheslav L Istomin

CiteSeerX

Proceedings of XLIII International Summer SchoolConference APM 2015
On the pulse pneumatic transportation of metal
radioactive waste materials at atomic electric
power stations
Dmitriy V. Voronin, Vyacheslav L. Istomin
voron@hydro.nsc.ru
Abstract
A problem of metal particles movement in a tube under action of a pulse
gas flow was numerically and experimentally solved. Comparison of compu-
tational and experimental data was carried out. On the basis of researches
the optimum characteristics of the work of pulse pneumatic transportation of
metal radioactive waste materials are determined. Modeling was performed
within the framework of model of non-stationary two-dimensional motion of
ideal compressible media on the basis of laws of conservation of mass, pulse
and energy in case of axial symmetry. The thermodynamic flow field has been
computed both in gas and solid phases. Processes of particles mutual inter-
actions, coalescence, fragmentation, interaction with a tube walls and motion
have been investigated in detail. Interface borders have been considered as
contact discontinuity surfaces, where a condition of a continuity of normal to
the surface component of a flow velocity vector and the continuity of normal
component of tension tensor were satisfied. Modeling was performed numer-
ically on the basis of the method of individual particles. The comparison of
the computational and experimental data confirms the reliability of numerical
algorithm. The optimum pipeline parameters (optimum nozzle diameter is 37
mm, pressure of gas in receiver chamber is about 8 MPa) are determined, at
which the effective pulse cleaning of pipelines from metal wastes with the least
expenses is possible. It was found that series of pulses is more effective mode
of transportation than a single pulse, having similar total power.
1 Introduction
Significant share in high radioactive waste materials, formed in factories on regenera-
tion of worked off nuclear fuels in nuclear electric power stations, make metal wastes
as fragments of constructional materials from processing nuclear reactors. One of
labor-consuming and dangerous operations in technological process of processing
reactors is the operation on transportation of firm wastes, as it is necessary to take
into account the danger of materials to an environment and their harmful influence
on health of the attendants and population. The various devices for transportation
of high radioactive waste materials are known [1, 2, 3]. Now most widespread is
their delivery to a burial place in containers by the specially equipped automobiles
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On the pulse pneumatic transportation of metal radioactive waste materials at
atomic electric power stations
Figure 1: The scheme of experimental installation of pulse pneumatic transportation:
1 - receiver; 2 - valve; 3 - nozzle; 4 - cover; 5 - bunker; 6 - metal pieces; 7 - pipeline;
8 - accumulating chamber.
or railway transportation. Such approach alongside with advantages has essential
lacks: in places of loading and the unloadings there are inevitable losses, that can
result in jamming the container, and the repair thus is necessary in view of a ra-
dioactivity. The best transport of firm radioactive wastes represents pipeline, based
on pneumatic transportation and allowing sharply to locate a zone of distribution
of radioactive particles, to improve sanitary - hygienic conditions. Such transport
has a high degree of automatisation and provides moving a material in a complex
line. Here occurrence of emergency conditions is possible as well, in case of a stop
of work of the device for pneumatic transportation at blocking, owing to fall of
operating pressure values. Especially it is essential for materials with high specific
density. However, the latter lack is possible to avoid, using pulsed pneumatic trans-
port [4]. The recent paper is devoted to theoretical and experimental determination
of various modes of operations of pulsed pneumatic transport devices, which com-
bines the advantages of usual pneumatic transport and is deprived of the mentioned
above lacks. This system is applied now at industrial facilities of ”Mayak” groop.
The gas was used as an inflator in the pipeline, as the clearing of a liquid is more
difficult problem. The scheme of experimental installation for research of parame-
ters of pulse pneumatic transportation is submitted in Fig. 1. A portion of metal
pieces was loaded into the bunker and closed by a cover. The gas (air) was pumped
into receiver chamber, and after opening of the special valve it penetrates in the
pipeline (where the pieces are transported to the accumulating chamber) through
a nozzle. In the experiments the simulators of metal pieces of firm wastes with
granular structure were used, which were obtained at their mechanical crushing in
cutting devices. The size of basic groop of pieces (particles) is about 30-40 mm.
A diameter of the pipeline is 250 mm. The purpose of the paper is a calculation
of the various characteristics of the process with the subsequent determination of
optimum parameters values, ensuring fast and effective clearing off the pipeline: a
nozzle diameter, pressure of gas in the receiver chamber and total gas charge.
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Proceedings of XLIII International Summer SchoolConference APM 2015
Figure 2: Isolines of gas velocity in the installation.
2 Modeling
Basing on experimental data (obtained with pneumatic transportation device) and
knowing its characteristics, we describe the statement of a model problem. The
scheme of simulated flow is submitted in Fig. 2. Initially motionless steel particle
or conglomerate of particles with diameter d0 (region 2) is placed within a pipeline
having diameter D0 (region 1). Regions 3 and 4 are the receiver (diameter 2D0) and
the nozzle correspondingly. The nozzle and the pipeline are initially separated by a
diaphragm. All the regions, except for 2, are filled with air. The gas is pumped in
regions 3 and 4 for obtaining increased values of initial pressure there. The initial
pressure of gas in region 1 is p0 = 1 bar. The whole system is under condition of
dynamic balance and has zero value of gas initial velocity in all the regions u0 = 0.
At the instant t = 0 the diaphragm is removed and propagation of gas pulse from the
nozzle within the pipeline starts at constant values of pressure p and gas velocity
(equal to sound velocity C0) at the nozzle. The mathematical model of flow is
based on the laws of conservation of mass, pulse and energy for two dimensional
non-stationary motion of two-phase compressible medium with obvious allocation
of borders between the phases in case of axial symmetry . The basic equations and
numerical method are stated in paper [5]. The meanings of characteristic constants
correspond to the experimental data described above and are chosen according to [6].
For the firm phase in system of units gram - centimeter-microsecond the following
values of characteristic constants have been used: a1 = 7, 78, a2 = 31, 18, b0 =
9, 591, b1 = 15, 676, b2 = 4, 634, c0 = 0, 3984, c1 = 0, 5306, φ0 = 9, 0, ρ0 = 7, 86; for
gas ρ0 = 0, 00122, γ = 1, 4. A diameter of the pipeline is D0 = 250 mm, diameter
of a particle or their conglomerate is d0 = 40 mm. Let’s note, that the problem was
solved numerically in dimensionless mode. One of dimensionless combinations of the
basic parameters of the problem (determining the flow process) was the ratio d = D0
dn
,
where dn is the nozzle diameter. Therefore proportional change of the geometrical
characteristics of the problem (at the fixed value of the ratio dn/d0) did not change
a flowfield of the basic thermodynamic parameters. Due to technological features
of pneumatic transportation device [4] the distance l between the particles and the
nozzle could not be less than 20 cm. According to computation results, at l > 20 cm
the main characteristics of the process poorly depend on this parameter, since the
losses of a pulse and energy owing to friction of gas at the wall of the pipeline are not
467
On the pulse pneumatic transportation of metal radioactive waste materials at
atomic electric power stations
Figure 3: Map of velocity u at the centre of the pipe at t = 22, 8µs.
taken into account in the model. Therefore the results stated below are obtained
at fixed l = 35 cm. One of the important technological constants determining
characteristic of pipeline transportation, is the velocity of particles starting off UT .
Usually it is considered as lower value of average gas velocity in a cross section of
the pipe, at which a particle of definite size is not soared in the flow any more. This
hydraulic characteristic of carrying ability of the flow can be considered [3], as the
characteristic of some limiting condition, when the frontal influence of a flow on a
particle causes its sliding along the wall of the pipe, and the elevating force tries to
lift it on some height. According to [3] we have
UT =
√
agd0/Fr, (1)
a =
ρ2
ρ
− 1, Fr = ψ1 +ψ2δ
2 (2)
Here, ρ, ρ2 are density of gas and particles accordingly, g is acceleration of force of
gravity, d0 is a diameter of particles, Fr is Froude number , δ is the ratio of the
diameter of a particle to the diameter of a pipe; ψ1, ψ2 are experimental constants.
For the characteristic geometrical sizes of the problem (as the change of the particle
form in course of time from just splintered to smoothed ones was taken into account
and ψ1 = 0, 7÷1, 35 according to [3]) the value of UT varies from 14,4 m/s up to 24,8
m/s. The maximal value of the velocity of particles starting off UT = 25 m/s was
taken in the numerical calculations stated below. To minimize the time of obtaining
UT , it is necessary to pick up the optimum size of a nozzle. The necessity of such a
nozzle for submission of gas into the pipeline is caused by two main reasons. First,
the velocity of a gas flow for steady motion of particles in the pipeline should be 2−3
times more than the velocity of particles starting off. Secondly, used in experiments
the receiver has limited volume.
The flow-field of gas velocities in the pipeline at instant t = 2ms from a beginning
of diaphragm breaking at the initial pressure value in the receiver P = 7 MPa is
submitted in Fig. 2. Twenty ranges of velocities in an interval from 0 up to 750 m/s
468
Proceedings of XLIII International Summer SchoolConference APM 2015
are represented here. The length of receiver is 70 cm. In experiments the duration
of a gas pulse τ, acting from the nozzle into the pipeline, is sometimes adjusted with
the help of a latch in the nozzle. The results of such a numerical modeling in the
pipeline are submitted in Fig. 3 at τ = 0, 8 ms for longitudinal velocity u at the
instant 1,1 ms from the moment of diaphragm break ( P = 8 MPa). Here region 1 is
gas at initial pressure p0 = 1 bar (ρ0 = 0, 001225g/cm
3), region 2 is for particles of
steel, 3 is a pulse, moving to the left hand side from the nozzle into the pipeline, with
compressed air at P = 8 MPa (ρ = 0, 098g/cm3). We name an interval between
the beginning of interaction of a particle with the pulse and moment of reaching the
meaning of UT as the time of obtaining of the velocity of particles starting off. Its
meaning was determined from the generated slides with a step of 0,2 ms, showing
the further stages of the process. For the recent variant such time is equal to 22, 8µs.
Here readout of z coordinate is conducted from the nozzle. The required velocity
of particles starting off was determined from a structure of longitudinal velocity at
the centre of the pipe. As it is visible from the figure, by this moment the particle
velocity begins to exceed the meaning of the velocity of particles starting off.
Table 1. Time dependence of achievement UT from pressure of working gas.
number of calculation initial pressure of gas, MPa time for achievement UT
1 1 -
2 3 46,00
3 4 34,00
4 5 26,00
5 6 23,60
6 7 23,20
7 8 22,80
8 9 22,40
9 10 21,80
Variations of time of reaching UT meanings are represented in Tab. 1. As it is
visible from the table, at the fixed nozzle diameter dn ∈ [10, 200] mm and P > 6
MPa the time of reaching the velocity of particles starting off begins poorly to
depend on growth of initial pressure values. As is clear from numerical simulations,
at the fixed pressure of gas in the receiver for meanings presented in Tab. 1, the
least time of achievement of the velocity of particles starting off corresponds there
the meaning d = 6, 8 . With the reduction of d , the gas in the pipeline has the
velocity insufficient for steady motion of particles, and at the very large diameter
of nozzle, the pulse of gas is short, i.e. the time of its influence on the particles is
insignificant. If d0 = 40 mm, then the optimum diameter of nozzle is 37 mm, that
is close to experimental data [4], where it is equal to 35 mm. In Fig. 4 we can see
the time diagram of reaching the value of the velocity of particles starting off UT
from the initial pressure of gas. It is visible from the diagram, that the time has
radical changes at pressure values diapason from 3 MPa up to 6 MPa, but at the
further increase of pressure its change are insignificant. Optimum parameter value
for the present scheme is pressure P = 8 MPa, the further increase is inexpedient,
since it will result in the over-expenditure of energy. In subsequent simulations we
use this meaning of pressure. Now we must determine the optimum charge of gas
469
On the pulse pneumatic transportation of metal radioactive waste materials at
atomic electric power stations
Figure 4: Time dependence of achievement of U from initial pressure of gas
that is necessary for the pipeline cleaning. The distance of particles motion (at
fixed nozzle diameter and variating pressure and the receiver volume) is important
factor here. Let’s note, that as the distance of transportation we consider one from
initial place up to the position of the inertia centre for the conglomerate of particles
after their motion under action of the pulse of gas. In technological installations
that distance is about tens meters. Such range is achieved, if average gas velocity
in cross section is 2-3 times higher than the velocity of particles starting off. For
the comparison with experimental data it was assumed in numerical simulations,
that the value of gas velocity u = 2, 5UT provides such a distance. The comparison
of experimental and numerical (continuous lines) data is presented in Fig. 5. The
deviations of numerical curves from experimental data do not exceed 7 percents. It
is visible from the figure, that with growth of the receiver volume at fixed initial
pressure of gas in it, the distance of particle motion initially grows linearly and at
achievement of some critical volume remains practically constant. At the increase
of initial pressure of gas in the receiver this curve moves above. Thus, there exists
an optimum technological volume of the receiver (about 0, 078m3), and its further
increase becomes inexpedient. In Tab. 2 the computation of the charge of gas is
presented at the fixed initial pressure P = 8 MPa. It is visible from the table, that
there is an optimum technological volume here as well, that at its further increase
the time of achievement of the velocity of particles starting off varies poorly. As well
as in the previous problem we determine the time of achievement of the velocity of
particles starting off UT . In experiments for breadboard models of pulse pneumatic
device [4] not a single pulse was used, but alternation of pulses. For the checking
of efficiency of such an approach, the simulations with two pulses were performed,
when the total duration is equal to one submitted in Fig. 3. All other values
470
Proceedings of XLIII International Summer SchoolConference APM 2015
Figure 5: Influence of the receiver volume and initial pressure of gas on the distance
of particles motion.
of a flow parameters of these problems are similar. As numerical study reveals,
the alternation of the phases of compression and rarefaction, that is usual for the
complex of two pulses, results in strong distortion of the form of the conglomerate of
particles owing to instability of interface border that promotes the development of
the splitting phenomena. Therefore alternation of pulses is more effective means of
clearing of the pipeline, than having pulse at fixed velocity and pressure that proves
to be true by the experimental data [4]. The numerical simulations confirm that with
increase of gas volume its duration of action is increased as well, but the meaning
Vopt = 0, 095m
3 is optimal, since at smaller volume the object exposed to influence
of a wave of compression, has not necessary velocity for steady motion. The results
of modeling on revealing of parameters for the optimum mode of transportation,
well coincide with parameters obtained by experimental way.
Table 2. Determination of the optimum charge of gas.
number of cal-
culation
time of
achievement
UT , µs
time of action,
µs
volume of gas
in a pulse, m3
the charge of
gas, kg
10 - 26,0 0,088 8,624
11 30,0 32,4 0,095 9,31
12 26,4 36,8 0,106 10,388
13 22,8 38,2 0,15 14,7
14 22,4 42,2 0,176 17,248
7 22,0 46,0 0,196 19,208
3 Conclusions
The problem of metal particles motion in a pipe under action of a pulsed gas flow
is numerically solved in the paper. The comparison of the numerical data with
experimental ones testifies about reliability of the numerical algorithm. The opti-
mum value of device parameters are determined (optimal nozzle diameter is about
471
On the pulse pneumatic transportation of metal radioactive waste materials at
atomic electric power stations
37 mm, pressure of gas in the receiver is about 8 MPa and appropriate gas charge
corresponds to the values), at which the effective pulse clearing of pipelines from
metal wastes with the least expenses is possible.
References
[1] Ginniff M. A burial place of radioactive wastes // Nuclear engineering abroad. -
1984. N 7. - P. 42.
[2] Borisov G.B., Saveliiev V.F. Processing and storage of metal wastes from regen-
eration of the worked out nuclear fuel // Nuclear engineering abroad. - 1978. N
8. - P. 23.
[3] Smoldyrev A.K. Pipeline transportation. - Moscow: Nedra, 1970, 272 pp.
[4] Istomin V.L. Pulse pneumatic transportation of metal radioactive wastes at nu-
clear power stations // Atomic Energy. - 1994. - V. 77. - N. 3. - P. 231.
[5] Voronin D.V., Istomin V.L. Modeling of pulse pneumatic transportation of metal
radioactive wastes from processing at nuclear power stations // Problems of
radioactive safety. - 2011 - 4 - P. 61.
[6] Loytsianskiy L.G. The mechanics of a liquid and gas. - Moscow: Nauka, 1987,
840 pp.
Dmitriy V. Voronin, Lavrentyev Institute of Hydrodynamics of SB RAS, Lavrentyev
str. 15, 630090, Novosibirsk, Russia
Vyacheslav L. Istomin, Lavrentyev Institute of Hydrodynamics of SB RAS, Lavren-
tyev str. 15, 630090, Novosibirsk, Russia
472


On the pulse pneumatic transportation of metal radioactive waste materials at atomic electric power stations

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On the pulse pneumatic transportation of metal radioactive waste materials at atomic electric power stations

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