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41
Arch. Min. Sci., Vol. 55 (2010), No 1, p. 41–48
Electronic version (in color) of this paper is available: http://mining.archives.pl
KATARZYNA SOCHA*, PAWEL LIGĘZA*
METHOD OF MEASUREMENT OF VELOCITY VECTOR FIELDS OF UNSTEADY REVERSE FLOWS
IN VENTILATION SYSTEMS
METODA POMIARU PÓL WEKTORA PRĘDKOŚCI NIESTACJONARNYCH PRZEPŁYWÓW
REWERSYJNYCH W SYSTEMACH WENTYLACYJNYCH
The balance of mass or volumetric fl ow of air in ventilation systems may be carried out on the basis
of the fl ow velocity fi eld assessment. The minimization of the measurement error of such a measure-
ment requires the application of a method allowing for determination of the magnitude, direction and
sense of the velocity vector in examined points of measurement space. In the case of unsteady fl ows,
the measurement method should additionally enable the measurements of variable signals changing in
a specifi c spectral range. The authors of this study have performed a research aimed to elaborate such
a measurement method.
This paper presents a hot-wire anemometric method for two-dimensional measurement of fl ow velo-
city vector. This method takes advantage of the specialist multi-wire measurement probe. The design of
the probe allows for the determination of magnitude, direction and the sense of the fl ow velocity vector.
Presented are the results of measurement probe calibration as well as of the analysis of errors of the fi t of
experimentally measured data to calibration data. In order to test the measurement method under reverse
fl ow conditions, an experimental measurement was performed at the measurement site which presented
a model of mining gallery with branching.
Keywords: ventilation systems, velocity fi elds, sense detection, hot-wire anemometry
Bilans masowego lub objętościowego strumienia powietrza w systemach wentylacyjnych może być
dokonywany w oparciu o wyznaczenie pola prędkości przepływu. Minimalizacja błędu takiego pomiaru
wymaga zastosowania metody pozwalającej na wyznaczenie wartości, kierunku i zwrotu wektora prędkości
w badanych punktach przestrzeni pomiarowej. Ponadto w przepływach niestacjonarnych metoda pomia-
rowa powinna umożliwiać pomiar sygnałów zmiennych w określonym zakresie spektrum widmowego.
Autorzy przeprowadzili badania zmierzające do opracowania takiej metody pomiarowej.
W pracy przedstawiono termoanemometryczną metodę pomiaru dwuwymiarowego wektora prędkości
przepływu. W metodzie tej wykorzystano specjalizowaną, wielowłóknową sondę pomiarową. Konstrukcja
sondy zapewnia możliwość wyznaczenia wartości, kierunku i zwrotu wektora prędkości. Zaprezentowano
* STRATA MECHANICS RESEARCH INSTITUTE OF THE POLISH ACADEMY OF SCIENCES, 27, REYMONTA STR., 30-059
KRAKOW, POLAND
42
wyniki wzorcowania sondy pomiarowej oraz analizę błędów dopasowania zmierzonych wartości do
danych wzorcowych. W celu przetestowania metody pomiarowej w warunkach przepływu rewersyjnego
wykonano pomiary na stanowisku będącym modelem chodnika kopalnianego z rozgałęzieniem.
Słowa kluczowe: systemy wentylacyjne, pola prędkości, detekcja zwrotu, termoanemometria
1. Introduction
The measurement of fl ow velocity vector is an important metrological application. The
knowledge of fl ow parameters is of particular importance with respect to the control of air con-
ditions in mines. Monitoring of air propagation in ventilation networks, air-ducts and demetha-
nization pipelines is an essential prerequisite of mine crew’s operational safety (Roszczynialski
et al., 1992). Also the phase of the ventilation network planning itself may be assisted by the
experimental verifi cation of numerical models at laboratory site (Mierzwiński & Popiołek,
1980). In many cases, the determination of the sense of fl ow vector in addition to information
considering the scalar value of fl ow velocity is necessary. The full information on fl ow velocity
vector allows for detection of reverse fl ows and recirculation possibly occurring in ventilation
networks. One of the very important issue is to perform the mass or volumetric balance of air
in ventilation systems. It may be obtained by means of the fl ow velocity fi eld determination.
The minimization of the measurement error of such a measurement requires the application of
a method allowing for determination of the magnitude, direction and the sense of the velocity
vector in examined points of measurement space. Moreover, considering the unsteady fl ows, the
measurement method should enable the measurement of variable signals changing in a specifi c
spectral range (Ligęza et al., 2006, 2008)
The hot-wire anemometry is a popular method of velocity vector measurement. In its classical
form, it only allows for the determination of velocity vector magnitude, not providing informa-
tion on the vector’s sense. Anemometers allowing for determination of direction and sense of
one-dimensional fl ow velocity vector can be found in literature (Downing, 1972; Mahler, 1982;
Kiełbasa, 1998, 2004). Nevertheless, solutions for determination of two-dimensional velocity
vector sense based on the hot-wire anemometric probes described in literature introduce signifi -
cant perturbances into examined fl ow and thus are not eligible for the realization of continuous
measurement (Al-Kayiem & Bruun, 1991; Venås et al., 1999). It therefore became reasonable
do develop a measurement method which would allow for the two-dimensional velocity vector
determination.
2. Method of measurement
For the determination of velocity vector in planar fl ows a specialized hot-wire anemometric
probe utilizing the phenomenon of mutual thermal interaction between the active elements of the
probe has been developed (Socha & Ligęza, 2007). One of such probe’s designs is presented in
fi gure 1a. It comprises four wires, which are pair-wise connected. Wires are made of a tungsten
fi bre 8 μm in diameter. Pairs of wires are placed in parallel 0.2 mm apart from each other and are
connected in series. The connection is shown in fi gure 1b. It is assumed that such a pair makes
up one hot-wire anemometric measurement element (between A and B supports) with a tap in the
43
middle (the C support) (Fig. 1b). The presented probe incorporates the wires which are placed
perpendicularly to each other in two parallel levels. Considering the orthogonal arrangement
of measurement wires, the Cartesian coordinate system may possibly be associated with them.
Owing to this, it is possible to determine the magnitude of both fl ow velocity components.
Fig. 1. a) model of the probe for fl ow velocity vector measurement,
b) voltage distribution on measuring wire
Us
C
AB
Uc
a) b)
The fl ow velocity vector measurement by means of the two-wire probe with taps is based
on the recording of two voltages for each single wire: the voltage Uc on the whole wire and volt-
age Us on its half. Based on voltages on whole wires, the fl ow velocity vector components are
calculated according to the following relationships (Ligęza & Socha, 2007):
()( )
()( )
2
222
1
111
2
222
1
111
22
22
yy
xx
n
ycy
n
ycy
o
y
n
xcx
n
xcx
o
x
aUbaUbv
aUbaUbv
-+-=
-+-=
(1)
where: aij, bij, nij are the model parameters, i stands for the wire identifi er (i = 1, 2),
and j is a component identifi er (j = x, y).
The fl ow velocity vector sense is determined based on difference in voltages on wire ends
according to the following relationship (Kiełbasa, 2004):
ii sici U
k
UU ××-=D 2 (2)
where: κi is a symmetrisation coeffi cient of voltages on ends of individual wires
(Kiełbasa, 2006).
44
Considering the sign of the voltage difference determined according to equation (2) in for-
mulas for fl ow velocity vector components (1), the following relationship is obtained:
()()
()()
2
222
1
111
2
222
1
111
22
1
22
2
)sgn(
)sgn(
yy
xx
n
ycy
n
ycy
o
y
n
xcx
n
xcx
o
x
aUbaUbUv
aUbaUbUv
-+-×D=
-+-×D=
(3)
Given the parallel arrangement of wire with respect to the fl ow direction, the voltage differ-
ences on this wire’s ends equals zero, while the magnitude of the vector component associated
with this wire reaches its maximal value. In the case of the fl ow perpendicular to the measuring
wire, the voltage difference reaches the maximal value and the associated vector component value
equals zero. Owing to this, the sign of vx component will be infl uenced by the sign of the ΔU2
voltage difference, while the sign of the vy will be affected by the ΔU1 voltage difference.
3. Measurement probe calibration
In order to determine the parameters aij, bij, nij (equation (1)) and κi (equation (2)),
a calibration of measurement probe rotated about its axis with the step of 30° given the fl ow
velocity from the range of 0.2 to 5 ms-1 changed with the step of 0.2 ms-1 was performed. The
results of calibration for several velocity values are presented in fi gure 2. Dashed line shows the
theoretical values of fl ow velocity vector components.
Fig. 2. Velocity vector components determined during the measurement probe calibration
a) b)
Since the velocity value and the angle of infl ow of the medium relative to the probe were
introduced during the experiments, the Cartesian system (vx, vy) was substituted by the polar system
(|v|, α) during the evaluation of the presented measurement method performance. In order to test
45
what is the infl uence of the preset fl ow velocity value on determined fl ow velocity vector module
or angle α, the mean-square error was calculated according to the following relationship:
å
=ç
ç
è
æ-
=
N
i
o
i
z
i
wd
ww
N1
2
1
e
ç
ç
è
æ
(4)
where: N — number of measurements performed for each velocity, w — in this case denotes
the modulus of the fl ow velocity vector or infl ow angle (α), and d — measurement range
(in this case, it is the maximal examined velocity 5 ms−1 or the angle of 360°).
The mean-square error is a measure of goodness of fi t of the value obtained in measurements
(wo) to preset value (wz) for all probe setups in function of preset fl ow velocity.
Figure 3 presents the mean-square error for velocity vector modulus as well as the medium
infl ow angle in function of preset velocity. Mean-square error determined for the velocity vector
modulus increases along with increasing velocity preset at the wind tunnel. It is caused by the
increasing infl uence of interference generated by the supports. In the case of mean-square error
calculated for medium infl ow angle, the maximal value was obtained at the velocity of 0.2 ms–1
and it equalled to 3·10–3. Considering the signifi cant difference in values, this point has been
removed from the graph. In the case of other fl ow velocities, the increase of velocity results in
insignifi cant increase of the angle error value, which is of the order of 1.4·10−4.
Fig. 3. Mean-square error for a) velocity modulus and b) infl ow angle
a) b)
4. Measurement site
For the purpose of the testing of the method allowing for determination of both velocity
vector components and vector sense, a simplifi ed model of air distribution in mine ventilation
network (Fig. 4) was developed. The air exchange in ventilation systems in mines is based on
46
forced air fl ow through the system of fans. In the model which has been developed, the presence
of two fans – one pushing the air in the main channel (A) and the second, drawing out the air in
the place of ramifi cation (B) was assumed.
Fig. 4. Simplifi ed model of ventilation system in mines
The model of the ventilation system was made of 1000-mm long PVC pipes with 110 mm
in diameter. The branching was simulated by means of the three-way pipe with the angle of
45° between the two longitudinal axes. Flow in the main channel was preset from the level of
the wind tunnel (A) with the length of 1500 mm and width of 190 mm. The tunnel outlet was
equipped with the exhaust nozzle of 110 mm in diameter. Maximal obtained velocity measured
at the tunnel outlet equalled 17 ms–1. Extracting fan equipped with the speed adjustment option
was installed at the end of side branching (B). Its purpose was to generate the continuous fl ow v’
(Fig. 5). For the purpose of air fl ow stabilization at the branching, a one meter long pipe (C)
was installed at its outlet. The probe was installed in the point marked p from above the pipe,
such that the measurement plane of the probe was overlapped with the plane indicated by the
axes of the model channels. The coordinate system was associated with lateral outfl ow, as it is
demonstrated in fi gure 5.
Fig. 5. Schematic diagram of the air fl ow in model of ventilation system in mine
47
5. Measurement experiment
The experiment was based on presetting the constant fl ow vr in the area of side branching,
and subsequent measurement of two-dimensional fl ow velocity vector in the point p for chang-
ing fl ow velocity in wind tunnel vz being in the range from 0 to 5 ms–1. The measurements were
performed with the sampling frequency of 1 kHz and averaging time of 1 s.
Figure 6 presents the projection of fl ow velocity vector in point p in function of the preset
velocity in wind tunnel for four different values of the vr velocity. Obtained fl ow velocity vec-
tors are caught in the point, the value of which corresponds to the fl ow velocity value preset in
the wind tunnel.
One may observe that in a situation in which the preset fl ow velocity in wind tunnel and
the forced velocity in branching are of the similar values (Fig. 6b-c), the change of the velocity
vector sense and direction occurs. On the other hand, the lack of the forced fl ow in branching
(Fig. 6a) or its very high value compared to the value of velocity in tunnel (Fig. 6d) results in
the sole change of the value of the fl ow velocity vector measured in point p.
Fig. 6. Projection of the fl ow velocity vector in point p (Fig. 5) for various values of forced fl ow parameters
in branching: a) vr ≈ 0 ms–1, b) vr ≈ 1 ms–1, c) vr ≈ 2 ms–1, d) vr ≈ 5 ms–1
a) b)
c) d)
48
6. Conclusion
This study presents a hot-wire anemometric method for the measurement of two-dimensional
fl ow velocity vector. In contrast to classical hot-wire anemometric probes, the probe presented
hereby allows for the determination of the changes in fl ow velocity vector direction and sense,
which is possible thanks to the application of the additional support connecting the two measuring
wires (sectional wire). The measurement algorithm presented in this paper enables the determi-
nation of the values of the velocity vector components as well as is allows for assessment of its
sense based directly on the measured voltages.
According to the results of the measurement experiment described here, the possibility of
the velocity vector determination under the conditions of reverse fl ows was confi rmed. As a result
of this measurement experiment, the complete system allowing for the measurement of both the
velocity vector components and the vector sense will be developed.
This scientifi c work was supported by Polish Ministry of Science and Higher Education
grant no. N N524 391734 (2008-2009)
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Received: 22 July 2009
