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Measurement of gas flow in short ducts, also rectangular
Flow Measurement and Instrumentation 30 (2013) 1–9
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Measurement of gas flow in short ducts, also rectangular Piotr Ostrowski n, Leszek Remiorz Institute of Power Engineering and Turbomachinery, Silesian University of Technology, ul. Konarskiego 18, 44-100 Gliwice, Poland
a r t i c l e i n f o
abstract
Article history: Received 23 April 2012 Received in revised form 1 August 2012 Accepted 18 September 2012 Available online 29 October 2012
This paper presents a discussion of the system of the measurement of the gas flow (of air or flue gases) dedicated particularly for use in rectangular ducts with short straight sections and with considerable cross-section dimensions (above 1 m). The measurement is conducted at a necking – the duct inset – with a single-point sensor such as the Prandtl tube. The measuring method may be used in newly designed air and flue gas ducts, as well as in those already in service, such as air conditioning or ventilation systems and power boilers. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Gas flow meter Flues and vents Short duct Rectangular duct Large cross-section duct
1. Introduction The control of combustion quality in power boiler furnaces is based on the measurement of the composition of flue gases – usually the concentration of oxygen – conducted by means of a zirconia sensor in a large cross-section convective duct, which obviously limits the reliability of the air excess ratio evaluation. The evaluation of the average air excess ratio can be improved by using a matrix of zirconia sensors built into a selected measuring cross-section of the flue, which still does not allow an ongoing evaluation of primary air distribution to the burners or secondary air distribution to the OFA nozzles. In view of the common use of secondary methods of reducing NOx emissions or additives that improve combustion such as kaolinites, it is also important to evaluate the reduction zone both in the furnace and on the waterwalls, and to measure the flue gas mass flow. The inconveniences mentioned above can be avoided by using gas flow meters (e.g. of air or flue gases) [1]. Gas flow measurement in pipelines is one of the fundamental measurements in technology (including boiler technology [2,3]) and it is performed by means of many methods [4,5,6,7]. In particular, gas flow measurements in pipelines with a diameter of up to 1.0 m may be made by means of standardized methods of the measurement of the pressure drop at the throttling element (Venturi methods). Based on [4,5] and some standards [8,9] it is known that the gas velocity profile in the pipeline crosssection immediately before the flow meter results from the 3D
n
Corresponding author. Tel.: þ48 32 2371368; fax: þ48 32 2372680. E-mail address: [email protected] (P. Ostrowski).
0955-5986/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.flowmeasinst.2012.09.010
spatial arrangement and from the applied pipeline fittings. Hence, it is asymmetrical but with a continuous surface. Depending on the flow characteristics, to normalize the profile, it is necessary to use a straight section with the length of 20–40 ID’s. Therefore, flow meters need straight pipeline sections before and after the measuring point which are quite long [10]. The lengths of these sections are determined by the flow measurement standards [8,9]. Moreover, flow meters involve a significant and permanent pressure drop which depends on velocity and density. For closed ducts with a rectangular cross-section or for pipelines with a diameter exceeding 1.0 m, standards [8,9] recommend measurements by means of the Prandtl tube (also: [11,12]) at n m points of division of the flow cross-section, which in the case of industrial measurements is a non-stationary method and practically unfeasible. The inconveniences resulting from the non-stationary character of the measurement are avoided owing to the development of averaging tubes [13,14], which have found numerous applications. Among others, it is possible to use them in the power industry [11,15]. Based on experience (as well as on design recommendations) it is known that the average linear velocity in low-pressure air and flue gas pipelines is included in the range of 5–15 m/s. Therefore, the averaging tubes feature (for gases) a low difference in the pressure measurement (e.g. for cold air it is around 145 Pa maximum). They also need straight measuring sections before and after the measuring points, result in a permanent pressure drop of approximately 2–10%, and involve resonance risk [13]. Another problem, which often appears in existing gas pipelines, is the changeability of the geometrical dimensions of the measuring cross-section, caused for example by the pollution of the pipeline
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P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
internal surfaces at low gas velocities, which substantially increases the uncertainty of the measurement. In professional power engineering air-flue gas cycles [2], as well as in heat engineering and ventilation systems, the most common are closed ducts with a large and rectangular cross-section which feature short straight sections [10] and relatively low linear velocities of the fluid of about 5–10 m/s.
BB
9
A
1 11 2 B
A
3
4
6
7
8 5 10
AA B
Fig. 1. Diagram of the gas flow meter. (1) Duct, (2) Normalizer, (inset) (3) Confusor, (4) Quasi-steady cross-section, (5) Diffuser, (6) Screw joint, (7) Blocking, (8) FM sensor, (9) DP meter, (10) Flat side walls, and (11) Baffle plate (option).
This paper presents a concept of the measurement method and of the structure of a gas flow meter [16] which may be used in ducts with a large rectangular and circular cross-section which feature short straight sections and low linear velocities of the fluid. The meter may find application in air-flue gas systems such as those used in power and heat engineering, air-conditioning and ventilation.
2. Description of the gas flow meter The concept of the gas flow measurement makes use of the fact that for a balanced, quasi-planar profile which is close to the average value of the velocity of the fluid at the measuring crosssection, the measurement of the fluid linear velocity can be made with a Prandtl tube or with a thermal anemometer at one selected point of the cross-section, which allows the calculation of the gas flow value as the product of the measured average velocity and of the area of the flow cross-section with a planar profile. The diagram illustrating the flow meter concept is presented in Fig. 1. The characteristic feature of the gas flow meter is that a non-movable flow normalizer 2 with a cross-section of the Venturi tube (inset) is built into duct 1; screw joint 6 with blocking 7 is built into the duct wall; the blocking fixes the movable sensor 8 of an point flow meter in a normalized planar velocity profile. The normalizer system may also include a planar baffle plate 11 which precedes the Venturi tube 2. The normalizer
Fig. 2. Modeling results—velocity profiles in measuring cross-sections: Inlet, I and II cross-sections, respectively.
Fig. 3. Modeling results—velocity distribution in the flow section of the measuring inset: (a) duct set 2 without the baffle plate (b) duct set 3 with the baffle plate.
Fig. 4. Modeling results—charts of pressure loss at the flow meter: (a) duct set 2 without the baffle plate/gas velocity 10.17 m/s (b) duct set 3 with the baffle plate/gas velocity 6.84 m/s.
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
3
Venturi tube 2, built into the duct with a rectangular crosssection, is composed of two symmetrical walls being a mirror image of each other, which make up the confusor part 3, with a quasi-steady cross-section 4, and the diffuser part 5; both these parts are closed by flat side walls 10 of the duct 1. The normalizer Venturi tube 2 built in the duct 1 with a circular cross-section has the shape of an axially symmetrical Venturi tube composed of the confusor part 3, with a quasi-steady cross-section 4, and the diffuser part 5. An additional characteristic of the measurement made with a normalizing Venturi tube is the fact that a much higher increase in linear velocity is obtained, i.e. there is a rise in the value of the measured pressure difference. Another premise which decides about the application values of the flow meter is the fact that pressure drops are contained at an acceptable level of a dozen or so per cent, which is obtained by way of appropriate selection of the flow meter geometrical dimensions.
to ensure that a quasi-planar (balanced) velocity profile is obtained at low local losses In a MATLAB program, the distribution of the gas velocity and the static pressure change curves at the length of the measuring inset for sets with and without the baffle plate are determined. They are presented in Figs. 3 and 4. With the criteria of the minimum pressure drop at the venturi and the simplicity of manufacture in mind, the structural form of the measuring venturi is determined as one consisting of three components: a confusor with the convergence angle of 301, a confusor with the convergence angle of 1.51 and a diffuser with a divergence angle of 12.51 with a necking of b ¼(0.3y0.4)B, where B is the size of the longer side of the duct with a rectangular cross-section A B. The used radial fan with the dimensions of the outflow window of A B¼ 170 300 mm2 and the assumed necking of b ¼ 0.333 determine the size of the venturi presented in Fig. 5.
3. Modeling results of the flow through the measuring inset
4. The test stand measurement results
The design of the measuring stand was preceded by an extensive series of model testing in the ANSYS environment to simulate different structural forms of the measuring inset – among others, nozzles (confusors) and Venturi tubes composed of a confusor and a diffuser were considered. The assumed velocity profile upstream the normalizing venturi at a section with the dimensions of 170 300 mm2 is taken as the boundary conditions – (cross-section in Fig. 6). The results of the flow modeling at the cross-sections at the end of the confusor (cross-section I in Fig. 6) and at the beginning of the diffuser (cross-section II in Fig. 6) are presented in Fig. 2. Appropriate geometrical characteristics of the flow meter are selected
The measurements are conducted at a test stand (Fig. 6) fitted with a radial fan, a forcing duct with a rectangular cross-section 170 300 mm2 and a flow meter inset made of zinc coated sheet, in accordance with Fig. 5. The system of local air velocity measurement is fitted with a Prandtl tube with a j of 3.18 mm manufactured by DWYER, with the EJA120 pressure difference converter with a range of 0y0.1 to 1.0 kPa made by YOKOGAWA. Other test stand components are: a static pressure meter, an air thermometer and hygrometer, and an S71200 controller with an analog input signal module made by SIEMENS. The measuring cross-sections are divided into 36 fields with an equal area—in the geometrical center of each field the local velocity is measured. The testing schedule assumed determination of velocity profiles at 3 measuring cross-sections, i.e. at the outflow window of the fan, and at 2 cross-sections of the flow meter: at the beginning and at the end of the 1.51 confusor. Based on the measurement results, the average velocity w4 in 4 central fields is calculated and then compared to the average velocity w36 which is calculated for the entire measuring cross-section, and the obtained calibration number k ¼w36/w4 is used to evaluate the correctness of the gas flow measurements conducted in accordance with the presented concept. The measurements of the air velocity profile are conducted for the sets of the measuring stand as presented in Table 1. The velocity measurement results are developed by means of a MATLAB program and presented in the form of air velocity fields, where:
1000
170
100
105 300
1,5° 12,5°
30° 180
200
470 Inserts material : galvanized sheet 1,0 mm
Fig. 7 presents the velocity profile at the fan outflow window; it features strong asymmetry and variation in local velocities (set 1),
Fig. 5. Dimensions of the measuring inset used in the testing.
I-st cross-section profile measurement
II-nd cross-section profile measurement
A
B
C
A
B
Inlet cross-section profile measurement
baffle plate
radial fan frequency converter
A-A option
B-B 100
300 170
C
confusor
C-C 300
170
gate valve
diffuser
300 170
Fig. 6. The measuring stand—location of measuring cross-sections: Inlet, I, and II.
4
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
Fig. 8 presents velocity profiles at cross-sections I and II for the duct fitted with a measuring inset without the baffle plate (set 2), Fig. 9 presents velocity profiles at cross-sections I and II for the duct fitted with a measuring inset and with the baffle plate (set 3).
Table 2 lists average values of the air velocity measurements w36 for the entire measuring profile (36 measuring points) and of the average velocity w4 at 4 central measuring points, as well as the calculated calibration number k ¼ w36/w4 which is an evaluation index of the correctness of the mass flow measurements made in accordance with the presented concept. The dependence of the calibration number k on the fluid velocity for both measuring sets and the location of the measuring cross-sections are presented in Fig. 10. Fig. 11 presents pressure drops determined by way of measurement for the pipeline sets 2 and 3. The description of the velocity axis corresponds to the average velocity converted to gas velocity in a 300 170 mm2 duct.
5. Results of velocity profile modeling The correctness of the calculations is verified in an ANSYS program; the measurement results assumed for digital modeling are those obtained at the test stand. The assumed velocity profile upstream the normalizing venturi at a section with the dimensions of 170 300 mm2 is taken as the boundary conditions; this profile is equal to the assumed profile measured at the Inlet cross-section, and the modeling results are presented in Figs. 12 and 13. The modeling results confirm the correctness of the measuring concept.
6. Uncertainty of measurement by means of Prandtl tube of the volume flow of gas with a constant composition The gas volume flow V (m3/h) is determined as the product of the cross-section area (circular cross-section is assumed) and the flow
Table 1 Measuring stand sets. Set Duct equipment
Straight sections 3pcs 0 Dekw downstream Straight section 1pc þinset( quasi-Venturie profile)þ straight sections 2pcs Straight section 1pcþ baffle plate þinset (quasi-Venturie profile) þ straight sections 2pcs
300
300
250
250
150
100
Cross-section I 100 170 mm2
Cross-section II 90 170 mm2
4.5 Dekw downstream 4.5 Dekw downstream
4.66 Dekw downstream 4.66 Dekw downstream
9.5 8.5 200
7.5 6.5 5.5 4.5
Y, mm
3.2 3.1 3 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2
200
Y, mm
1 2 3
Inlet cross-section 170 300 mm2
3.5
150
2.5 1.5 0.5 -0.5
100
-1.5 -2.5 -3.5 -4.5
50
50
0
0 0
50
100 X, mm
150
0
50
100
150
X, mm
Fig. 7. Air velocity profiles in the Inlet cross-section (pipeline set 1) for a low (about 405 m3/h) and a high (about 810 m3/h) fan output.
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
Y, mm
60
40
20
0 0
20
40
60
80
100
120
140
160
10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
100 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
80
Y, mm
80
60
40
20
0 0
20
40
60
Y, mm
60
40
20
0 40
60
80
100
120
140
160
20 20 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
60
40
20
0 0
20
0 80 100 X, mm
120
140
160
20
40
60
Y, mm
60
40
20
0 20
40
60
80 X, mm
100
80
100
120
140
160
100 27 26.5 26 25.5 25 24.5 24 23.5 23 22.5 22 21.5 21 20.5 20 19.5 19
80
60
40
20
0 0
20
40
60
80
100
120
140
160
X, mm
80
0
27 26.5 26 25.5 25 24.5 24 23.5 23 22.5 22 21.5 21 20.5 20 19.5 19
Y, mm
40
60
160
80
120
140
160
40 39.5 39 38.5 38 37.5 37 36.5 36 35.5 35 34.5 34 33.5 33 32.5 32 31.5 31 30.5 30 29.5 29 28.5 28 27.5 27
100 32.4 80
31.9 31.4
Y, mm
Y, mm
60
40
140
X, mm
80
20
120
19 18.5 18 17.5 17 16.5 16 15.5 15 14.5 14 13.5 13 12.5 12 11.5 11
X, mm
0
100
100
Y, mm
80
20
80 X, mm
X, mm
0
5
60
30.9 30.4
40
29.9 29.4
20
28.9 28.4
0 0
20
40
60
80
100
120
140
160
X, mm
Fig. 8. Air velocity profiles in measuring cross-sections I and II in four velocity ranges (pipeline set 2 without the baffle plate): measuring cross-section I (left); measuring cross-section II (right).
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
80
Y, mm
60
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
80
Y, mm
60
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
80
Y, mm
60
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
12 12 11 11 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
27 27 26 26 25 25 24 24 23 23 22 22 21 21 20 20 19 19 18 18 17
100
80
60
40
20
0 0
20
40
60
80
100
120
140
160
100 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
80 Y, mm
Y, mm
60
11 11 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
60 40 20 0 0
20
40
60
80 100 X, mm
120
140
160
100 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
80 Y, mm
80
60 40 20 0 0
20
40
60
80 100 X, mm
120
140
160
100 20 20 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
80 Y, mm
6
60 40 20 0 0
20
40
60
80 100 X, mm
120
140
160
Fig. 9. Air velocity profiles in measuring cross-sections I and II in 4 velocity ranges (pipeline set 3 with the baffle plate): measuring cross-section I (left), measuring crosssection II (right).
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
7
Table 2 Measurement results. Set
Cross-section
Calibration number j ¼ w36/w4
Average value of velocity (m/s) w36 (At 36 points)
Average jav
w4 (At 4 points)
2 (Without baffle plate)
I II
9.04 8.21
17.98 16.01
25.94 22.83
34.17 30.10
9.37 8.37
18.71 16.34
26.91 23.57
35.17 30.53
1.038 1.021
1.041 1.021
1.038 1.033
1.032 1.014
1.037 1.022
3 (With baffle plate)
I II
4.71 3.82
10.02 8.48
14.45 12.37
19.15 16.31
4.89 3.82
10.24 3.89
14.60 12.24
19.36 16.16
1.038 1.00
1.022 0.989
1.010 0.989
1.011 0.991
1.020 0.992
Fig. 10. Dependence of calibration number j on the gas velocity.
Fig. 11. Pressure losses for set 2 and set 3 of the measuring pipeline.
Fig. 12. Modeling results: pipeline set 2 without the baffle plate; the vertical axis–air velocity profiles [m/s] in the Inlet, I and II cross-sections.
rate [8]: V¼
Due to air compressibility, the correction coefficient is
Y d2 4
!
ae SQRT 2 K 0 K u Dpd =r
ð1Þ
e ¼ 120, 18
Dpd ps
ð2Þ
8
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
Fig. 13. Modeling results: pipeline set 3 with the baffle plate; the vertical axis–air velocity profiles [m/s] in the Inlet, I and II cross-sections. Table 3 Uncertainty of measurement.
DV_ =V_ (%)
d (mm)
2
0.929 0.889 0.511 0.51
250 500 1000 2000
0.00000225 0.00000225 0.00000225 0.00000225
Da=a
2
De=e
0.000000000024 0.000000000024 0.000000000024 0.000000000024
2 Dd=d Þ2
0:5 Dy=y Þ2
0.000000639 0.000000160 0.000000040 0.000000010
0.0000136 0.0000136 0.0000136 0.0000136
0.00000956 0.00000956 0.00000956 0.00000956
0:5 Ds=s Þ2
2 0:5Dt=t 0.000000653 0.000000653 0.000000653 0.000000653
Fig. 15. Measurement at the Accredited Laboratory. Fig. 14. Measurement in ventilation/air-conditioning ducts.
and density is K 0 ps K 0 T Rg
r¼
ð3Þ
where a is the Prandtl tube calibration coefficient, d is the pipeline inside diameter (m), Dpd is the pressure difference (Pa), ps is the gas static pressure (Pa), T ¼tc þ273.16 is the gas temperature (K), Rg is the individual gas constant, K0 is the uncertainty of the measuring converter (PLC analog signal input module), and Ku is the uncertainty resulting from the Prandtl tube setting angle. If p ¼ K 0 K u pd ,
s ¼ K 0 ps ,
t ¼ K 0 tc
ð4Þ
and if
d¼
Dd d
W ¼ K0Ku
,
Dp p
s¼
,
Ds s
,
t¼
Dt
DV V
2
¼ þ
2
Da
a
þ
2
De
e
2 ð0:5ÞDs
s
þ
2 2Dd
þ
d 0:5Dt
t
þ
7. Examples of industrial applications The single-point method is used in air mass flow measurements in air-conditioning cycles in the automotive industry (Fig. 14) for on-line measurements of the heat balance carried out according to Standard ISO: 50001:2011 [17], at a test stand (Fig. 15) at the Accredited Laboratory, as well as in a system of the measurement of the steam boiler secondary air distribution (investment in progress).
ð5Þ
t
8. Summary
The uncertainty of indirect measurement of the gas flow, where standard deviation is the measure, is
Example results of the uncertainty of the measurement of the volume flow of gas with a constant composition (where standard deviation is the measure) are presented in Table 3. The uncertainty related to the determination of the correction coefficient due to compressibility (De/e)2 is defined for the working point: Dp¼200 Pa and ps ¼105 Pa.
2 0:5DW
W
2 ð6Þ
This paper presents the method of a single-point measurement of the air (or flue gas) mass flow at the central point of a planar measuring cross-section. A preliminary study of the shape and of the dimensions of the measuring section was conducted using numerical models, and the results were used to design a test stand. The stand, composed of a radial fan and a segmented rectangular duct, was fitted with a flow area necking which limited the cross-section
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
area to 33%. A possibility of fitting the duct with an additional baffle plate before the measuring section was also ensured. Measurements of air velocity profiles were conducted with the Prandtl tube at selected cross-sections of the duct, and the results were presented in the form of the field of velocity isolines and the calibration number. The calibration number for the necking without the baffle plate in the measuring cross-section after the confusor is jav ¼1.037, and jav ¼1.022 before the diffuser; for the necking with the baffle plate the values of the calibration number are jav ¼1.020 and 0.992, respectively. The measurement results were entered into a numerical model as the boundary conditions for which velocity profiles were calculated and pressure drops were determined along the entire measuring section. Pressure drops along the measuring section for the set with and without the baffle plate are presented in Fig. 11 – the velocities are average velocities of the fluid in the full 300 170 mm2 duct. As a form of supplement, the uncertainty of the gas (air or flue gas) flow single-point measurement with the Prandtl tube was evaluated for the flow in a pipeline with an equivalent circular cross-section. For the diameters of d 41000 mm the uncertainty of the measurement falls to the value of about 0.5%. The obtained results make it possible to state that the proposed method of a single-point air (or flue gas) measurement, incorporating the correction coefficient jav, satisfies the requirements of industrial measurement and that it may be used in short ducts with a rectangular cross-section with an equivalent diameter 41000 mm. It should be added that the measuring set may be applied in new ducts and in those which are already in use at very reasonable investment costs. The Authors intend to conduct further experimental studies and model testing of the flow meter. References [1] Pronobis M. Modernization of steam generators. Warsaw: WNT; 2002 [in Polish].
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[2] Yang X. Flow characteristic and velocity measuring of primary air in the pipe. Yi Qi Yi Biao Xue Bao/Chinese Journal of Scientific Instrument 2006;27(Suppl.):1194–5. [3] Xue Z. Development and realization of air flow on-line monitoring system in utility boiler based on AC induction. Advanced Materials Research 2012 4831–6. [4] LaNasa & Upp Fluid Flow Measurement. A practical guide to accurate flow measurement. 2nd ed.Elsevier; 2002. [5] Parr EA. Industrial control handbook. 3rd ed. Oxford OX2 8DP: B-H Ltd; 1998 [chapter 5]. [6] Rup K, Malinowski L, Sarna P. Measurement of flow rate in square-sectioned Duct Bend. Journal of Theoretical and Applied Mechanics 2011;49(2): 301–11. [7] Zeng XY, Chi ZH, Zheng MG, Sun GG, Zhang GX, Wang JQ. Experiment research on air flow rate measurement using tracer gas method. Advanced Materials Research 2012;374–377:520–3. [8] Standard PN-ISO 5221. Air distribution and air diffusion—rules to methods of measuring air flow rate in and air handling duct; December 1994. [9] Standard PN-EN ISO 5167. Measurement of fluid flow by means of differential devices inserted in circular cross-section conduits running full; June/July 2005. [10] Zhu X, Zhao Z, Zhang Q. Measuring and calibrating flow rate of primary air for medium speed mills by numerical simulation. In: Proceedings of the 2011 2nd international conference on mechanic automation and control engineering, MACE 2011; 2011. Art. no. 5987203, p. 1386–9. [11] Winters D, Johnson AK. Properly measured duct flow. Chemical Processing 2011;74(10):39–42. [12] Wu H, Zou Z, Huang C, Wang F, Li H, Wang Z. Study on the inaccuracies of air velocity measured by pitots with different outer diameter in a air duct. In: Proceedings of the international conference on computer distributed control and intelligent environmental monitoring, CDCIEM 2011; 2011. Art. no. 5748172, p. 1815–8. [13] Torbar averaging pitot tubes economical flow metering solutions for gases, liquids and steam. Torbar_EN_ Issue 1—Brochure ABB. [14] Ostrowski P, Wecel D. Patent P 379723. Averaging tube for continuous fluid mass flow measurement, especially in pipelines; 2006 [in Polish]. [15] Stan´da J, Go´recki J, Andruszkiewicz A, Kubas K.. Air mass flow meter in a rectangular duct PAR r.7 nr 7-8 str.46-9 [in Polish]. [16] Ostrowski P, Pronobis M, Kalisz S, Remiorz L, Wejkowski R. Patent applications P.393836, EP12460004. Method and meter for the measurement of gas flux in short closed ducts of large cross section area, particularly in boiler air/ flue gas and ventilation circuits; 2011,2012) [in Polish]. [17] Standard ISO 50001:2011. Energy management systems—requirements with guidance for use; June 2011.
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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Measurement of gas flow in short ducts, also rectangular Piotr Ostrowski n, Leszek Remiorz Institute of Power Engineering and Turbomachinery, Silesian University of Technology, ul. Konarskiego 18, 44-100 Gliwice, Poland
a r t i c l e i n f o
abstract
Article history: Received 23 April 2012 Received in revised form 1 August 2012 Accepted 18 September 2012 Available online 29 October 2012
This paper presents a discussion of the system of the measurement of the gas flow (of air or flue gases) dedicated particularly for use in rectangular ducts with short straight sections and with considerable cross-section dimensions (above 1 m). The measurement is conducted at a necking – the duct inset – with a single-point sensor such as the Prandtl tube. The measuring method may be used in newly designed air and flue gas ducts, as well as in those already in service, such as air conditioning or ventilation systems and power boilers. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Gas flow meter Flues and vents Short duct Rectangular duct Large cross-section duct
1. Introduction The control of combustion quality in power boiler furnaces is based on the measurement of the composition of flue gases – usually the concentration of oxygen – conducted by means of a zirconia sensor in a large cross-section convective duct, which obviously limits the reliability of the air excess ratio evaluation. The evaluation of the average air excess ratio can be improved by using a matrix of zirconia sensors built into a selected measuring cross-section of the flue, which still does not allow an ongoing evaluation of primary air distribution to the burners or secondary air distribution to the OFA nozzles. In view of the common use of secondary methods of reducing NOx emissions or additives that improve combustion such as kaolinites, it is also important to evaluate the reduction zone both in the furnace and on the waterwalls, and to measure the flue gas mass flow. The inconveniences mentioned above can be avoided by using gas flow meters (e.g. of air or flue gases) [1]. Gas flow measurement in pipelines is one of the fundamental measurements in technology (including boiler technology [2,3]) and it is performed by means of many methods [4,5,6,7]. In particular, gas flow measurements in pipelines with a diameter of up to 1.0 m may be made by means of standardized methods of the measurement of the pressure drop at the throttling element (Venturi methods). Based on [4,5] and some standards [8,9] it is known that the gas velocity profile in the pipeline crosssection immediately before the flow meter results from the 3D
n
Corresponding author. Tel.: þ48 32 2371368; fax: þ48 32 2372680. E-mail address: [email protected] (P. Ostrowski).
0955-5986/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.flowmeasinst.2012.09.010
spatial arrangement and from the applied pipeline fittings. Hence, it is asymmetrical but with a continuous surface. Depending on the flow characteristics, to normalize the profile, it is necessary to use a straight section with the length of 20–40 ID’s. Therefore, flow meters need straight pipeline sections before and after the measuring point which are quite long [10]. The lengths of these sections are determined by the flow measurement standards [8,9]. Moreover, flow meters involve a significant and permanent pressure drop which depends on velocity and density. For closed ducts with a rectangular cross-section or for pipelines with a diameter exceeding 1.0 m, standards [8,9] recommend measurements by means of the Prandtl tube (also: [11,12]) at n m points of division of the flow cross-section, which in the case of industrial measurements is a non-stationary method and practically unfeasible. The inconveniences resulting from the non-stationary character of the measurement are avoided owing to the development of averaging tubes [13,14], which have found numerous applications. Among others, it is possible to use them in the power industry [11,15]. Based on experience (as well as on design recommendations) it is known that the average linear velocity in low-pressure air and flue gas pipelines is included in the range of 5–15 m/s. Therefore, the averaging tubes feature (for gases) a low difference in the pressure measurement (e.g. for cold air it is around 145 Pa maximum). They also need straight measuring sections before and after the measuring points, result in a permanent pressure drop of approximately 2–10%, and involve resonance risk [13]. Another problem, which often appears in existing gas pipelines, is the changeability of the geometrical dimensions of the measuring cross-section, caused for example by the pollution of the pipeline
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internal surfaces at low gas velocities, which substantially increases the uncertainty of the measurement. In professional power engineering air-flue gas cycles [2], as well as in heat engineering and ventilation systems, the most common are closed ducts with a large and rectangular cross-section which feature short straight sections [10] and relatively low linear velocities of the fluid of about 5–10 m/s.
BB
9
A
1 11 2 B
A
3
4
6
7
8 5 10
AA B
Fig. 1. Diagram of the gas flow meter. (1) Duct, (2) Normalizer, (inset) (3) Confusor, (4) Quasi-steady cross-section, (5) Diffuser, (6) Screw joint, (7) Blocking, (8) FM sensor, (9) DP meter, (10) Flat side walls, and (11) Baffle plate (option).
This paper presents a concept of the measurement method and of the structure of a gas flow meter [16] which may be used in ducts with a large rectangular and circular cross-section which feature short straight sections and low linear velocities of the fluid. The meter may find application in air-flue gas systems such as those used in power and heat engineering, air-conditioning and ventilation.
2. Description of the gas flow meter The concept of the gas flow measurement makes use of the fact that for a balanced, quasi-planar profile which is close to the average value of the velocity of the fluid at the measuring crosssection, the measurement of the fluid linear velocity can be made with a Prandtl tube or with a thermal anemometer at one selected point of the cross-section, which allows the calculation of the gas flow value as the product of the measured average velocity and of the area of the flow cross-section with a planar profile. The diagram illustrating the flow meter concept is presented in Fig. 1. The characteristic feature of the gas flow meter is that a non-movable flow normalizer 2 with a cross-section of the Venturi tube (inset) is built into duct 1; screw joint 6 with blocking 7 is built into the duct wall; the blocking fixes the movable sensor 8 of an point flow meter in a normalized planar velocity profile. The normalizer system may also include a planar baffle plate 11 which precedes the Venturi tube 2. The normalizer
Fig. 2. Modeling results—velocity profiles in measuring cross-sections: Inlet, I and II cross-sections, respectively.
Fig. 3. Modeling results—velocity distribution in the flow section of the measuring inset: (a) duct set 2 without the baffle plate (b) duct set 3 with the baffle plate.
Fig. 4. Modeling results—charts of pressure loss at the flow meter: (a) duct set 2 without the baffle plate/gas velocity 10.17 m/s (b) duct set 3 with the baffle plate/gas velocity 6.84 m/s.
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
3
Venturi tube 2, built into the duct with a rectangular crosssection, is composed of two symmetrical walls being a mirror image of each other, which make up the confusor part 3, with a quasi-steady cross-section 4, and the diffuser part 5; both these parts are closed by flat side walls 10 of the duct 1. The normalizer Venturi tube 2 built in the duct 1 with a circular cross-section has the shape of an axially symmetrical Venturi tube composed of the confusor part 3, with a quasi-steady cross-section 4, and the diffuser part 5. An additional characteristic of the measurement made with a normalizing Venturi tube is the fact that a much higher increase in linear velocity is obtained, i.e. there is a rise in the value of the measured pressure difference. Another premise which decides about the application values of the flow meter is the fact that pressure drops are contained at an acceptable level of a dozen or so per cent, which is obtained by way of appropriate selection of the flow meter geometrical dimensions.
to ensure that a quasi-planar (balanced) velocity profile is obtained at low local losses In a MATLAB program, the distribution of the gas velocity and the static pressure change curves at the length of the measuring inset for sets with and without the baffle plate are determined. They are presented in Figs. 3 and 4. With the criteria of the minimum pressure drop at the venturi and the simplicity of manufacture in mind, the structural form of the measuring venturi is determined as one consisting of three components: a confusor with the convergence angle of 301, a confusor with the convergence angle of 1.51 and a diffuser with a divergence angle of 12.51 with a necking of b ¼(0.3y0.4)B, where B is the size of the longer side of the duct with a rectangular cross-section A B. The used radial fan with the dimensions of the outflow window of A B¼ 170 300 mm2 and the assumed necking of b ¼ 0.333 determine the size of the venturi presented in Fig. 5.
3. Modeling results of the flow through the measuring inset
4. The test stand measurement results
The design of the measuring stand was preceded by an extensive series of model testing in the ANSYS environment to simulate different structural forms of the measuring inset – among others, nozzles (confusors) and Venturi tubes composed of a confusor and a diffuser were considered. The assumed velocity profile upstream the normalizing venturi at a section with the dimensions of 170 300 mm2 is taken as the boundary conditions – (cross-section in Fig. 6). The results of the flow modeling at the cross-sections at the end of the confusor (cross-section I in Fig. 6) and at the beginning of the diffuser (cross-section II in Fig. 6) are presented in Fig. 2. Appropriate geometrical characteristics of the flow meter are selected
The measurements are conducted at a test stand (Fig. 6) fitted with a radial fan, a forcing duct with a rectangular cross-section 170 300 mm2 and a flow meter inset made of zinc coated sheet, in accordance with Fig. 5. The system of local air velocity measurement is fitted with a Prandtl tube with a j of 3.18 mm manufactured by DWYER, with the EJA120 pressure difference converter with a range of 0y0.1 to 1.0 kPa made by YOKOGAWA. Other test stand components are: a static pressure meter, an air thermometer and hygrometer, and an S71200 controller with an analog input signal module made by SIEMENS. The measuring cross-sections are divided into 36 fields with an equal area—in the geometrical center of each field the local velocity is measured. The testing schedule assumed determination of velocity profiles at 3 measuring cross-sections, i.e. at the outflow window of the fan, and at 2 cross-sections of the flow meter: at the beginning and at the end of the 1.51 confusor. Based on the measurement results, the average velocity w4 in 4 central fields is calculated and then compared to the average velocity w36 which is calculated for the entire measuring cross-section, and the obtained calibration number k ¼w36/w4 is used to evaluate the correctness of the gas flow measurements conducted in accordance with the presented concept. The measurements of the air velocity profile are conducted for the sets of the measuring stand as presented in Table 1. The velocity measurement results are developed by means of a MATLAB program and presented in the form of air velocity fields, where:
1000
170
100
105 300
1,5° 12,5°
30° 180
200
470 Inserts material : galvanized sheet 1,0 mm
Fig. 7 presents the velocity profile at the fan outflow window; it features strong asymmetry and variation in local velocities (set 1),
Fig. 5. Dimensions of the measuring inset used in the testing.
I-st cross-section profile measurement
II-nd cross-section profile measurement
A
B
C
A
B
Inlet cross-section profile measurement
baffle plate
radial fan frequency converter
A-A option
B-B 100
300 170
C
confusor
C-C 300
170
gate valve
diffuser
300 170
Fig. 6. The measuring stand—location of measuring cross-sections: Inlet, I, and II.
4
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
Fig. 8 presents velocity profiles at cross-sections I and II for the duct fitted with a measuring inset without the baffle plate (set 2), Fig. 9 presents velocity profiles at cross-sections I and II for the duct fitted with a measuring inset and with the baffle plate (set 3).
Table 2 lists average values of the air velocity measurements w36 for the entire measuring profile (36 measuring points) and of the average velocity w4 at 4 central measuring points, as well as the calculated calibration number k ¼ w36/w4 which is an evaluation index of the correctness of the mass flow measurements made in accordance with the presented concept. The dependence of the calibration number k on the fluid velocity for both measuring sets and the location of the measuring cross-sections are presented in Fig. 10. Fig. 11 presents pressure drops determined by way of measurement for the pipeline sets 2 and 3. The description of the velocity axis corresponds to the average velocity converted to gas velocity in a 300 170 mm2 duct.
5. Results of velocity profile modeling The correctness of the calculations is verified in an ANSYS program; the measurement results assumed for digital modeling are those obtained at the test stand. The assumed velocity profile upstream the normalizing venturi at a section with the dimensions of 170 300 mm2 is taken as the boundary conditions; this profile is equal to the assumed profile measured at the Inlet cross-section, and the modeling results are presented in Figs. 12 and 13. The modeling results confirm the correctness of the measuring concept.
6. Uncertainty of measurement by means of Prandtl tube of the volume flow of gas with a constant composition The gas volume flow V (m3/h) is determined as the product of the cross-section area (circular cross-section is assumed) and the flow
Table 1 Measuring stand sets. Set Duct equipment
Straight sections 3pcs 0 Dekw downstream Straight section 1pc þinset( quasi-Venturie profile)þ straight sections 2pcs Straight section 1pcþ baffle plate þinset (quasi-Venturie profile) þ straight sections 2pcs
300
300
250
250
150
100
Cross-section I 100 170 mm2
Cross-section II 90 170 mm2
4.5 Dekw downstream 4.5 Dekw downstream
4.66 Dekw downstream 4.66 Dekw downstream
9.5 8.5 200
7.5 6.5 5.5 4.5
Y, mm
3.2 3.1 3 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2
200
Y, mm
1 2 3
Inlet cross-section 170 300 mm2
3.5
150
2.5 1.5 0.5 -0.5
100
-1.5 -2.5 -3.5 -4.5
50
50
0
0 0
50
100 X, mm
150
0
50
100
150
X, mm
Fig. 7. Air velocity profiles in the Inlet cross-section (pipeline set 1) for a low (about 405 m3/h) and a high (about 810 m3/h) fan output.
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
Y, mm
60
40
20
0 0
20
40
60
80
100
120
140
160
10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
100 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
80
Y, mm
80
60
40
20
0 0
20
40
60
Y, mm
60
40
20
0 40
60
80
100
120
140
160
20 20 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
60
40
20
0 0
20
0 80 100 X, mm
120
140
160
20
40
60
Y, mm
60
40
20
0 20
40
60
80 X, mm
100
80
100
120
140
160
100 27 26.5 26 25.5 25 24.5 24 23.5 23 22.5 22 21.5 21 20.5 20 19.5 19
80
60
40
20
0 0
20
40
60
80
100
120
140
160
X, mm
80
0
27 26.5 26 25.5 25 24.5 24 23.5 23 22.5 22 21.5 21 20.5 20 19.5 19
Y, mm
40
60
160
80
120
140
160
40 39.5 39 38.5 38 37.5 37 36.5 36 35.5 35 34.5 34 33.5 33 32.5 32 31.5 31 30.5 30 29.5 29 28.5 28 27.5 27
100 32.4 80
31.9 31.4
Y, mm
Y, mm
60
40
140
X, mm
80
20
120
19 18.5 18 17.5 17 16.5 16 15.5 15 14.5 14 13.5 13 12.5 12 11.5 11
X, mm
0
100
100
Y, mm
80
20
80 X, mm
X, mm
0
5
60
30.9 30.4
40
29.9 29.4
20
28.9 28.4
0 0
20
40
60
80
100
120
140
160
X, mm
Fig. 8. Air velocity profiles in measuring cross-sections I and II in four velocity ranges (pipeline set 2 without the baffle plate): measuring cross-section I (left); measuring cross-section II (right).
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
80
Y, mm
60
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
80
Y, mm
60
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
80
Y, mm
60
40
20
0 0
20
40
60
80 100 X, mm
120
140
160
12 12 11 11 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
27 27 26 26 25 25 24 24 23 23 22 22 21 21 20 20 19 19 18 18 17
100
80
60
40
20
0 0
20
40
60
80
100
120
140
160
100 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
80 Y, mm
Y, mm
60
11 11 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3
60 40 20 0 0
20
40
60
80 100 X, mm
120
140
160
100 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
80 Y, mm
80
60 40 20 0 0
20
40
60
80 100 X, mm
120
140
160
100 20 20 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11
80 Y, mm
6
60 40 20 0 0
20
40
60
80 100 X, mm
120
140
160
Fig. 9. Air velocity profiles in measuring cross-sections I and II in 4 velocity ranges (pipeline set 3 with the baffle plate): measuring cross-section I (left), measuring crosssection II (right).
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
7
Table 2 Measurement results. Set
Cross-section
Calibration number j ¼ w36/w4
Average value of velocity (m/s) w36 (At 36 points)
Average jav
w4 (At 4 points)
2 (Without baffle plate)
I II
9.04 8.21
17.98 16.01
25.94 22.83
34.17 30.10
9.37 8.37
18.71 16.34
26.91 23.57
35.17 30.53
1.038 1.021
1.041 1.021
1.038 1.033
1.032 1.014
1.037 1.022
3 (With baffle plate)
I II
4.71 3.82
10.02 8.48
14.45 12.37
19.15 16.31
4.89 3.82
10.24 3.89
14.60 12.24
19.36 16.16
1.038 1.00
1.022 0.989
1.010 0.989
1.011 0.991
1.020 0.992
Fig. 10. Dependence of calibration number j on the gas velocity.
Fig. 11. Pressure losses for set 2 and set 3 of the measuring pipeline.
Fig. 12. Modeling results: pipeline set 2 without the baffle plate; the vertical axis–air velocity profiles [m/s] in the Inlet, I and II cross-sections.
rate [8]: V¼
Due to air compressibility, the correction coefficient is
Y d2 4
!
ae SQRT 2 K 0 K u Dpd =r
ð1Þ
e ¼ 120, 18
Dpd ps
ð2Þ
8
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
Fig. 13. Modeling results: pipeline set 3 with the baffle plate; the vertical axis–air velocity profiles [m/s] in the Inlet, I and II cross-sections. Table 3 Uncertainty of measurement.
DV_ =V_ (%)
d (mm)
2
0.929 0.889 0.511 0.51
250 500 1000 2000
0.00000225 0.00000225 0.00000225 0.00000225
Da=a
2
De=e
0.000000000024 0.000000000024 0.000000000024 0.000000000024
2 Dd=d Þ2
0:5 Dy=y Þ2
0.000000639 0.000000160 0.000000040 0.000000010
0.0000136 0.0000136 0.0000136 0.0000136
0.00000956 0.00000956 0.00000956 0.00000956
0:5 Ds=s Þ2
2 0:5Dt=t 0.000000653 0.000000653 0.000000653 0.000000653
Fig. 15. Measurement at the Accredited Laboratory. Fig. 14. Measurement in ventilation/air-conditioning ducts.
and density is K 0 ps K 0 T Rg
r¼
ð3Þ
where a is the Prandtl tube calibration coefficient, d is the pipeline inside diameter (m), Dpd is the pressure difference (Pa), ps is the gas static pressure (Pa), T ¼tc þ273.16 is the gas temperature (K), Rg is the individual gas constant, K0 is the uncertainty of the measuring converter (PLC analog signal input module), and Ku is the uncertainty resulting from the Prandtl tube setting angle. If p ¼ K 0 K u pd ,
s ¼ K 0 ps ,
t ¼ K 0 tc
ð4Þ
and if
d¼
Dd d
W ¼ K0Ku
,
Dp p
s¼
,
Ds s
,
t¼
Dt
DV V
2
¼ þ
2
Da
a
þ
2
De
e
2 ð0:5ÞDs
s
þ
2 2Dd
þ
d 0:5Dt
t
þ
7. Examples of industrial applications The single-point method is used in air mass flow measurements in air-conditioning cycles in the automotive industry (Fig. 14) for on-line measurements of the heat balance carried out according to Standard ISO: 50001:2011 [17], at a test stand (Fig. 15) at the Accredited Laboratory, as well as in a system of the measurement of the steam boiler secondary air distribution (investment in progress).
ð5Þ
t
8. Summary
The uncertainty of indirect measurement of the gas flow, where standard deviation is the measure, is
Example results of the uncertainty of the measurement of the volume flow of gas with a constant composition (where standard deviation is the measure) are presented in Table 3. The uncertainty related to the determination of the correction coefficient due to compressibility (De/e)2 is defined for the working point: Dp¼200 Pa and ps ¼105 Pa.
2 0:5DW
W
2 ð6Þ
This paper presents the method of a single-point measurement of the air (or flue gas) mass flow at the central point of a planar measuring cross-section. A preliminary study of the shape and of the dimensions of the measuring section was conducted using numerical models, and the results were used to design a test stand. The stand, composed of a radial fan and a segmented rectangular duct, was fitted with a flow area necking which limited the cross-section
P. Ostrowski, L. Remiorz / Flow Measurement and Instrumentation 30 (2013) 1–9
area to 33%. A possibility of fitting the duct with an additional baffle plate before the measuring section was also ensured. Measurements of air velocity profiles were conducted with the Prandtl tube at selected cross-sections of the duct, and the results were presented in the form of the field of velocity isolines and the calibration number. The calibration number for the necking without the baffle plate in the measuring cross-section after the confusor is jav ¼1.037, and jav ¼1.022 before the diffuser; for the necking with the baffle plate the values of the calibration number are jav ¼1.020 and 0.992, respectively. The measurement results were entered into a numerical model as the boundary conditions for which velocity profiles were calculated and pressure drops were determined along the entire measuring section. Pressure drops along the measuring section for the set with and without the baffle plate are presented in Fig. 11 – the velocities are average velocities of the fluid in the full 300 170 mm2 duct. As a form of supplement, the uncertainty of the gas (air or flue gas) flow single-point measurement with the Prandtl tube was evaluated for the flow in a pipeline with an equivalent circular cross-section. For the diameters of d 41000 mm the uncertainty of the measurement falls to the value of about 0.5%. The obtained results make it possible to state that the proposed method of a single-point air (or flue gas) measurement, incorporating the correction coefficient jav, satisfies the requirements of industrial measurement and that it may be used in short ducts with a rectangular cross-section with an equivalent diameter 41000 mm. It should be added that the measuring set may be applied in new ducts and in those which are already in use at very reasonable investment costs. The Authors intend to conduct further experimental studies and model testing of the flow meter. References [1] Pronobis M. Modernization of steam generators. Warsaw: WNT; 2002 [in Polish].
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[2] Yang X. Flow characteristic and velocity measuring of primary air in the pipe. Yi Qi Yi Biao Xue Bao/Chinese Journal of Scientific Instrument 2006;27(Suppl.):1194–5. [3] Xue Z. Development and realization of air flow on-line monitoring system in utility boiler based on AC induction. Advanced Materials Research 2012 4831–6. [4] LaNasa & Upp Fluid Flow Measurement. A practical guide to accurate flow measurement. 2nd ed.Elsevier; 2002. [5] Parr EA. Industrial control handbook. 3rd ed. Oxford OX2 8DP: B-H Ltd; 1998 [chapter 5]. [6] Rup K, Malinowski L, Sarna P. Measurement of flow rate in square-sectioned Duct Bend. Journal of Theoretical and Applied Mechanics 2011;49(2): 301–11. [7] Zeng XY, Chi ZH, Zheng MG, Sun GG, Zhang GX, Wang JQ. Experiment research on air flow rate measurement using tracer gas method. Advanced Materials Research 2012;374–377:520–3. [8] Standard PN-ISO 5221. Air distribution and air diffusion—rules to methods of measuring air flow rate in and air handling duct; December 1994. [9] Standard PN-EN ISO 5167. Measurement of fluid flow by means of differential devices inserted in circular cross-section conduits running full; June/July 2005. [10] Zhu X, Zhao Z, Zhang Q. Measuring and calibrating flow rate of primary air for medium speed mills by numerical simulation. In: Proceedings of the 2011 2nd international conference on mechanic automation and control engineering, MACE 2011; 2011. Art. no. 5987203, p. 1386–9. [11] Winters D, Johnson AK. Properly measured duct flow. Chemical Processing 2011;74(10):39–42. [12] Wu H, Zou Z, Huang C, Wang F, Li H, Wang Z. Study on the inaccuracies of air velocity measured by pitots with different outer diameter in a air duct. In: Proceedings of the international conference on computer distributed control and intelligent environmental monitoring, CDCIEM 2011; 2011. Art. no. 5748172, p. 1815–8. [13] Torbar averaging pitot tubes economical flow metering solutions for gases, liquids and steam. Torbar_EN_ Issue 1—Brochure ABB. [14] Ostrowski P, Wecel D. Patent P 379723. Averaging tube for continuous fluid mass flow measurement, especially in pipelines; 2006 [in Polish]. [15] Stan´da J, Go´recki J, Andruszkiewicz A, Kubas K.. Air mass flow meter in a rectangular duct PAR r.7 nr 7-8 str.46-9 [in Polish]. [16] Ostrowski P, Pronobis M, Kalisz S, Remiorz L, Wejkowski R. Patent applications P.393836, EP12460004. Method and meter for the measurement of gas flux in short closed ducts of large cross section area, particularly in boiler air/ flue gas and ventilation circuits; 2011,2012) [in Polish]. [17] Standard ISO 50001:2011. Energy management systems—requirements with guidance for use; June 2011.