Journal of Science & Technology 101 (2014) 035-040
Combination of Second-Order Interpolation with Loop Transformation for Measuring Fluid Parameters in Multi-Chanel System
Pham Ngoc Thang Hung Yen University of Technology and Education
Khoai Chau. Hung Yen, Viet Nam Received: May 16, 2013; accepted April 22, 2014
Abstract
The fluid path systems have been widely used in many industries and civil society. In order to maintain the stability of system and avoid relative emergencies, we have to measure and monitor important parameters of fluid such as the temperature, pressure and flow This study presents one method for designing the multi-channel measuring system that includes modem digital data processing as miens processing, programmable logic controllers, and field-programmable gate array. By using the measured information processing algorithm by combination method of a second-order interpolation through three succeeding data points with the loop transformation, not only errors of system are significantly reduced but also data processing speed is improved The results calculated by using the MATLAS program have shown the ability to reduce errors of measurement devices
Keywords: Multi-channel system, Field-programmable gate array. Loop transfonnation.
1. Introduction
The important fluid parameters are temperature, pressure, specific volume, and mass flow. In order to improve accuracy of measurement for these parameters, we should make non-linear adjustments of transformation function of the primary transformation devices (PTD) and decrease enors of the secondary transformation devices (STD) [1]. In the flow measurement, moreover, we should determine characteristic parameters of fluid as the flow coefficient, specific capacity, and so on.
Because of behavior of mfluence quantines and variety of measurement environment, values of these parameters can no p e o s y spe fy and 1 ose I a e to be approx a e y a c a ed by o p ca ed method. Recen y he d ec n easu emen s o temperature and p essu e he non nea d us men method of the ansfo na on tun onfo h PTD by a second-order nterpo a on hrou h h ee succeed ng data pomts m sma nter\as and eno educ on fo the STD were d scussed and analysed [ ] The solutions for reducing enors in the indirect measurement, however, have not been inplemented so far
m the present study, we presented combination of a second-order interpolation through three succeedmg data pomts with the loop
transformation for a multi-channel system, which have been designed and analysed with the purposes of simplification the hardware structure to improve accuracy and save cost, the muln-channel measuring devices [3-5]- This system can measure parameters such as the temperature, pressure, specific capacity, and fiow of fluid- The solutions for the non-luiear adjustment method of the fransformation function for the PTD, enor reduction or enor exclusion of the STD, and determination of the fiow of fluid have been implemented with the inexpressive conditions of specific capacity, specific volume, and flow coefficient-
2. Method of measuring flow through differential pressure by usmg interpolation and loop transformations
2.1 Measuring flow through measuring differential pressure
The fiow of fluid is measured by method of difference of pressure (differential pressure) To make differential pressure, standard tight tube, which has type of shield or suction cone (Venmri pipe and Dall pipe), is manufactured [6], Fig 1 presents structure diagram of standard tight tube that has type of suction cone and differenUal pressure chart of pipe's length I.
[6]:
Flow of gas in the pipeline is determined z
Corresponding author. Tel, (+84) 912,287.247 Emaib phamngocthangutehy@graaiI com
? - Q - & Fj2-AP/p
Journal of Science & Technology 101 (2014) 03S-040 where a is the fiow coefficient, e is the adjustment
coefficient, Fo (F2) is the output cross section of suction cone, AP is the differenfral pressure, and p the is specific volume of gas.
The flow coefficient a is a complex fianction It depends on parameters such as dynamic viscosity, diameter of input pipe, and ratio F2/F1 of suction cone. The adjustment coefficient e depends of ratios of A P / p , F2/F1 and adiabatic coefficient K that is a fiinction of temperature and pressure.
Equation (1) is wntten as
Q = K4AP (2)
K = ^ " (3)
Coefficient K can be regarded as fiow adjustment coefficient. The flow adjustment coefficient depends on parameters such as density, viscosity, gas speed, size of standard tight pipe and suction cone, smooth of pipe's wall, differential pressure, and temperature of gas in pipe
In fact, coefficients a and E are chosen from monograph chart or are approximately calculated by using loop method [6]. Selection process for parameters is complex and long lime Therefore, establishment of characteristic of flow adjustment coefficient for measuring flow is necessary.
2.2 Establishment for characteristic of flow adjustment coefficient by loop method
Step I- Set standard flow (Qj, Q2, ..,, Q,) in fiill-
Slep 2. Measure conelative differential pressure (APi,AP2, ...,AP,)-
^/^'
Fig, 1, Type of suction cone of Ught tube and differential pressure chart
Step 3: Calculate coefficients (K|, K2, .., K,) by following equation.
Step 4' Interpolate to determine relationship between Ki and APi,
2.3 Application of the Second-order Interpolation and Loop Transformation in Measuring Flow
To measure flow, we need to measure differential pressure AP|. We determined space and interpolation fijnction based on AP| and characteristic K = f(APi), To calculate flow adjustment coefficienl Ki for specific measurement environment and standard tight tube (STT), we solve interpolation equation. The flow of gas on standard tight tube is determined through equation (1) when we know value K],
From determinmg characteristic of the flow adjustment coefficient and measuring gas flow by using loop transformation and the second-order interpolation through three succeeding data points, we can establish library of characteristics of the flow adjustment coefficient for specific fluid environment and the STT, This method allows us to decrease selection steps and not to need calculatmg coefficients a and e in flow measurement 3. Multi-channel measuring system for measuring temperature, pressure and flow of fluid 3.1 Structure and principle of system
Fig. 2 shows structure diagram of multi- channel measuring system. The present system Is proposed to measure temperature, pressure, and flow in fluid environment (e,g,, steam pipes, alarm-service for parameters of line-out of industrial boilers, indusfrial tonefaction system, and civil heating).
Diagram of system consists of blocks as follows:
The PTD I for measuring pressure. The PTD 2 for measuring temperature; The PTDs 3 and 4 for measuring pressures P and P", respectively, with the aim of determination of flow through differenlial pressure method; standard converters (SCs I, 2, 3, and 4) with output signal conesponding to nexl converter of analog-to-digital converter (ADC);
digital signal processor (DSP); pattern generator flow (PGF); switch (SW); digital display (DD); and controller (C),
System is established through principle of demultiplex of pressure and temperature in combmation with loop measurement of secondaiy standard quantity and the second-order interpolation of tranfonnation function.
Journal of Science & Technology 101 (2014) 035-040
|Qx
STT
PGF
i'x 1 |Vx 1 1
^1 PTDI | - - ^ SC I 1 62 - ^ PTD 2 p > | SC2 1 ]
93 I
—*\ PTD 3 \~*\ SC3 | - ^
- J - ^ PTD4 | — ^ SC4 [-»
1 T,P, p, AP.Q
1 DD H DSP \*-\ ADC |-*-^
Fig. 2. Structure of multi-chaimel system for measuring temperature, pressure, and flow of fluid
Symbols in Fig. 2 are presented as follows; Px IS mput pressure; Vx is output quatity of the PTDI;
Tv IS mput temperture; Uy is output quantity of the PTD2; p is required measurement density; Qx is input flow; P and P' are input pressures for measuring flow by using the pressure difference method, V and V are output quantities of the PTD3 and PTD4, respectively, Qj -r Q, are standard flow; AP is pressure difference; 6i, 62, 63, and dt are normalization factors; T, P, p, AP, and Q are display results of temperature, pressure, density, pressure difference, and measured flow, respectively.
This system has two mam steps as follows.
Firstly, enors and quantities such as temperature, pressure and density of fluid are adjusted and calculated. Secondly, enor and flow quantity of fluid are adjusted and calculated by differential pressure method. Programs for adjustmg enor and calculating temperature, pressure, and flow by using the second- order interpolation method through three succeeding data points combined with loop fransformation are implemented in the block DSP in Fig. 2, The results displayed on the DD are values of required temperature, pressure, and flow quantities.
3.2 Program for determining of temperature, pressure, and density of fluid
Program of enor adjustment and determination of temperature, pressure, and density is implemented through algorithm chart shown in Fig. 4 of [2] Therein, X is pressure Px, Y is temperahire Ty, Z IS requirement density, p, of fluid environmenh Input data of program consist of data table of the
PTD for measunng pressure U, = ((J,) (n points), data table of the PTD for measuring temperanire Vj = f(P,) (m points), density data table p.j = f^T,, Pj), mput standard voltage values Y.^ and Yjs-
Program is implemeted through three main steps
Step I: Measure pressure by applying the second-order interpolation through three succeeding data points combined with loop fransformation for excluding enor of the ADC. If error of the ADC is second-order equation, the transformation function of the ADC will be second-order equation. If interpolation method uses three input standard voltage values and three conelative measured results of the ADC, the second-order interpolation function will be nansformation function of the ADC. Value, which we need to measure, is the solution of this interpolation equation In other words, the value of requirement quantity does not depend on enor of the ADC.
The procedures for measuring input standard voltage of the ADC and excluding enor the ADC by interpolation were implemented in our previous report [2].
Step 2. Measure temperature by second-order interpolation through three succeeding data points combined with loop fransformation to exclude enor the ADC similarly to step 1,
Steps 1 and 2 were implemented on one ADC only. Therefore, the enors ADC were excluded by using two loops of pressure and temperature in one program when establishing program.
Step 3- The process for measuring density is as follows:
- Determine interpolation space of density Pressure P is supposed to be close to pressure P,. Density data space (p,-i,j p,j, and p,.no), which consist of three columns (i-I, 1, and i+I) and m rows G = I ^ m), IS selected
- Determine characteristic of density- pressure We find m interpolation equations based on combination of 3 density data at each row of m rows of temperature in interpolation space with three correlative pressures P,-i, P„ and P,-.: To estahhsh interpolation characteristic curve consisting of m points pi, p2, ,, , pm, we solve m interpolafion equations by using method given at steps 1 and 2, Charactenstic of density-temperature interpolation, therefore, only depends on temperature at one pre- defined pressure P.
- Determine density
Journal of Science & Technology 101 (2014) 035-040 Algorithm of determination of density is the
same as algonthm for detemining temperature and pressure by second-order interpolation at steps 1 and 2.
3.3 Program for determining the flow of fluid Fig. 3 presents the algorithm scheme for determmmg coefficient K, difference pressure, and flow.
Adjustment process and calculation of flow value consist of main steps as follows; (a) input data, (b) calculate pressures P and P', (c) calculate values AP| by using loops, (d) calculate K| through equation (1), (e) determine differentia! pressure characteristic, charactenstic of coefficient Ki, and APi, (t) calculate Ki, (g) calculate measured flow Qi through equation (2).
3.4 Results of non-linear error adjustment program and calculated results in measurement system
By using MATLAB program, we established adjustment program for enor and calculated temperature, pressure, and flow of fluid for mulfi- channe! system. For the purpose of illustration the accuracy of the present method, the following data can be setup in the program,
- Data for calculating pressure, temperature and density data table for converting pressure-resistor (PTDI), data table for converting heat-voltage 11111 (PTD2), density table (29.88 - 192,6 kg/m^) with 12 columns of pressure (10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 29, 30) Mpa and 5 rows of temperahire (420, 440, 460, 480, 500) "C [6], and the normalization factors e, - 0.04 A and 62 = 200.
- Data for calculating flow by differential pressure method: standard flow equipment (Q^ = 0.5, 1.0, 1.5, 2.0, 2,5, and 3.0) mVs, data table for converting pressure-resistor with 12 data points (therein, pressures change from 10 Mpa to 30 Mpa and resistors change from 6 95 £i to 22.91 il).
Absolute error of the ADC is supposed to he non-lmear and is given by a fiill second-order equation, given as'
AN = 2 + 0.5*Y + 0,15*Y^
The standard input voltages of the ADC are 0, O.I,...,andl-0 V.
The following calculation results of program, which was modeled by MATLAB program, were convert relative error in measurements of pressure Px, temperature Ty. and density p, pressures P and P';
pressure difference AP|, flow adjustment coefficient Ki; flow Qi; and enor m measuring flow AQi
- V a l u e t a b l e o f U i , P i ; l - l - t - Standard quafrties: Qi - Qi - Measured results of ADC
Calculate pressure P |
Calculate pressure P'
r^n
Calculate differential | _ pressure AP|
Establish characteristics of differential pressure APi,AP2 AP,
Determine APi
Fig. 3. Algorithm scheme for measuring flow by using difference pressure method
- Measuremental enors of Px were very small at the mput data of 10, 12, .„, and 30 MPa and did not exceed ± 0 08013% at the middle points of the input data (i.e, 11, 13, „., and 29 5 MPa);
- Measuremental enors of Ty were very small at the input data of 420, 440, ..., and 500 "C and did not exceed ± 0.09846% at the middle points of the input data (i e., 430, 450,..., and 490)*'C;
- Measuremental enors of density al those points did not exceed ± 0.1105%. These results are given in Table 1.
- Measuremental enors of flow did not exceed + 0,0034 mVs conesponding to convert enors of + 0.136%. Theseresuhs are given in Table 2 and Fig. 4, - which IS characteristic of flow adjustment coefficient
Journal of Science & Technology 101 (2014) 035-040
Table I The relative error of measuremental results for Table 2. Measuremental results of pressure P and P', density of water vapour at several points between the pressure difference API. flow adjustment coefficient KI, input data (Sf^i) flow QI, and measuremental error of flow AQI
\ P x T \
430 450 470 490
\ Px T \ ^
430 450 470 490
II 0.0020 0.0091 0.0II3 0.0012
-
0.0376 0.0491 0.0014 0.0126
13 0.0304 0.0041 0.0136 0.0164 23 0.0113 0.0136 0.0012 0.0128
15 0.0403 0 0052 0.0015 0 0582 25 0.0882 0.0675 0.0847 0.0424
17 0.0083 00117 0,0214 0,0132 27 0.0342 0.0988 0.1015 0.0367
19 0.0150 0.0263 0,0372 0,0596 29,5 00143 0 1105 0,0339 0,0132 Nole: Px (l\4Pa) and TfC)
btt 1 Measuremental results
|QS 1 0.5 1 P 112.201
| p ' 116.128 p i 3 9272 JKI 0,2523
|QI 0.4999 1,0 14 093 17 465 3.3719 0.5445 0,9998 [iQi [o.OOOl 0.0002
1,5 15.832 18.793 2.9607 0.8712 1.4990 0 0010
2.0 17 789 20,466 2,6769 1.224 1,9999 0.0001
2.5 20.098 22,547 2,4485 1.5987 2.5016 0.0016
3.0 22.292 24,584 2 2919 1,9966 2.9814 0 0034
Fig. 4. Characteristic of flow adjustment coefficient From these results, it is very clear to have following remarks.
(1) With effect of pre-defmed flow, the present loop fransformation method is used for detennining characteristic of flow adjustment coefficient through differential pressure measurements. The second-order interpolation method through three succeeding data pomts is used for calculatmg pressure and flow adjustment coefficient.
(2) The present method excluded select steps and is used to calculate coefficient of flow ct and adjustment coefficient e in flow measurement
(3) Measurement process can be established from two independent steps as follows: (1) establish characteristic of flow adjustment coefficient (or library of this characteristic) and (u) measure flow with characteristic of established flow adjustment coefficient.
Note: Qtl: Quantity. Q,. Qi and AQifrnVs). P, P' and /iPi(MPa)
4, Conclusion
Combination of the second-order interpolation through three succeeding data points and loop fransformation is suitable method for determining the fransformation function which given by data table;
and for adjusting the second measurement enor of measurement device, Enor adjustment, which is implemented by combination of the second-order interpolation through three succeeding data points and loop transformation of standard input voltage in measurements for temperature, pressure, specific volume, and mass flow, allows ADC to exclude enor and have Imear range. For measuring flow by measunng differential pressure, loop transformation IS used for determining characteristic of fiow coefficient and it is adjusted through differential pressure and standard flow. The second-order interpolation method through three succeedmg data points IS used for calculating pressure and flow adjustment coefficient Concurrently, to exclude steps of selecfion, we calculate flow coefficient a and adjustment coefficient E. The present results were examined and proven by MATLAB program. The present method has been used to establish systems for measuring the parameters of fluid in diversity environment with high accuracy.
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Journal of Science & Technology 101 (2014) 035-040
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