error analysis of the measurement system of chcp

8/8/2019 Error Analysis of the Measurement System of CHCP

http://slidepdf.com/reader/full/error-analysis-of-the-measurement-system-of-chcp 1/34



3

(5.2) Haiger ................................................................................................... 28

[6] Energy/Heat balance of Blumenhaus Bade CHCP plant and error calculationfrom the data .................................................................................................... 30

(6.1) Procedure and Formula for heat/energy balance ................................... 30

(6.2) Heat flow through different circuits ...................................................... 31

[7] Conclusion .................................................................................................. 33

References ........................................................................................................ 34



4

List of Figures

Figure3.1 Accuracy limits according to class A ................................................ 10

Figure3.2 Accuracy limits according to class B ................................................ 11

Figure3.3 Accuracy limits according to class 1/3B ........................................... 11

Figure3.4 Logarithmic graph of ultrasonic device from manufacturer .............. 12

Figure3.5 Relative error graph of ultrasonic device derived from the logarithmic

graph ................................................................................................................ 13

Figure3.6 Logarithmic graph of magnetic inductive device from manufacturer 14

Figure3.7 Relative error graph of magnetic inductive device derived from the

logarithmic graph ............................................................................................. 14

Figure3.8 Error graph of mechanical device 1 from manufacturer .................... 15

Figure3.9 Relative error graph of mechanical device 1 derived from the

manufacturer graph .......................................................................................... 16

Figure3.10 Error graph of mechanical device from manufacturer ..................... 17

Figure3.11 Relative error graph of mechanical device 2 derived from the

manufacturer graph .......................................................................................... 17

Figure4.1 Plant layout of Blumenhaus Bade ..................................................... 19

Figure4.2 Plant layout of Haiger ...................................................................... 22



5

List of Tables

Table 2.1 Temperature accuracy classes………………………………………7

Table 4.1 List of measured quantities at Blumenhaus Bade………………….19

Table 4.2 List of measured quantities at Haiger………………………………23

Table 5.1 Calculated heat fluxes at Blumenhaus Bade………………………..25

Table 5.2 Calculated heat fluxes at Haiger…………………………………….26

Table 6.1 Comparison of heat flux relative error values of different circuits…. 28

Table 7.1 Recommended measuring instruments for different heat fluxes …….32



6

[1] Introduction :

(1.1) Types of errors -

(i) Systematic errors- Errors that tend to be in one direction, either positive ornegative. Some of the sources are:

Instrumental errors- Errors that arise from the imperfect design orcalibration of the measuring instrument (Zero error in the instrument).

Errors due to imperfection in experimental technique- Errors that arisefrom effects of external conditions or any unfavorable conditions duringexperiments.

Personal errors- Errors that arise due to an individual’s bias, lack of proper setting of the apparatus or individual’s carelessness in taking observationswithout observing proper precautions.

Systematic errors may be estimated to a certain extent and the necessary corrections may beapplied to the readings.

(ii) Random errors- Errors that occur irregularly and hence are random with respect tosign and size. These can arise due to random and unpredictable fluctuations inexperimental conditions.

(1.2) Absolute and relative errors -

(i) Absolute error- The magnitude of the difference between the true value of thequantity and the individual measurement value is called Absolute Error of themeasurement.In the absence of any other method of knowing the true value normally the truevalue is the arithmetic mean of the measured values.

|ΔA| = A mean – A; ΔA = A mean ± A …. (1.1)

Thus we can say that the actual value isAmean – ΔA mean ≤ A ≤ A mean + ΔA mean …. (1.2)

(ii) Relative error- The ratio of the mean absolute error (ΔA mean ) to the mean value of the quantity measured is called Relative Error.

|ΔA|relative = |ΔA |mean / A mean …. (1.3)



7

(1.3) Error propagation law - When several quantities are measured then errors in all themeasurements combine and so the error propagation law can be used. Actually there are rulesfor addition, subtraction, product and division. Suppose we are measuring two quantities Aand B.

(i) Error of a sum or a difference- Here A and B have a me asured value A±ΔA andB±ΔB respectively, where ΔA and ΔB are their absolute errors. So the total errorfor Z is Z=A+B. Thus for addition…

Z±ΔZ = (A±ΔA) + (B±ΔB) …. (1.4)

So the maximum value of error can be|ΔZ| = |ΔA| + |ΔB| …. (1.5)

The same rule applies for subtraction.

‘When two quantities are added or subtracted, the absolute error in the finalresult is the sum of the absolute errors in the individual quantities’ .

(ii) Error of a product or a division- Here if Z=AB.

Z±ΔZ = (A±ΔA)(B±ΔB) Z±ΔZ = AB ± BΔA ± AΔB ± ΔAΔB

By ignoring the quant ity ΔAΔB as this product is small compared to other terms andso

Z±ΔZ = AB ± BΔA ± AΔBThis form can be used for the absolute error calculations.The relative error is then …

(Z+ ΔZ)/Z = 1 ± (ΔZ/Z) = 1 ± (ΔA/A) ± (ΔB/B) ΔZ/Z = (ΔA/A) + (ΔB/B) …. (1.6)

‘When two quantitie s are multiplied or divided, the relative error in the result isthe sum of the relative error of individual quantities’.

(1.4) DIN norms for different accuracy classes of measured quantities of CHCP - Temperature – DIN EN 60751 Volumetric flow rate – DIN 1434 For heat flux( ) both of these accuracy classes can be used and heat flux depends on

the manufacturer of the heat flux measuring device. /1/



8

[2] List of accuracy classes and its ranges for measured quantities of

CHCP -

(2.1) Temperature - According to DIN EN 60751, measuring instruments for temperatureare mainly having three classes

Table 2.1 Temperature accuracy classes

Classes Ranges Accuracy limitsClass A ( -30°C to 300°C) ±(0.15K + 0.002*T)Class B ( -50°C to 500°C) ±(0.30K + 0.005*T)Class 1/3B ( 0°C to 150°C) ±1/3(0.30K + 0.005*T)

Temperature accuracy limit for Class A (T A) = ± (0.15K + 0.002*T)

T = Temperature in °C

Here mainly temperature sensor pairs or a single temperature sensor are used. With the helpof a temperature sensor pair the temperature difference of any circuit can be obtained and thusit gives us the heat flux of that circuit. In the case of temperature sensor pairs both sensorsalways belong to the same accuracy class i.e. both sensors will be A and A, B and B or 1/3Band 1/3B, and thus the accuracy limit can be calculated from the single accuracy class. Fromthe data sheets of the manufacturer (Thermo Sensor) accuracy limits are ±0.05% between 0°C

to 100°C. Though the accuracy limits are shown in the graphs below in the section [3]. /2/

(2.2) Volumetric flow rate - According to DIN EN ISO 5167 the measurement of volumetric flow rate has three accuracy classes

(1) 1 = ± (1 + 0.01 p / ), not more than ±3.5%(2) 1 = ± (2 + 0.02 p / ), not more than ±5%(3) 1 = ± (3 + 0.05 p / ), not more than ±5%

Here p(m3 /h) = Nominal value of the flow sensor given by manufacturer, This value

is a permanent value of the volumetric flow rate measured withthe device according to DN showing the diameter of the inlet duct of the device.

(m 3 /h) = Actual volumetric flow rate

Having an approximation about the value to be measured, DN type and accordingly thenominal value of volumetric flow rate can be selected. The volumetric flow ranges are mainlydependent on the particular application and the manufacturer of the device. Here mainly threetypes of measuring instruments for volumetric flow rate measurement are used, which are US(Ultrasonic device), MID (Magnetic inductive device) and Mechanical device. Accuracy

limits are shown in the graphs below and it can be seen that MID devices are the mostaccurate devices for volumetric flow measurement. /3/



9

(2.3) Heat flux - Accuracy classes and ranges for heat flux mainly depend on themanufacturer and the application of the instrument.

Here also mainly three types of instruments are used, which are dependent on the temperature

difference, volumetric flow rate and the medium and the absolute temperature of the medium.

In both the plants Ultrasonic devices are used for direct heat flux measurements in compactconditions while magnetic devices are used for indirect heat flux measurement. Moreover theerror of heat flux measurements can be calculated with the help of the error propagation lawwith two quantities which are temperature and volumetric flow rate.



10

[3] Graphical representation of different accuracy classes with tolerance

ranges -

(3.1) Temperature classes – Here graphs for the temperature range between 0°C to 150°Care shown. DIN EN 60751 for different accuracy classes. The 12 values of temperature hasbeen taken and the graph has been made for values between (-30°C to 300°C). These graphsfor different classes (Class A, Class B and Class 1/3B) are shown below./2/

(i) Class A – (-30°C to 300°C)

Figure3.1 Accuracy limits according to class A

In class A we can see that the maximum absolute error reaches at 0.75K at 300°C. Theabsolute error for this temperature range lies between 0.09K to 0.75K. From this absoluteerror values the relative errors can be calculated with the help of formula given below

Trelative = |ΔT |mean / T mean …. (3.1)

For Class B and Class 1/3B the accuracy limits can be seen from the graphs shown below.The relative error value is given by the formula above.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-50 0 50 100 150 200 250 300 350

Positive accuracy limit Negative accuracy limit

c c u r a c y

l i i t s i n

( K )

Temperature °C



11

(ii) Class B – (-50°C to 500°C)

Figure3.2 Accuracy limits according to class B

(iii) Class 1/3B – (0°C to 150°C)

Figure3.3 Accuracy limits according to class 1/3B

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 20 40 60 80 100 120 140 160


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 20 40 60 80 100 120 140 160


c c u r a c y

l i i t s i n

( K )

Temperature °C

c c u r a c y

l i i t s i n

( K )

Temperature °C



12

Thus from these graphs it can be seen that class 1/3B has the highest accuracyamong all the accuracy classes of temperature sensors.

(3.2) Volumetric flow classes – The graphs for volumetric flow rate depend on the

manufacturer. As shown in DIN 1434 the classes of volumetric flow rate sensors contain p and in the formula. p is the nominal value of volumetric flow rate and as said earlier it canbe chosen according to the application.

(i) Ultrasonic flow rate device:-

According to DIN EN ISO 5167 Class 2 for ultrasonic volumetric flow rate measurementdevice (US) [By aqua metro ]. The device can be chosen in the range between 1.5m 3 /h to25m 3 /h.

Model number/Name: AMFLO SONIC UFA-114

For the device used here has the nominal value of volumetric flow rate i.e. p is 2.5 m 3 /h, asthe device is of DN 20 type. /4/

Figure3.4 Logarithmic graph of ultrasonic device from manufacturer

The method of getting absolute value volumetric flow rate curve is shown here.

Here Q p = 2.5m3

/h Multiplying Q p with the first point of a logarithmic volumetric flow rateabsolute volumetric flow rate can be obtained as shown here

Error

(m 3/h)



13

p(absolute) = p * 0.01 = 2.5m 3 /h * 0.01 = 0.025 m 3 /h

Figure 3.4 shows the logarithmic graph given by the manufacturer. Here the nominal value of the volumetric flow rate is 2.5m 3 /h, and so by multiplying this value with x-axis the absolute

value of volumetric flow rate can be obtained as shown above by keeping the y-axis valuessame as the manufacturer graph. From this relative error graph is made as shown below infigure 3.5. Now onwards all the logarithmic graphs have been converted into absolute valueby the same method as shown above.

Figure3.5 Relative error graph of ultrasonic device derived from the logarithmic graph

(ii) Magnetic inductive device:-

According to DIN EN ISO 5167 for magnetic inductive volumetric flow rate measuringdevice (MID) [By aqua metro ], the range of this device is between 1.5 m 3 /h to 60m 3 /h.

Model number/Name: AMFLO MAG Smart The nominal value of volumetric flow rate is p is 3.7m 3 /h, as the DN type usedhere is DN25 type. /4/ The values used in the graph are

i = Qmin = 0.14 m 3 /h p = 3.7 m 3 /h s = 7 m 3 /h

As described above the graph shown below is also a logarithmic graph given by themanufacturer. As the nominal value of volumetric flow rate is 3.7m 3 /h, and the methoddiscussed above can be used for the absolute volumetric flow rate graph.

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 3 3.5 4


(m 3/h)

Error

%



14

Figure3.6 Logarithmic graph of magnetic inductive device from manufacturer

Figure3.7 Relative error graph of magnetic inductive device derived from thelogarithmic graph

Thus the accuracy of the volumetric flow measurement device depends on the manufacturer

of the apparatus, here it is aquametro .

-8

-6

-4

-2

0

2

4

6

8

0 0.5 1 1.5 2 2.5 3 3.5 4


Error

%

(m 3/h)

Error

% (m 3/h)



15

(iii) Mechanical device 1:-

The graph of the accuracy class for mechanical device from aquametro, with water

temperature 20°C is shown below. From here graphs shown below are for DN 25 and as wellfrom the manufacturer data sheet.

Model number/Name: AQUA Concept cold water /4/

The nominal value of volumetric flow rate p is 6.3m 3 /hr, as per DN25 type. The graphshown below is having values as follows

1 = Minimum flow rate = 0.039 m 3 /h

2 = Transition flow rate = 0.063 m3

/h 3 = Permanent flow rate = 6.3 m 3 /h 4 = Overload flow rate = 7.9 m 3 /h

This graph can be read by the values given and from that it is clear that accuracy limit rangesbetween ± 2%. From Typische Fehlerkurve it is clear that volumetric flow rate measuredbelow 2 is having the highest accuracy limits fluctuation.

Figure3.8 Error graph of mechanical device 1 from manufacturer

Error

%

(m 3/h)



16

Figure3.9 Relative error graph of mechanical device 1 derived from the manufacturergraph

(iv) Mechanical device 2:-

The graph of accuracy class for mechanical device 2 from aquametro is shown below. Heregraphs are obtained as DN 25 and as well from the manufacturer data sheet.

Model number/Name: Series 417/M-TFXKA

The nominal value of volumetric flow rate p is 3.5m 3 /h, as per DN25 type. /4/

The values given in the graphs are as follows

min = 0.065 m 3 /h = Minimum flow rate tr = 0.35 m 3 /h n = 3.5 m 3 /h

This graph can be read by the values given and from that it is clear that accuracy limit rangesbetween ± 1%.

Thus from all these graphs and discussion we can conclude that MID devices arehaving the highest accuracy amongst all.

-6

-4

-2

0

2

4

6

0 1 2 3 4 5 6 7 8


Error

%

(m3

/h)



17

Figure3.10 Error graph of mechanical device from manufacturer

Figure3.11 Relative error graph of mechanical device 2 derived from the manufacturergraph

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

Accuracy limit

Error

%

(m 3/h)



18

[4] List of monitored measuring data –

(4.1) Blumenhaus Bade -

Table 4.1 List of measured quantities at Blumenhaus Bade /6/

Quantity Name Sign InstrumentType

Accuracy class

Ambient Temperature T 1 Pt 100 1/3 DIN(B)

Room Temperature T 2 Pt100 1/3 DIN(B)

CHP Exhaust Temperature 1(T abgas 1 ) T 3 Thermocouple Class B

CHP Exhaust Temperature 2(T abgas 2 ) T 4 Thermocouple Class B

CHP Forward flow Temperature(T vorlauf )

CHP Reverse flow Temperature(T rücklauf )

T5

T6

Pt100(Sensor pair)

Class A

Boiler Temperature(peak load) T 7 Thermocouple Class B

Buffer tank upper Temperature(T oben ) T 8 Pt100 1/3 DIN(B)

Buffer tank middle Temperature(T mittel ) T 9 Pt100 1/3 DIN(B)

Buffer tank lower Temperature(T unten ) T 10 Pt100 1/3 DIN(B)

Hot water Temperature(T ww) T 11 Pt100 1/3 DIN(B)

Cold water Temperature(T kw) T 12 Pt100 1/3 DIN(B)

Forward flow Temperature to HK-1,HK-2and HK-3 (T vorHK1-3 )

T13 Pt100 1/3 DIN(B)

Reverse flow Temperature from HK-1and HK-2(T rückHK1+2 )

T14 Pt100 1/3 DIN(B)

Reverse flow Temperature fromHK-3(T rückHK-3 )

T15 Pt100 1/3 DIN(B)

Secondary heat Circuit inlettemperature(T HT-IN-SEK )

T16 Pt100 1/3 DIN(B)



19

Figure4.1 Plant layout of Blumenhaus Bade /6/



20

Secondary heat Circuit outlettemperature(T HT-OUT-SEK )

T17 Pt100 1/3 DIN(B)

THT-IN

(Heat input to chiller)

THT-OUT (Heat output from chiller)

T18

T19

Pt100(Sensor pair)

Class A

TMT-OUT (Output temperature of MTcircuit)

TMT-IN (Input temperature of MT circuit)

T20

T21

Pt100(Sensor pair)

Class A

TNT-OUT (Output temperature of NTcircuit)

TNT-IN (Input temperature of NT circuit)

T22

T23

Pt100(Sensor pair)

Class A

TNT-SOLL (Control signal of cold control) T 24 Direct measurement Direct voltage signal

TGAS T25 Thermocouple ?

VGAS (Total gas consumption) 1 Mechanical ?

VCHP (2.5 m 3 /h) 2 Ultrasonic ±2%

VWW (1.5 m 3 /h) 3 Mechanical max. ± 2%

VHK1+2 (2 m 3 /h) 4 Mechanical max. ± 2%

VHK3 (2 m 3 /h) 5 Mechanical max. ± 2%

VHT (1.6 m 3 /h) 6 Mechanical ±1%

VMT (3.7 m 3 /h) 7 MID ±2%



21

(4.2) Haiger -

Table 4.2 List of measured quantities at Haiger /6/

Garage Temperature (T _Garage ) T 1 Pt100 1/3 DIN(B)

Room 1 Temperature (T _Raum_1 ) T 2 Pt100 1/3 DIN(B)




CHP 1 Exhaust Temperature (T _Abgas_1 ) T 6 Thermocouple Class B



CHP in Temperature (T _BHKW_IN ) T 9 Pt100 (Sensor Pair) Class A

CHP out Temperature (T _BHKW_OUT ) T 10 Pt100 (Sensor Pair) Class A

Heat buffer upper Temperature (T _SP_oben ) T 11 Pt100 1/3 DIN(B)

Heat buffer middle Temperature(T _SP_mitte )

T12 Pt100 1/3 DIN(B)

Heat buffer lower Temperature(T _SP_unten )

T13 Pt100 1/3 DIN(B)

Cold buffer upper Temperature(T _SPK_oben )

T14 Pt100 Class A

Cold buffer middle Temperature(T _SPK_mitte )

T15 Pt100 Class A



22

Figure4.2 Plant layout of Haiger/6/



23

Warm water heating from chiller wasteinput Temperature (T _WW_VW_IN )

Warm water heating from chiller waste

output Temperature (T _WW_VW_OUT )

T17

T18

Pt100 (Sensor Pair) Class B

Heat input to chiller (T _HT_IN )

Heat output from chiller (T _HT_OUT )

T19

T20

Pt100 (Sensor Pair) Class A

Input temperature of MT circuit (T _MT_IN )

Output temperature of MT circuit(T _MT_OUT )

T21

T22


Input temperature of NT circuit (T _NT_IN )

Output temperature of NT circuit(T _NT_OUT )

T23

T24


Input temperature of secondary NT circuit(T _NT_IN_sek )

Outputput temperature of Secondary NTcircuit (T _NT_OUT_sek )

T25

T26

Pt100 (Sensor Pair) Class B

Control signal of cold control (T _NT_Soll ) T 27 Direct measurement _

T_Gas T28 Thermocouple _

Boiler Temperature (T _Kessel ) T 29 Thermocouple _

VGAS 1 Pulse

VCHP (6 m 3 /h) 2 Ultrasonic ±2%

VHT (6 m 3 /h) 3 Ultrasonic ±2%

VMT (6 m 3 /h) 4 Ultrasonic ±2%

VNT (6 m 3 /h) 5 Ultrasonic ±2%



24

VSPK(6 m 3 /h) 6 Ultrasonic ±2%

Heat flow from buffer SP-2 to SP-1

(QWW )

Q1 Ultrasonic heat flow ±3%

Heat flow from SP-1 to HK-1 (Q HK) Q 2 Ultrasonic heat flow ±3%

Heat flow from HK-1 to buffer SP-1(Q _SP2 )

Q3 Ultrasonic heat flow ±3%

Heat flow boiler to buffer (Q Kessel ) Q 4 Ultrasonic heat flow ±3%



25

[5] Statement of different accuracy limits for heat flux of CHCP plants –

In both the plants i.e. Blumenhaus Bade and Haiger the accuracy limits of heat fluxes are tobe measured. Though the plants have heat flux measuring devices, the intention of the reportis to calculate the heat flux accuracy limits from the volumetric flow rate and the temperatureaccuracy limits. These values can be calculated with the help of error propagation law.

The values to be analyzed are shown below in the tables and can be obtained by the accuracylimits of temperature sensor pairs and the volumetric flow measurement devices.

The tables given below present the accuracy limits for heat fluxes to be measured and thedescription is given below.

(5.1) Blumehaus Bade :-

Here the accuracy limits of different heat fluxes values are to be measured in BlumenhausBade CHCP plant. These are Q NT, QMT, QHT , QBHKW, QWW , QHK1+2, QHK3 .

The heat flux accuracy limit can be calculated from the error propagation law. Errorpropagation law for multiplication and division says that

‘When two or more quantities are multiplied or divided, the relative error in the resultis the sum of the relative error of individual quantities’.

According to heat flux equation as shown below heat flux depends on four parameters andthat are temperature difference, flow rate, density and specific heat capacity.

Q = V*ρ*C p* ΔT …. (5.1)

Density is a function of temperature and pressure. Neglecting the density error due to pressurechanges and considering density error due to temperature dependency calculation is shownbelow.

As well Specific heat capacity is also a function of temperature and then in calculationdependency of specific heat capacity on temperature is shown. Thus the error in temperatureis considered as the error in density and specific heat capacity.

According to error propagation law the accuracy limit for the heat flux can be calculated withthe relative error values of individual quantities i.e.

ΔQ/Q= ΔΔT/ ΔT+ ΔV/V + Δρ / ρ + Δ Cp / C p …. (5.2)

Thus the relative heat flux errors calculated through this law is presented in the table below.The temperature accuracy limits are given in K.

As the maximum absolute error of temperature sensor pair is ±0.05K between 0°C to 150°Cas given by the manufacturer(Thermo Sensor AG) and so that value is considered for heat flux



26

calculation and i.e. for Q NT, QMT, QHT, QBHKW for Blumenhaus Bade plant and Q NT, QMT, QHT,

QBHKW, QWWV for Haiger plant.

The relative accuracy limit of temperature and volumetric flow rate can be seen in the graphs

as well the absolute values can be converted into relative value by the equation shown below. /1/

|ΔA|relative = |ΔA|mean / A mean

Example of calculation of relative error of heat flux is shown below.

ΔQ BHKW / Q BHKW = ΔΔTBHKW / ΔTBHKW + ΔVBHKW /V BHKW + Δρ BHKW / ρBHKW + ΔC pBHKW /

CpBHKW …. (5.3)

The temperature difference mean value of BHKW circuit is 12 K. Relative error of temperature is

ΔΔTBHKW / ΔTBHKW = (0.05K/12K)*100 = ±0.4%

Density is a function of temperature and pressure. The pressure dependency is very less andneglecting the density changes due to pressure only temperature is taken into account. Fromthe table given in www.simetric.co.uk/si_water , density relative error is calculated as shownbelow.

If temperature changes by 0.1°C, the density changes in small amount. From the data given inthe web-site shown above 10 density readings are taken into account and by deriving themean value relative error is calculated and the maximum value of relative error of density is±0.01% at 80°C. This temperature is maximum possible temperature in the circuits of CHCPplants. /8/

Specific heat capacity is a function of temperature also. The relative error in specific heatcapacity can be calculated by two methods as shown below.

(I) From the data given in Heat and mass transfer book by Domkundwar.(II) From the differentiation of the equation shown below.

Cp = C p0 + αT + αT 2

Here α is a constant value.

Cp0 = Specific heat capacity at 0°C temperature

T = Temperature

By taking the simple way of finding relative error from method (I) and with same procedureas shown for the density, the specific heat capacity relative error value is ±0.04%. The method

is to notice the specific heat capacity change with 0.1°C temperature change. /7/

http://www.simetric.co.uk/si_water






27

The volumetric flow rate device used here is Ultrasonic device and relative error value for thatis ±2%.

Applying all these values to equation (5.3)

ΔQ BHKW / Q BHKW = (±0.4%) + (±0.01%) + (±0.04%) + (±2%) =.±2.45%

The method shown here is used for the relative error calculation of all the heat fluxes indifferent circuits. /6/

Table 5.1 Calculated heat fluxes at Blumenhaus Bade

Heatflux

Temperature Sensor

Pair

Temperaturedifferenc

e(K)

Temperature

relativeaccuracy limit

Densityrelative

accuracylimit

Specificheat

capacityrelative

accuracylimit

Volumetricflow rate

device

Flowrate

relativeaccuracy limit

Heat fluxrelative

accuracylimit

QNT T23 - T 22 5 ±1% ±0.01 ±0.04% V 8

(MID)

±2% ±3.05%

QMT T21 - T 20 10 ±0.2% ±0.01 ±0.04% V 7

(MID)±2% ±2.25%

QHT T18 – T19 7 ±0.7% ±0.01 ±0.04% V 6

(Mechanical)±1% ±1.75%

QBHK

W T05 – T06 12 ±0.4% ±0.01 ±0.04% V 2

(US)±2% ±2.45%

QWW T11 – T12 20 ±0.2% ±0.01 ±0.04% V 3

(Mechanical)

±2% ±2.25%

QHK1

+2 T13 – T14 10 ±0.5% ±0.01 ±0.04% V 4


QHK3 T13 – T15 20 ±0.2% ±0.01 ±0.04% V 5




28

(5.2) Haiger :-

Here the accuracy limits of different heat fluxes values are to be measured in Haiger CHCPplant. These are Q NT, QMT, QHT , QBHKW, QWW , QHK, QWWV .

The heat flux accuracy limit can be calculated from the error propagation law. Errorpropagation law for multiplication and division says that

‘When two or more quantities are multiplied or divided, the relative error in the resultis the sum of the relative error of individual quantities’.

According to heat flux equation as shown below heat flux depends on four parameters andthat are temperature, flow rate, density and specific heat capacity.

Q = V*ρ* cp* ΔT …. (5.1)

Density is a function of temperature and pressure. Neglecting the density error due to pressurechanges and considering density error due to temperature dependency calculation is shownbelow.

As well Specific heat capacity is also a function of temperature and then in calculationdependency of specific heat capacity on temperature is shown. Thus the error in temperatureis considered as the error in density and specific heat capacity.

According to error propagation law the accuracy limit for the heat flux can be calculated with

the relative error values of individual quantities i.e.

ΔQ/Q= ΔΔT/ ΔT+ ΔV/V + Δρ / ρ + Δ cp / c p …. (5.2)

Thus the relative heat flux errors calculated through this law is presented in the table below.The temperature accuracy limits are given in K.

As the maximum absolute error of temperature sensor pair is ±0.05° C between 0°C to 150°cas given by the manufacturer(Thermo Sensor AG) /5/ and so that value is considered for heatflux calculation and i.e. for Q NT, QMT, QHT, QBHKW for Blumenhaus Bade plant and Q NT, QMT,

QHT, QBHKW, QWWV for Haiger plant.

The relative accuracy limit of temperature and volumetric flow rate can be seen in the graphsas well the absolute values can be converted into relative value by the equation shown below.

/1/

|ΔA|relative = |ΔA|mean / A mean



29

Table 5.2 Calculated heat fluxes at Haiger

Heatflux

Temperature

SensorPair

Temperatu

redifference(K)

Temperature

relativeaccuracylimit

Densityrelative

accuracy limit

Specific heat

capacityrelativeaccuracy limit

Volumetricflow rate

device

Flowrate

relativeaccur

acylimit

Heat fluxrelative

accuracylimit

QNT T23 - T 24 5 ±1% ±0.01% ±0.04% V 5 (US)

±2% ±3.05%

QMT T21 - T 22 5 ±1% ±0.01% ±0.04% V 4

(US)±2% ±3.05%

QHT T19 – T20 7 ±0.7% ±0.01% ±0.04% V 3

(US)

±2% ±2.75%

QBHKW T09 – T10 12 ±0.4% ±0.01% ±0.04% V 2

(US)±2% ±2.45%

QWW T20 – T21 20 ±0.2% ±0.01% ±0.04% V 6

(US)±2% ±2.25%

QHK T22 – T23 10 ±0.5% ±0.01% ±0.04% V 3

(US)±2% ±2.55%

QWWV T17 – T18 20 ±0.2% ±0.01% ±0.04% V 1




30

[6] Energy/Heat balance of Blumenhaus Bade CHCP plant and errorcalculation from the data

Theoretically and i.e. with the help of the error propagation laws the values of relative errorsfor different heat fluxes are shown and discussed. Now from the actual data of BlumenhausBade plant the relative error calculation is shown below.

(6.1) Procedure and Formula for heat/energy balance :-

The data measured have temperature and volumetric flow rate values for different circuits andso one can calculate heat flux (Q) with the formula

= *cp* ΔT …… (6.1)

Here with the values of the volumetric flow rate the mass flow rate can be calculated easily if the density of heat transfer fluid is known from the formula

= *ρ …… (6.2)

And so

= *ρ*c p* ΔT ……. (6.3)

= Heat flux (W)

= Volumetric flow rate (m 3 /h)

ρ = Density (kg/ m 3)

cp = Specific heat capacity (kJ/kg*K)

ΔT = Temperature difference (K)

= Mass flow rate (kg/hr)

In these plants two circuits i.e. HT circuit and MT circuit have water and glycol mixtures asheat transfer fluid. The percentage of water in the mixture is 80% while 20% is glycol. Theremaining circuits use water as heat transfer fluid. Specific heat capacity and density of themixture can be calculated from the formula given below.

cp mix = (x 1* c p 1) + (x 2* c p 2)

ρ mix = (x 1* ρ 1) + (x 2* ρ 2)

x1 and x 2 are the percentages of the component in the mixture. From these formulas c p and ρ of the mixture can be calculated if these two values for an individual component are known.

From this formula density and specific heat capacity value for the mixture of water (80%) andglycol (20%) are shown below.



31

cp mix = 3.35 kJ/kg*K

ρ mix = 1022.64 kg/ m 3

The circuits HK1+2 and HK3 are not in use during summer because of no need of heating.Thus the heat flux values in these circuits are zero. /6/

(6.2) Heat flow through different circuits :-

Here heat flux values for all circuits have been calculated with the help of equation (6.3). Forparticular time heat flux value relative accuracy is calculated as shown below.

By determining the temperature difference and volumetric flow rate value at the particularpoint relative error can be found as shown in section /5/. Eight points have been taken intoconsideration to find out the maximum and minimum relative error values from the one daydata of Blumenhaus Bade plant. From these eight points two points are at maximum andminimum heat flux values. It has been seen that at the minimum heat flux values accuracy of measurement is not good.

Here time interval during which the device is on stand still is neglected and the values atsteady state are considered. The example of relative error calculation from measured data isshown below.

ΔQ BHKW / Q BHKW = ΔΔTBHKW / ΔTBHKW + ΔVBHKW /V BHKW + Δρ BHKW / ρBHKW + ΔC pBHKW /

CpBHKW …. (6.4 )

The temperature difference at peak point of heat flux curve is 11.52 K from the data of measurement. Relative error of temperature is

ΔΔTBHKW / ΔTBHKW = (0.05K/11.52K)*100 = ±0.43%

As well density and specific heat capacity are the functions of temperature and so these bothquantities have the relative error as described above.

The volumetric flow rate device used here is Ultrasonic device and measured value of

volumetric flow rate is 0.632m 3 /h. From the graph of the US device the relative error value is±2.5 %.

Applying all these values to equation (5.3)

ΔQ BHKW / Q BHKW = (±0.43%) + (±0.01%) + (±0.04%) + (±2.5%) =.±2.98%

The method shown here is used for the relative error calculation of all the heat fluxes indifferent circuits. /6/



32

Table 6.1 Comparison of heat flux relative error values of different circuits

Heat flux ( )(kW)

Average heatflux value )

(kW)

Maximum heatflux relative

error%

Minimum heatflux relative

error%

Relative erroras per

theoretical lawin %QBHKW 9.6978 ±2.98 ±2.35 ±2.45

QMT 10.26 ±15.76 ±3.1 ±2.25

QHT 7.38 ±8.22 ±1.95 ±1.75

QNT 3.89 ±9.08 ±4.07 ±3.05

QWW 5.4929 ±6.85 ±3.05 ±2.25

The heat flux values for the WW circuit varies too much because it is only used when hotwater is required for domestic application e.g. for taking bath. /7/

As well volumetric flow rate measuring device of NT circuit is not working at the momentand so heat flux in NT circuit is calculated by doing heat balance of adsorption chiller and

obtained by the formula

QNT = Q MT - Q HT …….. (6.4)



33

[7] ConclusionHere conclusion can be made that results obtained of relative error by doing energy balanceare quite reliable and one can make prediction of an error value from this work. Even thoughthere is a variation in the relative error value obtained by energy balance of the plant andreasons for that are shown below.

The reasons of variation in relative error value are listed below.

Here density is a function of temperature and pressure while specific heat capacity is afunction of temperature. But effect due to pressure change is neglected here.

As well in calculation of heat flux value for NT circuit, heat loss is ignored while heatbalancing around the adsorption chiller.

As well due to periodic operation of an adsorption chiller the mean value and error

from data is high. Uncertainty of WW circuit as discussed earlier. As well imperfection in experimental technique/procedure and personal errors.

As well table shown below is the recommendation for temperature sensor pair and volumetricflow rate device for different heating circuits.

Table 7.1 Recommended measuring instruments for different heat fluxes

Heat flux ( )(kW)

Average heat fluxvalue )

(kW)

Temperature sensorpair class

Flow measuringdevice

QBHKW 9.6978 Class 1/3B Ultrasonic

QMT 10.26 Class 1/3B Mechanical

QHT 7.38 Class 1/3B Ultrasonic

QNT 3.89 Class 1/3B MID

QWW 5.4929 Class A Mechanical

The recommendations are mainly based on the measured values and by keeping in mind that,the values to be measured are high then high accuracy class devices are to be used and thevalues to be measured are low then low accuracy class devices should be used.

Thus the error calculation of the whole CHCP plant can be done easily with the help of thework shown here.



References

/1/ Benenson, W. Harris, J.W.Stöcker, H. Lutz

Hand book of Physics, (e-book), 2001

http://www.amazon.com/Handbook-Physics-Walter-Benenson/dp/0387952691

/2/ DIN EN 60751, Industrielle Platin -Widerstandsthermometer

Genauigkeitsklassen der Temperatur, 1996

/3/ DIN EN ISO 5167,

Measurement of fluid flow by means of pressure differential devices inserted in circular cross-

section conduits running full -- Part 1: General principles and requirements, 2003

/4/ Aquametro data sheets for volumetric flow rate

Aquametro AG, Ringstrasse 75, CH-4106 Therwil, Switzerland

/5/ THERMO SENSOR data sheets for temperature sensor pairs

Thermo Sensor GmbH, Slemens strasse. 36. 59199, Bönen, Germany

/6/ Solar Institute Jülich data sheet for plants of CHCP plants

Heinrich-Mußmann-Str. 5, 52428 Jülich, Germany

/7/ Arora, Domkundwar

A course in Heat and mass transfer, sixth edition

Dhanpat Rai and company, 4779/23, Ansari Road Darya Ganj, New Delhi –

110002, 2004

/8/ www.simetric.co.uk/si_water



http://de.wikipedia.org/wiki/Widerstandsthermometer





http://de.wikipedia.org/wiki/Widerstandsthermometer


error analysis of the measurement system of chcp

Documents