Research Article Preliminary Development of Thermal Power ...

Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor

Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo

School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China

Correspondence should be addressed to Fan Zhang hdhxyzf126com

Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014

Academic Editor Jiejin Cai

Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR

1 Introduction

SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area

For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]

According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published

IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967

We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays

H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092

2 Science and Technology of Nuclear Installations

READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop

Figure 1 H-Power modules diagram

enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le

100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions

2 Theoretical Modeling

The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine

H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis

21 Thermodynamic Properties Subroutine

211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine

We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume

which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated

Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured

The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2

212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid

22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]

As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875

1is obtained by (1) taking pressure loss Δ120596

caused by the existence of orifice plate into account

1198751= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 12057319) (2)

H-Power adopted the following equation for flow ratemeasurement

119902119898=

119862

radic1 minus 1205734120576 sdot

1205871198892

4radic2Δ119875120588

119906 (3)

where 119902119898

is mass flow rate 120573 is ratio of 119889 (diameter oforifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588

119906

is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows

119862 = 05961 + 002611205732minus 0216120573

8+ 0000521(

106120573

Re119863

)

07

+ (00188 + 00063119860) 12057335(106

Re119863

)

03

+ (0043 + 0080119890minus101198711 minus 0123119890

minus71198711) (1 minus 011119860)

1205734

1 minus 1205734

minus 0031 (1198721015840

2minus 08119872

1015840

2

11

) 12057313

+ sdot sdot sdot

(4)

Science and Technology of Nuclear Installations 3

Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1)

ℎ(kJkgminus1)

119904(kJkgminus1Kminus1)

119906(kJkgminus1)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 2273150 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4

R 3 iterativecomputations

Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97

If119863 lt 7112mm (4) should add the following term

0011 (075 minus 120573) (28 minus119863

254) (5)

As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re

119863 which is

dependent on 119902119898in turn so the calculation of mass flow rate

119902119898has to be iteratedDiameters in the formula for calculating should be cor-

rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter

is 119889119896) on the plate the 119889 should be corrected by the following

equation

119889 = 1198891198981 + 055(

119889119896

119889119898

)

2

(6)

where the 119889119898have already been corrected by temperature as

follows

119889119898= 1198890+ 1198890120582 (119905 minus 119905

0) (7)

where 1198890is the measurement value under the standard

temperature 1199050 120582 is the coefficient of linear expansion and

119905 is the operating temperature


Pressure measuring point

Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa

Figure 3 Pressure measuring schematic by orifice plate

Re119863is the Reynolds number calculated by119863 (diameter of

internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation

Re119863=

4119902119898

120583120587119863 (8)

where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine

1198711(= 1198971119863) is the ratio of the distance from the upstream

tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows

1198711=

0 corner tappings

1 119863 and 119863

2tappings

254

119863flange tappings

119860 = (19000120573

Re119863

)

08

1198721015840

2=

211987110158402

1 minus 120573

(9)

11987110158402(= 11989710158402119863) is the ratio of the distance from the down-

stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows

1198711015840

2=

0 corner tappings

047 119863 and 119863

2tappings

254


(10)

The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42

23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above

Pump

Reactor

Turbine

Condenser

Control rods

Figure 4 Sketch of SCWR with one loop

the critical point of water (119879119888= 647096K 119901

119888= 22064MPa)

The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4

The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation

119882 = 119876 timesΩ

Ω0

times(119867ℎminus 119867119888)

1000(MW) (11)

where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω

0(trmin) is the

ideal speed of pump and 119867ℎminus 119867119888(kjkg) is the difference

between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine

24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5

Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second


Pump

Reactor

Turbine

Condenser

Pressurizer Steam generator

Control rods

Figure 5 Sketch of SCWR with two loops

loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR

Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation

119882119877=

119873

sum119894=1

119882SG119894

minus119882ΔPr (12)

where the 119882119877is the core thermal power (MW) 119882SG

119894

is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882

ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor

The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876119890and specific enthalpy 119867

119890flows into the steam generator

through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876

119901and specific enthalpy 119867

119901 The

thermal power in ith steam generator can be calculated withfollowing equation

119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)

where119867V is thewet steam enthalpy in steam generator export119867119901is the blowdown enthalpy119876

119901is the flow rate of blowdown

in second loop 119867119890is the feedwater enthalpy in second loop

and 119876119890is the flow rate of feedwater in second loop

The feed water satisfies the law of conservation of mass asfollows

119876119890= 119876V + 119876119901 (14)

Simplify (13) and (14)


where feedwater enthalpy 119867119890and blowdown enthalpy 119876

119901

are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876

119890can be obtained from flow rate

calculation subroutine and the flow rate of blowdown 119876119901is

a measured valueThe wet steam always consists of saturated steam and

saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation

119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)

where the 119867V119904 is the enthalpy of saturated steam and 119867119897119904is

the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine

3 Uncertainty Analysis of Double-Loop SCWR

The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula

Δ119882

119882= [

119899

sum119894=1

[119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [119882ΔPr119882

Δ(119882ΔPr)

119882ΔPr

]

2

]

12

(17)

where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882

ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop

Δ119882SG119894Δ119882

le [Δ119882SGΔ119882

]119872

(18)

where [Δ119882SGΔ119882]119872

is the max uncertainty of each steamgeneration

Assuming that

119882SG119894119882

=1

119894 (19)

We can obtain the following equation

Δ119882

119882=

1

119894[Δ119882SG119882SG

]

2

119872

+ [119882ΔPr119882

timesΔ119882ΔPr

119882ΔPr

]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater

Core heat production

Entranceheat loss

Pump

PumpChargingstream operation

streamLetdown

Reactor

Pressurizer

Figure 6 Heat balance principle diagram of double-loop SCWR

31 The Calculation of Δ119882119878119866119882119878119866 The following equation

can be obtained by error propagation formula

Δ119882SG119882SG

=

[[[[[

[

[119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [119867119890119876119890

119882SG

Δ119867119890

119867119890

]

2

+ [119867119901119876119901

119882SG

Δ119867119901

119867119901

]

2

+[119876119890(119867V minus 119867119890)

119882SG

Δ119876119890

119876119890

]

2

+ [119876119901(119867V minus 119867119901)

119882SG

Δ119876119901

119876119901

]

2

]]]]]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909]

2

+ [119867V119904

119867V119909Δ119867V119904

119867V119904]

2

+[119867119890119904

119867V(1 minus 119909)

Δ119867119890119904

119867119890119904

]

2

]

12

(21)

Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range

Δ (1 minus 119909)

1 minus 119909=

119909

1 minus 119909

Δ119909

119909= 1 (22)

Equation (22) can be deduced by the above formula

Δ119909

119909=1 minus 119909

119909 (23)

Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows

Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (Δ119867V119904

119867V119904)

2

119891

]

12

(24)

and the uncertainty caused by pressure measurement can becalculated by following equation

(Δ119867V119904

119867V119904)119875V

=119875V

119867V119904

10038161003816100381610038161003816100381610038161003816

120597119867V119904

120597119875V

10038161003816100381610038161003816100381610038161003816

Δ119875V

119875V (25)

where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement

120597119867V119904

120597119875V= 120591119877119879

119904

43

sum119894=1

119899119894119869119894(120591 minus 05)

119869119894minus1119868119894(01119875V

119901lowast)

119868119894minus1

(1

119901lowast)

(26)

where 119868119894 119869119894 119899119894

is given in IAPWS-IF97 and 120587 =

01119875V119901lowast120591 = 119879

lowast119905119890 119901

lowast= 1MPa 119879lowast = 540K and

119877 = 0461526 kJ kgminus1Kminus1


(Δ119867V119904119867V119904)2

119891is the uncertainty caused by the calculation

of water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97

32 The Calculation of Δ119867119890119904119867119890119904 The uncertainty of sat-

urated water enthalpy Δ119867119890119904119867119890119904

and feedwater enthalpyΔ119867119890119867119890can be estimated by the method the same as

Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902

119898119902119898can be

described by the following equation

120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)

The uncertainty of discharge coefficient is given by

119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)

If 120573 gt 05 and Re119863lt 10000 the above values should add

the following relative uncertainty

+05 (30)

The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)

for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can

be estimated by the following equation

120590119863=005 times 119889119894 times 2

radic3= 005 times 119889

119894times 115 (31)

where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distribution

The volume elasticity coefficient of water is quite largedetermining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows

(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)

and the uncertainty caused by temperature measurement canbe calculated by following equation

(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)

Table 2 The main parameters reference design of the US SCWR

Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs

Table 3 The input and output values calculated by H-Power

Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW

Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above

The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by

experience values

4 Validation of H-Power Code

41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present

The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3

42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II

Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument

It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation


Table 4 Input parameters of H-Power using the values of Qinshan Phase II

Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261

Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power

Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088

5 Conclusions

The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998

[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005

[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010

[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009

[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010


[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003

[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008

[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997

[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries

[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000

[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003

[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009

[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


READDT

THPROP

OUTPUT

ERCALC

NUSOLV

FLOWRT

READDT

OUTPUT

NUSOLV

H-Power

2 loops

1 loop

Figure 1 H-Power modules diagram

enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le

100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions

2 Theoretical Modeling

The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine

H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis

21 Thermodynamic Properties Subroutine

211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine

We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume

which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated

Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured

The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2

212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid

22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]

As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875

1is obtained by (1) taking pressure loss Δ120596

caused by the existence of orifice plate into account

1198751= 119875me + 119875119886 + Δ120596 (1)

Δ120596 = Δ119875 times (1 minus 12057319) (2)

H-Power adopted the following equation for flow ratemeasurement

119902119898=

119862

radic1 minus 1205734120576 sdot

1205871198892

4radic2Δ119875120588

119906 (3)

where 119902119898

is mass flow rate 120573 is ratio of 119889 (diameter oforifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588

119906

is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows

119862 = 05961 + 002611205732minus 0216120573

8+ 0000521(

106120573

Re119863

)

07

+ (00188 + 00063119860) 12057335(106

Re119863

)

03

+ (0043 + 0080119890minus101198711 minus 0123119890

minus71198711) (1 minus 011119860)

1205734

1 minus 1205734

minus 0031 (1198721015840

2minus 08119872

1015840

2

11

) 12057313

+ sdot sdot sdot

(4)


Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1)

ℎ(kJkgminus1)


119906(kJkgminus1)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 2273150 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus119863

254) (5)


119863 which is





equation

119889 = 1198891198981 + 055(

119889119896

119889119898

)

2

(6)


follows

119889119898= 1198890+ 1198890120582 (119905 minus 119905

0) (7)






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902119898

120583120587119863 (8)




1198711=

0 corner tappings

1 119863 and 119863

2tappings

254


119860 = (19000120573

Re119863

)

08

1198721015840

2=

211987110158402

1 minus 120573

(9)



1198711015840

2=

0 corner tappings

047 119863 and 119863

2tappings

254


(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 timesΩ

Ω0

times(119867ℎminus 119867119888)

1000(MW) (11)


0(trmin) is the






Pump

Reactor

Turbine

Condenser


Control rods




119882119877=

119873

sum119894=1

119882SG119894



119894







119901 The








119876119890= 119876V + 119876119901 (14)




119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)





Δ119882

119882= [

119899

sum119894=1

[119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [119882ΔPr119882

Δ(119882ΔPr)

119882ΔPr

]

2

]

12

(17)



Δ119882SG119894Δ119882

le [Δ119882SGΔ119882

]119872

(18)

where [Δ119882SGΔ119882]119872


Assuming that

119882SG119894119882

=1

119894 (19)


Δ119882

119882=

1

119894[Δ119882SG119882SG

]

2

119872

+ [119882ΔPr119882

timesΔ119882ΔPr

119882ΔPr

]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer




Δ119882SG119882SG

=

[[[[[

[

[119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [119867119890119876119890

119882SG

Δ119867119890

119867119890

]

2

+ [119867119901119876119901

119882SG

Δ119867119901

119867119901

]

2

+[119876119890(119867V minus 119867119890)

119882SG

Δ119876119890

119876119890

]

2

+ [119876119901(119867V minus 119867119901)

119882SG

Δ119876119901

119876119901

]

2

]]]]]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909]

2

+ [119867V119904

119867V119909Δ119867V119904

119867V119904]

2

+[119867119890119904

119867V(1 minus 119909)

Δ119867119890119904

119867119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909=

119909

1 minus 119909

Δ119909

119909= 1 (22)


Δ119909

119909=1 minus 119909

119909 (23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(Δ119867V119904

119867V119904)119875V

=119875V

119867V119904

10038161003816100381610038161003816100381610038161003816

120597119867V119904

120597119875V

10038161003816100381610038161003816100381610038161003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum119894=1

119899119894119869119894(120591 minus 05)

119869119894minus1119868119894(01119875V

119901lowast)

119868119894minus1

(1

119901lowast)

(26)

where 119868119894 119869119894 119899119894


01119875V119901lowast120591 = 119879

lowast119905119890 119901




(Δ119867V119904119867V119904)2







119898119902119898can be


120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)



+05 (30)




120590119863=005 times 119889119894 times 2


119894times 115 (31)



(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)


(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)







experience values












5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Table1Com

paris

onof

calculationresults

betweenH-Pow

erroutinea

ndIAPW

S-IF97

Region

Parameters

Given

byV(m

3kgminus1)

ℎ(kJkgminus1)


119906(kJkgminus1)

Subregion1

119879=300K

IF97

000100215168

11533

1273

0392294792

11232

4818

119875=3MPa

H-Pow

er00010021516

11533

127302

03922947924

11232481798

119879=300K

IF97

971180894119890minus4

184142828

0368563852

10644

8356

119875=80MPa

H-Pow

er97118089119890minus4

18414282773

03685638523

10644

835621

Subregion2

119879=300K

IF97

394913866

25499114

5852238967

241169160

119875=00035MPa

H-Pow

er39491386637

25499114

508

852238966

7324116915976

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825

Subregion3

119879=66315K

119875=24MPa

IF97

0005613

250075

50320

23660

H-Pow

er00056134399

25007519610

50320333072

23660291590

119879=72315K

119875=50MPa

IF97

0002487

228444

45892

21601

H-Pow

er00024874366

22844399286

458922040321

21600680674

Subregion5

119879=1500K

IF97

13845509

521976

855

965408875

452749310

119875=05MPa

H-Pow

er13

845508987

521976

85512

96540887533

45274931018

119879=2000K

IF97

00311385219

657122604

85364

0523

563707038

119875=30MPa

H-Pow

er00311385218

65712260386

85364

052311

56370703825


Input p T

27315 le T le 2273150 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus119863

254) (5)


119863 which is





equation

119889 = 1198891198981 + 055(

119889119896

119889119898

)

2

(6)


follows

119889119898= 1198890+ 1198890120582 (119905 minus 119905

0) (7)






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902119898

120583120587119863 (8)




1198711=

0 corner tappings

1 119863 and 119863

2tappings

254


119860 = (19000120573

Re119863

)

08

1198721015840

2=

211987110158402

1 minus 120573

(9)



1198711015840

2=

0 corner tappings

047 119863 and 119863

2tappings

254


(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 timesΩ

Ω0

times(119867ℎminus 119867119888)

1000(MW) (11)


0(trmin) is the






Pump

Reactor

Turbine

Condenser


Control rods




119882119877=

119873

sum119894=1

119882SG119894



119894







119901 The








119876119890= 119876V + 119876119901 (14)




119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)





Δ119882

119882= [

119899

sum119894=1

[119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [119882ΔPr119882

Δ(119882ΔPr)

119882ΔPr

]

2

]

12

(17)



Δ119882SG119894Δ119882

le [Δ119882SGΔ119882

]119872

(18)

where [Δ119882SGΔ119882]119872


Assuming that

119882SG119894119882

=1

119894 (19)


Δ119882

119882=

1

119894[Δ119882SG119882SG

]

2

119872

+ [119882ΔPr119882

timesΔ119882ΔPr

119882ΔPr

]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer




Δ119882SG119882SG

=

[[[[[

[

[119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [119867119890119876119890

119882SG

Δ119867119890

119867119890

]

2

+ [119867119901119876119901

119882SG

Δ119867119901

119867119901

]

2

+[119876119890(119867V minus 119867119890)

119882SG

Δ119876119890

119876119890

]

2

+ [119876119901(119867V minus 119867119901)

119882SG

Δ119876119901

119876119901

]

2

]]]]]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909]

2

+ [119867V119904

119867V119909Δ119867V119904

119867V119904]

2

+[119867119890119904

119867V(1 minus 119909)

Δ119867119890119904

119867119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909=

119909

1 minus 119909

Δ119909

119909= 1 (22)


Δ119909

119909=1 minus 119909

119909 (23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(Δ119867V119904

119867V119904)119875V

=119875V

119867V119904

10038161003816100381610038161003816100381610038161003816

120597119867V119904

120597119875V

10038161003816100381610038161003816100381610038161003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum119894=1

119899119894119869119894(120591 minus 05)

119869119894minus1119868119894(01119875V

119901lowast)

119868119894minus1

(1

119901lowast)

(26)

where 119868119894 119869119894 119899119894


01119875V119901lowast120591 = 119879

lowast119905119890 119901




(Δ119867V119904119867V119904)2







119898119902119898can be


120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)



+05 (30)




120590119863=005 times 119889119894 times 2


119894times 115 (31)



(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)


(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)







experience values












5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Input p T

27315 le T le 2273150 le p le 100

Error and quit

Error and quit

R 5

R 1 R 2 R 2

T T

T

T

T

T

T

T

T

T

P le 10 T ge 107315

F

F

FF

F

F

F

F

F

T le 647096

ps(T)

ps(T)

p = ps

T le 62315 T ge 86315

p23(T)

p lt p23

p lt p23

= 00013

= +

Output result

End

p gt ps

R 4




0011 (075 minus 120573) (28 minus119863

254) (5)


119863 which is





equation

119889 = 1198891198981 + 055(

119889119896

119889119898

)

2

(6)


follows

119889119898= 1198890+ 1198890120582 (119905 minus 119905

0) (7)






Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902119898

120583120587119863 (8)




1198711=

0 corner tappings

1 119863 and 119863

2tappings

254


119860 = (19000120573

Re119863

)

08

1198721015840

2=

211987110158402

1 minus 120573

(9)



1198711015840

2=

0 corner tappings

047 119863 and 119863

2tappings

254


(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 timesΩ

Ω0

times(119867ℎminus 119867119888)

1000(MW) (11)


0(trmin) is the






Pump

Reactor

Turbine

Condenser


Control rods




119882119877=

119873

sum119894=1

119882SG119894



119894







119901 The








119876119890= 119876V + 119876119901 (14)




119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)





Δ119882

119882= [

119899

sum119894=1

[119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [119882ΔPr119882

Δ(119882ΔPr)

119882ΔPr

]

2

]

12

(17)



Δ119882SG119894Δ119882

le [Δ119882SGΔ119882

]119872

(18)

where [Δ119882SGΔ119882]119872


Assuming that

119882SG119894119882

=1

119894 (19)


Δ119882

119882=

1

119894[Δ119882SG119882SG

]

2

119872

+ [119882ΔPr119882

timesΔ119882ΔPr

119882ΔPr

]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer




Δ119882SG119882SG

=

[[[[[

[

[119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [119867119890119876119890

119882SG

Δ119867119890

119867119890

]

2

+ [119867119901119876119901

119882SG

Δ119867119901

119867119901

]

2

+[119876119890(119867V minus 119867119890)

119882SG

Δ119876119890

119876119890

]

2

+ [119876119901(119867V minus 119867119901)

119882SG

Δ119876119901

119876119901

]

2

]]]]]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909]

2

+ [119867V119904

119867V119909Δ119867V119904

119867V119904]

2

+[119867119890119904

119867V(1 minus 119909)

Δ119867119890119904

119867119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909=

119909

1 minus 119909

Δ119909

119909= 1 (22)


Δ119909

119909=1 minus 119909

119909 (23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(Δ119867V119904

119867V119904)119875V

=119875V

119867V119904

10038161003816100381610038161003816100381610038161003816

120597119867V119904

120597119875V

10038161003816100381610038161003816100381610038161003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum119894=1

119899119894119869119894(120591 minus 05)

119869119894minus1119868119894(01119875V

119901lowast)

119868119894minus1

(1

119901lowast)

(26)

where 119868119894 119869119894 119899119894


01119875V119901lowast120591 = 119879

lowast119905119890 119901




(Δ119867V119904119867V119904)2







119898119902119898can be


120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)



+05 (30)




120590119863=005 times 119889119894 times 2


119894times 115 (31)



(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)


(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)







experience values












5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















Steam generator

Orificeplate

+ Δ120596

Δ120596

Pme + Pa

Pme + Pa




Re119863=

4119902119898

120583120587119863 (8)




1198711=

0 corner tappings

1 119863 and 119863

2tappings

254


119860 = (19000120573

Re119863

)

08

1198721015840

2=

211987110158402

1 minus 120573

(9)



1198711015840

2=

0 corner tappings

047 119863 and 119863

2tappings

254


(10)



Pump

Reactor

Turbine

Condenser

Control rods



119888= 22064MPa)



119882 = 119876 timesΩ

Ω0

times(119867ℎminus 119867119888)

1000(MW) (11)


0(trmin) is the






Pump

Reactor

Turbine

Condenser


Control rods




119882119877=

119873

sum119894=1

119882SG119894



119894







119901 The








119876119890= 119876V + 119876119901 (14)




119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)





Δ119882

119882= [

119899

sum119894=1

[119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [119882ΔPr119882

Δ(119882ΔPr)

119882ΔPr

]

2

]

12

(17)



Δ119882SG119894Δ119882

le [Δ119882SGΔ119882

]119872

(18)

where [Δ119882SGΔ119882]119872


Assuming that

119882SG119894119882

=1

119894 (19)


Δ119882

119882=

1

119894[Δ119882SG119882SG

]

2

119872

+ [119882ΔPr119882

timesΔ119882ΔPr

119882ΔPr

]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer




Δ119882SG119882SG

=

[[[[[

[

[119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [119867119890119876119890

119882SG

Δ119867119890

119867119890

]

2

+ [119867119901119876119901

119882SG

Δ119867119901

119867119901

]

2

+[119876119890(119867V minus 119867119890)

119882SG

Δ119876119890

119876119890

]

2

+ [119876119901(119867V minus 119867119901)

119882SG

Δ119876119901

119876119901

]

2

]]]]]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909]

2

+ [119867V119904

119867V119909Δ119867V119904

119867V119904]

2

+[119867119890119904

119867V(1 minus 119909)

Δ119867119890119904

119867119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909=

119909

1 minus 119909

Δ119909

119909= 1 (22)


Δ119909

119909=1 minus 119909

119909 (23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(Δ119867V119904

119867V119904)119875V

=119875V

119867V119904

10038161003816100381610038161003816100381610038161003816

120597119867V119904

120597119875V

10038161003816100381610038161003816100381610038161003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum119894=1

119899119894119869119894(120591 minus 05)

119869119894minus1119868119894(01119875V

119901lowast)

119868119894minus1

(1

119901lowast)

(26)

where 119868119894 119869119894 119899119894


01119875V119901lowast120591 = 119879

lowast119905119890 119901




(Δ119867V119904119867V119904)2







119898119902119898can be


120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)



+05 (30)




120590119863=005 times 119889119894 times 2


119894times 115 (31)



(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)


(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)







experience values












5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Pump

Reactor

Turbine

Condenser


Control rods




119882119877=

119873

sum119894=1

119882SG119894



119894







119901 The








119876119890= 119876V + 119876119901 (14)




119901






119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)





Δ119882

119882= [

119899

sum119894=1

[119882SG119894119882

Δ119882SG119894119882SG119894

]

2

+ [119882ΔPr119882

Δ(119882ΔPr)

119882ΔPr

]

2

]

12

(17)



Δ119882SG119894Δ119882

le [Δ119882SGΔ119882

]119872

(18)

where [Δ119882SGΔ119882]119872


Assuming that

119882SG119894119882

=1

119894 (19)


Δ119882

119882=

1

119894[Δ119882SG119882SG

]

2

119872

+ [119882ΔPr119882

timesΔ119882ΔPr

119882ΔPr

]

2

12

(20)


Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer




Δ119882SG119882SG

=

[[[[[

[

[119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [119867119890119876119890

119882SG

Δ119867119890

119867119890

]

2

+ [119867119901119876119901

119882SG

Δ119867119901

119867119901

]

2

+[119876119890(119867V minus 119867119890)

119882SG

Δ119876119890

119876119890

]

2

+ [119876119901(119867V minus 119867119901)

119882SG

Δ119876119901

119876119901

]

2

]]]]]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909]

2

+ [119867V119904

119867V119909Δ119867V119904

119867V119904]

2

+[119867119890119904

119867V(1 minus 119909)

Δ119867119890119904

119867119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909=

119909

1 minus 119909

Δ119909

119909= 1 (22)


Δ119909

119909=1 minus 119909

119909 (23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(Δ119867V119904

119867V119904)119875V

=119875V

119867V119904

10038161003816100381610038161003816100381610038161003816

120597119867V119904

120597119875V

10038161003816100381610038161003816100381610038161003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum119894=1

119899119894119869119894(120591 minus 05)

119869119894minus1119868119894(01119875V

119901lowast)

119868119894minus1

(1

119901lowast)

(26)

where 119868119894 119869119894 119899119894


01119875V119901lowast120591 = 119879

lowast119905119890 119901




(Δ119867V119904119867V119904)2







119898119902119898can be


120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)



+05 (30)




120590119863=005 times 119889119894 times 2


119894times 115 (31)



(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)


(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)







experience values












5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Electric heater

Steamgenerator

Blowdown

Feedwater


Entranceheat loss

Pump


streamLetdown

Reactor

Pressurizer




Δ119882SG119882SG

=

[[[[[

[

[119867V(119876119890 minus 119876119901)

119882SG

Δ119867V

119867V]

2

+ [119867119890119876119890

119882SG

Δ119867119890

119867119890

]

2

+ [119867119901119876119901

119882SG

Δ119867119901

119867119901

]

2

+[119876119890(119867V minus 119867119890)

119882SG

Δ119876119890

119876119890

]

2

+ [119876119901(119867V minus 119867119901)

119882SG

Δ119876119901

119876119901

]

2

]]]]]

]

12

Δ119867V

119867V= [[

119909

119867V(119867V119904 minus 119867119890119904)

Δ119909

119909]

2

+ [119867V119904

119867V119909Δ119867V119904

119867V119904]

2

+[119867119890119904

119867V(1 minus 119909)

Δ119867119890119904

119867119890119904

]

2

]

12

(21)


Δ (1 minus 119909)

1 minus 119909=

119909

1 minus 119909

Δ119909

119909= 1 (22)


Δ119909

119909=1 minus 119909

119909 (23)


Δ119867V119904

119867V119904= [(

Δ119867V119904

119867V119904)

2

119875V

+ (Δ119867V119904

119867V119904)

2

119891

]

12

(24)


(Δ119867V119904

119867V119904)119875V

=119875V

119867V119904

10038161003816100381610038161003816100381610038161003816

120597119867V119904

120597119875V

10038161003816100381610038161003816100381610038161003816

Δ119875V

119875V (25)


120597119867V119904

120597119875V= 120591119877119879

119904

43

sum119894=1

119899119894119869119894(120591 minus 05)

119869119894minus1119868119894(01119875V

119901lowast)

119868119894minus1

(1

119901lowast)

(26)

where 119868119894 119869119894 119899119894


01119875V119901lowast120591 = 119879

lowast119905119890 119901




(Δ119867V119904119867V119904)2







119898119902119898can be


120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)



+05 (30)




120590119863=005 times 119889119894 times 2


119894times 115 (31)



(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)


(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)







experience values












5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















(Δ119867V119904119867V119904)2







119898119902119898can be


120575119902119898

119902119898

= ((120575119862

119862)

2

+ (120575120576

120576)

2

+ (21205734

1 minus 1205734)

2

(120575119863

119863)

2

+(2

1 minus 1205734)

2

(120575119889

119889)

2

+1

4(120575Δ119901

Δ119901)

2

+1

4(1205751205881

1205881

)

2

)

12

(27)


119862 =

(07 minus 120573) 01 le 120573 le 02

05 02 le 120573 le 06

(1667120573 minus 05) 06 le 120573 le 075

(28)


09 (075 minus 120573) (28 minus119863

254) (29)



+05 (30)




120590119863=005 times 119889119894 times 2


119894times 115 (31)



(Δ120588

120588) = [(

Δ120588

120588)

2

119905119890

+ (Δ120588

120588)

2

119891

]

12

(32)


(Δ120588

120588)119905119890

=119905119890

120588

10038161003816100381610038161003816100381610038161003816

120597120588

120597119905119890

10038161003816100381610038161003816100381610038161003816

Δ119905119890

119905119890 (33)







experience values












5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















5 Conclusions




References



















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















Research Article Preliminary Development of Thermal Power ...

Documents

Transcript of Research Article Preliminary Development of Thermal Power ...