research article preliminary development of thermal power
TRANSCRIPT
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
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
119863flange tappings
(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
6 Science and Technology of Nuclear Installations
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)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
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)
Science and Technology of Nuclear Installations 7
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
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
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Wind EnergyJournal of
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Nuclear EnergyInternational Journal of
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High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
119863flange tappings
(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
6 Science and Technology of Nuclear Installations
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)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
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)
Science and Technology of Nuclear Installations 7
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
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
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FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
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High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
119863flange tappings
(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
6 Science and Technology of Nuclear Installations
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)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
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)
Science and Technology of Nuclear Installations 7
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
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
4 Science and Technology of Nuclear Installations
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
Science and Technology of Nuclear Installations 5
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
119863flange tappings
(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
6 Science and Technology of Nuclear Installations
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)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
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)
Science and Technology of Nuclear Installations 7
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
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Science and Technology of Nuclear Installations 5
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
119863flange tappings
(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
6 Science and Technology of Nuclear Installations
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)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
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)
Science and Technology of Nuclear Installations 7
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
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
6 Science and Technology of Nuclear Installations
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)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
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)
Science and Technology of Nuclear Installations 7
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
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Science and Technology of Nuclear Installations 7
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
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
8 Science and Technology of Nuclear Installations
(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)
If119863 lt 7112mm (10) should add the following term
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
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Science and Technology of Nuclear Installations 9
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
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
10 Science and Technology of Nuclear Installations
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014