SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems, which has higher thermal power efficiency than current pressurized water reactor. It is necessary to perform the thermal equilibrium and thermal power calculation for the conceptual design and further monitoring and calibration of the SCWR. One visual software named HPower was developed to calculate thermal power and its uncertainty of SCWR, in which the advanced IAPWSIF97 industrial formulation was used to calculate the thermodynamic properties of water and steam. The ISO51674: 2003 standard was incorporated in the code as the basis of orifice plate to compute the flow rate. New heat balance model and uncertainty estimate have also been included in the code. In order to validate HPower, an assessment was carried out by using data published by US and Qinshan Phase II. The results showed that HPower was able to estimate the thermal power of SCWR.
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems, which has higher thermal power efficiency than current pressurized water reactor. Compared to the currently running water coolant reactors, SCWR has the higher thermal efficiency and safety, which makes it a more promising advanced nuclear energy system. The concept of SCWR was originally put forward by Westinghouse and GE (General Electric) in the 1950s and preliminarily studied by the United States and the former Soviet Union from 1950s to 1960s. In the 1990s, Dobashi et al. [
For reactor operating more safely, stably, and economically, the accurate calibration for real thermal power has important significance in reactor design and analysis. It is necessary to develop a special thermal power calculation code for SCWR, while there is no available program published in the world. This paper preliminarily developed visual software named HPower to calculate SCWR thermal power and its uncertainty based on heat balance method, which has been applied to current PWRs [
According to the various conceptual SCWR designs [
IAPWS is an international nonprofit association concerned with the properties of water and steam, particularly thermodynamic properties. In 1997, IAPWS adopted the “IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam” for industrial use [
We have done lots of researches and work in comparing IAPWSIF97 with IFC67 in several aspects. The result showed that IAPWSIF97 improves significantly in boundary consistency and accuracy and calculation speed [
HPower adopted IAPWSIF97 to calculate thermodynamic properties (including specific volume, specific enthalpy, and viscosity) of water. The code covers all range of IAPWSIF97
The modules of HPower are given in Figure
HPower modules diagram.
HPower provides a visual interface for users and has high module independence, which makes it a practical code in SCWR analysis.
The range of IAPWSIF97 is divided into five subareas; each of them has a basic equation. To make the program more concise and readable, this subroutine used the compiling method of modularization; that is, separate districts of thermodynamics equation were written into separate subroutine.
We can directly obtain the thermophysical properties from pressure and temperature values using the basic equations except region 3. Subregion 3 does not have the formula which can calculate other various thermal parameters directly through the temperature and pressure; it can only rely on iteration calculation. In this subroutine, the first pressure calculation uses temperature and a small specific volume which was chosen as initial value. If the difference between the calculated value of pressure and user input values is positive, the value of specific volume increases incremental quantity ratio by half and continues the iteration until the pressure difference is less than condition of convergence. The iteration is over and other properties can be calculated.
Through this kind of iteration and close proximity to the input value by increasing incremental quantity in halving bisection method, not only the disadvantages of the increased specific volume increment are too small to calculate quickly was avoided, but also the accuracy of calculation can be ensured.
The subroutine of water and steam thermodynamic properties has been totally developed according to the flow chart shown in Figure
Flow chart of thermodynamic properties subroutine based on IAPWSIF97.
In order to do the verification, we list the calculation results together with those given by IAPWSIF97 in Table
Comparison of calculation results between HPower routine and IAPWSIF97.
Region  Parameters  Given by 





Subregion 1 

IF97  0.00100215168  115.331273  0.392294792  112.324818 

HPower  0.0010021516  115.33127302  0.3922947924  112.32481798  

IF97 

184.142828  0.368563852  106.448356  

HPower 

184.14282773  0.3685638523  106.44835621  


Subregion 2 

IF97  39.4913866  2549.91145  8.52238967  2411.69160 

HPower  39.491386637  2549.9114508  8.5223896673  2411.6915976  

IF97  0.0311385219  6571.22604  8.53640523  5637.07038  

HPower  0.0311385218  6571.2260386  8.5364052311  5637.0703825  


Subregion 3 

IF97  0.005613  2500.75  5.0320  2366.0 
HPower  0.0056134399  2500.7519610  5.0320333072  2366.0291590  

IF97  0.002487  2284.44  4.5892  2160.1  
HPower  0.0024874366  2284.4399286  4.58922040321  2160.0680674  


Subregion 5 

IF97  1.3845509  5219.76855  9.65408875  4527.49310 

HPower  1.3845508987  5219.7685512  9.6540887533  4527.4931018  

IF97  0.0311385219  6571.22604  8.53640523  5637.07038  

HPower  0.0311385218  6571.2260386  8.5364052311  5637.0703825 
The main feedwater flow rate of the steam generator can be measured by orifice plate, which is widely used in measurement of fluid flow. This part is based on the ISO 5167 standard in [
As the schematic diagram shown in Figure
Pressure measuring schematic by orifice plate.
HPower adopted the following equation for flow rate measurement:
As we can see from the above equation, discharge coefficient
Diameters in the formula for calculating should be corrected due to the difference of temperature between working condition and measurement. If there is drain hole (diameter is
The uncertainty of the feedwater flow measured and calculated by orifice plate and relevant equations will be given in Section
In singleloop type SCWR, the coolant is supercritical water which will be operated above the critical point of water
Sketch of SCWR with one loop.
The thermal power in this type can be calculated with thermal balance using measured values, including inlet and outlet temperatures, working pressure, flow rate of coolant, and the practical speed of pump. The thermal power
Some conceptual designs of doubleloop SCWR have been put forward, like CANDUSCWR with a steam generator proposed by Dr. William Fatoux [
Sketch of SCWR with two loops.
Heat balance method in this type of SCWR is based on the steam generator approximation enthalpy balance. HPower calculate the thermal power of reactor by the theory of heat balance, which obtains thermal power (of generator) in second loop from primary loop through the measurement values of temperature, pressure, and flow rate in the second loop, counting the internal heat loss in at the same time. The advantages of the working conditions of second loop for easy measurement makes it an important method of obtaining thermal power of the doubleloop SCWR.
Figure
Heat balance principle diagram of doubleloop SCWR.
The main physical process occurring in the steam generator is as follows: unsaturated water with the mass flow rate
The feed water satisfies the law of conservation of mass as follows:
Simplify (
The wet steam always consists of saturated steam and saturated water, which is determined by vapour fraction
The relative uncertainty of thermal power given in (
Assuming that
We can obtain the following equation:
The following equation can be obtained by error propagation formula:
Assume that the uncertainty of saturated water in the wet steam is “1” as in (
The uncertainty of saturated water enthalpy
The relative uncertainty of mass flow rate
The uncertainty of discharge coefficient is given by
If
If
The uncertainty of expansibility factor
The uncertainty of internal diameter of the pipe line can be estimated by the following equation:
The volume elasticity coefficient of water is quite large determining that its compressibility is very small, so the influence of pressure on the density can be ignored. The uncertainty of feed water density
The calculation procedures and method of the parameters are the same as the
The relative uncertainty of
We have done the verification of singleloop program in HPower using the main parameters design by Jacopo Buongiorno as in Table
The main parameters reference design of the US SCWR.
Parameter  Value 

Thermal power  3575 MWth 
Operating pressure  25 MPa 
Reactor inlet temperature  280°C 
Reactor outlet temperature  510 
Reactor mass flow rate  1843 kg/s 
The calculation result of thermal power 3564.3396 MW given in Table
The input and output values calculated by HPower.
Input parameter  Value 

Operating pressure  25 MPa 
Reactor inlet temperature  280°C 
Reactor outlet temperature  520°C 
Reactor mass flow rate  1843 kg/s 
Ideal pump speed  1900 tr/min 
Practical pump speed  1850 tr/min 
Output parameter  Value 
Cold leg enthalpy  1230.2407 kj/kg 
Hot leg enthalpy  3216.4985 kj/kg 
Thermal power  3564.3396 MW 
Due to the lack of design data of SCWR, the validation of this part has been done by using the values of Qinshan Phase II [
Input parameters of HPower using the values of Qinshan Phase II.
Parameters  Values 

Orifice diameter in reference (m)  0.2417 
Feedwater pipe diameter in reference (m)  0.36374 
Steam pipe diameter in reference (m)  0.739 
Orifice linear expansion coefficient (m/m°C)  0.0000166 
Feedwater pipe linear expansion coefficient (m/m°C)  0.0000121 
Steam pipe linear expansion coefficient (m/m°C)  0.0000121 
Orifice reference temperature (°C)  20 
Feedwater pipe reference temperature (°C)  20 
Steam pipe reference temperature (°C)  20 
Feedwater pressure difference (KPa)  182.1147 
Feedwater temperature (°C)  228.920334 
Feedwater pressure (MPa)  7.11855 
Steam pressure (MPa)  6.941479 
Blowdown flow rate (t/h)  20.757261 
Comparison between the results of the values of Qinshan Phase II and HPower.
Parameters  Qinshan Phase II  HPower 

Feedwater density (kg/m^{3})  833.12894  832.69758 
Feedwater enthalpy (kj/kg)  986.18622  986.07354 
Saturated water enthalpy (kj/kg)  1264.3947  1265.5310 
Saturated steam enthalpy (kj/kg)  2774.1882  2773.0492 
Steam enthalpy (kj/kg)  2772.6784  2771.5417 
Blowdown enthalpy (kj/kg)  1264.3947  1265.531 
Discharge coefficient  0.603068  0.606047 
Feedwater flow rate (t/h)  1948.4789  1957.6866 
Generator thermal power (MW)  958.2318  970.94089 
Feedwater flow rate uncertainty  0.007236  0.006088 
Although the main calculation result trend of SCWR is same as CNP650 of Qinshan Phase II, there is many detail differences in thermodynamic properties of water and steam and uncertainties calculation. The inconsistencies in Table
It is a valid way to verify the HPower while the main calculation process of both PWR and SCWR is the same and there is no particular data of SCWR fitting for the code. The result in Table
The thermal power calculation code HPower for SCWR was developed based on heat balance method, which can be easily applied in designs and operation. In this paper thermodynamic properties calculation subroutine based on IAPWSIF97 has been verified, and the uncertainty analysis has been proposed. The validation of HPower has been carried out in two parts: singleloop SCWR by the data given by Jacopo Buongiorno and doubleloop SCWR by the values of Qinshan Phase II. Although Qinshan Phase II is a PWR, the result can show that HPower is valid because the main calculation process of both PWR and SCWR is the same. In the future, the validation will be carried out using the values of SCWR when published.
The authors declare that there is no conflict of interests regarding the publication of this paper.