A combined cycle that combines AWM cycle with a nuclear closed Brayton cycle is proposed to recover the waste heat rejected from the precooler of a nuclear closed Brayton cycle in this paper. The detailed thermodynamic and economic analyses are carried out for the combined cycle. The effects of several important parameters, such as the absorber pressure, the turbine inlet pressure, the turbine inlet temperature, the ammonia mass fraction, and the ambient temperature, are investigated. The combined cycle performance is also optimized based on a multiobjective function. Compared with the closed Brayton cycle, the optimized power output and overall efficiency of the combined cycle are higher by 2.41% and 2.43%, respectively. The optimized LEC of the combined cycle is 0.73% lower than that of the closed Brayton cycle.
With the development of the world economy, the total energy consumption increases steadily. The consumption of the energy, especially fossil energy resources, causes and accelerates the occurrence of many environmental problems. Nuclear energy is an efficient energy source that plays an important role in current energy demand. Because of its inherent safety, the high temperature gascooled reactor (HTGR) has attracted many attentions of the researchers. To ensure the high efficiency of nuclear power plant, reasonable thermodynamic cycle should be used. Despite the higher efficiency of HTGR, a large amount of waste heat is discharged from the precooler of the nuclear closed Brayton cycle. Thus, research topics focus on recovery and utilization of this low grade thermal energy.
At present, the waste heat of the closed Brayton cycle can be recovered by several ways, as follows: desalination, Organic Rankine Cycle (ORC), Kalina cycle, and ammoniawater combined power/cooling cycle. Soroureddin et al. [
Meanwhile, many investigations focused on the design and optimization of waste heat recovery system. Some studies optimized the system according to the net power output, cooling output, first law efficiency, and second law efficiency [
According to the studies proposed in the public literatures, few investigations focused on the system economic analysis of the combined cycle, especially the evaluation of the levelized energy cost (LEC). In this paper, a combined cycle, in which a power/cooling cogeneration cycle is integrated into the nuclear closed Brayton cycle, is proposed to recover and utilize the waste heat rejected from the precooler of the closed Brayton cycle. Based on a detailed parametric analysis, a multiobjective function
A schematic diagram of the proposed combined cycle is shown in Figure
Schematic diagram of the combined cycle.
The helium flowing out from the gas turbine flows into the hot side of the recuperator where the helium is cooled to about 400 K. To reduce the compressor power consumption, the helium should be cooled to about 300 K before flowing into the compressor. Thus, the ammoniawater power/cooling cycle (AWM), proposed by Goswami [
An ammoniawater mixture (state 8) is pumped to a high pressure (state 9) and heated to boil off ammonia (state 12). The vapor is enriched in ammonia by condensing a part of the vapor in a rectifier (state 14). The condensate is richer in water and returned to the boiler (state 13). The ammonia vapor, which is almost pure ammonia, can be expanded in a turbine to exit at a very low temperature (state 15). After expansion in the turbine to generate power, low temperature ammonia first provides cooling capacity in the cooler (state 16) and is absorbed by low concentration solution from the boiler in an absorber, to form the basic ammoniawater liquid solution to complete the cycle (state 8) [
The following assumptions are used in this work:
The system operates in a steady state condition.
Changes in kinetic and potential energies are neglected.
The pressure loss due to the frictional effects is neglected.
The turbine and the pump in the combined cycle have isentropic efficiencies [
The ammoniawater solution leaving the absorber (state 8) is a saturated liquid at low pressure.
A MATLAB code has been developed to carry out the numerical simulations for this combined cycle. The thermodynamic properties of the states in the closed Brayton cycle are evaluated by REFPROP 9.0. The thermodynamic properties of the states of the bottom cycle (AWM cycle) are evaluated by the method proposed by Xu and Goswami [
To simplify the calculation, just one operation condition of the closed Brayton cycle is selected according to the literature [
The energy relations for the equipment of combined cycle are listed in Table
Energy relations for the equipment of closed Brayton cycle and AWM cycle.
Cycle  Equipment  Energy equations 

Closed Brayton cycle  Reactor core 

Turbine 


Recuperator 


Precooler 


Compressor 




AWM cycle  Boiler 

Rectifier 


HT recuperator 


Absorber 


Turbine 


Cooler 


Pump 


Throttle valve 

For the combined cycle, the net power output can be defined as follows:
To verify the developed thermodynamic models for AWM cycle, the available data in the literature are used. The comparisons between the simulation results and those reported in the published literature are presented in Table
Comparison between the properties of the present work and those from the published literature [
State 












 
8  280.0  2.0  −214.1  −214.4  −0.1060  −0.1061  0.53  0.53 
9  280.0  30.0  −211.4  −211.6  −0.1083  −0.1084  0.53  0.53 
11  378.1  30.0  246.3  246.7  1.2907  1.2924  0.53  0.53 
12  400.0  30.0  1547.2  1549.8  4.6102  4.6223  0.9432  0.9451 
13  360.0  30.0  205.8  206.1  1.1185  1.1201  0.6763  0.6760 
14  360.0  30.0  1373.2  1374.1  4.1520  4.1546  0.9921  0.9938 
15  257.0  2.0  1148.9  1177.6  4.5558  4.6702  0.9921  0.9938 
16  280.0  2.0  1278.7  1284.6  5.0461  5.0734  0.9921  0.9938 
17  400.0  30.0  348.2  347.9  1.5544  1.5563  0.4147  0.4269 
18  300.0  30.0  −119.0  −120.7  0.2125  0.2105  0.4147  0.4269 
To evaluate the thermoeconomic performance of the combined cycle, levelized energy cost (LEC) is analyzed in this paper. Because the aim of this paper is to evaluate the effect of AWM cycle on the thermodynamic and economic performances of the combined cycle, the HTGR plant (closed Brayton cycle) specific cost is assumed to be 1073$/kW [
Then, the capital investment of AWM cycle is calculated. According to the literature [
The heat exchanger area can be expressed as follows:
Heat transfer coefficients for heat exchangers [
Component  Heat transfer coefficient (W/m^{2}K) 

Absorber  800 
Separator  900 
Cooler  1000 
Recuperator  800 
The overall heat transfer coefficient of the boiler can be calculated as follows [
The heat transfer coefficient of the helium in the shell is calculated by the following equations:
For the above equations,
The capital costs of the AWM system consist of the heat exchanger, pump, and turbine costs and are expressed as follows [
Coefficients required for the cost evaluation for each component [
Components 











Turbine  3.15140  0.5890  0  0  0  0  0  0  0  3.50 
Pump  3.5790  0.3210  0.0290  0.1680  0.3480  0.4840  1.80  1.51  1.80  Equation ( 
Heat exchanger  3.2138  0.2688  0.07961  −0.064991  0.05025  0.01474  1.80  1.50  1.25  Equation ( 
Specifications of the combined cycle [
Parameters  Value 


358.8 

0.85 

1179.1 

301 

67.6 

0.85 

0.85 

398.8 

855.4 

31.0 
The capital cost
The coefficients of
Thus, the cost of the AWM system in the year 1996
According to the time value of money, the cost of closed Brayton system in the year of 2006 and the AWM system in the year of 1996 are converted into the capital costs in the year of 2015, respectively, and the total cost of the combined cycle (
The capital recovery factor (CRF) is defined as follows:
For each year, the operation hour of the system is calculated as follows:
In the combined system, the levelized energy cost (LEC) can be calculated by (
A simple thermodynamic optimization or economical optimization might draw different results, because it is difficult to ensure a global costeffective cycle design. Thus, the optimizations on both the thermodynamics and economics are simultaneously needed in the assessment of the combined cycle. Regarding this, overall efficiency
The first objective function
The second objective function
The first objective function
In this paper, the method of linear weighted evaluation function is adopted to solve the objective function optimization model [
The absorber pressure is the outlet pressure of ammoniawater turbine. If the absorber pressure is high, the working fluid cannot expand fully in the turbine, and both the power output and overall efficiency decrease in turn (Figures
Variation of power output of combined cycle with absorber pressure.
Variation of overall efficiency of combined cycle with absorber pressure.
Variation of LEC of combined cycle with absorber pressure.
Variation of
As shown in Figures
Variation of power output of combined cycle with turbine inlet pressure.
Variation of overall efficiency of combined cycle with turbine inlet pressure.
As shown in Figure
Variation of LEC of combined cycle with turbine inlet pressure.
Variation of
Figure
Variation of power output of combined cycle with turbine inlet temperature.
Because the increasing turbine inlet temperature increases cooler inlet temperature, the equivalent work of cooling capacity (
Variation of overall efficiency of combined cycle with turbine inlet temperature.
As shown in Figure
Variation of LEC of combined cycle with turbine inlet temperature.
Variation of
Figures
Variation of power output of combined cycle with ammonia mass fraction.
Variation of overall efficiency of combined cycle with ammonia mass fraction.
Figure
Variation of LEC of combined cycle with ammonia mass fraction.
Variation of
In this work, SA (Simulated Annealing) is employed to obtain the optimum combination of the key parameters. For the optimization, the constraints are simplified as follows:
Subject to:
The selection of the abovementioned parameters for this optimization is according to the literatures [
Table
Results of the closed Brayton cycle.
Parameters  Value 


593.64 

46.6% 

276.90 
LEC 
0.0711 
Table
Optimization results.
Parameters  Optimization results 



Comparing with closed Brayton cycle, the combined cycle reduces the LEC slightly. The optimized LEC of combined cycle is 0.73% lower than that of the closed Brayton cycle. The reason is that the AWM utilizes the waste heat and adds the power output and the cooling capacity to the closed Brayton cycle. However, the total capital investment increases due to the combined AWM system.
In this paper, a combined cycle, which combines AWM cycle and a nuclear closed Brayton cycle to recover the waste heat rejected from the precooler, is proposed. A detailed parametric study and optimization are carried out for this combined cycle according to the thermodynamics and economics performances. The combined cycle can potentially be used to improve the power output and overall efficiency. The power output and overall efficiency of the combined cycle increase with increasing turbine inlet temperature and ammonia mass fraction, but the turbine inlet temperature and the ammonia mass fraction are limited by the heat source temperature and the absorb pressure, respectively. Compared with the closed Brayton cycle, the optimized power output and overall efficiency increase by 2.41% and 2.43%, respectively. LEC increases with decreasing absorber pressure and turbine inlet temperature. The optimized LEC of the combined cycle is 0.0706 USD/(kWh), which is 0.73% lower than those of the closed Brayton cycle.
The authors declare that there are no competing interests regarding the publication of this paper and regarding the funding that they have received.
This present research was supported by the Chinese Natural Science Fund (Project no. 51306216) and the Fundamental Research Funds for the Central University (Project no. CDJ2R13140016).