Potential advantages of coupling supercritical CO2 Brayton cycle to water cooled small and medium size reactor

Nuclear Engineering and Design 245 (2012) 223–232

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Potential advantages of coupling supercritical CO2 Brayton cycle to water cooled small and medium size reactor Ho Joon Yoon a,b,1,2 , Yoonhan Ahn a,1 , Jeong Ik Lee a,b,∗ , Yacine Addad b,2 a b

Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology 373-1 Guseong-dong Yuseong-gu, Daejeon, 305-701, South Korea Department of Nuclear Engineering, Khalifa University of Science, Technology & Research (KUSTAR). P.O. Box 127788, Abu Dhabi, United Arab Emirates

a r t i c l e

i n f o

Article history: Received 22 August 2011 Received in revised form 5 January 2012 Accepted 12 January 2012

a b s t r a c t The supercritical carbon dioxide (S-CO2 ) Brayton cycle is being considered as a favorable candidate for the next generation nuclear reactors power conversion systems. Major benefits of the S-CO2 Brayton cycle compared to other Brayton cycles are: (1) high thermal efficiency in relatively low turbine inlet temperature, (2) compactness of the turbomachineries and heat exchangers and (3) simpler cycle layout at an equivalent or superior thermal efficiency. However, these benefits can be still utilized even in the watercooled reactor technologies under special circumstances. A small and medium size water-cooled nuclear reactor (SMR) has been gaining interest due to its wide range of application such as electricity generation, seawater desalination, district heating and propulsion. Another key advantage of a SMR is that it can be transported from one place to another mostly by maritime transport due to its small size, and sometimes even through a railway system. Therefore, the combination of a S-CO2 Brayton cycle with a SMR can reinforce any advantages coming from its small size if the S-CO2 Brayton cycle has much smaller size components, and simpler cycle layout compared to the currently considered steam Rankine cycle. In this paper, SMART (System-integrated Modular Advanced ReacTor), a 330 MWth integral reactor developed by KAERI (Korea Atomic Energy Institute) for multipurpose utilization, is considered as a potential candidate for applying the S-CO2 Brayton cycle and advantages and disadvantages of the proposed system will be discussed in detail. In consideration of SMART condition, the turbine inlet pressure and size of heat exchangers are analyzed by using in-house code developed by KAIST–Khalifa University joint research team. According to the cycle evaluation, the maximum cycle efficiency under 310 ◦ C is 30.05% at 22 MPa of the compressor outlet pressure and 36% of flow split ratio (FSR) with 82 m3 of total heat exchanger volume while the upper bound of the total cycle efficiency is 37% with ideal components within 310 ◦ C. The total volume of turbomachinery which can afford 330 MWth of SMR is less than 1.4 m3 without casing. All the obtained results are compared to the existing SMART system along with its implication to other existing or conceptual SMRs in terms of overall performance in detail. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The steam-Rankine cycle was the most suitable power conversion system for a water cooled reactor for more than 60 years. It has demonstrated a good efficiency and system reliability when the reactor operating temperature is below 350 ◦ C. Nowadays, gas Brayton cycles, especially supercritical CO2 (S-CO2 ) cycle, come

∗ Corresponding author at: Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology 373-1 Guseong-dong Yuseonggu, Daejeon, 305-701, South Korea. Tel.: +82 42 350 3829/+971 0 2 5018519; fax: +82 42 350 3810/+971 0 2 4472442. E-mail addresses: [email protected], [email protected] (H.J. Yoon), [email protected] (Y. Ahn), [email protected], [email protected] (J.I. Lee), [email protected] (Y. Addad). 1 Tel.: +82 42 350 3829; fax: +82 42 350 3810. 2 Tel.: +971 0 2 5018519; fax: +971 0 2 4472442. 0029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2012.01.014

into the spotlight with an emergence of Gen-IV reactor systems. As various coolants such as helium, carbon dioxide and sodium are considered for Gen-IV reactor systems, the maximum operating temperature of these reactor systems is now increased above 350 ◦ C to achieve higher efficiency than the past. In the case of high temperature reactors over 500 ◦ C, the S-CO2 cycle has been consistently confirmed that it will demonstrate better efficiency than the (super-heated) steam-Rankine cycle or even than the helium Brayton cycle at equal operating temperature. The S-CO2 cycle also has a simple layout and relatively smaller component size compared to other power conversion cycles with the help of printed circuit heat exchanger (PCHE) technology. These advantages may result in lowering the capital cost and overcoming any physical size restriction. These advantages can also bring a reduction to the construction period and make S-CO2 cycle economically more feasible (Dostal et al., 2004).

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Brayton cycle) will be discussed with main parameters like cycle efficiency and the size of components in detail.

Nomenclature AR CL c Deq f h Hte S tte Y Z ˇ    ω

blade aspect ratio lift coefficient chord length of blade equivalent diffusion ratio function from the radial equilibrium equation blade height tailing-edge boundary layer shape factor pitch length tailing-edge blade thickness energy loss coefficient for turbine loading factor relative angle Stagger angle blade solidity momentum thickness pressure loss coefficient for compressor

In recent years, a small and medium size reactor (SMR) is gaining attention from the technical community in parallel with Gen-IV reactor systems. A SMR which has its capacity around 50–300 MWth is consisted of small and modularized components. Comparing to conventional large capacity reactors, these smaller in sizes bring high mobility and a reduction in construction period. Furthermore, slightly lower efficiency of SMRs can be compensated by various utilizations of nuclear energy like seawater desalination, district heating and propulsion. However, due to these characteristics of SMRs, coupling SMRs to the S-CO2 cycle can enhance the existing advantages of SMRs, such as reduction in size, capital cost, construction period and so forth. One of the examples for SMRs is SMART (System-integrated Modular Advanced ReacTor), a 330 MWth integral reactor being developed by KAERI (Korea Atomic Energy Institute) for multipurpose utilization, which incorporated all the latest safety features of the pressurized water reactor technology into the design as well as utilizing new technologies such as passive safety, system simplification and modularization, innovations in manufacturing and installation (Lee, 2010). In this paper, SMART is considered as a potential candidate for applying the SCO2 Brayton cycle to improve the existing advantages of SMR, and potential advantages of the combined system (SMART + S-CO2

2. Backgrounds 2.1. Various types of small and medium size reactors As the nuclear power plant becomes larger, the initial investment to construct a large plant increases which results in higher financial risk for a business entity with limited resources. Most developing countries which do not have experience of building the nuclear power plant or countries with small grid size cannot easily afford the large size nuclear power plants. Therefore, they are becoming more interested in a SMR technology which has less risk on financial side and at the same time involves less perturbation to their original electricity grid. A SMR produces electricity of 10–100 MWe . As more and more attention is given to a SMR, each nuclear nation around the world is researching and designing various types of reactors. The SMRs can be classified with their operating coolants such as water, helium, sodium and so on. Table 1 shows several light water typed SMRs currently under development in various countries. Some reactors are based on conventional nuclear power plant technologies with some modifications and adjustments. Other reactors are based on nuclear propulsion technology such as nuclear submarine, aircraft carrier, icebreaker and barge (Kim, 2010). Developing status varies from conceptual design stage to license approval stage. 2.2. SMART (System-integrated Modular Advanced ReacTor) KAERI is developing SMART for various purposes for nuclear energy application. As Fig. 1 shows, the principal feature of SMART is an integrated system which all the components of the primary system that can be potentially sources of accidents were removed and integrated in to the primary pressure vessel by adopting a cassette type steam generator. SMART can be utilized not only for electricity production but also for desalination, and district heating. The thermal power of SMART is now 330 MWth ; if it only produces electricity, its electricity generation capacity is around 100 MWe . If it combines electric generation with desalination, it can produce 90 MWe of electricity and 40,000 tons of fresh water daily. KAERI expects one SMART reactor can supply the electricity and water for a 100,000-person-living city (Lee, 2010). The operating range of

Table 1 Light water reactor typed SMRs under development in nuclear nations. Model

Developer/nation

Planned deployment

CAREM

CNEA & INVAP/Argentina

Northwestern Formosa Province of Argentina

MWe

IRIS

Westinghouse/USA

KLT-40

OKBM/Russia

MRX mPower

JAERI/Japan Babcock & Wilcox/USA

After shut-down of IRIS project Under development of SMR based on AP1000. Under construction near to Vilyuchinsk/complete date (expect): 2012 – Clinch River Breeder Reactor in Oak Ridge

NuScale

Nuscale Power/USA

–

NP-300

Technicatome (Areva)/France

Developed for submarine power supply

100–300

SMART

KAERI/Korea

–

100

VK-300

Atomenergoproekt/Russia

Kola and Primorskaya in the far east/Start operating 2017–2020

300

27

200 35 30–100 125

45

Status Completion of conceptual design, thermo-hydraulic, performance test. Plan to build a prototype Under development Proven by icebreaker Plan to use a different purpose. Under development Under NRC pre-application License approval: 2012 Constructing date: 2015 Domestic supply of components Under NRC pre-application License approval: 2012 Operating date: 2018 Development completion for submarine power supply Applied for DA: 2010 Plan of license approval: 2012 BWR type. Plan to operate 2017-2029

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Fig. 1. SMART reactor developed by KAERI (Lee et al., 2009).

SMART is as same as conventional PWR, which is 315 ◦ C and 15 MPa at primary side. It has cassette typed steam generator having 59 m3 volumes inside an integrated loop. 2.3. Supercritical CO2 (S-CO2 ) Brayton cycle A Brayton cycle operating fluid is at single phase (mostly gas) and is consisted of compressors, heat exchangers, and turbines. The Brayton cycle is generally used in gas turbine technologies for power generation purpose or aircraft propulsion, which is generally an open cycle. However, for a nuclear application the closed Brayton cycle is necessary to reduce risks of public exposed by an accidental release of radioactivity from a nuclear power plant. During the development of the next generation reactor technologies the helium Brayton cycle has been the most studied gas Brayton cycle. However, to gain economy, it requires over 900 ◦ C of high operating temperature, which is suited for high temperature heat source application. Under this condition, most structural materials face significant challenge to have reliable performances. If any cycle can be competitive in a wide range of operating temperature with reasonable efficiency, it can be applied not only to the next generation reactors but also to the current reactor systems as well (Dostal et al., 2004). In 1967, Feher compared several fluids such as ammonia, carbon dioxide, water for the application of the supercritical fluid cycle and found out that CO2 is the most appropriate candidate in a view of moderate temperature range, chemical stability and corrosiveness (Feher, 1967). Dostal analyzed several CO2 characteristics and noticed that the density is high and the compressibility is low near the critical point. Therefore, if the cycle is composed to take advantage of these characteristics, the total thermal efficiency becomes higher because the work in a compressor decreases and the work output from a turbine increases. However, the specific heat changes dramatically and that influences the inlet and exit temperatures of heat exchangers, therefore a special consideration of the heat exchanger design is required (Dostal et al., 2004). Reviewing the past study of S-CO2 cycle, recompressing cycle had been selected as the most promising option. Fig. 2 is

Fig. 2. The cycle efficiency comparison reconstructed from works of Dostal et al.

reconstructed from Dostal’s works. It shows efficiencies of superheated steam cycle, supercritical steam cycle, helium Brayton cycle with two inter-coolers and supercritical CO2 recompression cycle. The advantages and identified issues for coupling the S-CO2 cycle to SMRs are: (1) High efficiency: Many researchers compared the S-CO2 cycle efficiency under high temperature condition for the next generation reactors. As Fig. 2 shows, S-CO2 cycle always shows higher efficiency than selected helium cycle and comparable efficiency with superheated steam cycle in certain temperature range (Dostal et al., 2004). However, one point that has to be stressed in Fig. 2 is that below 350 ◦ C there is no calculated efficiency for comparison. Since our interest is in the range of 310 ◦ C (core outlet temperature of SMART or less for other water cooled SMRs), an analysis for estimating the efficiency is necessary since the trend of efficiency with respect to turbine inlet temperature shows a non-linear behavior. (2) Compactness of turbomachinery: S-CO2 cycle that shows high efficiency does not need large components such as low pressure turbines in a steam cycle. From Ref. Dostal et al. (2004), it was already demonstrated that the size of a turbine in the S-CO2 cycle is the smallest compared to those of steam and helium cycles. Because the S-CO2 cycle has higher operating pressure than the steam cycle, its fluid density is high and its turbine shows very compact size as much as one tenth of a steam cycle turbine. As the fluid is compressed near the critical point, the size of a compressor is much smaller than that of a helium cycle compressor and becomes comparable with a pump in the steam cycle. In summary, although the S-CO2 cycle operates with supercritical gas, the size of turbomachinery is very compact. However, the advantage of turbomachinery sizes have to be re-calculated and verified for the case of coupling the S-CO2 cycle to a SMR, since the turbine inlet temperature has changed which results in different cycle operating conditions.

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Fig. 3. The layout of S-CO2 recompressing Brayton cycle.

3. S-CO2 cycle coupled with SMART 3.1. Cycle layout and analysis method This study will be mainly based on the S-CO2 recompressing cycle coupled to SMART as shown in Fig. 3. In the cycle, S-CO2 flows to a turbine after absorbing heat from the reactor through IHX (intermediate heat exchanger) (point 1). After generating electricity, the fluid goes through high temperature recuperator (HTR) and low temperature recuperator (LTR) (points 2–4) and the flow is divided: one goes to a precooler (PC) where the remaining heat is rejected to the surrounding and the other goes to a recompressing compressor (points 4–8). The reason why the flow is sent to a recompressing compressor is to save rejected heat and increase the total thermal efficiency of the cycle. After the precooler, S-CO2 goes to the main compressor (points 5–6). Then, the fluid receives heat from the low temperature recuperator (point 7) and two flows merge before entering the high temperature recuperator (points 8–9). After the high temperature recuperator, the fluid is transported to the reactor (point 10) and the total process begins all over again. In order to assess the S-CO2 recompressing cycle coupled to SMART an in-house code developed by KAIST (Korea Advanced Institute of Science and Technology) research team (Jeong et al., 2010) was modified to estimate the proposed system performance. This code has several subroutines for each component such as a turbine, a compressor and a heat exchanger. This code can optimize cycle operating conditions for given layout by maximizing thermal efficiency of the cycle. The total mass flow rate of the cycle is determined from the calculated temperature and pressure of each component. Since the detailed structure and the verification of the cycle code were already well

summarized in Ref. Jeong et al. (2010), it will not be repeated here in detail. Even though the turbomachineries in the S-CO2 cycle are expected to be compact, the volume of S-CO2 heat exchangers can be larger compared to water heat exchangers due to: (1) inherently less heat transfer capability of the fluid itself, (2) single phase heat transfer shows smaller heat transfer capability than two phase heat transfer (e.g. steam generator vs. IHX), which can compromise the advantage rooting from the cycle physical size. With this aspect, a PCHE is introduced instead of conventional IHX. Therefore, the size of each heat exchanger is estimated as well as the efficiency of the total cycle. In the adopted cycle layout, there are several heat exchangers: IHX, HTR, LTR and PC. All these heat exchangers are assumed to be PCHE type, since PCHE was considered to be one of the best solutions for reducing the size of gas to gas heat exchanger in the previous work (Dostal et al., 2004). The size of each heat exchanger was reduced from the heat exchanger design from the previous work (Jeong et al., 2010) by reflecting the amount of power handled by the cycle. In the cycle code, a heat exchanger performance is estimated by dividing the channel into a number of given meshes. This is because the S-CO2 Brayton cycle experiences a dramatic change of fluid property, it cannot be fully analyzed through a simple log-mean temperature difference method. Temperature and pressure in each mesh are determined by considering heat transfer and friction pressure drop. Heat transfer coefficient is determined from Dittus-Boelter type correlation developed by Ngo et al., which is suited for PCHE type channels. The friction factor is also adopted from the same Ref. Ngo et al. (2007). Regarding the geometry of PCHE, channel diameter is 2 mm, gap of channel is 0.4 mm, and the thickness between hot and cold

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Table 2 Design specification of the S-CO2 cycle in SMART condition. Reactor outlet temperature (K) Max pressure (MPa) Precooler water side inlet temperature (K) Precooler water side outlet temperature (K) Flow split ratio

583.15

Turbine pressure ratio

1.88089

15 300.15

Turbine efficiency Compressor efficiency

0.9 0.89

305.15

0.89

IHX pressure drop (MPa)

0.13

Recompressing compressor Efficiency Precooler water side Pump efficiency Electric generator efficiency

0.3

0.75 0.98

channel is 1.5 mm. A PCHE was also designed on the basis of 0.1 MPa pressure drop within the channel. From these assumed design conditions, the effectiveness of PCHE is still over 98% (Heatric) and maximum temperature difference between reactor outlet temperature and turbine inlet temperature was held below 2 ◦ C. 3.2. Reference layout and operating points Initial preliminary design parameters were obtained through a sample calculation based on previous works (Dostal et al., 2004; Jeong et al., 2010) and these obtained results are set as the reference design values for this study. The reference design conditions are shown in Table 2 and reference design results are shown in Table 3. The parameters that authors think which represent realistic values and are taken from the previous works are: IHX pressure drop and efficiencies of turbomachineries in Table 2. These parameters will be investigated separately in the future to incorporate more realistic component design and to predict the performance of the proposed system better. The reference design result shows that the proposed cycle thermal efficiency is around 28.5%. This value is not far from the value we can expect from Fig. 2. The operating conditions at each point are indicated in Fig. 3 as well as in Fig. 4 in terms of temperature, pressure and entropy. 3.3. Ideal cycle analysis for the coupled system Before optimizing the cycle operating conditions, the upper bound of the combined system was evaluated by simply assuming all the components in the cycle are ideal to identify impact of realistic components on the cycle efficiency. For ideal cycle analysis, following assumptions were made. The first assumption is that there is no pressure drop through heat exchangers and 100% of the effectiveness between hot and cold channels, which is the definition of an ideal heat exchanger. The second assumption is that the process in turbomachineries is reversible adiabatic process, i.e. ideal turbomachinery. The third assumption is that since the efficiency of Brayton cycle can be sensitive to the pressure ratio as well as operating temperature range, the cycle efficiency will be evaluated with varying cycle pressure ratio with fixed minimum pressure at 7.7 MPa (main compressor inlet). The reason for a fixed Table 3 Reference results of the S-CO2 cycle in SMART condition. Thermal efficiency

28.5%

Volume of precooler (m3 )

21.6

Turbine work (MW) Recompressing compressor work (MW) Main compressor massflow (kg/s) Total massflow (kg/s)

164.6 44.3 1336.6 2193.2

Volume of H-T recuperator (m3 ) Volume of L-T recuperator (m3 ) Main compressor work (MW) Pump work (MW) Recompressing compressor massflow (kg/s) Recompressing fraction

24 36 24.8 0.23 856.6 39.1%

Fig. 4. (a) Pressure–temperature diagram of the Temperature–entropy diagram of the coupled system.

coupled

system.

(b)

minimum pressure is due to the dramatic change of CO2 properties near the critical point (Dostal et al., 2004). Thus, the inlet condition of main compressor is fixed at 305.15 K and 7.7 MPa for all the calculations. The cycle pressure ratio is defined as the ratio of the main compressor outlet pressure to the inlet pressure and the investigated pressure ratio range is from 1.7 to 3.2. This corresponds to the range of maximum cycle pressure from 13 MPa to 25 MPa. The recompressing fraction is defined as the ratio of the main compressor mass flow rate to the total mass flow rate in the cycle. Fig. 5 shows the trend of the cycle efficiency vs. the pressure ratio for ideal cycle assumption, while heat exchanger volumes, recompressing fraction, compressor inlet pressure and temperature are fixed at constant with reference values mentioned above. The total cycle efficiency increases steadily with increasing pressure

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Fig. 5. Total cycle efficiency and mass flow rate for ideal cycle analysis.

ratio since the net work produced by turbomachineries gradually increases, while the CO2 mass flow rate decreases due to the heat balance. The upper bound of total cycle efficiency is varying from 32% to 37% when the outlet pressure of compressor is changing from 13 MPa to 25 MPa. The case of ideal turbomachinery shows better efficiency than that of ideal heat exchangers. In other words, the benefit from improving the performance of turbomachinery from the reference design is more important to enhance the system efficiency than to improve the effectiveness of heat exchanger from the reference point. 4. Optimization of S-CO2 recompressing cycle This chapter explains the optimization process of the proposed design. The optimized values are: (1) cycle pressure ratio, (2) length of heat exchangers (recuperators and precooler) and (3) flow split ratio (FSR). 4.1. Pressure ratio The optimization of cycle pressure ratio is the first step to design a Brayton cycle (Dostal et al., 2004). Unlike the ideal cycle realistic turbomachineries efficiency, heat exchanger effectiveness and pressure drop must be taken into the consideration. The turbomachineries efficiency varies with the type, design and the pressure ratio (Wang et al., 2005), but it is assumed to be constant in this study and the values are specified in Table 2. There are two reasons why the pressure ratio of the proposed system has to be investigated: (1) change of the turbine inlet temperature and (2) safety of the SMR primary system. For the first reason, since most of the previous studies focused on coupling the S-CO2 cycle to the next generation reactor system with high turbine inlet temperature (above 500 ◦ C), the optimum pressure ratio is found for that particular operating condition. Thus, for the newly proposed system the effect of pressure ratio on the cycle efficiency has to be re-calculated to confirm the optimal pressure ratio with lower turbine inlet temperature (around 310 ◦ C). The second reason is due to the fact that most of previous conventional safety systems of

Fig. 6. Cycle efficiency and mass flow rate by pressure ratio and volume effect.

PWRs and SMRs are based on the primary side coolant insurgent to the secondary side when there is a steam generator tube rupture while the proposed system can have reversed situation if the S-CO2 cycle maximum pressure is over the primary side pressure (15 MPa). Therefore, if there is no significant impact on the cycle efficiency even though the maximum pressure of the S-CO2 cycle is lowered below the 15 MPa, similar safety systems design and operation philosophy can be maintained. The calculation result shows that the optimal cycle efficiency is 29.85% at 22 MPa of the compressor outlet pressure and 30% of flow split ratio as shown in Fig. 6. When the compressor outlet pressure is 15 MPa, the efficiency reduction is only 2.4% compared to the maximum efficiency at 22 MPa. It is observed from Fig. 6 that the cycle efficiency is not significantly influenced by the pressure ratio when the performance of turbomachinery is fixed and the pressure ratio of the cycle is over 2, which is consistent with the observation from Dostal et al.’s work (Dostal et al., 2004). For the safety purpose mentioned above, if the maximum pressure of the S-CO2 cycle limited under the primary side pressure of SMART (15 MPa), the cycle efficiency is only decreased by 2.4%, even though the maximum pressure decreased over 7 MPa from the optimum pressure at 22 MPa. To understand why optimum pressure ratio exists for the SCO2 Brayton cycle, the power production and consumption from each turbomachinery are analyzed for different pressure ratio. Fig. 7 shows the effect of pressure ratio on the total net power production of the cycle along with power production of turbine, and power consumptions of main compressor and recompressing compressor. It is noted that for the given condition, the water pumping power does not have a significant impact on the total net power produced, since the compressor inlet conditions are fixed above critical conditions. Therefore, the water pumping power is neglected from Fig. 7. The optimal pressure ratio exists due to two competing effects. The first effect is the increase in the power production from the turbine when the pressure ratio is increased and the second effect is the increase in the power consumption from two compressors when the pressure ratio is increased. After 22 MPa compressor outlet pressure the increase in compressor power consumption

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Fig. 7. The effect of pressure ratio on power of turbomachineries.

exceeds the increase in power production from the turbine due to increase in the cycle pressure ratio, and before 22 MPa the situation is reversed. This observation was similarly made by previous work as well (Dostal et al., 2004). Thus, this result demonstrates that the optimization result for higher turbine inlet temperature reactor system application can be repeatedly used for the proposed system in this paper, since the impact from non-linear CO2 property variation on the power cycle performance is very similar regardless of the turbine inlet temperature. However, even though the trend is similar, the total effect of pressure ratio on the cycle for the proposed system is milder than the system of high turbine inlet temperature. 4.2. Heat exchanger geometry The effect of heat exchangers’ total volume on the total cycle efficiency is shown in Fig. 6 as well. Each individual heat exchanger volume was reduced or increased from the reference design by 10% respectively by decreasing/increasing the total number of channels in the PCHE type heat exchanger. The cycle efficiency becomes higher as the heat exchanger heat transfer area increases. This result implies that even at 15 MPa cycle pressure, further optimization of the cycle through component sizing can increase the total cycle efficiency which can be comparable to the current SMART thermal efficiency 30.3% with steam-Rankine cycle (Chang, 2002). In other words, if the reference configuration is re-optimized for the lower pressure ratio, the decrement of the cycle efficiency can be further reduced. Therefore, the impact of coupling S-CO2 cycle to SMRs can be minimized while the cycle efficiency is maintained at reasonable value. As shown in Fig. 6, the total cycle efficiency is slightly affected by volume of heat exchanger. A larger volume of heat exchanger brings better efficiency but not much. Thus, geometry with limited volume of HX needs to be well designed to enhance the total cycle efficiency for better cost effectiveness. There are three major components in heat exchangers which are required to be optimized in the proposed system: the recuperator, the pre-cooler and the intermediate heat exchanger. All heat exchangers are zigzag type PCHE which shows high performance of gas to gas heat transfer

Fig. 8. Total cycle efficiency by the different heat exchanger length. (*OL denotes an optimal length).

with a compact size. For the preliminary design of IHX, the calculated parameters showed a performance of 98.59% effectiveness, 0.15 MPa pressure drop, and 13.1 m3 volume for 330 MWth of heat transfer between primary and secondary side. HTR, LTR and PC geometry is also analyzed based on the reference condition. Fig. 8 shows the total cycle efficiency affected by the length of heat exchangers (HTR, LTR and PC). To maintain the same volume as the reference design, the number of channels in the PCHE was reduced while the length is increased proportionally. Thus, the effectiveness and pressure drop increase by increasing the length of PCHE. From the calculation, the optimized length of each heat exchanger is suggested as 0.75 m for HTR, 1.5 m for LTR, and 1.25 m for PC as marked in Fig. 8. 4.3. Flow split ratio The effects of split ratio on the cycle efficiency are analyzed based on the reference condition at 15 and 22 MPa of cycle pressure. The analyzed results with two different pressures are shown in Fig. 9. The split ratio is defined as the recuperated amount of mass flow divided by the total mass flow rate. The optimal flow split ratio is varying with the different pressure ranges. The optimal FSR at 22 MPa is 36% with 30.05% of maximum cycle efficiency while the optimal FSR at 15 MPa is 46% with 29.03% of maximum cycle efficiency. For better understanding, the case of 15 MPa of cycle pressure was mainly focused on following explanation. If the flow split ratio is zero, it means simple cycle layout without recompressing compressor. In the case of no recompressing, the maximum achievable efficiency is only 24%. In the case of ideal turbomachinery and heat exchanger, the total cycle efficiency is increased up to 40% when the flow split ratio is 50%. But in a real system with real components, the maximum efficiency is 29% at 46% of flow split ratio. And, a temperature difference at merging point is 10 ◦ C. The reason why the total efficiency decreases after reaching the maximum efficiency can be explained by works of turbomachineries as shown in Fig. 10. When the recuperated flow rate increases,

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Dostal et al.’s results were based on zero temperature difference at merging points and they used PCHE with straight channel. Meanwhile, Jeong et al. evaluated 5 ◦ C of temperature gap and they applied PCHE with zigzag channel. The zigzag channel typed PCHE was selected for this study and Jeong et al.’s reference values are adopted. The temperature difference is 10 K at 46%. And, the difference is less than 5 K over 48%. Although the cycle efficiency is highest at 46% of the split ratio, 48% of the split ratio is recommended until the thermal striping issue is fully resolved. 5. Turbomachinery design 5.1. Design process

Fig. 9. Cycle efficiency and temperature difference at merging point with varying flow split ratio (15 MPa, 22 MPa).

the total mass flow rate of system also increases. More mass flow rate results in more turbine work. But, as the work consumed by recompressing compressor exceeds the work generated by turbine after 46% of flow split ratio, the net work done by turbomachineries decreases. To optimize the split ratio, the temperature difference at the merging point should be considered as well. The temperature difference can cause thermal striping which can deteriorate long term material integrity (Lee et al., 2009). When more heat is recuperated, the inlet temperature of the IHX becomes higher. From previous research, the temperature difference was less than 5 ◦ C.

The uniqueness for designing S-CO2 turbomachineries is that the property variation within the turbomachineries is far from the ideal gas assumption. Therefore, estimating the enthalpy change or pressure variation within the turbomachineries has to be performed on the basis of real gas properties. The modifications to the ideal gas base turbomachinery design tools to incorporate the SCO2 property variation were already suggested in works of Wang et al. (2005) and demonstrated some success. The KAIST–Khalifa University joint research team has developed an in-house turbomachinery design code based on works of Wang et al. for axial type turbomachineries along with some added new features. All the thermodynamic properties of S-CO2 are calculated from the NIST property subroutines. At the early stage of turbomachinery design, the efficiency of a turbomachinery is dependent on the estimated pressure losses. There are four kinds of primary loss sources. Before further discussion, it should be noted that the experimental data and respective empirical correlation for the pressure losses are not well established for the S-CO2 turbomachineries so far. Recently, the Sandia National Laboratory (SNL) reported preliminary results from a compression loop experiment. According to their results, the observed performance map data agree extremely well with the predictions based on a real gas compressor model up to now (Wright et al., 2010). Therefore, until there are experimental data that indicate current real gas based loss models are incorrect, the most general and widely applicable loss models in the literatures, were selected and used in the design code.First, the profile loss is generated by boundary layer growth and blade wake on the blade surface and is represented by wake momentum thickness, solidity, and flow angle. Lieblein correlations (Lieblein, 1959) are used for estimating the loss of compressor, Balje–Binsley correlations (Balje and Binsley, 1968) are selected for that of turbine. The annulus loss is associated with the end-wall boundary layers, and the secondary flow loss is due to the cascade and trailing vortices. Vavra and Howell’s correlation (Vavra, 1974; Horlock, 1973) are used for predicting the secondary loss and the end-wall loss of compressor. The annulus loss and the secondary flow loss for turbine can be calculated together by Kacker–Okapuu (Kacker and Okapuu, 1982). - Lieblein correlation for profile loss in compressors: ωprofile = 2 ×

te c

 × cos ˇ2



cos ˇ1 cos ˇ2

2

2Hte 3Hte − 1



te  1− Hte × c cos ˇ2

−3 (1)

/c = 0.00138e1.1127Deq

 te + 0.0025 and Hte = 1.26 + where, 0.795(Deq − 1)1.681 - Vavra’s correlation for the secondary loss in compressors:



ωsecond flow = Fig. 10. The work of turbomachinery with varying flow split ratio (15 MPa).

0.04CL2 

cos2 ˇ1 ¯ cos3 ˇ



(2)

H.J. Yoon et al. / Nuclear Engineering and Design 245 (2012) 223–232

231

- Howell’s correlation for end-wall loss in compressors: ωend-wall = 0.02

 S   cos2 ˇ  1

h

(3)

¯ cos3 ˇ

- Balje–Binsley correlation for profile loss in turbine:



t cos2 2 1−(1−Hte ) ∗ − te t



Yp = 1 −

t 1−Hte  ∗ − te t

1 − 2 sin2 2





2

1− Hte  ∗ −



+ sin2 2 1 − Hte  ∗ − tte t

2 

tte t

2

− 1− (1 + Hte )  ∗ −

tte t

 (4)

where * and Hte are the boundary layer momentum thickness and the trailing-edge boundary layer form factor. - Kacker–Okapuu correlation for annulus loss and secondary flow loss in turbine: Ys = 0.0334f(AR)

 cos ˛  2

cos ˇ1

Z

(5)

The design variables are operating conditions, number of stages and flow coefficient, which is the ratio of axial velocity to mean blade rotating velocity. The design variables are modified to avoid excessive aerodynamic loading that can cause stall during nominal operation while the size of each designed turbomachinery was minimized.

Fig. 11. The effect of pressure ratio on tip diameter (TD) and axial length (AL) of turbomachinery.

5.2. Size variation of turbomachinery with pressure ratio Size and actual performance of axial type turbomachineries in the S-CO2 cycle were previously investigated by Wang et al. (2005). Major conclusions drawn from the work are the following: small Mach number; significant gas bending stress; small tip diameter and high hub/tip ratio; wide and thick blades; short blade height and low aspect ratio; high chord Reynolds number; and a flat annulus flare. They are also very compact in terms of dimensions and number of stages, compared to other machines in different type of power conversion systems. As mentioned earlier, the previous research works focused on combining the S-CO2 cycle with the next generation reactor system which operates above 500 ◦ C. In this study, the proposed S-CO2 cycle is combined with SMART which is operating at maximum temperature of 310 ◦ C. Therefore, not only the cycle efficiency and heat exchangers vary from the previous study but also the size of turbomachinery has to be estimated for different condition.The effect of pressure ratio on geometry of turbomachineries between 15 and 20 MPa are shown in Fig. 11. Since all the turbomachineries are designed with fixed tip diameter geometry, the diameter shown in Fig. 11 represents tip diameter for all stages in each turbomachinery. When the pressure ratio was decreased from 2.5 (20 MPa) to 1.9 (15 MPa), both of the diameters and the axial length of turbomachinery are increased. Even though the geometry was enlarged according to the decreasing of pressure ratio, the total volume change of turbomachinery was from 1.1 m3 to 1.4 m3 without casing. As a result, all the turbomachineries can be fitted within 1 m of diameter and 1.6 m of axial length of cylindrical geometry regardless of the pressure ratio. In other words, an entire turbomachinery system fits into volume of 1.4 m3 and it will have considerably less weight compared to the steamRankine system. This means that the whole (balance of plant) BOP can be easily modularized. The effect of pressure ratio on the isentropic efficiency of turbomachinery is shown in Fig. 12 as well. With the decrease of pressure ratio, isentropic efficiency of each component is decreased; that of main turbine reduced from 96.9 to 92.3: that of main compressor from 91.7 to 84.8: that of recompressing compressor from 93.8 to 88.6. However, more detailed analysis regarding the designed turbomachinery has to be followed to validate and identify if the design is sound under all the possible

Fig. 12. The effect of pressure ratio on isentropic efficiency of turbomachinery.

operating conditions and modes of these components. Furthermore, radial type turbomachineries will be investigated to identify the best suitable type for the proposed system during normal operating condition as well as off-design operation. 6. Summary and conclusion The S-CO2 Brayton cycle has higher efficiency (∼40%) and much smaller cycle footprint in high temperature and high pressure operating conditions (∼500 ◦ C, ∼20 MPa) compared to other power cycles. Therefore, previously the S-CO2 Brayton cycle was studied

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for the application of the next generation nuclear reactor system with high operating temperature. However, as it was suggested by KAIST–Khalifa University joint research team, coupling the S-CO2 Brayton cycle to a SMR such as SMART can be another potential option where the S-CO2 Brayton cycle can improve the system performance significantly. In order to assess the potential benefits appropriately, the effects of various operating conditions and design options for cycle components were considered in this paper. Although the cycle was identified to possess better efficiency in high operating temperature region (∼550 ◦ C) previously, still the efficiency of the S-CO2 cycle within SMR operating condition showed a comparable efficiency to the existing steam-Rankine cycle for SMRs (∼30%) at optimum pressure ratio. The evaluated results are summarized as follows: 1. The upper bound of total cycle efficiency with ideal system components is varying from 32% to 37% when the outlet pressure of compressor is changing from 13 MPa to 25 MPa. Improving the performance of turbomachinery from the reference design is more effective to enhance the system efficiency than that of heat exchanger. 2. The efficiency of a cycle with realistic components is not significantly influenced by the pressure ratio when the performance of turbomachinery is fixed, which is consistent with the observation from previous work. The maximum cycle efficiency is 29.85% at 22 MPa of the compressor outlet pressure and 30% of FSR. However, even though the maximum cycle pressure is reduced to the level of SMART primary side pressure 15 MPa, the net efficiency is only reduced by 2.4%, which implies that the S-CO2 cycle can have less impact on the total nuclear system design. 3. The total cycle efficiency is slightly affected by volume of heat exchangers. A larger volume of heat exchanger brings better efficiency but not that significant. When the volumes of heat exchangers are fixed as the reference values which are 24 m3 of HTR, 36 m3 of LTR, and 21.6 m3 of PC, the optimized length of each heat exchangers are estimated at 0.75 m for HTR, 1.5 m for LTR, and 1.25 m for PC. 4. The cycle efficiency can be further decreased by considering the pressure drop due to piping and plenum in a component. However, from a sensitivity study to address the uncertainty in the system pressure drop estimation, it was identified that even the whole system pressure drop was assumed to be two times higher than the calculated value; still the cycle efficiency was reduced by less than 0.3%. Therefore, at current stage the underestimation of the total pressure drop in the proposed system seems to have a limited effect on the system performance. 5. The simple cycle layout without a recompressing compressor at 15 MPa of the compressor outlet pressure can achieve only 24% of the cycle efficiency. Increased recompressing flow leads to better efficiency and less temperature difference at merging point. The maximum cycle efficiency is 29% at 46% of flow split ratio. 6. When the pressure ratio was decreased from 2.5 (20 MPa) to 1.9 (15 MPa), both of the diameters and the axial length of turbomachinery are increased. Even though the geometry was enlarged in accordance with the decrease of pressure ratio, the total volume change of turbomachinery was only from 1.1 m3 to 1.4 m3 without casing. 7. Since the primary side pressure of SMART is at 15 MPa, and the existing system usually postulates primary to secondary coolant insurgence, the effect of maximum S-CO2 cycle pressure reduction to 15 MPa to avoid any impact on the current SMR primary

system design due to the coupling was investigated. As a result, the total cycle efficiency is reduced only by 1.8% when the maximum pressure is at 15 MPa and this can be further improved by optimizing the heat exchanger designs. In conclusion, according to preliminary results we discussed above, potentially the entire BOP system with the S-CO2 cycle can be modularized into a single component, and it can be even fitted inside the SMR pressure vessel while the efficiency is comparable to the current steam-Rankine cycle. This advantage can increase the competitiveness of SMRs by reducing the capital cost further which in turn reduces the financial risk involved, easier operation and management, and provides the possibility to transport the system by various means for various purposes. In the future, more thorough optimization of the proposed system will be performed to enhance the efficiency while reducing the total size of all the cycle components. The transient behavior will be considered as well to identify the characteristic of the proposed system under different operating conditions. Furthermore, the radial turbomachineries will be designed as well to compare pros and cons of both radial and axial turbomachineries for the proposed system. Acknowledgments The authors gratefully acknowledge that this research was financially supported by the Korean Ministry of Education, Science and Technology and by the Khalifa University for Science, Technology and Research. References Balje, O.E., Binsley, R.L., 1968. Axial Turbine Performance Evaluation. Part A- LossGeometry Relationship. Journal of Engineering for Power Transctions of the ASME, 341–348. Chang, M., 2002. Basic Design Report of SMART, Technical Report-2142, KAERI, Korea. Dostal, V., Driscoll, M.J., Hejzlar, P., 2004. A Supercritical Carbon Dioxide Cycle for Next Generation Nuclear Reactors, Thesis, MIT-ANP-TR-100. Feher, E.G., 1967. Supercritical thermodynamic power cycle, Douglas Paper No.4348, presented to the IECEC, Miami Beach, Florida, August 13-17. Heatric homepage. http://www.heatric.com/diffusion bonded exchangers.html. Horlock, J.H., 1973. Axial Flow Turbines: Fluid Mechanics and Thermodynamics. Krieger Pub, pp. 148–176. Jeong, W.S., Lee, J.H., Lee, J.I., Jeong, Y.H., NO, H.C., Kim, J.H., 2010. Potential improvements of supercritical CO2 Brayton cycle by mixing other gases with CO2 . In: Proceedings of NUTHOS-8, The 8th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Operation and Safety, Shanghai, China, October 10–14. Kacker, S.C., Okapuu, U., 1982. A mean line prediction method for axial flow turbine efficiency. Journal of Engineering for Power, Transaction of the ASME 104, 111–119. Kim, K.K., 2010. SMART research and nuclear energy for the ocean utilization. In: KAIST Fusin Forum, Daejeon, Korea, October 6. Lee, W.J., 2010. The SMART reactor. In: The 4th Annual Asian-Pacific Nuclear Energy Forum, California, U.S.A., June 18–19. Lee, J.I., Hu, L.-W., Saha, P., Kazimi, M.S., 2009. Numerical analysis of thermal striping induced high cycle thermal fatigue in a mixing tee. Nuclear Engineering and Design 239, 833–839. Lieblein, S., 1959. Loss and stall analysis of compressor cascades. ASME Journal of Basic Engineering 81, 387–400. Ngo, T.L., et al., 2007. Heat transfer and pressure drop correlations of microchannel heat exchangers with S-shaped and zigzag fins for carbon dioxide cycles. Experimental Thermal and Fluid Science 32, 560–570. Vavra, M.H., 1974. Aero-Thermodynamics and Flow in Turbomachines. John Wiley & Sons, New York, pp. 439–470. Wang, Y., Guenette, G.R., Hejzlar, P., Driscoll, M.J., 2005. Aerodynamic Design of Turbomachinery for 300 MWe Supercritical Carbon Dioxide Brayton Power Conversion System, Topical Report, MIT-GFR-022. Wright, S.A., Radel, R.F., Vernon, M.E., Rochau, G.E., Pickard, P.S., 2010. Operation and Analysis of a Supercritical CO2 Brayton Cycle, SAND2010-0171, Sandia Report.