Natural Circulation Capability Research Articles

Radial Basis Function Surrogate Model-Based Optimization of Small Light-Weight Lead-Bismuth Reactor Core

Owing to their high miniaturization potential and strong natural circulation capability, lead-bismuth reactors have been widely employed for nuclear energy utilization as well as military and civilian applications. However, there is a need to optimize the design of these reactors. To solve the complex high-dimensional nonlinear single-/multiobjective optimization problem of lead-bismuth reactors, we proposed a single-/multiobjective optimization method (termed as RBF-OLHS-NGA/NSGA II method) for optimizing the reactor core, which is based on the radial basis function (RBF) surrogate model (for prediction), orthogonal Latin hypercube sampling, niche genetic algorithm (for single-objective optimization), and nondominated sorting genetic algorithm (for multiobjective optimization). In view of this approach, the design optimization procedure of the lead-bismuth reactor based on RBF (DOPPLER-R) was developed, which combined the reactor Monte Carlo (RMC) code and the steady-state thermo-hydraulic analysis calculation (STAC) code to sample, predict, and optimize reactor core parameters. Furthermore, the single-/multiobjective optimization approach was verified by considering the core fuel loading and active zone volume of SPALLER-4 as the optimization objectives. The results show that the RBF surrogate model can accurately and rapidly predict the core characteristic parameters of lead-bismuth reactors. When compared to the value calculated using the RMC code, the relative error associated with the predicted effective multiplication factor ( <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> </math> ) is within ±0.1%. Compared to the unoptimized values, the single-objective optimized fuel loading reduced by 400 kg, multiobjective optimized fuel loading decreased by 455–493 kg (optimization ratio of 78%–84%), and active zone volume reduced by 166362–182888 cm3 (optimization ratio of 72%–79%). These results prove that the proposed optimization method is feasible, exhibits high efficacy, and can provide new technical ideas for single-/multiobjective optimization of multiphysics, multivariable, and multiconstraint lead-bismuth reactors.

Safety analysis of representative accidental transients for a 100 MWe small modular LBE-cooled reactor

Nuclear energy plays an important role in the green low-carbon energy. The lead-based reactor is one of the most popular small modular reactor types. The pre-conceptual design of a 100 MW(e) small modular lead-bismuth eutectic cooled reactor was developed by Shanghai Nuclear Engineering Research &amp;amp; Design Institute CO., LTD. to meet the market demand of advanced small-scale nuclear plant. Representative accidents were analyzed for the 100 MW(e) small modular lead-bismuth reactor using ATHLET/MOD 3. The result shows that under the design basis conditions, the performance of the reactor can meet the safety criteria with the protection system working normally. The coolant solidification in the primary circuit under these transients should be prevented. Under the design extension condition, the highest cladding temperature is much lower than the melting point. In the unprotected reactivity insertion condition, there may be a short time of local melting of the fuel, which also meet the acceptance criteria. The safety analysis demonstrated the passive safety of the design with the negative temperature coefficient, strong natural circulation capability, and the passive residual heat removal system.

Analysis of fuel performance under normal operation conditions of MicroURANUS: Micro long-life lead-bismuth-cooled fast reactor

An innovative ultra-long-life lead-bismuth eutectic (LBE)-cooled fast reactor called MicroURANUS has been designed to prevent severe accidents. It utilizes the remarkable natural circulation capability of the LBE coolant. Furthermore, it can be operated at 60 MWth without refueling for 30 effective full-power years (EFPY). In this study, the thermal and mechanical performance of the highest linear power rod of MicroURANUS was evaluated by modifying the fuel performance code FRAPCON-4.0, which is the normal operation fuel performance code for light water reactors (LWRs). A plutonium generation model was added to consider changes in the physical properties of the UO2 fuel. Furthermore, mechanical and oxidation models of 15–15Ti were added, and the coolant models were modified for liquid metal. According to the unique design of MicroURANUS, a maximum low linear power density of 12.5 kW/m ensures that the highest linear power rod can operate below the safety limit. A low fuel temperature provides a large safety margin for fuel melting, as well as low-pressure build-up fission gas release. In addition, low inlet and outlet coolant temperatures of 250 and 350°C cause the cladding to display a low degree of swelling (a maximum diametral strain of 1.5%) while maintaining high mechanical integrity with negligible cumulative damage fraction (CDF). The modified fuel performance code for lead-cooled fast reactors exhibited the capability to be utilized for fuel performance evaluation and design feedback of MicroURANUS.

Assessment of Modified RELAP5 MOD3.2 Against LBE Natural Circulation Test Loops

Motivated by the significant natural circulation capability of lead–bismuth eutectic (LBE)–cooled systems, the RELAP5 MOD3.2 code was modified for the analysis of LBE-cooled reactors and non-nuclear systems. The thermo-physical properties of LBE have been incorporated into the code without affecting the code’s original performance; new heat transfer correlations for liquid metal have been implemented. For the purpose of validating the modified code, experimental results of two different LBE natural circulation test loops were compared with the code simulation results. The first one was a natural circulation setup process test at a power of 22.5 kW performed at the Natural Circulation Experimental (NACIE) facility. The simulated inlet and outlet LBE temperatures across the heat source and mass flow rate of LBE agreed well with the test data. The second one was natural circulation conditions under five different power levels conducted at the Natural Circulation Capability Loop (NCCL) facility. The LBE temperature difference and mass flow rate under different power levels predicted by the code were consistent with the experimental data. Generally speaking, the modified code gives acceptable results, and the code could be applied for further LBE systems thermal-hydraulic analysis.

Enhanced safety characteristics of SMART100 adopting passive safety systems

SMART100 is a small sized integral type pressurized water reactor (PWR) with a rated thermal power of (Chung et al., 2015) 365 MW, which adopts various inherent and passive design features to enhance safety. Most of the primary circuit components, such as the core, reactor coolant pumps, steam generators, and a steam pressurizer are contained in a single leak-tight reactor pressure vessel. Due to the integral reactor design, the large pipes connecting the major components are removed. Thus, the possibility of a large break loss of coolant accident (LBLOCA) is inherently eliminated and the natural circulation capability is improved during the transient. Also, SMART100 has inherent design characteristics of the large primary coolant inventory per unit thermal power, low core power density, and increased secondary system design pressure. Due to these design characteristics, SMART100 can enhance the mitigation capability to a wide range of initiating events. In addition to these inherent safety design features, the safety goals of SMART100 are enhanced by the passive safety systems such as the passive residual heat removal system (PRHRS) (Bae et al., 2001) and passive safety injection system (PSIS). To confirm the enhanced safety of SMART100, deterministic safety analyses were performed for the safety related design basis events (SRDBEs). The results of the analyses using an evaluation model of the TASS/SMR-S code and conservative initial/boundary conditions and assumptions show that the acceptance criteria for the fuel integrity, system integrity, and radiation doses specified in the safety review guidelines are well met. Therefore, the passive safety systems of SMART100 adequately mitigate the consequences of all SRDBEs and maintain the plant in a safe shutdown condition without any AC power or operator action for at least 72 h.

Study of Flow and Heat Transfer Characteristics of Lead-Based Liquid Metals in a Turbulent Tube Flow and the Impacts of Roughness

Lead-based liquid metals (LLMs) such as lead–bismuth eutectic (LBE) and lead, are currently the most interesting candidate coolants for fast reactors because of their excellent physical properties, which can improve safety and reduce costs. However, in comparison to other liquid metals, previous research on the flow and heat-transfer characteristics of LLMs has been limited. Therefore, this work carried out flow and heat-transfer experiments in LBE flowing through a circular tube in the Natural Circulation Capability Loop (NCCL) facility. The results show a significantly higher friction factor than that of water flowing in a smooth pipe. Furthermore, the Nusselt numbers were found to be lower than those found in data in the literature for experiments carried out in a smooth tube at low Péclet numbers, while they were higher at high Péclet numbers. Therefore, theoretical analyses were performed for LLMs flowing in both smooth and rough pipes, and the impacts of roughness on the heat transfer of an LLM were examined. The theoretical relations for a smooth pipe and a rough pipe were validated using experimental data from the literature and the results of the NCCL experiments, respectively. The results of the theoretical relation for a smooth pipe fitted the literature data well. The derived theoretical relation for a rough pipe with a relative roughness of 0.004 fitted the NCCL data best. Moreover, it was established from the theoretical analysis that roughness has two competitive impacts on the heat transfer of an LLM: it reduces conductive heat transfer while enhancing convective heat transfer. Because conductive heat transfer is important for liquid metals, even with turbulent flow, a small roughness will lead to heat-transfer deterioration at low Péclet numbers, and it may even deteriorate across the whole typical Péclet-number range. This discovery has important implications for the thermal–hydraulic design of LLM reactors, because corrosion and erosion by an LLM will lead to a rough surface after long operating times.

SPARK-NC: A Lead-Bismuth-Cooled Small Modular Fast Reactor with Natural Circulation and Load Following Capabilities

In this study, a conceptual design was developed for a lead-bismuth-cooled small modular fast reactor SPARK-NC with natural circulation and load following capabilities. The nominal rated power was set to 10 MWe, and the power can be manipulated from 5 MWe to 10 MWe during the whole core lifetime. The core of the SPARK-NC can be operated for eight effective full power years (EFPYs) without refueling. The core neutronics and thermal-hydraulics design calculations were performed using the SARAX code and the natural circulation capability of the SPARK-NC was investigated by employing the energy conservation equation, pressure drop equation and quasi-static reactivity balance equation. In order to flatten the radial power distribution, three radial zones were constructed by employing different fuel enrichments and fuel pin diameters. To provide an adequate shutdown margin, two independent systems, i.e., a control system and a scram system, were introduced in the core. The control assemblies were further classified into two types: primary control assemblies used for reactivity control and power flattening and secondary control assemblies (with relatively smaller reactivity worth) used for power regulation. The load following capability of SPARK-NC was assessed using the quasi-static reactivity balance method. By comparing three possible approaches for adjusting the reactor power output, it was shown that the method of adjusting the coolant inlet temperature was viable, practically easy to implement and favored for the load following operation.

An experimental study on natural circulation flow characteristics under passive IVR-ERVC conditions

In vessel retention (IVR) of molten core debris via water cooling at the external surface of the reactor vessel is an important severe accident management feature of advanced passive plants. During postulated severe accidents, the heat generated by the molten debris relocated to the lower head of reactor pressure vessel needs to be removed continuously to prevent vessel failure.Besides the local critical heat flux (CHF) of outer wall surface which is of the first importance, a stable feature of natural circulation flow and an effective natural circulation capability within the external reactor vessel cooling (ERVC) channel tend to be rather crucial for the success of IVR. Under this circumstance, a full-height ERVC test infrastructure, reactor pressure vessel external cooling II test facility (REPEC-II) was designed and constructed in Shanghai Jiao Tong University (SJTU). During test campaign on the REPEC II facility, the one-dimensional natural circulation boiling flow characteristics with the experimental observation and measurement are investigated under IVR-ERVC conditions.Based on the abundant results acquired in the test campaign, it is attempt to evaluate the ERVC performances and trends under various practical engineered conditions in this paper. From this study, the following conclusions can be made: The influence of different power shapes on the two-phase natural circulation flow is not obvious, while the impact on the resistance characteristics of the outlet section is very significant. Among all the test conditions (power shapes, subcooling, flow path configuration and water level), the resistance characteristics of the outlet section change the most compared with other sections. It is expected that these conclusions may help designers to have a reliable estimate of the impact of some related engineered factors on real IVR-ERVC performance.

Experimental study on the natural circulation capability and heat transfer characteristic of liquid lead bismuth eutectic

The lead-bismuth eutectic(LBE)-cooled nuclear systems have significant natural circulation due to its large thermal expansion. Therefore, the passive safety of the reactor in postulated accidents is greatly improved. Moreover, the flow resistance and heat transfer characteristics are important to natural circulation ability of LBE-cooled system. In this paper, the natural circulation capability, the flow resistance and heat transfer characteristics were experimentally studied in the Natural Circulation Capability Loop(NCCL) facility. The research mainly includes four aspects: 1) start-up process of natural circulation; 2) capability of natural circulation; 3) flow resistance of LBE in an annular channel and 4) heat transfer in an annular channel. The results showed that a significant natural convection flow was generated in the experiment. Due to high thermal expansion of LBE, the natural circulation is quickly established and stabilized. The flow rate of natural circulation depends on the loop resistance and the temperature between heating section and cooling section. In our experiment, the maximum natural circulation flow rate was measured to be ∼0.81 kg/s. A new friction coefficient correlation was fitted and the results is slightly larger than the value calculated by the Blasius formula. For the convection heat transfer of liquid LBE in an annular channel, the heat conduction term is dominant, and the Nusselt number increases with the increase of Peclet number. Fitted experimental correlation of convection heat transfer of liquid LBE in annular channel is given.

Sub-channel analysis for Pb-Bi-cooled direct contact boiling water fast reactor

Pb-Bi-cooled direct contact boiling water fast reactor (PBWFR) featured with a direct-contact heat exchanger between lead-bismuth eutectic coolant and water could significantly simplify the primary system and enhance the natural circulation capability, meeting the potential needs for small modular reactor design. It is of great importance to conduct thermal-hydraulic analysis of the PBWFR core in detail. In this paper, a self-developed SUB-channel AnalysiS code SUBAS is adopted to study the thermal hydraulic characteristics of the PBWFR core. The fidelity and the reliability of the code have been preliminarily benchmarked. With SUBAS, the space grid is studied to figure out its impact on the temperature and flow distributions in each sub-channel. Besides, the application of space grids would increase the pressure drops and decreases the cross flow between adjacent sub-channels. To study the transient performance of the PBWFR core, the power transient and the inlet blockage accident are calculated by SUBAS. The results of the power transient show the cross-flow effect would be weakened in the sub-channel which has higher coolant temperature and larger mass flow rate. For the inlet blockage accident, the results indicate the influence of the small area blockage is relatively weak on the overall performance of the assembly but is significant on the local parameters. With consideration of time and space, the blockage influence only exists in a certain area. This research may provide contribution to the design of PBWFR.

Transient safety analysis for simplified accelerator driven system with gas-lift pump

Owing to remarkable advantage for transmutation of the long-lived nuclear waste, Accelerator Driven System (ADS) is one of the most promising systems in nuclear power field. In this study, the transient analysis of a simplified lead bismuth alloy cooling accelerator driven system with gas-lift pump has been numerically simulated. By using point reactor neutron kinetics equation and related thermal-hydraulic models, TASAR (Transient Analysis of Simplified ADS Reactor) code is developed. The five kinds of transient cases are simulated: Starting gas-lift pump (SG), Unprotected loss of flow (ULOF), Beam interruption (BI), Unprotected transient over current (UTOC), Unprotected transient overpower (UTOP). Meanwhile, the calculation results of TASAR code are validated by the experimental data of NACIE (Natural Circulation Experiment) facility. The analysis is as following: In SG and ULOF conditions, the introduction of gas-lift pump has a remarkable influence of loop natural circulation capability. In BT and UTOC conditions, the short-time beam cutting off and a 100% increase of the external neutron source would not lead to the immediate fuel melting. In UTOP condition, a reactivity jump of 2$ would not lead to the damage of fuel and the cladding. The above numerical results show that, the accelerator and gas-lift pump influence the loop mass flow rate and core temperatures of research system in this paper greatly, and the simplified accelerator driven system with gas-lift pump has a very good safety performance.

Experimental investigation of gas lift pump in a lead-bismuth eutectic loop

The gas lift pump has been used in the development of an Accelerator Driven System (ADS) nuclear reactor instead of mechanical pumps due to its simple mechanical structure. The two phase flow of Lead Bismuth eutectic (LBE)-inert gas in rising pipe could remarkably increase natural circulation capacity. This study aims to evaluate the performance of the gas lift pump and to conduct the relevant parametric study. As a result, the Natural Circulation Capability Loop (NCCL) test facility was designed and constructed. The height of the experimental loop is 4.5 m and the rising height is 3.5 m. The maximum temperature of the loop is 500 °C. The experiments about the gas lift pump in LBE were performed with risers of three different heights. The results showed that the LBE mass flow rate increases rapidly with an increase of argon flow rate when it is less than 300 NL/h. When the argon flow rate is larger than 300 NL/h, the growth of the LBE mass flow rate is reduced. The LBE mass flow rate increased process is accompanied by the transformation of the flow pattern. The variation trend of the LBE flow rate is consistent with the trend of the void friction in the riser. Under the same amount of argon gas injection, the LBE circulation ability increases as the height of the riser increased. Based on the experimental data and drift-flow model of Zuber and Findlay, a new correlation of the void fraction is obtained and the relative error between the calculated and the experimental value is within 30%. The purpose of this study is to reveal the enhancement mechanism of the natural circulation capacity of gas lift pump and to provide experimental data and model support for the design of ADS in China.

Flow characteristics of natural circulation in a lead–bismuth eutectic loop

Lead and lead-alloys are proposed in future advanced nuclear system as coolant and spallation target. To test the natural circulation and gas-lift and obtain thermal-hydraulics data for computational fluid dynamics (CFD) and system code validation, a lead–bismuth eutectic rectangular loop, the KYLIN-II Thermal Hydraulic natural circulation test loop, has been designed and constructed by the FDS team. In this paper, theoretical analysis on natural circulation thermal-hydraulic performance is described and the steady-state natural circulation experiment is performed. The results indicated that the natural circulation capability depends on the loop resistance and the temperature and center height differences between the hot and cold legs. The theoretical analysis results agree well with, while the CFD deviate from, the experimental results.

Development of Natural Circulation Analytical Model in Super-COPD Code and Evaluation of Core Cooling Capability in Monju During a Station Blackout

The capability of natural circulation for core cooling has been evaluated in detail for a station blackout (SBO) event induced by an earthquake and a subsequent tsunami hit. The evaluation was prompted by the accident at the Fukushima Daiichi nuclear power station of Tokyo Electric Power Company. The plant dynamics computer code Super-COPD was used for the evaluation, which has been validated by analyses of preliminary test results on the natural circulation in Monju. As a result, it was concluded that natural circulation of the sodium coolant will enable the decay heat from the core to be removed under such an SBO condition.

Research on enhancement of natural circulation capability in lead–bismuth alloy cooled reactor by using gas-lift pump

The gas-lift pump has been adopted to enhance the natural circulation capability in the type of lead–bismuth alloy cooled reactors such as Accelerator Driven System (ADS) and Liquid–metal Fast Reactor (LMFR). The natural circulation ability and the system safety are obviously influenced by the two phase flow characteristics of liquid metal–inert gas. In this study, LENAC (LEad bismuth alloy NAtural Circulation capability) code has been developed to evaluate the natural circulation capability of lead–bismuth cooled ADS with gas-lift pump. The drift flow theory, void fraction prediction model and friction pressure drop prediction model have been incorporated into LENAC code. The calculation results by LENAC code show good agreement with experiment results of CIRCulation Experiment (CIRCE) facility. The effects of the gas mass flow rate, void fraction, gas quality, bubble diameter and the rising pipe height or the potential difference between heat exchanger and reactor core on natural circulation capability of gas-lift pump have been analyzed. The results showed that in bubbly flow pattern, for a fixed value of gas mass flow rate, the natural circulation capability increased with the decrease of the bubble diameter. In the bubbly flow, slug flow, churn flow and annular flow pattern, with the gas mass flow rate increasing, the natural circulation capability initially increased and then declined. And the flow parameters influenced the thermal hydraulic characteristics of the reactor core significantly. The present work is helpful for revealing the law of enhancing the natural circulation capability by gas-lift pump, and providing theoretical basis of the optimization design of cooling and system safety.

Two-dimensional numerical simulation of single bubble rising behavior in liquid metal using moving particle semi-implicit method

Gas-lift pump in liquid metal cooling fast reactor (LMFR) is an innovative conceptual design to enhance the natural circulation ability of reactor core. The two phase flow characteristics of gas–liquid metal make significant improvement of the natural circulation capacity and reactor safety. It is important to study bubble flow in liquid metal. In present study, the rising behaviors of a single nitrogen bubble in 5 kinds of common stagnant liquid metals (lead bismuth alloy (LBE), liquid kalium (K), sodium (Na), potassium sodium alloy (Na–K) and lithium lead alloy (Li–Pb)) and in flowing lead bismuth alloy have been numerically simulated using two-dimensional moving particle semi-implicit (MPS) method. The whole bubble rising process in liquid was captured. The bubble shape, rising velocity and aspect ratio during rising process of single nitrogen bubble were studied. The computational results show that, in the stagnant liquid metals, the bubble rising shape can be described by the Grace's diagram, the terminal velocity is not beyond 0.3 m/s, the terminal aspect ratio is between 0.5 and 0.6. In the flowing lead bismuth alloy, as the liquid velocity increases, both the bubble aspect ratio and terminal velocity increase as well. This work is the fundamental research of two phase flow and will be important to the study of the natural circulation capability of Accelerator Driven System (ADS) by using gas-lift pump.

Experimental and computational investigation of a natural circulation system in Regional Energy Reactor-10 MW th

A small- and medium-sized nuclear reactor (SMR) has drawn attention because it is used for multi-purpose applications and the SMR has the virtue of being safer than a large-sized nuclear reactor. According to this tendency, the Regional Energy Research Institute for Next Generation (RERI) has been designing a Regional Energy Reactor-10 MW th (REX-10). REX-10 is an integral type pressurized water reactor (PWR), and is designed to remove heat by natural circulation to improve safety. To investigate the natural circulation characteristics of REX-10, we designed a REX-10 Test Facility (RTF) using the scaling law and carried out experiments in two parameters: heater power and primary pressure. The experimental results have shown that the heater power is the most important parameter of the natural circulation behavior. On the other hand, the primary pressure does not show remarkable effect on natural circulation. In addition, MARS code simulation has been conducted to compare the experimental results and its results show good agreement with the experimental data. Finally, evaluation of the capability of natural circulation was conducted. The result of the evaluation shows that the RTF is sufficiently capable of removing the thermal power of this system.

Design and safety optimization of ship-based small nuclear power reactors

Design and safety optimization of ship-based nuclear power reactors have been performed. The neutronic and thermo-hydraulic programs of the three-dimensional X– Y– Z geometry have been developed for the analysis of ship-based nuclear power plant. Quasi-static approach is adopted to treat seawater effect and quasi-static approach is also employed to treat neutronic aspect during safety analysis. The reactors are loop type lead–bismuth-cooled fast reactors with nitride fuel and with relatively large coolant pipe above reactor core, the heat from primary coolant system is directly transferred to water–steam loop through steam generators. The power level is 100–200 MW th and excess reactivity is about 1$. Three types of core were investigated in the optimization process: balance, tall, and pancake with five values of Z– Y size ratio. As the optimization results, the core outlet temperature distribution is changing with the elevation angle of the reactor system. The pancake core type has larger temperature distribution change as the elevation angle changes due to the sea wave. The natural circulation capability is good for safety. However, large driving head of natural circulation may cause large temperature fluctuation as the elevation angle changes.

Experimental study on natural circulation and its stability in a heavy liquid metal loop

Motivated by the increasing interest in heavy liquid metal (HLM) cooled fast reactors and accelerator driven system (ADS), the TALL test facility was designed and constructed at KTH to investigate the thermal-hydraulic characteristics of HLM. In this paper, the HLM natural circulation characteristics in a HLM loop were investigated with experiments in the TALL test facility. The study includes measurements on (1) start-up of natural circulation from different initial conditions; (2) stability of natural circulation; (3) effects of influencing parameters and (4) capability of natural circulation. The experimental data are compared to predictions with a relevant code (RELAP5). Significant natural convection flow was observed in the experiments. It was found that the natural circulation was easily established and stabilized. It took only a few minutes to have a stable natural circulation prevailing from cold conditions. The natural circulation flowrate depends on the loop resistance, and the temperature difference between the hot leg and the cold leg, as determined by the power level and the heat sink capacity. The experiments show that the maximum flowrate for the natural circulation is ∼0.5 kg/s (corresponding to ∼0.5 m/s in the heat exchanger), resulting in heat removal of ∼15 kW from the core tank, which is comparable to the capacity of ∼100 W/cm of the electric heater elements. The preliminary analysis performed with the RELAP5 code is in reasonable agreement with the experimental data.

Natural circulation capability of Pb-Bi cooled fast reactor: PEACER

First-principle calculations were performed to analyze the natural circulation heat removal from the core of a liquid metal reactor (LMR). The lead-bismuth (Pb-Bi) was chosen as the primary coolant for the LMR system. From the single channel analysis the temperature and the pressure drop are calculated along the fuel assembly. The total pressure drop of the core is less than 100kPa due to the large pitch-to-diameter ratio and the small height of the fuel pin. The natural circulation potential is a key characteristics of the LMR design. The steady-state momentum and energy equations are solved along the primary coolant path. The calculations are divided into two parts: an analytical model and a one-dimensional lumped parameter flow loop model. Results of the analytical model indicate that the elevation difference of 4.5m between thermal centers of the core and the steam generators could remove as much as 10% of the nominal operating reactor power. The flow loop model yielded the total pressure drop and the natural circulation heat removal capacity.