Supercritical Natural Circulation Loop Research Articles

Numerical Investigation of Thermohydraulic Characteristics in Supercritical CO2 Natural Circulation Loop with Spatially Varying Temperature

Investigation of thermohydraulic characteristics is highly significant for any natural circulation loop (NCL) applications. The physical properties of supercritical fluids are highly sensitive to temperature when they cross pseudo-critical points. In the current study, steady state thermohydraulic characteristics of NCL with a spatially varying temperature distribution on the source along with different orientations of the source and sink are numerically investigated. A three-dimensional rectangular NCL with a uniform diameter and constant length of source and sink is modeled. The temperature of the sink is held constant, while the temperature of the source varies spatially with local maximum and minimum temperatures. The system performance is investigated for four different operating pressures ranging from 8 to 12 MPa. The mass flow rate is observed to increase with increasing operating pressure for all orientations and heat load distribution at the source. The results also indicate that heat transfer degrades when the fluid crosses the pseudo-critical point. It has been noticed that spatially varying temperature distribution has a maximum of 48% heat transfer variation compared to the constant temperature distribution. Furthermore, a source or sink located in the horizontal leg performs better than the vertical leg.

Numerical investigation on the impact of circumferentially varying temperature on the buoyancy and heat transfer characteristics of supercritical CO2 natural circulation loop

The non-uniform heating in the supercritical natural circulation loop (SCNCL) and its associated heat transfer behaviour and buoyancy variation are not well understood. Since buoyancy is the primary force that drives fluid motion in the SCNCL, any factor affecting buoyancy will have an impact on overall performance. The present study investigated the circumferentially varying temperature (CVT) at the source, compared it to constant uniform temperature conditions, and examined the associated variation in buoyancy, and heat transfer characteristics. This study establishes a numerical model for a three-dimensional circular cross-section rectangular SCNCL. The SCNCL was examined at different pressures ranging from 8 MPa to 12 MPa, with 1 MPa pressure increments, to cover a wide range of applications. The results indicated that at 12 MPa pressure, the heat transfer rate and heat transfer coefficient decreased by a maximum of 14 % and 50 %, respectively, compared to that of constant uniform temperature. In contrast, the mass flow rate shows minimal variation between the CVT and a constant temperature condition. The fluid density increases significantly at higher pressure, resulting in decreased buoyancy generation in the loop. Therefore, for all cases, velocity increases up to 10 MPa and then begins to decrease. Thus, the peak velocity was observed at 10 MPa pressure. The CVT negatively impacts both horizontal and vertical heater configurations, leading to a reduction in overall performance. Additionally, non-uniform heating has a greater impact on the horizontal heater configuration compared to the vertical heater configuration.

Effect of operating regimes on the heat transfer and buoyancy characteristics of supercritical CO2 natural circulation loop - A numerical study

At present, 82% of global energy is generated by fossil fuels which produce substantial emissions and have a significant impact on the environment. Heat transfer devices play a vital role in enhancing the efficiency of power generation systems and mitigating environmental impact. Among various heat transfer devices, natural circulation loops (NCLs) assume significance due to their simplicity and safety. In the present study, numerical investigations were conducted on three-dimensional rectangular circular cross-section supercritical CO2-based NCL across three distinct operating regimes. These regions include the average temperature of NCL maintained near the widom line (near pseudo-critical region), away from the widom line (higher buoyancy region) and very far away from the widom line (deeply supercritical region). The results indicate that in all regions, there is an increase in both the mass flow rate and heat transfer rate as pressure increases. At a pressure of 14 MPa, the maximum heat transfer rate across all regions is observed. Although the higher buoyancy region exhibits a superior heat transfer rate, the near pseudo-critical region demonstrates efficient heat transfer capabilities. For example, at 11 MPa, the temperature difference in the higher buoyancy region exceeds that in the near pseudo-critical region by 73%. However, the reduction in heat transfer rate in the near pseudo-critical region is only 37% compared to the higher buoyancy regions. For low-temperature applications, the near pseudo-critical region effectively transfers heat. However, in high-temperature applications, the sink temperature should be kept in the liquid-like region to maximize system buoyancy.

The steady behavior of the supercritical carbon dioxide natural circulation loop

The steady state behavior of thermodynamically supercritical natural circulation loops (NCLs) is investigated in this work. Experimental steady state results with carbon dioxide are presented for supercritical pressures in the range of 80–120 bar, and temperatures in the range of 20–65 °C. Distinct thermodynamic states are reached by traversing a set of isochors. An equation for the prediction of the steady state of NCLs at supercritical pressures is presented, and its performance is assessed using empirical data. Changes of mass flow rate as a result of independent changes of thermodynamic state, heating rate, driving height and viscous losses are shown to be accurately captured by the proposed equation. Furthermore, close agreement between the predicted and measured mass flow rate is found when the measured equipment losses are taken into account for the comparison. Subsequently, the findings are put forward in aid of the development of safe, novel supercritical natural circulation facilities.

Dynamic characterization of supercritical natural circulation loop under periodic excitation

Characterization of supercritical natural circulation loop under the influence of periodic power profile has not been explored in open literature, despite the promise of producing intriguing dynamics. Present study employs a one-dimensional numerical model to explore the transients on imposing a sinusoidal excitation on the heater power. The resultant dynamics are found to be strongly correlated with the heat transfer regime. The time period of excitation plays a more dominating role compared to the amplitude in deciding the characteristics. System attains dynamic steady-state and persists with a periodic profile at both low and high power levels. But introduction of natural frequency emanates into flow reversal at power levels within the transition regime. Chaotic oscillations can be identified for an intermediate band of imposed frequency, transforming to bidirectional pulsing at higher time periods. Frequency locking within the chaotic zone and frequency pushing for double-periodic nature is also identified, and the appearance of chaos is substantiated using the Poincaré map.

Experimental study of pressure drop oscillation in a supercritical carbon dioxide natural circulation loop

Pressure drop oscillation (PDO) is a common type of instability in a two-phase system. The PDO may occur in a supercritical fluid system, with limited prior research on the matter. In this study, an experimental study on PDO of supercritical carbon dioxide (S-CO2) in a natural circulation loop has been carried out. The influence of thermal parameters and compressible volume has been investigated. The experimental result shows that PDO occurs in a natural circulation loop of supercritical carbon dioxide. The location and compressibility capacity of the pressurizer greatly impacts the instability characteristics of the natural circulation loop. The large volume pressurizer installed at the outlet of hot section helps to stabilize the system. The amplitude and the period are influenced by the heat flux and the location of the compressible volume. Increasing the heat flux will slightly increase the amplitude and decrease the period. This work helps to clarify the mechanism of PDO of S-CO2 in the natural circulation loop and provides a reference for the safe design and operation of S-CO2 energy conversion systems.

Numerical evaluation of static and dynamic stability characteristics of a supercritical CO[formula omitted]-driven natural circulation loop

The stability characteristics of closed supercritical natural circulation loop has hardly been explored owing to the mathematical complexity and absence of explicit boundary condition. Present numerical study investigates the nature of both static and dynamic instability in a rectangular loop with carbon dioxide as the working medium. Sharp deterioration in the steady-state circulation rate can be observed, consistent to existing multidimensional analyses. Loop exhibits Ledinegg instability for an intermediate range of heater power, characterized by multiple steady-state solutions. Appearance of static instability has been substantiated following the pressure drop versus mass flow rate profiles, leading to the development of the stability maps. Dynamic instability has also been identified by introducing perturbation during transient simulations, and the range of both static and dynamic instabilities conforms well with each other. A novel approach of approximating the location of the stability threshold using time-series data has also been proposed.

Numerical characterization of heat transfer deterioration in supercritical natural circulation loop and role of loop inclination

Thermalhydraulics of any supercritical natural circulation loop (sNCL) is strongly influenced by the choice of operating conditions and geometric configurations, and can experience severe deterioration in heat transfer characteristics and circulation rate under certain situations. Present study focuses on systematic identification of a quantifiable criterion for prior identification of such deterioration in a carbon dioxide-driven rectangular loop, subjected to a wide range of operating conditions and also with particular emphasis on loop inclination. Four distinct regimes of operation have been identified, primarily based on the temperature levels in the adiabatic arms. Operation is desirable to be restricted within the enhanced heat transfer regime, which offers large heat transfer rate and moderate level of fluid temperature. Inclination to vertical lowers the driving potential, thereby reducing the flow rate and forcing an early induction into the deteriorated heat transfer regime. Highest circulation rate corresponds to the heater power capable of equating the average loop temperature to the pseudocritical value at that pressure. Strong thermal asymmetry and density stratification has been observed in the horizontal sections, with local recirculation and non-uniform radial velocity profiles. Buoyancy parameter has been identified as a capable dimensionless quantity to predict the appearance of deterioration a priori. It can also be coupled with the average friction factor to quantify the critical power level, and a correlation has been suggested for the same.

A Study on the Effect of Geometry and Operating Variables on Density Wave Oscillation in a Supercritical Natural Circulation Loop

Nowadays, a prime technology in generation IV nuclear reactors, the supercritical water reactor (SCWR), is the main object of focus. The current article aims to develop a thermal hydraulic numerical model for predicting density wave oscillation (DWO) in a supercritical water natural circulation loop (SCWNCL). A one-dimensional thermal hydraulic mathematical model was developed. The numerical model consists of nonlinear mass, momentum, and energy conservation equations, which were discretized by applying the implicit finite difference technique. The numerical model was validated with experimental results, and numerical simulations were carried out to find the marginal stability boundary (MSB) and draw the stability map for the loop. Further, the effects of geometry (i.e., diameter and hot leg length) and operating parameters (i.e., inlet system pressure and friction factor) on the density wave oscillation of the SCWNCL were analyzed.

Steady-state and nonlinear stability analysis for the feasibility of different fluids in a supercritical natural circulation loop

A numerical model for a supercritical natural circulation loop is developed to examine the flow instabilities by nonlinear stability analysis. The supercritical natural circulation loop is a loop geometry, which is driven by natural circulation with supercritical fluids as a coolant. A mathematical formulation is developed to study the steady-state and transient solution procedure for supercritical natural circulation loop. This mathematical model is then used to perform various parametric studies with different supercritical fluids (water, [Formula: see text], R134a, ammonia, R22, propane, and isobutane). The behavior of all the fluids is analyzed on identical geometrical and operating conditions. A comprehensive numerical study of the nonlinear stability analysis is presented with particular emphasis on the feasibility of various fluids in a natural circulation loop environment. The 50% increment in loop diameter and height increased the stable operating zones and shifted the marginal stability boundary upward respectively by approximately three times and 25–40% of the previous value. However, further increase in diameter and height reduces the increment of stable operating zones; hence the marginal stability boundary shifts upward marginally than the previous value. Furthermore, the marginal stability boundaries are generated to identify the stable and unstable zones for the available geometrical and operating conditions.

Numerical investigation of steady state characteristics and stability of supercritical water natural circulation loop of a heater and cooler arrangements

The present paper studies the thermal-hydraulic behaviour of the rectangular supercritical natural circulation loop (SCNCL) using numerical model of one dimensional. Then the results of this model is confirmed with experimental and benchmark results. Variations with several geometric parameters like loop diameter, riser length, and heater length and operating conditions like heater inlet enthalpy, pressure, friction factor, and inlet and exit loss coefficient on steady-state performance are investigated for various orientations like HHHC, HHVC, VHVC and VHHC of the heater and cooler. The chances of existing static instability (Ledinegg excursion) has been investigated, which reveals that it can arise only in a low inlet enthalpy condition, far from the suggested various orientations of heater and cooler.

Identification of stable zone via linear stability analysis of supercritical water natural circulation loop

A mathematical model for supercritical water natural circulation loop (SCWNCL) is developed to study flow instabilities by linear stability analysis. The SCWNCL is a loop geometry, which is driven by natural circulation with supercritical water (SCW) as a coolant. A mathematical approach is developed to couple thermal-hydraulic (TH) model and neutron point kinetics (NPK) model. This nuclear coupled model is then used to perform a linear asymptotic stability analysis of the steady state of SCWNCL. A comprehensive numerical study of the linear asymptotic stability analysis is presented with particular emphasis on the effects of coupling. As a result of coupling, a transition from unstable to the stable region and vice-versa is observed for some governing parameter values, which is significantly different from the TH model. Furthermore, the stable operating zone’s are investigated by taking appropriate geometrical and operating conditions via stability analysis.

Mathematical modeling and numerical investigation of density wave instability of supercritical natural circulation loop

In present paper, a mathematical model based on the one dimensional nonlinear mass, momentum and energy conservation equations has been developed to study the density wave instability (DWI) in horizontal heater and horizontal cooler supercritical water natural circulation loop (HHHC-SCWNCL). The one dimensional nonlinear mass, momentum and energy conservation equations are discretized by using finite difference method (FDM). The numerical model is validated with the benchmark results (NOLSTA model). Numerical simulations are performed to find the threshold stability zone (TSZ) and draw the stability map for natural circulation loop. Further, effect of change in diameter and riser height on the density wave instability of SCWNCL has been investigated.

Numerical analysis of influence of geometry and operating parameters on Ledinegg and dynamic instability on supercritical water natural circulation loop

In this work a numerical investigation is performed to analyze a rectangular supercritical water natural circulation loop (R-SCWNCL) from thermal-hydraulic point of view with the specific work to predict Ledinegg instability and dynamic instability in a rectangular shape supercritical water natural circulation loop using a thermal–hydraulic model which is based on nonlinear mass, axial momentum and energy conservation equations. The thermal–hydraulic (TH) model has been validated against a result available in the literature. A SCWNCL of rectangular shape is analyzed and numerical simulations are carried out to obtain a marginal stability zone (MSZ) in its operating regime and relevant system. Further parametric studies have been performed to find out the impact of loop riser height (loop height), loop diameter and system pressure on the Ledinegg instability.

Comparative computational appraisal of supercritical CO2-based natural circulation loop: effect of heat-exchanger and isothermal wall

Natural circulation loop (NCL) is a geometrically simple heat transfer device in which fluid flow occurs due to density gradient of loop fluid, induced by the temperature difference between the source and the sink. NCL has an inherent problem of instability caused by the combined effect of buoyancy, friction and inertia forces at varying operating conditions, and hence it requires an elegant solution of instability. The primary objective of the present work is to do a comparative study on the dynamic performance between two different configurations of NCL based on supercritical CO2, i.e. (i) NCL with isothermal heater and a cold heat-exchanger (ISO-CHX), and (ii) NCL with hot and cold heat-exchangers (HHX-CHX). To explore these NCLs, two-dimensional transient computational fluid dynamics studies have been carried out on the stability of supercritical CO2-based natural circulation loop. Results are obtained for different operating pressures and temperatures in the form of mass flow rate and velocity variation with respect to time. Results show the higher instabilities in both side heat-exchanger loop than an isothermal heater with heat-exchanger loop. At a lower rate of heat input at source in the HHX-CHX loop, the mass flow is bidirectional, whereas it is unidirectional in the ISO-CHX loop at all level of heat input. It is also observed that as pressure increases, flow instability also increases. Obtained results are validated with the published experimental and numerical data and found in good agreement.

Influence of geometric parameters on thermalhydraulic characteristics of supercritical CO2 in natural circulation loop

Deterioration of mass flow rate in supercritical natural circulation loops, accompanied by rapid decline in the heat transfer coefficient, is a phenomenon reported both experimentally and theoretically in recent years. It is generally recognised as the consequence of fluid temperature crossing the pseudocritical limit throughout the loop and sets a practicable limit for loop operation. Present study investigates the dependence of such flow-induced deterioration on the associated geometric parameters, with an aim of identifying guidelines for a safer design. Accordingly a computational model of a rectangular loop, with source and sink in opposite horizontal arms, is developed and employed to explore the influence of geometric variables, including diameter, height, width, inclination, corner bends, and heating and cooling lengths and their orientations. Reduction in loop diameter and increase in adiabatic length in the horizontal arms are found to lead towards early initiation of deterioration, while the presence of an optimum loop height is envisaged. Length of heater is predicted to have minimal influence. However, a longer sink is found to be favorable, as that corresponds to a lower level of heat transfer coefficient for identical power supply. Positioning of the source and sink, and the specifications of the corner bends are also observed to impose trivial effect on the overall loop thermalhydraulics, apart from enforcing a pre-defined flow direction and minor centrifugal action respectively. Inclining the loop to vertical results in substantial reduction in the flow rate, owing to lower effective buoyancy, without significantly tampering the initiation of deterioration.

Experimental research and theoretical analysis of flow instability in supercritical carbon dioxide natural circulation loop

In the last decade, supercritical carbon dioxide power cycle has attracted worldwide attention. The characteristics of flow instability are critical for the design and safe operation of supercritical carbon dioxide power cycle. In the present paper, theoretical and experimental study was carried out to investigate the characteristics of flow instabilities in supercritical carbon dioxide natural circulation loop. A new explanation of the mechanism of flow oscillation in supercritical carbon dioxide natural circulation has been put forward. It found that the pressure fluctuation, which resulted from the variation of heat transfer mode, might be amplified under the condition of appropriate non-dimensional pressure drop in supercritical fluids natural circulation loop. Effects of typical thermal parameters on flow instabilities of supercritical carbon dioxide natural circulation were discussed in detail. Results showed that, for supercritical fluids natural circulation system, an increase in the system pressure and the local resistance coefficient in the cold section, and a decrease in the local resistance coefficient in the hot section could enhance the system stability.

Numerical Comparison of Thermalhydraulic Aspects of Supercritical Carbon Dioxide and Subcritical Water-Based Natural Circulation Loop

Abstract Application of the supercritical condition in reactor core cooling needs to be properly justified based on the extreme level of parameters involved. Therefore, a numerical study is presented to compare the thermalhydraulic performance of supercritical and single-phase natural circulation loops under low-to-intermediate power levels. Carbon dioxide and water are selected as respective working fluids, operating under an identical set of conditions. Accordingly, a three-dimensional computational model was developed, and solved with an appropriate turbulence model and equations of state. Large asymmetry in velocity and temperature profiles was observed in a single cross section due to local buoyancy effect, which is more prominent for supercritical fluids. Mass flow rate in a supercritical loop increases with power until a maximum is reached, which subsequently corresponds to a rapid deterioration in heat transfer coefficient. That can be identified as the limit of operation for such loops to avoid a high temperature, and therefore, the use of a supercritical loop is suggested only until the appearance of such maxima. Flow-induced heat transfer deterioration can be delayed by increasing system pressure or lowering sink temperature. Bulk temperature level throughout the loop with water as working fluid is higher than supercritical carbon dioxide. This is until the heat transfer deterioration, and hence the use of a single-phase loop is prescribed beyond that limit.

Numerical modeling of supercritical CO2 natural circulation loop

The objective of this research project is to estimate steady state characteristics of supercritical natural circulation loop (SCNCL) using computational methodology and to compliment on-going experimental investigation of the same at the authors’ organization. For computational investigation, a couple of in-house codes are developed. At first, formulation and a corresponding computer program for the SCNCL based on conservation equations written in 1D framework is developed. Comparison of 1D code results with experimental data showed that, under some operating conditions, there is deviation between computed results and experimental data. To improve predictive capability, it was thought to model the SCNCL using conservation equations in 2D axi-symmetric framework. An existing 2D axi-symmetric code (named NAFA), which was developed and validated for supercritical fluid flow in pipes, is modified for natural circulation loop (NCL) geometry. The modified code, named NAFA-Loop, is subsequently used to compute the steady state characteristics of the SCNCL. These results are compared with experimental data. The steady state characteristics such as the variation of mass flow rate with power, velocity and temperature profiles in heater and cooler are studied using NAFA-Loop. The computed velocity and temperature fields show that the flow is hydro-dynamically and thermally developing at various sections of the loop. Such a situation where in some parts of the loop is fully developed and some other part is developing, is more accurately computed by CFD codes than 1D codes. One-Dimensional codes employ fully developed flow correlations for friction factor and heat transfer throughout the loop, hence show deviation from actual behavior of loop. The advantages and shortcomings of 1D as well as 2D models are discussed in the paper.Steady state characteristics of SCNCL are found to be much different than those of sub-critical low pressure NCLs. The computed steady state characteristics are also compared with Swapnalee correlation for SCNCL. Analysis of temperature fields in SCNCL show the existence of normal enhanced and deteriorated heat transfer regimes as observed by previous investigators.

Working regime identification for natural circulation loops by comparative thermalhydraulic analyses with three fluids under identical operating conditions

Computational investigation for comparative thermalhydraulic analyses of rectangular natural circulation loops is performed to propose a guideline for selecting the working fluid and nature of the loop, subcritical or supercritical, under identical levels of operating parameters like pressure, heating power and coolant temperature. A 3-d uniform-diameter loop geometry is developed with horizontal heating and cooling. Heating is provided in constant heat flux mode, whereas cooling is through a constant temperature sink. Due to favourable thermophysical properties and environmental conformity, water, CO2 and R134a are selected as possible working fluids. Operational parameters are set so as to have sub- to supercritical condition for CO2, supercritical for R134a and single-phase liquid for water. Mass flow rate for supercritical fluid rapidly increases with heater power, when the fluid is allowed to cross the pseudocritical point during its passage through the heater, and exhibits a maxima. Drastic fall in mass flow rate can be observed beyond the maxima, accompanied by a jump in maximum fluid temperature and a rapid decline in sink-side heat transfer coefficient. That can be identified as heat transfer deterioration in supercritical natural circulation loops, a highly undesirable situation from loop safety point of view. Allowable working range of heater power can be enhanced by increasing system pressure and decreasing sink temperature. For any specified set of operating conditions, CO2-based supercritical loops are better choice till the appearance of maxima, whereas single-phase water-based loops are preferable beyond that limit due to consistently-higher level of heat transfer coefficient. R134a can substitute water at higher powers owing to the lesser inventory requirement and similar level of maximum fluid temperature, but may suffer from chemical stability issues.