Rectangular Natural Circulation Loop Research Articles

A novel magnetohydrodynamic power generation system using low-temperature liquid metal coupled with a rectangular single-phase natural circulation loop

A novel magnetohydrodynamic power generation system using low-temperature liquid metal coupled with a rectangular single-phase natural circulation loop

Linear and Nonlinear Stability Analysis of Molten Salt Natural Circulation Loop

Abstract A molten salt natural circulation loop (MSNCL) has been setup to study the steady-state, transient, and stability characteristics of molten nitrate salt, mixture of sodium nitrate, and potassium nitrate in 60:40 ratios by weight. Natural circulation experiments in a temperature range of 290 °C–600 °C have been performed. A semi-analytical linear model was derived for stability analysis of rectangular natural circulation loops with conventional localized surface heating and cooling. The developed model includes the effect of wall thermal inertia, variable internal heat transfer coefficient, finite secondary side heat transfer coefficient at cooler, and heat losses for predicting the stability map. These effects are incorporated considering their significant role in modeling high-temperature molten salt-based natural circulation systems. The developed model has been first validated with the experimental data of water loop available in literature. The developed model is then validated with the experimental data generated in MSNCL. Validation of in-house developed nonlinear model has also been performed against the same experimental data. The comparison of both linear and nonlinear stability analysis with the experimental data shows good agreement and articulates the importance of various parameters which have been included in the developed model.

Experimental and analytical study on the stability of a low aspect ratio single-phase natural circulation loop coupled to a parabolic trough collector

Use of passive heat transport systems in renewable energy eliminates operator and external power requirements, thereby reducing the cost. Hence, a horizontal heater and horizontal cooler rectangular natural circulation loop (NCL) of low L/D (110) and aspect ratio (0.54) is coupled to a parabolic trough in the present work. Experimental investigations of the loop's steady state and stability characteristics were carried out at various powers corresponding to the solar irradiances using water as the heat transfer fluid. SolTrace was used to determine the heat loads at different direct normal irradiance (DNI) for the selected loop and trough dimensions. The upper threshold for stability was experimentally observed for the first time and reported here. Stability analysis carried out for different loop diameters revealed that the power at which the upper threshold of instability occurs reduces significantly with increase in loop diameter, enabling its observation in the low-pressure low temperature loop employed in the present study. Stabilizing techniques like orifice insertion and loop inclinations were also studied in detail. The results showed stability at higher heat loads (> 350 DNI), while the instability at lower heat loads can be curbed using an orifice (β = 0.5) or a loop inclination (> 4°). The small inclination can eliminate multiple steady state solutions and hence stabilizes the loop. Besides, the reduction in natural circulation flow rate with inclination is much smaller compared to the orifice making its heat transport capability higher. Additionally, the steady state results were validated with 1-D analytical model giving a good match.

Stabilization of single phase rectangular natural circulation loop of larger diameter using orifice plate

Experimental investigations on the dependence of the stability threshold on different operating procedures have been carried out in a uniform diameter rectangular loop with orifice plates. The investigations revealed that there is no unique stability threshold for the different operating procedures with orifice confirming the existence of a hysteresis region just as in the loop without orifice. The hysteresis region can be further categorized into unconditionally stable, conditionally stable and unconditionally unstable regions even with the orifice plates. The stability region is found to increase with the introduction of the orifices. The predicted dimensionless steady state flow rate with orifice is found to be in good agreement with the data. One dimensional linear stability analysis accounting for the effective length of the orifices and elbows have been used to predict the stability map. The 1-D analysis can qualitatively predict the stabilizing effect of the orifice plates. However, the stable experimental data is not well characterized by the stability map predicted by the 1-D linear stability analysis which is attributed to the 3-D nature of the flow, the heat losses and the wall thermal inertia which are neglected in the 1-D analysis.

Effect of geometrical and operating parameters on performance of a rectangular two-phase natural circulation loop

Natural Circulation Loops (NCLs) find application in a wide range of engineering devices and it is often necessary to predict and ensure the performance of such loops under various operating conditions. In this paper analytical expressions are presented in non-dimensional form for steady-state mass flow rate in typical rectangular, two-phase natural circulation loops having Vertical-Heater Vertical-Cooler (VHVC) and Vertical-Heater Horizontal-Cooler (VHHC) configurations. The normalized loop mass flow rates are expressed in terms of several geometrical and operating variables such as, normalized heat input, density ratio, volume/diameter of heater and cooler sections, aspect ratio of loop, inlet subcooling, fractional length of heater and cooler sections, two-phase friction multiplier and the loss coefficient at heater inlet. The analytical mass flow rate expressions are first validated using published data for various loops and shown to reasonably capture the gravity and friction dominated regimes in two-phase pipe flow. Parametric studies are then conducted to elucidate the effect of key variables on steady-state loop mass flow rates. For the chosen geometrical configuration of the loops, the possibility of existence of multiple steady-state solutions is checked for the entire range of values used in this study for each variable. The discussions in this paper are limited to explaining the influence of individual variables by comparing with a base case analysis.

Effect of Geometrical and Operating Parameters on Performance of a Rectangular Two-Phase Natural Circulation Loop

Effect of Geometrical and Operating Parameters on Performance of a Rectangular Two-Phase Natural Circulation Loop

Stability enhancement in large diameter rectangular natural circulation loops using flow restrictors

Single-phase natural circulation loops (SPNCL) finds application in district heating reactors and low-power pressurized water reactors. It is not only adopted as a backup operation mode during accidental scenarios but also as the normal operating mode in several small and medium-sized advanced nuclear power plants. Stable operation is desired in such plants for smooth power generation and hence, the stability analysis of single-phase natural circulation systems assumes significance. The horizontal heater and horizontal cooler combination produce a maximum flow rate for a specific heater power but also is the most unstable compared to other configurations. Out of many instability restraining techniques, the orifice plate has been targeted by very few. The present experimental study focuses on the effect of using orifice plates (β = 0.90, 0.77, 0.64, and 0.51) on the stability of the 38.89 mm diameter rectangular loop with a horizontal heater and cooler configuration. The various operating procedures (start-up from rest, power raise from a stable steady-state, and power step down from an unstable state) have shown different stability/instability thresholds. Further, a hysteresis phenomenon was observed between the operating procedure of power raise from a stable state and the power step down from an unstable state, both exhibiting different stability thresholds. The increase in the stability threshold for β = 0.9, 0.77, and 0.64 for the operating procedure of start-up from rest was 75%, 110%, and 225% respectively compared to without orifice. Since the heater power was limited to 1100 W, the orifice of β = 0.51 was seen to be completely stable for the entire range of all three operating procedures for the same cooler conditions. From the loss coefficient (K), the effective length of the loops for β = 0.9, 0.77, 0.64, and 0.51 increased by 0.36, 1.32, 4.72, and 21.8 m respectively. Accordingly, the steady-state analytical solution with and without orifice found a good agreement with the experimental results. Thus, the present experimental investigations show that with the judicious choice of the flow restrictor, an unstable natural circulation system can be stabilized although the steady-state flow decreases.

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.

Effective utilization of CuO/water nanofluid potential in the natural circulation loop

Nanofluid potential in a rectangular natural circulation loop has been carried out through numerical investigation. A rectangular loop of dimension 110 cm length, 100 cm width in which 90 cm length of the heating and cooling sections is considered, respectively. The loop is filled with water-based CuO nanofluid with volumetric concentrations 1%, 2%, and 3%. Firstly, the validation of experimental results available in the literature is validated using the present numerical model. The potential of CuO nanofluids is utilized subjected to various inlet boundary conditions temperature and mass flow rate of cold and hot working fluids. The results show that CuO nanofluid can enhance the fluid flow and thermal performance of the loop. It is observed that heat transfer enhancement diminished with vol 3% because of dominating buoyancy forces. The study found that enhancement in heat transfer 5.33% and mass flow rate of 21.29% for CuO vol 2% nanofluid than water.

Non-linear dynamics of single phase rectangular natural circulation loop

The future nuclear reactors are being engineered to function completely on the phenomena of thermosiphoning. These reactors are equipped with various natural circulation-based systems which offer several benefits. The linear stability analysis examines the stability for such systems for small perturbations. If perturbations are slightly large, linear stability fails to fathom the stability of the system. In such cases, it becomes imperative to perform non-linear stability analysis. In the present work, a rectangular natural circulation loop has been simulated for small as well as large perturbations to underscore the importance of non-linear stability analysis. The key objectives of the present work include identification of the subcritical Hopf bifurcation and unravelling the repercussions of larger perturbation on the system in each region of the parametric space. The unfolding of dynamics from unstable limit cycles to chaos and then back to stable fixed points have been investigated through numerical simulations.

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.

Investigation of a nanofluid-based natural circulation loop

The Natural Circulation Loop (NCL) has many applications in nuclear and renewable energy systems including solar heaters and geothermal power derivation. Applying nanofluids in NCL has distinctive advantageous, including higher stability and effectiveness of NCL. The present study is a numerical investigation of a rectangular single-phase natural circulation loop utilizing Water, water-based Al2O3, and TiO2 nanofluids as working fluids. Both steady-state and transient simulations are in good agreement with experimental data. The effects of heating power and nanoparticle concentration on the stability and flow transitions were investigated in this study. Flow rate and heat transfer capacity enhancement were significantly observed by applying nanofluids in NCL compared to Water. The comparison of effectiveness factor, temperature difference over heater, and mass flow rate of NCL utilize different working fluids, revealed thermal performance improvement by particle concentration increment, and this is more considerable for the nanofluids containing bigger particle size.

Investigations on the dependence of the stability threshold on different operating procedures in a single-phase rectangular natural circulation loop

During the past years, several studies were focused on the instability of single-phase rectangular natural circulation systems. However, experimental identification of instability threshold and categorization of instability regimes is of prime interest in many industrial applications which have been addressed by very few researchers that too limited to lower diameter loops only. Hence, in the present study, a larger diameter rectangular loop with horizontal heater horizontal cooler (HHHC) configuration has been designed to generate single phase natural circulation data on the steady state and stability behavior. Effect of different operating procedures (i.e., start-up from rest, power raising from stable steady state, and power reduction from an unstable state) on stability behavior are studied. Most of the oscillatory regimes are identified and noticed that the operating procedure can influence the instability threshold. The instability threshold was found to increase with the lowering of the coolant temperature and increasing its flow rate. The operating procedures i.e., power raising from stable steady state and start-up from rest gave the maximum and minimum values of the stability threshold respectively. As opposed to this, the minimum instability threshold in smaller diameter loops was reported for the operating procedure with power reduction from an unstable state. The experimental results confirm the occurrence of the hysteresis phenomenon. Due to the larger diameter and lower Lt/D ratio of the loop, all the oscillatory behaviors were aperiodic in nature in contrast to the observations in smaller diameter loops.

Experimental analysis of four parallel single-phase natural circulation loops with small inner diameter

In this paper, results from a new experimental setup consisting of four rectangular natural circulation loops are presented. The loops are vertically oriented, parallel and connected at the bottom; each one has an independent heat source of variable power and a common heat sink, and are studied under different configurations with varying parameters. The loops are symmetrical with 7 mm inner diameter, using distilled water as the working fluid transporting heat from the source to the heat sink by means of natural circulation. The experimental data are compared with the Vijayan’s correlation showing a good agreement.

Analysis of a single-phase natural circulation loop with hybrid-nanofluid

Abstract A rectangular single-phase natural circulation loop (NCL) has numerous industrial applications such as nuclear reactors, geothermal systems, solar water heating systems, gas turbine blade cooling, electrical machine rotor cooling, and electronic device cooling. To establish the heat transport capability of a NCL, it is important to realize the mass flow rate. Commonly, water has been considered as working fluid. In this paper, a hybrid nanofluid (Al2O3-Cu-water) is considered as working fluid. Firstly, the governing equations are written for the NCL. Then the dimensionless form of governing equations are solved. The influence of cooler length, heater length, tubes diameter, loop height, loop inclination angle, the concentration of nanoparticles, the power of the heater and the type of working fluid on the loop temperature distribution and loop mass flow rate are scrutinized. The results illustrate that the steady-state mass flow rate goes up with augmenting the heater power, the loop height, the loop diameter and the concentration of nanoparticles whereas it abates with rising the loop inclination angle. The results discovered that the steady-state mass flow augments 34.8% if the loop diameter increases 20% at ϕ = 2%. Also, the Reynolds number reaches a maximum value (Ress = 1303.5) at ϕ = 6% for hybrid nanofluid.

Transient thermo-hydraulics and performance characteristics of single-phase natural circulation loop using hybrid nanofluids

Transient analysis of vertical heating and horizontal cooling rectangular single-phase natural circulation loop with various water-based hybrid nanofluids (Al2O3 + Ag, Al2O3 + Cu, Al2O3 + TiO2, Al2O3 + CNT, Al2O3 + Graphene) with 1% volumetric concentration is studied numerically. Temporal fluctuation and time required to attain the steady-state, transient mass flow rate and energy-exergy performance parameters (effectiveness and total entropy generation) using hybrid nanofluids are compared with water. The effect of power input and geometry parameter (diameter and height) of the loop on transient performances is studied as well. The result reveals that the fluctuation of mass flow rate and time required to attain the steady-state are less for hybrid nanofluids as compared to water. However, platelet and cylindrical shaped nanoparticles yield a lower stability as compared to spherical shaped. The mass flow rate is enhanced with hybrid nanofluids, except Al2O3 + CNT and Al2O3 + Graphene, as compared to water. The energy-exergy performance of hybrid nanofluids is higher than water. The maximum increment in mass flow rate is shown by Al2O3 + Ag hybrid nanofluid (3%), whereas Al2O3 + Graphene shows the highest increment in effectiveness (25.4%) and highest decrement in total entropy generation (14.3%) as compared to water. Smaller diameter and lower height of loop are found preferable for the flow stability.

1-D semi-analytical modeling and parametric study of a single phase rectangular Coupled Natural Circulation Loop

The study of heat exchangers with both the hot and cold fluid sides driven by buoyancy forces is an area of considerable interest due to their inherent passivity and non-existence of moving parts. The current study aims to study such heat exchange devices employing the basic Coupled Natural Circulation Loop (CNCL) systems. A one dimensional (1-D) Fourier series based semi-analytical model of the basic CNCL system is proposed. A 3-D CFD validation is performed to validate the developed 1-D model. The non-dimensional numbers such as Grashof number, Fourier number, Stanton number and Reynolds number, which determine the system behavior are identified and a detailed parametric study is performed. Both vertical and horizontal CNCL systems are considered along with the parallel and counter flow configurations. The heater-cooler location greatly influences the behavior of CNCL system. The vertical CNCL always exhibits counter flow configuration whereas the horizontal CNCL system may exhibit parallel or counter flow arrangement depending on the heater-cooler location and initial flow conditions.

Experimental Studies on Nanofluid-Based Rectangular Natural Circulation Loop

The main objective of the present study is to carry out experimental investigation on thermal performance of the nanofluid-based rectangular natural circulation loop (NCL). For this study, an experimental test rig is fabricated with heater as heat source, and tube in tube heat exchanger as heat sink. For the experimentation, three different nanofluids are used as working fluids. The nanometer-sized particles of silicon dioxide (SiO2), copper oxide (CuO), and alumina (Al2O3) are dispersed in distilled water to produce the nanofluids at different volume concentrations ranging from 0.5% to 1.5%. Experiments are carried out at different power inputs and different cold fluid inlet temperatures. The results indicate that NCL operating with nanofluid reaches steady-state condition quickly, when compared to water due to its increased thermal conductivity. The steady-state reaching time is reduced by 12–27% by using different nanofluids as working fluids in the loop when compared to water. The thermal performance parameters like mass flow rate, Rayleigh number, and average Nusselt number of the nanofluid-based NCL are improved by 10.95%, 16.64%, and 8.10%, respectively, when compared with water-based NCL. At a given power input, CuO–water nanofluid possess higher mass flow rate, Rayleigh number and Nusselt number than SiO2–water and Al2O3–water nanofluids due to better thermo-rheological properties.

Numerical and experimental analysis of a rectangular single-phase natural circulation loop with asymmetric heater position

A simple rectangular natural circulation loop (NCL) consists of a heater, a cooler, cold leg and hot leg. The main aim of an NCL is to reject heat from heat sources to heat sinks with the use of a mechanical pump. NCL is used in various energy systems, such as solar heaters, nuclear reactors, geothermal power production and engine and computer cooling. In this study, a simple rectangular single-phase NCL with an asymmetric heater is numerically analyzed with respect to tested experimental data. First governing equations, i.e., mass, momentum, and energy balance equations are derived. Then, these equations are written in dimensionless form with proper definitions of the dimensionless parameters. The boundary conditions of NCL are heater power and cooler temperature that are modeled by modified Grashof number and modified Stanton number, respectively. A continuous friction law is used for numerical solution of governing equations that are applicable for the laminar, transition and turbulent flow regimes. The governing equations are solved for both the steady state and transient. The equations of the transient state are solved with both linear and nonlinear methods. In most of the earlier literature, a stability map has been reported that is only applicable for laminar or turbulent flows. But in the present work, a stability map is obtained, which is valid for all the three regions (laminar, transition, and turbulent). Finally, the experimental data are compared with the numerical results.

A semi-analytical model for linear stability analysis of rectangular natural circulation loops

A semi-analytical model for stability analysis of natural circulation loops (NCL) with conventional localized surface heating and cooling is derived based on linear stability analysis (LSA) methodology. Considerations for local pressure losses, wall thermal inertia and finite secondary side heat transfer coefficient at cooler are given in this model. Heat losses are also incorporated to extend the scope of the model to high temperature loops like those operating with pressurized water, molten salts and liquid metals. A new parameter space is introduced for representing the stability maps. This parameter space gives a direct representation of operating variables and focuses on stability behavior at only feasible (theoretically) operating conditions for a given loop. The model is validated against the experimental data of two rectangular natural circulation loops from literature. The stability maps generated by this LSA model are further verified by simulating the dynamic behavior of NCL at various operating conditions. This is accomplished by numerically solving the non-linear governing equations of NCLs. A study is performed to find the effect of some aspects like wall thermal inertia on stability behavior of natural circulation loops. Local pressure losses and wall thermal inertia are found to have considerable effect on the stability behavior of the loops studied.