Two-phase natural circulation in a toroidal loop

This is an experimental study of the overall behaviour of two-phase flow and heat transfer in a closed toroidal loop. Heat input and output are at opposite ends of a diameter. The magnitude of the heat input and the inclination of the loop are the two independent parameters whose influence is determined. Three different regions of operation with phase change are observed. Boiling at the evaporator section can be without bubbling, or with bubbling but with or without liquid carry over. The efficiency of the system as a heat transport device is determined and found to be better under liquid carry over conditions. A simple theoretical model of bubble formation and rise is also discussed.     

Single-phase natural circulation in a tilted square loop

Natural circulation of water in a tilted square loop of circular cross-section is studied in this paper. Heating is by an electrical resistance and cooling through a heat exchanger. Heating and cooling are at opposite sides of the square loop. The natural convection flow is determined experimentally as a function of the heating flux and the tilt angle. Multiplicity of steady-state velocities is experimentally confirmed.

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Einphasiger Naturumlauf in einem geneigten quadratischen Loop

Zusammenfassung In dem Aufsatz wird der Naturumlauf von Wasser in einem geneigten quadratischen Loop mit Rohren kreisförmigen Querschnittes behandelt. Die Beheizung erfolgt über einen elektrischen Widerstand und die Kühlung über einen Wärmetauscher. Heizung und Kühlung sind auf den gegenüberliegenden Seiten des quadratischen Loops angeordnet. Der Naturumlauf wird experimentell als Funktion des Wärmestromes und des Neigungswinkels bestimmt. Es wird die Vielfältigkeit von stationären Geschwindigkeiten experimentell bestätigt.

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Nomenclature Q input heat flow - V fluid velocity - V _m maximum fluid velocity - tilt angle - _c critical tilt angle - T temperature difference     

Thermal hydraulic modeling of a natural circulation loop

 The experiment was carried out on the test loop HRTL-5, which simulates the geometry and system design of a 5 MW nuclear heating reactor. The analysis was based on a one-dimensional two-phase flow drift model with conservation equations for mass, steam, energy and momentum. Clausius–Clapeyron equation was used for the calculation of flashing front in the riser. A set of ordinary equations, which describes the behavior of two-phase flow in the natural circulation system, was derived through integration of the above conservation equations for the subcooled boiling region, bulk boiling region in the heated section and for the riser. The method of time-domain was used for the calculation. Both static and dynamic results are presented. System pressure, inlet subcooling and heat flux are varied as input parameters. The results show that subcooled boiling in the heated section and void flashing in the riser have significant influence on the distribution of the void fraction, mass flow rate and flow instability of the system, especially at low pressure. The response of mass flow rate, after a small disturbance in the heat flux is shown, and based on it the instability map of the system is given through experiment and calculation. There exists three regions in the instability map of the investigated natural circulation system, namely, the stable two-phase flow region, the unstable bulk and subcooled boiling flow region and the stable subcooled boiling and single phase flow region. The mechanism of two-phase flow oscillation is interpreted. Received on 24 January 2000     

Transient heat and mass transfer in a natural circulation loop

Comprehensive work has been performed by theoretical and numerical methods in order to study the steady state, transient and stability characteristics of a double diffusive natural circulation loop. It was found that the behavior of the flow in the system depends on the initial conditions and on the location of the state in the seven-parameter space of the thermal and saline Rayleigh numbers,Ra _T ,Ra _S , the modified Prandtl and Schmidt numbers,Pr, Sc, the dimensionless heat and mass transfer coefficients,H _T ,H _S , and the “aspect ratio” (between the height and width) of the loop, γ. Numerical results are presented here, showing the flow in each of the five regions formed in the stability chart. The steady state solutions include convection (constant velocity flow), conduction (no-flow) and periodic with constant amplitude and frequency. Two main new results were obtained: long term periodic oscillations where the amplitude is not symmetric around the conduction solution, and an overshoot of the velocity in transients before reaching the stable convection solutions. In the monotonic instability region of the conduction solution, convection solutions (constant velocity flow) develop, and in the global stability region the flow decays to the conduction solution (no flow), regardless of the initial conditions.     

Conjugate heat transfer simulation of a rectangular natural circulation loop

In this article, conjugate heat transfer characteristics of a single-phase rectangular natural circulation loop were investigated numerically. Effects of the wall thermal conductivity and the wall thickness on the heat transfer behavior in a circulation loop with fixed geometrical configuration were investigated in detail. The presence of axial conduction through thick and highly conductive loop wall tends to strengthen markedly the buoyancy-induced circulating flow in the loop at lower Ra*.     

An analytical model for the determination of stability boundaries in a natural circulation single-phase thermosyphon loop

In this paper, an extension of previous analyses of natural circulation in a simple single-phase loop is presented. Assuming more general correlations for the friction factor and the heat transfer coefficient, an analytical model describing the system is obtained and a parametric representation of its dynamic behaviour is achieved. On this basis, stability maps can be drawn. A preliminary validation of the analytical model has been carried out by using an independent program developed for the analysis of stability in natural circulation loops. The aim of the present work is to provide a simple analytical tool devoted to the stability analysis of a reference single-phase loop. This model can be applied in a relatively wide range of conditions and regimes to provide benchmark solutions for thermal-hydraulic codes and related nodalisations.     

Two dimensional analysis of transient flow and heat transfer in a natural circulation loop

The transient heat transfer, fluid flow and pressure in a natural circulation loop have been studied under laminar flow conditions. Most studies of these systems have utilized a onedimensional approach which requires a priori specifications of the friction and the heat-transfer coefficients. In the present work the variation of the friction and heat-transfer coefficients are determined. Detailed pressure, temperature and velocity distributions are presented.     

Inlet throttling effect on the boiling two-phase flow stability in a natural circulation loop with a chimney

 Experiments have been conducted to investigate an effect of inlet restriction on the thermal-hydraulic stability. A Test facility used in this study was designed and constructed to have non-dimensional values that are nearly equal to those of natural circulation BWR. Experimental results showed that driving force of the natural circulation at the stability boundary was described as a function of heat flux and inlet subcooling independent of inlet restriction. In order to extend experimental database regarding thermal-hydraulic stability to different inlet restriction, numerical analysis was carried out based on the homogeneous flow model. Stability maps in reference to the core inlet subcooling and heat flux were presented for various inlet restrictions using the above-mentioned function. Instability region during the inlet subcooling shifted to the higher inlet subcooling with increasing inlet restriction and became larger with increasing heat flux. Received on 17 January 2000     

惯性平台稳定回路基于Backstepping的动态滑模控制(英文)

针对带不匹配不确定非线性干扰的惯性平台稳定回路跟踪控制问题,提出了基于backstepping的动态滑模控制方法。首先,建立了惯性平台稳定回路的等价模型,该模型由一个线性模型加上一个不确定的非线性函数组成。然后,基于backstepping方法设计了带渐近稳定滑模面的动态滑模控制器,解决了模型不匹配的问题,并提高了系统的鲁棒性。进而应用Lyapunov稳定性理论证明了所设计的控制器不仅能保证闭环系统的稳定性,而且可以通过选择适当的控制器参数来调整跟踪误差的收敛率。最后,仿真结果表明,基于backstepping的动态滑模控制方法与PID控制方法相比,提高了系统的跟踪精度,增强了鲁棒性。     

Influence of thermal boundary conditions on the dynamic behaviour of a rectangular single-phase natural circulation loop

Natural circulation of distilled water and FC43 has been experimentally investigated in a rectangular loop characterized by internal diameter of 30 mm and total length of 4.1 m. The aim of the present study is to analyse the influence of thermal boundary conditions on the flow regimes inside the pipes and on the stability of the system. The new aspect of the present research is the possibility of tuning the heat sink temperature in a range between −20 °C and +30 °C by means of a cryostat. This kind of analysis could be useful for the design of systems characterized by a wide range of environment temperatures, as for example for aerospatial applications. The other parameters investigated were the heat flux transferred to the fluid, which varied between 0.1 kW and 2.5 kW, and the thermo-physical properties of the working fluid. The system showed both stable and unstable behaviour. In particular, in the case of FC43 the loop was more unstable and it was characterized by higher velocities and frequencies compared to the case of distilled water.It was found that the stability threshold could be crossed by varying only the heat sink temperature, demonstrating the importance of this boundary condition on the dynamics of the system. Different flow regimes and fluid velocities were observed. In the case of steady-state flow, Vijayan’s correlation (Vijayan et al., 2000) was tested and found to give good agreement with experimental data. Linear stability analysis was made following the Vijayan’s model. In particular, the effect of heat sink temperature was considered in the dimensionless Stanton number based on the overall heat transfer coefficient at the heat sink. Finally, Ultrasound Pulsed Doppler Velocimeter (UPDV) was used on a natural circulation loop for the first time, and gave a preliminary validation of the traditional fluid velocity measurement method based on the frequency analysis.     

Experimental investigation on the flow instability behavior of a multi-channel boiling natural circulation loop at low-pressures

Natural circulation as a mode of heat removal is being considered as a prominent passive feature in the innovative nuclear reactor designs, particularly in boiling-water-reactors, due to its simplicity and economy. However, boiling natural circulation system poses many challenges to designer due to occurrence of various kinds of instabilities such as excursive instability, density wave oscillations, flow pattern transition instability, geysering and metastable states in parallel channels. This problem assumes greater significance particularly at low-pressures i.e. during startup, where there is great difference in the properties of two phases. In light of this, a parallel channel loop has been designed and installed that has a geometrical resemblance to the pressure-tube-type boiling-water-reactor, to investigate into the behavior of boiling natural circulation. The loop comprises of four identical parallel channels connected between two common plenums i.e. steam drum and header. The recirculation path is provided by a single downcomer connected between steam drum and header. Experiments have been conducted over a wide range of power and pressures (1–10 bar). Two distinct unstable zones are observed with respect to power i.e. corresponding to low power (Type-I) and high power (Type-II) with a stable zone at intermediate powers. The nature of oscillations in terms of their amplitude and frequency and their evolution for Type-I and Type-II instabilities are studied with respect to the effect of heater power and pressure. This paper discusses the evolution of unstable and stable behavior along with the nature of flow oscillation in the channels and the effect of pressure on it.     

Measurements in a natural convection loop

Fluid temperature measurements are reported for a natural convection loop operating in the steady state regime. Averaged and fluctuating measurements were made for a toroidal thermosyphon oriented in the vertical plane that was heated over the lower half and cooled over the upper half. The measurements were made along the tube diameter at the entrance and exit of the heating sections for heat inputs from 1400 to 8410 w/m². The amplitude of the temperature fluctuations exceeded 10 °C near the inner walls indicating the effects from recirculating flow regions at the entrances to the heating and cooling sections.

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Messungen in einem Kreislauf mit Naturumlauf

Zusammenfassung Es wird über Messungen der Fluid-Temperatur in einem mit freier Konvektion stationär betriebenen Kreislauf berichtet. Die Messungen wurden bei leichten Fluktuationen an einem toroidalen Thermosyphon mit vertikaler beheizter Platte durchgeführt, bei dem die untere Hälfte beheizt und die obere gekühlt war. Die Temperaturenmessungen wurden über den Rohrdurchmesser am Eintritt und Austritt der beheizten Strecke für Wärmestromdichten von 1400-8410 w/m² durchgeführt. Die Amplituden der Temperaturfluktuationen überstiegen 10 K in der Nähe der inneren Wand und zeigten dabei Rezirkulationseffekte der Strömung am Eintritt des beheizten und des gekühlten Abschnitts an.

     

An experimental investigation of single-phase natural circulation behavior in a rectangular loop with Al2O3 nanofluids

In this paper, the natural circulation behavior in a rectangular loop was investigated experimentally with water and different concentration of Al₂O₃ nanofluids (0.3–2% by wt. and particle size 40–80 nm). It was demonstrated that, not only the flow instabilities are suppressed but also the natural circulation flow rates are enhanced with nanofluids. The enhancement in natural circulation flow rate and suppression of instabilities were found to be dependent on the concentration of nanoparticles in water.     

Analysis of flow instabilities at the natural circulation loop DANTON with regard to non-linear effects

The natural circulation loop DANTON at the Dresden University of Technology was designed to investigate the thermohydraulic properties of integrated reactor concepts with a natural circulation driven primary loop. It is not possible to reach a stable two-phase flow in the loop without passing flow instabilities. At an equilibrium of heating and cooling power the flow oscillations can exist at nearly constant frequencies and amplitudes. The oscillating mass flow signal had been investigated by various methods: (a) autocorrelation function, (b) Fast Fourier transformation, (c) estimation of a temporal Liapunov-exponent and (d) reconstruction of the system attractor in a three-dimensional phase space. The selected time-series express a non-linear behaviour, however, they are not chaotic. In comparison to the usual methods the applied analysing methods yield additional information about system frequencies, sensitiveness to disturbances and properties due to non-linear and chaotic behaviour in a natural circulation loop. Received on 17 January 2000     

Steady state and stability characteristics of single-phase natural circulation in a rectangular loop with different heater and cooler orientations

Effect of the heater and cooler orientations on the single-phase natural circulation was studied in a rectangular loop. From steady state considerations, the maximum flow for a specified operating condition is achievable for the orientation with both the heater and the cooler horizontal. However, this orientation is found to be least stable and the orientation with both heater and cooler vertical is found to be most stable. Three oscillatory modes were observed in the experiments, two of which are observable only for certain heat addition paths. A hysteresis (conditionally stable) regime wherein stable or unstable flow can prevail depending on the operating procedure is also observed. Generalized steady state equation valid for all the orientations is possible whereas generalized stability equation is possible for a given orientation and flow direction. Steady state flow rate can be predicted with reasonable accuracy using the generalized equation. The stability map predicted by the generalized equation is found to be highly conservative in that its unstable zone is much larger than that observed in the experiments. Both the linear and the nonlinear stability analyses gave the same stability map for identical initial conditions. With nonlinear analysis, it was possible to reproduce the observed unstable oscillatory modes albeit at significantly different power levels. Also, the predicted limit cycles were significantly different in shape which is attributed to the multidimensional nature of the flow especially during the low flow part of the oscillation cycle.     

Experiments on thermal characteristics of a natural circulation loop with latent heat energy storage under cyclic pulsed heat load

 An experimental investigation has been made of thermal characteristics of a rectangular, annular single-phase natural circulation loop with the inner tube filled with a solid–liquid phase change material (PCM) under cyclic pulsating heat load. A rectangular, annular loop of 150 cm in height and 75 cm in width was constructed with an annular gap of 0.6 cm, within which water was filled. The inner tube of the annular loop was filled with a PCM (n-Eicosene) or air. Under the cyclic pulsating heat load, temperature field within the water-filled annular loop with PCM- or air-filled inner tube was found to evolve into a steady periodic variation for the range of parameters considered. The water temperature and/or its fluctuating amplitude along the heated or cooled sections of the loop with the PCM-filled inner tube were found to be markedly lower than those measured in the loop with the air-filled inner tube under the identical conditions. On the other hand, along the insulated sections of the loop a somewhat minute difference in temporal variations of the water temperatures exists between the loops with PCM- and air-filled inner tube. In addition, at the outer wall along the cooled section, a time-periodic variation of temperature was detected in synchronizing with the pulsating heat load. Parametric effects of varying amplitude and time-period of the pulsating heat input, as well as of varying the inlet coolant temperature of the cooling jacket were investigated. Received on 30 June 2000 The authors are grateful for the support for this study from National Science Council of Republic of China in Taiwan under the Project Nos. NSC87-2212-E006-054 and NSC88-2212-E006-022.     

Experiments in a single-phase natural circulation mini-loop

This study reports an experimental investigation related to a rectangular single-phase natural circulation mini-loop, which consists of two horizontal copper tubes (heat transfer sections) and two vertical tubes (legs) made of copper, connected by means of four glass 90° bends. The loop inner diameter is 4 mm. The lower heating section consists of an electrical heating wire made of nicromel on the outside of the copper tube; the upper cooling system consists of a coaxial cylindrical heat exchanger with a water–glycol mixture, set at controlled temperature and flowing through the annulus. The loop has an imposed heat flux in the lower heating section and an imposed temperature in the cooler. The mini-loop was placed onto a table which can assume different inclinations. The parameters investigated during the experiments were: power transferred to the fluid and inclination of the loop. The preliminary results show a stable behaviour with a steady temperature difference across the heat sinks. It has been confirmed that the fluid velocity is very small (order of millimetres per second).     

The influence of the wall thermal capacity and axial conduction over a single-phase natural circulation loop: 2-D numerical study

 In this paper the natural circulation phenomenon of a differentially heated single-phase natural circulation loop has been numerically investigated. The conservation equations of mass, momentum and energy are solved using a two-dimensional finite difference method. The preliminary results will be presented. The transient and steady-state behavior of the circuit has been investigated. The dependency of the temperature and velocity field on the power input and the wall thermal capacity has been analyzed, as well as the relationship between the most important non-dimensional numbers (Nusselt, Reynolds and the friction factor versus the modified Grashof number). A comparison of the numerical results is made with conventional one-dimensional analysis and with the experimental data. Generally, a good agreement is achieved in the stable region. Received on 17 January 2000     

Navier-Stokes analysis of a circulation control airfoil

The two-dimensional, compressible, mass-averaged Navier-Stokes equations are used to investigate flows about a typical circulation control airfoil. The governing equations are solved using the implicit approximate-factorization algorithm of Beam-Warming with a modified algebraic eddy viscosity model. Results are compared with experimental data, and excellent agreement is obtained. The effects of different jet momentum coefficients and angles of attack on the flow are studied. The mechanism of genenating large lift by circulation control is discussed.     

Investigation of the stability of a natural circulation two-pass boiler

In this paper, the results of a theoretical analysis of the static flow instability, namely the reverse flow, for a two-pass steam generator (see Fig. 1) will be presented. The aim of the work was the development of design criteria to avoid the reversal of flow. To determine the critical heat absorption ratio between the two riser systems of a two-pass boiler several dynamic simulations of a warm start-up of the two-pass boiler with different heat absorption ratios, different heat profiles along the lower heated riser system 1 and modified geometry of the boiler (influence of the flow resistance) are done. On the basis of the results of this investigations it can be shown that for every natural circulation system with unequally heated risers and a common downcomer a special critical heat absorption ratio exists. The investigations clearly indicate that such types of steam generators should be designed only in that way that the operation below the critical heat absorption ratio is possible. The modification of the flow resistance in the riser systems can help to extend the range of stable operation.