Density Wave Oscillations Research Articles

Effect of Liquid Density Differences on Boiling Two-Phase Flow Stability

In order to investigate the effect of considering liquid density dependence on local fluid temperature in the thermal-hydraulic stability, a linear stability analysis is performed for a boiling natural circulation loop with an adiabatic riser. Type-I and Type-II instabilities were to investigate according to Fukuda-Kobori's classification. Type-I instability is dominant when the flow quality is low, while Type-II instability is relevant at high flow quality. Type-II instability is well known as the typical density wave oscillation. Neglecting liquid density differences yields estimates of Type-II instability margins that are too small, due to both a change in system-dynamics features and in the operational point. On the other hand, neglecting liquid density differences yields estimates of Type-I stability margins that are too large, especially due to a change in the operational point. Neglecting density differences is thus non-conservative in this case. Therefore, it is highly recommended to include liquid density dependence on the fluid subcooling in the stability analysis if a flow loop with an adiabatic riser is operated under the condition of low flow quality.

Analysis of External Cooling of the Reactor Vessel During Severe Accidents

An analysis is presented of the integral behavior of the external cooling of a reactor vessel by natural circulation during a severe accident to investigate the feasibility of the in-vessel retention strategy for a high-power reactor by using the RELAP5/MOD3 computer code. It is shown that two-phase flow instability phenomena, including natural-circulation oscillation and density wave oscillations, affect the local thermal margin at the reactor vessel wall. The heat load on the reactor vessel is simplified as a uniform heat flux load of 600 kW/m2 in the base case. A sensitivity study for the effect of the inlet K factor, nonuniform heat flux distribution, inlet flow area, and subcooling of the pool water is performed to evaluate the local thermal margin. The results of the analysis show that natural-circulation cooling is marginal at this level of heat flux. It also clearly indicates that a system level of analysis for two-phase natural circulation, including the sensitivity study on the design parameters, is necessary to ensure successful implementation of the external cooling.

Effects of ship motions on natural circulation of deep sea research reactor DRX

DRX is a very small integral type PWR (750 kW t) for a scientific deep-sea research bathyscaph. The core having a small amount of steam is cooled by natural circulation and pressurized by self-pressurization. During operation of the bathyscaph in a deep sea or near the water surface, a ship inclination or ship motions will affect the reactor behavior. This paper describes the effect of a heeling or a heaving on the thermal hydraulic behavior of reactor system, which is analyzed by retran-02/grav improved so to simulate the effect of ship motions. The dynamics has a feature of nuclear power-natural circulation flow coupling under the condition of external forces. The analysis shows that ship inclination induces the core flow to decrease but reactor power recovers to the initial level without help of the reactor automatic control system. The heaving makes the core flow and the reactor power oscillate in phase with heaving, which are different from a density wave oscillation. Oscillation amplitudes of the flow and the power have peaks at the heaving period of 5 s. The peaks are due to resonance of the natural circulation flow and the heaving. An effective measure to suppress this oscillations due to heaving is to pressurize the primary loop by filling non-condensable gas. The density wave oscillation occurs when the reactor power increases over the rated power, and the boundary of its occurrence is analytically revealed. Under the condition of both density wave oscillation and heaving, the system shows to oscillate with the overlapped effect.

Theoretical and experimental study on density wave oscillation of two-phase natural circulation of low equilibrium quality

A theoretical and experimental study of density wave oscillation (DWO) in natural circulation is presented in this paper. Experiments were performed on a natural circulation test facility. The influences of mass flow rate, pressure, inlet subcooling, heat flux and exit quality on DWO were analyzed. The marginal stability boundary (MSB) of DWO was obtained. A criterion of two-phase natural circulation, which predicts the stability thresholds, was developed by lumped parameter method. It is a function of non-dimensional parameters, such as phase change number N pch, subcooling number N sub, Froude number, Fr, geometry number N l and friction number τ. The geometry number and friction number are first defined in this paper. A correlation of DWO period was also obtained, it is also a function of the above non-dimensional parameters. The results of the present criterion and period correlation were compared with those of the experimental data and references. It is shown that they agree very well.

Theoretical Study on Density Wave Oscillation of Two-Phase Natural Circulation under Low Quality Conditions

A theoretical study of the Density Wave Oscillation (DWO) of a natural circulation loop is presented in this paper. The nonlinear analysis based on the drift flux model is performed. The momentum equation is integrated around a closed loop, and the energy equation is integrated separately for every component. The equations are solved numerically using the Gear method, suitable for solving nonlinear stiff equations, with a newly developed Nonlinear Time Domain Computer Code (NTDCC). The Marginal Stability Boundary (MSB) of DWO of the low Temperature Heating Reactor (THR) designed in China was obtained by NTDCC. The results obtained by NTDCC are in good agreement with the experimental results.

BWR Regional Instability Analysis by TRAC/BF1-ENTRÉE—I: Application to Density-Wave Oscillation

In this study, applicability of the TRAC/BF1-ENTRÉE code to regional instability was demonstrated in two parts. In Part I, fidelity of numerical models was studied with regard to the density-wave oscillation. Based on the FRIGG-4 loop test, predictability of the code has been demonstrated. An appropriate time integration scheme was explored, and it was found that the numerical viscosity can be minimized by applying the semi-implicit method and specifying the material Courant number close to unity. Applicability of the code was studied for simulating parallel channel configurations. The bypass channel effect was quantified as a function of its flow area and power level. The influence of flow mixing at the upper and lower plena was studied.

Importance of Delayed Neutrons on the Coupled Neutronic-Thermohydraulic Stability of a Natural Circulation Heavy Water–Moderated Boiling Light Water–Cooled Reactor

The coupled neutronic-thermohydraulic stability characteristics of a natural circulation heavy water-moderated boiling light water-cooled reactor was investigated analytically considering the effects of prompt and delayed neutrons. For this purpose, the reactor considered is the Indian Advanced Heavy Water Reactor. The analytical model considers a point kinetics model for the neutron dynamics, a homogeneous two-phase flow model for the coolant thermal hydraulics, and a lumped heat transfer model for the fuel thermal dynamics. A higher mode of oscillation having a frequency much greater than the density-wave oscillation frequency was observed if prompt neutrons alone were considered. The occurrence of a higher mode of oscillation was found to be dependent on the concentration of delayed neutrons, the void reactivity coefficient, and the fuel time constant. The core inlet subcooling is found to have different effects on the decay ratio of the fundamental and higher modes of oscillations. The influences of void reactivity coefficient and fuel time constant on the fundamental and higher modes of oscillations were also found to be opposite in nature.

The physical mechanism of core-wide and local instabilities at the Forsmark-1 BWR

During the last 15 years, the problem of BWR instabilities has attracted the attention of a number of researchers. In 1996, an unusual instability event occurred at Forsmark-1 in which superimposed on the classical, fundamental spatial mode oscillations, there were relatively large-amplitude, highly localised oscillations. Subsequent time-series analysis of the local power range monitor (LPRM) signals resulted in very different decay ratios for the two sides of the core (from ≈0.2 to ≈1.0), an inexplicable result. Furthermore, noise analysis-based localisation techniques pointed towards the existence of two strong ‘perturbation sources’ in the two halves of the core, one of them coinciding with the radial position of an unseated bundle. Motivated by these findings and the fact that as was found later, at least one bundle was unseated, the code RAMONA3-12 was used in order to try to simulate these experimental findings, by assuming that in some bundles, there are relatively large amplitude thermohydraulic perturbations. These perturbations (which are in fact density wave oscillations) were excited by modifying the inlet loss coefficients of the bundles in question.

Density Wave Oscillation Beyond Dryout under Forced Circulation.

The objective of the present experimental investigation is mainly to clarify experimentally the threshold of the density wave oscillation beyond the dryout condition of the boiling channels in the case of constant flow rate. The flow instability experiments under forced circulation were conducted with two channels, one holds high power heater bundle up to 6 MW and the other one holds low power heater bundle up to 200 kW. The high power heater bundle consists of 36-rods, which are made of Inconel claddings, Ni-Cr heater elements and BN insulators. In case of raising heating power, the pump rotation was controlled to keep the flow rate. Flow instability threshold was confirmed with the approach that the heating power was raised higher after the dryout of cladding was detected. Three experiments under different flow rate conditions were conducted. As a result, the instability threshold was measured beyond the dryout condition. The measured results were compared with available data. The prediction capability of a thermal hydraulic code was also validated partially by the experimental results.

Theoretical Study on Density Wave Oscillation of Two-Phase Natural Circulation under Low Quality Conditions.

A theoretical study of the Density Wave Oscillation (DWO) of a natural circulation loop is presented in this paper. The nonlinear analysis based on the drift flux model is performed. The momentum equation is integrated around a closed loop, and the energy equation is integrated separately for every component. The equations are solved numerically using the Gear method, suitable for solving nonlinear stiff equations, with a newly developed Nonlinear Time Domain Computer Code (NTDCC). The Marginal Stability Boundary (MSB) of DWO of the low Temperature Heating Reactor (THR) designed in China was obtained by NTDCC. The results obtained by NTDCC are in good agreement with the experimental results.

Density Wave Oscillation Beyond Dryout under Forced Circulation

The objective of the present experimental investigation is mainly to clarify experimentally the threshold of the density wave oscillation beyond the dryout condition of the boiling channels in the case of constant flow rate. The flow instability experiments under forced circulation were conducted with two channels, one holds high power heater bundle up to 6 MW and the other one holds low power heater bundle up to 200 kW. The high power heater bundle consists of 36-rods, which are made of Inconel claddings, Ni-Cr heater elements and BN insulators. In case of raising heating power, the pump rotation was controlled to keep the flow rate. Flow instability threshold was confirmed with the approach that the heating power was raised higher after the dryout of cladding was detected. Three experiments under different flow rate conditions were conducted. As a result, the instability threshold was measured beyond the dryout condition. The measured results were compared with available data. The prediction capability of a thermal hydraulic code was also validated partially by the experimental results.

Flow excursion phenomenon and its mechanism in natural circulation

An experiment was performed on the test loop (HRTL-5), which simulates the geometry and system design of a 5-MW nuclear heating reactor. In a wide range of inlet subcoolings, different flow modes, such as single-phase stable flow, subcooled boiling stable flow, subcooled boiling static flow excursion, density-wave oscillation and stable two-phase flow in the natural circulation system have been described. The phenomenon and mechanism of the static flow-excursion, which has never been studied well on this field, is especially interpreted. The experimental results show that, in the process of flow excursion, the mass flow rate and the inlet temperature decreases, while the exit temperature increases smoothly. As the process of the excursion continues for about 1 h, short period dynamic flow oscillation occurs, which can only be seen in the process of this static flow excursion, and has also never been studied well. These static and dynamic flow instabilities combine together and continue for about 2 h, then a point is reached, at which the static flow excursion disappears, but the dynamic flow oscillation continues. The mechanism of the static flow excursion is interpreted through two sets of curves for flow resistance pressure drop and driven head in natural circulation, and one curve for the natural circulation operation under special thermohydraulic condition. The study of the flow excursion and its concerned dynamic flow oscillation is of great significance for the development of the nuclear heating reactor under natural circulation.

Thermo-hydraulic instability of boiling natural circulation loop induced by flashing (analytical consideration)

An analytical study is presented on the thermo-hydraulic stability of a boiling natural circulation loop with a chimney at low pressure start-up. The effect of flashing induced by the pressure drop in the channel and the chimney due to gravity head on the instability is considered. A method to analyze linear stability is developed, in which a drift-flux model is used. The analytical result of a stability map agrees very well with the experimental one obtained in a previous report. Instability does not occur when the heater power is too low to generate voids in the chimney and only natural circulation of single phase can be induced. Instability tends to occur when boiling occurs only near the chimney exit due to flashing. This instability phenomenon has some similarities with density wave oscillation, such as the phase difference of temperature between the boiling region and non-boiling region, and the oscillation period which is near to the time required for fluid to pass through the chimney. However, there are also some differences from density wave oscillation, such as the boiling region is very short, and pressure fluctuation can affect void fraction fluctuation.

Determining parameters where pressure drop oscillations occur in a boiling channel using singularity theory and the D-partition method

Sustained oscillations have been experimentally observed when a surge tank is introduced up stream of a boiling channel. This dynamic state arises from an instability of the steady state of the system. These low-frequency oscillations are called pressure drop oscillations to distinguish them from the high-frequency density wave oscillations of boiling channels under constant pressure drop. The conditions under which these oscillations arise are that the steady-state operating point should be in the negative slope region of the boiling channel pressure drop characteristic and in the positive-slope region of the system pressure drop characteristic. The steady state should also be unique in the system pressure drop characteristic i.e. there should be no coexisting steady states. Under these conditions when this state is dynamically unstable the system shows sustained oscillations having a low-frequency. In this paper we discuss how the parameter values where these conditions are satisfied can be determined analytically and elegantly using results from the D-partition method and the singularity theory. The former allows us to determine regions in parameter space where an operating point is stable while the latter allows us to obtain different regions in parameter space where the bifurcation diagrams are qualitatively different. The superposition of results of these theories is used to determine parameter values where pressure drop oscillations occur. The predictions are verified with numerical simulations of the original nonlinear model for a horizontal channel.

Experimental Study of Two-Phase Flow Oscillation in Natural Circulation

The experiment was performed on the test loop HRTL-5, which simulates the geometry and system design of the 5-MW nuclear heating reactor developed by the Institute of Nuclear Energy Technology, Tsinghua University. The flow behavior for a wide range of inlet subcoolings, in which the flow experience varies from single- to two-phase, is described in a natural circulation system at different pressures (p = 0.1, 0.24, and 1.5 MPa). Several kinds of flow instability are investigated, including geysering, flashing-related flow instability, and high-frequency flow oscillation at p = 0.1 and 0.24 MPa, as well as low steam quality density wave oscillation at p = 1.5 MPa. The mechanisms of geysering, which has new features, and flashing-related flow instability, which has never been studied well enough in this field, are particularly interpreted. The experimental results show the following: First, for a low-pressure natural circulation system, the two-phase flow is unstable in most inlet subcooling conditions, and the two-phase stable flow can be reached only with very low inlet subcoolings. Second, at high inlet subcoolings, the flow instability is dominated by subcooling boiling in the heated section, and at intermediate inlet subcoolings, it is dominated by void flashing in the adiabatic long riser. Third, in the two-phase stable flow region, the conditions for boiling out of the core, namely, single-phase flow in the heated section and two-phase flow in the riser due to vapor flashing, can be realized. The experimental results are of significance for the design and accident analysis of vessel and swimming pool–type natural circulation nuclear heating reactors.

Coupling of density wave oscillations in parallel channels with high order modal kinetics: application to BWR out of phase oscillations

In this paper, we study the behavior of a system formed by two parallel channels coupled to a multimodal kinetics. The first problem that arises is the calculation of the reactivity coefficients for the higher modes. This problem is solved by means of the introduction of distribution factors for a given reactor region which depend on the involved modes. We have also performed a detailed analysis of the different instability types which can be obtained from the model changing the boundary conditions and the feedback gains of the fundamental and first harmonic modes.

TRANSIENT AND TIME-AVERAGED BOILING HEAT TRANSFER OF THE OSCILLATORY TWO-PHASE FLOW IN HELICAL COILS

The transient and time-averaged boiling heat transfer characteristics of water during density wave oscillations are studied experimentally. A horizontally positioned helical coiled tube is used as test section and is heated with alternating current. The measurement of the fluid temperatures at different positions within one cross section indicate that the test section departs from saturation, a significant superheat occurs, and postdryout heat transfer is reached during the transient. It is interesting that fluid temperatures at different positions of the same cross section are not oscillating in the same phase but are rather delayed from tube outer side to inner side, while the wall temperatures in one cross section are oscillating in the same phase. The time-averaged boiling heat transfer of the oscillatory two-phase flow is different from that of the steady-state flow by its dependence upon the frequency and amplitude of the oscillation. The boiling heat transfer coefficient of the oscillatory flow is less than that of the steady-state flow and this difference can be even enlarged in a high mass quality region. Based on the analysis of heat transfer phenomenon, a set of dimensionless parameters is defined to embody the oscillatory boiling characteristics and a correlation is proposed to predicate the boiling heat transfer coefficient during the oscillation.

Flow excursion phenomenon in natural circulation at nuclear heating reactor conditions / Das Phänomen der Durchsatzschwankungen beim Naturumlauf in einem nuklearen Heizreaktor

The experiment was performed on the test loop (HRTL-5), which simulates the geometry and system design of a 5 MW nuclear heating reactor. In a wide range of inlet subcoolings different flow features, such as single phase stable flow, subcooled boiling stable flow, subcooled boiling static flow excursion, density wave oscillation and stable two phase flow in the natural circulation system have been described. The phenomenon and mechanism of static flow excursion, which has never been studied well in this field, is especially interpreted. The experimental results show that static flow excursion exists under certain inlet subcooling condition, in which only subcooled boiling occurs in the heated section. In the process of flow excursion the mass flow rate and the inlet temperature decreases, while the exit temperature increases smoothly. As the process of excursion continues for about 1 hour, bubbles enter in the flow channel resulting in short period dynamic flow oscillation which can only be seen in the process of this static flow excursion and has also never be studied well. These static and dynamic flow instabilities combine for about 2 hours. Then a point is reached, at which the static flow excursion stops, but the dynamic flow oscillation continues. The study of flow excursion and its concerned dynamic flow oscillation is of great significance for the development of nuclear heating reactor under natural circulation.

Linear Analysis of Thermo-hydraulic Instabilities of the Advanced Heavy Water Reactor (AHWR)

Analysis was carried out to predict the threshold of instability for Ledinegg type and density wave oscillations for the Indian Advanced Heavy Water Reactor (AHWR) which is a Natural Circulation Pressure Tube Type Boiling Water Reactor. The mathematical model considers homogeneous two-phase flow and the conservation equations are solved analytically to obtain the steady state thermo-hydraulic characteristics and flow stability map. The model was applied for the AHWR concept after it had been validated with the test data obtained from a simple forced circulation loop with small parallel boiling channels and from the High Temperature Loop (PNC). The results indicate that the proposed design configuration of the AHWR may experience both Ledinegg type (static instability) and Type-I and Type-II density wave oscillations depending on the operating condition. The effects of various geometric and operating parameters on these types of instabilities were studied. It can be seen from the results that the Ledinegg type instability is suppressed with an increase in pressure and disappears when the operating pressure is higher than 0.7MPa. But the density wave instability may occur even at 7 MPa. In addition, it is found that for parallel multiple channels operating under natural circulation condition, the stability of density wave instability is not always enhanced by increasing the throttling coefficients at the inlet of channels.

Stability of small diameter airlift pumps

In an airlift pumping process, air is injected into the pipe containing the fluid to be transferred. Small diameter airlift pumps are, in particular, used for corrosive or radioactive liquids. However, for certain combinations of the geometrical parameters and air flow rate, they may become unstable. In this case, the flow at the riser outlet pulsates strongly, which cannot be accepted for many applications. An airlift pump involves three different regions, e.g. a single phase liquid flow and a separate single phase gas flow upstream of the air injection device and a two-phase flow downstream. The instabilities are due to density wave oscillations in the two-phase flow. Depending on the liquid flow inertia, friction effects and gas flow compressibility, the density waves are sustained or not. The present study is based upon a detailed description of the steady state flow in a small diameter airlift pump. A linear stability analysis is performed and assessed against an extensive set of experimental data. Both the experimental and analytical results show that the influencing parameters have complex effects and strongly interact: the same variation of a parameter may have opposite effects, i.e. stabilizing or destabilizing, depending on the values of the other parameters. The effect of the compressibility of the gas flow between the regulating valve and the air-injection device is shown to be very important. The analysis presented leads to a numerical model that can be considered as a practical tool for airlift performance and stability analysis.