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During operation in the sea the reactor natural circulation behaviors are affected by ship rolling motion. The development of an analysis code and the natural circulation behaviors of a reactor simulator under rolling motion are described in this paper. In the case of rolling motion, the primary coolant flow rates in the hot legs and heating channels oscillated periodically, and the amplitude of flow rate oscillation was in direct proportion to rolling amplitude, but in inverse proportion to rolling period. The total mass flow rate also oscillated with half the rolling period, and the average total mass flow rate was less than that in steady state. In the natural circulation under a rolling motion, the flow rate oscillations in the hot legs were controlled by the tangential force; however, the mass flow rate oscillations in the total natural circulation and the heating channels were a result of the combined action of the change of inclination angle, flow resistance, and the extra force arising from the rolling motion. The extra tangential force brought about intense flow rate oscillations in the hot legs, which resulted in increasing total flow resistance; however the extra centrifugal force played a role in increasing thermal driving head.

Apart from designed as land-based nuclear power plants, another significant application of small and medium sized LWRs is to be mounted on barges as floating nuclear power plants FNPPs (FNPPs) or as propulsion power of commercial cargo ship or icebreaker, such as SMART and KLT-40s. However, during operation in the sea, the ship inclination or rolling motion will affect the reactor thermal hydraulics, especially for natural circulation behaviors. The effects of ship motion focus on two principles. Firstly, inclination decreases the height difference between the source (core) and sink (SG) and thus decreases the thermal driving head of natural circulation. Secondly, inertial forces imparted by the ship rolling motion in addition to the gravity act upon the primary coolant, which control the natural circulation flow rate with the loop resistances together. The direction and magnitude of inertial forces depend on the position with respect to rolling axis, rolling amplitude, and period. So the natural circulation behaviors under ship motion conditions are much more complicated than those operated on the land.

Experimental studies [

To understand the natural circulation behaviors of the integral type marine reactor under rolling motion conditions, a scaled test facility was built in Institute of Nuclear and New Energy Technology of Tsinghua University (INET) and a one-dimensional time-domain simulation program development was synchronized with test facility design. This paper describes the physical models and solution method in the program and the natural circulation behaviors of the reactor simulator under rolling motion condition based on the analysis results.

The test facility is a reactor simulator (natural circulation test loop) mounted on rolling equipment shown schematically in Figure

Geometry parameters of test facility.

Items | Number | Length (m) | Flow area (m^{2}) |
---|---|---|---|

Inlet section | 3 | 0.306 | 0.00237 |

Heating channel | 3 | 1.08 | 0.00178 |

Mid riser | 3 | 0.575 | 0.00126 |

Riser | 1 | 1.59 | 0.0104 |

Hot leg | 2 | 0.67 | 0.0113 |

Heat exchanger | 2 | 1.6 | 0.00246 |

Downcomer | 2 | 1.951 | 0.00594 |

Lower plenum | 1 | 1.34 | 0.0113 |

(a) Configuration of the test facility. (b) Relation between test section and real reactor system. (c) Connection of electrical heating tubes.

Be similar to study the fluid mechanics of rotating machinery that is often best analyzed in a rotating frame of reference, a noninertial frame of reference with the same rolling motion of test facility was chosen in our study. In a noninertial frame of reference, the continuity and energy equations are unchanged but the momentum equation must be modified. The extra body force term that arises from the motion of the noninertial frame must be added to the right of momentum equation to take account of the motion of the frame.

One-dimensional single phase conservation equations of hydrodynamic component can be written as follows:

mass continuum equation:

momentum continuum equation:

energy continuum equation:

The extra acceleration

The three terms in the right side of (

Figure

Three-dimensional spatial information of a control volume in noninertial frame of reference.

The parameters of rolling motion were defined as follows:

rolling angle:

rolling angle speed:

rolling angel acceleration:

The component of extra acceleration along main flow direction in our test facility was described by the following equation:

During rolling,

The friction factor model used in the code was simply an interpolation scheme linking the laminar, laminar-turbulent transition, and turbulent flow regimes. The laminar friction factor was calculated as

The friction factor in the transition region between laminar and turbulent flows was computed by reciprocal interpolation as

The turbulent friction factor is given by the Zigrang-Sylvester [

The wall heat transfer coefficient

In the code,

The Nusselt number for laminar flow was set to the analytical value for fully developed flow with a constant heat flux boundary condition. Thus,

The Nusselt number for fully developed turbulent flow was that of Weisman [

The Nusselt number for natural circulation was given by

The constitute correlations discussed above were widely used in analysis codes. Although these accuracy for real cases of the test loop should be verified, it was the best choice in our studies before deep experimental studying.

To solve (

Nodalization of a flow channel.

For single phase flow, during a small time interval, we can assume

Then (

Integrating (

Fluid enthalpy at the joint of control volumes was obtained by using upwind scheme as

In the code, temperature

For simplicity, the long expressions were replaced by single variables:

Combining (

Integrating (

And the integrating can be solved approximately as follows:

Nodalization of test facility.

loop 1 composed of left heating channel, middle risers, right heating channel, and part of lower plenum,

loop 2 composed of right heating channel, middle risers, heating channel 2, and part of lower plenum,

loop 3 composed of left heating channel, riser, left hot leg, left heat exchanger, downcomer, and part of lower plenum,

loop 4 composed of right heating channel, riser, right hot leg, right heat exchanger, downcomer, and part of lower plenum,

Applying the mass continuity, we can obtain

In the code, Gaussian elimination is used to solve (

The node model for test facility is shown in Figure

The transient simulation began with the variation of body force due to rolling motion. During the transient simulation, the feed water mass flows and total heating power kept being identical with those in steady state. Analyses were carried out for 3 s, 8 s, 13 s, 18 s, and 23 s rolling periods and 5°, 10°, 22.5°, and 45° rolling amplitude with heating power 175 kw, operating pressure 5 MPa.

A case of natural circulation mass flow rates and subcooling of heating channels outlet under rolling motion was shown in Figure

Natural circulation behavior under rolling condition.

Figure

Mass flow rate under the same rolling period, different rolling amplitude, (a) left heating channel, (b) left hot leg.

Figure

Mass flow rate under the same rolling amplitude, different rolling period, (a) left heating channel, (b) left hot leg.

Mass flow rate of heating channels under rolling period 23 s, rolling amplitude 45°.

Natural circulation flow rates under rolling motion were affected by extra forces, thermal driving head, and flow resistance. The extra force varied with the rolling angle. On the other hand, the thermal driving head also varied with the inclination angle, and flow resistance varied with velocity. Therefore, it was difficult to judge how much do these three factors contribute to overall thermal hydraulic behaviors ostensibly. If the natural circulation was only affected by thermal driving head decrease due to inclination, the normalized total natural circulation mass flow was always less than unit. However, as shown in Figure

The mechanisms of influence of rolling motion can be interpreted by the analysis of extra forces. Figure

Analysis of extra forces arising from rolling.

From above discussion, it was concluded that in the natural circulation under rolling motion, the flow rates oscillations in hot legs were controlled by tangential force; however, the mass flow rate oscillations of total natural circulation and heating channels were a result of the combined action of the change of inclination angle, flow resistance, and extra force due to rolling motion. The centrifugal force and thermal driving head varied periodically with half the rolling period, and the tangential force varied periodically with the same rolling period, so the oscillation waveforms of left and right heating channels depended on the quantity of the centrifugal force, the tangential force, and thermal driving head, that was why there were two maximum and minimum in one period shown in Figure

Figure

Average normalized total mass flow rates of different rolling cases.

A transient system analysis code was developed to study natural circulation under motion condition. The momentum equation was modified and it adopted the fluid mechanics in noninertial frame of reference. The natural circulation behavior of integral type marine reactor simulator under rolling condition can be concluded as follows.

The heat and flow symmetry between heating channels and hot legs were broken. The flow rates of hot legs and left and right heating channels oscillated periodically with the same rolling period; however, the flow rates of middle heating channel and total mass flow rate oscillated with half rolling period. The average total mass flow rate in rolling motion was less than that in steady state.

The tangential forces along the pipes were in two circles, which generate theoretical flows in outer and inner loops. The superposition of theoretical flows and flows driven by density difference resulted in the oscillation of hot legs and left and right heating channels.

Natural circulation behaviors in rolling motion were results of the combined action of the variation of inclination angle, flow resistance (extra tangential force), and extra centrifugal force. Extra tangential force caused intense flow rates oscillation of hot legs, which resulted in increasing total flow resistance; however extra centrifugal force played a role in increasing the thermal driving head.

Area of cross section, m^{2}

Heat transfer correction factor

Hydraulic equivalent diameter, m

Thermal equivalent diameter, m

Rod diameter, m

Extra tangential force

Extra centrifugal force

Extra acceleration, m/s^{2}

Extra acceleration component along axial, m/s^{2}

Grashofnumber

Gravityacceleration = −9.8 m/s^{2}

Gravity acceleration component along axial, m/s^{2}

Pressure drop, Pa

Enthalpy, J/kg

Thermal conductivity, w/m

Nusseltnumber

Nusselt number for laminar flow

Nusselt number for turbulent flow

Nusselt number for natural convection

Thermal perimeter, m

Prandtl number

Velocity, m/s

Mass flow rate, kg/s

Intersection angle between main stream and

Intersection angle between main stream and

Intersection angle between main stream and

Density, kg/m^{3}

Friction factor

Friction factor for laminar flow

Friction factor for turbulent flow

Rolling angle, rad

The maximum rolling angle, rad

Angle velocity, rad/s

Rolling period, s

Angle acceleration, rad/s^{2}

Rolling frequency

Roughness.

The authors declare that there is no conflict of interests regarding the publication of this paper.