Thermalhydraulic behavior of electrically heated rod during a critical heat flux transient

Thermalhydraulic Behavior of Electrically Heated Rod during a Critical Heat Flux Transient

Rita de Cássia Fernandes de Lima

Mechanical Engineering Department. Universidade Federal de Pernambuco

Av. Acad. Hélio Ramos, s/n

50740-530 Recife. PE. Brazil

[e-mail]

Pedro Carajilescov

Mechanical Engineering Department. Universidade Federal Fluminense

Rua Passo da Pátria,156

24210-240 Niterói. RJ. Brazil

[e-mail]

In nuclear reactors, the occurrence of critical heat flux leads to fuel rod overheating with clad fusion and radioactive products leakage. To predict the effects of such phenomenon, experiments are performed using electrically heated rods to simulate operational and accidental conditions of nuclear fuel rods. In the present work, it is performed a theoretical analysis of the drying and rewetting front propagation during a critical heat flux experiment, starting with the application of an electrical power step from steady state condition. After the occurrence of critical heat flux, the drying front propagation is predicted. After a few seconds, a power cut is considered and the rewetting front behavior is analytically observed. Studies performed with various values of coolant mass flow rate show that this variable has more influence on the drying front velocity than on the rewetting one.

Keywords: Critical heat flux, rewetting front, drying front, thermalhydraulics, numerical simulation

Introduction

The power generation of a nuclear reactor is limited by the coolant capability of removing the heat generated inside the fuel rods. In PWR type reactor, this capability is determined by the occurrence of critical heat flux (CHF), also called by DNB (Departure from Nucleated Boiling). Fuel rods overheating, due to the occurrence of a boiling crisis, during a power transient, can yield clad fusion with radioactive products leakage to the coolant. To predict this type of phenomenon, it is a common practice to perform simulations of the reactor operational and transient conditions in thermalhydraulic loops, utilizing electrically heated rods. Such simulations represent an important aspect of the reactor safety analysis.

When a critical heat flux occurs, the heated surface is covered by a vapor blanket, which will spread over the rod length with a so called drying front propagation velocity. Considering that vapor has a very low thermal conductivity, the local heat transfer coefficient is drastically reduced, provoking very high local temperatures. When the power is turned off, the wetting of the surface is re-established with a rewetting front propagation velocity. Since those electrically heated rods are very expensive, during a DNB experiment, it is necessary to turn the power off very quickly in order not to damage the rods. The prediction of the drying and rewetting front propagation, for a given experiment, can be used to establish the amount of time available for the experiment without rod damage. Several authors have studied this problem. Gunnerson & Yackle (1981) establish the difference between quench and rewetting. Yu et alii (1977) analyze the quench process on hot surfaces using bidimensional conduction. The work treats the subcooled and saturated rewetting for pressures from 1 to 69 bar. Olek et alii (1988) study the rewetting in descendent films. They consider the problem as a heat conjugated problem. Carlson (1989) analyses the expansion of the CHF region in direct heated rods. He takes into consideration also the thermocouple locations and the mechanism through which the drying front is detected by them.

The present work, analyzes the thermal behavior of a typical electrically heated rod with indirect heating, as shown in Figure 1, during a step transient of the electrical power. From a steady state condition, at a given power, it is imposed a 10% power step of its initial value in order to produce the CHF. It is, then, observed the effect of pressure and flow rate in the drying and rewetting front propagation velocities.

Theoretical Model

Consider the universally adopted test section, with indirect heating, shown schematically in Figure 1. Heat is generated in the electrical resistance by an electrical current, is conducted axially and radially, and is removed by the water flowing longitudinally along the rod. The heat transfer coefficient is a function of the local coolant conditions.

In order to analyze the thermal behavior of this system, it was considered:

• circular symmetry of the electrical heaters;

• uniform axial heat generation;

• no heat losses through the ends of the rod;

• constant thermal properties of the materials of the rod;

• homogeneous model for the water two-phase flow.

For the several regions of the rod, the heat conduction equation can be written as:

where T is the rod temperature; k, the thermal conductivity; r , the density and c_p , the specific heat of each material. The volumetric heat generation, q’’’, is zero for all material except for the electrical resistance.

According to Silva Neto et alii(1983), the lumped form of the energy equation for the water coolant can be written as:

where q" is the heat flux received by the coolant; A is the cross section area of the channel; p is the rod perimeter and h_{f ,}r_f and G are the enthalpy, density and mass flux of the coolant, respectively.

The coupling between the rod and the flow is established by the surface heat removal given by:

where k_clad is the thermal conductivity of the cladding; h_ref is the heat transfer coefficient between cladding and coolant; T_f is the coolant temperature and R_ext =R₄, the outer radius of the cladding.

The correlations presented in ^{Appendix A} were considered for the heat transfer coefficient, taking into account the several heat transfer regimes. Although several different correlations can be found in literature, these were considered adequate for the present situation.

The heat conduction equation for the rod was solved by the finite control volume method with an implicit formulation. For the water enthalpy, equations were solved iteratively.

To take into account the surface-water coupling, in any length of the coolant channel, the sequence shown in Figure 2, with the variables T_wall, h_ref and q" defined in ^{Appendix A}, was adopted.

Results

A computational program was developed to analyze the critical heat flux for a several types of transients. Here the classical case of a step power transient is presented. At t=0s, the variable q_o’ (the linear power density) is increased by 10% from its steady state value of 16 600 W/m, in order to reach the CHF. The new level is then maintained for 4.0 s and then the electric power is cut off. The entire transient lasts 4.5 s.

The tables below show the physical and geometric parameters used. The electrically heated rod is composed of a Ni-Cr ( 18 to 20% Cr and 8 to 12% Ni ) resistance, a MgO electric insulator and stainless steel ( type 349 ) cladding. The time step used in discretization is 5 x 10 ^-2 s. The numbers of nodes considered are: five in the internal insulator, nine in the resistance, four in the internal insulator and four in the cladding. The axial interval is equal to 10^-2 m.

The variation of the heat transfer coefficient versus height in the coolant channel, for several time instants, is shown in Fig. 3. Since the heat transfer coefficient for subcooled boiling is function of the wall temperature, it is observed that it will rise steadily until saturation is reached. After saturation, its value remains constant. When CHF occurs near the end of the channel, the heat removal degrades and the heat transfer coefficient suffers a severe drop as observed. This heat transfer crisis tends to travel to lower heights as time increases, which corresponds to a drying front propagation. For t = 4.0 s, the heat transfer coefficient drop is as large as 97%. When the power is cut off, the heat transfer coefficient drops along the rod due to the reduction of the rod superficial temperature.

Figure 4 shows the flow quality, where three different boiling regions can be observed, separated by the inflections of the curves. The first one separates the region of forced convection and subcooled boiling from the region of saturated boiling. The second inflection divides this last region from the post-dryout region. Near the entrance, a sharp increase in flow quality is observed, followed by a smooth increase when the CHF phenomenon occurs. There is a reduction in the quality growth, indicating the position and instant of time where it takes place. This behavior can be explained by the reduction of the superficial flux and consequently a smaller increase of the enthalpy. The maximum flow quality in this transient is equal to 0.57 at the outlet of the channel at t = 4.0 s.

The effect of the heat transfer regimes reflects on the clad temperature as shown in Fig.5. A maximum increase of 22% is seen in the clad temperatures when the boiling crisis phenomenon occurs. Clad melting can be avoided if the electric power supply is interrupted. Some clad points show temperature rise of 118 oC/s. As a result their temperatures could reach values as high as 1100^oC in less than 7.0 s.

The propagation of the drying and rewetting fronts is represented in Figure 6, for several mass flow rates. For mass flow rate equal to 0.0535 m/s, the drying front has a mean velocity of 4.6 cm/s. For the rewetting one, this velocity is 2.4 cm/s. The front velocities presented in Figs.6, ⁷ e ⁸ are mean velocities which are calculated dividing the maximum distance reached by the front by the correspondent time interval. The mass flow influence on the velocities is also shown. Variations of + 20% and - 20% on the reference case (= 0.0535 kg/s) are applied. It is noted that, as this variable rises, the drying velocity also rises from 4.6 to 4.9 cm/s, while the rewetting one goes from 2.4 to 4.4 cm/s. The CHF does not occur immediately after the power step, due to the radial and axial thermal resistances and condutances of the indirect heated rod. The time delay observed is reduced from 1.0 s to 0.8 s as the mass flow rate increases.

In order to observe the pressure influence on the reported velocities, the same transient is then analyzed under the coolant pressure of 8.0 MPa. Its inlet temperature is now equal to 280 ^oC. A 41% reduction in the pressure value has a strong influence on the rewetting front velocity: an increase of 936%. Otherwise there is a little influence on the drying one: it goes from 3.8 to 3.2 cm/s. These comparisons are shown in ^{Fig. 7}. The pressure also has considerable influence on the time delay which varies from 1.9 s to 1.4 s as the pressure changes from 8.0 MPa to 13.5 MPa.

The influence of the inlet mass flow rate was also investigated for the 8.0 MPa coolant pressure. Other authors have shown that this parameter has accentuated influence on the rewetting velocity at low pressures until 6.9 MPa. The test with a lower pressure was done to validate the model. The result obtained with the present model shown in ^{Fig. 8} and confirms the trend. Note that the inlet mass flow rate has a smaller effect in the drying front. For a 20% reduction in mass flow the rewetting front velocity is reduced in 29.5%: It varies from 24.7 to 17.4 cm/s.

Conclusions

The present work analyzes the front propagation velocity for the drying out and rewetting processes, during the occurrence of critical heat flux in electrically heated simulators of nuclear fuel rods, caused by a power step. This study is very important in the simulation of nuclear power plants as well as in metallurgical problems. At the occurrence of CHF, the amount of time required to cut off the electric power used in the heating of the simulator needs to be quantified. After the p ower cut off, the surface is rewetted when the temperature of the wall is less than the critical one. The two phenomena were analyzed individually by several authors (Carlson (1989), Olek et al. (1988), Griffith et al.(1988)) and there were no information about the amount of time available for the operation of the protection systems. Specially, there were few informations about rewetting, studied before only for descending films at low pressures. The work here presented supplies part of this lack of information.

Due to the radial and axial thermal resistances and capacitances of the indirect heating of the rod, the critical heat flux does not occur immediately after the power step. A certain time delay is observed. This time delay is reduced by increasing the pressure or the mass flow rate. In the beginning of the occurrence of CHF, the velocity of the propagation of the drying front is very high, being reduced gradually to an approximately constant value, around 4.6 cm/s. After the power cut off, the rewetting front presents a very large velocity of propagation, which is greatly affected by the system pressure and mass flow rate. The rewetting velocities were 24.7 cm/s and 2.4 cm/s for pressures of 8.0 MPa and 13.5 MPa, respectively. For the case of pressure of 8.0 MPa, the rewetting front propagation velocities were 17.4 cm/s and 24.7 cm/s for flow rates of 0.0471 kg/s and 0.0539 kg/s, respectively.

At the spot where the occurrence of CHF first starts, it was observed that the temperature increases at a rate of 118° C/s, which indicates that the wall temperature would reach its temperature limit, estimated around 1100° C, in approximately 7s. This is the amount of time available to turn off the electrical power supply. This observed heating rate is much larger than the value obtain by Mosaad (1988).

Additional details of the present work can be obtained in Lima (1997).

Acknowledgements

The authors thank to FACEPE ( Fundação de Apoio à Ciência e Tecnologia do Estado de Pernambuco) for the support given to this work.

a) Forced convection: DITTUS - BOELTER’s correlation (BJORNARD (1977)).

where k is the coolant thermal conductivity; De , the hydraulic diameter of the channel; Re, the Reynolds number; and Pr , the Prandtl one.

b) Nucleate boiling: THOM’s correlation (TONG & WEISMAN, (1979)).

where T_wall = external temperature of the cladding; T_sat = saturation temperature; q"_SUP = heat flux; e p = pressure.

The transition between forced convection and nucleate boiling may be abrupt. This problem can be solved using the suggestion of Rohsenow(1961) that considers the heat flux divided into two parts:

where the first term refers to the convection in the absence of bubbles and the second is the heat transfer only affected by the bubble movement, without convection. In the present work the first term is calculated using h_ref obtained from Eq. A.1 and the last one by Eq. A.2.

c) Critical heat flux: EPRI correlation (EPRI Report, 1983).

where A and C are constants which are dependent from pressure, is the local flow quality local, and , the inlet flow quality; is the local heat flux and q"_CHF , the critical heat flux.

d) Transition boiling: Bjornard’s correlation (BJORNARD,1977).

where q"_TB is the heat flux in the transition boiling region, and q"_MSFB is the heat flux at the Leidenfrost temperature (T_MSFB ).

e) Minimum heat flux (Leidenfrost point): BJORNARD’s correlation (1977).

where T_HN is the homogeneous nucleation temperature. This is the temperature at which the nucleation occurs spontaneously in the liquid in the absence of preferred nucleation sites. It is function of the pressure and can be predicted using standard nucleation theory. It can be obtained by the following expression of the TRAC -PF1 handbook:

where DP = 3203.6 - P, ( in psia) and T_HN in ⁰F.

f) Film boiling: modified Groeneveld’s correlation (BJORNARD, (1977)).

where: Y = two-phase flow factor of Miropol’skiy, x = flow quality; Pr_wall = Prandtl number evaluated at temperature T_wall; G = coolant mass flux; De = hydraulic diameter of the channel; m_g = dynamic viscosity - gaseous phase; r_g = coolant density - gaseous phase; r_f = coolant density - liquid phase; k_g.= thermal conductivity –gaseous phase.

Manuscript received: February 1998. Technical Editor: Angela Ourivio Nieckele.

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Appendix A

Publication Dates

• Publication in this collection
  13 Sept 2001
• Date of issue
  2000

History

• Received
  Feb 1998