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The main purpose of this study is to apply a two-fluid mathematical model to numerical simulation of two phase flow at low-pressure condition. Although models of sub-cooled boiling flow at one-dimension and high-pressure have been studied extensively, there are few equivalent studies for numerical simulation at two-dimension and low-pressure (1–2 bar) conditions. Recent literature studies on sub-cooled boiling flow at low-pressure have shown that empirical models developed for high-pressure situations are not valid at low-pressures. Since the mathematical model used in this study is accomplished at low-pressure, the transport equations for the variables of each phase are substituted in low-pressure. The governing equations of two-phase flow with an allowance to inter-phase transfer of mass, momentum and heat, are solved using a two-fluid; non-equilibrium model. The finite volume discretization scheme is used to create a linearized system of equations that are solved by SIMPLE staggered grid solution technique for a rectangular channel.
Improvement of the void fraction prediction of our model for the case of low-pressure sub-cooled flow boiling conditions was achieved. It is found that the heat transfer due to evaporation and surface quenching is higher than that by convection. Good agreement is achieved with the predicted results against the experimental data’s available in the literatures for a number of test cases.
Introduction
Boiling occurs when the temperature of the heater surface exceeds the saturation temperature, thus causing bubble formation. If the bulk temperature of the liquid is below saturation, the process is known as sub-cooled boiling. Sub-cooled flow boiling
is an important heat transfer regime in nuclear reactors. The proper prediction of the void fraction profile and other important parameters under sub-cooled flow boiling conditions is of primary importance in thermal-hydraulic safety analysis of nuclear reactors. In the nuclear area, ensuring the safe operation of a power or research reactor is of paramount importance especially where nuclear safety analyses concern the ability to predict the void fraction distributions and other two-phase flowparameters in sub-cooled boiling conditions. In the present state-of-the-art, the
two-fluid model can be considered as the most detailed and accurate macroscopic formulation of the thermal-hydraulic dynamics of two-phase flowsystems(KonĖcar andMavko, 2003). Within the flow field equations, expressed by conservation of mass,momentumand energy for each phase, interfacial transfer terms appear in each of
the equations to couple the different phasic effects. These terms determine the rate of phase changes and the degree of mechanical and thermal non-equilibrium between phases. Much success of the two-fluid model depends on these essential closure relations, which should be modelled accurately.
Most available sub-cooled boiling flow models are developed and tested at high-pressure (above 10 bar), and one-dimension conditions typical of power reactors, but there are few equivalent studies for numerical simulation at two-dimension and
low-pressure conditions. For a number of years, an internationally coordinated effort has been carried out, focusing on continuous development and validation of best-estimate thermalhydraulic computer codes, e.g. RELAP5, TRAC, CATHARE and ATHLET. These codes are used to perform predictive safety analyses of system transients, e.g. loss-of-coolant accidents (Petelin et al., 1994; Parzer et al., 1995; Wang and Mayinger, 1995; Tuunanen et al., 2000). According to the analyses of Woodruff et al. (1996), Hari et al. (1998), Hari and Hassan (2002), Tu and Yeoh
(2002,2006), Ustinenko et al. (2007), the codes, which have been developed and validated for high-pressure conditions, cannot be applied to low-pressure conditions without adequate modifications.
Extensive studies have addressed stability at low-pressure startup of natural circulation BWRs. Aritomi et al. (1992) and Chang et al. (1992,1993) conducted basic studies on instabilities under lowpressure condition in a parallel channel natural circulation loop using a two-fluid model. Tu and Yeoh (2002) improved the CFX1
code for the sub-cooled boiling flow at low-pressure condition and applied it to numerical simulation of vertical boiling channel. They found a reasonable agreement with the experimental results of Zeitoun and Shoukri (1997). Anglart (1993) studied the sub-cooled boiling at low-pressure condition in a vertical channel. He found
that the rate of vapor generated in low-pressure condition is higher than that in high-pressure condition. Recently, Mi et al. (1998) further developed the CFX sub-cooled boiling model and validated the model against Bartolomei et al.’s (1982) high-pressure boiling experiments.
The main objective of this study is to apply a two-fluid mathematical model to numerical simulation of two-phase flow in a vertical boiling channel at low-pressure condition, which is appropriate for research reactors. Our simulation is accomplished at low-pressure, therefore the interfacial area phenomena are substituted in low-pressure. Since the sensitivity of boiling to various parameters is much higher at low-pressure, in order to show all of the effects are properly captured, the predicted results are compared with the experimental data’s of Zeitoun and Shoukri (1997) for several test cases.
Conclusion
A two-dimensional; non-equilibrium two-fluid mathematical model was applied to predictions of low-pressure; low-flow subcooled boiling, using the phasic correlations being suitable for low-pressure condition. Improvement of the void fraction prediction of our model for the case of low-pressure sub-cooled flow
boiling conditionswas achieved. Applied numerical method in this work is in the good agreement with existing experimental data’s in low-pressure condition. It is found that the buoyancy force plays an important role on the void fraction evolvement. Density of bubbles is maximum near the walls and due to diffusion phenomena its effectiveness is developed to center of channel. With increasing in length of channel void fraction is increased, due to convection of bubble. Also because the effects of buoyancy and drag forces, the vapor velocity is increasing rapidly along the channel. It is found that the heat transfer due to evaporation and surface quenching is higher than that by convection.
Finally, it should be noted that, in high flow rates, some kind of additional phenomena such as bubbles coalescence and break-up appears, therefore in order to consider these effects, it is necessary to equip the formulation with a turbulence model.
Introduction
Boiling occurs when the temperature of the heater surface exceeds the saturation temperature, thus causing bubble formation. If the bulk temperature of the liquid is below saturation, the process is known as sub-cooled boiling. Sub-cooled flow boiling
is an important heat transfer regime in nuclear reactors. The proper prediction of the void fraction profile and other important parameters under sub-cooled flow boiling conditions is of primary importance in thermal-hydraulic safety analysis of nuclear reactors. In the nuclear area, ensuring the safe operation of a power or research reactor is of paramount importance especially where nuclear safety analyses concern the ability to predict the void fraction distributions and other two-phase flowparameters in sub-cooled boiling conditions. In the present state-of-the-art, the
two-fluid model can be considered as the most detailed and accurate macroscopic formulation of the thermal-hydraulic dynamics of two-phase flowsystems(KonĖcar andMavko, 2003). Within the flow field equations, expressed by conservation of mass,momentumand energy for each phase, interfacial transfer terms appear in each of
the equations to couple the different phasic effects. These terms determine the rate of phase changes and the degree of mechanical and thermal non-equilibrium between phases. Much success of the two-fluid model depends on these essential closure relations, which should be modelled accurately.
Most available sub-cooled boiling flow models are developed and tested at high-pressure (above 10 bar), and one-dimension conditions typical of power reactors, but there are few equivalent studies for numerical simulation at two-dimension and
low-pressure conditions. For a number of years, an internationally coordinated effort has been carried out, focusing on continuous development and validation of best-estimate thermalhydraulic computer codes, e.g. RELAP5, TRAC, CATHARE and ATHLET. These codes are used to perform predictive safety analyses of system transients, e.g. loss-of-coolant accidents (Petelin et al., 1994; Parzer et al., 1995; Wang and Mayinger, 1995; Tuunanen et al., 2000). According to the analyses of Woodruff et al. (1996), Hari et al. (1998), Hari and Hassan (2002), Tu and Yeoh
(2002,2006), Ustinenko et al. (2007), the codes, which have been developed and validated for high-pressure conditions, cannot be applied to low-pressure conditions without adequate modifications.
Extensive studies have addressed stability at low-pressure startup of natural circulation BWRs. Aritomi et al. (1992) and Chang et al. (1992,1993) conducted basic studies on instabilities under lowpressure condition in a parallel channel natural circulation loop using a two-fluid model. Tu and Yeoh (2002) improved the CFX1
code for the sub-cooled boiling flow at low-pressure condition and applied it to numerical simulation of vertical boiling channel. They found a reasonable agreement with the experimental results of Zeitoun and Shoukri (1997). Anglart (1993) studied the sub-cooled boiling at low-pressure condition in a vertical channel. He found
that the rate of vapor generated in low-pressure condition is higher than that in high-pressure condition. Recently, Mi et al. (1998) further developed the CFX sub-cooled boiling model and validated the model against Bartolomei et al.’s (1982) high-pressure boiling experiments.
The main objective of this study is to apply a two-fluid mathematical model to numerical simulation of two-phase flow in a vertical boiling channel at low-pressure condition, which is appropriate for research reactors. Our simulation is accomplished at low-pressure, therefore the interfacial area phenomena are substituted in low-pressure. Since the sensitivity of boiling to various parameters is much higher at low-pressure, in order to show all of the effects are properly captured, the predicted results are compared with the experimental data’s of Zeitoun and Shoukri (1997) for several test cases.
Conclusion
A two-dimensional; non-equilibrium two-fluid mathematical model was applied to predictions of low-pressure; low-flow subcooled boiling, using the phasic correlations being suitable for low-pressure condition. Improvement of the void fraction prediction of our model for the case of low-pressure sub-cooled flow
boiling conditionswas achieved. Applied numerical method in this work is in the good agreement with existing experimental data’s in low-pressure condition. It is found that the buoyancy force plays an important role on the void fraction evolvement. Density of bubbles is maximum near the walls and due to diffusion phenomena its effectiveness is developed to center of channel. With increasing in length of channel void fraction is increased, due to convection of bubble. Also because the effects of buoyancy and drag forces, the vapor velocity is increasing rapidly along the channel. It is found that the heat transfer due to evaporation and surface quenching is higher than that by convection.
Finally, it should be noted that, in high flow rates, some kind of additional phenomena such as bubbles coalescence and break-up appears, therefore in order to consider these effects, it is necessary to equip the formulation with a turbulence model.
By : Said Talebi, Farshad Abbasib, Hadi Davilu
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