atw Vol.

atw Vol. 63 (2018) | Issue 4 ı April

| | Fig. 1.

Schematic representation of horizontal flow and different morphologies.

(Algebraic Interfacial Area Density

Model) is developed for detection of

the local morphology and corresponding

switch between them [16]. The

recently developed GENTOP- model

combines both concepts. GENTOP

(Generalized Two-Phase Flow) approach

is able to simulate co-existing

large-scaled (continuous) and smallscaled

(polydispersed) structures [17].

All these models are validated for adiabatic

cases without any phase change.

Therefore, the start point of the current

work project is using the available

models and integrating phase transition

and con densation models into

them. In the current work as initial

stages the AIAD model has been used

since in this model 2 continues phases

should be considered and it is less complicated

compare to GENTOP model

which also considers a polydispersed

phase. In the proceeding sections a

more detail explanation of AIAD model

will be given.

2 CFD model formulation

In the current work a multi-field twophase

CFD approach is used with

ANSYS CFX 17.2 in order to simulate

the condensation inside horizontal

pipe flows. The mass, momentum and

energy equations can be defined,

respectively, as follow:

• Mass conservation equation:

(1)

where S Mi describes user specified

mass source.

χ iβ the mass flow rate per unit volume

from phase β to phase i.

• Momentum conservation equation:

(2)

where S mi is the momentum source

caused by external body forces

and user defined momentum

sources.

M i is the interfacial forces acting

on phase i due to the presence

of other phases.

χ + iβ v β – χ + βi v i is the momentum

transfer induced

by mass transfer.

• The total energy equation:

(3)

where: h tot is the total enthalpy

related to static enthalpy by:

(4)

T i , λ i represents the temperature

and the thermal conductivity

of phase i.

S Ei describes external heat sources.

Q i is interphase heat transfer

to phase i across interfaces

with the other phase.

χ + iβ h βs – χ + βi h is denotes the interphase

mass transfer.

In ANSYS CFX in order to describe the

phase change which occurs due to the

interphase heat transfer, the Thermal

Phase Change Model has been introduced

[30]. This model is particularly

useful in simulation of the condensation

of saturated vapor. The heat

flux from the interface to phase i and

phase β is:

q i = h i (T sat – T i ) (5)

q β = h β (T sat – T β ) (6)

where h i , h β and T sat are heat transfer

coefficients of the phase i and phase

β and the saturation temperature,

respectively. ṁ iβ is the mas flux from

phase β to phase i. H is and H βs are the

interfacial enthalpy values which

come into and out of the phase due

to phase change which occurs. By

usage of the total heat balance

equation the interphase mas flux can

be determined as follow:

| | Fig. 2.

3D geometry of the pipe and mesh of the cross section.

(7)

ṁ iβ > 0 → H is = H i,sat , H βs = H β (8)

ṁ iβ < 0 → H is = H i , H βs = H β,sat (9)

In the current work, the steam

con sidered to be in saturation temperature.

Therefore, the heat flux

from the steam to the interface equals

zero since both are in saturation

temperature. As a result, the interphase

mass flux formula can be

written as:

(10)

In this work in order to model the heat

transfer coefficient the Hughes and

Duffy model has been used which is

based on the SRT model [9]. They

used the Surface Renewal Theory

(SRT) and the Kolmogorov turbulent

length scale theory to find a correlation

for heat transfer coefficient.

Therefore, the heat transfer coefficient

was derived as:

(11)

where ε is the turbulent dissipation, v l

is the kinematic viscosity and λ is the

thermal conductivity.

3 Computational grid and

boundary conditions

In Figure 2 the pipe and the boundary

conditions are shown. The pipe is

horizontal and has 1 m length

and 0.043 m diameter. In order to

define a mesh for the pipe ANSYS

ICEM software is used. Due to the

higher importance of the wall region

compare to the middle of the pipe,

the mesh near the wall needs to be

finer than the mesh in the pipe

center. The number of nodes is

1,250,000.

Mass flow rate

[Kg/s]

Temperature

(k)

Inlet 0.5 537.1

Wall - 312.18

outlet outflow -

ENVIRONMENT AND SAFETY 239

CFD Modeling and Simulation of Heat and Mass Transfer in Passive Heat Removal Systems

Environment and Safety

ı Amirhosein Moonesi, Shabestary, Eckhard Krepper and Dirk Lucas

atw Vol. 63 (2018) | Issue 4 ı April 238 ENVIRONMENT AND SAFETY CFD Modeling and Simulation of Heat and Mass Transfer in Passive Heat Removal Systems Amirhosein Moonesi, Shabestary, Eckhard Krepper and Dirk Lucas This paper is presenting the CFD-modelling and simulation of condensation inside passive heat removal systems. Designs of future nuclear boiling water reactor concepts are equipped with emergency cooling systems which are passive systems for heat removal. The emergency cooling system consists of slightly inclined horizontal pipes which are immersed in a tank of subcooled water. At normal operation conditions, the pipes are filled with water and no heat transfer to the secondary side of the condenser occurs. In the case of some accident scenarios the water level may decrease in the core, steam enters the emergency pipes and due to the subcooled water around the pipe, this steam condenses. The emergency condenser acts as a strong heat sink which is responsible for a quick depressurization of the reactor core. This procedure acts passive i.e. without any additional external measures. The actual project is defined to model the phenomena which are occurring inside the emergency condensers. The focus of the project is on detection of different morphologies such as annular flow, stratified flow, slug flow and plug flow and also modeling of the laminar film which is occurring during the condensation near the wall. The condensation procedure inside the pipe is determined by two important phenomena. The first one is wall condensation and the second one is the direct contact condensation (DCC). The Algebraic Interfacial Area Density (AIAD) concept is used in order to model the interface between liquid and steam. In the next steps the Generalized Two-Phase Flow ( GENTOP) model will be used to model also the dispersed phases which are occurring inside the pipe. Finally, the results of the simulations will be validated by experimental data which will be available in HZDR. In this paper the results of the first part are presented. 1 Introduction Condensation plays a crucial role in the emergency condenser of passive heat removal systems of nuclear power plants. Passive safety systems do not need any external power supplies and they mostly depend on physical phenomena such as natural circulation and gravity driven flows. In order to assess the performance of passive safety systems and their efficiency mostly one-dimensional codes are used such as ATHLET, RELAP and TRACE. These codes are able to calculate most of the phe nomena in power plants; however, they cannot reflect the 3D phenomena. Therefore, Computational Fluid Dynamics (CFD) methods should be used to simulate and predict the complex multiphase flow structure. Despite the previous research being done on the two-phase flow behavior, this phenomenon needs much more investigations. The two-phase flow patterns and transition between vapor and liquid are studied by Thome and Hajal et al. [1, 2]. They introduced a logarithmic mean void fraction (LMe) method in order to calculate the vapor void fractions which change from the low pressure up to the critical pressure point. Moreover, they proposed a new heat transfer model based on the same simplified flow structures that have been used in the flow boiling model of Kattan et al. [3]. The model can predict the local condensation heat transfer coefficient for different flow regimes such as annular, intermittent, stratified-wavy fully stratified and wavy flow. Many attempts have been done to investigate the mass transfer between liquid and gas phase in condensation. Lee et al. [4] introduced a model for prediction of the mass transfer. They assumed that the interface between liquid and steam is on saturation temperature and introduced an iterative technique in order to reach to desired boundary condition inside each cell. This model depends on a relaxation factor which needs to be tuned. The tuning needs many trial and error simulations which is time-consuming and doesn’t have any predictive capabilities. Moreover, there are empirical or semi-empirical methods to calculate the mass transfer in the interface. Strubelj et al. [5] by using ANSYS CFX and NEPTUNE_CFD [6] code tried to simulate Direct Contact Condensation (DCC) in stratified flows. In DCC the phase change occurs due to the direct contact interaction of subcooled water and saturated steam. The defined phase change mass flux depends on thermal conductivity of the liquid and Nusselt number of the liquid. The Nusselt number was calculated by Coste et al. [7] based on Surface Renewal Theory (SRT) [8]. The SRT theory calculates the mass transfer according to the renewal period of eddies and the liquid turbulent properties. Hughes and Duffey [9] used the surface renewal theory and the Kolmogorov turbulent length scale theory to define a correlation for the heat transfer coefficient. They considered that the heat removal from interface occurs by smallest turbulent scales. This model will be introduced more detailed in the next sections. This correlation is validated for Pressurized Thermal Schock (PTS) phenomenon by Egorov [10] and Apanasevich [11]. Further to Hughes correlation, Shen et al. [12] developed another correlation for calculation of heat transfer coefficient based on the surface renewal theory. Ceuca et al. [13] used both of these correlations in order to simulate the direct contact condensation for the LAOKOON facility [14]. By comparison of Hughes and Duffey correlation with Shen correlation, Ceuca et al. [13] concluded that both of the models provide accurate results for the horizontal stratified quasi-steady state. Evidently, many attempts have been done in the modeling of con densation inside the pipes. The goal of the current work is modeling of the transition between different mor phologies which are occurring during the condensation inside the pipe ( Figure 1). In order to do that, several CFD models such as IMUSIG, AIAD and GENTOP which have been developed in HZDR in cooperation with ANSYS are available. The Inhomo geneous MUSIG model considers the bubble size distribution and is used for modeling the small-scaled dispersed gas phase [15]. The AIAD Environment and Safety CFD Modeling and Simulation of Heat and Mass Transfer in Passive Heat Removal Systems ı Amirhosein Moonesi, Shabestary, Eckhard Krepper and Dirk Lucas

atw Vol. 63 (2018) | Issue 4 ı April | | Fig. 1. Schematic representation of horizontal flow and different morphologies. (Algebraic Interfacial Area Density Model) is developed for detection of the local morphology and corresponding switch between them [16]. The recently developed GENTOP- model combines both concepts. GENTOP (Generalized Two-Phase Flow) approach is able to simulate co-existing large-scaled (continuous) and smallscaled (polydispersed) structures [17]. All these models are validated for adiabatic cases without any phase change. Therefore, the start point of the current work project is using the available models and integrating phase transition and con densation models into them. In the current work as initial stages the AIAD model has been used since in this model 2 continues phases should be considered and it is less complicated compare to GENTOP model which also considers a polydispersed phase. In the proceeding sections a more detail explanation of AIAD model will be given. 2 CFD model formulation In the current work a multi-field twophase CFD approach is used with ANSYS CFX 17.2 in order to simulate the condensation inside horizontal pipe flows. The mass, momentum and energy equations can be defined, respectively, as follow: • Mass conservation equation: (1) where S Mi describes user specified mass source. χ iβ the mass flow rate per unit volume from phase β to phase i. • Momentum conservation equation: (2) where S mi is the momentum source caused by external body forces and user defined momentum sources. M i is the interfacial forces acting on phase i due to the presence of other phases. χ + iβ v β – χ + βi v i is the momentum transfer induced by mass transfer. • The total energy equation: (3) where: h tot is the total enthalpy related to static enthalpy by: (4) T i , λ i represents the temperature and the thermal conductivity of phase i. S Ei describes external heat sources. Q i is interphase heat transfer to phase i across interfaces with the other phase. χ + iβ h βs – χ + βi h is denotes the interphase mass transfer. In ANSYS CFX in order to describe the phase change which occurs due to the interphase heat transfer, the Thermal Phase Change Model has been introduced [30]. This model is particularly useful in simulation of the condensation of saturated vapor. The heat flux from the interface to phase i and phase β is: q i = h i (T sat – T i ) (5) q β = h β (T sat – T β ) (6) where h i , h β and T sat are heat transfer coefficients of the phase i and phase β and the saturation temperature, respectively. ṁ iβ is the mas flux from phase β to phase i. H is and H βs are the interfacial enthalpy values which come into and out of the phase due to phase change which occurs. By usage of the total heat balance equation the interphase mas flux can be determined as follow: | | Fig. 2. 3D geometry of the pipe and mesh of the cross section. (7) ṁ iβ > 0 → H is = H i,sat , H βs = H β (8) ṁ iβ < 0 → H is = H i , H βs = H β,sat (9) In the current work, the steam con sidered to be in saturation temperature. Therefore, the heat flux from the steam to the interface equals zero since both are in saturation temperature. As a result, the interphase mass flux formula can be written as: (10) In this work in order to model the heat transfer coefficient the Hughes and Duffy model has been used which is based on the SRT model [9]. They used the Surface Renewal Theory (SRT) and the Kolmogorov turbulent length scale theory to find a correlation for heat transfer coefficient. Therefore, the heat transfer coefficient was derived as: (11) where ε is the turbulent dissipation, v l is the kinematic viscosity and λ is the thermal conductivity. 3 Computational grid and boundary conditions In Figure 2 the pipe and the boundary conditions are shown. The pipe is horizontal and has 1 m length and 0.043 m diameter. In order to define a mesh for the pipe ANSYS ICEM software is used. Due to the higher importance of the wall region compare to the middle of the pipe, the mesh near the wall needs to be finer than the mesh in the pipe center. The number of nodes is 1,250,000. Mass flow rate [Kg/s] Temperature (k) Inlet 0.5 537.1 Wall - 312.18 outlet outflow - ENVIRONMENT AND SAFETY 239 CFD Modeling and Simulation of Heat and Mass Transfer in Passive Heat Removal Systems Environment and Safety ı Amirhosein Moonesi, Shabestary, Eckhard Krepper and Dirk Lucas