**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 poly- dispersed

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