Heat transfer engineering an international journal, tập 32, số 5, 2011

Heat Transfer Engineering, 32(5):359–368, 2011
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457632.2010.483851

Boiling of R404A Refrigeration
Medium Under the Conditions of
Periodically Generated Disturbances
´
TADEUSZ BOHDAL and WALDEMAR KUCZYNSKI
Thermal Engineering and Refrigerating Engineering, Koszalin University of Technology, Koszalin, Poland

An attempt was made to evaluate the impact of external, periodically generated disturbances on the boiling process of the
refrigeration medium in a flow. The experimental investigations were conducted under the conditions of periodic changes
(increase and fading) of the mass flux density of the refrigeration medium for constant refrigeration chamber heat loads. This
led to a change of the pressure and temperature along the path of the flow of the medium in a coil tube of the evaporator. It was
confirmed that the boiling process of the refrigeration medium in a flow exhibits wave properties, which are characterized by
finite values of the displacements of the disturbances. By way of dimensional analysis, nondimensional dependences were
determined that specify the velocity of the displacement of the pressure change signal and the temperature change signal.
The investigations were conducted with the use of an environmentally friendly R404A refrigeration medium.

INTRODUCTION
The principle of operation of some power engineering machines and devices is based on the use of the phase changes of an
energy medium in a thermodynamic cycle. An energy medium
is understood to be both an energy carrier and a thermodynamic
medium that is subject to changes and that participates in energy
conversion in a direct or indirect manner. Energy media include,
among others, water, refrigeration media, and water saline solutions. It has been established that phase changes of energy media
that occur in evaporators and condensers in machines and devices are very “sensitive” to any disturbances that occur during
operation, including both external and internal disturbances [1].

External disturbances are usually the result of an interaction
between various components of the system. For example, they
are the result of the work of automatic elements, disturbances
of the work of machines (e.g., pumps, turbines, compressors),
and power stoppages. The causes of the occurrence of internal
disturbances can generally be divided into two groups. They
can be directly embedded in the mechanism of phase changes
or in the structure and properties of the working medium. Both
external and internal disturbances can be of an individual [2] or

Address correspondence to Professor Tadeusz Bohdal, Thermal Engineering
and Refrigerating Engineering, Koszalin University of Technology, Koszalin,
Poland. E-mail:

periodic [3–5] nature; i.e., they can be periodically generated
with a specific amplitude and frequency.
Impulse and periodically generated disturbances cause specific phenomena, which trigger the following changes: (a) an
abrupt drop or increase of the pressure of the medium, (b) a
decay or an increase of the mass flux density, (c) an increase or
a drop of the resistances of the medium flow, and (d) periodic
problems connected with the starting of the device.
A two-phase system of liquid (either a gas, or a single or
multicomponent fluid) is a set of particles of a substance with
two states of aggregation, which are separated by an interface.
The interaction between particular phases and the displacement
velocity of a disturbance triggered by an external or internal
cause depend on the internal structure of the system. This can
be clearly seen via the example of the propagation of a sound
wave in an adiabatic two-phase system. The velocity of a sound
wave depends, above all, on the value of the filling degree φ and

the pressure of the two-phase mixture. The sound velocity in
a two-phase mixture increases together with an increase of the
pressure. However, this tendency only occurs up to a specific
value of the pressure (whose value depends from the filling
degree) and then, with adequately high pressures, it is almost
constant and is equal to 1300 m/s [6].
During the propagation of the wave of disturbances in a
two-phase one-component mixture with thermal parameters
determined for the states on the saturation line, the propagation
of the wave of disturbances causes a periodic change of the local

359


360

´
T. BOHDAL AND W. KUCZYNSKIRH

pressure values. In turn, this results in a continuous process of
phase changes. On the boundary of the phases, a condensation
process occurs locally when the pressure increases; when the
pressure decreases, an evaporation process occurs. The local
values of the parameters of the two-phase system change,
including the saturation pressure pS , saturation temperature
TS , density ρ, dryness degree x, and filling degree ϕ. These
phenomena cause the “damping effect” associated with the
dissipation of energy and the change of the propagation velocity
of the disturbances [7–9].
In a two-phase system, in nonequilibrium conditions, an evolution of the disturbance signals occurs. A two-phase flow also

possesses dispersion wave properties, which are evident in the
fact that the propagation velocity of small disturbances depends
on their frequency [6, 10]. It should be emphasized that a close
examination of the mechanism of the displacement of disturbances in a two-phase medium is very important in order to
guarantee the stable operation of machines and devices. The
determination of the velocity of these disturbances plays a vital
part in the description of the operation of thermal and refrigeration systems under conditions of an automatic control, by
preventing breakdowns and minimizing of their results [11–13].

BOILING PROCESS OF THE MEDIUM IN A COIL TUBE
An evaporator constitutes the basic element of a refrigeration
system; it is important in determining the effectiveness of its
operation. The use of the disposable surface of the heat exchange
of the evaporator usually constitutes the basic criterion of the
optimization of the whole system [10].
A considerable number of evaporators in fan air coolers with
small and medium outputs are usually fed with a refrigeration
medium with the aid of thermostatic expansion valves. However,
these days, a new generation of automatic cooling devices is
being used increasingly frequently in the form of electronic expansion valves or whole systems of automatic control for filling
evaporators with the medium. The “saturation” of a refrigerating
system with any type of electronic element and computer assistance, or with a monitoring system, makes it more susceptible
to any disturbance that occurs during operation. A disturbance
of the operation of a system that feeds the evaporator has an
impact on the boiling process of the refrigeration medium used.
The boiling of a refrigeration medium in a flow is usually
considered to be a phenomenon that occurs in coil tubes composed of horizontal or vertical straight pipes connected with
elbows for vapor dryness values between x = 0 to 1. However, it
happens that the boiling process is incomplete and it takes place
between x > 0 to x < 1 (e.g., x = 0.3 to 0.9), which is practically

in the area of saturated damp vapor [14].
If the cooler is fed with the medium with the aid of a thermostatic or electronic expansion valve, then the refrigeration
medium flows to the expansion valve in the form of a liquid that
has not been heated up to the saturation temperature. During the
heat transfer engineering

T

TS
TF
∆ΤS
TS

0
two - phase zone

one-phase zone

L

Figure 1 Division of coil tube length L into the zones of two-phase and singlephase flow in the case where the coil tube is fed through the expansion valve.

flow through the expansion valve, a damping conversion occurs
(the medium expands while it does not perform any external
work). During this time, a part of the liquid passes to the vapor
state, while the temperature of the medium is lowered to the
evaporation temperature level. The remaining liquid evaporates
during the flow through the coil tube. If the quantity of the refrigeration medium that evaporates in the evaporator is too small for
the boiling process to occur on the whole length of the coil tube,
then after the completion of the phase change of boiling (sometimes referred to as proper boiling), the dry saturated vapor is

overheated. In fan air coolers, the active length L of the coil
tube can be divided into two sections: a two-phase length (zone)
(in which heat exchange during boiling in a flow occurs) and
a single-phase length (zone) (in which a convective exchange
of the heat of a single-phase medium, i.e., overheated vapor,
occurs)—see Figure 1. The size of the overheating zone can be
adjusted by changing the setting of a thermostatic expansion
valve or the time characteristics of an electronic valve.
The occurrence of disturbances in the feeding “mechanism”
of the evaporator, for example, in the form of an instantaneous
decrease or fading of the mass rate of flow of the medium, is crucial for its correct operation. In the present paper, the results of
experimental investigations of the boiling process of the R404A
refrigeration medium in a coil tube are presented for the case
where periodically generated disturbances are present. The determination of the impact of these disturbances on the operation
of the entire refrigerating system has a substantial cognitive and
application-focused significance on the construction, operation,
and economic analysis of the system.

EXPERIMENTAL FACILITY
The experimental investigations of the boiling process were
conducted on a measuring facility, which is schematically presented in Figure 2. Its main elements include an isolated refrigeration chamber 1 and the air cooler 2 tested placed in it, which
vol. 32 no. 5 2011


´
T. BOHDAL AND W. KUCZYNSKIRH

361

Figure 2 Schematic diagram of the experimental facility: 1, isolated refrigeration chamber; 2, lamelled air cooler; 3, flow channel of the lamelled block of the air

cooler; 4, compressor and condensation installation (components of the installation: COM, piston compressor; CON, water-chilled condenser; LPS, low-pressure
control system; HPS, high-pressure control system; TL, tank with the liquid R404A medium; 5, cutoff valve; 6, a classical flow rate measuring system; 7, Massflow
type electronic flowmeter; 8, computer measuring and recording system; 9, pressure measuring and recording system; 10, temperature measuring and recording
system; 11, inspection opening; 12, feeding block; 13, filter/dewaterer; 14, evaporator of auxiliary refrigeration system; 15, electric air heater; 16, measurement of
the environment parameters.

constituted an element of a single-stage compressor refrigeration system. Air cooler 2 was fed with R404A refrigerant from
refrigeration and condensation installation 4, which is equipped
with the following subassemblies: a piston compressor COM (a
compressor of K373H/4P-102Y type), a condenser CON chilled
with water, a liquid tank TL, and control instrumentation. From
the liquid tank TL, the R404A refrigeration medium flowed
through the filter–dewaterer 13 and inspection hole 11 for the
flow-rate measuring systems. The liquid refrigeration medium
flowed to the feeding system 12 and the air cooler 2 placed in
a flow channel 3. Additional control elements were placed in
the test chamber 1; i.e., an electric air heater 15 and evaporators
14 were placed on the sidewalls inside chamber 1 and were fed
from an auxiliary refrigeration system. A forced air movement
through the cooler tested was realized with the aid of an axial
fan, with the possibility of an adjustment of the volumetric rate
of airflow (Figure 3). The experimental facility allowed us to
investigate the scope of a constant adjustable level of the heat
load in the test chamber [15].
The main element of the fan cooler was a heat exchanger:
an evaporator made in the form of a single coil tube lamelled
block, whose dimensional diagram is given in Figure 4.
Over the length of the coil tube of the lamelled block L =
13.86 m, 12 sensors for pressure measurements and 12 sensors
for temperature measurements were placed at regular intervals.

In each of the 12 cross sections of the coil tube, there was one
heat transfer engineering

piezoelectric sensor for pressure measurements and one thermoelectric sensor for the measurements of the temperature of
the medium (Table 1). A dimensional diagram of the arrangement of the sensors along the length of the coil tube is given in
Figure 5.
The computer system used for the measurement, control, and
registration of the basic parameters of the refrigeration medium,
air, and environment constituted an integral component of the
experimental facility. This system included the following: (a)
NiCr–Ni type thermoelectric sensors with 0.35 mm diameter
Ventilator

Exchanger

Channel

Figure 3 Schematic diagram of cooler housing in channel.

vol. 32 no. 5 2011


´
T. BOHDAL AND W. KUCZYNSKIRH

362
480 [mm]

TEV

360 [mm]

L1

Figure 4 Measurement diagram of lamelled block viewed from the side of air
inflow.

thermocouple wires (for which individual calibration characteristics were previously made) were included in the system of
voltage amplifiers along with a computer converter card for the
voltage measurement, PCL 818HG type; (b) piezoelectric pressure sensors (the ICP type with a M102A07 symbol), which
cooperate with the tare system and a computer voltage measuring card; and (c) a MASS2100-type electronic Massflow
flowmeter, manufactured by the Danfoss company, with software, which was included in the measuring and data processing
system.
All of the impulses obtained from the temperature, pressure,
and flow rate measuring sensors were converted into voltage
signals and were supplied to the computer system.
It is evident from the conducted analysis that the temperature
values were determined with an accuracy of ±0.1◦ C and the
densities of heat flux q and mass flux (wρ) were measured with
an accuracy of ±6%. The velocities of the displacements of
the pressure and temperature changes were determined with an
accuracy of ±10%.
The scope of the experimental investigations conducted was
limited by the capabilities of the measuring facility. They allowed us to make measurements related to the following: (a)
Table 1 Arrangement of the cross sections where sensors for pressure and
temperature measurements were placed

1
2
3

4
5
6

L3

L4

L5

L6

L7

L8

L9

L10

L11

L12

Figure 5 Schematic diagram of the distribution of sensors for measuring the
temperature and pressure of the refrigeration medium during flow in the coil
tube (where TEV is the thermostatic expansion valve).

the density of the mass flux of the refrigeration medium (wρ) =
0 to 300 kg/(m2-s), (b) the boiling temperature of the medium

Ts = 0 to –40◦ C, and (c) the density of the heat flux q = 0 to
6000 W/m2.

RESULTS OF EXPERIMENTAL INVESTIGATIONS

440 [mm]

Number

L2

Distance from feeding
block

Number

Distance from feeding
block

L1 = 855 mm
L2 = 1965 mm
L3 = 3073 mm
L4 = 4183 mm
L5 = 5250 mm
L6 = 6377 mm

7
8
9
10

11
12

L7 = 7484 mm
L8 = 8582 mm
L9 = 9772 mm
L10 = 10,887 mm
L11 = 11,977 mm
L12 = 13,081 mm

heat transfer engineering

In the present paper, the notion of a “periodically generated
disturbance” is to be understood as a disturbance produced by
feeding the evaporator with a refrigeration medium, in conditions of a change of the time to open and close the valve that
supplies the medium to the coil tube. Such an action results in
an increase or a decay of the mass flux density of the R404A
medium. This, in turn, results in periodic changes of the pressure and temperature along the flow path in the coil tube. In the
experimental investigations, a single coil tube lamelled block
was used, while an additional cutoff was installed on the coil
tube inlet (thus allowing the disturbances to be turned off).
In the experiments, it was assumed that a constant opening
and closing time of the cutoff valve was realized in the measuring
session. While the opening time of the valve was always constant
for all of the measuring series (5 s), the closing time of the valve
in the individual measuring series varied and was τc = 5, 10,
15, 20, 25, and 30 s. The sum of the opening and closing times
constituted the duration of the period that formed the basis
for the determination of the frequencies of the disturbances
generated f [mHz] (f = 100, 67, 50, 40, 33, 29 mHz).

Figures 6 to 8 present example characteristics of the course of
the mass rate flow of the R404A refrigeration medium (Figure
6), changes of the evaporation pressure (Figure 7), and the temperature profile (Figure 8). For the purpose of the construction
of the pressure and temperature characteristics presented, the
registration of the pressure and temperature by sensors denoted
with subsequent numbers (given according to Figure 5) was
taken into account. The introduction of periodic disturbances
resulted in the occurrence of the pulsation of the medium flow
rate. During the period of the closing of the cutoff valve, the
medium was “sucked off” by the compressor from the coil tube.
Because of this, there was a pressure drop and an increased
overheating of the vapor. This caused gradual increase in the
temperature of refrigerant in the monophase area of the tubular
channel. At the same time, in the two-phase boiling area, the
boiling temperature of refrigerant decreased, which depends on
vol. 32 no. 5 2011


´
T. BOHDAL AND W. KUCZYNSKIRH

Figure 6 Changes of mass rate flow m˙ of the R404A refrigeration medium
during periodic disturbances; initial value m˙ = 50 [kg/h].

the absolute pressure. Opening of the valve resulted in the reversal of the process. An inflow of a new portion of refrigerant
caused a pressure increase in the channel, which in turn resulted
in an increase of the vaporization temperature and a decrease
of the overheating of vapors on the outlet from the pipe coil.
The changes of the pressure and temperature of the refrigeration
medium that occur during its flow in a coil tube with periodic

disturbances are characterized by a “time shift.” This proves the
finite velocity with which the signals of these values relocate
after the opening or closing of the cutoff valve. Therefore, it
can be recognized that there is a reaction with a wave nature,
which is characterized by two velocities: vp (the velocity of the
relocation of the pressure change signal), and vT (the velocity of
the temperature change relocation). The commencement of the
boiling process results in an intensification of the heat exchange,
which is manifested by a decrease of the channel wall temperature. For this reason, the relocation of the signal produced by
a decreased temperature can be identified with the relocation of
the front of the boiling medium, i.e., the so-called boiling front,
which displaces with velocity vT [10, 16, 17].

Figure 7 Course of changes of pressure p0 in time τ of the medium flow in
the coil tube.

heat transfer engineering

363

Figure 8 Temperature profile T of the medium in time τ during its flow in the
coil tube.

During experimental investigations, boiling of the medium
was realized under the conditions of periodical external disturbances. Opening or closing of the cutoff valve resulted in a
periodical change of refrigerant parameters under nonstationary conditions. The consequence of the disturbances occurring
was the formation of a pressure wave, which relocated along
the channel. It is the opinion of the authors that the relocation of the pressure wave was the reason for the formation of a
temperature wave as a secondary effect. However, no large temperature changes of the medium or of the tubular channel wall
were observed. It means this does not involve such temperatures,

which should be the result of the value of the saturation pressure change in the channel. This is the result of the impact of the
thermal inertia of the system as well as a significant frequency
of disturbances generated. The investigations demonstrated that
velocities vp and vT depend, among other things, on the size of
the disturbance triggered, which is characterized by the pressure drop p. Figure 9 presents as an example an experimental
dependence vp = f ( p). The size of the pressure drop p that
occurs during periodically generated disturbances depends on
the mass flux density in the coil tube. This phenomenon is the
result of the work of the compressor, which sucks in the refrigeration medium vapor from the evaporator. When the cutoff valve
from the inlet of the medium to the coil tube is closed, there is
a pressure drop. The longer the valve is closed, the greater the
pressure drop is. Once the cutoff valve is opened again (with a
greater reduction of the pressure in the evaporator), an increase
of the medium flow rate occurs. Figure 10 presents the dependence of the mass flux density (wρ) of the R404A refrigeration
medium on the pressure drop p. The mass flux density (wρ)
exerts a substantial influence on the values of velocities vp and
vT , as shown in Figure 11.
It is evident from the conducted investigations that velocities
vp and vT differ from one another with regard to their values,
as the velocity of the pressure signal relocation changed between 45 and 330 m/s, while the velocity of the boiling front
relocation was substantially smaller, and ranged from close to
vol. 32 no. 5 2011


364

´
T. BOHDAL AND W. KUCZYNSKIRH

Figure 9 Dependence of the pressure change displacement velocity vp on the

pressure drop p generated by closing the cut-off valve; vp = f ( p).

Figure 10 Dependence of the mass flux density (wρ) of the refrigeration
medium on the pressure drop p.

Figure 12 Dependence of the temperature change displacement velocity vT in
the coil tube on the velocity vp of the pressure signal displacement.

zero to 4.5 m/s. Low values of vT serve to confirm the results
obtained by the authors of reference [8], where a model was
given to enable the determination of the boiling front forming
velocity on the surface heated. It was assumed in the analysis
that the boiling front velocity on the surface heated depends on
local liquid overheating TS and the thermophysical properties
of the refrigerant in saturated conditions. The obtained results
of theoretical computations were compared with the results of
experimental investigations. The experiments were conducted
for the range of low-pressure values and a high-value liquid
overheating (up to 155 K) was obtained. This corresponded to
a boiling front velocity vT of up to 35 m/s. The authors of reference [18] confirm that with higher absolute pressures, such large
velocities vT are not achieved. In practice, it is not possible to
overheat a liquid by dozens of degrees Kelvin because the boiling process commences spontaneously at a substantially lower
liquid overheating value. This results in a substantial reduction
of velocity vT even to values approaching zero. Experimental
investigations also demonstrated that the velocities of the relocation of the pressure signal vp and temperature signal vT are
interdependent, which is shown in Figure 12.

ANALYSIS OF EXPERIMENTAL RESULTS

Figure 11 Dependence of the pressure change displacement velocity vp on the

mass flux density (wρ) of the refrigeration medium; vp = f (wρ).

heat transfer engineering

The experimental investigations of the influence of periodic
disturbances on the boiling process of a refrigeration medium
demonstrated that there is a direct interdependence between
the propagation velocity of the pressure disturbances vp and
the relocation velocity of the temperature change signal vT and
the frequency of the disturbances applied. An increase of the
disturbances generation frequency resulted in a velocity drop
distribution change of pressure signal vp and temperature signal
vT . This frequency was described with the aid of nondimensional
number Ta, which takes into account the ratio of the time τo
required to open the valve on the inlet of the medium to the coil
vol. 32 no. 5 2011


´
T. BOHDAL AND W. KUCZYNSKIRH

365

took into consideration Buckingham’s
theorem, according
to which the number of non-dimensional modules is equal to
the number of independent physical parameters reduced by the
number of basic measurements in the SI system (such as meter,
second, and kilogram) [19, 20].
The relocation velocity of the pressure change vp signal triggered by periodic disturbances was made functionally dependent on the following parameters:

v p = f ( p, ps , ν, d, w, τo , τc )

Figure 13 Dependence of the pressure change displacement velocity vp in the
coil tube on the nondimensional Ta number.

tube to the total time of its being closed τc and opened τo :
Ta =

τo
τc + τo

where: vp is the relocation velocity of the pressure change signal
[m/s], p is the oscillation amplitude of the boiling pressure during disturbances [N/m2], ps is the average evaporation pressure
of the refrigeration medium [N/m2], d is the internal diameter
of the coil tube [m], w is the average velocity of the two-phase
mixture of the refrigeration medium [m/s], τo is the time of
opening of the valve on the medium inlet to the coil tube [s], τc
is the time of closing of the valve on the medium inlet to the
coil tube [s], and ν is the kinematic coefficient of the viscosity
of the two-phase mixture [m2/s], which is defined as:

(1)

The time of the opening of the valve was constant and was τo
= 5 s, while an increase of the value of the closing time of the
valve τc corresponded to a drop of the frequency of disturbances
f and caused a reduction of the value of the nondimensional
number Ta. Ta represents, in an indirect manner, the force of
the disturbances acting on the system [9, 10]. This determines
the dependence of the speed of the pressure change vp and the

velocity of the relocation of the temperature change signal vT
from the Ta number (Figures 13 and 14).
An attempt was made to generalize, in the form of a regression function, the experimental results obtained. The problem
concerned the description of the relocation velocity of the pressure change vp signal and the temperature change vT signal. For
this purpose, dimensional analysis procedures were used that

(2)

ν=

µTPF
ρTPF

(3)

with
1
µTPF

=

1
1−x
1
1
1−x
+
and
=
+

µg
µ1
ρTPF
ρg
ρl

(4)

It is evident from the assumptions accepted that the relocation
velocity of a triggered disturbance was made dependent on its
amplitude, frequency, and the physical properties of the refrigeration medium. The frequency of the disturbances is indirectly
covered by the time of the opening and closing of the valve at the
medium inlet to the evaporator. The size of the pressure oscillation amplitude p depends on the change of the dryness level
x and the filling degree ϕ of the boiling refrigeration medium.
A drop of the medium boiling pressure results in an increase of
the values of x and ϕ while a rise of the pressure makes these
values lower.
By way of a dimensional analysis [19], Eq. (2) was converted
to the following form:
B
v+
p = A × ReT P F ×

p+

C

× T aD

(5)

where:
v

Figure 14 Dependence of the temperature change displacement velocity vT in
the coil tube on the nondimensional Ta number.

heat transfer engineering

p
v+
p = w is the nondimensional velocity (determined via the
ratio of the relocation velocity of the pressure change signal
to the two-phase mixture velocity).
ReT P F = (wρ)×d
is the nondimensional Reynolds number for a
µT P F
two-phase flow.
p + = p0p is the nondimensional pressure drop (as a ratio of
the pressure oscillation amplitude and the boiling pressure of
the refrigeration medium).
Ta is a nondimensional number that takes into account the relationship between the time τo of the opening of the valve on

vol. 32 no. 5 2011


366

´
T. BOHDAL AND W. KUCZYNSKIRH

Figure 15 Dependence of the nondimensional velocity vp +cal calculated from
Eq. (3) on the value obtained from experimental measurements of vp +exp .

the inlet of the medium to the coil tube and the total time of
its being closed τc and opened τo , as described by Eq. (1).
The calculation of the leading constant A and exponents B,
C, and D in Eq. (5) was carried out with the use of the nonlinear regression model. In this model, the maximum likelihood
method was used, which constitutes an alternative to the method
of the sum of the least squares. The standard deviation of the
value observed from the one expected was determined with the
use of the applied model, which is the so-called loss function. A
maximization of the likelihood function (selection of the proper
parameters that fulfill this condition) was conducted with the
quasi-Newton and Symplex method, which was carried out using standard computational modules in the Statistica software
package [20].
The following values of the unknowns occurring in Eq. (5)
were obtained:
A = 489 × 104 , B = −1.05, C = 0.07, D = −0.76
with a variance of 92% and a correlation coefficient of 0.91.
The values of the nondimensional experimental velocity v +
p
were compared with the results of calculations according to
dependence (5). A satisfactory compatibility was obtained in
the range of ±25%, which is presented in Figure 15.
In an analogous manner, the value of nondimensional velocity vT + was determined, which takes into account the displacement of the temperature change vT . Its value was made
functionally dependent from the following parameters:
vT = f ( T, Ts , ν, d, w, τo , τc )

(6)

where additional denotations were introduced: vT is the displacement velocity of the temperature change signal [m/s], T
is the amplitude of the temperature oscillations caused by disturbances [K], and Ts is the average boiling temperature of the
refrigeration medium [K].
heat transfer engineering

Figure 16 Dependence of the nondimensional velocity vT +cal calculated from
Eq. (5) on the value obtained from experimental measurements of vT +exp .

After the application of the dimensional analysis, a dependence was obtained in the following form:
vT+ = A × ReTB P F ×

T+

C

× T aD,

(7)

where:
vT+ = vwT is the nondimensional velocity determined via the
ratio of the displacement velocity of the temperature change
signal vT to the velocity of the two-phase mixture.
T + TTs is the nondimensional temperature drop determined
via the ratio of the temperature amplitude to the boiling temperature of the refrigeration medium T0 [K].
The following values of constants were obtained for Eq. (7):
A = 107 × 105 , B = −1.05, C = 1.43, D = −0.76
with a variation of 92% and a correlation coefficient of 0.94.
The value of the experimental nondimensional velocity vT+

was compared with the results of calculations according to dependence of Eq. (7). A satisfactory compatibility was obtained
in the range of ±25%, which is presented in Figure 16.
Empirical dependences of Eqs. (5) and (7) were checked
with regard to the following range of parameters: saturation
temperature Ts = (0 to –40◦ C); saturation pressure ps = (0.1
to 0.24 MPa); mass flux density (wρ) = (50 to 300 kg/m2-s);
displacement velocity of the pressure change signal vp = (40
to 330 m/s); displacement velocity of the temperature change
signal vT = (1 to 4.50 m/s); nondimensional number Ta = (0.14
to 0.50); and criterion number ReTPF = (2280 to 12800).
In a two-phase medium with a boiling refrigeration medium,
the pressure is strictly related to the saturation temperature value.
In view of this fact, dependence of Eq. (7) (which allows the
value of the nondimensional displacement velocity of the temperature change signal vT+ to be determined) can be transformed
to a form where the nondimensional temperature drop T + is
replaced with the nondimensional pressure drop p+:
vT+ = 107 × 105 × Re−1.05
T PF ×
vol. 32 no. 5 2011

p+

0.11

× T a −0.76 ,

(8)


´

T. BOHDAL AND W. KUCZYNSKIRH

Dependences of Eqs. (7) and (8) are identical and can be
used alternatively, depending on the assumptions accepted and
the current requirements.

CONCLUSIONS
An attempt was made to assess the impact of periodically
generated external disturbances on the boiling process of a refrigeration medium in a flow. The experimental investigations
were conducted under conditions whereby periodic changes (an
increase and a decay) of the mass flux density of the refrigeration medium were made for constant heat load levels of the
refrigeration chamber. This led to periodic changes of the pressure and temperature along the path of the flow of the medium
in the coil tube of the evaporator. The investigations were carried out with the use of an environmentally friendly R404A
refrigeration medium. Based on an analysis of the boiling of
the refrigeration medium under the conditions of periodically
generated disturbances, the following were established:
1. The boiling process of the refrigeration medium in a flow
exhibits wave properties, which are characterized by two velocities: vp , the displacement velocity of the pressure change
signal; and vT , the displacement velocity of the temperature
change signal;
2. Velocities vp and vT depend on the parameters of the twophase medium and the magnitude of the disturbance generated, which are described by the value of the pressure drop
p or temperature drop T.
3. There is an analogy in the displacement of the pressure
change signal and the temperature change signal, which is
manifested by an interdependence between the values of
the velocities vp and vT ; a higher value of velocity vp corresponds to a higher value of velocity vT , and vice versa. This is
also confirmed by the notation given by empirical equations
(3)–(6).
4. The displacement velocity of the disturbances in a boiling
refrigeration medium depends on the frequency of their generation. This is taken into account in the nondimensional Ta

number, which constitutes the ratio of time τo of the opening
of the valve at the inlet of the refrigeration medium (from the
coil tube) to the total time of its closing τc and opening τo .
5. The dependences worked out on the basis of the experimental investigations allow one to determine the displacement
velocity of the pressure change signal vp and the temperature
change signal velocity vT generated with periodic disturbances.
NOMENCLATURE
d
f
L

internal diameter of coil tube [m]
frequency [s−1]
length of coil tube [m]
heat transfer engineering

m˙
p
p
q
Re
T
T
Ta
v
w
(wρ)
x

367

mass rate of flow [kg/h]
pressure [MPa]
pressure drop (pressure amplitude during disturbances)
[MPa]
heat flux density [W/m2]
Reynolds number
temperature [◦ C]
temperature drop (temperature amplitude during disturbances) [K]
dimensionless number that covers the frequency of the
disturbances generated
velocity of displacement of disturbances [m/s]
velocity [m/s],
mass flux density [kg/m2-s]
dryness level

Greek Symbols
ϕ
µ
ν
ρ
τ

filling level, relative air humidity
dynamic viscosity coefficient [kg/m-s]
kinematic viscosity coefficient [m2/s]
density [kg/m3]
time [s]

Subscripts

c
cal
exp
F
g
l
o
p
s
T
TPF

shutting of cutoff valve
calculation value
experimental value
medium
gas
liquid
opening of cutoff valve
pressure
saturation, overheating
temperature
two-phase flow

Superscript
+

dimensionless quantity

REFERENCES

[1] Bergles, A. E., Review of Instabilities in Two-Phase System, Hemisphere Publishing Corporation, Bristol, UK,
1977.
[2] Bohdal, T., Investigation of Boiling of Refrigerating
Medium Under Conditions of Impulse Disturbances, International Journal of Experiental Heat Transfer, vol. 17,
no. 2, pp. 103–117, 2004.
[3] Wedekind, G. L., An Experimental Investigation Into the
Oscillatory Motion of the Mixture–Vapor Transition Point
vol. 32 no. 5 2011


368

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]
[13]

[14]
[15]

[16]

´
T. BOHDAL AND W. KUCZYNSKIRH

In Horizontal Evaporating Flow, Journal of Heat Transfer,
vol. 93, pp. 47–54, 1971.
Xu, J., Zhou, J., and Gan, Y., Static and Dynamic Flow
Instability of a Parallel Microchannel Heat Sink at High
Heat Fluxes, Energy Conversion and Management, vol. 46,
pp. 313–334, 2004.
Yuncu, H., Yildirim, O. T., and Kakac, S., Two-Phase Flow
Instabilities in a Horizontal Single Boiling Channel, Applied Sciences Research, vol. 48, pp. 83–104, 1991.
Nakoryyakov, V. E., Pokusaev, B. G., and Shreiber, I. R.,
Wave Propagation in Gas–Liquid Media, ed. A. E. Bergles,
CRC Press, Boca Raton, FL, 1993.
Bilicki, Z., Latent Heat Transport in Forced Boiling Flow,
International Journal of Heat and Mass Transfer, vol. 26,
no. 4, pp. 539–565, 1983.
Cao, L., Kakac¸, S., Liu, H. T., and Sarma, P. K., The
Effects of Thermal Non-Equilibrium and Inlet Temperature
on Two-Phase Flow Pressure Drop Type Instabilities in an
Upflow Boiling System, International Journal of Thermal
Science, vol. 39, pp. 88–905, 2000.
Gabaraev, B., Kovalev, S. A., Molochnikov, Yu. S.,
Soloviev, S. L., and Usatikov, S. V., Boiling Curve in Temperature Wave Region, International Journal of Heat and

Mass Transfer, vol. 46, pp. 139–148, 2003.
Bohdal, T., Reasons of Phase Change Instabilities in Energy Conversion Media, Koszalin University of Technology Press, Koszalin, Poland, 2006 (in Polish).
Bohdal, T., Bilicki, Z., and Czapp, M., Development of
Nucleate Boiling in an Annular Clearance, International
Journal of Heat and Technology, vol. 19, no. 2, pp. 33–37,
2001.
Carey, V. P., Liquid–Vapor Phase-Change Phenomena,
Hemisphere, Washington, DC, 1992.
¨ Karsli, S., and Yilmaz, M., Experimental InComakli, O.,
vestigation of Two Phase Flow Instabilities in a Horizontal
in Tube Boiling System, Energy Conversion and Management, vol. 4, pp. 249–268, 2002.
Nigmatulin, R. I., Dynamics of Multiphase Media, Hemisphere, New York, 1990.
Bohdal, T., and Kuczy´nski W., Investigation of Boiling of
Refrigeration Medium Under Periodic Disturbance Conditions, International Journal of Experimental Heat Transfer, vol. 18, no. 3, pp. 135–151, 2005.
Mitrovic, J., and Fauser, J., Propagation of Two-Phase
Fronts During Boiling Of Superheat Liquids, Proc. 2nd
European Symp. “Fluids in Space,” Naples, Italy, 1996.

heat transfer engineering

[17] Pavlenko, A. N., and Lel, V. V., Model of Self-Maintaining
Evaporation Front for Superheat Liquids, Proceedings of
the Third International Conference on Multiphase Flow,
ICMF’98, Lyon, France, pp. 366–374, 1998.
[18] Pavlenko, A. N., and Lel V. V., Approximate Simulation
Model of a Self-Sustaining Evaporation Front, Thermophysics and Aeromechanics, vol. 6, no. 1, pp. 105–117,
1999.
[19] Kukiełka, L., Podstawy Bada´n In˙zynierskich, Koszalin
University of Technology Press, Koszalin, Poland, 2000
(in Polish).

[20] Sobczak, M., Statystyka, Wydanie II Poprawione,
Wydawnictwo Naukowe PWN, Warszawa, Poland, 1994
(in Polish).
Tadeusz Bohdal is the Vice-Rector for Research and
Co-operation with Industry and he is head of the Chair
of Thermal Engineering and Refrigerating Engineering of the Koszalin University of Technology, Poland.
He is also a member of the Commission B1 of the
International Institute of Refrigeration in Paris. His
general scientific interests are heat transfer during
flow boiling and condensation, intensification of heat
transfer in refrigeration and air-conditioning heat exchangers, and application of thermomechanics and
refrigeration in power engineering. He is author or co-author of seven books,
more than 220 publications in national and international scientific journals,
and more than 130 unpublished reports and expert documents for industrial
and engineering centers. He has supervised six completed Ph.D. dissertations and more than 150 completed M.Sc. theses in refrigeration and power
engineering.

´
Waldemar Kuczynski
is a graduate of the Koszalin
University of Technology, Poland. Since 1999, he has
been working as the Chair of Thermal Engineering
and Refrigerating Engineering. In the year 2002, he
was awarded the title of master of science in the field
of machine construction and operation in the specialty
of thermal engineering. In the years 2002–2007, he
was a Ph.D. student at the Faculty of Mechanical Engineering of the Koszalin University of Technology.
In the year 2008, under a project of the State Committee for Scientific Research, he defended his doctoral thesis entitled “Boiling
Testing in Refrigerant Flow under the Conditions of Periodically Generated
Disturbances.” Since September 2008, he has been the head of the laboratory

of the Chair of Thermal Engineering and Refrigerating Engineering. He is the
co-author of 20 articles, and a joint contractor of seven research projects (and
the manager of one of these). His chief interests focus on the issues of wave
phenomena and instability during the condensation and boiling of refrigerants
in conventional channels and in mini-channels.

vol. 32 no. 5 2011


Heat Transfer Engineering, 32(5):369–383, 2011
Copyright C Taylor and Francis Group, LLC
ISSN: 0145-7632 print / 1521-0537 online
DOI: 10.1080/01457632.2010.483857

Investigation of Thermal Striping in
Prototype Fast Breeder Reactor
Using Ten-Jet Water Model
R. KRISHNA CHANDRAN,1 INDRANIL BANERJEE,2 G. PADMAKUMAR,2
and K. S. REDDY1
1

Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India
Experimental Thermal Hydraulics Section, Fast Reactor Technology Group, Indira Gandhi Centre for Atomic Research,
Kalpakkam, India

2

A two-dimensional numerical analysis has been carried out to study the phenomenon of thermal striping in a prototype fast
breeder reactor using a 10-jet water model that represents a row of the reactor core consisting of fuel and blanket zones. The
above-core structures in the reactor are modeled with a porous lattice plate and solid core cover plate. The Reynolds stress

model is used for simulating the turbulence characteristics of jet mixing phenomena. When the ratio of hot jet velocity to
cold jet velocity is equal to 1, maximum fluctuations of temperature have been observed. Also the temperature fluctuations
reduced gradually beyond a hot jet to cold jet velocity ratio of 1.0. The lattice plate is found to be more prone to thermal
striping as compared to the core cover plate.

INTRODUCTION
The thermal striping phenomenon came to the attention of
nuclear scientists during early 1990. Design of any liquid-metalcooled fast breeder reactor (LMFBR) must be preceded by detailed analysis of the thermal striping phenomenon. The coolant
(sodium) attains different temperatures when it is made to pass
through the fuel and blanket zones of the LMFBR core. The
temperature difference between the hot jet and cold jet can be as
high as 150◦ C. The turbulent oscillating jets interact with each
other, giving rise to high magnitudes of temperature fluctuations. Highly conducting sodium makes it easy to transfer the
temperature fluctuations to the adjacent solid structures without
any loss due to boundary-layer attenuation. This results in the
thermal fatigue of the solid structures and thereby their failure
by generation of cracks in the structures. This phenomenon is referred to as thermal striping. The thermal striping phenomenon
was identified to be occurring in stages, which include: (1) generation of temperature fluctuations in the fluid due to the mixing

Address correspondence to Dr. K. S. Reddy, Department of Mechanical
Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
E-mail:

of different temperature jets, (2) reduction of fluctuations in the
near surface due to boundary layer, (3) conveyance of the fluctuations to the solid surfaces, (4) conduction of fluctuations within
the solid material, and (5) thermal fatigue leading to the failure of structure by the initiation of a crack. The entire thermal
striping phenomena can be attributed to the incomplete mixing
of the different-temperature jets.
A very limited literature is available related to thermal hydraulic studies of thermal striping. The effect of working fluid
on the temperature fluctuation phenomena has been studied by

Moriya and Ohshima [1]. It was found that the average and root
mean square (RMS) temperatures were functions of Reynolds
and Peclet numbers. If the Reynolds number and Peclet number
are sufficiently large (Re > 20,000 and Pe > 600) both in the
prototype and in the model, then the working fluid has no influence on the mixing characteristics. Water or air can be used
instead of sodium for conducting temperature fluctuation studies
at high values of Reynolds and Peclet numbers. Ohshima et al.
[2] elaborated on the status of four temperature fluctuation phenomena: thermal stratification, thermal striping, core–plenum
interaction, and free surface sloshing. Experimental analysis of
a single-jet and a three-jet model with two hot jets surrounding a cold jet was conducted by Tokuhiro and Kimura [3] using ultrasound Doppler velocimetry. The properties like mean

369


370

R. KRISHNA CHANDRAN ET AL.

velocity, RMS velocity, mean temperature, and standard deviation of temperature have been found at different heights from
the inlet of the jets. The heat transfer characteristics of sodium
to the nearby solid structures were experimentally studied using
parallel triple jets by Kimura et al. [4]. The three-dimensional
flow field in a mixing T-junction was studied by Hirota et al. [5].
The experiments were done by varying the velocity ratio of the
hot jet and cold jet, as well as the aspect ratio of the channel.
Ushijima et al. [6] used a second-order closure turbulence
model to perform a numerical analysis on non-isothermal coaxial jets and compared this with experimental results. Muramatsu
and Ninokata [7] used an algebraic stress model (ASM) to conduct a numerical analysis for predicting the temperature fluctuation phenomena. Kasahara [8] analyzed the possibility of crack
initiation and propagation due to thermal striping by conducting structural analysis on a tee junction of the PHENIX reactor.
Low-Reynolds-number turbulent stress and heat flux equation

models (LRSFM) and the k-ε model have been used to simulate
the experimental data of three-jet model by Nishimura et al. [9].
LRSFM gave good predictions of mean temperature as well as
oscillatory motion of the jets. The k-ε model underpredicted the
mixing effect and gave high-temperature fluctuation intensity.
A comparison of the k-ε model and LRSFM has been made using the three-jet model experimental data by Kimura et al. [10].
A quasi-direct numerical simulation was also conducted along
with the turbulence models. Jung and Yoo [11] showed that the
large eddy simulation (LES) can successfully produce time history of turbulence variables. Prediction of thermal striping in a
three-jet situation was carried out using two-layer, shear stress
transport and elliptic relaxation turbulence models by Choi and
Kim [12].
Suyambazhahan et al. [13] conducted numerical analysis of a
single non-isothermal jet and found that high-frequency oscillations are mainly due to forced convection. The thermal striping
phenomena in the Indian prototype fast breeder reactor (PFBR)
were predicted by Velusamy et al. [14], who estimated that
the temperature fluctuations were within the accepted limits of
safety. A direct numerical simulation (DNS) calculation was performed at four localized regions of the reactor at specific velocity and temperature. Suyambazhahan et al. [15] found out mean
flow structure and oscillation characteristics of temperature and
velocity fields of non-isothermal twin parallel jets numerically.
Gao and Voke [16] conducted LES studies for the study of
thermally inhomogeneous jets impinging on a plate. The study
focused on the mechanisms that influence the generation and
transportation of thermal eddies. Voke and Gao [17] showed
that a one-dimensional conduction model is enough to describe
the thermal behavior of the solid plate in impinging jet studies.
Wakamatsu et al. [18] carried out impinging jet experimental
studies using water and sodium as the working fluids to assess
the difference in their physical characteristics. Distance between
the nozzle and the plate was found to affect the fluctuations in

temperature significantly. Comparing the surface attenuation ratios using water and sodium, it was observed that for the same
value of velocity the sodium attenuation ratios were smaller. A
heat transfer engineering

Figure 1 A simplified diagram showing the hot and cold jets coming out of
LMFBR core.

boundary-layer model was proposed to predict the attenuation
of temperature near the surface, and it was found to give good
results compared to the experimental values. Krishna Chandran et al. [19] carried out a numerical analysis simulating the
thermal striping phenomena in a 1/5 scale water model of the
prototype fast breeder reactor (PFBR) primary circuit. Two nonisothermal water jets impinge on a lattice plate placed above the
jets. A Reynolds stress turbulence model is used to evaluate the
temperature fluctuations near the plate.
Most of the studies just described were limited to a threejet model analysis without considering the above-core structural
geometry. An actual reactor core consists of a number of parallel
jets coming out of the fuel and blanket zones. It is possible that
the interaction among these jets is entirely different from that of
a two-jet or three-jet model. The above-core geometry also plays
an important role in the mixing characteristics of multiple jets.
Therefore, it is important to study the thermal striping behavior
of multiple parallel jets near the solid structures. In the present
study a 10-jet water model representing a 1/5 scale model of
PFBR is numerically analyzed. The 10-jet model corresponds
to a half row of the reactor core. Thus it represents, to some
extent, the geometry and thereby the physical phenomena close
to the reactor conditions. The numerical procedure, after taking
due care on geometrical and hydraulic aspects, can be extended
to the actual reactor conditions.

MATHEMATICAL FORMULATION
The schematic of the core of a fast breeder reactor having
a number of fuel and blanket zones is shown in Figure 1. The
coolant sodium at uniform temperature enters the base of the
core and passes through the different zones. The coolant absorbs different amounts of heat and thus comes out at different
temperatures. Above the reactor core, a lattice plate used for
supporting the core-monitoring thermo wells is placed. The lattice plate, being porous, allows the streams to pass through it.
vol. 32 no. 5 2011


R. KRISHNA CHANDRAN ET AL.

371

plate, called the core cover plate, is placed at y/d = 10.4 from
the inlet. Both plates are made to resemble the corresponding
plates in the reactor.
The governing equations in Cartesian form for the 10-jet
model can be written as follows [20–22].
Continuity equation:
∂ρ ∂(ρUi )
+
=0
∂t
∂ xi

(1)

Momentum equation:
1 ∂P

∂
DUi
=−
+
Dt
ρ ∂ xi
∂x j

ν

∂Ui
− < ui u j >
∂x j

(2)

Earlier studies have shown the ability of the Reynolds stress
model (RSM) in forecasting the thermal striping phenomena
effectively [9, 10]. It has been found to accurately predict the
thermal striping phenomena compared to the k-ε model and to be
less time-consuming compared to direct numerical simulation
without losing much accuracy. Therefore, it has been decided
to use the Reynolds stress model for the present turbulence
modeling. The model used standard wall functions for the near
wall treatment after ensuring through a detailed analysis that the
wall y+ values are above 30 and below 300.
The Reynolds stress equation [23] is
D < ρu i u j >
Dt

=−

∂ Ti jk
+ Pi j + Ri j − εi j
∂ xk

(3)

D<ρu u >

Figure 2 Geometry of the 10-jet model.

Above the lattice plate, a core cover plate is also placed on which
the thermo wells are mounted. These two plates are much affected by the thermal mixing of the out coming hot and cold
jets from the reactor core. Hence, the analysis is carried out
to find out the temperature fluctuations near these two solid
structures.
The geometry and boundary conditions selected for the analysis are shown in Figure 2. Ten jets having 25 mm diameter each
are introduced into a chamber with an outlet provided on the
side wall as shown in Figure 2. The seven hot jets correspond
to the jets coming out of the fuel zone and the three cold jets
correspond to the jets coming out of the blanket zone of the
reactor. The region above the control plug has been modeled as
one with no jet. In actual reactors the flow through the control
plug subassembly is very low compared to other subassembly
outlet velocities. Hence in the analysis this has been treated as
one with no jets coming out of the subassembly. In the present
study, a numerical simulation of the mixing of 10 jets is analyzed at different velocity ratios. Two steel plates are placed in
the flow zone, which prevents direct motion of the fluid upwards.
The bottom porous plate (φ = 0.30) is called the lattice plate

and is at a distance of y/d = 3.8 from the inlet. The top solid
heat transfer engineering

i j
where
is the total derivative given by the sum of the
Dt
time derivative ( ∂t∂ (ρ < u i u j >)) and the convection term Cij
given by ( ∂∂xk (ρu k < u i u j >)).
Tijk is the transport of Reynolds stresses, given by

Ti jk = ρ < u i u j u k > + < u i p > δ jk + < u j p > δik
−µ

∂ < ui u j >

(4)

∂ xk

Pij is the production term, given by
Pi j = −ρ < u i u k >

∂U j
∂Ui
− ρ < u j uk >
∂ xk
∂ xk

(5)

Rij is the redistribution or pressure-strain term, given by
Ri j = p

∂u j
∂u i
+
∂ xi
∂x j

(6)

and εij is the dissipation tensor, given by
εi j = 2µ

∂u i ∂u j
∂ xk ∂ xk

(7)

Of these terms, the convective term of the total derivative,
the production term, and the last term of the Reynolds stress
transport do not have to be modeled. But in order to close
the equations, the turbulent part of the transport equation, the
vol. 32 no. 5 2011


372

R. KRISHNA CHANDRAN ET AL.

production strain, and dissipation terms are modeled. The turbulent diffusion term (first two terms of the Reynolds stress
∂<u u >
transport term) is modeled as ∂∂xk ( µσkt ∂ xi k j ) where the value
of σk is taken as 0.82. The pressure-strain term is modeled
as Ri j = φi j,1 + φi j,2 + φi j,w . Here the slow pressure-strain
is modeled as φi j,1 = −C1 ρ kε [< u i u j > − 23 δi j k] where C1
= 1.8. The rapid pressure-strain term is given by φi j,2 =
−C2 Pi j − Ci j − 13 δi j (Pkk − Ckk ) . In this equation, C2 =
0.6, and φi j,w is the wall-reflection term. The dissipation tensor
can be modeled as εi j = 23 δi j ρε. The turbulent viscosity in the
2
above equations is taken as µt = ρCµ kε where Cµ = 0.09.
The turbulent kinetic energy (k) equation is expressed as
∂
∂
∂
(ρkUi ) =
(ρk) +
∂t
∂ xi
∂x j

µt ∂k
σk ∂ x j

+

1
Pii − ρε (8)

2

Here the value of σk is 0.82.
The turbulent dissipation (ε) equation is given by
∂
∂
∂
(ρε) +
(ρεUi ) =
∂t
∂ xi
∂x j
+ Cε1

µt ∂ε
σε ∂ x j

1 Pii ε
ε2
− Cε2
2 k
k

(9)

The turbulence modeling constants have the following values: σε = 1.0, Cε1 = 1.44, and Cε2 = 1.92.
The Reynolds stress model uses an analogy between heat and
momentum transfer to model the energy equation. The equation
is given by
∂

∂
∂
(ρUi T ) =
(ρT ) +
∂t
∂ xi
∂x j

λf +

µt
Prt

∂T
∂x j

(10)

The value of Prt is 0.85.
Within the solid plate only conduction is present. The
corresponding governing equation is given by
∂2T
ρCs ∂ T
=
.
∂ xi ∂ xi
λs ∂t

(11)

In the porous lattice plate the momentum equation will be
ρf

1 ∂Ui
1
∂Ui
+ 2 Ui
ϕ ∂t
ϕ
∂ xi

∂T
∂ xi

Initial and Boundary Conditions
The domain was assumed initially to be stagnant and at a
temperature equal to 50◦ C. The temperature of the hot jet was
taken as 70◦ C and that of the cold jet as 30◦ C. Five different hot
jet to cold jet velocity ratios—0.35, 0.50, 1.0, 2.0, and 3.0—were
used for the analysis. The Reynolds number of the hot jets was
always above 20,000. The Reynolds number of the cold jets has
been varied. The jets were assumed to have a top-hat velocity
profile at the inlet. All the inlets were assumed as velocity inlets,
while outflow was taken at the outlet. A turbulent intensity of
5% was assumed for all the incoming jets since the flow was a
medium turbulent one. The walls were taken as adiabatic with
no-slip boundary condition.
The viscous resistance [23] is given by

(13)

where λe f f = ϕλ f + (1 − ϕ) λs .
The assumptions made in the mathematical formulation include: (a) The flow is two-dimensional, (b) properties of the
heat transfer engineering

(14)

where Dp is the plate hole diameter.
The inertial resistance [23] is given by
1 A p /A f
β=
β
tp

∂
∂
(ϕρ f C f T f + (1 − ϕ) ρs Cs Ts ) +
ρ f Ui C f T f
∂t
∂ xi
λe f f

The available computational fluid dynamics (CFD) software
FLUENT 6.2 was used for the numerical analysis. A detailed
grid independence study was conducted to find out the suitable
mesh size. For the analysis, the grid size has been varied in steps
of 33,600, 52,500, 93,300, 134,400 and 210,000. The variation
in properties using 134,400 and 210,000 was less than 2%.
Hence it was decided to use a model with 134,400 grids. The
energy equation has been solved with a residual of 10−8, whereas

momentum, continuity, Reynolds stress, k, and ε equations have
been solved with a residual of 10−6. A time step of 0.001 s has
been selected in order to completely capture the temperature
fluctuations during the flow. Implicit formulation with secondorder accuracy was used for the unsteady equations. In order to
have second-order accuracy for the temporal discretization, the
values of the variable for the previous two time steps have been
used in the calculations.

150 (1 − ϕ)2
1
= 2
K
Dp
ϕ3

The corresponding energy equation will be

∂
∂ xi

NUMERICAL PROCEDURE

∂p
µ
=−
− Ui − βρ f |U | Ui
∂ xi
K
(12)

=

fluid are linearly varying with temperature, (c) the flow is incompressible, (d) there is no effect of buoyancy, and (e) the flow
is unsteady.

2

−1

(15)

where β is a coefficient based on the ratio of porous plate hole
diameter to its thickness. Ap is the area of the plate and Af is the
free area for flow.
Based on the preceding equations, a viscous resistance of
1.125 × 107 m−2 and inertial resistance of 1140 m−1 were taken
for the lattice plate. Between the core cover plate and the fluid,
conjugate heat transfer was assumed to correlate conductive and
vol. 32 no. 5 2011


R. KRISHNA CHANDRAN ET AL.

373

convective heat transfer. The equation that couples the conductive heat transfer between the fluid and solid region is
λs

∂T
∂x

= λf
s

∂T
∂x

(16)
f

the boundary and initial conditions can be expressed mathematically as
T = 323 K, U = 0 at t = 0 for the entire domain

(17)

T = 343 K, U = Uh for the hot jets

(18)

T = 343 K, U = Uc for the cold jets

(19)

U = 0 at the walls

(20)

RESULTS AND DISCUSSION
Validation of Numerical Procedure
The numerical procedure has been validated with the experimental data reported in Tokuhiro and Kimura [3]. A comparison of present numerical procedure with the three-jet model

data in terms of nondimensional mean (θ) and RMS (θRMS )
temperatures is shown in Figure 3. The nondimensional mean
temperature is defined as
θ=

(T − Tc )
(Th − Tc )

(21)

and the nondimensional RMS temperature is given as:
θ R M S = TR M S 100/(Th − Tc )

(22)

The mean temperature distribution along the transverse and
axial directions show the numerical and experimental results
are closely matching with a maximum deviation of about 12%
(Figure 3a and b). Some deviation can be seen in the outer edges
of the jets (Figure 3a). This might be because the time simulated was not enough for the outer domains to attain a closer
value with the experimental data. It must be noted that the initial condition of mean jet temperature was assumed in the study
and the flow was simulated for a period of 20 s only. Very
close to the inlet there was departure from the experimental data
possibly because the turbulence model is incapable of predicting in the developing regions of the jets (Figure 3b). Similarly
good agreement can be seen for the experimental and numerical
results of RMS temperature distribution in the region of interest (Figure 3c). The model correctly predicted the maximum
temperature fluctuation that was measured in the experiment.
As in the case of mean temperature, variations were seen for
the outer edges of the jets. The analysis was for a period of
20 s and the initial condition assumed in the analysis might

heat transfer engineering

Figure 3 Validation of the numerical model using three-jet model data: (a)
nondimensional mean temperature distribution along transverse direction, (b)
nondimensional mean temperature distribution along axial direction, and (c)
nondimensional RMS temperature distribution along transverse direction.

vol. 32 no. 5 2011


374

R. KRISHNA CHANDRAN ET AL.

have resulted in the deviation in the edges of the jets. However, the numerical procedure was able to correctly predict the
mixing behavior of the jets. Since a comparatively good result
was obtained from the numerical procedure, it was decided to
use Reynolds stress model for carrying out the thermal striping
analysis.

Variation of Nondimensional Mean Temperature
The variation of nondimensional mean temperature near the
plates and near the inlet has been investigated. The variation of
nondimensional mean temperature at Uh /Uc = 0.35 is shown in
Figure 4a. At y/d = 0.8 the temperatures were equal to the inlet
temperatures. Even near the lattice plate (y/d = 3.6), there was
not much variations in the temperature. Near the core cover plate
(y/d = 10.2), temperature became uniform and was observed to
be about 80% of the temperature difference between the jets.
Even though the flow was cold jet dominated, the temperature

was closer to hot jet temperature because of the large number of
hot jets in the flow. Same observations were seen for the Uh /Uc
= 1.0 case with the temperatures near the core cover plate
showing slightly higher magnitudes of temperature (Figure 4b).
For the hot jet dominated flow (Uh /Uc = 3.0), temperatures
were almost equal to hot jet temperature at y/d = 0.8 and y/d
= 3.6 except at the end of the plate (Figure 4c). At y/d =
10.2, the temperature everywhere was very close to the hot
jet temperature. As the velocity ratio was increased, the width
of the region having temperature equal to or near the hot jet
temperature value also increased; i.e., as long as the velocity of
the hot jet is higher compared to the cold jet, mean temperatures
near the solid regions approach the hot jet temperature values.
Variation of Nondimensional RMS Temperature
The nondimensional temperature fluctuations near the plates
were found out during the analysis for different velocity ratios.
The nondimensional RMS temperatures for Uh /Uc = 0.35
indicate that the temperature fluctuations increase from 5%
at y/d = 0.8 to about 10% at y/d = 3.6 (Figure 5a). Most of
the region had uniform temperature fluctuations below 10% at
y/d = 0.8, whereas at y/d = 3.6 after x/d = 8 the fluctuations
increased in large magnitudes. Even 20% temperature fluctuation was observed between x/d = 8 and x/d = 11. The large
magnitudes of temperature fluctuations correspond to regions
where improper mixing between the hot and cold jets takes
place. The locations where a drop in temperature fluctuations
was seen must be where the mixing between the jets was proper.
For Uh /Uc = 1.0, the temperature fluctuations observed were
5% up to x/d = 9.5 and raised to 10% thereafter at y/d = 0.8. At
y/d = 3.6 fluctuations were higher, equal to 10% everywhere
except at the end of the plate (Figure 5b). Here the fluctuations

were suddenly raised to 21% which must be due to interactions
between the hot and the cold jets. At y/d = 10.2, the fluctuations
heat transfer engineering

Figure 4 Variation of nondimensional mean temperature for (a) Uh /Uc = 0.35,
(b) Uh /Uc = 1.0, and (c) Uh /Uc = 3.0.

vol. 32 no. 5 2011


R. KRISHNA CHANDRAN ET AL.

375

were of uniform magnitude of 13% throughout the region of
interest. The hot jet dominated flow also showed (Figure 5c)
that temperature fluctuations are increasing in magnitude with
height from 3% at y/d = 0.8 to 8% and 12% near the lattice
plate and core cover plate, respectively. A steep increase was
noted at the edge of the plate, which means the mixing region
has been shifted to the edge of the plate. From Figure 5 it
can be seen that the width of uniform temperature fluctuation
regions increased with height. Also near the core cover plate
the temperature fluctuations remain uniform throughout the
region.

Variation of Nondimensional Mean Transverse Velocity
Nondimensional mean transverse velocities were calculated
to analyze the deflection of the jets near the plates. The mean
transverse velocities are nondimensionalized by the following

equation as:
ψx =

Ux
U I Max

(23)

The variation of mean transverse velocity with y/d indicates
that there is not much transverse movement of the streams at y/d
= 0.8 and y/d = 3.6 (Figure 6). Due to the resistance offered
by the porous lattice plate there is some deflection, which, however, is minimal. At y/d = 10.2, the transverse velocity increases
slowly and reaches its maximum at the edges of the core cover
plate (x/d = 0.5 and x/d = 11). There is a transverse movement
of the jets taking place due to solid core cover plate. The porous
lattice plate completely allows the jets to pass through without
deflecting them. The trends are similar, irrespective of the relative magnitudes of velocity of the jets. With the existence of
seven hot jets, it is possible that the dominance of cold jet over
hot jet do not have much effect on the flow.

Variation of Properties with Velocity Ratios

Figure 5 Variation of nondimensional RMS temperatures for (a) Uh /Uc =
0.35, (b) Uh /Uc = 1.0, and (c) Uh /Uc = 3.0.

heat transfer engineering

The variation of different parameters is studied at fixed locations for various values of the velocity ratios to study the
effect of velocity ratio on the mixing phenomenon. Near the inlet of the jets (y/d = 0.8), the nondimensional mean temperature
profiles in all the cases fall on the same points except near the

walls indicating that interaction between the jets is minimum
(Figure 7a). The variation of nondimensional temperature for
different velocity ratios near the lattice plate is shown in Figure
7b. As Uh /Uc increases, the width of the hot temperature region
increases. For Uh /Uc < 1, the temperature above the jets reduced
slightly from the hot jet temperature value due to the effect of
the dominant cold jet streams. The temperature profiles had a
much clearer indication of the dominance of the jets near the
core cover plate, where the cold jet dominated flow had values
of nondimensional temperatures about 0.8 in the hot jet region
vol. 32 no. 5 2011


376

R. KRISHNA CHANDRAN ET AL.

Figure 6 Variation of nondimensional mean transverse velocities for
(a) Uh /Uc = 0.35, (b) Uh /Uc = 1.0, and (c) Uh /Uc = 3.0.

heat transfer engineering

Figure 7 Variation of nondimensional mean temperatures at (a) y/d = 0.8,
(b) y/d = 3.6, and (c) y/d = 10.2.

vol. 32 no. 5 2011


R. KRISHNA CHANDRAN ET AL.

(Figure 7c). The hot jet dominated flow has values almost equal
to the hot jet temperature.
The variations of nondimensional RMS temperature profiles
at different velocity ratios near the inlet (y/d = 0.8) are shown
in Figure 8a. This indicates that the temperature fluctuations
were lowest above the hot jet region in all the situations. The
lowest fluctuations were for cold jet dominated flow and the
highest was for the hot jet dominated case. There was a rise in
fluctuations in the control rod region due to the mixing of the
two hot jet streams. The fluctuations rose to higher magnitudes
above the cold jet region. The maximum fluctuations were observed for Uh /Uc = 3. Near the lattice plate the hot jet dominated
flows showed minimum and uniform fluctuations except at the
right edge of the plate (Figure 8b). As the value of Uh /Uc was
reduced, the magnitudes of temperature fluctuations increased
and the width of uniform fluctuation zone reduced. At Uh /Uc =
0.35, the fluctuations started to increase at x/d = 8. High fluctuations of temperature were observed from x/d = 8 to x/d = 11 in
this case. The maximum fluctuations were observed in the unity
velocity ratio case, but they were spread only for a very small
width. The points of highest temperature fluctuations should be
the region of interaction between the hot jet and the cold jet
where mixing between the jets is not complete. There was a
reduction in fluctuation after an increase in all five cases where
good mixing lead to lower fluctuations in temperature. The fluctuations became almost uniform and of equal magnitudes for all
the cases near the core cover plate (Figure 8c). It is seen that the
fluctuations show maximum values near the lattice plate. After
the porous lattice plate the streams might have mixed well so
that as they moved on the fluctuations reduced.
The turbulent intensity (I) is the ratio of the root mean square
of turbulent velocity fluctuations to the mean velocity. The turbulent intensity plots at y/d = 0.8 are shown in Figure 9a. The
values are higher only at the regions of interaction of the jets,

i.e., the control rod region, the region between the hot and cold
jets and the edges of the extreme jets. The same trend was observed near the lattice plate as well but with the width of high
turbulent intensity region increasing and maximum turbulent
intensity reducing (Figure 9b). The increase in width of the high
turbulent intensity region indicates that as the jets move upward
the diffusion between parallel jets and consequent mixing lead
to a larger domain where high velocity fluctuations occur. The
turbulent intensity has become almost uniform except at the
edges of the plate near the core cover plate (y/d = 10.2) (Figure
9c). The streams coming out of the lattice plate mix properly
and thus the identity of the control plug region is lost above
the lattice plate. Thus, almost uniform turbulent intensity was
observed in the entire region below the core cover plate except
at the ends.
There was only marginal transverse movement of the jets
at y/d = 0.8, which is near the inlet of the jets (Figure 10a).
This small movement cannot be accounted for by any physical
phenomena but only because of the turbulent nature of the jets.
Near the lattice plate, a small movement of the jets in transverse
direction was observed (Figure 10b). But even this magnitude
heat transfer engineering

377

Figure 8 Variation of nondimensional RMS temperatures at (a) y/d = 0.8,
(b) y/d = 3.6, and (c) y/d = 10.2.

vol. 32 no. 5 2011

378

R. KRISHNA CHANDRAN ET AL.

Figure 9 Variation of turbulent intensity at (a) y/d = 0.8, (b) y/d = 3.6, and
(c) y/d = 10.2.

heat transfer engineering

Figure 10 Variation of nondimensional mean transverse velocity at (a) y/d =
0.8, (b) y/d = 3.6, and (c) y/d = 10.2.

vol. 32 no. 5 2011


R. KRISHNA CHANDRAN ET AL.

379

Figure 12 Velocity vectors in the domain below the core cover plate.

was less, as the porous lattice plate passed most of the fluid
through it. The transverse movements become significant near
the core cover plate, as the plate is completely solid, which
deflects the entire fluid stream to the sides (Figure 10c).
The nondimensional axial velocities are expressed as
ψy =

Uy
U I Max

(24)

The axial velocity profile at y/d = 0.8 showed that the jets
had not lost their individual identity (Figure 11a). One is still
moving mostly independent of the other jet, with a top-hat velocity profile. Near the lattice plate the jets got spread out and
the interaction between the jets started (Figure 11b). So the
profile became more of uniform nature. There was significant
movement past the plate, as can be seen by the magnitudes of
nondimensional axial velocity profiles. Near the core cover plate
(y/d = 10.2) the movement upward was zero between x/d = 0.5
and x/d = 11 due to the solid structure (Figure 11c). The jets
moved at very high velocities through the sides of the plate (0
< x/d < 0.5 and 11 < x/d < 14).
Spectral Distribution of Properties

Figure 11 Variation of nondimensional mean axial velocity at (a) y/d = 0.8,
(b) y/d = 3.6, and (c) y/d = 10.2.

heat transfer engineering

A typical velocity vector plot is shown in Figure 12 in which
the jets have uniform velocity. The mixing in the control plug
region can be clearly seen from this diagram. A mixing zone
above the lattice plate can also be seen. The nondimensional
RMS temperature distribution in the region below the core cover
plate can be seen in Figure 13. It can be seen that when the hot
jet is dominating, the region of high fluctuation has shifted
to the extreme right end of the domain. Fluctuation near the
lattice plate and core cover plate is less. As the velocity ratio

was reduced to 1.0, the region of high fluctuation widened.
In addition, higher fluctuations can be seen near the plates.
vol. 32 no. 5 2011


380

R. KRISHNA CHANDRAN ET AL.

Figure 14 Maximum nondimensional RMS temperature as a function of velocity ratio.

When the flow became cold jet dominated (Uh /Uc = 0.35) the
domain of mixing increased, leading to high magnitudes of
temperature fluctuation near the lattice plate. It can be seen
that just behind the lattice plate high values of temperature
fluctuation are recorded. This might be due to the mixing of
the jets. As the jets come out of the lattice plate, mixing occurs
due to a resistance to flow offered by the lattice plate. As the
mixing becomes good, the fluctuations near the core cover plate
become less. Hence the lattice plate is more prone to the failure
due to thermal striping phenomena.

Figure 13 Nondimensional RMS temperature contours in the domain for (a)
Uh /Uc = 3.0, (b) Uh /Uc = 1.0, and (c) Uh /Uc = 0.35.

heat transfer engineering

Figure 15 Location of maximum temperature fluctuation as a function of
velocity ratio.

vol. 32 no. 5 2011


R. KRISHNA CHANDRAN ET AL.

Variation of Temperature Fluctuation With Velocity Ratio
Figure 14 shows a plot of maximum magnitude of RMS temperature fluctuation as a function of velocity ratio at different
locations. The highest fluctuations are recorded near the lattice
plate, with the maximum being at the unity velocity ratio case.
Moreover, as the velocity ratio is increased beyond 1.0 the temperature fluctuation near the lattice plate is reduced. For all the
different cases of velocity ratios the temperature fluctuations
remain almost the same near the core cover plate, which was
less than that near the lattice plate, due to good mixing beyond
the lattice plate. Figure 15 shows the location of maximum temperature fluctuation recorded near the lattice plate as a function
of the velocity ratio. It can be seen that as the velocity ratio
increases, the location of highest temperature fluctuation gets
shifted to the right. Therefore, by enhancing the velocity ratio,
the solid region that is subjected to high temperature fluctuations
can be reduced.

CONCLUSIONS

K
LMFBR
p
p’
P
Pe
Pii , Pij
Prt

Rij
Re
RSM
t
tp
T
TRMS
Tijk
u
u’
U
x, y
y+

A numerical analysis of thermal striping in the PFBR has
been carried out using a 10-jet water model with seven hot
and three cold jets. Turbulence modeling has been done using
the Reynolds stress model (RSM). Based on the analysis the
following conclusions were arrived at:

Greek Symbols

• Maximum temperature fluctuations near the solid structures
occur for the unity velocity ratio situation.
• The lattice plate is more prone to thermal striping failure
compared to the core cover plate.
• As the velocity ratio is increased, the location of highest temperature fluctuations shifts to the right. By increasing the
velocity ratio, the solid region subjected to high temperature
fluctuation can be reduced.
• Beyond a velocity ratio of 1.0, the temperature fluctuations

reduces as the velocity ratio increases.
• The numerical scheme can be extended to actual reactor conditions after taking due care for geometric and hydraulic aspects.

δ
ε
εij
θ
θRMS
λ
µ
µt
ν
ρ
σk , σε

β
β’

φ
x

NOMENCLATURE
Ap
Af
C
Cij
C1 , C2 , Cε1 , Cε2 , Cµ
d
Dp
I

k

y

area of the porous plate (m2)
free area for flow through the porous
plate (m2)
specific heat of solid (J/kg-K)
convection term (kg/m-s3)
turbulence modeling constants
diameter of the jet (m)
plate hole diameter (m)
turbulent intensity
turbulent kinetic energy (m2/s2)
heat transfer engineering

381

permeability (m2)
liquid-metal-cooled fast breeder reactor
instantaneous pressure (Pa)
pressure fluctuations (Pa)
mean pressure (Pa)
Peclet number
turbulence production term (kg/m-s3)
turbulent Prandtl number
redistribution or pressure-strain term
(kg/m-s3)
Reynolds number
Reynolds stress model

time (s)
plate thickness (m)
mean temperature (K)
RMS temperature fluctuations (K)
transport of Reynolds stresses (kg/s3)
instantaneous velocity (m/s)
velocity fluctuations (m/s)
mean velocity (m/s)
coordinates
dimensionless distance from the wall

inertial resistance (m−1)
coefficient based on the ratio of porous
plate hole diameter to its thickness
Kronecker delta
turbulent dissipation rate (m2/s3)
dissipation tensor (kg/m s3)
nondimensional mean temperature
nondimensional RMS temperature
thermal conductivity (W/m-K)
dynamic viscosity (kg/m-s)
turbulent viscosity (kg/m-s)
kinematic viscosity of the fluid (m2/s)
density (kg/m3)
turbulence modeling constants
pressure-strain term
porosity
nondimensional mean transverse velocity
nondimensional mean axial velocity

Subscripts
c
eff
f
h
i, j, k
I Max
s
w
x, y
vol. 32 no. 5 2011

cold jet
effective
fluid
hot jet
general spatial indices
maximum value at inlet
solid
wall
coordinates


382

R. KRISHNA CHANDRAN ET AL.

REFERENCES
[1] Moriya, S., and Ohshima, I., Hydraulic Similarity in the
Temperature Fluctuation Phenomena of Non-Isothermal

Coaxial Jets, Nuclear Engineering and Design, vol. 120,
pp. 385–393, 1995.
[2] Ohshima, H., Muramatsu, T., Kobayashi, J., and Yamaguchi, A., Current Status of Studies on Temperature Fluctuation Phenomena in LMFBRs, IAEA Specialist Meeting
on Correlation Between Material Properties and Thermohydraulics Conditions in Liquid Metal Cooled Fast Reactors (LMFRs), Aix-en-Provence, France, 1994.
[3] Tokuhiro, A., and Kimura, N., An Experimental Investigation on Thermal Striping Mixing Phenomena of a Vertical Non-Buoyant Jet With Two Adjacent Buoyant Jets
as Measured by Ultrasound Doppler Velocimetry, Nuclear
Engineering and Design, vol. 188, pp. 49–73, 1999.
[4] Kimura, N., Miyakoshi, H., and Kamide, H., Experimental
Investigation on Transfer Characteristics of Temperature
Fluctuation From Liquid Sodium to Wall in Parallel TripleJet, International Journal of Heat and Mass Transfer, vol.
50, pp. 2024–2036, 2007.
[5] Hirota, M., Asano, H., Nakayama, H., Asano, T., and
Hirayama, S., Three-Dimensional Structure of Turbulent
Flow in Mixing T-Junction, JSME International Journal,
vol. 49, pp. 1070–1077, 2006.
[6] Ushijima, S., Tanka, N., and Moriya, S., Turbulence Measurements and Calculations of Non-Isothermal Coaxial
Jets, Nuclear Engineering and Design, vol. 122, pp. 85–94,
1990.
[7] Muramatsu, T., and Ninokata, H., Thermal Striping Temperature Fluctuation Analysis Using the Algebraic Stress
Turbulence Model in Water and Sodium, JSME International Journal, vol. 35, pp. 486–496, 1992.
[8] Kasahara, N., Evaluation of Thermal Striping Phenomena at a Tee Junction of LMFR Piping System with Numerical Methods (II), Thermomechanical Calculations,
Proc. 15th International Conference on Structural Mechanics in Reactor Technology, Seoul, Korea, pp. IV-209–
IV-216, 1999.
[9] Nishimura, M., Tokuhiro, A., Kimura, N., and Kamide, H.,
Numerical Study on Mixing of Oscillating Quasi-planar
Jets With Low Reynolds Number Turbulent Stress and Heat
Flux Equation Models, Nuclear Engineering and Design,
vol. 202, pp. 77–95, 2000.
[10] Kimura, N., Nishimura, M., and Kamide, H., Study on
Convective Mixing for Thermal Striping Phenomena (Experimental Analyses on Mixing Process in Parallel TripleJet and Comparisons Between Numerical Methods), JSME

International Journal, vol. 45, pp. 592–599, 2002.
[11] Jung, J. H., and Yoo, G. J., Analysis of Unsteady Turbulent
Triple Jet Flow With Temperature Difference, Journal of

heat transfer engineering

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]
[22]
[23]

Nuclear Science and Technology, vol. 41, pp. 931–942,
2004.

Choi, S. K., and Kim, S. O., Evaluation of Turbulence
Models for Thermal Striping in a Triple Jet, Journal of
Pressure Vessel Technology, vol. 129, pp. 583–592, 2007.
Suyambazhahan, S., Sarit K. Das, and Sundararajan,
T., Hydrodynamic and Thermal Oscillations in a NonIsothermal Laminar Jet, International Journal of Heat and
Mass Transfer, vol. 47, pp. 3957–3969, 2004.
Velusamy, K., Natesan, K., Selvaraj, P., Chellapandi, P.,
Chetal, S.C., Sundararajan, T., and Suyambazhahan, S.,
CFD Studies in the Prediction of Thermal Striping in an
LMFBR, Benchmarking of CFD Codes for Application to
Nuclear Reactor Safety (CFD4NRS), Munich, Germany,
pp. 253–263, 2006.
Suyambazhahan, S., Das, S. K., and Sundararajan, T., Numerical Study of Flow and Thermal Oscillations in Buoyant Twin Jets, International Communications in Heat and
Mass Transfer, vol. 34 pp. 248–258, 2007.
Gao, S., and Voke, P. R., Large-Eddy Simulation of Turbulent Heat Transport in Enclosed Impinging Jets, International Journal of Heat and Fluid Flow, vol. 16, pp.
349–356, 1995.
Voke, P. R., and Gao, S., Numerical Study of Heat Transfer
From an Impinging Jet, International Journal of Heat and
Mass Transfer, vol. 41, pp. 671–680, 1998.
Wakamatsu, M., Nei, H., and Hashiguchi K., Attenuation
of Temperature Fluctuations in Thermal Striping, Journal
of Nuclear Science and Technology, vol. 32, pp. 752–762,
1995.
Krishna Chandran, R., Banerjee, I., Padmakumar, G., and
Reddy, K. S., Numerical Analysis of Thermal Striping
Phenomena using a Two Jet Water Model, Engineering
Applications of Computational Fluid Mechanics, vol. 4,
pp. 209–221, 2010.
Incropera, F. P., and DeWitt, D. P., Fundamentals of Heat
and Mass Transfer, 5th ed., John Wiley and Sons, New

York, 2006.
Nield, D. A., and Bejan, A., Convection in Porous Media,
2nd ed., Springer, New York, 1999.
Pope, S. B., Turbulent Flows, Cambridge University Press,
Cambridge, 2000.
Fluent Inc., Fluent 6.2 User’s Guide, Lebanon, NH, 2005.
R. Krishna Chandran is a scientific officer at the
Safety Research Institute, Atomic Energy Regulatory Board, Kalpakkam, India. His current research
interest is in safety analysis related to fast breeder
reactors particularly decay heat removal system and
thermal striping studies. He obtained his M.Tech. in
thermal engineering from Indian Institute of Technology Madras. He is a graduate in Mechanical Engineering from the University of Kerala.

vol. 32 no. 5 2011