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

Analysis of a counterflow heat exchanger with a heat source in the hot fluid stream was presented in detailfor minimum and maximum heat capacity rate of the hot fluid[10] for which the a

Copyright
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 KUCZY ´ NSKI

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

ma-chines 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

solu-tions It has been established that phase changes of energy media

that occur in evaporators and condensers in machines and

de-vices 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: tadeusz.bohdal@tu.koszalin.pl

periodic [3–5] nature; i.e., they can be periodically generatedwith a specific amplitude and frequency

Impulse and periodically generated disturbances cause cific phenomena, which trigger the following changes: (a) anabrupt drop or increase of the pressure of the medium, (b) adecay or an increase of the mass flux density, (c) an increase or

spe-a drop of the resistspe-ances of the medium flow, spe-and (d) periodicproblems connected with the starting of the device

A two-phase system of liquid (either a gas, or a single ormulticomponent fluid) is a set of particles of a substance withtwo states of aggregation, which are separated by an interface.The interaction between particular phases and the displacementvelocity of a disturbance triggered by an external or internalcause depend on the internal structure of the system This can

be clearly seen via the example of the propagation of a soundwave in an adiabatic two-phase system The velocity of a soundwave depends, above all, on the value of the filling degreeφ andthe pressure of the two-phase mixture The sound velocity in

a two-phase mixture increases together with an increase of thepressure However, this tendency only occurs up to a specificvalue of the pressure (whose value depends from the fillingdegree) and then, with adequately high pressures, it is almostconstant and is equal to 1300 m/s [6]

During the propagation of the wave of disturbances in atwo-phase one-component mixture with thermal parametersdetermined for the states on the saturation line, the propagation

of the wave of disturbances causes a periodic change of the local

359

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

T S, 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

evo-lution 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

distur-bances 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

refrig-eration 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

ex-pansion 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

assis-tance, 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

com-posed 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

ther-mostatic 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

two - phase zone one-phase zone

single-phase 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 externalwork) During this time, a part of the liquid passes to the vaporstate, while the temperature of the medium is lowered to theevaporation temperature level The remaining liquid evaporatesduring the flow through the coil tube If the quantity of the refrig-eration medium that evaporates in the evaporator is too small forthe boiling process to occur on the whole length of the coil tube,then after the completion of the phase change of boiling (some-times 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 beadjusted by changing the setting of a thermostatic expansionvalve 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 instantaneousdecrease or fading of the mass rate of flow of the medium, is cru-cial for its correct operation In the present paper, the results ofexperimental investigations of the boiling process of the R404Arefrigeration medium in a coil tube are presented for the casewhere periodically generated disturbances are present The de-termination of the impact of these disturbances on the operation

of the entire refrigerating system has a substantial cognitive andapplication-focused significance on the construction, operation,and economic analysis of the system

EXPERIMENTAL FACILITY

The experimental investigations of the boiling process wereconducted on a measuring facility, which is schematically pre-sented in Figure 2 Its main elements include an isolated refrig-

eration chamber 1 and the air cooler 2 tested placed in it, which

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

refrigera-tion 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

piezoelectric sensor for pressure measurements and one moelectric sensor for the measurements of the temperature ofthe medium (Table 1) A dimensional diagram of the arrange-ment of the sensors along the length of the coil tube is given inFigure 5

ther-The computer system used for the measurement, control, andregistration of the basic parameters of the refrigeration medium,air, and environment constituted an integral component of theexperimental facility This system included the following: (a)NiCr–Ni type thermoelectric sensors with 0.35 mm diameter

Channel

Ventilator

Exchanger

heat transfer engineering vol 32 no 5 2011

thermocouple wires (for which individual calibration

charac-teristics 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

pres-sure sensors (the ICP type with a M102A07 symbol), which

cooperate with the tare system and a computer voltage

mea-suring card; and (c) a MASS2100-type electronic Massflow

flowmeter, manufactured by the Danfoss company, with

soft-ware, 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

al-lowed us to make measurements related to the following: (a)

temperature measurements were placed

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

T s= 0 to –40◦C, and (c) the density of the heat flux q= 0 to

6000 W/m2

RESULTS OF EXPERIMENTAL INVESTIGATIONS

In the present paper, the notion of a “periodically generateddisturbance” is to be understood as a disturbance produced byfeeding the evaporator with a refrigeration medium, in condi-tions of a change of the time to open and close the valve thatsupplies the medium to the coil tube Such an action results in

an increase or a decay of the mass flux density of the R404Amedium This, in turn, results in periodic changes of the pres-sure and temperature along the flow path in the coil tube In theexperimental investigations, a single coil tube lamelled blockwas used, while an additional cutoff was installed on the coiltube inlet (thus allowing the disturbances to be turned off)

In the experiments, it was assumed that a constant openingand closing time of the cutoff valve was realized in the measuringsession While the opening time of the valve was always constantfor all of the measuring series (5 s), the closing time of the valve

in the individual measuring series varied and wasτc= 5, 10,

15, 20, 25, and 30 s The sum of the opening and closing timesconstituted the duration of the period that formed the basisfor 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 ofthe mass rate flow of the R404A refrigeration medium (Figure6), changes of the evaporation pressure (Figure 7), and the tem-perature profile (Figure 8) For the purpose of the construction

of the pressure and temperature characteristics presented, theregistration of the pressure and temperature by sensors denotedwith subsequent numbers (given according to Figure 5) wastaken into account The introduction of periodic disturbancesresulted in the occurrence of the pulsation of the medium flowrate During the period of the closing of the cutoff valve, themedium was “sucked off” by the compressor from the coil tube.Because of this, there was a pressure drop and an increasedoverheating of the vapor This caused gradual increase in thetemperature of refrigerant in the monophase area of the tubularchannel At the same time, in the two-phase boiling area, theboiling temperature of refrigerant decreased, which depends on

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

re-versal 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

temper-ature 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]

the coil tube.

coil tube.

During experimental investigations, boiling of the mediumwas realized under the conditions of periodical external dis-turbances Opening or closing of the cutoff valve resulted in aperiodical change of refrigerant parameters under nonstation-ary conditions The consequence of the disturbances occurringwas the formation of a pressure wave, which relocated alongthe channel It is the opinion of the authors that the reloca-tion of the pressure wave was the reason for the formation of atemperature wave as a secondary effect However, no large tem-perature changes of the medium or of the tubular channel wallwere observed It means this does not involve such temperatures,which should be the result of the value of the saturation pres-sure change in the channel This is the result of the impact of thethermal inertia of the system as well as a significant frequency

of disturbances generated The investigations demonstrated that

velocities vp and vTdepend, among other things, on the size ofthe disturbance triggered, which is characterized by the pres-sure 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 onthe mass flux density in the coil tube This phenomenon is theresult of the work of the compressor, which sucks in the refriger-ation medium vapor from the evaporator When the cutoff valvefrom the inlet of the medium to the coil tube is closed, there is

a pressure drop The longer the valve is closed, the greater thepressure drop is Once the cutoff valve is opened again (with agreater reduction of the pressure in the evaporator), an increase

of the medium flow rate occurs Figure 10 presents the dence of the mass flux density (wρ) of the R404A refrigerationmedium on the pressure drop
p The mass flux density (wρ) exerts a substantial influence on the values of velocities vpand

depen-v T, as shown in Figure 11.

It is evident from the conducted investigations that velocities

v p and vT differ from one another with regard to their values,

as the velocity of the pressure signal relocation changed tween 45 and 330 m/s, while the velocity of the boiling frontrelocation was substantially smaller, and ranged from close toheat transfer engineering vol 32 no 5 2011

be-Figure 9 Dependence of the pressure change displacement velocity v pon the

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

medium on the pressure drop
p.

mass flux density (w ρ) of the refrigeration medium; v p = f (wρ).

the coil tube on the velocity v pof the pressure signal displacement.

zero to 4.5 m/s Low values of vT serve to confirm the resultsobtained by the authors of reference [8], where a model wasgiven to enable the determination of the boiling front formingvelocity on the surface heated It was assumed in the analysisthat the boiling front velocity on the surface heated depends onlocal liquid overheating
T Sand the thermophysical properties

of the refrigerant in saturated conditions The obtained results

of theoretical computations were compared with the results ofexperimental investigations The experiments were conductedfor the range of low-pressure values and a high-value liquidoverheating (up to 155 K) was obtained This corresponded to

a boiling front velocity vTof up to 35 m/s The authors of ence [18] confirm that with higher absolute pressures, such large

refer-velocities vTare not achieved In practice, it is not possible tooverheat a liquid by dozens of degrees Kelvin because the boil-ing process commences spontaneously at a substantially lowerliquid overheating value This results in a substantial reduction

of velocity vT even to values approaching zero Experimentalinvestigations also demonstrated that the velocities of the relo-

cation of the pressure signal vp and temperature signal vT areinterdependent, which is shown in Figure 12

ANALYSIS OF EXPERIMENTAL RESULTS

The experimental investigations of the influence of periodicdisturbances on the boiling process of a refrigeration mediumdemonstrated that there is a direct interdependence between

the propagation velocity of the pressure disturbances vp and

the relocation velocity of the temperature change signal vTandthe frequency of the disturbances applied An increase of thedisturbances generation frequency resulted in a velocity drop

distribution change of pressure signal vpand temperature signal

v T This frequency was described with the aid of nondimensional number Ta, which takes into account the ratio of the time τorequired to open the valve on the inlet of the medium to the coil

Figure 13 Dependence of the pressure change displacement velocity v pin the

coil tube on the nondimensional Ta number.

tube to the total time of its being closedτcand openedτo:

The time of the opening of the valve was constant and wasτo

= 5 s, while an increase of the value of the closing time of the

valveτccorresponded 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 vpand 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

regres-sion function, the experimental results obtained The problem

concerned the description of the relocation velocity of the

pres-sure change vp signal and the temperature change vTsignal For

this purpose, dimensional analysis procedures were used that

the coil tube on the nondimensional Ta number.

took into consideration Buckingham’s  theorem, according

to which the number of non-dimensional modules is equal tothe number of independent physical parameters reduced by thenumber of basic measurements in the SI system (such as meter,second, and kilogram) [19, 20]

The relocation velocity of the pressure change vpsignal gered by periodic disturbances was made functionally depen-dent on the following parameters:

trig-v p = f (
p, ps , ν, d, w, τ o , τ c) (2)

where: vpis the relocation velocity of the pressure change signal[m/s],
p is the oscillation amplitude of the boiling pressure dur-

ing disturbances [N/m2], psis 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 ofopening 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 thecoil tube [s], andν is the kinematic coefficient of the viscosity

of the two-phase mixture [m2/s], which is defined as:

with

1µTPF =

1

µg

+1− x

µ1and 1ρTPF =

x and the filling degreeϕ 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 thesevalues lower

By way of a dimensional analysis [19], Eq (2) was converted

to the following form:

v+

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)

Ta is a nondimensional number that takes into account the

rela-tionship between the timeτoof the opening of the valve onheat transfer engineering vol 32 no 5 2011

Figure 15 Dependence of the nondimensional velocity v p+calcalculated from

Eq (3) on the value obtained from experimental measurements of v p+exp.

the inlet of the medium to the coil tube and the total time of

its being closedτcand openedτo, 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

nonlin-ear 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

us-ing 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

ve-locity vT+was determined, which takes into account the

dis-placement of the temperature change vT Its value was made

functionally dependent from the following parameters:

v T = f (
T, Ts , ν, d, w, τ o , τ c) (6)

where additional denotations were introduced: vT is the

dis-placement velocity of the temperature change signal [m/s],
T

is the amplitude of the temperature oscillations caused by

dis-turbances [K], and Tsis the average boiling temperature of the

refrigeration medium [K]

calcalculated from

Eq (5) on the value obtained from experimental measurements of v T+

v+

T = v T

w is the nondimensional velocity determined via the

ratio of the displacement velocity of the temperature change

signal vTto the velocity of the two-phase mixture

T +
T

T s is the nondimensional temperature drop determinedvia the ratio of the temperature amplitude to the boiling tem-

perature of the refrigeration medium T0[K]

The following values of constants were obtained for Eq (7):

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 thevalue of the nondimensional displacement velocity of the tem-perature change signalv+

T to be determined) can be transformed

to a form where the nondimensional temperature drop
T+isreplaced with the nondimensional pressure drop
p+:

v+

T = 107 × 105× Re−1.05

T P F ×

p+0.11 × T a −0.76 , (8)

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

re-frigeration 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

refriger-ation medium were made for constant heat load levels of the

refrigeration chamber This led to periodic changes of the

pres-sure and temperature along the path of the flow of the medium

in the coil tube of the evaporator The investigations were

car-ried 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

ve-locities: vp, the displacement velocity of the pressure change

signal; and vT, the displacement velocity of the temperature

change signal;

2 Velocities vp and vTdepend on the parameters of the

two-phase medium and the magnitude of the disturbance

gener-ated, 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

corre-sponds 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

gen-eration This is taken into account in the nondimensional Ta

number, which constitutes the ratio of timeτoof the opening

of the valve at the inlet of the refrigeration medium (from the

coil tube) to the total time of its closingτcand openingτo

5 The dependences worked out on the basis of the

experimen-tal investigations allow one to determine the displacement

velocity of the pressure change signal vpand the temperature

change signal velocity vT generated with periodic

ϕ filling level, relative air humidity

µ dynamic viscosity coefficient [kg/m-s]

ν kinematic viscosity coefficient [m2/s]

ρ density [kg/m3]

τ time [s]

Subscripts

c shutting of cutoff valve

cal calculation value

exp experimental value

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Manage-ment, vol 4, pp 249–268, 2002.

[14] Nigmatulin, R I., Dynamics of Multiphase Media,

Hemi-sphere, New York, 1990

[15] Bohdal, T., and Kuczy´nski W., Investigation of Boiling of

Refrigeration Medium Under Periodic Disturbance

Condi-tions, International Journal of Experimental Heat

Trans-fer, vol 18, no 3, pp 135–151, 2005.

[16] 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

[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, physics and Aeromechanics, vol 6, no 1, pp 105–117,

Thermo-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 ing of the Koszalin University of Technology, Poland.

Engineer-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 ex- changers, 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 disserta- tions and more than 150 completed M.Sc theses in refrigeration and power engineering.

Waldemar Kuczy ´nski 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 En- gineering of the Koszalin University of Technology.

In the year 2008, under a project of the State mittee 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

Com-of the Chair Com-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.

Copyright
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

1Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India

2Experimental Thermal Hydraulics Section, Fast Reactor Technology Group, Indira Gandhi Centre for Atomic Research,

Kalpakkam, India

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-metal-cooled fast breeder reactor (LMFBR) must be preceded by

de-tailed 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

fluctua-tions 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

re-ferred to as thermal striping The thermal striping phenomenon

was identified to be occurring in stages, which include: (1)

gen-eration 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: ksreddy@iitm.ac.in

of different temperature jets, (2) reduction of fluctuations in thenear surface due to boundary layer, (3) conveyance of the fluctu-ations to the solid surfaces, (4) conduction of fluctuations withinthe solid material, and (5) thermal fatigue leading to the fail-ure of structure by the initiation of a crack The entire thermalstriping phenomena can be attributed to the incomplete mixing

of the different-temperature jets

A very limited literature is available related to thermal draulic studies of thermal striping The effect of working fluid

hy-on the temperature fluctuatihy-on phenomena has been studied byMoriya and Ohshima [1] It was found that the average and rootmean square (RMS) temperatures were functions of Reynoldsand Peclet numbers If the Reynolds number and Peclet numberare sufficiently large (Re> 20,000 and Pe > 600) both in the

prototype and in the model, then the working fluid has no fluence on the mixing characteristics Water or air can be usedinstead of sodium for conducting temperature fluctuation studies

in-at high values of Reynolds and Peclet numbers Ohshima et al.[2] elaborated on the status of four temperature fluctuation phe-nomena: thermal stratification, thermal striping, core–plenuminteraction, and free surface sloshing Experimental analysis of

a single-jet and a three-jet model with two hot jets ing a cold jet was conducted by Tokuhiro and Kimura [3] us-ing ultrasound Doppler velocimetry The properties like mean

surround-369

velocity, RMS velocity, mean temperature, and standard

devi-ation 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

coax-ial jets and compared this with experimental results Muramatsu

and Ninokata [7] used an algebraic stress model (ASM) to

con-duct a numerical analysis for predicting the temperature

fluctua-tion phenomena Kasahara [8] analyzed the possibility of crack

initiation and propagation due to thermal striping by

conduct-ing 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

us-ing 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

his-tory 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

oscilla-tions 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

per-formed at four localized regions of the reactor at specific

veloc-ity 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

ra-tios using water and sodium, it was observed that for the same

value of velocity the sodium attenuation ratios were smaller A

LMFBR core.

boundary-layer model was proposed to predict the attenuation

of temperature near the surface, and it was found to give goodresults compared to the experimental values Krishna Chan-dran et al [19] carried out a numerical analysis simulating thethermal striping phenomena in a 1/5 scale water model of theprototype fast breeder reactor (PFBR) primary circuit Two non-isothermal water jets impinge on a lattice plate placed above thejets A Reynolds stress turbulence model is used to evaluate thetemperature fluctuations near the plate

Most of the studies just described were limited to a jet model analysis without considering the above-core structuralgeometry An actual reactor core consists of a number of paralleljets coming out of the fuel and blanket zones It is possible thatthe interaction among these jets is entirely different from that of

three-a two-jet or three-jet model The three-above-core geometry three-also plthree-ays

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 presentstudy a 10-jet water model representing a 1/5 scale model ofPFBR is numerically analyzed The 10-jet model corresponds

to a half row of the reactor core Thus it represents, to someextent, the geometry and thereby the physical phenomena close

to the reactor conditions The numerical procedure, after takingdue 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 Thecoolant sodium at uniform temperature enters the base of thecore and passes through the different zones The coolant ab-sorbs different amounts of heat and thus comes out at differenttemperatures Above the reactor core, a lattice plate used forsupporting the core-monitoring thermo wells is placed The lat-tice plate, being porous, allows the streams to pass through it

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

af-fected 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

anal-ysis 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

ana-lyzed 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

plate, called the core cover plate, is placed at y/d= 10.4 fromthe inlet Both plates are made to resemble the correspondingplates in the reactor

The governing equations in Cartesian form for the 10-jetmodel can be written as follows [20–22]

Earlier studies have shown the ability of the Reynolds stressmodel (RSM) in forecasting the thermal striping phenomenaeffectively [9, 10] It has been found to accurately predict thethermal striping phenomena compared to the k-ε model and to beless time-consuming compared to direct numerical simulationwithout losing much accuracy Therefore, it has been decided

to use the Reynolds stress model for the present turbulencemodeling The model used standard wall functions for the nearwall treatment after ensuring through a detailed analysis that thewall y+ values are above 30 and below 300

The Reynolds stress equation [23] is

D < ρu

i uj >

Dt = −∂T i j k

∂x k + Pi j + Ri j − εi j (3)where D <ρui u

production strain, and dissipation terms are modeled The

tur-bulent diffusion term (first two terms of the Reynolds stress

transport term) is modeled as ∂x ∂

∂x k ) 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

can be modeled as εi j = 2

3δi jρε The turbulent viscosity in theabove equations is taken as µt= ρCµk2

∂k

∂x j

+1

2P ii− ρε (8)Here the value ofσkis 0.82

The turbulent dissipation (ε) equation is given by

The Reynolds stress model uses an analogy between heat and

momentum transfer to model the energy equation The equation



∂T

∂x j

(10)

The value of Prtis 0.85

Within the solid plate only conduction is present The

corresponding governing equation is given by

The assumptions made in the mathematical formulation

in-clude: (a) The flow is two-dimensional, (b) properties of the

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

in-is unsteady

NUMERICAL PROCEDURE

The available computational fluid dynamics (CFD) softwareFLUENT 6.2 was used for the numerical analysis A detailedgrid independence study was conducted to find out the suitablemesh 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 Theenergy equation has been solved with a residual of 10−8, whereasmomentum, continuity, Reynolds stress, k, andε equations havebeen solved with a residual of 10−6 A time step of 0.001 s hasbeen selected in order to completely capture the temperaturefluctuations during the flow Implicit formulation with second-order accuracy was used for the unsteady equations In order tohave second-order accuracy for the temporal discretization, thevalues of the variable for the previous two time steps have beenused in the calculations

Initial and Boundary Conditions

The domain was assumed initially to be stagnant and at atemperature equal to 50◦C The temperature of the hot jet wastaken as 70◦C and that of the cold jet as 30◦C Five different hotjet to cold jet velocity ratios—0.35, 0.50, 1.0, 2.0, and 3.0—wereused for the analysis The Reynolds number of the hot jets wasalways above 20,000 The Reynolds number of the cold jets hasbeen varied The jets were assumed to have a top-hat velocityprofile at the inlet All the inlets were assumed as velocity inlets,while outflow was taken at the outlet A turbulent intensity of5% was assumed for all the incoming jets since the flow was amedium turbulent one The walls were taken as adiabatic withno-slip boundary condition

The viscous resistance [23] is given by

where Dpis the plate hole diameter

The inertial resistance [23] is given by

Based on the preceding equations, a viscous resistance of1.125× 107m−2and inertial resistance of 1140 m−1were takenfor the lattice plate Between the core cover plate and the fluid,conjugate heat transfer was assumed to correlate conductive and

convective heat transfer The equation that couples the

conduc-tive heat transfer between the fluid and solid region is

T= 323 K, U = 0 at t = 0 for the entire domain (17)

T= 343 K, U = Uhfor the hot jets (18)

T= 343 K, U = Ucfor the cold jets (19)

RESULTS AND DISCUSSION

Validation of Numerical Procedure

The numerical procedure has been validated with the

exper-imental data reported in Tokuhiro and Kimura [3] A

compar-ison 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

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

simu-lated was not enough for the outer domains to attain a closer

value with the experimental data It must be noted that the

ini-tial 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

predict-ing in the developpredict-ing 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

inter-est (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

nondimensional mean temperature distribution along transverse direction, (b) nondimensional mean temperature distribution along axial direction, and (c) nondimensional RMS temperature distribution along transverse direction.

heat transfer engineering vol 32 no 5 2011

have resulted in the deviation in the edges of the jets

How-ever, 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

fluctu-ation 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

(b) U h /U c = 1.0, and (c) U h /U c = 3.0.

Figure 5 Variation of nondimensional RMS temperatures for (a) U h /U c =

0.35, (b) U h /U c = 1.0, and (c) U h /U c = 3.0.

were of uniform magnitude of 13% throughout the region ofinterest The hot jet dominated flow also showed (Figure 5c)that temperature fluctuations are increasing in magnitude withheight from 3% at y/d = 0.8 to 8% and 12% near the latticeplate and core cover plate, respectively A steep increase wasnoted at the edge of the plate, which means the mixing regionhas been shifted to the edge of the plate From Figure 5 itcan be seen that the width of uniform temperature fluctuationregions increased with height Also near the core cover platethe temperature fluctuations remain uniform throughout theregion

Variation of Nondimensional Mean Transverse Velocity

Nondimensional mean transverse velocities were calculated

to analyze the deflection of the jets near the plates The meantransverse velocities are nondimensionalized by the followingequation as:

ψx= U x

U I Max

(23)The variation of mean transverse velocity with y/d indicatesthat 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, ever, is minimal At y/d= 10.2, the transverse velocity increasesslowly and reaches its maximum at the edges of the core coverplate (x/d= 0.5 and x/d = 11) There is a transverse movement

how-of the jets taking place due to solid core cover plate The porouslattice plate completely allows the jets to pass through withoutdeflecting them The trends are similar, irrespective of the rel-ative magnitudes of velocity of the jets With the existence ofseven hot jets, it is possible that the dominance of cold jet overhot jet do not have much effect on the flow

Variation of Properties with Velocity Ratios

The variation of different parameters is studied at fixed cations for various values of the velocity ratios to study theeffect of velocity ratio on the mixing phenomenon Near the in-let of the jets (y/d= 0.8), the nondimensional mean temperatureprofiles in all the cases fall on the same points except near thewalls indicating that interaction between the jets is minimum(Figure 7a) The variation of nondimensional temperature fordifferent velocity ratios near the lattice plate is shown in Figure7b As Uh/Ucincreases, the width of the hot temperature regionincreases For Uh/Uc< 1, the temperature above the jets reduced

lo-slightly from the hot jet temperature value due to the effect ofthe dominant cold jet streams The temperature profiles had amuch clearer indication of the dominance of the jets near thecore cover plate, where the cold jet dominated flow had values

of nondimensional temperatures about 0.8 in the hot jet regionheat transfer engineering vol 32 no 5 2011

Figure 6 Variation of nondimensional mean transverse velocities for

(a) U h /U c = 0.35, (b) U h /U c = 1.0, and (c) U h /U c = 3.0.

(b) y/d = 3.6, and (c) y/d = 10.2.

(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

ob-served 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/Ucwas

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

fluctu-ations 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

fluc-tuations 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

tur-bulent 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

ob-served 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

(b) y/d = 3.6, and (c) y/d = 10.2.

heat transfer engineering vol 32 no 5 2011

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

0.8, (b) y/d = 3.6, and (c) y/d = 10.2.

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.

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

ψy= U y

U I Max

(24)The axial velocity profile at y/d= 0.8 showed that the jetshad not lost their individual identity (Figure 11a) One is stillmoving mostly independent of the other jet, with a top-hat ve-locity profile Near the lattice plate the jets got spread out andthe interaction between the jets started (Figure 11b) So theprofile became more of uniform nature There was significantmovement past the plate, as can be seen by the magnitudes ofnondimensional axial velocity profiles Near the core cover plate(y/d= 10.2) the movement upward was zero between x/d = 0.5and x/d= 11 due to the solid structure (Figure 11c) The jetsmoved at very high velocities through the sides of the plate (0

< x/d < 0.5 and 11 < x/d < 14).

Spectral Distribution of Properties

A typical velocity vector plot is shown in Figure 12 in whichthe jets have uniform velocity The mixing in the control plugregion can be clearly seen from this diagram A mixing zoneabove the lattice plate can also be seen The nondimensionalRMS temperature distribution in the region below the core coverplate can be seen in Figure 13 It can be seen that when the hotjet is dominating, the region of high fluctuation has shifted

to the extreme right end of the domain Fluctuation near thelattice plate and core cover plate is less As the velocity ratiowas reduced to 1.0, the region of high fluctuation widened

In addition, higher fluctuations can be seen near the plates.heat transfer engineering vol 32 no 5 2011

Figure 13 Nondimensional RMS temperature contours in the domain for (a)

velocity ratio.

Variation of Temperature Fluctuation With Velocity Ratio

Figure 14 shows a plot of maximum magnitude of RMS

tem-perature 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

tem-perature 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

tem-perature 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

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:

• 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

tem-perature 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

con-ditions after taking due care for geometric and hydraulic

as-pects

NOMENCLATURE

Ap area of the porous plate (m2)

Af free area for flow through the porous

plate (m2)

Cij convection term (kg/m-s3)

C1, C2, Cε1, Cε2, Cµ turbulence modeling constants

k turbulent kinetic energy (m2/s2)

LMFBR liquid-metal-cooled fast breeder reactor

Pii, Pij turbulence production term (kg/m-s3)

Rij redistribution or pressure-strain term

β’ coefficient based on the ratio of porous

plate hole diameter to its thickness

i, j, k general spatial indices

[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

Yam-aguchi, A., Current Status of Studies on Temperature

Fluc-tuation Phenomena in LMFBRs, IAEA Specialist Meeting

on Correlation Between Material Properties and

Thermo-hydraulics Conditions in Liquid Metal Cooled Fast

Reac-tors (LMFRs), Aix-en-Provence, France, 1994.

[3] Tokuhiro, A., and Kimura, N., An Experimental

Investi-gation on Thermal Striping Mixing Phenomena of a

Ver-tical 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

Triple-Jet, 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

Mea-surements 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

Tem-perature Fluctuation Analysis Using the Algebraic Stress

Turbulence Model in Water and Sodium, JSME

Interna-tional Journal, vol 35, pp 486–496, 1992.

[8] Kasahara, N., Evaluation of Thermal Striping

Phenom-ena at a Tee Junction of LMFR Piping System with

Nu-merical Methods (II), Thermomechanical Calculations,

Proc 15th International Conference on Structural

Me-chanics 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

(Ex-perimental Analyses on Mixing Process in Parallel

Triple-Jet 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

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

2004

[12] 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.

[13] Suyambazhahan, S., Sarit K Das, and Sundararajan,T., Hydrodynamic and Thermal Oscillations in a Non-

Isothermal Laminar Jet, International Journal of Heat and Mass Transfer, vol 47, pp 3957–3969, 2004.

[14] 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,

[16] Gao, S., and Voke, P R., Large-Eddy Simulation of

Tur-bulent Heat Transport in Enclosed Impinging Jets, national Journal of Heat and Fluid Flow, vol 16, pp.

Inter-349–356, 1995

[17] 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

[18] 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,

[21] Nield, D A., and Bejan, A., Convection in Porous Media,

2nd ed., Springer, New York, 1999

[22] Pope, S B., Turbulent Flows, Cambridge University Press,

Cambridge, 2000

[23] 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 tory 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 Tech- nology Madras He is a graduate in Mechanical En- gineering from the University of Kerala.

Regula-Indranil Banerjee is a scientific officer at the

Ex-perimental Thermal Hydraulics Section of the Indira

Gandhi Centre for Atomic Research, India He has

eight years of experience in thermal hydraulic

analy-sis and experiments for fast breeder reactors (FBRs).

His research interests include design and planning of

thermal hydraulic experiments for FBRs and

compu-tational fluid dynamics He graduated in mechanical

engineering from Jadavpur University, India.

G Padmakumar is head of the Sodium

Experi-ments and Hydraulics Division, Fast Reactor

Tech-nology Group, Indira Gandhi Centre for Atomic

Re-search He is a graduate in mechanical engineering

and has obtained his M.S degree He has undergone a

one-year orientation course in nuclear engineering at

BARC, Mumbai, India His current research focuses

on thermal hydraulics of fast reactors His areas of

expertise include design of experiments in water, air

and sodium.

K S Reddy is an associate professor in the

Depart-ment of Mechanical Engineering at Indian Institute of Technology Madras, Chennai He received his doc- torate in the area of solar energy from IIT Delhi in

1999 His main research interests are renewable ergy systems, energy conservation, and heat transfer

en-in two-phase systems He has co-authored more than

70 refereed journal and conference publications He

is currently working on concentrating solar power, hydrogen production using solar energy, energy ef- ficency, heat transfer in two-phase systems, and nuclear reactor thermal hy- draulics.

heat transfer engineering vol 32 no 5 2011

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457632.2010.483863

Analysis of a Parallel-Flow Heat

Exchanger with a Heat Source

M EL HAJ ASSAD and VOITTO W KOTIAHO

Department of Energy Technology, Aalto University School of Science and Technology, Aalto, Finland

In this work, a modified analysis of a parallel-flow plate heat exchanger that takes into account a volumetrically uniform

heat source in the hot fluid is presented New expressions for the number of transfer units (NTU) and effectiveness of the

heat exchanger are derived These expressions are verified against the conventional effectiveness–NTU relations in the limit

of zero heat source rate This situation is of interest in applications such as the ammonia–water absorption absorber heat

exchanger where a heat source is generated in the solution side The model studies two cases based on the minimum and

maximum heat capacities of the hot fluid The results show that the number of transfer units and the effectiveness of the heat

exchanger are the same for both cases The analysis is applied to the absorber heat exchanger Expressions of effectiveness

and number of transfer units of a counterflow heat exchanger with a heat source in the hot fluid stream are also given from

minimum and maximum heat capacities points of view.

INTRODUCTION

Heat exchangers are widely used in many thermal systems

Condensers, boilers, intercoolers, and preheaters are some

ex-amples of heat exchanger devices used in power plants Heat

exchanger performance can be characterized by finding its

ef-fectiveness A powerful and useful method for heat exchanger

analysis is the one relating effectiveness (ε) and number of

trans-fer units (NTU) The conventionalε–NTU analysis given in heat

exchanger textbooks [1–7], to the authors’ knowledge, does not

take into account the volumetric source of thermal energy in

the hot fluid stream Currently, there is no analytical solution

available in the literature for the performance of a parallel-flow

heat exchanger with thermal energy volumetric source in the hot

fluid stream

The basic motivation behind this work is due to the

observa-tions made in an experimental work [8] on a large-aspect-ratio

absorber used in an ammonia–water absorption chiller In that

experimental work, it was observed that for certain experimental

conditions, the solution temperature at the exit of the

counter-flow heat exchanger was higher than or identical to the

solu-tion temperature at the inlet of the counterflow heat exchanger,

despite the fact that the solution inlet temperature at the heat

exchanger inlet was close to the ambient temperature

Address correspondence to Dr Mamdouh El Haj Assad, Department of

Energy Technology, Aalto University School of Science and Technology, PO

Box 14100, 00076, Aalto, Finland E-mail: mamdouh.assad@hut.fi

Based on the experimental work just described [8], analyticalanalysis to determine the overall heat transfer coefficient of acounterflow heat exchanger with heat source in the hot fluidstream was presented [9] but nothing was mentioned about theε–NTU analysis Analysis of a counterflow heat exchanger with

a heat source in the hot fluid stream was presented in detailfor minimum and maximum heat capacity rate of the hot fluid[10] for which the analytical solution of the heat exchangereffectiveness and number of units were not the same for bothcases, as in conventional heat exchangers Therefore, there was aneed to study both cases (minimum and maximum heat capacity)for parallel-flow heat exchangers with a heat source in the hotfluid stream

The objective of this work is to present a closed form alytical solution for the ε–NTU relation for any parallel-flowheat exchanger in the presence of volumetric source of thermalenergy in the hot fluid stream and then to apply this analysis to

an-an absorber

MATHEMATICAL MODEL

Consider a parallel-flow plate heat exchanger in which there

is a heat source (g) in the hot fluid stream The inlet tures of the hot and cold fluids are T1and t1, respectively, and

tempera-the outlet temperatures of tempera-the hot and cold fluids are T2and t2,respectively In the analysis, it is assumed that this heat source

is uniform and constant over the length of the heat exchanger.

Other assumptions for the analysis are that fluid specific heats

are constant, overall heat transfer coefficient is constant, and

there is no heat transfer between the exchanger and the

sur-roundings

The heat balance of the hot fluid can be written as

d φ = dg − ( ˙mc p)T d T (1)where φ is the heat rate of the heat exchanger, g is the heat

source rate, m is the mass flow rate, c˙ p is the specific heat

at constant pressure, T is the hot fluid temperature, and the

subscript T refers to the hot fluid.

The heat balance of the cold fluid is

where t is the cold fluid temperature and the subscript t refers

to the cold fluid

The heat transfer rate between the hot and cold fluids that

define the overall heat transfer coefficient is expressed as

where U is the overall heat transfer coefficient, W is the

heat exchanger width, and x is the axial direction of the heat

exchanger

The overall energy balance over the entire length of the heat

exchanger can be obtained by integrating Eq (1) as

φ = g + ( ˙mcp)T (T1− T2) (4)

where g can be obtained from dg = g

L d x by using the

uni-form heat source assumption and the subscripts 1 and 2 refer,

respectively, to the inlet and exit conditions

Combining Eqs (1)–(3), the temperature variation of the hot

fluid, cold fluid and their difference along the axial direction of

the heat exchanger are, respectively, obtained as

where ˙C T = ( ˙mcp)T and ˙C t = ( ˙mcp)t are, respectively, the

heat capacity rate of the hot and cold fluids and L is the heat

With the boundary condition at the heat exchanger inlet, the

temperature difference at x∗ = 0 is θo = T1− t1, then thesolution of Eq (8) is obtained by

−Dx∗

(9)where

Case 1

In this case we assume that the minimum heat capacity is

on the hot fluid side and the maximum heat capacity is on thecold side, so C˙T = ˙Cmin, which means that the maximumtemperature difference occurs in the hot fluid, i.e.,
Tmax =

T1−T2, and ˙C t = ˙Cmaxindicates that the minimum temperaturedifference occurs in the cold fluid, i.e.,
Tmin= t2− t1.The effectiveness of the heat exchanger is defined by

Cmax is the heat capacity ratio

The maximum temperature difference is obtained as

θ2− A D



(15)where

heat transfer engineering vol 32 no 5 2011

θ2= T2− t2= θo(1− ε − Rε) + ˙g

Cmin

(17)Using Eqs (11), (15), (16), and (17) and defining the number

θo(1− ε − Rε) + A − A

D

(18)

The effectiveness of the heat exchanger can be obtained from

In this case we assume that the maximum heat capacity is on

the hot fluid side and the minimum heat capacity is on the cold

side, in other words, ˙C T = ˙Cmax, i.e.,
Tmin = T1− T2, and

˙

C t = ˙Cmin, i.e.,
Tmax= t2− t1

In a way similar to that in case 1, the number of transfer units

θo(1− ε − Rε) + A − A

D

(20)

The effectiveness of the heat exchanger can be obtained from

Equation (18) is identical to Eq (20) and Eq (19) is

iden-tical to Eq (21), which is not the case for a counterflow heat

exchanger with a heat source [10]

Considering a conventional parallel-flow heat exchanger

where there is no heat source in the hot fluid, i.e., g = 0 (

A = 0), then number of transfer units NTU of Eqs (18) and

(20) will be the same for both cases, which is

1+ Rln

1

1− (1 + R)ε



(22)Then Eq (22) gives the effectiveness of the parallel-flow heat

For R = 0 and N T U → ∞, the heat exchanger

effective-ness is obtained from Eq (24) as

ε =θo+ A

As N T U → ∞ and g = 0, the heat exchanger effectiveness

is obtained from Eq (24) as

Counterflow Heat Exchanger

We summarize the results obtained in reference [10] for acounterflow heat exchanger in which there is a heat source g inthe hot fluid stream

Case 1: ˙ C T = Cmin The number of transfer units and heatexchanger effectiveness are, respectively,

ε =



θo−A B

 

exp (N T U (1−R)) − 1+ A exp (N T U (1 −R))

θoexp (N T U (1 − R)) − R

(28)where

1

ε =



θo− A B

heat source ( g = 0), so Eqs (27) and (30) and Eqs (28) and(31) become, respectively,

lit-1.0 0.8

0.6 0.4

0.6 0.4

0.2 0.0

18 19 20 21 22 23 24 25 26

RESULTS AND DISCUSSION

An experimental study was used to analyze the microchannel

absorber with a counterflow heat exchanger [8] In this absorber,

a weak solution of ammonia–water was constrained to flow in a

microchannel, while ammonia vapor was bubbled through its top

porous wall A coolant that flows in a counterflow arrangement

to the weak solution removed the heat absorption that is released

by the microchannel fluid

Figure 1 presents the hot fluid temperature distribution along

the heat exchanger for fixed thermal conductance of 2W/K,

the hot fluid heat capacity rate of 2W/K, the hot fluid inlet

temperature of 25◦C and the cold fluid inlet temperature of 15◦C

The results presented in Figure 1 are obtained for extremely high

cold fluid heat capacity rate ( Ct → ∞), in other words, exit

and inlet temperatures of the cold fluid are equal, i.e., t1 =

t2 = 15oC For given values of the heat source, the hot fluid

temperature variation along the heat exchanger is obtained by

using Eq (9)

Figure 1 shows that as the heat source value increases, the hot

fluid temperature at the exit increases The g= 0 line in Figure

1 corresponds to the distribution without heat source in the hot

fluid As g= 20W, the exit hot fluid temperature reaches the

inlet hot fluid temperature, i.e., T1 = T2 = 25oC, this can be

seen from Eq (4) for g= φ

Based on the numerical values given above, Eq (19) can

be used to calculate the effectiveness of the heat exchanger for

which the minimum heat capacity rate is on the hot fluid side

The variation of the effectiveness of parallel-flow heat exchanger

with the heat source rate for R= 0 is given in Figure 2 based

on the data used in Figure 1

Figure 2 presents the variation of heat exchanger

effective-ness with heat source rate for different number of transfer units

As it can be seen from Figure 2, the heat exchanger effectiveness

30 25 20

15 10 5

0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

30 25 20

15 10 5

0

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

NTU=1 NTU=10

ε

g (W)

is monotonically increasing with heat source rate Figure 2 alsoshows that for a given heat source rate, increasing the number

of transfer units results in an increase in heat exchanger

effec-tiveness As N T U → ∞, the heat exchanger effectiveness will

be ε = θo +A

θo for R = 0 Figure 2 shows that for this infinitenumber of transfer units, the heat exchanger effectiveness will

be larger than 1 for heat source rate larger than 0 and it will be

equal to 1 for g= 0, which can be seen from Eq (25).Figure 2 also shows that the effectiveness of the heat ex-changer reaches 1, i.e., ε = 1 when the heat source rate is

g = 20W for N T U = 1, which is the case when g = φ,

and hence all heat source rate is transferred to the cold fluid.The general variation of heat exchanger effectiveness with the

number of transfer units for R = 0.5, ˙CT = 2W/K, and

θo = 10◦C( T

1 = 25◦C and t

1 = 15◦C) is presented in

10 9 8 7 6 5 4 3 2 1 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

10 9 8 7 6 5 4 3 2 1 0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

g=0 W g=5 W g=10 W g=15 W g=20 W

ε

NTU

heat transfer engineering vol 32 no 5 2011

30 25

20 15

10 5

NTU=15 NTU=20 NTU →∝

ε

g (W)

Figure 3 for different values of heat source rate according to

Eqs (19) or (21) Figure 3 shows that increasing the heat source

rate and number of transfer units, increases the heat exchanger

effectiveness The figure shows that the heat exchanger

effec-tiveness can be higher than 1 as the heat source rate and number

of transfer units increase

The variation of heat exchanger effectiveness with heat

source rate is illustrated in Figure 4 for different values of

num-ber of transfer units Figure 4 shows that there is no remarkable

change in the heat exchanger effectiveness for R = 0.5, which

is not the case for R = 0 as shown in Figure 2 As N T U → ∞,

the heat exchanger effectiveness will be ε = θo +A

θo(1+R).

CONCLUSIONS

A modified analysis of a parallel-flow heat exchanger with a

uniform heat source in the hot fluid stream was presented

Mod-ified equations for the heat exchanger effectiveness and number

of transfer units were derived These modified equations were

presented for the cases when the hot fluid has minimum heat

capacity rate and maximum heat capacity rate The results show

that these two cases are identical to each other, which is not the

case for a counterflow heat exchanger with a heat source The

analysis presented in this work is very useful in many

applica-tions such as ammonia–water absorber heat exchanger

More-over, it demonstrates an analytical procedure in order to analyze

and explain data obtained from parallel-flow heat exchangers

with a heat source in the hot fluid stream Analytical

expres-sions are also given to analyze the performance of counterflow

heat exchanger with a heat source in the hot fluid stream

NOMENCLATURE

A parameter defined in Eq (10), K

B parameter defined in Eq (29)

c p specific heat at constant pressure, J/kg-K

˙

C heat capacity rate, W/K

D parameter defined in Eq (11)

R heat capacity ratio

T hot fluid temperature,◦C

t cold fluid temperature,◦C

U overall heat transfer coefficient, W/m2-K

[7] Lampinen, M J., El Haj Assad, M., and Kotiaho, V., Heat

Transfer Textbook, Helsinki University of Technology, No.

155, Espoo, Finland, 2008

[8] Jenks, J., and Narayanan, V., An Experimental Study of

Ammonia–Water Bubble Absorption in a Large Aspect

Ra-tio Microchannel, ASME Paper No IMECE2006-14026,

pp 243–249, 2006

[9] Narayanan, V., Kanury, M., and Jenks, J., Heat Exchanger

Analysis Modified to Account for a Heat Source, ASME

Journal of Heat Transfer, vol 130, no 12, p 124502,

2008

[10] El Haj Assad, M., and Kotiaho, V., Analysis of a

Counter-flow Heat Exchanger With a Heat Source, ICEGES 2009,

Amman, Jordan, November 10–12, pp 1–5, 2009

M El Haj Assad is a teaching research scientist of

energy technology at Aalto University School of ence and Technology, Finland He received his Ph.D.

Sci-in applied thermodynamics from Aalto University Sci-in

1998 He studied at Middle East Technical sity, Turkey, where he obtained his B.E and M.S degrees His research interests include irreversible thermodynamics, heat exchangers, and energy con- version systems.

Univer-Voitto W Kotiaho is a research scientist of energy

technology at Aalto University School of Science and Technology, Finland He received his M.S from Aalto University in 1997 His research interests in- clude scientific computing and heat exchanger de- sign.

heat transfer engineering vol 32 no 5 2011

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457632.2010.483868

Dynamic Characteristics of a

Free-Flow-Channel Heat Exchanger

NA QIN,1 JUN ZHAO,1 YAN JING XIANG,1and PENG ZHI HAO2

1Thermal Department, Mechanical Engineering School, Tianjin University, Tianjin, China

2Department of Electronics and Information Engineering, Tianjin Institute of Urban Construction, Tianjin, China

The performance of sewage heat exchangers plays an important role in the sewage source heat pump systems when the

sewage does not enter the heat pump unit directly, especially when untreated sewage is used as heat or cold source In this

article, a free-flow channel heat exchanger is proposed to be used in an untreated sewage source heat pump system First

the article designs the sizes of heat exchanger according to the real system requirements, and then it models and analyzes

dynamic characteristics on the simulink platform The transfer functions that are suitable for the heat exchanger are deduced.

The analysis shows that the wall temperature is 9.1◦C when the untreated sewage and water temperatures at the inlet are 15

and 7◦C, respectively The result is obtained when considering the temperature at the outlet is affected by the temperature

at the inlet The variable quantity of water temperature at the outlet is affected greatly by the variable quantity of water

temperature at the inlet and the variable quantity of sewage temperature at the outlet by the variable quantity of sewage

temperature at the inlet Besides, the measured values of water temperatures at the inlet and outlet are also observed from

the real system where the free-flow channel heat exchanger is adopted The variable quantities of water temperature at the

outlet are calculated according to the measured values, and are compared with the model results deduced by the transfer

functions The comparative result shows that the differences between the measured and model results of water temperature

variable quantities at the outlet range from −1 to 1◦C, thus getting the water temperatures at the outlet according to the

model results The differences of the water temperature at the outlet between the measured values and the deduced results

are from −0.5 to 0.5◦C It illustrates the temperature at the outlet can be estimated by modeling the temperature variable

quantity at the outlet.

INTRODUCTION

Sewage has great potentials to be a cold or heat source [1]

A heat pump system using sewage as an energy source allows

the use of low-cost off-peak electricity, has no outdoor unit to

make noise or spoil the appearance of the building where it is

installed, and combines cooling/heating and hot-water heating

in a single unit In addition, it has outstanding energy-saving

effect since it is operated at a high coefficient of performance

(COP) without air pollution [2] It can save more than 60% of

electricity compared to an electric boiler, and more than 50%

of fuel compared to a coal-fired unit [3] Comparing with air,

earth, and groundwater, urban sewage has great advantages such

Financial support was provided by National Major Project of Scientific and

Technical Supporting Programs of China During the 11th Five year Plan Period,

Grant No 2006BAJ03A06.

Address correspondence to Ms Na Qin, Thermal Department,

Mechan-ical Engineering School, Tianjin University, Tianjin 300072, China E-mail:

qina1108@yahoo.com.cn

as high thermal capacity, large heat transfer coefficient, no need

to intake and recharge well, and also the suitable temperatureboth in winter and summer [4, 5] Although sewage treatmentplants generally reduce chemicals and nutrients, they providelittle control over the temperature of effluents As a result, thesewage that is released into the natural water cycle is generallywarmer than the natural water and the resulting changes to thenatural water body can affect the quality of the water resources[6] Therefore, the sewage heat recovery has attracted the interiorresearch field in recent years Several types of sewage heatpump systems are widespread in those developed countries ofnorthern Europe [7, 8] In 2000, the first project of a treatedsewage source heat pump system was established in Gao BeidianSewage Plant in Beijing At the beginning of 2004, the firstuntreated sewage source heat pump project of mainland Chinahad begun to be operated in Miyun Sewage Treatment Plant inBeijing [9]

In most untreated sewage-source heat pump systems, theextract quantity of heat or cold from the untreated sewage isrealized by the heat exchange with the water rather than the re-

Figure 1 Free-flow-channel heat exchanger schematic diagram.

frigerant The approach is applied to the majority of the real heat

pump systems Urban sewage has lots of contaminants and

so-lutes If there is no simple and economical filtration, it is much

easier to plug the heat exchanger and the pipeline equipment

[10, 11] With the increasing application of untreated sewage as

the heat or cold resource, the performance of a sewage heat

ex-changer in the whole heat pump system is of great importance

In an untreated sewage source heat pump system,

shell-and-tube heat exchangers are usually selected as the heat exchange

equipments [12], while plate heat exchangers or immersion heat

exchangers are also used in some real systems Although the

untreated sewage is filtered through the equipment, the

foul-ing and the decrease of coefficient of heat transfer are still

the serious problems of these heat exchangers, and the shorter

maintenance period of these exchangers also leads to much

labor

In this condition, a free-flow-channel heat exchanger is

presented to be applied to an untreated sewage source heat

pump system [13] The article gives the design sizes, research

on the dynamic characteristics, and finally verifies the

trans-fer functions of the heat exchanger through the real system

operation

Free-Flow-Channel Heat Exchanger Principle

Figure 1 shows the schematic diagram of the heat exchanger

[14] The water flows in the heat exchange pipes and the

un-treated sewage flows in the channel as the non-hydraulic filling

The free flow of untreated sewage can ensure higher velocity,

wash away large impurities, and thus can decrease the

ther-mal resistance of the wall region The special structure of the

heat exchanger facilitates the cleaning and maintenance of heat

transfer surfaces, which can even be performed while the system

operates Besides, the special structure also decreases the

foul-ing formation and simplifies the design of the heat exchanger,

and reduces the total initial investment of the whole heat pump

system

Heat load (kW)

Sewage inlet temperature ( ◦C)

Sewage outlet temperature ( ◦C)

Water inlet temperature ( ◦C)

Water outlet temperature ( ◦C)

DYNAMIC MODEL Model Basis

The free-flow-channel heat exchanger is adopted in a realsystem using untreated sewage as the heat source Its designneeds to satisfy some design parameters of the real system whichare shown in Table 1

Design and Calculation

The mass flow of untreated sewage is given by Eq (1) andthe mass flow of water by Eq (2) [15],

where ˙m sis the mass flow of untreated sewage and ˙ m wis the

mass flow of water, Q is the heat load, csis the specific heat of

untreated sewage and c w is the specific heat of water, ts1, ts2arethe separate temperatures of untreated sewage at the inlet and

outlet respectively, and t w1 , t w2are the temperatures of water

at the inlet and outlet, respectively

The internal diameters of heat exchange pipes are set as 20

mm and the water velocity is set as 1.5 m/s The Reynoldsnumber of water side is given by Eq (3):

Rew= v w d i

where Rewis the Reynolds number of water side, v w is thewater velocity, and νwis the water kinematic viscosity The heattransfer coefficient is deduced from the Nusselt number given

Figure 2 Set dimensions of heat transfer surface.

should be lower than 4.3 m/s It is set as 1.5 m/s to satisfy both

the turbulence flow condition and design margin

The Nusselt number of untreated sewage follows Eqs (5)

where N us is the Nusselt number of untreated sewage, Resis

the Reynolds number of untreated sewage and Prsis the Prandtl

number of untreated sewage

The total heat transfer coefficient can be obtained from

where K is the total heat transfer coefficient, h wis the water

heat transfer coefficient, r f is the fouling thermal resistance,

δb is the wall surface thickness of heat exchange pipes, λb

is the conductivity factor of heat exchange pipes, hs is the

heat transfer coefficient of untreated sewage, and r w is the

water thermal resistance The numbers of heat transfer pipes are

figured out from Eq (8):

where Ac is the cross-sectional area of heat exchange pipes,

ρwis the water density, n is the number of heat exchange pipes,

and diis the internal diameter of heat exchange pipes The sizes

of the heat exchanger are calculated and shown as Table 2

Established Model

Possessing distributed-parameter property, heat exchangers

appear to be of special dynamic characteristics, which are

re-flected by the transfer functions The transfer functions of thefree-flow channel heat exchanger depend on the following threeequations [17]:

where tb is the wall temperature of heat exchange pipes, A wand

A s are the heat exchange areas of water and untreated sewage,

respectively, cbis the specific heat of heat exchange pipes, and

m bis the mass of heat exchange pipes

Equations (9) and (10) can be transformed into Eqs (12) and(13) The parameters a and b are defined as Eq (14)

2+a + 1
t w1 2cb m b · s − hs A s

2b2+b − 2− hw A w2a

2+a − 2(16)Another incremental representation is given based on Eq (12),

Table 3 Values of some short equations

where
t w1 and
t w2 are the variable quantities of water

temperature at the inlet and outlet, respectively

Then the variable quantities of water and untreated sewage

temperatures at the outlet are deduced as Eqs (18) and (19),

2−b2+b+1
t s1 2cb m b · s − hs A s

 2b2+b − 2− h w A w 2a

2+a − 2

+ 2a

2+a ·

h w A w2−a2+a+1
t w1 2cb m b · s−hs A s

 2b2+b−2−hw A w2a

2+a−2+2− a

2−b2+b+1
t s1 2cb m b · s−hs A s

 2b2+b−2−hw A w2a

2+a−2+2− b

 2b2+b − 2− h w A w 2a

2+a − 2 (19)where
t s1 and
t s2 are the variable quantities of untreated

sewage temperature at the inlet and outlet, respectively

ANALYSIS OF THE RESULTS

Table 3 shows the calculated results of several short equations

that are obtained according to the results in Table 2

The transfer function of the wall temperature is obtained

as shown by expression (20) The numerator means the signal

source composed of two parameters: untreated sewage and water

temperatures at the inlet; the denominator means the transfer

function where the parameter s is the Laplace operator Figure 3

shows the signal diagram of the wall temperature in the simulink

environment [18]

t b= t s1 + 1.6t w1

1 6.01s+2.87 Transfer Fcn

simout

To Workspace

Scope

26.2 Constant

Suppose the wall temperature is 0◦C at the initial time.Figure 4, which contains four different curves, shows the re-sults of wall temperature of heat exchange pipes From Eq (12)

we can see that the wall temperature is related to the sewage andwater temperature at the inlet The wall temperature is 9.1◦Cwhen the sewage and water temperatures at the inlet are 15 and

7◦C, respectively It decreases to 0.5◦C when the sewage andwater temperatures at the inlet are 15 and 6◦C, respectively.However, it is about 8.8◦C when the sewage and water tem-peratures at the inlet are 14 and 7◦C, respectively When boththe water and sewage temperatures at the outlet are known, thewall temperature can be deduced by Eq (11) The result is givenwhen not considering the effect of the temperature at the inlet onthe temperature at the outlet In such a case the wall temperature

is about 9.6◦C, which is the highest in Figure 4

The transfer function about the water side is given by Eq.(18), and the simplified results are shown as expressions (23)and (24) when only the influence of water or untreated sewage

heat transfer engineering vol 32 no 5 2011

w w

+

∆t

=

∆t

16.361.6

1 2

results are shown as expressions (23) and (24)

Figure 5 shows the variable quantities of water temperature at

the outlet on which the variable quantities of untreated sewage

and water temperature at the inlet show different effects Both

of the temperature variable quantities at the inlet are 1◦C It

can be seen that the variable quantity of water temperature at

the inlet has greater influence on the variable quantity of water

temperature at the outlet

Figure 6 shows the variable quantities of untreated sewage

temperature at the outlet on which the variable quantities of

sewage and water temperature at the inlet show different

ef-fects Both of the temperature variable quantities at the inlet are

also 1◦C The result shows that the variable quantity of sewage

1 2

86.527

12 s

s s

temperature at the outlet is affected more greatly by the variablequantity of sewage temperature at the inlet

EXPERIMENTAL VERIFICATION

The real system where the free-flow channel heat exchanger

is adopted has been operated for a heating season To verify thetransfer functions discussed in the previous section, we need

to observe the temperatures at the inlet and outlet of the heatexchanger The transfer function shown as expression (13) ischosen for the verification From the beginning of the heat sup-ply, we monitor the whole system with the testing equipmentshown in Figures 7 and 8 The important equipment in Figure

7 are data recorders and PT1000 sensors, which are used forobserving the water temperatures at the inlet and outlet of theevaporator, condenser, and heat exchanger Figure 8 shows theTransport P7878 ultrasonic flowmeter used for observing theflux of untreated sewage and the water

Table 4 Water temperatures at the inlet and outlet ( ◦C)

Table 4 shows water temperatures at the inlet and outlet of

the heat exchanger There are two groups of data measured on

the very day of the experiment: The data in the first line mean

the temperatures at the inlet; the data in the second line mean

the temperatures at the outlet

We get the variable quantities of water temperature at the

inlet and put them into expression (22) Then the variable

quan-tities of water temperature at the outlet are deduced as the model

results The temperature variable quantities at the outlet are as

the measured results according to the data in Table 4 These two

temperature variable quantities on the very day of the

experi-ment are compared and shown in Figures 9 to 14 The

compar-ative results on December 4, 2008, show the best coincidence

because the temperature fluctuation at the inlet is the most

mod-erate However, Figures 13 and 14 do not show the coincidence

quite well The reason for the error lies in a large fluctuation of

the temperature at the inlet on those two days, which causes a

large change of the temperature at the outlet Both of the two

figures also illustrate that the temperature at the inlet should be

controlled in a narrow range This just proves that the transfer

function expresses the control characteristics to the temperature

tem-perature variable quantities at the outlet.

From Figure 15 it can be seen that the differences between themeasured and model results of temperature variable quantities

at the outlet are from−1 to 1◦C Furthermore, it is easy to duce the water temperature at the outlet according to the modelresults, which is compared with the measured data in Table 4.The comparative results, given as Figure 16, show the differ-ences are in the range from−0.5 to 0.5◦C In this condition, themeasured and model differences of water temperature variablequantities at the outlet from−1 to 1◦C are permissible Figure

de-16 also indicates that the water temperature at the outlet drops

on the average by 11.5◦C as the weather turns cold gradually

tem-peratures at the outlet.

Due to its perfect application to sewage, a free-flow-channel

heat exchanger is chosen as the key equipment to transfer heat in

the untreated sewage source heat pump system The conclusions

drawn through this research on dynamic characteristics of the

heat pump system are:

First, the wall temperature is affected by both untreated

sewage and the water temperatures at the inlet The wall

temper-ature is 9.1◦C when the untreated sewage and water temperatures

at the inlet are 15 and 7◦C, respectively It decreases to 0.5◦C

when the untreated sewage and water temperatures at the inlet

are 15 and 6◦C, respectively And it is about 8.8◦C when the

untreated sewage and water temperatures at the inlet are 14 and

7◦C, respectively When both of the temperatures at the outlet

are known, the wall temperature is 9.6◦C, which is the highest

Second, the variable quantity of water temperature at the

inlet has greater influence on the variable quantity of water

temperature at the outlet than the variable quantity of untreated

sewage temperature at the inlet, while the variable quantity of

untreated sewage temperature at the inlet has greater influence

on the variable quantity of untreated sewage temperature at the

outlet than the variable quantity of water temperature at the inlet

If the water or sewage temperature at the inlet is adjusted, its

temperature at the outlet needs to be paid more attention to, for

guaranteeing the temperature variable quantity at the outlet not

exceeding its set value

Third, the differences between measured and model results of

water temperature variable quantities at the outlet are from−1

to 1◦C The water temperature at the outlet, which is compared

with the measured data, is deduced according to the model

results The comparison shows that the difference is in the range

from−0.5 to 0.5◦C In this condition, the differences of water

temperature variable quantities at the outlet from−1 to 1◦C are

permissible

Fourth, the transfer functions of the water side can be applied

to the indirect estimation of water temperature at the outlet The

analytical method also can be used for the performance analysis

of other heat exchangers

The transfer function of the sewage side is not verified

be-cause the sewage temperatures at the inlet are not observed The

further work that should be done is to verify it and then estimate

the sewage temperatures at the outlet according to the model

d diameter of heat exchange pipe, m

h heat transfer coefficient, W/ m2-K

1

K total thermal resistance, m2-K/W

l length of heat exchange pipe, m

m mass, kg

˙

m mass flow rate, kg/s

N u Nusselt number

N number of heat exchangers

n number of heat exchange pipes

b heat exchange pipes

c cross section of heat exchange pipes

REFERENCES

[1] Felix, S., Sewage Water: Interesting Heat Source for

[4] Liang, Z M., Yang Y., and Ying, L Z., The Application

Prospect of Sewage Source Heat Pumps, China Water & Wastewater, vol 19, pp 41–43, 2003.

[5] Jun, Y., and Dong, X W., The Feasibility Analysis of

Cycle Using the Sewage Heat Energy, China Water & Wastewater, vol 16, pp 28–30, 2000.

heat transfer engineering vol 32 no 5 2011