International Journal of Heat and Mass Transfer 53 (2010) 3721–3732

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier.com/locate/ijhmt

The effect of pulsed electric fields on horizontal tube side convective condensation
H. Sadek, C.Y. Ching *, J. Cotton
Department of Mechanical Engineering, McMaster University, Hamilton, Canada L8S 4L7

a r t i c l e i n f o a b s t r a c t

Article history: The effect of pulsed electric fields on two-phase flow patterns, heat transfer and pressure drop in horizon-
Received 4 January 2010 tal tube side convective condensation was investigated. Experiments were performed for an applied pulse
Received in revised form 12 April 2010 voltage of 8 kV at pulse repetition rates in the range of 0.5 Hz–1.5 kHz and duty cycles of 25%, 50% and
Available online 12 May 2010
75%. Three mass fluxes of 55, 100, and 150 kg/m2 s were tested with an average vapour quality of 45%
which corresponds to an initially stratified flow. The voltage was applied through a central electrode
Keywords: along the centerline of the tube. Changing the pulse repetition rate and duty cycle results in different flow
Two-phase flow
patterns and therefore in different values of heat transfer and pressure drop. For a given mass flux, the
Electrohydrodynamics
Heat transfer
heat transfer enhancement due to the applied voltage decreased with the pulse repetition rate and
Pressure drop reached a plateau. The pressure drop ratio, however, increased with pulse repetition rate and reached
Pulse electric fields a maximum before decreasing with a further increase in pulse repetition rate.
Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction represents the force acting on the free charges in the presence of
an electric field (also known as the Coulomb force). This force is
Active control of heat transfer and fluid flow is very important usually dominant for single-phase flow and can contribute to heat
in many engineering applications, such as in refrigeration, air con- transfer in two-phase flows by increasing convection in the individ-
ditioning, energy, and heat recovery systems. In most cases, con- ual phases. The dielectrophoretic component represents the force
ventional control techniques rely on quasi-steady control of the due to the spatial change of the permittivity of the dielectric med-
inlet flow conditions at the heat exchanger such as the average ium as a result of temperature gradients and/or differences in the
temperature, flow rate and bypass [1]. A promising technique for phases. The electrostrictive force is caused by both the inhomoge-
active heat transfer control, without changing the initial flow con- neity in the electric field strength and the variation in the dielectric
ditions, is by using electrohydrodynamics (EHD). Electrohydrody- constant of the medium with temperature and density. In two-
namics refers to the coupling between the flow field and a high- phase flows such as in convective boiling and condensation, the
voltage electric field. This coupling induces an electric body force dielectrophoretic and electrostrictive forces (polarization forces)
within the fluid which can induce secondary motions which dis- are dominant and significant at the vapour–liquid interface due to
turb the boundary layer near the surface and/or cause two-phase the large difference in permittivity between the two-phases, [4,5].
redistributions, and therefore change the heat transfer and pres- This force can cause interfacial instabilities and force the liquid with
sure drop. EHD can be applied relatively non-intrusively, using higher permittivity to move to regions of higher electric field. This
simple electrode designs. It is a relatively robust technique since phenomenon is usually referred to as liquid extraction [6] and can
it is non-mechanical, and can be configured for a high degree of result in phase redistribution in two-phase flows.
local control. The relative importance of the different components of the EHD
The total EHD force induced by the electric fields on the fluid is body force can be determined by evaluating the key dimensionless
expressed as [2,3] numbers in the governing differential momentum equation. The
    additional electric body force in the momentum equation can be
f 000 ¼ q E  1 E2 re þ 1 r qE2 @ e : ð1Þ represented by the EHD number, Ehd, and the Masuda number,
e e
2 2 @q T Md, [3,7];

The three terms on the right-hand side of (1) represent the electro- I o L3 E2 eo L2 T o ð@ es =@TÞ
phoretic, dielectrophoretic, and electrostrictive components of the Ehd ¼ Md ¼ : ð2Þ
q o m le A
2 2qo m2
electric body force, respectively. The electrophoretic component
The electrohydrodynamic forces will have a significant effect on
* Corresponding author. Tel.: +1 905 525 9140x24998. the fluid flow if Md/Re2  1 and/or Ehd/Re2  1 [3,4]. The Md and
E-mail address: chingcy@mcmaster.ca (C.Y. Ching). Ehd numbers are dependant on the nature of the flow (single-phase

0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijheatmasstransfer.2010.04.023
3722 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732

Nomenclature

A area, m2 T temperature, K
cppw specific heat of the water through the preheater, Trefsub refrigerant inlet temperature (subcooled), K
J kg1 K -1 T Sav g average surface temperature, K
cpref specific heat of the refrigerant, J kg1 K1 Tsat saturation temperature, K
cpw specific heat of the water through the test section, TwPRE, i water temperature at preheater inlet, K
J kg1 K1 TwPRE, o water temperature at preheater outlet, K
D duty cycle of the applied pulse wave V voltage, V
E electric field strength, V m1 x mass vapour quality
Ehd EHD number, defined by Eq. (2) DTRTD RTD temperature difference across the test section, K
f Fanning friction factor
fe000 electric body force per unit volume, N m3 Greek
h heat transfer coefficient, W m2 K1 e dielectric permittivity, N V2
hlv latent heat of vapourization, J kg1 eo dielectric permittivity of free space (8.854  1012),
I current, A N V2
L characteristic length, m es dielectric constant
m_w water mass flow rate in the test section, kg s1 le ion mobility, m2 V1 s1
m_ ref refrigerant mass flow rate, kg s1 m kinematic viscosity, m2 s1
m_ wPRE water mass flow rate in the water preheater, kg s1 q density, kg m3
Md Masuda number, defined by Eq. (2) qe charge density, C m3
QPRE heat transfer rate from the water and electric preheat-
ers, W Subscripts
Qw test section heat transfer rate, W i inlet
Re Reynolds number l, L liquid
T time period of the applied pulse wave, s o reference, outlet

or two-phase), electrode geometry, fluid properties and the applied more advantageous compared to DC voltages as different combina-
voltage. For example, in two-phase flows, the presence of the tions of pressure drop and heat transfer could be achieved by vary-
liquid–vapour interfaces can result in large electric interfacial ing the different voltage parameters.
forces due to the discontinuity of the electric properties across While there is agreement in the literature that EHD presents a
the interface. Here, the interfacial Masuda number can be several promising active technique for heat transfer control, there is a lack
orders of magnitude higher than the vapour EHD number, which of understanding of the interdependence of the redistribution of
implies that the dominant force acting on the liquid–vapour inter- the two-phase flow patterns due to the application of AC/pulse
face are the dielectrophoretic and electrostrictive forces. voltage and the heat transfer and pressure drop. The objective of
There have been several studies on EHD heat transfer enhance- this study is to experimentally determine the effect of pulse repe-
ment and detailed reviews are given by [8–10]. The effect of DC tition rate and duty cycle of high-voltage pulsed electric fields on
electric fields on tube side convective condensation heat transfer flow pattern redistributions, heat transfer and pressure drop for
using a concentric wire electrode configuration was investigated tube side convective condensation. This is important to identify
by [11–15]. In general, EHD is found to enhance heat transfer, the range of heat transfer and pressure drop that can be achieved
and the augmentation level decreases with an increase of the mass by varying the voltage waveform parameters. The details of the
flux and the vapour quality. Increasing the mass flux decreases the experimental facilities, uncertainty analysis, and data reduction
ratios, Md/Re2 and Ehd/Re2, and therefore decreases the effect of are presented in Section 2. The experimental results are presented
EHD on two-phase flow. The heat transfer enhancement in two- and discussed in Section 3, followed by the conclusions of this
phase flow is mainly attributed to the phase redistribution caused study.
by the induced interfacial electric forces [16–18,14]. These interfa-
cial forces can cause liquid extraction from the vicinity of the heat
transfer surface to the regions of the high electric fields, and thus 2. Experimental facility and data reduction
increase the convective condensation heat transfer.
Most previous research on EHD-enhanced tube side convective The test facility is a closed loop charged with refrigerant R-134a
condensation has been performed under applied DC voltages as shown schematically in Fig. 1. In this instance, R134a was se-
[8,19,9,10]. There have been fewer studies on the effect of alternat- lected because it is one of the most common refrigerants used in
ing electric fields on the flow pattern redistributions, heat transfer industrial refrigeration systems, and also because of the large dif-
and pressure drop [20–24]. Cotton et al. [20] applied a 60 Hz AC ference in permittivity between the liquid and vapour phases.
signal using a coaxial wire electrode in two-phase flow and found The main difference in the use of different working fluids would
that the application of the high-voltage induced an oscillatory flow be in the EHD force at the liquid–vapour interface due to the differ-
where liquid droplets were observed to oscillate radially in the ences in the liquid and vapour permittivity, and in the voltage at
lower portion of the tube. Small liquid spouts or jets were observed which breakdown occurs. The refrigerant is circulated throughout
on the upper half above the electrode, which was attributed to the the loop by a gear pump located at the exit of the condenser. The
continuous transition between flow regimes due to the approxi- refrigerant inlet quality to the test section can be controlled by
mate on/off electric field. The effect of different AC/Pulse waveform two separate heating sections: direct electric heating and water
parameters (e.g. frequency, pulse repetition rate, duty cycle, and heating in a plate-type heat exchanger. The refrigerant exiting
amplitude) on tube side convective condensation using a central the heat exchanger is directed into the horizontal test section via
high-voltage electrode configuration were investigated by [21– a straight length of 0.55 m (50 diameters) tubing to achieve fully
24]. The results showed that using AC/pulse applied voltages was developed conditions. Leaving the test section, the refrigerant
 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732 3723

T
Relief Valve
~ Rotameter
T Condenser
Water Water Out Chiller
IIn Tank
Pump
T
Sight
T Tube
T
P
Water Out Water In

Condenser
Turbine PID
Water Outlet
Flow Controller
Meters

T
~
Test Section T P Relief Valve

T
T
High Voltage Pressure Transducer
Water
Amplifier Preheater
T

Relief Valve P T
Ceramic Isolation Fittings
~
Constant
Preheated
P T Sections
Heat Flux ~
Evaporators P T Relief Valve

Filter
Turbine Flow Meters

Gear
Pump

Fig. 1. Schematic diagram of test facility.

Dimensions in mm
200 250 300
Water
outlet
R134a
inlet

T1s T2s T3s

Viewing
Refrigerant Water
window for 75 75 75 75
outlet inlet
high speed
camera
Pressure
Transducer

Ø 3.18 Wire Electrode

Ts-t

Ts-s2 Ts-s1 10.2 12.7 19.05 26.67

Ts-b

Spacer Design

Fig. 2. Schematic diagram of the test section.

enters a 30 kW coaxial single-pass condenser to return the refrig- counter-current heat exchanger as depicted in Fig. 2. The outer
erant two-phase mixture to its original liquid state before entering water jacket is constructed from a 30 cm length of clear PVC with
the pump. The test section consists of a horizontal single tube inner diameter of 19 mm and wall thickness of 3.8 mm. The inner
3724 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732

tube containing the two-phase refrigerant is a stainless steel tube Table 1

with an outer diameter of 12.7 mm and an inner diameter of Uncertainties in calculated parameters.

10.2 mm. A 3.2 mm diameter stainless steel rod electrode was used Parameter Maximum percentage error (%)
to apply the electric field across the annular gap formed by the Heat flux (W/m ) 2
±9.2
electrode and the surface of the inner stainless steel tube. The Heat transfer coefficient (W/m2 K) ±12.0
electrode is concentric with the inner tube forming an annulus as Reynolds number ±3.0
shown in Fig. 2. The width of the annular gap is maintained along Average quality ±10.4

the entire length of the test section by three non-conducting

spacers at intervals of 75 mm. The spacers were machined out of
non-conducting material Delrin (dielectric constant of approxi- where V1 and V2 are the voltage drop across the two sections of the
mately 2.5) and occupy approximately 20% of the cross-sectional electric preheater. The maximum pressure drop across the test sec-
flow area, as shown in Fig. 2. The outside surface temperature of tion is less than 0.4% of the absolute pressure, therefore the effect of
the inner test section tube is measured with 0.5 mm O.D. T-Type the change in the pressure between the inlet and the exit of the test
thermocouples, with absolute uncertainty of ±0.23 K, embedded section on the two-phase refrigerant properties can be neglected.
in the tube at three axial locations, 75 mm apart. Each location The refrigerant outlet quality is calculated by applying an energy
contains four thermocouples, at the bottom, top and the two sides. balance across the test section such that
The inlet and outlet temperature of the refrigerant and the water
are measured by 1.6 mm O.D. T-Type thermocouple probes for Qw
xo ¼ xi  : ð7Þ
the refrigerant side and 6 mm O.D. resistance temperature detec- _ ref hlv
m
tors (RTD) for the water side. The dimensions of the test section An uncertainty analysis of the experimental results was per-
and the thermocouple locations are depicted in Fig. 2. The water
formed as outlined by Kline and McClintock [25], and are summa-
flow rate to the test section is measured using a turbine flow meter rized in Table 1. In addition, to confirm the accuracy of the
with an accuracy of ±4% of the reading.
experimental measurements, an energy balance was performed
The pressure drop across the test section is measured with an by comparing the power extracted from the refrigerant by the con-
8.62 kPa (1.25 psi) differential pressure transducer, with an accu-
denser and the test section condenser to the power input by the
racy of 0.25% of the full scale connected to the test section via preheaters. The energy balance was found to be within ±15% for
6.35 mm O.D. tubing. The tubing is passed through a water jacket
all test conditions, providing confidence in the efficacy of the mea-
to condense any vapour in the tubes in order to equalize the hydro- surement and analysis techniques.
static head on each side of the transducer. A viewing section made
of transparent quartz tube coated with an electrically transparent
conductive film of tin oxide is located at the outlet of the test sec- 3. Results and discussion
tion for visual observations of the flow. The grounded transparent
viewing section ensures the continuation of the elecric field within The effect of pulse repetition rate on two-phase flow patterns,
the viewing section. A high speed camera with a frame rate of heat transfer and pressure drop is studied for a pulse voltage of
2000 fps is used for visualizing and recording the flow pattern. 8 kV with three different duty cycle values of 25%, 50%, and 75%.
The electric field was established by connecting the voltage output The duty cycle is defined as the percentage ratio between the volt-
from a high-voltage amplifier to the center electrode. The chilled age on duration time of the pulse to the time period of a complete
water loop, needed to supply the cooling water to the test section, cycle. The experiments were performed at mass fluxes of 55, 100,
consists of a chiller, turbine flow meters and resistance tempera- and 150 kg/m2 s and average vapour quality of 45% which corre-
ture detectors (RTD). The chiller has a cooling capacity range up sponds to stratified flow with the liquid level below the electrode
to 7.3 kW for temperature range from 5 °C to 35 °C with a resolu- (without EHD). This particular quality was used here because it re-
tion of 0.5 °C. The heat flux extracted from the test section can sulted in a maximum heat transfer for an applied DC voltage of
be controlled by controlling either or both the water flow rate 8 kV in an earlier study [14]. The smallest value of the mass flux
and/or the outlet temperature from the chiller. was selected based on the range of the turbine flow meter
Excluding the thermal resistance of the stainless tube, which is available.
one order of magnitude lower than the inner convective thermal To better understand the transient response of the two-phase
resistance, the refrigerant side average heat transfer coefficient in flow to an applied high-voltage, the effect of a step input voltage
the tube can be approximated by on the two-phase redistribution was initially investigated [26].
The flow images showing the response of the flow starting from
¼ Qw
h ; ð3Þ 0.005 s prior to applying the step input voltage for mass flux of
AðT sat  T Sav g Þ
55 kg/m2 s and quality of 35% is shown in Fig. 3. Before the voltage
where Qw is the heat extracted by the coolant water from the con- is applied, the two-phase flow pattern is stratified wavy with the
densing refrigerant within the test section, given by liquid–vapour interface just below the electrode, Fig. 3(a). At the
instant of application of the voltage (t = 0 s), liquid is extracted
_ w cpw ðDT RTD Þ;
Qw ¼ m ð4Þ
from the liquid stratum toward the electrode due to the induced
where T Sav g is the average of the surface temperatures. The refriger- interfacial electric forces, Fig. 3(b). At 0.005 s, the liquid extraction
ant inlet quality, xin, is obtained from the energy balance across the is more intense, forming high-intensity liquid–vapour interaction
electric and water preheaters such that regions below the electrode (Fig. 3(c) and (d)). At a time of around
0.02 s, the liquid can be seen pushed radially outwards from the
Q PRE
m_ ref  cpref ðT sat  T ref sub Þ central electrode in the form of twisted liquid cones, Fig. 3(e).
xin ¼ ð5Þ For simplicity, these flow patterns will be referred to as ‘‘twisted
hlv ;in
cone” patterns hereafter. The amount of liquid extracted from
and QPRE is the net heat input by the electric and water preheaters the bottom stratum increases as time increases from 0.02 to
as determined by 0.04 s (Fig. 3(e)–(g)). With a further increase in time, the liquid–va-
  pour interactions below the electrode stay intense while the inten-
Q PRE ¼ ½IðV 1 þ V 2 Þ þ m_ wPRE cppw ðT wPRE;i  T wPRE;o Þ ; ð6Þ sity of the liquid ‘‘twisted cone” patterns start to decrease and
 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732 3725

Fig. 3. Transient response of two-phase flow due to an applied step voltage of 8 kV.

eventually diminish at steady state (Fig. 3(h) and (k)). These tran- Similar two-phase distribution characteristics are observed for
sient two-phase flow patterns are expected to result in different a pulse repetition rate less than 10 Hz. Increasing the pulse repeti-
heat transfer and pressure drop characteristics compared to the tion rate in this range decreases the time duration of the liquid
case of an applied steady DC electric field. Understanding and ‘‘twisted cone” patterns but sustains the liquid–vapour interaction
manipulating these transient flow patterns using pulsed electric below the electrode. The flow images for a pulse repetition rate of
fields will provide a means of using electrohydrodynamics for con- 10 Hz, (Fig. 5) show liquid columns (liquid extraction) between the
trolling heat transfer and pressure drop in thermal systems. As a bottom stratum and the central electrode, but no liquid above the
first step, the effect of a pulse voltage waveform on the flow and electrode. This is because the voltage on time duration is less than
heat transfer is investigated here. the time needed to initiate the transient flow patterns (estimated
The effect of 1 Hz, 50% duty cycle 8 kV pulse wave voltage on as 0.025 s from the step input voltage experiments). Therefore,
the two-phase flow patterns at mass flux of G = 55 kg/m2 s and there is no formation of liquid ‘‘twisted cone” patterns around
average quality of 45% is shown in Fig. 4. The figure shows 12 the circumference of the electrode but the liquid–vapour interac-
images equally distributed over one cycle of the applied pulse volt- tions below the electrode are sustained.
age. At this pulse repetition rate, the duration of the voltage on and The flow patterns for a pulse repetition rate greater than 10 Hz
off periods are large enough for the two-phase flow to fully re- are shown in Fig. 6. There is no significant difference in the two-
spond to the applied pulse voltage. In this case, the flow exhibits phase flow patterns throughout the cycle and therefore, each case
similar phase distribution characteristics observed in the 8 kV step is represented by a flow image and a schematic diagram (Fig. 6(b)–
input voltage case (Fig. 3). The flow pattern oscillates between a (d)). The liquid–vapour interactions due to the pulse voltage re-
stratified wavy flow observed at 0 kV (Fig. 4(a, b, l)), the ‘‘twisted sults in the formation of liquid droplets which oscillate with the
cone” transient flow patterns (Fig. 4(d–h)) and the 8 kV DC applied same frequency as the pulse repetition rate of the applied voltage.
voltage flow patterns (Fig. 4(i)). In the pulse repetition rate range, 10 Hz < f < 100 Hz (Fig. 6(b)), the
3726 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732

Fig. 4. Flow pattern redistributions for a 1 Hz, 50% duty cycle pulse wave between 0 and 8 kV at a mass flux of G = 55 kg/m2 s and quality x = 45% (pictures equally distributed
along one cycle, i.e. time between frames is 83.3 ms).

liquid droplets are able to respond to the applied voltage and an increase of the pulse repetition rate till it diminishes at pulse
therefore increasing the pulse repetition rate increases the fre- repetition rate of 200 Hz. The results confirm the flow visualization
quency of the liquid droplet oscillations. For pulse repetition rates results which showed that the two-phase flow responds to the ap-
greater than 100 Hz (Fig. 6(c)–(d)), the liquid droplets cannot com- plied pulse voltage up to approximately 100 Hz. Beyond this, the
pletely respond to the applied voltage and the amplitude of the li- flow response diminishes till it can no longer respond to the ap-
quid droplet oscillations decreases with an increase of pulse plied pulse voltage.
repetition rate. The response continues to decrease till there is
no significant effect of the pulse repetition rate on the two-phase 3.1. Heat transfer and pressure drop
flow patterns at 400 Hz (Fig. 6(d)).
The flow images were analyzed using a commercial image pro- The effect of EHD on heat transfer and pressure drop during
cessing software to track the droplets and estimate the FFT spectra two-phase flow convective condensation can be attributed to three
of the droplet oscillations. Representative FFT spectra of the drop- factors: (i) liquid extraction from the bottom stratum to the core of
let oscillations for an 25% duty cycle and 8 kV amplitude pulse the test section which reduces the thermal resistance due to the
wave voltage for the same flow conditions (mass flux of stratified liquid layer [3,4,18], (ii) destabilization of the thermal
G = 55 kg/m2 s and average quality of x = 45%) are shown in boundary layer at the heat transfer surface for both the liquid stra-
Fig. 7. A distinct peak is observed at the same frequency as the tum and the annular liquid film due to the applied electric field
pulse repetition rate of the applied voltage in the frequency range [27] and (iii) thinning of the circumferential liquid film which
from 20 Hz till 100 Hz. The magnitude of the peak decreases with might lead to pseudo drop-wise condensation [28,29]. The increase
 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732 3727

Fig. 5. Flow pattern redistributions for a 10 Hz, 50% duty cycle pulse wave between 0 and 8 kV at a mass flux of G = 55 kg/m2 s and quality x = 45% (pictures equally
distributed along one cycle, i.e. time between frames is 8.3 ms).

in pressure drop due to EHD can, in addition to the above mecha- and 8 kV with no transient effects during each pulse period. The
nisms, be attributed to the momentum transfer at the central elec- heat transfer and pressure drop ratios for the 8 kV DC case were ta-
trode in the present configuration. This can be significant due to ken as 2.5 and 4.2 as reported in [15]. The effect of pulse repetition
the electrically induced liquid–vapour interactions at the electrode rate on heat transfer can be divided into three regions. In the first
surface, which will not be reflected in the heat transfer. The pres- region, or pulse repetition rate less than about 5 Hz, the heat trans-
sure drop penalty can be alleviated by a change in the electrode de- fer ratio is higher than the weighted average value for all three
sign and would be specific to the heat exchanger configuration. For duty cycles. The higher heat transfer for the pulse voltage com-
example, for a rectangular cross section, the electrode could be at pared to the weighted average can be attributed to the higher heat
the top wall, which will eliminate the additional momentum trans- transfer associated with the transient ‘‘liquid twisted cone” flow
fer at the central electrode as in this experiment. patterns which is not accounted for in the weighted average heat
The effect of pulse repetition rate on heat transfer and pressure transfer values. The greater the number of liquid ‘‘twisted cone”
drop ratios for duty cycles of 25%, 50% and 75% at mass flux of patterns indicates that more liquid is being extracted away from
55 kg/m2 s and average quality of 45% is shown in Fig. 8. The heat the heat transfer surface and therefore a higher heat transfer.
transfer and pressure drop ratios are defined as the ratios of the Increasing the pulse repetition rate in this range (less than 5 Hz),
heat transfer coefficient and pressure drop with applied voltage decreases the time duration of the liquid ‘‘twisted cone” patterns
to that without an applied voltage, respectively. The horizontal and therefore decreases the heat transfer ratio. In the second re-
lines in Fig. 8 represent the weighted average of the heat transfer gion (5 Hz < f < 40 Hz), the heat transfer is less than the weighted
and pressure drop ratios based on the percent time of the voltage average. Increasing the pulse repetition rate in this range dimin-
‘‘on” period assuming that the flow is quasi steady between 0 kV ishes the liquid ‘‘twisted cone” patterns until they completely
3728 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732

Fig. 6. Flow pattern redistributions for 50% duty cycle pulse wave between 0 and 8 kV for (a) 10 Hz, (b) 75 Hz, (c) 250 Hz, (d) 400 Hz. Mass flux of G= 55 kg/m2 s and quality
x = 45%.

disappear for f > 10 Hz. The liquid–vapour interactions below the however, the ratio increases with an increase in the duty cycle. The
electrode are decreased and therefore the heat transfer ratio is de- flow visualization results (Fig. 6(b)–(d)) for this pulse repetition
creased. For the 25% duty cycle, the variation of the heat transfer rate range show no liquid extraction above the electrode. This is
ratio with frequency is not very pronounced. There is a small de- because the voltage on period in this range is less than the time
crease initially with pulse repetition rate and then it remains needed for the liquid to be extracted towards the high-voltage
nearly constant (1.4) for pulse repetition rates greater than electrode (0.025 s). The flow visualization results, however, show
10 Hz. This is likely because the fraction of time which the flow a continuous formation and destruction of liquid droplets which
is subjected to the 8 kV (25% of the time period) is not sufficient oscillate with the same frequency as the applied voltage up to
to cause significant liquid extraction. In this case, the main reason 100 Hz. Although the frequency of the droplet oscillations follows
for the heat transfer enhancement is the electrically induced li- the pulse repetition rate of the applied voltage, the value of the
quid–vapour interactions in the bottom section of the channel heat transfer ratio remains relatively unchanged in this pulse rep-
which destabilize the thermal boundary layer. For the 75% duty cy- etition rate range. This suggests that the heat transfer enhance-
cle, the fraction of time at which the two-phase flow is subjected to ment in this range is mainly due to the destabilization of the
the applied voltage is higher than for the other two duty cycles. thermal boundary which is not significantly affected by the oscilla-
This leads to higher heat transfer ratios (2.4 at 0.5 Hz and 1.65 at tions of the droplets. The heat transfer ratio in this range (pulse
40 Hz) because of a greater amount of liquid extraction from the repetition rate greater than 40 Hz) remains relatively constant at
bottom stratum. 1.3, 1.4 and 1.6 for 25%, 50% and 75% duty cycle, respectively. These
In the third region, for pulse repetition rate greater than 40 Hz, values lie between the values at applied DC voltage of 0 kV (heat
the heat transfer ratio is nearly constant for the three duty cycles; transfer ratio of 1) and 8 kV (heat transfer ratio of 2.7). The heat
 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732 3729

1200 Applied pulse voltage of 20 Hz voltage or electric field as seen from Eq. (1). Thus, the average heat
transfer value obtained from applied voltages at 0 kV and 8 kV will
be greater than the value at the average voltage in this case.
840 Measuring the heat transfer associated with the transient
40 Hz ‘‘twisted cone” flow patterns is not currently possible due to the
Power spectrum density

short time duration of these flow patterns compared to the time re-
400
sponse of the temperature and pressure sensors. A simple interpo-
60 Hz lation scheme to estimate the heat transfer coefficients associated
with the transient flow patterns is developed here. The overall heat
transfer for a typical pulse wave voltage with a time period, T, and
150
80 Hz duty cycle, D, (Fig. 9) can be divided into three components: (i) the
heat transfer prior to the application of the high-voltage (i.e. at
0 kV), (ii) heat transfer associated with the transient flow patterns,
140
100 Hz and (iii) heat transfer after the transients have diminished (i.e. DC
high-voltage). The overall heat transfer coefficient can be ex-
pressed as
70
200 Hz      
D D D
h¼ 1 h0 kV þ s htransient þ ð1  sÞ h8 kV ; ð8Þ
100 100 100
10 20 40 60 80 100 200
where (D/100)T is the voltage on time duration and s(D/100)T is the
Frequency (Hz)
time duration of the transient flow patterns, h0kv, h8kV and htransient
Fig. 7. FFT spectra for typical droplets oscillations for 25% duty cycle applied pulsed are the heat transfer coefficients corresponding to 0 kV (without
voltage. EHD), 8 kV DC and transient flow patterns respectively. Knowing
h, h0kV, h8kV, and s from experimental measurements, the heat trans-
fer coefficient associated with the transient flow patterns (htransient)
a 4.0 can be estimated using Eq. (8). The time duration of the transient
flow patterns for mass flux of 55 kg/m2 s and average quality of
3.5 45% estimated from the flow visualization is 0.55 s. With h0kV and
h8kV as 2673 W/m2 K and 6461 W/m2 K, the htransient values for the
Heat transfer ratio

3.0 different applied voltage are given in Table 2. The average value
of htransient is 7241 W/m2 K, which is 10% to 15% higher than the va-
2.5 lue at 8 kV DC applied voltage.
The pressure drop characteristics with the pulse repetition rate
2.0
is different to that of the heat transfer (Fig. 8(b)). This is mainly due
to the presence of the central high-voltage electrode which con-
tributes significantly to the pressure drop across the test section.
1.5
For the 25% duty cycle, the pressure drop ratio increases from 1.5
at a pulse repetition rate of 0.5 Hz to approximately 2.58 at a pulse
1.0
0.1 1 10 100 1000 10000 repetition rate of 100 Hz. In the low pulse repetition rate range
Pulse repetition rate (Hz) (f < 10 Hz), where liquid extraction from the bottom stratum oc-
curs in the form of liquid ‘‘twisted cone” patterns, the pressure
drop is less than that for the DC weighted average. This indicates
b 4.0
that the increase in the pressure drop due to these transient flow
3.5
patterns is less than the increase in pressure drop for the 8 kV
DC case. Increasing the pulse repetition rate increases the oscilla-
Pressure drop ratio

tions of the liquid–vapour interactions below the electrode and

3.0
the liquid droplets and therefore increases the pressure drop ratio

2.5
Applied voltage (kV)

2.0

1.5

1.0
0.1 1 10 100 1000 10000
Pulse repetition rate (Hz)
Flow patterns

τ (D/100)T
Fig. 8. The effect of pulse repetition rate on (a) heat transfer and (b) pressure drop,
M 25% duty cycle, h 50% duty cycle, }75% duty cycle, – weighted average 25%, - - 0 kV flow Transient flow 8 kV flow
weighted average 50%, -  - weighted average 75%. Heat flux of q00 = 5.7 kW/m2 and patterns patterns patterns
average quality of xavg = 45%.

T
transfer values, for pulse repetition rate greater than 40 Hz, are less
Ti
Time (sec)
( )
than those for the weighted average. This can be attributed to the
non-linear relationship between the EHD force and the applied Fig. 9. Schematic representation of one pulse including the transient effects.
3730 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732

Table 2 in pressure drop during the voltage on period, which increases

Heat transfer coefficient associated with the transient flow patterns (htransient). with the duty cycle and (ii) an increase in pressure drop due to
Time duration of the transient flow patterns = 0.55 s the oscillations of the liquid vapour interface and the liquid drop-
25% duty cycle 50% duty cycle 75% duty cycle lets, which increases with the pulse repetition rate. At lower duty
cycles (25%), the latter effect is more significant than that due to
0.5 Hz 7377 7850 8592
1 Hz 7271 7271 7277
the voltage on period. Therefore the effect of pulse repetition rate
2 Hz 6901 6929 7349 will be more significant causing higher rates of change in pressure
4 Hz 6745 6469 6868 drop compared to the higher duty cycles. Increasing the duty cycle
Average value 7241 decreases the impact of the change in the pulse repetition rate and
Standard deviation 7.7% therefore decreases the rate of change of pressure drop with pulse
repetition rate. Increasing the duty cycle increases the time avail-
able for the two-phase flow to respond and therefore increases
the pulse repetition rate at which the maximum pressure drop
till it exceeds that for the DC weighted average at pulse repetition occurs.
rate of about 8 Hz and reaches a maximum value of 2.58 at 100 Hz. The effect of duty cycle on heat transfer ratio and pressure drop
For pulse repetition rate greater than 100 Hz, the pressure drop de- ratio for pulse repetition rate of 1 Hz, 50 Hz and 800 Hz is shown in
creases with an increase of pulse repetition rate. This is mainly be- Fig. 10. The 0% duty cycle corresponds to the no-applied voltage
cause the response of the two-phase flow (and the liquid droplets) case. For the same pulse repetition rate, increasing the duty cycle
to the applied voltage decreases with a resultant decrease in inten- increases the effective value of the applied voltage and therefore
sity of the liquid–vapour interactions and therefore the pressure increases heat transfer and pressure drop till they reach the corre-
drop. The spectral analysis of the liquid droplet oscillations shows sponding values of 8 kV DC applied voltage at 100% duty cycle. The
no response of the liquid droplets to the applied signals for fre- results of Fig. 10 are consistent with the previous section, where
quencies greater than 100 Hz. the heat transfer ratio is higher at 1 Hz compared to 50 Hz and
For the 50% and 75% duty cycles, the pressure drop characteris- 800 Hz as the longer voltage on time duration provides sufficient
tics are qualitatively similar to the 25% duty cycle. There are two time to complete the liquid extraction. The pressure drop ratio is
main differences between the trends for the different duty cycles; higher at 50 Hz compared to 1 Hz and 800 Hz due to the droplet
the first is that the initial rate of increase and decrease of the pres- oscillations which increase the momentum transfer between the
sure drop ratio are higher for the 25% duty cycle compared to the two-phase flow and the center electrode.
50% and 75% duty cycles. The effect of the applied pulse voltage The effect of pulse repetition rate for a 50% duty cycle pulse
on pressure drop can be attributed to two factors: (i) an increase wave applied voltage on heat transfer and pressure drop for the

a 5.0
a 3.5
4.5

4.0 3.0
Heat transfer ratio

3.5
Heat transfer ratio

2.5
3.0
2.0
2.5

2.0 1.5

1.5 1.0
1.0
0.5
0.5
0.0
0.0
0.1 1 10 100 1000 10000
0 10 20 30 40 50 60 70 80 90 100
Frequency (Hz)
Duty cycle (%)

b 5.0 b 3.5
4.5
3.0
4.0
Pressure drop ratio
Pressure drop ratio

3.5 2.5

3.0 2.0
2.5
1.5
2.0
1.0
1.5

1.0 0.5
0.5
0.0
0.0 0.1 1 10 100 1000 10000
0 10 20 30 40 50 60 70 80 90 100 Frequency (Hz)
Duty Cycle (%)
Fig. 11. Effect of pulse repetition rate on (a) heat transfer ratio and (b) pressure
Fig. 10. Effect of duty cycle on (a) heat transfer and (b) pressure drop, M 1 Hz, h drop ratio for 50% duty cycle, 0 to 8 kV applied pulse wave (h G = 57 kg/m2 s, }
50 Hz, }800 Hz. Heat flux of q00 = 5.7 kW/m2 and average quality of xavg = 45%. G = 100 kg/m2 s, M G = 150 kg/m2 s).
 H. Sadek et al. / International Journal of Heat and Mass Transfer 53 (2010) 3721–3732 3731

25.0 three ranges. At the low pulse repetition rate range, the two-phase
flow responds to the induced EHD forces, and liquid is extracted
20.0
from the bottom stratum to the center electrode and then pushed
radially outwards in the form of liquid ‘‘twisted cone” patterns.
Increasing the pulse repetition rate in this range increases the rep-
h/Δp (m/sK)

15.0 etition of the extraction cycle and therefore increases heat transfer
and pressure drop. In the mid pulse repetition rate range, the two-
10.0 phase flow does not have sufficient time to complete the extraction
cycle which leads to lower heat transfer values compared to the
lower pulse repetition rate range. In this range, the two-phase flow
5.0
patterns are characterized by liquid–vapour interface oscillations
between the center electrode and the bottom stratum, with liquid
0.0 droplet oscillations. Increasing the pulse repetition rate in this
0 20 40 60 80 100 120 140 160 range decreases heat transfer and increases pressure drop. In the
Mass flux (kg/m2s) high pulse repetition rate range, increasing the pulse repetition
rate decreases both the interfacial and droplet oscillations and
Fig. 12. Effect of mass flux on heat transfer to pressure drop ratio for M 8 kV DC
applied voltage and 8 kV amplitude pulse wave applied voltage with therefore decreases the heat transfer and pressure drop till the
different pulse repetition rates and duty cycles. two-phase flow patterns resembles that for an applied DC voltage
case.
The advantage of a pulse applied voltage is that it provides a
three different mass fluxes (57 kg/m2 s, 100 kg/m2 s and 150 kg/ wider range of heat transfer and pressure drop compared to an ap-
m2 s) are shown in Fig. 11. The pulse repetition rate has a qualita- plied DC voltage. The different characteristics of the pulse voltage
tively similar effect on heat transfer and pressure drop ratios at the compared to the DC case are due to the formation of two-phase
different mass fluxes. The heat transfer ratio decreases from 1.9 to flow patterns that are not present in the DC case. These two-phase
1.4 as the pulse repetition rate is increased from 1 Hz to 800 Hz for flow patterns can be controlled by manipulating the pulse repeti-
mass flux of 57 kg/m2 s. For mass fluxes 100 kg/m2 s and 150 kg/ tion rate and the duty cycle of the applied pulse voltage. This
m2 s, the heat transfer ratio decreases from 1.4 and 1.2 at 1 Hz to makes the system more amenable to control, which is absent if
1.1 at 800 Hz. The maximum pressure drop decreases from 3.5 at using either DC voltages or passive heat transfer techniques. While
57 kg/m2 s to 2.4 and 2.1 at 100 kg/m2 s and 150 kg/m2 s for the the quantitative results from this study would be dependent on the
same pulse repetition rate of 80 Hz. These results are consistent electrode geometry and working fluid, the main conclusions of this
with the dimensionless analysis of the governing differential study with respect to the control using AC electric fields would, in
momentum equation [15], which shows that the effect of EHD will general, be valid. The electrode geometry would need to be opti-
be significant if the interfacial Masuda number (Md) is in the same mized for maximum heat transfer while minimizing pressure drop,
order of the square of liquid Reynolds number (Re2l ). For the same and would depend on the particular application.
amplitude and duty cycle, increasing the mass flux decreases the
ratio (Md=Re2l ) and therefore decreases the effect of EHD on heat
transfer and pressure drop over the entire range of pulse repetition
rate. At mass flux of 57 kg/m2 s, the dimensionless ratio (Md=Re2l ) is References
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