Accepted Manuscript Enhancement of convection heat transfer using EHD conduction method Mostafa Mirzaei, Majid Saffar-Avval PII: DOI: Reference:
S0894-1777(17)30411-9 https://doi.org/10.1016/j.expthermflusci.2017.12.022 ETF 9312
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
21 October 2017 16 December 2017 24 December 2017
Please cite this article as: M. Mirzaei, M. Saffar-Avval, Enhancement of convection heat transfer using EHD conduction method, Experimental Thermal and Fluid Science (2017), doi: https://doi.org/10.1016/j.expthermflusci. 2017.12.022
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Enhancement of convection heat transfer using EHD conduction method Mostafa Mirzaei a, Majid Saffar-Avval b1
a. Ph.D. Candidate, Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran, Email:
[email protected] b. Professor of Mechanical Engineering, Amirkabir University of Technology, Energy and Control Center of Excellence, Tehran, Iran, Email:
[email protected]
Abstract Laminar forced convection heat transfer in an annulus is enhanced using electrohydrodynamics (EHD) technique. A novel EHD-enhanced double pipe heat exchanger is designed and incorporated with six pairs of electrodes. An experimental setup is constructed to investigate heat transfer enhancement, pressure drop and power consumption in the double pipe. The finite volume method is employed to solve the governing equations of EHD conduction pumping, Navier-Stokes and energy. The numerical results are in agreement with the experimental results and demonstrated that in the considered range of the parameters, heat transfer enhances up to 50% with low electric power consumption and the method is more effective in lower Reynolds numbers. An effectiveness parameter is introduced which considers both heat transfer enhancement and pumping power consumption. Increasing applied voltage will improve performance until an optimum voltage which generates a cross-stream flow comparable to main-stream inlet flow. The flow patterns of the induced cross-stream flow are investigated using numerical simulation. Keywords: EHD, Conduction pumping, Heat transfer enhancement, Laminar forced convection, Experimental and numerical analysis
1
Corresponding author: Professor of Mechanical Engineering Department, Head of Energy and Control Center of Excellence, Amirkabir University of Technology, P. O. Box 1591-634311, Fax: +98-21-66419736, Email: mavval @aut.ac.ir
1. Introduction Single phase heat transfer enhancement is a widely interesting subject of research in the thermal engineering field which is known since 1920s. The increasing demand for higher heat transfer rates and energy saving concerns in recent decades brought the subject more attractive. Several heat transfer enhancement methods are introduced in the literature, which are divided into two categories of passive and active methods [1]. Comparing to other methods utilizing electrostatic field to enhance heat transfer, known as EHD method, despite its safety considerations, has some principal advantages, including: simple manufacturing, quick response and ease of controlling, low power consumption and maintenance costs due to the absence of moving parts. A wide range of applications for EHD method is reported in the literature consisting of: pumping [2], single phase heat transfer [3,4], boiling [5,6], condensation [7,8], mixing [9], and liquid jets [10]. There are many studies concerning electrohydrodynamic enhancement of heat transfer [11–14]. Kasayapananad and Kiatsiriroat studied heat transfer enhancement in a partially open square cavity with different wire electrode arrangements [11]. Grassi et al. studied heat transfer enhancement in an annulus flow due to ion injection from sharp electrodes, experimentally [12,13]. Lakeh and Molki used a corona jet to locally enhance natural convection heat transfer in a pipe [14]. Sahebi and Alemrajabi studied EHD enhanced natural convection heat transfer of an inclined heated plate with corona jet, experimentally [15]. These works showed that heat transfer can be significantly enhanced by EHD mechanism. All of the above-mentioned papers considered an EHD method known as ion-drag pumping which utilizes a wire-plate or needle-plate electrode configuration to generate a corona wind. Ion-drag pumping deals with injection of ions from a sharp metal electrode into the fluid which results the degradation of the working fluid and electrode. On the contrary, EHD conduction pumping is a modern concept compared to the ion drag pumping mechanism. It is associated with the nonequilibrium process of dissociation of neutral species and recombination of generated ions in a finite thickness in the vicinity of electrodes which is known as hetrocharge layer. In the hetrocharge layer, the dissociation rate exceeds the recombination rate, therefore there is a continuous rate of charge
generation and the electric field forces the charges inside hetrocharge layers to move toward the electrodes. A special configuration of electrodes in a non-symmetric shape results a net useful flow. The conduction pumping phenomenon occurs in an electric field lower than that of the ion injection field intensity (between 1kV/cm and 100kV/cm [16]). It doesn’t have the mentioned disadvantages of ion-drag pumping mechanisms besides consuming lower electric power. Also flush mounted electrodes in conduction pumping do not alter flow geometry. Theoretical model of conduction pumping was firstly presented by Atten and Seyed-Yagoobi [17], and it was further developed in other researches [18–20] following the initiative study of Jeong and Seyed-Yagoobi [19] who studied the circulation of an isothermal dielectric liquid inside an enclosure using the proposed EHD conduction model. A number of experimental studies in different electrode configurations are implemented by different researchers on conduction pumping and the theoretical model is validated against their results [21–23]. Also, Gharraei et al. 2014 studied EHD conduction pumping of dielectric liquid film numerically [24]. They showed that ion mobility difference and electrodes’ configuration are two major factors affecting the conduction pumps. Sobhani et al. 2015 investigated the fully developed falling film flow in the presence of conduction pumping, experimentally [25]. Gharaei et al. 2015 studied hydrodynamic behavior of developing laminar wavy falling film, in the presence of electrohydrodynamic conduction phenomenon [26]. There are a limited number of publications focusing on the heat transfer enhancement with conduction pumping mechanism. Yazdani and Seyed-Yagoobi conducted a series of numerical studies on the forced convection heat transfer enhancement in some geometries. They generated high impinging jet velocities with EHD conduction method, allowing for effective removal of heat from the heated surfaces [27]. In another work they studied EHD-conduction pumping of liquid film in the presence of evaporation and concluded that the EHD-conduction induced flow have good overall heat transfer performance, because of the local flow circulations [28]. They also studied application of the EHD conduction phenomenon for heat transfer enhancement of channel flow in macro and microscales. The microscale case showed better enhancement because the EHD conduction dominated the external pressure gradient, also the enhancement level degraded as the Reynolds number increased [29], and
finally Yazdani and Seyed-Yagoobi 2014 showed heat transfer of backstep flow can be enhanced using the EHD conduction method [30]. In the only experimental study in the literature about heat transfer enhancement with EHD conduction, Nourdanesh and Esmaeilzadeh studied heat transfer enhancement of free surface liquid film with flush mounted electrodes [31]. In this study, heat transfer from film surface to the above air was enhanced considerably by EHD conduction method. There is no experimental study available in the literature regarding EHD-enhanced forced convection heat transfer with conduction pumping mechanism in internal flows. In this paper, flow and heat transfer enhancement of a dielectric fluid in an annulus due to an external electric field is experimentally investigated for the first time. A novel EHD-enhanced double pipe heat exchanger is constructed and its effectiveness is evaluated. Effectiveness parameter as a proper tool which considers both effect of heat transfer and pressure drop is calculated. A numerical finite volume code based on EHD conduction pumping model is developed to study the flow pattern and induced crossstream flows. The effect of Re and applied voltage on the heat transfer enhancement and pressure drop and power consumption is studied thoroughly. 2. Problem statement The geometry of the problem and configuration of the electrodes which are used to enhance heat transfer in the annulus are shown in Fig.1 and the dimensions are provided in table 1. The outer wall of the annulus is insulated while heat is transferred to the fluid from inner wall. Flush mounted electrodes are placed on the outer wall of the annulus to impose no extra pressure drop to the flow.
Fig.1 sketch of the geometry and dimensional parameters
Table 1. Dimensions of the geometry di (mm)
do (mm)
L (mm)
HV (mm)
G (mm)
i (mm)
o (mm)
9.5
29
494 / 506 / 518
6
15
3/5/7
40
According to previous studies, i.e. Gharraei et al. [32], Yazdani and Seyed Yagoobi [33] the pumping direction of EHD pumps is determined by mobility difference of charges and asymmetry of electrodes. If ionic mobility of positive and negative charges were identical and high voltage and ground electrodes have equal size, there would be no net flow generation and only local flow circulation occurs. This behavior is not desired In the EHD pumps, but for the sake of heat transfer enhancing purposes even such circulation may have benefits. Electrode configuration is designed based on the following assumptions to have a maximum pressure generation: -
In the case of symmetric electrodes if negative charge mobility is higher than positive charge mobility, the net flow generation of conduction EHD pump would be from cathode to anode electrode [24].
-
If negative and positive charges have identical mobility the net flow generation would be from narrower electrode to wider electrode [34].
The working fluid is transformer oil with properties presented in Table 1 and its negative charge mobility is higher than its positive one. High voltage wire is connected to the narrower electrode and it is placed on the left side of the ground electrode, therefore, the generated flow of EHD pump is in the same direction as external flow. Table 2. Electrical and thermophysical properties of the working fluid Property
Value [26]
Permittivity (F/m)
18.41 × 10-12
Electrical conductivity (S/m)
1.2 × 10-12
Density (kg/m3)
895.5
Dynamic Viscosity (Pa.s)
0.011
Specific Heat (J/kg.K)
1856 [35]
Thermal conductivity (W/m.K)
0.13 [35]
Thermal expansion coefficient
0.0007
Positive charge mobility (m2/V.s)
0.18 × 10-8
Negative charge mobility (m2/V.s)
0.35 × 10-8
3. Experimental setup and methods In order to study EHD enhanced convection heat transfer in an annulus, a test loop was constructed as shown in Fig.2. The test section of the experimental setup is a double pipe heat exchanger consisting Teflon parts as outer pipe and a copper tube as the inner pipe. Oil flows through the space between pipes and hot water flows through the inner pipe. The setup is designed to feed a steady flow of oil with constant head and temperature to the test section. A pump is used to transfer the oil from cooling tank to the constant head tank. The constant head tank is located at approximately 1 meter above the test section and it is incorporated with an overflow pipe which keeps the oil level constant by returning excess fluid to the cooling tank. Another centrifugal pump is used to supply a high mass flow rate of water to the inner pipe of test section to ensure that the temperature drop of water is maintained small enough to assume that wall temperature is constant. The test section is instrumented with four pt-100 class B temperature sensors with an accuracy of 0.03ºC at the inlet and outlet of both inner and outer pipes. Testo 454 data logger is used to transfer the temperature data to a computer with 1 second intervals. A Rosemount 3051 differential pressure transmitter measures the pressure drop in the annulus with an accuracy of 0.1 Pa. Heating tank is equipped with two 2kW electrical submerged heaters and a temperature controller with pt-100 sensor to maintain a constant water temperature of 55ºC. Also, the cooling tank is equipped with a refrigeration cooler and a temperature controller to maintain a constant oil temperature of 20ºC. The oil flow rate is measured using bucket and stopwatch method.
The high voltage electrodes are connected to a high-voltage DC power supply (D-RC Series from FNM Inc. with a digital connection to a computer for input and output).
Fig. 2. Schematic diagram of the experimental setup
3.1. Test section design The test section consists of 6 EHD pumps and an inlet and outlet port as it is shown in Fig.2. In order to generate a uniform flow at the inlet, a perforated plate is placed in the inlet port. Each EHD pump consists of a PTFE electrode holder with an outer diameter of 40mm, a pair of electrodes and a ring spacer (if needed). Neighbor EHD pumps are separated with PTFE tubes with an inner diameter of 29mm to form a part of the outer wall of the annulus. The outer surface of these tubes is threaded to fit in the electrode holder. High voltage and ground electrodes are flush rings made from a copper tube with the inner diameter of 29 mm and form a part of the outer wall of annulus. The high voltage and ground wires are connected to the corresponding electrodes with screws 120 degrees apart from
each other. Minimum electrode gap is 3 mm in the base case, but it is increased to 5 and 7 mm with PTFE ring spacers in some cases. This novel design can be used in double pipe heat exchangers without many modifications.
Fig. 3. The double pipe with EHD pumps and measurement instruments in the test Section
Fig. 4. Electrode holder with a pair of electrodes
3.2. Data reduction Heat transfer coefficient is calculated using Eq. (1):
h
Q
(1)
As (Tw T in )
In which As is area of the inner surface of annulus, Q is total heat transfer and is calculated from Eq (2) considering a constant specific heat which is an acceptable assumption due to the small temperature increase in our experiments:
Q mc p T out T in oil
(2)
Wall temperature is calculated as follows:
Tw Twater Q R th ,tube R th ,water Twater
di ln d 2t i 1 Q 2 k cu L hin A s
(3)
Because of the high mass flow rate of water in the tube, the temperature reduction of water is about 0.05°C which almost equals temperature sensor uncertainty. The inner tube is made from copper which has a high thermal conductivity, therefore, the wall temperature is approximated by Eq. (4):
Tw
Twater ,out Twater ,in 2
Q hin As
(4)
Nusselt number is calculated as: Nu
hD H k
(5)
Heat transfer enhancement ratio is defined as the ratio of Nusselt number at voltage V to the Nusselt number at the same flow rate in the absence of EHD effect.
e
Nu EHD Nu 0
(6)
3.3. Uncertainty analysis In each experiment the following data are directly measured: inlet and outlet temperature of oil and water, pressure drop across the test section, voltage, electric current, time, volume, and water flow rate. Each measured value has an uncertainty which is defined as an interval around the measured value, where the exact value of the parameter lies with a certain probability. The accuracy of measurements are shown in Table 3, but it has to be clarified how these uncertainties are propagated into the uncertainty of derived quantities such as heat transfer enhancement. The uncertainty of property R which is computed from the independent variables Vi with uncertainties of Uvi is given in Eq. (7):
R U R Uvi i 1 V i n
2
(7)
Calculated uncertainty for heat transfer coefficient in all of the considered cases is in the range of 2%3.5%. Maximum uncertainty in the heat transfer enhancement ratio is 6%. The percent share of each measurement in the final uncertainty of the heat transfer coefficient is shown in table 4. It can be seen that almost 74 percent of the uncertainty is due to volume measurement and 26% is related to the other measurements. It was one of our limitations because of the low flow rates of the oil at the small Reynolds numbers. It should be mentioned that in general, the bucket and stopwatch method is assumed to be an accurate method because its uncertainty can be reduced by increasing the time of measurement (and also using larger bucket). The volume error could be reduced by using a bucket with more accurate scales, but the maximum uncertainty of 6% in the heat transfer enhancement ratio shows that it is a good enough measurement. In the results section, the calculated uncertainty in each parameter will be shown with error bars in graphs.
Table 3. Instruments and their accuracy parameter
instrument
accuracy
Toil ,in ,Toil ,out ,Twater ,in ,Twater ,out
Testo pt-100
0.03 °C
P
Rosemont 3051
0.09 Pa
V
FNM HV35P D-RC high voltage power supply
100 V
I
FNM HV35P D-RC high voltage power supply
1 µA
time
Stopwatch
0.3 s*
Volume
2000cc Scaled cylinder
100 cc
Water flow rate
Flownetix 100 series
0.3 L/min
d i ,do
Vernier caliper
0.05 mm
* human reaction time according to NIST stopwatch and timer calibrations 960-12 [36] Table 4. Effect of each measurement on the uncertainty of Nu in a case with Nu = 11.34±0.33 parameter
% of uncertainty in Nu
T oil ,in
6.5 %
T oil ,out
7.9 %
Twater ,in
0.05 %
Twater ,out
0.05 %
Volume
73.9 %
time
3.27 %
di
7.2 %
do
0.8 %
4. Governing equations and numerical method The considered problem of forced convection heat transfer in the presence of electric field in an annular which investigated experimentally revealed a great heat transfer enhancement, but it didn’t present the mechanism of this effect. The electric field induces cross-stream flows in the form of vortices and changes flow pattern which leads to heat transfer enhancements. In order to be able to study the flow pattern and obtain the detailed knowledge of heat transfer enhancement mechanism under the effect of an electric field the proposed problem is investigated numerically. 4.1. Theoretical model of conduction pumping The theoretical model of EHD conduction pumping is developed by Atten and Seyed-Yagoobi [17] and it is improved by Jeong and Seyed-Yagoobi [19], considering the effect of fluid motion in the charge conservation equations. The electric field is governed by Maxwell equations and the fluid motion is governed by NavierStokes equations. The effect of electric field on the fluid motion is modeled by including an electric force in the basic Navier-Stokes equations. Both of the electric field intensity (in the Maxwell equation) and the electric force (in the Navier-Stokes equations) are related to the net charge density in the fluid, therefore, in addition to above-mentioned equations, the equation of conservation of both positive and negative charges should be solved considering production-recombination of charges as well as charges transfer. The following assumptions are considered in the model: -
Incompressible fluid with constant properties,
-
Steady state flow,
-
No charge injection from electrodes.
EHD conduction pumping mechanism is based on the electric forces which act on electric charges in the fluid. The charges are produced because of the dissociation-recombination process of neutral species as follows. A B AB kd
(8)
kr
In thermodynamic equilibrium, the relationship between the equilibrium charge densities and the concentration of neutral species can be represented by the following equation:
kd N kr neq peq ,
(9)
peq neq Recombination coefficient is constant and calculated by Langevin’s approximation [37]: kr
b b
(10)
Dissociation rate is not constant in the domain and is known that the electric field can enhance the dissociation rate effectively. Two models for field dependency of dissociation rate are introduced previously. Plumly [38] model presented in Eq. (12) is used by Gharraei et al. [24]. Eq. (11) shows Onsager model [39] which is used in several EHD conduction pumping simulations like [19,40]. Both models seem to have reasonable results, therefore, the Onsager model is adopted in this work.
2e3/2 E '/ kd kd 0 f E ' kd 0 exp kBT '
e3/ 2 E '/ I1 2 kd kd 0 f E ' kd 0 , 2kBT '
(11)
(12)
In which I1 is the modified Bessel function of the first kind, order one. There are three mechanisms for movement of charges, including electric mobility, convection, and diffusion. Considering these three mechanisms, the charge conservation equation would be as follows:
(13)
(14)
' . b p' E ' p' u ' D' p' kd N kr p ' n'
' . b n' E ' n' u ' D' n' kd N kr p ' n'
Where p’ and n’, are positive and negative charge densities produced by dissociation – recombination process of neutral species. The diffusion coefficients are calculated from Eq. (15): D
b k BT ' e
(15)
Electric field intensity is governed by Maxwell’s equations:
' . E ' q ' p ' n' (16)
E ' ' ' The other governing equations of the system includes: continuity, momentum, and energy. The continuity equation for incompressible steady state flow:
u ' 0
(17)
The Momentum equation with source term for electric body force:
u '. 'u ' ' P ' '2u ' Fe
(18)
The electric body force can be expressed as Eq.(19):
1 1 Fe q ' E ' E ' 2 ' ' E ' 2 2 2 T
(19)
The second and third terms in the electric body force will be vanished, because density and permittivity of working fluid are assumed to be constant, therefore, only the first term known as Coulomb force or electrophoretic force is present in the model. The energy equation with Joule heating term is as follows:
c pu '. 'T ' k '2 T ' E '2
(20)
Considering the presented equations, the following dimensionless parameters are defined as:
x
T ' T in x u' P' ,u , P 2 , T , d bV / d T / d 2
' E' p' n' , E , p , n , V V /d neq neq
br
b b
, neq
1 br neqV V ,J , b b c p b T c p T
(21)
neq d 2 b V Re EHD , Co , M , V b 2 D k T B , Pr b V e Non-dimensional form of governing equations can be written as:
u 0
u . u
1 Re EHD
2
P
1 2u MC o p n E Re EHD
.E C o p n E
. b nE nu b n 1 b C f E pn . pE pu p 1 b r C o f E pn r
r
1 . u .T T Re Pr EHD
r
(22)
o
2 JE
4.2. Boundary conditions The following boundary conditions are applied to the equations of section 4.1 and are solved numerically. The no-slip condition leads to zero velocity of fluid on walls and electrodes. A uniform velocity of Uin and temperature of Tin are considered at the inlet of the annulus. The inner wall of the annulus is kept at constant temperature of Tin+ΔT. Since the outer wall is insulated, the zero gradient
boundary condition is used for its temperature. Neglecting presence of electric double layer near the solid insulator walls, the Neumann boundary conditions are applied for the positive and negative charge densities and the electric potential at the walls of the annulus (except on the electrodes). At the high voltage electrode:
1; p 0; n.n 0
(23)
At ground electrode:
0; n.p 0; n 0
(24)
Other walls:
n. 0; n.p 0; n.n 0
(25)
4.3. Derived parameters The total rate of heat transfer from the hot wall is calculated by integration of heat flux over the wall. Nusselt number is defined by equation (27). In the absence of EHD effects the heat transfer from hot wall to the fluid is by forced convection, therefore the heat transfer enhancement parameter is defined by equation (28).
Q
k (n .T ) dA mc p T out T in
(26)
hot wall
Nu
e
Q DH As T k
Nu Nu 0
(27)
(28)
Where Nu0 is the Nusselt number at zero voltage which means forced convection Nusselt number without electric field effect.
Apparent friction factor is a non-dimensional measure of pressure loss in the duct and is defined by Eq. (29).
f app
P 4L 2 1 / 2 U in D H
(29)
Power consumption is consists of two parts as defined by Eq. (30); pumping power and electric power.
Power Powerpumping Powerelec P U in Ac VI
(30)
5. Numerical method The finite volume method on a 2D grid in an axisymmetric domain is employed to solve governing equations numerically. PISO algorithm is used for pressure velocity coupling. Convective terms in the momentum equations discretized in a first order upwind scheme based on the flow direction. A second order upwind scheme based on the electrical field is applied to convective terms of charge density equations. All of the equations are fully coupled. The coupled equations are solved simultaneously in a pseudo transient frame with time marching until the steady state solution is obtained with a maximum normalized residual of 1e-6. In all considered cases, the problem of grid independency is obtained by refining the mesh sizes. In each step, the grid numbers are doubled and the total heat transfer is compared to the corresponding value of the last mesh size until the difference between the two consecutive steps becomes less than one percent.
6. Results and discussions Experimental and numerical results, including heat transfer enhancement, pressure drop and power consumption in different cases are presented in this section. Also, charge distribution and induced
flow characteristics and their effect on the heat transfer enhancement are explained using numerical results. 6.1. Data collection In each experiment, Reynolds number and the flow rate are fixed by a valve and when the system reaches a steady state, temperature and pressure and flow rate are measured and recorded. Then high voltage power supply is started and applied voltage is increased in 4kV steps. At each step data collection is done when the system reaches a new steady state. This process continues to maximum voltage of 20 kV and then voltage is decreased step by step and data are collected in the reverse order. During the entire experiment the valve position is not changed and the flow rate is constant. It should be emphasized that pressure drop in the valve and piping is much larger than the pressure drop in the test section, therefore, a little change in the pressure drop in the test section due to electric field cannot affect the flow rate. 6.2. Heat transfer enhancement The main objective of the experiment is to evaluate the amount of heat which transfer from the hot inner pipe to the fluid in the annulus and increase it by using electric field. Fig. 5 shows Nusselt number as a function of applied voltage at different Reynolds numbers. It can be seen that numerical results have a satisfactory agreement with experimental results which confirms the validity of the results. There are an average error of 10% between the numerical and experimental results. The final errors between numerical and experimental results are higher than the reported uncertainties, because in the uncertainty analysis only random errors arising from measurements are considered. There are also some inevitable systematic errors which reduce the accuracy of the results and could not be exactly simulated numerically. For example in the simulation, the inner and outer surface of the annulus are assumed to be smooth and straight while it is not true in the experiments. The copper tube is not completely straight and horizontal, it is a little deflected in the construction. The electrodes and outer tube have same inner diameter, but they may have a little misalignment which will introduce extra disturbance to the flow. These disturbance have more effect at lower
Reynolds numbers. They increase the Nusselt number even at the zero voltage, therefore, the enhancement would underestimated at these cases (Fig.6). It is evident from the figure that heat transfer increases as applied voltage increases in all Reynolds numbers. Heat transfer enhancement ratio is presented in Fig. 6. It can be observed that electric field has more enhancement at lower Reynolds numbers and the enhancement ratio is smaller at larger Reynolds numbers. The numerical results showed that applied voltage of 24 kV in the considered configuration of electrodes with 5 mm electrode gap increases the heat transfer 50% and 21% at Reynolds numbers of 10 and 30 respectively. Which means that, the EHD heat transfer enhancement is more effective at lower Reynolds numbers. Electric forces tend to improve heat transfer by pushing the fluid toward the hot wall, and higher Reynolds number means more inertia in the fluid and more resistance against these forces.
Fig. 5. Experimental and numerical Nusselt number and as a function of applied voltage at different Reynolds Numbers and d=5mm
Fig. 6. Experimental and numerical heat transfer enhancement ratio as a function of applied voltage at different Reynolds Numbers and d=5mm
Fig. 7. Effect of electrode gap on enhancement ratio at Re=20
The effect of the electrode gap on the heat transfer enhancement is shown in the Fig. 7. All 3 cases with applied voltage up to 20 kV are in the range of conduction pumping and ion injection is not take place in none of them. The heat transfer enhancement ratios are very close to each other, but the smaller electrode gap shows slightly better heat transfer enhancement, especially at higher voltages. 6.3. Pressure drop and power consumption The proposed heat transfer enhancement is taking along with an increase in pressure drop and some electric power consumption and one should consider these two drawbacks carefully to choose the range of the parameters in which the EHD heat transfer enhancement method can be useful. As a measure of pressure loss in the test section Fig. 8 shows apparent friction factor with and without the effect of electric field. In the absence of electric field, fRe is approximately constant and changes between 24.75 at Reynolds number of 5 and 25.15 at Reynolds number of 50. Results show a drastic increase in friction factor at low Reynolds numbers. At the Reynolds number of 5, the friction factor has a 3 fold and 5 fold increase by applying an electric voltage of 8 and 16 kV respectively, but this increment sharply decreases as Reynolds number increases, i.e. the voltage of 8 kV only imposes 3% increase to the friction factor at Reynolds number of 50.
Fig. 8. Apparent friction factor as a function of Reynolds number with and without EHD
Presented results in fig 6 and fig 8 showed that increasing voltage increases both heat transfer and pressure drop which means the required pumping power increases too. In order to justify the effectiveness of an enhancement method its pumping power increase should be considered as well, therefore, the Nusselt number is plotted as a function of pumping power in Fig.9a. The Nusselt number at different voltages can be compared to each other at a constant power. It is clear that even with the equal power consumption the Nusselt number increases as voltage increases. In order to quantify this comparison, the effectiveness parameter is defined as the ratio of the Nusselt number at a voltage to the Nusselt number of a case without electric field but with the same power consumption. The effectiveness of greater than unity shows that the rate of heat transfer enhancement is more than the rate of power consumption increase. It is clear from Fig. 9b that effectiveness parameter is more than unity and increases as voltage increases, but it decreases as Reynolds number increases. It shows the advantage of the EHD conduction method in the low Reynolds numbers which has a high amount of heat transfer enhancement and low pressure drop increment and low power consumption. The EHD conduction method is more effective at low Reynolds numbers because as Reynolds number increases the bulk main-stream flow overcomes the produced electric cross-stream flow. A strange behavior is seen in the Fig. 9b at the Reynolds number of 10 in which the effectiveness parameter have a small increase from 16kV to 24 kV. The reason behind this behavior will be cleared in the next section in which the cross-stream flows are investigated numerically.
a
b
Fig. 9. a) Nusselt number as a function of pumping power b) Effectiveness parameter as a function of Reynolds number
The experimental measurement of electric current shows zero current in many cases. Numerical results show that in the considered range of parameters, electric power consumption of all 6 electrode pairs is smaller than 50µW. It is smaller than the minimum value that could be measured by our instruments, therefore, power consumption results are not presented. It is only concluded that the
electric power consumption is negligible compare to pumping power and it is not an issue in this problem. 6.4. Charge distribution and flow patterns Presented experimental and numerical results showed that the electric field successfully enhances heat transfer in the setup but the question of how this happens is still to be answered. Fig. 10 shows contours of net charge density in the vicinity of electrode pair No.3. These contours are repeated near each electrode periodically only the first and last pair have slightly different shapes. Net charge density distribution shows that hetrocharge layers are constructed near electrodes on the outer wall of annulus and the thickness of the hetrocharge layer increases as voltage increases until it reaches the inner wall.
4 kV
8 kV
16 kV
24 kV
Fig 10. Net charge distribution (left) and flow streamlines (right) in different applied voltages at Re=10
The streamlines of the flow in different EHD Reynolds numbers are plotted in Fig. 10. It can be seen that the electric body force pushes the fluid away from the outer wall in the region between
electrodes. This results in a small deviation from a straight line in the fluid streamline at 4 kV. Increasing applied voltage and electric force will cause generation of two separate vortices near each electrode. More increase in the applied voltage strengthens and enlarges the vortices and eventually breaks them into smaller vortices. These cross-stream flows are responsible for heat transfer enhancement by removing heat from the hot wall and transferring it to the main-stream flow.
0 kV
4 kV
8 kV
16 kV
24 kV
Re = 5
Re = 10
Fig 11. Effect of electric field on non-dimensional isotherms at Re=5 and Re=10 Fig. 11 shows distortion of non-dimensional isotherms due to different applied voltages at Reynolds number of 5 and 10. In the absence of electric field, the thermal boundary layers are smooth and their thickness is related to the local heat flux from the wall. The thinner boundary layer at Reynolds number of 10 in comparison with the Reynolds number of 5 leads to higher heat flux and higher total heat transfer rate. When electric field applies the isotherms align themselves with streamlines near the inner wall of the annulus, therefore, the isotherms squeezed under the vortices and the thermal boundary layer decrease in these areas which results a higher local heat transfer coefficient.
Fig 11. Maximum transverse velocity as a function of applied voltage at different Reynolds numbers A good measure of the strength of cross-flow streams is the maximum of induced transverse velocity in the domain. Fig. 11 reports maximum transverse velocity as a function of applied voltage. It can be seen that the maximum transverse velocity increases as voltage increases. It should be clarified that, the transverse velocity reported in Fig.11 is scaled by inlet velocity. The inlet velocity is proportional to Reynolds number, therefore, a maximum non-dimensional transverse velocity of 1.15 at Re=5 and V=12kV means that the induced flow has a velocity of 1.15 times of the external main-stream flow. In the lower Reynolds number cases, there is an optimum voltage in which the transverse velocity is maximized it means that, induced transverse velocity increases with applied voltage increase until the transverse velocity almost equals the main-stream inlet velocity. As it was shown previously in the Fig. 9b. It would not be effective to increase the voltage beyond this optimum voltage. Conclusion The application of EHD conduction method for forced convection heat transfer enhancement in an annulus at Reynolds numbers between 5 and 50 was investigated experimentally and numerically. An
effectiveness parameter defined to evaluate the advantage of proposed double pipe heat exchanger design. The experimental results had a good agreement with numerical results with an average error of 10%. The induced flow patterns and heat transfer enhancement considering a wide range of Reynolds and voltages were studied numerically and the following main conclusions can be highlighted: -
Electric field in the considered range of parameters effectively enhances heat transfer up to 50% for transformer oil compared to the forced convection heat transfer in the absence of electric field.
-
The EHD induced flow consumes a small amount of electric power which is negligible compared to the amount of pumping power and the heat transfer. The conduction method can be used in the practical heat exchangers to enhance the heat transfer and reduce the size of the heat exchanger without high extra power consumption.
-
Electric field also increases pressure drop in the heat exchanger, but the heat transfer enhancement outweighs pumping power increase as the effectiveness parameter is greater than unity. At the Reynolds number of 10 the effectiveness parameter is 1.18 and 1.3 at applied voltages of 8 kV and 16 kV respectively.
-
Effectiveness parameter increases as voltage increases and Reynolds number decreases therefore the EHD method is more effective at lower Reynolds numbers.
-
At low Reynolds numbers, an optimum voltage was observed in which the effectiveness parameter was maximized. This optimum voltage corresponds to the voltage which generates a transverse cross-stream flow comparable to main-stream inlet velocity. It would not be effective to increase the voltage beyond this optimum voltage. This is helpful in the designing process of an enhanced heat exchanger.
-
In the gap between electrodes, the electric force is toward the outside and pushes the fluid away from the wall and improve the heat convection.
-
Electric field generates two separate vortices near each electrode. The vortices break at high voltages.
-
Cross-stream flows had a maximum transverse velocity of almost equal to inlet velocity, which leads to a maximum effectiveness. This fundamental illustration of the concept of heat transfer enhancement by EHD conduction method
Nomenclature
N n Nu P p Pr Q q Re Rth t T u V Vmax
Area, m2 Charge mobility constant, m2/Vs Electrical dimensionless parameter Specific heat constant, J/kgK Diameter, m Charge diffusion constant, m2/s Hydraulic diameter, m Heat transfer enhancement ratio, Electron charge = 1.60217662 × 10-19 c Electric field strength, V/m Apparent friction factor Electric body force density, N/m3 Heat transfer coefficient, W/m2K Electric current, A Joule heating dimensionless parameter Thermal conductivity, W/mK Boltzmann universal constant = 1.38064852 × 10-23 m2kg/s2K Dissociation rate Recombination rate Length, m Electrical dimensionless parameter Mass flow rate, kg/s Neutral species density Normal direction, Negative charge density, c/m3 Nusselt number Pressure, Pa Positive charge density, c/m3 Prandtl number Total heat transfer, W Net charge density, c/m3 Reynolds number Thermal resistance, K/W Tube thickness, m Temperature, K Velocity, m/s Voltage, V Maximum transverse velocity, m/s
Greek letters α ε η μ ν ξ
Thermal diffusivity, m2/s Electric permittivity F/m, Effectiveness Electrode length ,m Dynamic viscosity, Pas Kinematic viscosity, m2/s Distance (between electrodes), m
A b Co cp d D DH e E fapp Fe h I J k kB kd kr L M
ρ σ φ ω
Density, kg/m3 Electrical conductivity, S/m Electrical potential, V Dissociation rate constant
Subscripts and Superscripts 0 Without electric field effect Negative charge + Positive charge c Cross section (area) EHD With electric field effect eq Equilibrium G Ground electrode HV High voltage electrode i Inner in Inlet o Outer out Outlet r Ratio (ngative to positive) s Surface (area) w Wall ‘ Dimensional parameters
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Highlights:
Heat transfer enhancement using EHD conduction mechanism is investigated. Effectiveness parameter evaluated considering heat transfer and pumping power. The method was more effective in low Reynolds numbers. Investigating the cross-stream flows reveals an optimum voltage.
