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Experimental optimization of ion wind generator with needle to parallel plates for cooling device
International Journal of Heat and Mass Transfer 84 (2015) 35–45
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental optimization of ion wind generator with needle to parallel plates for cooling device Dong Ho Shin, Joon Shik Yoon, Han Seo Ko ⇑ School of Mechanical Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do 440-746, Republic of Korea
a r t i c l e
i n f o
Article history: Received 4 September 2014 Received in revised form 15 December 2014 Accepted 3 January 2015
Keywords: Ion wind Electrode Cooling performance Heat transfer Voltage
a b s t r a c t An efficient cooling system is needed for Light Emitting Diode (LED) devices since they consume 70% of the applied power as heat. Thus, much research on cooling devices has been performed this century. However, most of the developed systems do not have high enough cooling efficiency, and are accompanied with other demerits such as noise, weight, and size problems. Therefore, an ion wind generator was suggested for use as a new cooling device in this study. The characteristics of the ion wind from the needle to parallel plate electrodes were analyzed for developing optimized cooling devices. Temperature changes induced by the ion wind were measured under various conditions for quantitative analysis. The efficient cooling performance of the ion wind was confirmed by the experimental and numerical results. Finally, optimization of the ion wind generator as a cooling device was accomplished. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Although Light Emitting Diodes (LEDs) have the highest energy efficiency among lighting devices, they still consume 70% of the applied power as heat [1]. Thus, proper temperature performance is required for LEDs to enhance the lighting efficiency and avoid thermal damage [1–4]. The general methods employed for cooling LEDs are natural convection with a heat sink and forced convection with a fan. However, in the case of natural convection with a heat sink, lower cooling performance is obtained than for forced convection, and other demerits such as heavy weight and large size are also present. In addition, forced convection with a fan also has many disadvantages such as noise, vibration, short lifetime, and large size, since it contains mechanical moving part [2–4]. Thus, an ion wind generator using corona discharge was suggested for a new cooling device for LEDs in this study because it overcomes all the demerits of the other cooling devices. Corona discharge has been used for industrial applications for a few decades now (e.g., electrostatic precipitators). Thus, much research has been performed for the development of applications using corona discharge, for which the ion wind generator is the most representative work. The ion wind is a flow of air induced by ions and electrons from the corona discharge, and it is also commonly called corona wind in atmospheric conditions. Ion wind research has actively progressed since Robinson’s work [5] in last ⇑ Corresponding author. E-mail address: [email protected] (H.S. Ko). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.01.018 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
five decades. The study of ion wind can be classified into two parts: analyzing the characteristics of ion wind in various electrode arrangements, and verifying its cooling performance in various conditions. Study on the characteristics in various electrode arrangements has been performed since the 1960’s, and many cases such as plate to plate [6], parallel plates [7], wire to cylinder [8], wire to plate [8], rod to plate [9], sphere to sphere [9] and needle to plate [10] have been studied so far. However, a needle to parallel plate-type electrode arrangement was developed in this study, since there is relatively insufficient research data on this arrangement even though it has a simple and more appropriate structure for the micro cooling of LEDs. Study on the verification of the cooling performance and application of ion wind has recently been performed widely. Kalman [11], Molki [12], Go [13], and Sheu [14] proved the cooling performance of ion wind for wire to plate, wire to cylinder, wire to flat plate, and point to flat plate electrode arrangements. Kasayapanand [15] analyzed the cooling performance of ion wind for a vertical fin array using the computational fluid dynamics technique, and Chen [16] verified the cooling performance of ion wind for LED devices by measuring the thermal resistivity of the LEDs. In the present study, the cooling performance of ion wind by the needle to parallel electrodes was analyzed by measuring the temperature distribution, and was quantitatively verified by calculating the heat transfer coefficient and enhancement factor. From the results, important parameters defining the cooling performance of ion wind were discovered, and empirical correlations were derived. Finally, the advantage of using the ion wind
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Nomenclature P Fe Q Qe qe h Ts T1 i
q u L
pressure electric force applied heat total amount of space charges total amount of space charge in unit length heat transfer coefficient surface temperature ambient temperature discharge current in unit length density of air velocity of ion wind length of plate
generator as an effective tool for cooling the LED was confirmed, and optimization of the generator using the needle to parallel plate electrodes was performed through use of the empirical correlations. 2. Theoretical background
Lc k V E d H D
K He R
c d V c ¼ mv g 0 dr 1 þ pffiffiffiffiffi ln r dr
d¼
2.2. Numerical study The range of the operating voltage of ion wind is defined as that between the onset voltage and the spark-over voltage in this study. In general, ion wind occurs right after occurrence of the corona discharge, and the onset voltage of the corona discharge, in the case of wire to cylinder electrodes, is defined by Eq. (1), named Peek’s law [17].
ð1Þ
where mv is an irregularity factor to account for the condition of the wires, g 0 is a disruptive electric field, c is an empirical dimensional constant, r and d are the radius and distance between the wires, and d is an air density factor with respect to SATP (25 °C, 76 cm Hg) (Eq. (2)).
2.1. Generation mechanism of ion wind If an electric field is applied between a sharply curved electrode (discharge electrode) and a blunt surface electrode (collecting electrode), a micro current starts flowing in the place between the electrodes called the discharge area. A corona discharge then occurs at the tip of the discharge electrode when the applied voltage in the discharge electrode is high enough to reach the threshold voltage. Air molecules are ionized into ions and electrons by the local discharge at the tip. In the range of the corona operating voltages, the same phenomenon is repeated to generate a considerable amount of ions and electrons in the discharge area, which is called an electron avalanche. The charged ions and electrons move in the opposite directions due to their polarities as space charges. As shown in the experimental setup of Fig. 1, the ions move to the plate electrodes while the electrons move to the needle electrode. Since heavy ions move in the discharge area, the ions transfer their moving inertia into the air molecules by collision between the accelerated ions and air molecules. Thus, the flow of air molecules occurs, which is called ion wind or corona wind.
characteristic length conductivity of air applied voltage applied electric field intensity distance between electrodes needle position diffusivity coefficient dielectric permittivity ion mobility heat loss resistance
q PT 0 ¼ qSATP P0 T
ð2Þ
The definition of the spark-over voltage of ion wind has shown little discrepancy between studies, unlike the definition of the onset voltage. In this study, the spark-over voltage of the ion wind was defined as the transition voltage from the glow corona discharge to the spark discharge, which is called a spark over. When an electric field is applied in the discharge area, the burst corona discharge occurs, making a fine current for the flow between the electrodes at the low voltage section near the onset voltage [17]. If the applied voltage becomes higher, the streamer and glow corona discharge occur to make a very stable electric field zone in the discharge area [17]. Thus, the discharge current has an exponential relation with the applied voltage in this section [18]. However, if the applied voltage becomes even higher, spark discharge occurs, making a spark noise and an electric shock wave. By the spark over, the discharge current rapidly increases and the ion wind velocity starts to decrease with a large undulation. Thus, the spark-over voltage in the present study was defined as the finishing voltage section of the ion wind. To study the ion wind, the electric field and the space charge should be considered at first. The electric field E is given by Eq. (3).
E ¼ rV
ð3Þ
And, the electric potential V is obtained by solving the Poisson’s equation as follows:
r2 V ¼
q
ð4Þ
where V is the electric potential, q is the space charge density and is the dielectric permittivity of free space. The momentum transfer between the moving space charges and the air molecules is defined by the charge transport equation as follows:
r ðDrq K rVqÞ þ U rq ¼ 0
Fig. 1. Mechanism of ion wind generation.
ð5Þ
where D is the diffusivity coefficient of ions, U is the velocity of airflow and K is the ion mobility in an electric field. The second term of Eq. (5) is the conduction force to define the motion of the ions under the electric field relative to entire air flow which is the main force to make the momentum transfer mechanism. Since it has a preponderant role in the momentum transfer mechanism, the other two terms
D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
(convection, diffusion) were ignored in this study. Thus, the current density generated by the moving space charges is reduced to the following form.
J ¼ KqE
ð6Þ
Since this system is assumed to be a steady state condition, the current density should also be conserved by the following equation.
rJ ¼0
ð7Þ
The evolution of the space charge density in the drift zone is reduced to the following form (Eq. (8)), by substituting Eq. (6) into Eq. (7) and solving the divergence using Eqs. (3) and (4).
r qrV ¼
q2
ð8Þ
And, the electric force applied to the space charges in the discharge area is expressed by Eq. (9)[19].
1 1 de 2 f e ¼ Q e E jEj2 re þ r q jEj 2 2 dq
ð9Þ
where the first term of the right-hand side in Eq. (9) is the Coulomb force which acts on the space charges in the electric field. The Coulomb force is the main factor which controls the moving speed of the space charges in the discharge area. The second and third terms are the forces due to the permittivity gradient and the electrostriction, respectively. These two terms are often neglected in the conditions of a single phase flow (air) in atmospheric pressure [20]. The velocity of the ion wind is calculated by Eq. (10), called the Navier–Stokes’s equation.
@~ v ~ ~ 1~ 1 þ ðv rÞv ¼ F rp þ mr2~ v @t q q
ð10Þ
where ~ v is the velocity of air, p is the pressure, q is the density, m is the viscosity of air, and F is the external volume force. Eq. (11) can be simply derived from Eq. (10) with some basic assumptions, such as incompressible, inviscid, and steady-state conditions.
1 qU 2 ¼ 2
Z
Fe
ðF e ¼ Q e EÞ
ð11Þ
where Q e is the amount of the space charges and E is the electric intensity in the discharge area. The heat transfer coefficient was calculated by Eq. (12), Newton’s cooling law, to analyze the cooling performance of the ion wind using the experimental data of temperature distribution in this study.
Q ¼ hAðT s T 1 Þ
ð12Þ
where Q is the applied thermal energy, h is the heat transfer coefficient, T s is the surface temperature, and T 1 is the air temperature. The enhanced cooling performance of the ion wind can be quantitatively analyzed using Eqs. (13) and (14).
Enhancement factor ¼
hion forced ðT s T 1 Þfree ¼ hfree ðT s T 1 Þion forced
ð13Þ
ðhion forced hfree Þ 100 hfree
ð14Þ
Enhancement ratio ½% ¼
where g is the gravitational acceleration, Lc is the characteristic length of the surface, and U is the fluid velocity. The empirical correlation of the local Nusselt number on the flat plate is derived as Eq. (17) [21]. 1=3 Nux ¼ 0:453 Re1=2 x Pr
ReL ¼
gbðT s T 1 ÞðLÞ3
m2 ULc
m
3. Experimental setup In this study, the velocity and temperature were measured to analyze the characteristics of the ion wind under various conditions, as shown in Fig. 2. An ion wind generator with a needle to parallel plate was fabricated for the experiment. The electrode intervals, needle positions and length of the plates were controlled to measure the velocity in various conditions, as shown in Figs. 3 and 4, respectively. The needle electrode and the plate electrode were made of pure steel. Table 1 shows the specific dimensions of the test materials. The stages, which had a 20 mm travel range, were installed to change the electrode interval and the position of the needle. The TSI velocity meter using a hot wire was used to measure the velocity. The temperature of the hot wire installed in the probe of the velocity meter increased by the applied electric current. After it stared cooling down by the applied flow, the temperature was measured for the calculation of the velocity. The heat loss of the hot wire can be calculated by Eq. (18).
qffiffiffiffiffiffi 2 He ¼ Ri ¼ ðT w T f Þ A þ B D V f
ð18Þ
where He is heat loss, R is resistance, I is current, A and B are coefficients, Vf is velocity of the fluid, Tw is a temperature of the hot wire, and Tf is a temperature of the fluid. The coefficients A and B were determined by the calibration of the velocity meter before the experiment using a fan. The probe of the velocity meter was installed parallel to the needle electrode outside the plate electrodes. The distance between the probe and the needle electrodes was fixed by 4 cm. The resolution of the velocity meter was 0.01 m/s and its maximum measurement error was 3%. The diameter and the length of the probe were 3 and 10 mm, respectively, which fit well with the plate interval. Yang [22] claimed that the corona-driven flow can ensure a greater speed close to the wall than a pressure differential flow, due to the continual Coulombic force applied to the fluid through the duct. It is true that the direction and position of the ionic wind are very complicated. However, the velocity meter using the hot wire was a proper device for the ion wind flow since the distance and the angle between the probe and the needle electrodes could be kept constant. The test area was protected from external air flow by a chamber which was maintained at the air temperature of 25 °C and the relative humidity of 25%. A high voltage DC power supplier with a
ð15Þ
ð16Þ
ð17Þ
where Pr is the Prandtl number.
where hfree and hion forced are the heat transfer coefficients of natural convection and the ion wind, respectively. The Grashof number and Reynolds number were calculated by Eqs. (15) and (16) as follows:
GrL ¼
37
Fig. 2. Schematic diagram of experimental setup.
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Fig. 3. Ion wind generator for various electrode intervals.
4. Development of correlations
Fig. 4. Ion wind generator for various needle positions and length of plates.
Table 1 Specifications of the ion wind generator. Components
Specifications (mm)
Needle (length diameter tip) Plate (thickness width length) Distance between needle and plate Needle position
2 2 0.015 2 10 (10, 20, 30) 3–15 0–15
maximum voltage of 30 kV was used to make the high electric field intensity. The discharge current was estimated by measuring the current at the plate electrodes with a multi meter. The power consumed making the ion wind was estimated by multiplying the measured current with the applied voltage. A heat plate was made for the temperature measurement test using a copper plate and a nicrome wire, which was attached to the bottom of the copper plate by a thermally conductive adhesive. T-type thermocouples were attached to the surface of the copper plate near the center area. An insulator was attached to ensure convective heat transfer occurred only at the top surface of the copper plate. The temperature of the copper plate was measured to be 75 °C in the air, and the constant heat flux was calculated to be 580 W/m2. Conduction and convection heat transfer were considered, and radiation was neglected in this case[11]. The heat plate was installed with the velocity meter, as shown in Fig. 2, to investigate an impinging jet flow of the ion wind on the surface. The uncertainty of the measurement device was listed in Table 2. The total measurement error of the device was estimated as 2.1% in this study.
The correlations (Eqs. (21)–(25)) were derived by the commercial software ‘‘Minitab Ver.16’’ which uses a multiple regression analysis method. The regression analysis is a statistical process for an estimation of relationships among variables. There are many techniques for modeling and analyzing several variables, when a focus is on the relationship between a dependent variable and one or more independent variables. Among them, an ordinary least square regression method was used for the parametric study in this case. The P-value in this method is the probability of obtaining the observed sample results when the null hypothesis is actually true. The P-value should be smaller than or equal to a previously chosen threshold value which is called the significance level (0.05 in this case) to have a high credibility. It suggests that if the observed data is false with the assumption that the null hypothesis is true, the hypothesis must be rejected and the other hypothesis should be selected for accepting the data as true. If the P-value is less than 0.05, strong presumption is ensured against the null hypothesis. And, the R-square value was calculated for the error measurement to validate the correlations. The R-square value denoted by R2 indicates how well data fits a statistical model. The main purpose of calculating the value is the prediction of future outcomes of the testing of the hypotheses on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, as the proportion of total variation of outcomes explained by the model. The R-square value can be calculated by the following Eq. (19). The developed correlations explained in this study have R-square values higher than 0.95 in all cases.
P 2 ðy f i Þ R2 ¼ 1 P i 2 Þ ðyi y
ð19Þ
Table 2 Uncertainty of experimental devices. Parameter (measured, calculated or referenced)
Uncertainty interval
Confidence limit (%)
Thermo couple hTtype-GL820i High voltage (DC) hSHV30M 15KV Pi Ventilation meter hTSI-9565Ai Multimeter (voltage) hCD771i Multimeter (current) hCD771i Total error
±0.5 °C ±0.8 V ±0.015 m/s ±0.1 mV ±0.1 lA
99 99 97 99.5 98.6 2.1%
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is a where yi is an experimental value, fi is a predicted value and y mean of the experimental value. Also, the relative error was calculated for comparison between the experimental results and the calculated results using Eq. (20).
Relativ e error ¼
Experimental data calculated data 100 Experimental data
5. Results and discussion 5.1. Voltage–current relation The relationship between the onset and spark-over voltages and the electrode intervals is shown in Fig. 5 and Table 3. The onset voltages observed experimentally were slightly lower than those calculated from Peek’s law by about 1–1.5 kV. This error was due to the different geometry of the electrodes. It should be noted that the discharge electrode in the present case was the needle, which was different from the wire used in Peek’s case. It is generally considered that a needle tip has a more proper topology for focusing of the electric field intensity onto one point than that of a wire. Thus, the onset voltage of the needle electrode could be lower than that of the wire electrode. Therefore, a modified Peek’s law (Eq. (21)) was developed for the case of the needle to the parallel plate electrodes using the data in Table 3.
ð21Þ
where r is the tip diameter of the needle electrode and d is the electrode interval. In order to calculate the spark-over voltages, the arrangement and topology of the electrode, properties of the air, the discharge current and the air pressure should be considered [18]. However, since it is too complicated to investigate all parameters for each case, an experimental approach is the most appropriate way to predict the spark-over voltages. Thus, an empirical correlation for calculating the spark-over voltage in the case of the needle to parallel plate electrodes was developed, shown as Eq. (22).
V spark ¼ 3:57 e61:3d=r ½kV
Electrode interval [mm] Onset [kV] Spark-over [kV]
3 3.1 4.5
4 3.5 5.1
5 3.8 5.6
6 4.2 6.6
8 4.7 7.7
10 5 9.3
12 5.6 10.1
ð20Þ
From the multiple regression method, the dimensionless parameters d/r and L/d were deduced for the application of the developed correlations against different electrode geometries. The range of variation of the corresponding parameters are 200 6 d=r 6 1334 and 2 6 L=d 6 3:3 in this study.
c d d ¼ 1:8 ln V on ¼ mv g 0 dr 1 þ pffiffiffiffiffi ln 4r 3:73r dr
Table 3 Average onset and spark-over voltages by electrode interval.
ð22Þ
where d is the electrode interval and V spark is the spark-over voltage. The experimental results of the onset and spark-over voltages
Fig. 5. Experimental results of onset and spark-over voltages according to electrode interval.
according to the electrode interval are shown in Fig. 5. The calculated data almost matched with the experimental data under these conditions, within the relative error rate of 5%. Thus, the optimized voltage supplier and the electric system are expected to be set up using these results. Figs. 6–8 show the measured current in the ground electrode according to the electrode intervals, needle positions and length of the plates, respectively. A distinct tendency was shown in Fig. 6, while the differences were too insignificant to be distinguished in Figs. 7 and 8. It was illustrated that the current decreased under the same voltage if the electrode interval increased, as shown in Fig. 6. It was also confirmed that the electric field intensity in the discharge area decreased as the distance between the needle tip and the plate electrode increased, by Coulmb’s law [23] as expressed by Eq. (3). It is clear that the electrode interval had a more significant effect on the electric field intensity than did the needle positions and the length of the plates. The current density and the electric field intensity were found to have almost the same values over different needle positions since the electrode interval did not change. The corona current data in Fig. 7 shows some fluctuation unlike the current data in Figs. 6 and 8 since the current was measured where the needle electrodes were placed between the plate electrodes. The measurement error of the current could occur in a moment when the discharge area became quite unstable as the needle electrodes were placed between the plate electrodes. The curvature of the stick part of the needle electrode was much larger than that of the tip. Thus, the local electric field intensities on the stick and the tip were quite different from each other. Moreover, the surface roughness of the needle electrode was not uniform from the tip to the stick part. As a result, it was concluded that the electric field intensity in the discharge area became irregular to make the measurement error of the current on the plate electrode since the stick and the tip were placed together in the discharge area. In this point of view, the optimum position of the needle electrode is the rear corner of the plate electrode where H is zero in this case. The current slightly increased as the length of the plate was elongated from 1 to 4 cm as shown in Fig. 8 because the flowing current in the ground electrodes increased, which means the increased space charge density as the collecting area of the ions
Fig. 6. Experimental results of discharge current according to voltage for each electrode interval.
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D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 7. Discharge current according to voltage for various needle electrode positions.
The calculation results of Eqs. (23) and (24) were compared against published results by Yang [22] to verify the accuracy and the predictive ability of the developed correlations. As shown in Fig. 9, the calculation data fits well with the experimental data within 10% of relative error in error bars. It is considered that the difference of the curvature of the needle tip and the material of the electrode are the main error reasons. Fig. 9 shows that the fine current in the early voltage region is well predicted by Eq. (23), and the exponentially increased current after the transition voltage (6.2 kV) can be calculated by Eq. (24). Furthermore, the empirical correlation for the current of the corona discharge (Eqs. (23) and (24)) can be used to calculate the current (i) value in Eq. (30). Thus, the velocity of the ion wind can be predicted by Eqs. (23), (24) and (30) without any prior experiment. As a result, the predictive ability of Eq. (30) can be extended by Eqs. (23) and (24).
5.2. Voltage–velocity relation
Fig. 8. Discharge current according to voltage for various length of plates.
widened with the plate size. However, the increasing rate of the current according to the length of the plate electrodes decreased with increasing the plate length. In fact, it is hard to conclude clearly that the current increased in the case of the length of the plate electrodes longer than 2 cm, since the difference of the current is so small, less than 2 lA Therefore, it is a reasonable conclusion that the space charge density in the discharge area increased according to the length of the plate electrodes, only in the case of the length of the plate electrode shorter than 2 cm in this study. An empirical correlation was also derived to analyze the relationship between the voltage and the corona discharge current using the voltage–current experimental data. The current had an exponential relation with the applied voltage, as shown in Fig. 6, which is a common tendency shown by Townsend [24]. However, a linear relation between the voltage and current was observed around the range of relatively low voltage near the onset voltage in Fig. 6. It was considered that the electric field intensity in this section was too weak to produce enough electrons to develop the electron avalanche. Thus, the empirical correlations (Eqs. (23) and (24)) were developed to estimate the discharge current more accurately.
i1 ½lA=m ffi
0:241 þ 0:85 ðV V on Þ; d=r
i2 ½lA=m ffi 0:026 eð0:49 lnd=rþ3:93ÞV ; V t ¼ 3:54e5:06d=r
V on < V < V t
ð23Þ
V t < V < V spark
ð24Þ
The ion wind velocity was shown according to the plate intervals, needle positions and length of the plates in Figs. 10–12, respectively. The open symbols in Fig. 10 represent the experimental data and the red-plot is for the calculation data by the correlation (Eq. (30)). The ion wind velocity decreased for the same voltage as the electrode interval increased from 3 to 12 mm (Fig. 10). These results were caused by the decreased electric field intensity in the discharge area due to the widened electrode intervals under the same voltages, as explained previously. The electric field intensity decreased because of decreased inertial force of the space charges in the discharge area, as derived in Eqs. (9) and (10). Thus, it is concluded that the electrode interval (plate interval in this case) is the most important parameter determining the velocity of the ion wind. Fig. 11 shows the changes in velocity while the needle electrode moved from outside to inside the discharge area. The velocity of the ion wind decreased as the needle electrode moved into the discharge area from 0 to 15 mm. The generated electric potential from the needle electrode caused imbalance of the electric field in the discharge area since the needle was placed between the plates. Thus, a backward electric field vector could be generated from the needle electrodes to the rear edges of the plate electrodes to divide the flow of the ion wind into many directions (backward and forward). In fact, this phenomenon frequently occurs in this type of electrode arrangement. Kalman [10] also reported this phenomenon to occur in experiments with a wire to plate electrodes, causing experimental error which was explained by split of the flow into two opposite directions when the wire was placed between the plates.
ð25Þ
where d is the electrode interval, V on is the onset voltage, V spark is the spark-over voltage, and V t is the transition voltage form the linear function to the exponential function.
Fig. 9. Comparison of Eqs. (23) and (24) with current data reported by Yang [22].
D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 10. Experimental and calculated results of ion wind velocity according to voltage for various electrode intervals.
Fig. 11. Ion wind velocity according to voltage for various needle electrode positions.
Fig. 12. Ion wind velocity according to voltage for various lengths of plates.
Fig. 11 also shows that the velocity of the ion wind increased linearly when H (position of the needle electrode) was greater than 0 mm where the needle electrode was placed between the plate electrodes, unlike the observed logarithm tendency of the velocity according to the applied voltage in the case of H of 0 mm, because of the decreased velocity in the early voltage region by a generated reversal flow in the case of H greater than 0 mm. The backward electric field vectors were generated by the locally enhanced electric field intensity on the rear corner of the plate electrodes. Thus, the reversal flow of the ion wind occurred toward the rear corner of the plate electrodes from the tip, which resulted in the reduction of the measured velocity. The reversal flow could be reduced when the spark-over occurred since much higher electric field intensity was focused on the tip, thus the ion wind converged to the same velocity at the spark-over voltage.
41
Fig. 12 illustrates that the ion wind velocities were higher in the cases of the length of plate electrodes are longer than 2 cm than that which was 1 cm in length. The total device error was 2.1%, thus the error bars indicating the maximum error rate of 5% were marked in Fig. 12. Fig. 12 obviously shows the increased velocity in the case of the plate length of 2 cm compared with the case for the plate length of 1 cm. And, it also shows the small differences among the velocities in the cases of the plate length longer than 2 cm, which are in the range of the experimental errors. This means that the inertial force of the space charges in the cases of the length of the plate electrodes are longer than 2 cm was higher than for that of 1 cm plates, because the travel distance of the space charges increased by the lengthened induced electrodes (lengthened plate electrodes in this case), causing increased possibility to impact the air molecules near the plate electrodes. Thus, the velocity of the ion wind could be lower in the case of the 1 cm than that the 2 and 3 cm plates. It is considered however, that the inertial force of the space charges was almost same in the cases of the length of the plate electrodes are longer than 2 cm. Warburg [25] pointed out that the space charges have a limitation in the drift distance of the space charge from the ionization zone. Thus, the current distribution on the ground electrode shows the Warburg distribution. Sigmond [26] also found out that the active electrode area was circular where the field line angle between the needle tip and the flat plate electrodes was 60° for the needle to flat plate electrodes. Rashkovan [27] also observed almost same results with Sigmond’s research using the wire to parallel plate electrode configuration that the optimum angle for using the whole active electrode area was 34.5°. Thus, it is a reasonable conclusion that the theory of the space charge drift distance derived by Warburg can be applied to the present case. From this point of view, it is considered that the density of the space charge was not formed farther than 2 cm (drift limit) from the discharge electrodes. In this study, the optimum field line angle between the needle tip and the edge of the plate electrode was 30° and the optimum length of the plate electrode was 2 cm. Thus, it is predicted that the velocity of the ion wind would not show the discrepancy if the plate length was longer than 2 cm in this study. The fluctuation of the velocity is also shown in Fig. 12 in the case of the length of the plate electrodes of 1 and 2 cm, while the typical logarithm tendency of the velocity according to the applied voltage is observed in the case of the plate electrodes of 3 and 4 cm. The logarithm tendency of the velocity was not measured because of the generated fluctuation by the edge effect of the plate electrode. The edge effect occurred to focus the strong electric field intensity on the edge of the plate electrodes because the edge of the plate electrodes became closer to the tip (ion source). Thus, the ion wind can be divided into many directions, which causes the measurement error. As a result, the ion wind would fluctuate rather than show the typical logarithm tendency according to the voltage when the length of the plate is shorter than 2 cm in this case. From the theoretical analysis, an empirical correlation to calculate the velocity of the ion wind according to the voltages under various conditions was developed by the following steps. By Coulomb’s law, the electric field intensity was derived in Eq. (26).
E¼
V Delc
ð26Þ
where V is the applied voltage and Delc is the distance between the discharge electrode and the ground electrode. It was, however, assumed from the experimental results in the present study that the distance between the electrodes was the only parameter defining the electric field intensity in the discharge area. The electric field intensity is actually influenced by many variables such as properties of the materials and air, surface rough-
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ness, space charge distribution, etc [18,23]. Particularly, it is very hard to consider the effect of the space charge distribution due to its nonlinear characteristics. Thus, a modified and simplified numerical approach with basic assumptions is suggested in this study. The distance between the electrodes can be derived as follows (Fig. 13):
Delc
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ¼ d þ x2
ð27Þ
where d is the perpendicular distance between the needle electrode and the plate electrode. Eq. (28) was derived by substituting Eqs. (26) and (27) into Eq. (11) and multiplying the final outcome by two to consider the symmetric geometry. Finally, Eq. (30) was derived by solving the integral equation of Eq. (29).
1 2 qu ¼ 2
Z 0
L
Q e Edx ¼
Z 0
L
V 2 qe pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dx 2 d þ x2
1 2 qu ¼ 2 qe V ln ðsec hL þ tan hL Þ 2
ð28Þ
ð29Þ
where hL ¼ arctan ðL=dÞ, L is the length of the plate and qe is the total amount of space charges in the unit length. The discharge current per unit time was assumed to be equal to the amount of space charges in the discharge area. Thus, qe in Eq. (30) can be substituted by i in Eqs. (23) and (24). Finally, Eq. (30) was derived to calculate the velocity of the ion wind.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 u¼ i V lnðsec hL þ tan hL Þ 103 ½m=s
q
ð30Þ
where the diameter of the tip was 0.015 mm. The experimental data for the velocity of the ion wind was compared with the values calculated by Eq. (30) in Fig. 10. The average error rate was 6%, which tended to increase with the applied voltages. The error rate in the early stage was around 3%, but it increased to the maximum error rate of 12% at the spark-over voltages. This was considered to be for two reasons. The first is the electric power loss of the corona discharge. The joule heating, irregular electric spark and noise consumed the applied power to make the ion wind have lower velocity than that expected by Eq. (30). It was considered that the rising amount of electric power loss according to increasing applied voltage reduced the velocity of the ion wind to cause error. The second reason is the transition from uniform corona discharge to the imbalanced spark discharge at the spark-over voltages. Fig. 10 illustrates that the maximum error rate occurred at the spark-over voltages. The electric insulation of air in the discharge area started to destruct unstably due to occurrence of the spark discharge [17,18]. Thus, the generated space charges lost their mobility, reducing the inertial force. This phenomenon ended up reducing the velocity of the ion wind. In addition, the spark discharges caused undulation of the ion wind velocity due to the electric shock wave, which could cause an error rate. In summary, the electric power loss and spark discharge
Fig. 13. Schematic diagram of electrode arrangement.
which occurred at the spark-over voltages were the main reasons of the errors observed in Fig. 10. 5.3. Velocity–temperature relation The results of the surface temperature for the heat plate under ion wind at different electrode intervals of 8, 10 and 12 mm are shown in Fig. 14. From the results of the measured velocity, the electrode interval was selected as the only variable with the most significant influence on the characteristics of the ion wind. The surface temperature of the heat plate was initially at 75 °C, and it started decreasing right after the ion wind was applied on it. The maximum temperature difference was 12, 24, and 23 °C resulting from electrode intervals of 8, 10, and 12 mm, respectively. The Reynolds numbers of the ion wind according to the voltages for different electrode intervals are also shown in Fig. 15. The Reynolds numbers increased from 230 to 2115 with increase in the applied voltages, decreasing with increase of the electrode intervals under the same voltages because the velocity of the ion wind decreased with the electrode intervals as explained in Fig. 10. In other words, the Reynolds number of the ion wind tended to increase as the distance between the electrodes decreased. The heat transfer coefficient of the ion wind calculated by Eq. (12) increased with increasing voltages for the electrode intervals of 8, 10 and 12 mm, as shown in Fig. 16. The heat transfer coefficient for natural convection was about 12 W/m2. The heat source was made of a copper block and an insulator was attached under the copper to ensure that the convective heat transfer occurred only on the top surface of the heat source which was the target place where the ion wind was applied. However, the generated heat on the copper block reduced by the conduction through the insulator unexpectedly. Also, the radiation was neglected when the applied heat flux on the heat source was calculated because the radiation contribution on the heat transfer performance would be insignificant and the total applied heat flux was very small around 580 W/m2. The heat transfer coefficient in the case of the pure natural convection reduced to 5–6 W/m2 if those two main reasons were considered. Although the heat transfer coefficient in the case of the pure natural convection was measured higher than the real value in this experiment, the cooling performances of the ion wind were analyzed by the augmentation factor which excluded the influence of the measurement error in this case. The heat transfer coefficient started to increase linearly until the spark-over of the ion wind occurred. It was found that the heat transfer coefficient decreased at the same voltages by increasing the electrode intervals, as the Reynolds number of the ion wind decreased. Table 4 shows the maximum temperature difference and the heat transfer coefficient by the ion wind for various electrode intervals. The maximum heat transfer coefficients by the ion wind were observed to be 19, 23 and 22 W/m2 K with the
Fig. 14. Temperature according to voltage for various electrode intervals.
D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 15. Reynolds number according to voltage for various electrode intervals.
Fig. 16. Experimental results of heat transfer coefficient according to voltage for various electrode intervals.
Table 4 Experimentally measured temperature data of ion wind. Electrode intervals
Maximum voltage
Temperature difference
Heat transfer coefficient
8 [mm] 10 [mm] 12 [mm]
7.7 [kV] 9.3 [kV] 10.1 [kV]
19 [°C] 24 [°C] 23 [°C]
19 [W/m2 K] 23 [W/m2 K] 22 [W/m2 K]
applied voltages of 7.7, 9.3 and 10.1 kV for the electrode intervals of 8, 10 and 12 mm, respectively. The maximum heat transfer coefficients at the conditions of 10 and 12 mm were higher than that measured at the condition of 8 mm by about 5 W/m2 K because of the rise of the spark-over voltages. The maximum operating Reynolds numbers at the conditions of the electrode intervals of 10 and 12 mm were also higher by about 300–500 than that of the 8 mm interval since the maximum operating voltages increased. The heat transfer coefficient for the power consumed generating the ion wind was shown in Fig. 17. The heat transfer coefficient varied at the same power consumption for varying electrode intervals. In other words, more power (20–60 mW) was required to generate the ion wind for the same heat transfer coefficient at the electrode interval condition of 8 mm than at 10 and 12 mm. The increased flow rate by the enlarged outlet area of the ion wind was considered to enhance the cooling performance. The flow rate of the ion wind increased by about 0.01–0.02 m3/s as the electrode interval widened from 8 to 12 mm at the same voltages. Fig. 17 also illustrates the slope of the line, indicating that the heat transfer coefficient rate decreased with increasing power consumption because the possibility of electric power loss increased with increasing applied voltages. As the plasma zone was formed by
43
Fig. 17. Heat transfer coefficient according to power consumption for various electrode intervals.
the corona discharge, electric power loss occurred in the discharge area [17,23]. Thus, the applied electric power can be wasted as noise and light energies. More noise and light of the spark can be generated clearly near the range of the spark-over voltage. The discharge method used in the present research was a type of non-thermal plasma so called cold plasma, which was maintained in the atmospheric condition. Thus, the temperature of the surrounding air still unchanged, although the joule heating of the electrodes occurred at the tip. Wang [28] also reported that the comparison data between the results of the numerical modeling and the experiment, emphasized that the heat transfer performance was not highly affected by the joule heating effect. As a result, the joule heating at the tip did not influence the convective heat transfer on the heat source much. However, the energy loss was observed by the joule heating effect in this case. By those reasons, the rate of the heat transfer coefficient decreased with increasing applied power. However, it should be noted that the total amount of applied power measured at the DC power supplier was very low, at about 1–5 W. Even though the ion wind had a low conversion efficiency of the electric power to mechanical power (2–7.5%), it was found that the corona air pump, which has the same range of the efficiency with that of the conventional fans, offers higher air velocities [22]. Thus, developing an ion wind generator is a proper suggestion for cooling electronic devices like the LED, in the matter of cooling performance and energy saving. Figs. 18 and 19 show the enhancement factor and ratio calculated by Eqs. (13) and (14), respectively. The result of Gr=Re2 calculated by Eq. (15) is shown in Fig. 20. The enhancement factors were around one near the onset voltages, as shown in Fig. 18. This means that natural convection had a dominant effect on the heat transfer performance. In addition, the velocities of the ion wind near the
Fig. 18. Enhancement factor according to voltage for various electrode intervals.
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D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 19. Enhancement ratio according to voltage for various electrode intervals.
Fig. 21. Experimental and calculated results of Nusselt number according to Reynolds number for various electrode intervals.
experimental data of the Nusselt numbers were shown to have higher values than the results of Eq. (17) by about 60%. It should be noted that the flow conditions of the fluid in Eq. (17) and the present study are different from each other. Eq. (17) was for fluid flowing parallel to the surface, while the ion wind had an impinging flow to the center of the surface of the heat plate (Eq. (31)) in this study. Thus, the ion wind was considered to make a stagnation point at the center of the surface with large local Reynolds numbers. Therefore, the experimental data had higher values than those calculated by Eq. (17). 6. Conclusions
Fig. 20. Gr/Re2 according to voltage for various electrode intervals.
onset voltages were very low, under 0.1 m/s, and the Reynolds numbers were under 100, as shown in Figs. 10 and 15. If the applied voltages increased by more than 1 kV from the onset voltage, Gr=Re2 started to decrease very fast, as the effect of the ion wind on heat transfer increased. The enhancement factor and ratio also increased by the ion wind from 1 to 2.2 and 0% to 51%. These results can be used to quantitatively analyze the cooling performance of the ion wind. The cooling performance was increased by more than two times by the ion wind. In order to predict the cooling performance of the ion wind, the Re–Nu relation of the empirical correlation was developed in Eq. (31) where the distance from the needle to heat plate was fixed by 40 mm. Eq. (32) is the final form to calculate the heat transfer coefficient of the ion wind. 1=2
NuL ¼ 0:65 ReL Pr1=3
In the present study, the velocity and temperature were measured experimentally to analyze the characteristics of ion wind under various conditions for the needle to parallel plate electrode arrangement. The plate interval was observed to be the most important and serious factor defining the performance of the ion wind, while the needle position and the length of the plate showed little influence on performance. The maximum heat transfer coefficient was measured to be 23 W/m2 K at a 10 mm-electrode interval, for which the enhancement factor of the heat transfer coefficient was 2.2. The empirical correlations for predicting the operating voltages, the discharge current, the velocity and the heat transfer coefficient of the ion wind were derived. In addition, the reliability of the developed correlations was confirmed by comparing them with the experimental results. Finally, the optimal design of the ion wind generator with the needle to parallel plate electrode arrangement for cooling electronic devices could be proposed in this study.
ð31Þ Conflict of interest
1
havg ¼ ReL 2
k L
ð150 6 ReL 6 2100Þ
ð32Þ
The experimental and calculated results of the Nusselt numbers of the ion wind using Eq. (31) by the Reynolds numbers are shown in Fig. 21. The average error rate of Eq. (31) was about 4.5%. The error rate was especially higher near the onset and the spark-over voltages than in the middle section. Natural convection and the velocity undulation generated errors at the onset and spark-over voltages. Near the onset voltages, natural convection had a dominant effect on the performance of the heat transfer, although the results of Eq. (31) ignored the effect of natural convection. In addition, the velocity undulation was observed as explained in previous section, which caused the large error rate near the spark-over voltages. Therefore, the ranges of the onset and spark-over voltage should not be considered as the operating conditions for the optimization of the ion wind cooling devices. The dotted line in Fig. 21 represents the local Nusselt numbers calculated by Eq. (17). The
None declared. Acknowledgments This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Korean government (MEST) – South Korea (NRF2013R1A2A2A01068653). References [1] D.S. Jang, S.H. Yun, K.S. Lee, Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications, Int. J. Heat Mass Transfer 55 (2012) 515–521. [2] J.P. Meyer, J. Dirker, A.O. Adelaja, Condensation heat transfer in smooth inclined tubes for R134a at different saturation temperatures, Int. J. Heat Mass Transfer 70 (2014) 515–525.
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[15] N. Kasayapanand, Electrohydrodynamic enhancement of heat transfer in vertical fin array using computational fluid dynamics technique, Int. Commun. Heat Mass Transfer 35 (2008) 762–770. [16] I.Y. Chen, M.Z. Guo, K.S. Yang, C.C. Wang, Enhanced cooling for LED lighting using ionic wind, Int. J. Heat Mass Transfer 57 (2013) 285–291. [17] F.W. Peek, Dielectric Phenomena in High Voltage Engineering, second ed., McGraw-Hill, New York, 1920, pp. 38–71. [18] J.M. Meek, A theoretical determination of spark-over voltage for sphere gaps, J. Franklin Inst. 230 (2) (1940) 229–242. [19] A. Chattock, On the velocity and mass of ions in the electric wind in air, Philos. Mag. 48 (1899) 401–420. [20] B.L. Owsenek, J. Seyed-Yagoobi, Theoretical and experimental study of electrohydrodynamic heat transfer enhancement through wire-plate corona discharge, J. Heat Transfer 119 (1997) 604–610. [21] American Society for Metal, Metals Handbook, Properties and Selection of Metals, eighth ed., vol. 1, ASM, Metals Park, OH, 1961. [22] F. Yang, N.E. Jewell-Larsen, D.L. Brown, K. Pendergrass, D.A. Parker, I.A. Krichtafovitch, A.V. Mamishev, Corona driven air propulsion for cooling of electronics, in: Smit (Ed.), Xlllth International Symposium on High Voltage Engineering, Netherlands, 2003, ISBN 90-77017-79-8. [23] Z. Popovic, B.D. Popovic, Introductory Electromagnetics, Prentice Hall, Upper Saddle River, NJ, 2000, pp. 28–37. [24] L. Jacob, High Voltage Physics, first ed., Methuen & Co., Ltd, London, 1934, pp. 53–61. [25] E. Warburg, Handbuch der Physik, 14, Springer, Berlin, 1927, pp. 154–155. [26] R.S. Sigmond, Simple approximate treatment of unipolar space charge dominated coronas: the Warburg law and the saturation current, J. Appl. Phys. 23 (1982) 891, http://dx.doi.org/10.1063/1.330557. [27] A. Rashkovan, E. Sher, H. Kalman, Experimental optimization of an electric blower by corona wind, Appl. Therm. Eng. 22 (2002) 1587–1599. [28] H.C. Wang, N.E. Jewell-Larsen, A.V. Mamishev, Thermal management of microelectronics with electrostatic fluid accelerators, Appl. Therm. Eng. 51 (2013) 190–211.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental optimization of ion wind generator with needle to parallel plates for cooling device Dong Ho Shin, Joon Shik Yoon, Han Seo Ko ⇑ School of Mechanical Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do 440-746, Republic of Korea
a r t i c l e
i n f o
Article history: Received 4 September 2014 Received in revised form 15 December 2014 Accepted 3 January 2015
Keywords: Ion wind Electrode Cooling performance Heat transfer Voltage
a b s t r a c t An efficient cooling system is needed for Light Emitting Diode (LED) devices since they consume 70% of the applied power as heat. Thus, much research on cooling devices has been performed this century. However, most of the developed systems do not have high enough cooling efficiency, and are accompanied with other demerits such as noise, weight, and size problems. Therefore, an ion wind generator was suggested for use as a new cooling device in this study. The characteristics of the ion wind from the needle to parallel plate electrodes were analyzed for developing optimized cooling devices. Temperature changes induced by the ion wind were measured under various conditions for quantitative analysis. The efficient cooling performance of the ion wind was confirmed by the experimental and numerical results. Finally, optimization of the ion wind generator as a cooling device was accomplished. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Although Light Emitting Diodes (LEDs) have the highest energy efficiency among lighting devices, they still consume 70% of the applied power as heat [1]. Thus, proper temperature performance is required for LEDs to enhance the lighting efficiency and avoid thermal damage [1–4]. The general methods employed for cooling LEDs are natural convection with a heat sink and forced convection with a fan. However, in the case of natural convection with a heat sink, lower cooling performance is obtained than for forced convection, and other demerits such as heavy weight and large size are also present. In addition, forced convection with a fan also has many disadvantages such as noise, vibration, short lifetime, and large size, since it contains mechanical moving part [2–4]. Thus, an ion wind generator using corona discharge was suggested for a new cooling device for LEDs in this study because it overcomes all the demerits of the other cooling devices. Corona discharge has been used for industrial applications for a few decades now (e.g., electrostatic precipitators). Thus, much research has been performed for the development of applications using corona discharge, for which the ion wind generator is the most representative work. The ion wind is a flow of air induced by ions and electrons from the corona discharge, and it is also commonly called corona wind in atmospheric conditions. Ion wind research has actively progressed since Robinson’s work [5] in last ⇑ Corresponding author. E-mail address: [email protected] (H.S. Ko). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.01.018 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
five decades. The study of ion wind can be classified into two parts: analyzing the characteristics of ion wind in various electrode arrangements, and verifying its cooling performance in various conditions. Study on the characteristics in various electrode arrangements has been performed since the 1960’s, and many cases such as plate to plate [6], parallel plates [7], wire to cylinder [8], wire to plate [8], rod to plate [9], sphere to sphere [9] and needle to plate [10] have been studied so far. However, a needle to parallel plate-type electrode arrangement was developed in this study, since there is relatively insufficient research data on this arrangement even though it has a simple and more appropriate structure for the micro cooling of LEDs. Study on the verification of the cooling performance and application of ion wind has recently been performed widely. Kalman [11], Molki [12], Go [13], and Sheu [14] proved the cooling performance of ion wind for wire to plate, wire to cylinder, wire to flat plate, and point to flat plate electrode arrangements. Kasayapanand [15] analyzed the cooling performance of ion wind for a vertical fin array using the computational fluid dynamics technique, and Chen [16] verified the cooling performance of ion wind for LED devices by measuring the thermal resistivity of the LEDs. In the present study, the cooling performance of ion wind by the needle to parallel electrodes was analyzed by measuring the temperature distribution, and was quantitatively verified by calculating the heat transfer coefficient and enhancement factor. From the results, important parameters defining the cooling performance of ion wind were discovered, and empirical correlations were derived. Finally, the advantage of using the ion wind
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D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Nomenclature P Fe Q Qe qe h Ts T1 i
q u L
pressure electric force applied heat total amount of space charges total amount of space charge in unit length heat transfer coefficient surface temperature ambient temperature discharge current in unit length density of air velocity of ion wind length of plate
generator as an effective tool for cooling the LED was confirmed, and optimization of the generator using the needle to parallel plate electrodes was performed through use of the empirical correlations. 2. Theoretical background
Lc k V E d H D
K He R
c d V c ¼ mv g 0 dr 1 þ pffiffiffiffiffi ln r dr
d¼
2.2. Numerical study The range of the operating voltage of ion wind is defined as that between the onset voltage and the spark-over voltage in this study. In general, ion wind occurs right after occurrence of the corona discharge, and the onset voltage of the corona discharge, in the case of wire to cylinder electrodes, is defined by Eq. (1), named Peek’s law [17].
ð1Þ
where mv is an irregularity factor to account for the condition of the wires, g 0 is a disruptive electric field, c is an empirical dimensional constant, r and d are the radius and distance between the wires, and d is an air density factor with respect to SATP (25 °C, 76 cm Hg) (Eq. (2)).
2.1. Generation mechanism of ion wind If an electric field is applied between a sharply curved electrode (discharge electrode) and a blunt surface electrode (collecting electrode), a micro current starts flowing in the place between the electrodes called the discharge area. A corona discharge then occurs at the tip of the discharge electrode when the applied voltage in the discharge electrode is high enough to reach the threshold voltage. Air molecules are ionized into ions and electrons by the local discharge at the tip. In the range of the corona operating voltages, the same phenomenon is repeated to generate a considerable amount of ions and electrons in the discharge area, which is called an electron avalanche. The charged ions and electrons move in the opposite directions due to their polarities as space charges. As shown in the experimental setup of Fig. 1, the ions move to the plate electrodes while the electrons move to the needle electrode. Since heavy ions move in the discharge area, the ions transfer their moving inertia into the air molecules by collision between the accelerated ions and air molecules. Thus, the flow of air molecules occurs, which is called ion wind or corona wind.
characteristic length conductivity of air applied voltage applied electric field intensity distance between electrodes needle position diffusivity coefficient dielectric permittivity ion mobility heat loss resistance
q PT 0 ¼ qSATP P0 T
ð2Þ
The definition of the spark-over voltage of ion wind has shown little discrepancy between studies, unlike the definition of the onset voltage. In this study, the spark-over voltage of the ion wind was defined as the transition voltage from the glow corona discharge to the spark discharge, which is called a spark over. When an electric field is applied in the discharge area, the burst corona discharge occurs, making a fine current for the flow between the electrodes at the low voltage section near the onset voltage [17]. If the applied voltage becomes higher, the streamer and glow corona discharge occur to make a very stable electric field zone in the discharge area [17]. Thus, the discharge current has an exponential relation with the applied voltage in this section [18]. However, if the applied voltage becomes even higher, spark discharge occurs, making a spark noise and an electric shock wave. By the spark over, the discharge current rapidly increases and the ion wind velocity starts to decrease with a large undulation. Thus, the spark-over voltage in the present study was defined as the finishing voltage section of the ion wind. To study the ion wind, the electric field and the space charge should be considered at first. The electric field E is given by Eq. (3).
E ¼ rV
ð3Þ
And, the electric potential V is obtained by solving the Poisson’s equation as follows:
r2 V ¼
q
ð4Þ
where V is the electric potential, q is the space charge density and is the dielectric permittivity of free space. The momentum transfer between the moving space charges and the air molecules is defined by the charge transport equation as follows:
r ðDrq K rVqÞ þ U rq ¼ 0
Fig. 1. Mechanism of ion wind generation.
ð5Þ
where D is the diffusivity coefficient of ions, U is the velocity of airflow and K is the ion mobility in an electric field. The second term of Eq. (5) is the conduction force to define the motion of the ions under the electric field relative to entire air flow which is the main force to make the momentum transfer mechanism. Since it has a preponderant role in the momentum transfer mechanism, the other two terms
D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
(convection, diffusion) were ignored in this study. Thus, the current density generated by the moving space charges is reduced to the following form.
J ¼ KqE
ð6Þ
Since this system is assumed to be a steady state condition, the current density should also be conserved by the following equation.
rJ ¼0
ð7Þ
The evolution of the space charge density in the drift zone is reduced to the following form (Eq. (8)), by substituting Eq. (6) into Eq. (7) and solving the divergence using Eqs. (3) and (4).
r qrV ¼
q2
ð8Þ
And, the electric force applied to the space charges in the discharge area is expressed by Eq. (9)[19].
1 1 de 2 f e ¼ Q e E jEj2 re þ r q jEj 2 2 dq
ð9Þ
where the first term of the right-hand side in Eq. (9) is the Coulomb force which acts on the space charges in the electric field. The Coulomb force is the main factor which controls the moving speed of the space charges in the discharge area. The second and third terms are the forces due to the permittivity gradient and the electrostriction, respectively. These two terms are often neglected in the conditions of a single phase flow (air) in atmospheric pressure [20]. The velocity of the ion wind is calculated by Eq. (10), called the Navier–Stokes’s equation.
@~ v ~ ~ 1~ 1 þ ðv rÞv ¼ F rp þ mr2~ v @t q q
ð10Þ
where ~ v is the velocity of air, p is the pressure, q is the density, m is the viscosity of air, and F is the external volume force. Eq. (11) can be simply derived from Eq. (10) with some basic assumptions, such as incompressible, inviscid, and steady-state conditions.
1 qU 2 ¼ 2
Z
Fe
ðF e ¼ Q e EÞ
ð11Þ
where Q e is the amount of the space charges and E is the electric intensity in the discharge area. The heat transfer coefficient was calculated by Eq. (12), Newton’s cooling law, to analyze the cooling performance of the ion wind using the experimental data of temperature distribution in this study.
Q ¼ hAðT s T 1 Þ
ð12Þ
where Q is the applied thermal energy, h is the heat transfer coefficient, T s is the surface temperature, and T 1 is the air temperature. The enhanced cooling performance of the ion wind can be quantitatively analyzed using Eqs. (13) and (14).
Enhancement factor ¼
hion forced ðT s T 1 Þfree ¼ hfree ðT s T 1 Þion forced
ð13Þ
ðhion forced hfree Þ 100 hfree
ð14Þ
Enhancement ratio ½% ¼
where g is the gravitational acceleration, Lc is the characteristic length of the surface, and U is the fluid velocity. The empirical correlation of the local Nusselt number on the flat plate is derived as Eq. (17) [21]. 1=3 Nux ¼ 0:453 Re1=2 x Pr
ReL ¼
gbðT s T 1 ÞðLÞ3
m2 ULc
m
3. Experimental setup In this study, the velocity and temperature were measured to analyze the characteristics of the ion wind under various conditions, as shown in Fig. 2. An ion wind generator with a needle to parallel plate was fabricated for the experiment. The electrode intervals, needle positions and length of the plates were controlled to measure the velocity in various conditions, as shown in Figs. 3 and 4, respectively. The needle electrode and the plate electrode were made of pure steel. Table 1 shows the specific dimensions of the test materials. The stages, which had a 20 mm travel range, were installed to change the electrode interval and the position of the needle. The TSI velocity meter using a hot wire was used to measure the velocity. The temperature of the hot wire installed in the probe of the velocity meter increased by the applied electric current. After it stared cooling down by the applied flow, the temperature was measured for the calculation of the velocity. The heat loss of the hot wire can be calculated by Eq. (18).
qffiffiffiffiffiffi 2 He ¼ Ri ¼ ðT w T f Þ A þ B D V f
ð18Þ
where He is heat loss, R is resistance, I is current, A and B are coefficients, Vf is velocity of the fluid, Tw is a temperature of the hot wire, and Tf is a temperature of the fluid. The coefficients A and B were determined by the calibration of the velocity meter before the experiment using a fan. The probe of the velocity meter was installed parallel to the needle electrode outside the plate electrodes. The distance between the probe and the needle electrodes was fixed by 4 cm. The resolution of the velocity meter was 0.01 m/s and its maximum measurement error was 3%. The diameter and the length of the probe were 3 and 10 mm, respectively, which fit well with the plate interval. Yang [22] claimed that the corona-driven flow can ensure a greater speed close to the wall than a pressure differential flow, due to the continual Coulombic force applied to the fluid through the duct. It is true that the direction and position of the ionic wind are very complicated. However, the velocity meter using the hot wire was a proper device for the ion wind flow since the distance and the angle between the probe and the needle electrodes could be kept constant. The test area was protected from external air flow by a chamber which was maintained at the air temperature of 25 °C and the relative humidity of 25%. A high voltage DC power supplier with a
ð15Þ
ð16Þ
ð17Þ
where Pr is the Prandtl number.
where hfree and hion forced are the heat transfer coefficients of natural convection and the ion wind, respectively. The Grashof number and Reynolds number were calculated by Eqs. (15) and (16) as follows:
GrL ¼
37
Fig. 2. Schematic diagram of experimental setup.
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D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 3. Ion wind generator for various electrode intervals.
4. Development of correlations
Fig. 4. Ion wind generator for various needle positions and length of plates.
Table 1 Specifications of the ion wind generator. Components
Specifications (mm)
Needle (length diameter tip) Plate (thickness width length) Distance between needle and plate Needle position
2 2 0.015 2 10 (10, 20, 30) 3–15 0–15
maximum voltage of 30 kV was used to make the high electric field intensity. The discharge current was estimated by measuring the current at the plate electrodes with a multi meter. The power consumed making the ion wind was estimated by multiplying the measured current with the applied voltage. A heat plate was made for the temperature measurement test using a copper plate and a nicrome wire, which was attached to the bottom of the copper plate by a thermally conductive adhesive. T-type thermocouples were attached to the surface of the copper plate near the center area. An insulator was attached to ensure convective heat transfer occurred only at the top surface of the copper plate. The temperature of the copper plate was measured to be 75 °C in the air, and the constant heat flux was calculated to be 580 W/m2. Conduction and convection heat transfer were considered, and radiation was neglected in this case[11]. The heat plate was installed with the velocity meter, as shown in Fig. 2, to investigate an impinging jet flow of the ion wind on the surface. The uncertainty of the measurement device was listed in Table 2. The total measurement error of the device was estimated as 2.1% in this study.
The correlations (Eqs. (21)–(25)) were derived by the commercial software ‘‘Minitab Ver.16’’ which uses a multiple regression analysis method. The regression analysis is a statistical process for an estimation of relationships among variables. There are many techniques for modeling and analyzing several variables, when a focus is on the relationship between a dependent variable and one or more independent variables. Among them, an ordinary least square regression method was used for the parametric study in this case. The P-value in this method is the probability of obtaining the observed sample results when the null hypothesis is actually true. The P-value should be smaller than or equal to a previously chosen threshold value which is called the significance level (0.05 in this case) to have a high credibility. It suggests that if the observed data is false with the assumption that the null hypothesis is true, the hypothesis must be rejected and the other hypothesis should be selected for accepting the data as true. If the P-value is less than 0.05, strong presumption is ensured against the null hypothesis. And, the R-square value was calculated for the error measurement to validate the correlations. The R-square value denoted by R2 indicates how well data fits a statistical model. The main purpose of calculating the value is the prediction of future outcomes of the testing of the hypotheses on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, as the proportion of total variation of outcomes explained by the model. The R-square value can be calculated by the following Eq. (19). The developed correlations explained in this study have R-square values higher than 0.95 in all cases.
P 2 ðy f i Þ R2 ¼ 1 P i 2 Þ ðyi y
ð19Þ
Table 2 Uncertainty of experimental devices. Parameter (measured, calculated or referenced)
Uncertainty interval
Confidence limit (%)
Thermo couple hTtype-GL820i High voltage (DC) hSHV30M 15KV Pi Ventilation meter hTSI-9565Ai Multimeter (voltage) hCD771i Multimeter (current) hCD771i Total error
±0.5 °C ±0.8 V ±0.015 m/s ±0.1 mV ±0.1 lA
99 99 97 99.5 98.6 2.1%
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is a where yi is an experimental value, fi is a predicted value and y mean of the experimental value. Also, the relative error was calculated for comparison between the experimental results and the calculated results using Eq. (20).
Relativ e error ¼
Experimental data calculated data 100 Experimental data
5. Results and discussion 5.1. Voltage–current relation The relationship between the onset and spark-over voltages and the electrode intervals is shown in Fig. 5 and Table 3. The onset voltages observed experimentally were slightly lower than those calculated from Peek’s law by about 1–1.5 kV. This error was due to the different geometry of the electrodes. It should be noted that the discharge electrode in the present case was the needle, which was different from the wire used in Peek’s case. It is generally considered that a needle tip has a more proper topology for focusing of the electric field intensity onto one point than that of a wire. Thus, the onset voltage of the needle electrode could be lower than that of the wire electrode. Therefore, a modified Peek’s law (Eq. (21)) was developed for the case of the needle to the parallel plate electrodes using the data in Table 3.
ð21Þ
where r is the tip diameter of the needle electrode and d is the electrode interval. In order to calculate the spark-over voltages, the arrangement and topology of the electrode, properties of the air, the discharge current and the air pressure should be considered [18]. However, since it is too complicated to investigate all parameters for each case, an experimental approach is the most appropriate way to predict the spark-over voltages. Thus, an empirical correlation for calculating the spark-over voltage in the case of the needle to parallel plate electrodes was developed, shown as Eq. (22).
V spark ¼ 3:57 e61:3d=r ½kV
Electrode interval [mm] Onset [kV] Spark-over [kV]
3 3.1 4.5
4 3.5 5.1
5 3.8 5.6
6 4.2 6.6
8 4.7 7.7
10 5 9.3
12 5.6 10.1
ð20Þ
From the multiple regression method, the dimensionless parameters d/r and L/d were deduced for the application of the developed correlations against different electrode geometries. The range of variation of the corresponding parameters are 200 6 d=r 6 1334 and 2 6 L=d 6 3:3 in this study.
c d d ¼ 1:8 ln V on ¼ mv g 0 dr 1 þ pffiffiffiffiffi ln 4r 3:73r dr
Table 3 Average onset and spark-over voltages by electrode interval.
ð22Þ
where d is the electrode interval and V spark is the spark-over voltage. The experimental results of the onset and spark-over voltages
Fig. 5. Experimental results of onset and spark-over voltages according to electrode interval.
according to the electrode interval are shown in Fig. 5. The calculated data almost matched with the experimental data under these conditions, within the relative error rate of 5%. Thus, the optimized voltage supplier and the electric system are expected to be set up using these results. Figs. 6–8 show the measured current in the ground electrode according to the electrode intervals, needle positions and length of the plates, respectively. A distinct tendency was shown in Fig. 6, while the differences were too insignificant to be distinguished in Figs. 7 and 8. It was illustrated that the current decreased under the same voltage if the electrode interval increased, as shown in Fig. 6. It was also confirmed that the electric field intensity in the discharge area decreased as the distance between the needle tip and the plate electrode increased, by Coulmb’s law [23] as expressed by Eq. (3). It is clear that the electrode interval had a more significant effect on the electric field intensity than did the needle positions and the length of the plates. The current density and the electric field intensity were found to have almost the same values over different needle positions since the electrode interval did not change. The corona current data in Fig. 7 shows some fluctuation unlike the current data in Figs. 6 and 8 since the current was measured where the needle electrodes were placed between the plate electrodes. The measurement error of the current could occur in a moment when the discharge area became quite unstable as the needle electrodes were placed between the plate electrodes. The curvature of the stick part of the needle electrode was much larger than that of the tip. Thus, the local electric field intensities on the stick and the tip were quite different from each other. Moreover, the surface roughness of the needle electrode was not uniform from the tip to the stick part. As a result, it was concluded that the electric field intensity in the discharge area became irregular to make the measurement error of the current on the plate electrode since the stick and the tip were placed together in the discharge area. In this point of view, the optimum position of the needle electrode is the rear corner of the plate electrode where H is zero in this case. The current slightly increased as the length of the plate was elongated from 1 to 4 cm as shown in Fig. 8 because the flowing current in the ground electrodes increased, which means the increased space charge density as the collecting area of the ions
Fig. 6. Experimental results of discharge current according to voltage for each electrode interval.
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D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 7. Discharge current according to voltage for various needle electrode positions.
The calculation results of Eqs. (23) and (24) were compared against published results by Yang [22] to verify the accuracy and the predictive ability of the developed correlations. As shown in Fig. 9, the calculation data fits well with the experimental data within 10% of relative error in error bars. It is considered that the difference of the curvature of the needle tip and the material of the electrode are the main error reasons. Fig. 9 shows that the fine current in the early voltage region is well predicted by Eq. (23), and the exponentially increased current after the transition voltage (6.2 kV) can be calculated by Eq. (24). Furthermore, the empirical correlation for the current of the corona discharge (Eqs. (23) and (24)) can be used to calculate the current (i) value in Eq. (30). Thus, the velocity of the ion wind can be predicted by Eqs. (23), (24) and (30) without any prior experiment. As a result, the predictive ability of Eq. (30) can be extended by Eqs. (23) and (24).
5.2. Voltage–velocity relation
Fig. 8. Discharge current according to voltage for various length of plates.
widened with the plate size. However, the increasing rate of the current according to the length of the plate electrodes decreased with increasing the plate length. In fact, it is hard to conclude clearly that the current increased in the case of the length of the plate electrodes longer than 2 cm, since the difference of the current is so small, less than 2 lA Therefore, it is a reasonable conclusion that the space charge density in the discharge area increased according to the length of the plate electrodes, only in the case of the length of the plate electrode shorter than 2 cm in this study. An empirical correlation was also derived to analyze the relationship between the voltage and the corona discharge current using the voltage–current experimental data. The current had an exponential relation with the applied voltage, as shown in Fig. 6, which is a common tendency shown by Townsend [24]. However, a linear relation between the voltage and current was observed around the range of relatively low voltage near the onset voltage in Fig. 6. It was considered that the electric field intensity in this section was too weak to produce enough electrons to develop the electron avalanche. Thus, the empirical correlations (Eqs. (23) and (24)) were developed to estimate the discharge current more accurately.
i1 ½lA=m ffi
0:241 þ 0:85 ðV V on Þ; d=r
i2 ½lA=m ffi 0:026 eð0:49 lnd=rþ3:93ÞV ; V t ¼ 3:54e5:06d=r
V on < V < V t
ð23Þ
V t < V < V spark
ð24Þ
The ion wind velocity was shown according to the plate intervals, needle positions and length of the plates in Figs. 10–12, respectively. The open symbols in Fig. 10 represent the experimental data and the red-plot is for the calculation data by the correlation (Eq. (30)). The ion wind velocity decreased for the same voltage as the electrode interval increased from 3 to 12 mm (Fig. 10). These results were caused by the decreased electric field intensity in the discharge area due to the widened electrode intervals under the same voltages, as explained previously. The electric field intensity decreased because of decreased inertial force of the space charges in the discharge area, as derived in Eqs. (9) and (10). Thus, it is concluded that the electrode interval (plate interval in this case) is the most important parameter determining the velocity of the ion wind. Fig. 11 shows the changes in velocity while the needle electrode moved from outside to inside the discharge area. The velocity of the ion wind decreased as the needle electrode moved into the discharge area from 0 to 15 mm. The generated electric potential from the needle electrode caused imbalance of the electric field in the discharge area since the needle was placed between the plates. Thus, a backward electric field vector could be generated from the needle electrodes to the rear edges of the plate electrodes to divide the flow of the ion wind into many directions (backward and forward). In fact, this phenomenon frequently occurs in this type of electrode arrangement. Kalman [10] also reported this phenomenon to occur in experiments with a wire to plate electrodes, causing experimental error which was explained by split of the flow into two opposite directions when the wire was placed between the plates.
ð25Þ
where d is the electrode interval, V on is the onset voltage, V spark is the spark-over voltage, and V t is the transition voltage form the linear function to the exponential function.
Fig. 9. Comparison of Eqs. (23) and (24) with current data reported by Yang [22].
D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 10. Experimental and calculated results of ion wind velocity according to voltage for various electrode intervals.
Fig. 11. Ion wind velocity according to voltage for various needle electrode positions.
Fig. 12. Ion wind velocity according to voltage for various lengths of plates.
Fig. 11 also shows that the velocity of the ion wind increased linearly when H (position of the needle electrode) was greater than 0 mm where the needle electrode was placed between the plate electrodes, unlike the observed logarithm tendency of the velocity according to the applied voltage in the case of H of 0 mm, because of the decreased velocity in the early voltage region by a generated reversal flow in the case of H greater than 0 mm. The backward electric field vectors were generated by the locally enhanced electric field intensity on the rear corner of the plate electrodes. Thus, the reversal flow of the ion wind occurred toward the rear corner of the plate electrodes from the tip, which resulted in the reduction of the measured velocity. The reversal flow could be reduced when the spark-over occurred since much higher electric field intensity was focused on the tip, thus the ion wind converged to the same velocity at the spark-over voltage.
41
Fig. 12 illustrates that the ion wind velocities were higher in the cases of the length of plate electrodes are longer than 2 cm than that which was 1 cm in length. The total device error was 2.1%, thus the error bars indicating the maximum error rate of 5% were marked in Fig. 12. Fig. 12 obviously shows the increased velocity in the case of the plate length of 2 cm compared with the case for the plate length of 1 cm. And, it also shows the small differences among the velocities in the cases of the plate length longer than 2 cm, which are in the range of the experimental errors. This means that the inertial force of the space charges in the cases of the length of the plate electrodes are longer than 2 cm was higher than for that of 1 cm plates, because the travel distance of the space charges increased by the lengthened induced electrodes (lengthened plate electrodes in this case), causing increased possibility to impact the air molecules near the plate electrodes. Thus, the velocity of the ion wind could be lower in the case of the 1 cm than that the 2 and 3 cm plates. It is considered however, that the inertial force of the space charges was almost same in the cases of the length of the plate electrodes are longer than 2 cm. Warburg [25] pointed out that the space charges have a limitation in the drift distance of the space charge from the ionization zone. Thus, the current distribution on the ground electrode shows the Warburg distribution. Sigmond [26] also found out that the active electrode area was circular where the field line angle between the needle tip and the flat plate electrodes was 60° for the needle to flat plate electrodes. Rashkovan [27] also observed almost same results with Sigmond’s research using the wire to parallel plate electrode configuration that the optimum angle for using the whole active electrode area was 34.5°. Thus, it is a reasonable conclusion that the theory of the space charge drift distance derived by Warburg can be applied to the present case. From this point of view, it is considered that the density of the space charge was not formed farther than 2 cm (drift limit) from the discharge electrodes. In this study, the optimum field line angle between the needle tip and the edge of the plate electrode was 30° and the optimum length of the plate electrode was 2 cm. Thus, it is predicted that the velocity of the ion wind would not show the discrepancy if the plate length was longer than 2 cm in this study. The fluctuation of the velocity is also shown in Fig. 12 in the case of the length of the plate electrodes of 1 and 2 cm, while the typical logarithm tendency of the velocity according to the applied voltage is observed in the case of the plate electrodes of 3 and 4 cm. The logarithm tendency of the velocity was not measured because of the generated fluctuation by the edge effect of the plate electrode. The edge effect occurred to focus the strong electric field intensity on the edge of the plate electrodes because the edge of the plate electrodes became closer to the tip (ion source). Thus, the ion wind can be divided into many directions, which causes the measurement error. As a result, the ion wind would fluctuate rather than show the typical logarithm tendency according to the voltage when the length of the plate is shorter than 2 cm in this case. From the theoretical analysis, an empirical correlation to calculate the velocity of the ion wind according to the voltages under various conditions was developed by the following steps. By Coulomb’s law, the electric field intensity was derived in Eq. (26).
E¼
V Delc
ð26Þ
where V is the applied voltage and Delc is the distance between the discharge electrode and the ground electrode. It was, however, assumed from the experimental results in the present study that the distance between the electrodes was the only parameter defining the electric field intensity in the discharge area. The electric field intensity is actually influenced by many variables such as properties of the materials and air, surface rough-
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ness, space charge distribution, etc [18,23]. Particularly, it is very hard to consider the effect of the space charge distribution due to its nonlinear characteristics. Thus, a modified and simplified numerical approach with basic assumptions is suggested in this study. The distance between the electrodes can be derived as follows (Fig. 13):
Delc
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ¼ d þ x2
ð27Þ
where d is the perpendicular distance between the needle electrode and the plate electrode. Eq. (28) was derived by substituting Eqs. (26) and (27) into Eq. (11) and multiplying the final outcome by two to consider the symmetric geometry. Finally, Eq. (30) was derived by solving the integral equation of Eq. (29).
1 2 qu ¼ 2
Z 0
L
Q e Edx ¼
Z 0
L
V 2 qe pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dx 2 d þ x2
1 2 qu ¼ 2 qe V ln ðsec hL þ tan hL Þ 2
ð28Þ
ð29Þ
where hL ¼ arctan ðL=dÞ, L is the length of the plate and qe is the total amount of space charges in the unit length. The discharge current per unit time was assumed to be equal to the amount of space charges in the discharge area. Thus, qe in Eq. (30) can be substituted by i in Eqs. (23) and (24). Finally, Eq. (30) was derived to calculate the velocity of the ion wind.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 u¼ i V lnðsec hL þ tan hL Þ 103 ½m=s
q
ð30Þ
where the diameter of the tip was 0.015 mm. The experimental data for the velocity of the ion wind was compared with the values calculated by Eq. (30) in Fig. 10. The average error rate was 6%, which tended to increase with the applied voltages. The error rate in the early stage was around 3%, but it increased to the maximum error rate of 12% at the spark-over voltages. This was considered to be for two reasons. The first is the electric power loss of the corona discharge. The joule heating, irregular electric spark and noise consumed the applied power to make the ion wind have lower velocity than that expected by Eq. (30). It was considered that the rising amount of electric power loss according to increasing applied voltage reduced the velocity of the ion wind to cause error. The second reason is the transition from uniform corona discharge to the imbalanced spark discharge at the spark-over voltages. Fig. 10 illustrates that the maximum error rate occurred at the spark-over voltages. The electric insulation of air in the discharge area started to destruct unstably due to occurrence of the spark discharge [17,18]. Thus, the generated space charges lost their mobility, reducing the inertial force. This phenomenon ended up reducing the velocity of the ion wind. In addition, the spark discharges caused undulation of the ion wind velocity due to the electric shock wave, which could cause an error rate. In summary, the electric power loss and spark discharge
Fig. 13. Schematic diagram of electrode arrangement.
which occurred at the spark-over voltages were the main reasons of the errors observed in Fig. 10. 5.3. Velocity–temperature relation The results of the surface temperature for the heat plate under ion wind at different electrode intervals of 8, 10 and 12 mm are shown in Fig. 14. From the results of the measured velocity, the electrode interval was selected as the only variable with the most significant influence on the characteristics of the ion wind. The surface temperature of the heat plate was initially at 75 °C, and it started decreasing right after the ion wind was applied on it. The maximum temperature difference was 12, 24, and 23 °C resulting from electrode intervals of 8, 10, and 12 mm, respectively. The Reynolds numbers of the ion wind according to the voltages for different electrode intervals are also shown in Fig. 15. The Reynolds numbers increased from 230 to 2115 with increase in the applied voltages, decreasing with increase of the electrode intervals under the same voltages because the velocity of the ion wind decreased with the electrode intervals as explained in Fig. 10. In other words, the Reynolds number of the ion wind tended to increase as the distance between the electrodes decreased. The heat transfer coefficient of the ion wind calculated by Eq. (12) increased with increasing voltages for the electrode intervals of 8, 10 and 12 mm, as shown in Fig. 16. The heat transfer coefficient for natural convection was about 12 W/m2. The heat source was made of a copper block and an insulator was attached under the copper to ensure that the convective heat transfer occurred only on the top surface of the heat source which was the target place where the ion wind was applied. However, the generated heat on the copper block reduced by the conduction through the insulator unexpectedly. Also, the radiation was neglected when the applied heat flux on the heat source was calculated because the radiation contribution on the heat transfer performance would be insignificant and the total applied heat flux was very small around 580 W/m2. The heat transfer coefficient in the case of the pure natural convection reduced to 5–6 W/m2 if those two main reasons were considered. Although the heat transfer coefficient in the case of the pure natural convection was measured higher than the real value in this experiment, the cooling performances of the ion wind were analyzed by the augmentation factor which excluded the influence of the measurement error in this case. The heat transfer coefficient started to increase linearly until the spark-over of the ion wind occurred. It was found that the heat transfer coefficient decreased at the same voltages by increasing the electrode intervals, as the Reynolds number of the ion wind decreased. Table 4 shows the maximum temperature difference and the heat transfer coefficient by the ion wind for various electrode intervals. The maximum heat transfer coefficients by the ion wind were observed to be 19, 23 and 22 W/m2 K with the
Fig. 14. Temperature according to voltage for various electrode intervals.
D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 15. Reynolds number according to voltage for various electrode intervals.
Fig. 16. Experimental results of heat transfer coefficient according to voltage for various electrode intervals.
Table 4 Experimentally measured temperature data of ion wind. Electrode intervals
Maximum voltage
Temperature difference
Heat transfer coefficient
8 [mm] 10 [mm] 12 [mm]
7.7 [kV] 9.3 [kV] 10.1 [kV]
19 [°C] 24 [°C] 23 [°C]
19 [W/m2 K] 23 [W/m2 K] 22 [W/m2 K]
applied voltages of 7.7, 9.3 and 10.1 kV for the electrode intervals of 8, 10 and 12 mm, respectively. The maximum heat transfer coefficients at the conditions of 10 and 12 mm were higher than that measured at the condition of 8 mm by about 5 W/m2 K because of the rise of the spark-over voltages. The maximum operating Reynolds numbers at the conditions of the electrode intervals of 10 and 12 mm were also higher by about 300–500 than that of the 8 mm interval since the maximum operating voltages increased. The heat transfer coefficient for the power consumed generating the ion wind was shown in Fig. 17. The heat transfer coefficient varied at the same power consumption for varying electrode intervals. In other words, more power (20–60 mW) was required to generate the ion wind for the same heat transfer coefficient at the electrode interval condition of 8 mm than at 10 and 12 mm. The increased flow rate by the enlarged outlet area of the ion wind was considered to enhance the cooling performance. The flow rate of the ion wind increased by about 0.01–0.02 m3/s as the electrode interval widened from 8 to 12 mm at the same voltages. Fig. 17 also illustrates the slope of the line, indicating that the heat transfer coefficient rate decreased with increasing power consumption because the possibility of electric power loss increased with increasing applied voltages. As the plasma zone was formed by
43
Fig. 17. Heat transfer coefficient according to power consumption for various electrode intervals.
the corona discharge, electric power loss occurred in the discharge area [17,23]. Thus, the applied electric power can be wasted as noise and light energies. More noise and light of the spark can be generated clearly near the range of the spark-over voltage. The discharge method used in the present research was a type of non-thermal plasma so called cold plasma, which was maintained in the atmospheric condition. Thus, the temperature of the surrounding air still unchanged, although the joule heating of the electrodes occurred at the tip. Wang [28] also reported that the comparison data between the results of the numerical modeling and the experiment, emphasized that the heat transfer performance was not highly affected by the joule heating effect. As a result, the joule heating at the tip did not influence the convective heat transfer on the heat source much. However, the energy loss was observed by the joule heating effect in this case. By those reasons, the rate of the heat transfer coefficient decreased with increasing applied power. However, it should be noted that the total amount of applied power measured at the DC power supplier was very low, at about 1–5 W. Even though the ion wind had a low conversion efficiency of the electric power to mechanical power (2–7.5%), it was found that the corona air pump, which has the same range of the efficiency with that of the conventional fans, offers higher air velocities [22]. Thus, developing an ion wind generator is a proper suggestion for cooling electronic devices like the LED, in the matter of cooling performance and energy saving. Figs. 18 and 19 show the enhancement factor and ratio calculated by Eqs. (13) and (14), respectively. The result of Gr=Re2 calculated by Eq. (15) is shown in Fig. 20. The enhancement factors were around one near the onset voltages, as shown in Fig. 18. This means that natural convection had a dominant effect on the heat transfer performance. In addition, the velocities of the ion wind near the
Fig. 18. Enhancement factor according to voltage for various electrode intervals.
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D.H. Shin et al. / International Journal of Heat and Mass Transfer 84 (2015) 35–45
Fig. 19. Enhancement ratio according to voltage for various electrode intervals.
Fig. 21. Experimental and calculated results of Nusselt number according to Reynolds number for various electrode intervals.
experimental data of the Nusselt numbers were shown to have higher values than the results of Eq. (17) by about 60%. It should be noted that the flow conditions of the fluid in Eq. (17) and the present study are different from each other. Eq. (17) was for fluid flowing parallel to the surface, while the ion wind had an impinging flow to the center of the surface of the heat plate (Eq. (31)) in this study. Thus, the ion wind was considered to make a stagnation point at the center of the surface with large local Reynolds numbers. Therefore, the experimental data had higher values than those calculated by Eq. (17). 6. Conclusions
Fig. 20. Gr/Re2 according to voltage for various electrode intervals.
onset voltages were very low, under 0.1 m/s, and the Reynolds numbers were under 100, as shown in Figs. 10 and 15. If the applied voltages increased by more than 1 kV from the onset voltage, Gr=Re2 started to decrease very fast, as the effect of the ion wind on heat transfer increased. The enhancement factor and ratio also increased by the ion wind from 1 to 2.2 and 0% to 51%. These results can be used to quantitatively analyze the cooling performance of the ion wind. The cooling performance was increased by more than two times by the ion wind. In order to predict the cooling performance of the ion wind, the Re–Nu relation of the empirical correlation was developed in Eq. (31) where the distance from the needle to heat plate was fixed by 40 mm. Eq. (32) is the final form to calculate the heat transfer coefficient of the ion wind. 1=2
NuL ¼ 0:65 ReL Pr1=3
In the present study, the velocity and temperature were measured experimentally to analyze the characteristics of ion wind under various conditions for the needle to parallel plate electrode arrangement. The plate interval was observed to be the most important and serious factor defining the performance of the ion wind, while the needle position and the length of the plate showed little influence on performance. The maximum heat transfer coefficient was measured to be 23 W/m2 K at a 10 mm-electrode interval, for which the enhancement factor of the heat transfer coefficient was 2.2. The empirical correlations for predicting the operating voltages, the discharge current, the velocity and the heat transfer coefficient of the ion wind were derived. In addition, the reliability of the developed correlations was confirmed by comparing them with the experimental results. Finally, the optimal design of the ion wind generator with the needle to parallel plate electrode arrangement for cooling electronic devices could be proposed in this study.
ð31Þ Conflict of interest
1
havg ¼ ReL 2
k L
ð150 6 ReL 6 2100Þ
ð32Þ
The experimental and calculated results of the Nusselt numbers of the ion wind using Eq. (31) by the Reynolds numbers are shown in Fig. 21. The average error rate of Eq. (31) was about 4.5%. The error rate was especially higher near the onset and the spark-over voltages than in the middle section. Natural convection and the velocity undulation generated errors at the onset and spark-over voltages. Near the onset voltages, natural convection had a dominant effect on the performance of the heat transfer, although the results of Eq. (31) ignored the effect of natural convection. In addition, the velocity undulation was observed as explained in previous section, which caused the large error rate near the spark-over voltages. Therefore, the ranges of the onset and spark-over voltage should not be considered as the operating conditions for the optimization of the ion wind cooling devices. The dotted line in Fig. 21 represents the local Nusselt numbers calculated by Eq. (17). The
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