A three-dimensional numerical model that couples the electric field, velocity field, and temperature field is developed based on the commercial code COMSOL Multiphysics. The influences of several factors on convective heat transfer on a heated plate in the electric field generated by a needle electrode are observed. The factors are the applied voltage, the distance between the two electrodes, and the size of the ground plate. The results show that applied voltage is one of the most important factors for the convection heat transfer. The convection heat transfer efficiency significantly increases with the improvement of the applied voltage. From the perspective of the model size, the decrease of the distance between two electrodes and the size of the plate could improve the average convection heat transfer coefficient. Smaller ionic wind device needs lower applied voltage and less electric energy to obtain the same average convection heat transfer coefficient as the bigger one, which provides the theoretical basis for the potential of miniaturizing the ionic wind cooling device.
Air is widely applied as heat transfer medium due to its abundant amount and safety, but at the same time it is also a medium with poor heat transfer performance. Great efforts have been made for the enhancement of heat transfer for air. A method called ionic wind cooling which introduces the electric field to the enhancement of air convection heat transfer attracts many researchers’ interests recently. Ionic wind cooling is a technology based on the electrohydrodynamics (EHD) theory. By applying high-voltage electric field between a sharp electrode and a grounded surface in the air, molecules in the air are ionized and the positive ionized air molecules are accelerated by the electrostatic force. Then they transfer their kinetic energy to the neutral air molecules by collisions, thus leading to a movement of airflow. The advantages of ionic wind cooling include convenient control, low energy consumption, no moving parts, long lifespan, high potential of integration, and miniaturization.
In the past few years there have been many studies related to the flow and heat transfer characteristics of ionic wind and the development of ionic wind or EHD pumps. Moreau and Touchard [
To further strengthen the ionic wind, some researchers focus on the utilization of multielectrodes or multistage discharge structures. Huang et al. [
Given the above, it can be seen that a major part of studies is based on experiment tests, which can provide reliable test data, but is costly and time consuming. With the development of computer technologies and multiphysics simulation methods, numerical simulation begins to play a more important role. Compared to experiment, numerical simulations can provide more detailed information at much lower cost. The numerical simulation methods for the flow and heat transfer characteristics of ionic wind are still in progress. Most of the numerical studies mentioned in the literature above adopt two dimensional models, which are far away from the practical situation. The numerical methods of some researches are not clearly illustrated, especially for the determination of the space charge. Moreover, some simulation results even lack validation with experimental data. All of these motivate the present studies.
In this paper, a 3-dimensional needle-plate model will be established by using commercial code COMSOL Multiphysics. The establishment of the numerical model and the numerical method will be given in details. To verify the reliability of the numerical method, the numerical results will be compared with the experimental results from open literatures. The influence of different factors, including the voltage, the distance between the two electrodes, and the size of the ground plate on the heat transfer, will be discussed.
Governing equation for electric field is as follows:
The current continuity equation is
The three terms on the right side of the equation are expressed as charge conduction (the ion movement relative to the overall flow under the electric field), charge convection (charge movement generated by the air flow), and charge diffusion (thermal motion of charge), respectively. The ionic mobility
As the speed of ions is considerably higher than the speed of air flow, the influence of air flow on ionic movement could be ignored; that is, the influence of air velocity on current density could be ignored. Furthermore, the diffusion coefficient of ionic is so small that it can be also ignored. Thus, the electric current density in present study can be simplified as
The mass conservation equation is
The momentum equation is
The first term on the right side of the equation is Coulomb force. The second term is called dielectrophoretic force generated by the change of dielectric constant space. The third term is electrostrictive force, which is the gradient force due to the change of the dielectric constant and is caused by the different density. In this paper the working fluid is air, and among all the forces the Coulomb force is the majority. The electric field force can be simplified as
The energy equation is
Generally, there are two ways to determine the distribution of space charge in the simulation of ionic wind. The first one is to calculate the ionization zone (close to the corona electrode and in which air ionization occurs) and drift zone (located between the ionization zone and the ground electrode) at the same time and then analyze the motion of microscopic particle to calculate the detailed distribution of space charge. The second one is to calculate the drift region only by assuming a charge density value at the interface crossing the ionization zone and the drift area. The latter method is mostly adopted in numerical studies of ionic wind for the reason that, in the area of convection heat transfer, the major task is to investigate the macroscopic heat transfer phenomena in the drift region. Moreover, this kind of method can also avoid the difficulties in the simulation of ionization zone.
Careful attention needs to be paid on how to determine the charge density at the interface crossing the ionization zone and the drift area. In this paper, a method of try and error iteration is used. Firstly, a guessed charge density at the external surface of ionic zone is given to calculate the current, and the calculated intensity of electric current should be around the level of
In many cases, the experiment data is not available in advance and it is costly and time-consuming to obtain experimental data for the validation of every simulation case. Therefore, an empirical formula is adopted to calculate the current for needle-plate discharge structure when the experimental data are not available. The empirical formula is as follows [
According to Peek’s semiempirical formula [
The solution procedure of this paper is shown in Figure
Solution procedure.
The experimental model (Design A) in [
Calculation model.
The boundary conditions are shown in Figure
Boundary conditions of validation model.
Electrostatics | Charge transport | Fluid dynamics | Heat transfer | |
---|---|---|---|---|
A | Voltage applied | Surface charge density | No slip | Thermal insulation |
B | Grounded | Zero diffusive flux | No slip | Constant temperature |
C | Zero charge | Zero diffusive flux | Neutral pressure | Thermal insulation |
D | Zero charge | Zero diffusive flux | Neutral pressure | Thermal insulation |
Positions of boundaries.
Assumptions are made in this paper as follows according to the numerical studies done by other authors in the past [
The physical parameters used in the simulation are shown in Table
Physical parameters.
Parameters | Value |
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|
|
|
|
|
|
|
|
|
1.007 kJ/(kg·K) |
|
0.027 W/(m·K) |
By adjusting the density of grids in COMSOL Multiphysics, five grid systems with 36446, 71682, 133341, 336238, and 823603 cells are adopted for calculation. The difference in the average heat transfer coefficient between last two grid systems is around 1%, as shown in Figure
Grid independence test.
Grid system and gird quality check.
The electrostatic field distribution, space charge distribution, velocity field distribution, and temperature field distribution can be found in Figure
Results of the simulation (
Distribution of voltage
Distribution of space charge
Distribution of velocity
Distribution of temperature
The current value based on the simulation results can be derived by
Figure
Comparison of current.
The local convection heat transfer coefficient is defined by
The average convection heat transfer coefficient is expressed as
As shown in Figure
Comparison of heat transfer.
The physical models discussed in following parts are similar to the validation model. Based on the consideration of ongoing trends of microminiaturization of the ionic wind devices, smaller plate is employed in the simulation. Besides, considering the convenience of manufacture, the radius of the needle electrode is at the level of micrometer scale. Most of the boundary conditions of the models are the same as the validation model. The only difference is that the constant temperature condition is changed to constant heat flux condition for the plate, and the heat flux is
In this section six different voltages are investigated, including 4 kV, 4.5 kV, 5 kV, 6 kV, 7 kV, and 8 kV. The geometric dimension of the plate is 5 mm × 5 mm. The distance between two electrodes is 5 mm. And the radius of the needle electrode is
As shown in Figure
Effect of voltage on velocity and heat transfer.
In this section the effect of the distance between the needle electrode and the ground electrode on heat transfer will be discussed. Five different distances including 3 mm, 4 mm, 5 mm, 6 mm, and 7 mm are considered. The geometric dimension of the plate is
The change of the average convection heat transfer coefficients with the variation of the distance between two electrodes is shown in Figure
Effect of distance between two electrodes on heat transfer.
Effect of distance between two electrodes on current.
Effect of distance between two electrodes on velocity.
With fixed applied voltage (7 kV), fixed distance between two electrodes (4 mm), and fixed radius of the needle electrode (
Effect of plate area on velocity and heat transfer.
It can be found that the heat transfer coefficient decreases with the increase of the plate area (
Variation of local heat transfer coefficient along the central line (
In this section, the applied voltage is kept as 7 kV, and the ratios between the length of the square plate and the distance of two electrodes are 0.5, 1.0, and 1.5, respectively. As shown in Figure
Effect of the ratio between the length of the plate and the distance of two electrodes on heat transfer.
In Figure
Effect of different combinations of the distance between two electrodes and the voltage on heat transfer.
Electric power consumption and operation voltage of devices with different distances between two electrodes and fixed heat transfer enhancement ratio (
According to present study, the following main conclusions can be reached. The voltage is one of the main factors for the convection heat transfer under electric field, and the effectiveness of heat transfer is increased with the improvement of the voltage. The effectiveness of heat transfer increases with the diminution of the distance between the two electrodes and the area of the grounding plate. The smaller size is better for local ionic wind cooling under the same conditions. The smaller size ionic wind cooling device needs lower operation voltage and electric energy consumption to get higher heat transfer capacity. This provides an important theoretical support for the potential of the miniaturization of ionic wind devices and the application of ionic wind devices in the miniaturized and portable equipment.
Area, mm2
Space charge diffusion coefficient
Electric field intensity,
Breakdown electric field intensity,
Electric force, N
Current, A
Current density,
Length, mm
Electric power, W
Joule heat, W
Radius, mm
Temperature, K
Velocity, m/s
Voltage, V
Constant-pressure specific heat,
Distance between two electrodes, mm
Heat transfer coefficient,
Pressure, Pa
Space charge density,
Heat flux, W/m2.
Heat transfer enhancement ratio
Dielectric constant,
Heat conductivity coefficient,
Ionic mobility,
Kinematic viscosity,
Density,
Value of initial
Value under electric field
Value of EHD
Value of average
Value of air
Value of calculation
Electricity filed, electrode
Value of experiment
Value of natural convection
Value of ground electrode
Value of needle electrode
Value of numerical
Local value.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (no. 51206129), Fok Ying Tung Education Foundation, and the Fundamental Research Funds for the Central Universities.