A Two-Stage Electrohydrodynamic Gas Pump in a Rectangular Channel

SOTIRIOS J. TAMPOURIS, ANTONIOS X. MORONIS

Department of Electrical and Electronics Engineering,

University of West Attica,

250 Thivon & P. Ralli 12244, Egaleo,

GREECE

Abstract: - Electrohydrodynamic (EHD) fluid pumps generate physical flux in a dielectric fluid without using any

moving parts. The advantages of EHD pumps are implemented in a wide variety of applications especially when

miniaturization and/or noise absence are required, such as in cooling applications. Research efforts focus on

improving existing concepts of efficiency optimization. Researchers are recently considering the concept of

cascading stages, among other options. In this research, an experimental investigation of a two-stage wire-to-mesh

EHD air pump has been made, providing information on the air velocity generated and the electrical power

demand. Based on the testing results, a two-stage cascading EHD pump has significantly higher airflow velocity

and efficiency than the conventional single-stage design. The two-stage structure was found to preserve the

advantages of EHD pumping technology while being directly comparable in terms of EHD flow characteristics

with conventional mechanical fans of similar dimensions.

Key-Words: - Electrohydrodynamic (EHD) flow, EHD cooling, EHD pump, corona discharge, ionic wind, Finite

Element Analysis (FEA), wire-mesh electrodes.

Received: November 4, 2022. Revised: August 19, 2023. Accepted: September 29, 2023. Published: October 13, 2023.

1 Introduction

When a large potential difference is applied across

two asymmetric emitter-collector electrodes that are

submerged in a dielectric fluid, EHD effects result,

[1], [2]. Such combinations have the potential to

produce net flow, or "ionic wind," under specific

circumstances, which is attributed to the discharge

current flowing from a high voltage emitter towards a

grounded collector. Most of the research on the EHD

effect is focused on applications related to thrust and

fluid pumping, [3]. Numerous parametric research

studies have been released that evaluate different

electrode configurations, as EHD applications have

grown in popularity over the past decade, [6], [7] and

major attempts are being made to enhance their

general efficiency, [5], [8], [9], [10]. Nowadays the

most common methods of cooling electronic

components are mechanical fans and aluminum

heatsinks. Ηeatsinks require a large surface area to be

able to dissipate heat adequately. Characteristic of

the operation of mechanical fans is the noise, the

magnetic field, and the development of operating

temperature due to the moving parts. Two-stage EHD

pumps offer more reliable performance and are more

adaptive, according to new research, [11]. In, [18] the

authors presented a work on an Electrohydrodynamic

pump based on wire-to-mesh configuration for CPU

cooling. In this paper a comparison has been made

between single and two-stage pumps, showing the

benefits of the two-stage configuration. Also, a year

later, in, [19], scientific work on EHD flow

generation on a needle-to-ring configuration was

conducted. Scientists also explored the viability of

using EHD pumps. In, [20] the authors dealt with a

two-stage cascaded EHD gas pump showing the

benefits of the two-stage setup, while in, [21] the

performance of an Electro-hydrodynamic gas pump

fitted in a conical nozzle was evaluated, where the

applied voltage between Corona threshold and spark

over has been tested on different nozzle geometries.

The three nozzle configurations that have been tested

were found to perform differently depending on the

diameter ratios. In, [22], the authors study EHD

plasma thrusters for space applications, while

recently, in, [23], a study has been conducted on an

EHD pump comprising parallel plate electrodes with

good results. Additionally, experimental studies on

multi-stage air pumping arrangements under negative

corona discharge have been carried out with

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encouraging outcomes, [12]. Even though recent

studies have indicated that multi-stage electrode

layouts may hold great promise for enhancing the

effectiveness and efficacy of EHD devices, there

hasn't been much experimental research on this

subject.

The main goal of this work is to experimentally

evaluate the performance of a prototype two-stage

wire-to-mesh EHD air pump in a rectangular

channel, under a positive corona discharge, which is

a configuration that has not been studied in the

bibliography. The good performance and minimal

complexity of wire-to-plane arrangements, [3],

provide easy construction and lower costs. The wire-

to-mesh architecture is comparable to this particular

setup since the plane collector has been replaced by a

mesh made of multiple wires, which allows the air to

flow through it, while at the same time keeping the

electric field distribution almost similar to the wire-

plate configuration, along the gap between the

electrodes. On the other hand, positive corona

discharge is used because it is highly stable and

efficient, [13]. In the methodology section 2 that

follows, the overall design and the experimental set-

up of the prototype two-stage pump are presented,

along with the circuit that supplies the device with

high voltage. In section 3 the results of the obtained

simulations for the optimization of the geometrical

parameters of the prototypes and the experimental

measurements are presented, along with the physical

relationships that govern the phenomenon. Then a

comparison is made between a single-stage and a

two-stage EHD pump of similar size, showing the

clear advantages of the two-stage configuration.

Finally, in section 3.2 the two-stage prototype is

compared with other mechanical fans or alternative

EHD configurations found in the bibliography.

2 Methodology

The experimental two-stage EHD pump prototype

that is presented in this work is constructed by

cascading in series two wire emitter-mesh collector

sets, each maintaining a constant potential difference

between the corresponding emitter and collector. The

emitter electrodes are made of a thin wire stretched

across the opposite sides of a plexiglass rectangular

channel. The collector electrodes are placed opposite

to the corresponding emitters and consist of copper

wires forming a rectangular mesh, as shown in Figure

1.

Fig. 1: Experimental configuration of two-stage EHD

pump. E1 and E2 are the emitter electrodes, C1, C2

are the collector electrodes. The collector C1 and

emitter E2 are equipotential (shorted) and are

connected at the output of a high voltage divider with

input high DC voltage V so that C1 and E2 are held

at potential k.V, k being the division ratio of the

divider.

Parallel wires have been used instead of dense

mesh to minimize pressure drop at collectors C1 and

C2. A software simulation based on Finite Element

Analysis (FEA) has been conducted to optimize the

final geometrical dimensions of the EHD pump

prototype, assuming a distance of d=2 cm between

the two stages. The FEA analysis has been carried

out by using FEMM software, [24], to optimize

cross-sectional radii r, r` of the emitters and the

emitter-mesh gaps d1, d2, to achieve maximum

electric field intensity along the emitter-collector

gaps, for a given applied voltage V, as well as

maximum electric field volume energy density

around the electrodes, since the electric field is the

determining factor for the generation of ionic wind,

[2], [3], [15]. FEMM is a free electrostatic problems

solver, which has been used in previous works, [4],

[18], [20], and is based on well-known electric field

laws, to calculate the electric field.

The differential form of Gauss’ Law, defines that the

flux out of any closed volume is equal to the charge

contained within the volume



· D = ρ (1)

where ρ represents charge density.

Secondly, the differential form of Ampere’s law



×E = 0 (2)

Displacement and field intensity are also related to

one another via the constitutive relationship

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D = ε E (3)

where ε is the electrical permittivity of the medium

where the electric field is applied.

The software employs the scalar potential V

distribution in space, which is related to the electric

field intensity according to the formula:

E = −



V (4)

Since the vector identity ×ψ = 0 is valid for any

scalar ψ, Ampere’s loop law (2) is automatically

satisfied. Substituting into Gauss’ Law and applying

the constitutive relationship yields the second-order

partial differential equation

−ε



2V = ρ (5)

which applies over regions of homogeneous ε.

FEMM solves (5) for voltage V over a user-defined

domain with user-defined Dirichlet boundary

conditions, [24]. Typical boundary conditions in this

work have been the experimentally controlled

constant voltage values at the electrodes of the EHD

pump configuration.

The prototype pump has been subsequently built and

tested, to experimentally evaluate its overall

performance [24].

2.1 Experimental Setup

The necessary high voltage has been provided by a

Matsusada Precision W series variable High-Voltage

0-40kV generator. A high-voltage shielded DC cable,

supplies the EHD pump for the generation of the

electrical wind flow, after the onset of the corona

discharge current. To ensure that each stage of the

two-stage pump receives the necessary fraction of the

total voltage V a high voltage divider has been used.

High voltage measurements on the prototype pump

have been performed with an accuracy of 1% by

using a Peak Tech 2010 DMM multimeter along with

a Coline HV40B 1000:1 high-voltage probe. A

Thurlby 1503 microammeter with a sensitivity of

1nA has been used to acquire corona current

measurements. To measure the generated airspeed, a

Testo 405 hot wire anemometer (5% accuracy) has

been installed at a 2 cm distance from the grounded

collector C2 at the pump's output. Figure 2 shows the

experimental setup that has been used to evaluate the

pump prototype. Regarding the rectangular channel

dimensions, the flow cross section is 5cm high and

10cm wide and the overall channel length is 20cm.

Fig. 2: a) Measurement equipment configuration and

experimental set-up for two-stage EHD pump, b)

single-stage configuration. The rectangular channel

outer limits are also shown.

3 Results and discussion

According to the optimization process carried out by

the FEMM software to determine the required

geometrical characteristics of the presented EHD

pump configuration electrodes, a constant distance of

d=2cm and various Ni-Cr wire combinations for the

construction of emitters and collectors have been

examined. The resulting optimized geometric

configurations for the single-stage and two-stage

prototypes are given in Table 1 and Table 2,

respectively. These configurations ensure maximum

electric field intensity in the vicinity of the emitters

while, at the same time, retaining high spatial energy

density between the emitter-collector electrodes for a

given applied voltage difference. It should be noted

that in the two-stage configuration, the high voltage

division ratio k, according to Figure 1, is quite

important. For example, supposing that both emitters

have identical cross-sections (r=r`) a division ratio of

k=0.5 divides equally the total applied voltage V

between the two stages, but then the electric field

strength around emitter E2 is expected to be lower

than the corresponding electric field strength around

emitter E1, due to the deformation of the electric

field caused by collector C1 which is shorted with

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E2, as shown in Figure 1. To ensure that both stages

reach the threshold field for air-ionization

simultaneously, thus maximizing electric wind flow,

a suitable combination of electrode geometry

parameters and a suitable potential division ratio k is

required. As shown in Table 2, in this study a

combination of k=0.5 with different wire selections

for E1 and E2 construction, with r=90 μm and r`=30

μm, ensures that the electric field strength in the

vicinity of both emitters reaches almost identical

values, for a given applied potential V. This has been

verified by FEMM simulations, with a fine 10 μm

mesh and a maximum simulation error of 1.e-008. This

number specifies the stopping criterion for the linear

solver [24].

The electrical field intensity (E) and voltage (V)

distribution along the airflow axis, have been plotted

on a fine step of 10μm from simulations. This is

shown in Figure 3 for the two-stage configuration

according to Table 2. In addition, similar curves for

the single-stage EHD pump prototype of Table 1 are

given in Figure 4.

Fig. 3: The distribution V along the airflow axis for

the applied voltage of 17 kV across E1 and C1, while

E2 and C2 are kept at 8.5 kV (k=0.5).

Fig. 4: FEMM results for the single-stage EHD pump

for a voltage difference V of 10kV between the

emitter and collector.

Figure 5 shows the potential distribution in the

space between the electrodes in both the first and

second stages. The areas with red color have with

highest levels of potential in contrast to areas of light

blue color the level of the potential in the space is at

zero levels. Accordingly, Figure 6 shows the

distribution of the electric field. The value of the

electric field strength at emitter E1 is 1.92x107 V/m,

while the corresponding value at emitter E2 is

1.82x107 V/m.

Fig. 5: FEMM results for the electric potential

distribution in a two-stage configuration.

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Fig. 6: FEMM results for the electric field strength

distribution in a two-stage EHD pump.

3.1 Experimental Evaluation Results

The experimental setup shown in Figure 2 has been

used to evaluate the constructed EHD pump

prototypes in terms of the generated air velocity v

(m/s) at various voltage levels V (kV). The total

current flow I(μA) that is provided to the EHD pump

was also recorded. Throughout the experiments, the

room temperature averaged 24,3 °C, ranging from

19,6°C to 29,1°C. The relative humidity (RH)

averaged 43,6% ranging from 35,2% to 52,1%. In

terms of breakdown voltage, the two-stage

arrangement was limited to 41 kV, which was the real

measured maximum output of the high-voltage

generator, slightly above the 40 kV maximum output

rating provided by the generator specs.

The electric power consumption by the EHD

prototypes PE (W) has been calculated as:

 =  ·  (6)

The mechanical output power PW of the generated

airflow has been calculated as:

PW = 

      (7)

where A(m) is the rectangular channel’s cross-

section, ρ is the air density (1,17 kg/m3 at 29 °C) and

v (m/s) is the wind velocity.

Finally, the EHD pump’s overall efficiency, n, is

calculated with the ratio

 =  (8)

When ionized air molecules drift toward the

collector, corona discharges occur in the vicinity of

the emitter. Corona current is defined by

Townsend’s, [1], formula:

 =  󰇛

V0

)2 (9)

where I is the corona discharge current in µA, V is the

applied voltage in kV, Vo is the ionization inception

voltage in kV and k represents a constant term in

µA/2. According to the literature, k depends on

several variables, including electrode separation

distance, emitter and collector radius, ion mobility,

and dielectric permittivity, [1]. In this case, k

increases also with collector radius, and k and Vo

values, as given in Table 3 have been determined by

a least square fitting method on the current

experimental results. The study, [14], found through

a parametric study that the speed of the airflow is a

function of the square root of the Corona current

multiplied by an empirical constant term, according

to the expression:

v =  (10)

where v (m/s) is the wind velocity, I (μA) is the

Corona current in μΑ and K is a constant term. The

experimental results for the corona current in the

single-stage configuration are given in Figure 7.

Fig. 7: Experimental and theoretical corona discharge

current with the applied voltage in the single-stage

EHD pump prototype with r=90m, R=300μm,

a=1cm, and d=6cm.

The results for the two-stage configuration are

shown in Figure 8.

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Fig. 8: Two-stage pump experimental and theoretical

curve of corona current variation with the applied

potential difference, where the geometrical

parameters of the pump prototype are r=90μm,

r’=30μm, R=300μm, a=1cm, d1=d2=d3=2cm.

Table 3 shows ionization inception voltage V0

with collector radius R and emitter radius r, and the

constant k, according to equation (9), which equals

0.13 for the two-stage EHD configuration and 0.30

for the single-stage configuration, both of identical

overall length d=6cm, to obtain comparable results.

Fitting curves were drawn according to equation

(9) and the fit was very close. The inception voltage

was 17kV for the two-stage configuration and 22kV

for the single-stage configuration. In Figure 9 the

variation of air flow velocity v in relation to the

corona discharge current I is shown. The

experimental measurements were acquired from the

two-stage configuration and a comparison was made

with the theoretical curve, obtained from the equation

(10).

Fig. 9: Two-stage EHD pump experimental

measurements v=f(I).

The constant term K for the theoretical curve of

wind velocity, according to equation (10) was 0.24.

Also, the change of ionic wind velocity v with

applied voltage V has been examined, with the results

shown in Figure 10 for both EHD pump prototypes.

Fig. 10: EHD air velocity with voltage, on both

single-stage and two-stage EHD pumps.

In Figure 10 becomes clear the difference in the

ionization inception voltage between the single-stage

and two-stage prototypes, which is approximately

22%. The two-stage pump produces significantly

higher air velocity at the same voltage level than the

single stage, which is a clear advantage.

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Fig. 11: EHD air velocity v variation with electrical

input power according to equation (6).

This is consistent with the air velocity results

according to the input power usage, as given in

Figure 11. It is clear that for the same overall

dimensions, the two-stage EHD pump is more

efficient than the single-stage EHD pump. Moreover,

the operation of the single-stage configuration is

unstable because there is an increased risk of

undesirable breakdowns. Additionally, the results for

the pump efficiency n, as calculated by applying

equation (8) to the experimental data, are given in

Figure 12. Accordingly, the efficiency of the two-

stage EHD pump did not exceed 4.48%, while the

single-stage pump corresponding value had been

0.65%, which shows the advantage of the two-stage

configuration.

Fig. 12: Efficiency to air- velocity variation.

3.2 Mechanical Fans and other EHD

Configurations Compared with the Prototype

Two-Stage EHD Pump

A consequence of the operation of electronic

components is the generation of heat. This heat must

be reduced in intensity or transferred to the

environment, outside the device. In this case, the

most widely applied solution for cooling applications

is the choice of mechanical fans. Some advantages

and disadvantages characterize this selection. A big

disadvantage is the operating noise, the large air

outlet surface, and the limitations in the design when

they have to be placed in narrow spaces as in laptops,

where a quiet operation is also required. Other

disadvantages are the presence of moving parts,

which require lubrication, and the production of

additional heat generated by the operation of the

moving parts. Advantages include low operating

voltage typically 12v and high air speeds. EHD

pumps also function as thrusters in space

applications. Besides, EHD has become a well-

established technology in propulsion devices for

small satellites, such as CubeSats, [16], or food

drying, [17].

An overall comparison of the presented two-

stage EHD pump prototype with other high-quality

mechanical fans or alternative EHD configurations

found in the bibliography is given in Table 4.

The mechanical fans shown in the table are of

similar dimensions, with a diameter ranging from

80mm to 120 mm. The experimental results have

shown that in fact, the prototype is capable of

directly competing with mechanical fans in free air

while providing comparable energy efficiency and

virtually zero noise, which is an important aspect for

certain, applications.

4 Conclusion

Finite element analysis simulations have been used

to optimize the geometrical characteristics and,

consequently, the overall efficiency of a two-stage

wire-to-mesh EHD air pump, where the two stages

are cascaded in a series configuration. Since the

electric field is the governing factor determining the

produced air wind flow between the electrodes of the

EHD two-stage pump, an effort has been made to

maximize the electric field strength by proper design

of the electrodes, while at the same time, maintaining

the applied high voltage at the lowest possible value.

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The presented two-stage prototype has been

experimentally tested in comparison with a single-

stage prototype of equal length. The results have

shown the clear advantages of the two-stage

configuration over the single-stage configuration, in

terms of the lower required threshold voltage for air-

wind onset, and the higher air flow velocity and

higher overall efficiency as a ratio of the net

mechanical flow power output to the required

electrical power input.

It has been also shown that in a direct

comparison with commercial fans of similar

dimensions or other EHD pump configurations found

in the bibliography, the proposed prototype two-stage

pump is quite competitive.

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflict of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_

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