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Tutorial : Plasma Actuators and their numerical modeling

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Old   February 7, 2022, 06:08
Post Tutorial : Plasma Actuators and their numerical modeling
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* Introduction
The purpose of this post is not to ask questions. In this post, we are going to get acquainted with "plasma actuators" and talk about their numerical modeling.
I have asked questions here several times before, but unfortunately no one answered them. Recently, it seems that no one is willing to share their knowledge with others. So I decided to share what I know here because it might be useful for some people in the future. I apologize in advance for my English.

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* Flow Control
The purpose of flow control is to make desirable changes in the fluid flow and improve its behavior. From time immemorial, there have been various methods for controlling water flow and air flow; Including water canals, windbreaks in farms, windmills, etc.
Nowadays, in most vehicles and aerodynamic systems and fluid machines, flow control methods are used to control vortices and control current separation and noise reduction.

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* Modern methods of flow control
1- Active methods: These methods require energy or matter consumption; Including plasma actuators, synthetic jets, moving or vibrating surfaces, etc.
2- Passive methods: These methods do not require the consumption of energy or matter and are usually fixed and permanent; Including vortex generator, porous surface, groove, flow deflector, etc.
3- Combined methods: Simultaneous use of active and passive methods.

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* Plasma Actuators
They are one of the modern methods of flow control that work based on electric discharge. These actuators consist of two electrodes, cathode and anode, and are divided into different types based on the geometry and arrangement of the electrodes:
1- Corona discharge actuator
2- sliding discharge actuator
3- Dielectric barrier discharge (DBD) actuators
DBD actuator is the simplest, newest and most widely used type of plasma actuators, which consists of two flat electrodes. A dielectric insulator is placed between the two electrodes.
These actuators are mounted on aircraft wings, turbomachines blades or on the surface of vehicles and air flow passes over these actuators.
When the actuator is turned on, the electric field between the two electrodes ionizes part of the air above the electrode (boundary layer air) and creates plasma. The actuator then exerts a force on the plasma that increases the momentum of the flow in the boundary layer, thereby controlling the flow separation and vortices. The unit of this body force is N/m^3 and is added to the Navier-Stokes equations.

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* Numerical modeling of plasma actuator
Now suppose we want to simulate a DBD plasma actuator on a flat plate, cylinder or an airfoil in a numerical study (CFD) in ANSYS FLUENT software. There are several numerical models for plasma actuators, the most famous of which is Shyy et al. model. In this model, body force is applied in a triangular area:



p907887_.png

In this model, the body force components of the plasma actuator are defined as follows:



20220207_144111_1993772477.jpg

In the above relations, all parameters are constant except E. E is an electric field and is calculated according to the following equation:



20220207_144237_1581121446.jpg

The values of the parameters and relationships are in the following reference:

W. Shyy, B. Jayaraman, and A. Andersson; Modeling of glow discharge-induced fluid dynamics; JOURNAL OF APPLIED PHYSICS; VOLUME 92, NUMBER 11.

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* UDF
An example of a suitable UDF for a plasma actuator is as follows:

......................................
#include "udf.h"
DEFINE_SOURCE(plasma,c,t,dS,eqn)
{
real pos[ND_ND];
real source, x, y;
real m, b, k1, k2, E0, k3, Fx;
C_CENTROID(pos,c,t);
x=pos[0];
y=pos[1];
m=...
b=...
k1=...
k2=...
k3=...
E0=...
E=E0-k1*x-k2*y
Fx=k3*E


/* apply source term to triangular region */
/* y=mx+b is the lineAB equation */

if ((y>=0)&&(y<=(mx+b))&&(x>=0)&&(x<=((y-b)/m)))
{
source=Fx
dS=0
}
else
{
source=0
dS=0
}
C_UDMI(c,t,0)=source;
returne source;
}
......................................

And a similar UDF for Fy. After compiling the UDF, apply it to the plasma actuator from the following path:

cell zone condition >> triangular zone >> source terms >> x-momentum & y-momentum >> UDF


If anyone has a suggestion to complete this article, it could be useful for future researchers.
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