Electromagnetic boundary layer.

In summary, the conversation discusses the idea of using electromagnetic control to prevent flow separation on an airfoil surface. The Von Karman integral equation is mentioned as a method for avoiding flow separation, and the possibility of using a DC electrical battery to generate a potential field above the surface is proposed. The speaker is unsure of the equations that govern this process and asks for mathematical insight and clarification on the behavior of electrical charges in this scenario. The conversation ends with a request for a non-trivial solution to the problem.
  • #1
Clausius2
Science Advisor
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I want to comment with you this imaginary problem. I have not formulated it yet. But I would want your qualitative opinion about this. It is not anything new or revolutionary, because electromagnetic control of boundary layers have been proved yet. But I would want to understood mathematically the process. I hope this thread have more success than others usually un-answered, I'm starting to feel myself "understood". I am thinking seriously of moving into differential equation forum. Last times I have more success there. :biggrin: :biggrin:

There's a free air stream subsonic (Ma<<<1) over a plain surface. The initial data line is u=uo; v=0. (stream parallel to surface). Well, surely you know that it exists some methods for avoiding flow separation. One of them was improved by Von Karman, he proposed a flow suction trough the porous wall of the surface. Thus, it can be demonstrated by the Von Karman integral equation that such suction pushes forwards the critical point of separation.

After this introduction, and under the hypothesis I have no idea of Magneto-Hidrodinamics at all (I'm only 22, sure it will be time for it), let's imagine next experiment. The surface, which would be an airfoil one, is connected to a DC electrical battery. One of its electrodes, the positive one, is connected to mass, and the other is connected to airfoil surface. Then, the complete airfoil has a negative potential respect to mass. Because of Maxwell Equations, a potential field V is generated over the infinite semiplane above the surface. If fluid freestream has electrical conductivity, its electrical charges would sense such potential, and eventually positive charges would experiment an atraction force to the airfoil surface, avoiding at first glance the flow separation.

First of all, I'm not able to formule the problem. Since I do not understood which equations govern this event, I am not capable of judge its behaviour. Is the electrical field generated by the surface being perturbated by the flow?. I mean, does it exists a convective transportation of electrical field or something like this?. It can be resumed if I'm allowed to use the Laplace equation (derived from 1st Maxwell equation) in order to solve the static electrical potential field. And another question is: the air would be ionized passing over the surface, but what occurs with negative charges?. They would esperiment a repulsion force, wouldn't they?.

I want to simulate this process numerically, I think maths here are easy enough, because integration of the Parabolized Navier-Stokes equations are not a problem yet, but I'm not capable of seeing the link between Navier-Stokes and Maxwell equations. Surely there is some coupling between them.
 
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  • #2
Hmm... to start with - don't really understand what you're talking
about and what you're asking and why all the math.

I'll try to answer something, charges - electrons can be released from
a surface when they are supplied with enough energy- overcome
a certain potential barrier. This can be achieved if there's a high
enough potential drop - which happens in a conductor, and air
is also a conductor, though a poor one, and due to surface impacts
which provide enough energy for the charges to escape (could
also be chemical reactions which lower the potential barrier).

Live long and prosper.
 
  • #3
drag said:
Hmm... to start with - don't really understand what you're talking
about and what you're asking and why all the math.
.

The fact of I'm saying something with no sense is perhaps one of the solutions of my problem. But to be honest, I think this is the trivial solution. I hope for a non-trivial solution.
 
  • #4
What IS the problem ? You need to clarify.
 

What is an electromagnetic boundary layer?

The electromagnetic boundary layer refers to the region near a surface where the electromagnetic field experiences significant changes. This can occur due to interactions with the surface itself or with other objects in close proximity.

How is the electromagnetic boundary layer different from the physical boundary layer?

The electromagnetic boundary layer is a separate concept from the physical boundary layer. While the physical boundary layer refers to the region where fluid flow experiences changes near a surface, the electromagnetic boundary layer specifically deals with changes in the electromagnetic field near a surface.

What factors affect the thickness of the electromagnetic boundary layer?

The thickness of the electromagnetic boundary layer can be influenced by a variety of factors, including the electrical conductivity and permittivity of the surrounding medium, the strength and frequency of the electromagnetic field, and the geometry of the surface and nearby objects.

What is the significance of the electromagnetic boundary layer in practical applications?

The electromagnetic boundary layer plays a crucial role in many practical applications, such as in the design of antennas and sensors, electromagnetic interference shielding, and heat transfer in electronic devices. Understanding and controlling the electromagnetic boundary layer can lead to more efficient and effective designs.

How is the electromagnetic boundary layer studied and measured?

The electromagnetic boundary layer is typically studied through numerical simulations and experimental measurements using techniques such as boundary element methods and electromagnetic probes. It can also be characterized through theoretical models and analytical solutions for simplified cases.

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