Vortex Panel Method derivation

In summary, the conversation discusses the search for resources on the vortex panel method, specifically the derivation of the fundamental equations and the equations in a more usable form. The individual also mentions finding a book that covers panel methods and techniques, and asks for help in obtaining the numerics for a specific program.
  • #1
ChrisHarvey
55
0
Hi,

Can anybody tell me where I can find the complete derivation of the vortex panel method (book / webpage)? It's easy enough to see where the fundamental equation comes from, but completing the integration etc. to get it in the form of influence coefficients is beyond me. I have the solution, but no maths or explanation to go with it and I haven't found anything on the net.

Thanks,
Chris
 
Engineering news on Phys.org
  • #2
In case you're wondering exactly what equations I'm talking about, I've attached them to this post. Problem.GIF shows the fundamental equations. Solution.GIF shows the equations in the more usuable form, the derivation of which I can't find.
 

Attachments

  • Problem.GIF
    Problem.GIF
    3.6 KB · Views: 678
  • Solution.GIF
    Solution.GIF
    18 KB · Views: 740
  • #3
If anyone's interested, or somebody later digs up this topic, I've found a book that covers many different panel methods and techniques including the linear vortex panel method I mentionned above (different approach though to solving): "Low speed aerodynamics: from wing theory to panel methods" (Katz & Plotkin). It was very hard to get hold of, but was worth the effort.
 
  • #4
ChrisHarvey said:
In case you're wondering exactly what equations I'm talking about, I've attached them to this post. Problem.GIF shows the fundamental equations. Solution.GIF shows the equations in the more usuable form, the derivation of which I can't find.

how these equations are derived? anyone who can put these here?
 
  • #5
Hi All ,

Currently , i m using xfoil for sinmulation but i need the numerics of xfoil - viscous; vortex panel method with boundary layer analysis. Can anyone share with me

cxfoil
 

1. What is the Vortex Panel Method and how is it used in aerodynamics?

The Vortex Panel Method is a mathematical approach used in aerodynamics to analyze and predict the airflow over a three-dimensional body. It is based on the concept that the flow around a body can be represented by a series of vortex panels that interact with each other to create a net flow. This method is commonly used in the design and analysis of aircraft and other aerodynamic structures.

2. How is the Vortex Panel Method derived?

The Vortex Panel Method is derived from the fundamental equations of fluid dynamics, namely the Navier-Stokes equations. These equations are solved using numerical methods, such as the boundary element method, to obtain the distribution of vorticity along the surface of a body. From this, the velocity and pressure fields can be calculated to determine the aerodynamic forces and moments.

3. What are the assumptions made in the derivation of the Vortex Panel Method?

The Vortex Panel Method makes several simplifying assumptions, including: the flow is steady, incompressible, and inviscid; the vorticity is concentrated on the surface of the body; and the flow is two-dimensional. Additionally, it assumes that the vorticity distribution is constant along each panel and that the panels are aligned with the local flow direction.

4. What are the limitations of the Vortex Panel Method?

While the Vortex Panel Method is a useful tool for analyzing the aerodynamics of simple bodies, it has several limitations. It cannot model separated flow, viscous effects, or complex geometries. It also assumes that the flow is two-dimensional, which may not be accurate for some real-world scenarios. Additionally, the results obtained from this method are sensitive to the panel distribution and the angle of attack.

5. How does the Vortex Panel Method compare to other aerodynamic analysis techniques?

The Vortex Panel Method is a relatively simple and computationally efficient approach compared to other techniques, such as computational fluid dynamics (CFD) and wind tunnel testing. However, it is less accurate and cannot provide detailed information about the flow field. As such, it is often used in conjunction with other methods to obtain a more comprehensive analysis of the aerodynamics of a body.

Similar threads

Vortex Lattice Method - can anyone help?
    • Mechanical Engineering
Replies
1
Views
3K
Calculating Where to Push to Straighten a Rod
    • Mechanical Engineering
Replies
5
Views
2K
I Resources on the Derivation of generalized Stokes' theorem
    • Differential Geometry
Replies
11
Views
385
Antisymmetric modeling for panel method solver
    • Mechanical Engineering
Replies
1
Views
3K
Formula derivation connecting vertical water flowrate & horizontal distance moved by a suspended sphere
    • Introductory Physics Homework Help
6
Replies
207
Views
3K
I Derivation of normal Zeeman-Effect
    • Quantum Physics
Replies
5
Views
509
I Derivatives of Standard Functions
    • Calculus
Replies
17
Views
1K
Linear-Strength Vortex Unsteady Panel Method (2D)
    • Aerospace Engineering
Replies
2
Views
4K
Courses Math Methods Vs. Analysis Track
    • STEM Academic Advising
Replies
1
Views
1K
Electronics Using photos for project front panel labels/artwork
    • DIY Projects
Replies
30
Views
4K

Hot Threads

Recent Insights

Back
Top