Incompressible Potential Flow Analysis Using Panel Method

Incompressible Potential Flow Analysis Using Panel Method

ShahNor Basri, Norzelawati Asmuin & Aznijar Ahmad Yazid

Universiti Putra Malaysia

Jabatan Kejuruteraan Aeroangkasa

Fakulti Kejuruteraan,

Universiti Putra Malaysia, 43400 UPM SERDANG, Selangor D E, Malaysia.

kaa@eng.upm.edu.my

ABSTRACT

Incompressible potential flow problems are governed by LaplaceЎ¦s equation. In solving linear, inviscid, irrotational flow about a body moving at subsonic or supersonic speeds, panel methods can be used. Panel methods are numerical schemes for the solution of the problem. The tools at the panel-method user's disposal are the representation of nearly arbitrary geometry using surface panels of source-doublet-vorticity distributions, and extremely versatile boundary condition capabilities that can frequently be used for creative modeling. Panel-method capabilities and limitations, basic concepts common to all panel-method codes and different choices that were made in the implementation of these concepts into working computer programs are discussed.

Keywords

Panel method (fluid dynamics), incompressible potential flow, application programs (computer), computational fluid dynamics.

INTRODUCTION

Incompressible inviscid flow is governed by LaplaceЎ¦s equation. An extremely general method to solve this equation is the panel method. The flow may be about a body of any shape or past any boundary. Almost any boundary conditions, not just due to the fluid flow, can be solved. For 2-dimensional problems, the profile is approximated by a many-sided inscribed polygons. For 3-dimensional cases, a flat quadrilateral elements are used instead. The name Ў§panel methodЎЁ derived from these treatments of the body shape.

Proper design of an airfoil requires an accurate prediction of the pressure distribution. Initially, thin-airfoil theory is used to analyse or design airfoils. However, due to its deficiencies for multi-element airfoils, this theory is not much used these days. Among the shortcomings of this theory is the inability to take into account the effect of thickness distribution on the lift and moment coefficients as well as the results at areas nearer to the stagnation points are not good.

After TheodorsenЎ¦s work on single-element airfoil problems using a semi-analytic method in the 1930s, more work was performed to produce even more accurate prediction of pressure distributions on airfoils. These works are based on the distributions of sources and vortices or doublets. In order to avoid the inaccuracies of the thin-airfoil theory, the body surface must satisfy the flow-tangency conditions without approximations. Additionally, the singularities are distributed on the body surfaces rather than any other line within the body or the chord line. This technique could be used to treat any airfoils, including multi-elements airfoil to any desired accuracy and could also be extended to handle three-dimensional flows.

The methods of approximating the body surfaces by a collection of Ў§panelsЎЁ, are aptly named ЎҐpanel methodsЎ¦. There are various ways in setting-up this method. Using any combinations of sources, vortices or doublets the types of singularities used can be varied. The pioneering work using sources and vortices were conducted by Hess and Smith.

Computational work on fluid dynamics requires the calculation for the entire 3-dimensional field about the body. However, the panel method requires only calculation over the surface of the body when handling 3-dimensional field. This reduces the calculation, hence lowering computing time.

INCOMPRESSIBLE POTENTIAL FLOW

An inviscid, incompressible fluid is also sometimes called an ideal fluid, or perfect fluid. The Laplace equation is the governing equation for the solution of the problems of this inviscid, incompressible fluid.

The assumption made in solving LaplaceЎ¦s equation is that the flows satisfy the equations for continuity and irrotationality.

The equation for continuity, that is, the conservation of mass is given by

(1)

While the vector equation expressing irrotationality is