Convergence properties of panel methods

Bellamy-Knight, P. G.; Benson, Mike; Gerrard, J. H.; Gladwell, I.

doi:10.1016/0045-7825(89)90094-7

Cited by 11 publications

(13 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…makers [58], Katz and Plotkin [63], Oskam [88]). Such an O(h 2 ) super convergence was also noted by Bellamy-Knights et al [8] for the simulation of 2D potential flow about an elliptical cylinder for which they assumed that the phenomenon was probably due to error cancellation occurring only for convex body shapes. For our solid angle test case the unit strength dipole distribution, the exact solution being constant, and the evaluation of the solid angle in the panel mid point could also be factors contributing to this occurrence of super convergence.…”

Section: Solid Anglesupporting

confidence: 71%

Multilevel panel method for wind turbine rotor flow simulations

Garrel¹

View full text Add to dashboard Cite

SummaryThe ongoing trend in wind turbine development is towards larger rotors because of the resulting lower cost of energy. These large rotors lead to relatively flexible structures that are more susceptible to the unsteady aerodynamic loading occurring in normal operating conditions. An accurate prediction of these loadings is important for the design of an economically viable and technically reliable wind turbine. Simulation methods of wind turbine aerodynamics currently in use mainly fall into two categories: the first is the group of traditional low-fidelity engineering models and the second is the group of computationally expensive CFD methods based on the Navier-Stokes equations.For an engineering environment the search is for "medium fidelity" wind turbine simulation methods that bridge the gap between the computationally inexpensive low-fidelity methods and the computationally expensive CFD methods. The ultimate goal is a balanced mixture of higher accuracy of the representation of the physics and shorter simulation times for wind turbine aerodynamics simulation methods. This can be found in the combination of the theories for panel methods, integral boundary layer methods, strong viscous-inviscid coupling, and fluid structure interaction.The present study focuses on the development of the theory and the practical implementation of a fast multilevel integral transform in a computer program. We utilize this multilevel scheme in a low-order panel method. It is demonstrated that for the simulation of the wake flow of wind turbine rotors the computational burden is reduced from O(N 2 ) for a conventional panel method to O(N ) for the present method. This implies that the computational effort is reduced to grow linearly with problem size N , with N the number of panels.We consider the unsteady, incompressible flow around wind turbine rotors and assume the effects of viscosity to be confined to infinitesimal thin boundary layers and wake regions and assume irrotational flow elsewhere. These assumptions allows us to reduce the flow problem to the problem of solving the Laplace equation for a (scalar) velocity potential function. This makes it possible to reformulate the problem as an integral equation over the surface of the rotor and the wakes that emanate from the trailing edges of the rotating wind turbine blades.The mathematical model is discretized in the form of a low-order panel iii Multilevel Panel Method method. The implementation of the panel method is verified by considering the flow over a stationary ellipsoid in a uniform onset velocity field, the flow over a rotating ellipsoid in a fluid at rest, and by considering the flow over a high aspect ratio wing with elliptic planform with as cross-section a von Kármán-Trefftz airfoil. For the first two test cases the numerical results are compared with analytical solutions. The error in the velocity potential is shown to be O(h 2 ), with h a characteristic panel size. The third test case uses the analytical solution for the 2D von Kármán-Trefftz airfoil ...

show abstract

Section: Solid Anglesupporting

confidence: 71%

Multilevel panel method for wind turbine rotor flow simulations

Garrel¹

View full text Add to dashboard Cite

show abstract

“…straight-line panels of constant strength), the singularity strength and external velocity field converge only as 1/N. If, however, panel curvature is taken into account (maintaining constant panel strength) then the singularity strength and external velocity field converge as 1/N 2 These results led Bellamy-Knights et al [12] to re-examine the work of Hess [13]. Analysis of the velocity induced at the control point of a panel by that panel itself verified that panel curvature should be taken into account to allow the computed strength distribution and external velocity field to converge as 1/N 2.…”

Section: Discussionmentioning

confidence: 87%

“…Bellamy-Knights et al [12] compare the analytical singularity distributions presented here with the distributions predicted by panel methods of different order and for N = 16, 32, 64 and 128 where N is the number of panels. It is found numerically that for the 'zeroth'-order panel method (i.e.…”

Section: Discussionmentioning

confidence: 89%

Analytical surface singularity distributions for flow about cylindrical bodies

et al. 1989

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper exact analytical values of surface singularity distributions for two-dimensional potential flows are presented. A general formulation which provides an alternative to the Milne-Thomson theorem is presented for the circle, then distributions are obtained for flow about an ellipse. These solutions provide useful bench-mark test cases for examining the convergence properties in the development of some panel-method computer codes.

show abstract

“…Later papers, including those by his research students, further developed this theme (208)(209)(210)(211)(212)(213)(214) . However, by the late 1980s his attention turned to establishing exact analytical values of surface singularity distributions for potential flows about ellipses, thus providing bench-mark tests for the panel methods currently popular in aerodynamic calculations (215)(216)(217)(218)(219)(220) . In this he was joined initially by Jack Gerrard, the latter's research student Michael Benson, and Ian Gladwell of the Mathematics Department.…”

Section: The Department Of the Mechanics Of Fluids And Its Successorsmentioning

confidence: 99%

The Victoria University of Manchester’s contributions to the development of aeronautics

Ackroyd

2007

Aeronaut. j.

View full text Add to dashboard Cite

This issue of the Aeronautical Journal celebrates the 50th anniversary of the foundation of the Honours Degree Course in Aeronautical Engineering at the Victoria University of Manchester. The following article therefore describes the aeronautical research and teaching activities of that university up to its recent amalgamation with the University of Manchester Institute of Science and Technology (UMIST) to form the present-day University of Manchester. This juncture provides a further justification for recording the Victoria University’s achievements.Both the Victoria University and UMIST had their roots in the nineteenth century although, apart from the relatively brief period of the First World War, neither of them was particularly involved in aeronautics until after the Second World War. However, as Sections 6.0-10.0 seek to demonstrate, thereafter the Victoria University’s involvement became considerable. The preceding Sections describe the origins of the Victoria University and UMIST and, in the case of the former institution, the subsequent activities of its staff and graduates in engineering and mathematics which, although not always specifically aeronautical in content, nonetheless had a profound influence on the development of the aeronautical sciences.

show abstract

Convergence properties of panel methods

Cited by 11 publications

References 2 publications

Multilevel panel method for wind turbine rotor flow simulations

Multilevel panel method for wind turbine rotor flow simulations

Analytical surface singularity distributions for flow about cylindrical bodies

The Victoria University of Manchester’s contributions to the development of aeronautics

Contact Info

Product

Resources

About