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Airfoil Theory

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David A. Peters – One of the best experts on this subject based on the ideXlab platform.

  • Two-dimensional incompressible unsteady Airfoil Theory—An overview
    Journal of Fluids and Structures, 2008
    Co-Authors: David A. Peters
    Abstract:

    Abstract Two-dimensional unsteady Airfoil Theory has a history that dates back at least 75 years. Closed-form solutions have been obtained for Airfoil loads due to step response (either to a pitch input or to a gust), due to Airfoil oscillations in the frequency domain, and due to generalized Airfoil motions in the Laplace domain. It has also been shown that the response of airloads to Airfoil motions can be formulated in state space in terms of ordinary differential equations that approximate the Airfoil and flow field response. The more recent of these models are hierarchical in that the states represent inflow shape functions that form a convergent series in a Ritz–Galerkin sense. A comparison of the various approaches with each other and with alternative computational approaches yields insight into both the methodologies and the solutions.

T. Staubli – One of the best experts on this subject based on the ideXlab platform.

  • OSCILLATING RECTANGULAR AND OCTAGONAL PROFILES: MODELLING OF FLUID FORCES
    Journal of Fluids and Structures, 1998
    Co-Authors: S. Deniz, T. Staubli
    Abstract:

    Abstract Fluid forces acting on rectangular and octagonal cylinders oscillating without (α=0°) and with (α=10°) a mean incidence were measured in a water channel. Experimentally determined force coefficients and phase angles were compared to calculated coefficients determined using the “unsteady Airfoil Theory” and the “quasi-steady Theory”. The results showed that calculation of the time-dependent lift force coefficient according to the quasi-steady Theory can only be used at low oscillation frequencies. While the quasi-steady Theory does not account for fluid inertia, the unsteady Airfoil Theory models the forces resulting from the cylinder acceleration and modifies the lift force with a circulation function. Accordingly, unsteady Airfoil Theory may be applied to a broader frequency range. One advantage of the unsteady Airfoil Theory is that, in addition to the lift force, the phase angle between the lift force and cylinder displacement can be calculated. By virtue of knowing this phase angle, the ranges of positive energy transfer from the fluid to the cylinder can be determined and thereby the ranges of possible self-excited cylinder oscillations. The limits to the applications of both the unsteady Airfoil Theory and the quasi-steady Theory were examined in detail and discussed with respect to oscillation frequency and amplitude. Neither Theory is capable of encompassing the instability-induced phenomena such as resonance due to vortex shedding or phase jump. For rectangular and octagonal cylinders (prisms), the influence of the oscillation amplitude was investigated in detail, through both experiments and calculation, for several excitation frequencies of interest. One important result is that for the rectangular cylinder oscillating at a constant frequency, the direction of energy transfer between the fluid and the cylinder appeared to change as a function of oscillation amplitude.

Daniel T. Valentine – One of the best experts on this subject based on the ideXlab platform.

  • Thin Airfoil Theory
    Aerodynamics for Engineering Students, 2017
    Co-Authors: E.l. Houghton, P.w. Carpenter, Steven H. Collicott, Daniel T. Valentine
    Abstract:

    This chapter examines the potential- or ideal-flow Theory of low-speed Airfoils. The application of potential-flow Theory to solve for the pressure distribution on Airfoils (or wing sections) is described in detail. The application of the vortex solution of the Laplace equation is applied to simulate certain effects of real flows. The result is a powerful but elementary Airfoil Theory capable of wide exploitation. The design of an Airfoil to support a specified lift by applying camber and angle of attack is discussed. How circulation Theory via the application of distributions of vortex singularities is applied to model the effects of camber and angle on Airfoil performance is described. The Theory is applied to examine several aerodynamic problems including the flapped Airfoil and the application of a jet flap. A computational method to examine arbitrary shaped Airfoils that is based on the application of a surface distribution of singularities is introduced.

  • Chapter 7 – Wing Theory
    Aerodynamics for Engineering Students, 2017
    Co-Authors: E.l. Houghton, P.w. Carpenter, Steven H. Collicott, Daniel T. Valentine
    Abstract:

    Important results from potential flow and thin Airfoil Theory are applied to three-dimensional incompressible flow around a planar wing. The flow and loads on a single line vortex are studied and then extended to a simple horseshoe vortex. Horseshoe vortices are combined to develop Prandtl’s lifting line Theory. The Theory is then used to determine the loads on wings and how wing design choices affect such loads. Effects of aspect ratio, wing twist, varying Airfoil section, taper, and similar are described by lifting line Theory. Computational methods to extend beyond classical analysis are introduced.

S. Deniz – One of the best experts on this subject based on the ideXlab platform.

  • OSCILLATING RECTANGULAR AND OCTAGONAL PROFILES: MODELLING OF FLUID FORCES
    Journal of Fluids and Structures, 1998
    Co-Authors: S. Deniz, T. Staubli
    Abstract:

    Abstract Fluid forces acting on rectangular and octagonal cylinders oscillating without (α=0°) and with (α=10°) a mean incidence were measured in a water channel. Experimentally determined force coefficients and phase angles were compared to calculated coefficients determined using the “unsteady Airfoil Theory” and the “quasi-steady Theory”. The results showed that calculation of the time-dependent lift force coefficient according to the quasi-steady Theory can only be used at low oscillation frequencies. While the quasi-steady Theory does not account for fluid inertia, the unsteady Airfoil Theory models the forces resulting from the cylinder acceleration and modifies the lift force with a circulation function. Accordingly, unsteady Airfoil Theory may be applied to a broader frequency range. One advantage of the unsteady Airfoil Theory is that, in addition to the lift force, the phase angle between the lift force and cylinder displacement can be calculated. By virtue of knowing this phase angle, the ranges of positive energy transfer from the fluid to the cylinder can be determined and thereby the ranges of possible self-excited cylinder oscillations. The limits to the applications of both the unsteady Airfoil Theory and the quasi-steady Theory were examined in detail and discussed with respect to oscillation frequency and amplitude. Neither Theory is capable of encompassing the instability-induced phenomena such as resonance due to vortex shedding or phase jump. For rectangular and octagonal cylinders (prisms), the influence of the oscillation amplitude was investigated in detail, through both experiments and calculation, for several excitation frequencies of interest. One important result is that for the rectangular cylinder oscillating at a constant frequency, the direction of energy transfer between the fluid and the cylinder appeared to change as a function of oscillation amplitude.

E.l. Houghton – One of the best experts on this subject based on the ideXlab platform.

  • Thin Airfoil Theory
    Aerodynamics for Engineering Students, 2017
    Co-Authors: E.l. Houghton, P.w. Carpenter, Steven H. Collicott, Daniel T. Valentine
    Abstract:

    This chapter examines the potential- or ideal-flow Theory of low-speed Airfoils. The application of potential-flow Theory to solve for the pressure distribution on Airfoils (or wing sections) is described in detail. The application of the vortex solution of the Laplace equation is applied to simulate certain effects of real flows. The result is a powerful but elementary Airfoil Theory capable of wide exploitation. The design of an Airfoil to support a specified lift by applying camber and angle of attack is discussed. How circulation Theory via the application of distributions of vortex singularities is applied to model the effects of camber and angle on Airfoil performance is described. The Theory is applied to examine several aerodynamic problems including the flapped Airfoil and the application of a jet flap. A computational method to examine arbitrary shaped Airfoils that is based on the application of a surface distribution of singularities is introduced.

  • Chapter 7 – Wing Theory
    Aerodynamics for Engineering Students, 2017
    Co-Authors: E.l. Houghton, P.w. Carpenter, Steven H. Collicott, Daniel T. Valentine
    Abstract:

    Important results from potential flow and thin Airfoil Theory are applied to three-dimensional incompressible flow around a planar wing. The flow and loads on a single line vortex are studied and then extended to a simple horseshoe vortex. Horseshoe vortices are combined to develop Prandtl’s lifting line Theory. The Theory is then used to determine the loads on wings and how wing design choices affect such loads. Effects of aspect ratio, wing twist, varying Airfoil section, taper, and similar are described by lifting line Theory. Computational methods to extend beyond classical analysis are introduced.