This paper examines the application of Gauss’s principle of least constraint to the classical problem of the lift of a two-dimensional airfoil in ideal, incompressible fluid flow, including the role of the empirical Kutta condition that determines the airfoil circulation in classical theory. Gauss’s principle demonstrates that the fluid pressure field consists of two components: a constraint pressure field that enforces the continuity and nonpenetration constraints and an impressed pressure field of arbitrary strength that satisfies but does not influence any constraints. The analysis shows that a flow solution that minimizes the difference between the acceleration and the impressed pressure gradient is a valid solution of Euler’s equation. Furthermore, Gauss’s principle proves that ideal potential flow airfoil theory is incomplete and that a first principles closure condition cannot exist within potential flow. This reaffirms the view that an external, empirical condition is needed to complete classical airfoil theory, i.e., the Kutta condition. The paper also investigates and disproves a new variational theory of lift developed from Hertz’s principle of minimum curvature that is claimed to provide a closure condition based on first principles to replace the empirical Kutta condition of classical airfoil theory.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Application of Gauss’s Principle to the Classical Airfoil Lift Problem


    Beteiligte:

    Erschienen in:

    AIAA Journal ; 63 , 1 ; 6-20


    Erscheinungsdatum :

    01.01.2025




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




    Magnus Force Estimation Using Gauss’s Principle of Least Constraint

    Shorbagy, Mohamed / Taha, Haithem | AIAA | 2024


    High lift airfoil design method, high lift airfoil and aircraft

    YUAN MENG / QI SHIBING / QIN YOUHUA et al. | Europäisches Patentamt | 2023

    Freier Zugriff

    AIRFOIL WITH AUGMENTED LIFT

    MOLBECH ALLAN | Europäisches Patentamt | 2023

    Freier Zugriff

    AIRFOIL WITH AUGMENTED LIFT

    MOLBECH ALLAN | Europäisches Patentamt | 2023

    Freier Zugriff

    Improving Airfoil Lift Prediction

    Ramanujam, Giridhar / Ozdemir, Huseyin | AIAA | 2017