Reduced-order modeling of separated flow on an airfoil via the Principle of Minimum Pressure Gradient.

Analytical determination of circulation over airfoils has classically required ad hoc closure to potential-flow solutions via the Kutta-Zhukovsky condition. This empirically-derived closure, being kinematic in nature, is not strictly applicable to transient flows with appreciable boundary-layer thickness, or flow separation. Recently, "A Variational Theory of Lift," proposed minimality of curvature in the potential flow field, i.e. the outer solution, and subsequently "What Does Nature Minimize In Every Incompressible Flow?" supplements this foundation beyond potential-flows by a generalized Principle of Minimum Pressure Gradient, (PMPG). We continue the study into determining circulation in the "outer solution," by applying PMPG to a potential-flow outer solution coupled with an integral boundary-layer (IBL) method. The flow solutions determined using PMPG are compared to classical IBL solutions, and experimental data.