We celebrate the centennial of the momentum-integral approach, one of the most significant theoretical contributions of Theodore von Kármán, which is widely taught in the field of aerodynamics. After giving tribute to von Kármán, we discuss the broad impact of his approach, which dates back to 1921 and is often used in conjunction with Pohlhausen’s polynomial approximations. We then offer a compelling rational explanation for the long-standing Pohlhausen paradox, namely, the reason why higher-order polynomial approximations of the nearfield produce less accurate predictions of the skin friction coefficient and boundary-layer thickness than lower-order Pohlhausen polynomials. Not only do we clarify the root cause of the Pohlhausen paradox, but we also provide alternative solutions that enable us to extend the accuracy of the momentum-integral approach by two orders of magnitude. Lastly, we provide an essentially exact one-term solution to the widely cited Blasius equation, whose analytical treatment has eluded scientists since its inception in 1907.
Professor Joseph Majdalani
He is a Francis Chair of Excellence and Professor of Aerospace Engineering and has been a pioneering researcher in aerodynamics and rocket propulsion for more than 30 years. He is a prolific scholar and exemplary mentor who has been invited to present more than 100 seminars and plenaries worldwide. He has over 325 publications and 19,000 citations. As a well-recognized authority in the field, he has co-authored a leading McGraw-Hill textbook titled, Viscous Fluid Flow, 4th edition, and delivered the 2023 Von Kármán Lecture. He has advanced new formulations based on Kármán’s approach and organized a Special Collection in the Physics of Fluids titled, “Centennial of the Kármán-Pohlhausen Momentum-Integral Approach.” Professor Majdalani’s technical research focus is on advancing acoustic instability and rotating flow theories in the context of solid, liquid, and hybrid rocket engines. He has developed new effective methodologies that have been successfully applied to various rocket systems including the class of cyclonic VORTEX® rocket engines pioneered by ORBITEC and Sierra Space.