Separated and vortical flow occurs over every aircraft in flight. Through interactions with the airframe, the separation-induced vortices affect the overall vehicle performance, stability and control. The effects can either be favourable or adverse, prompting Elsenaar to term the vortex the ‘beauty and the beast in aerodynamics’ in his Lanchester Lecture.

On a broad-brush canvas of vortex-flow aerodynamics illustrated above, this paper attempts to cast a historical perspective on the theoretical modelling of vortices from wing edges as it developed over the past century. Such a blanket approach allows us to parallel the historic achievements, along with the frustrations, of aerodynamic design during Lanchester’s time with those of more recent times.

In the last decade of the 1800s Frederick Lanchester speculated correctly on the vortex theory of lift and the nature of the shear-layer wake shed from the trailing edge of a wing. In a sense the study of vortex-flow aerodynamics began with Lanchester. The theoretical model that evolved over the next three decades was linear, assumed attached flow, and enabled design of the sleek shapes of 400 mph WWII fighters.

New technology requires Computational Fluid Dynamics

The invention of the jet engine changed the game entirely. Planes flew faster and higher with wings that became swept and slender, and their aerodynamics became nonlinear. The theoretical models that had served low-speed design so well were useless for speeds approaching Mach 1. In the late 1940s and early 1950s substantial guesswork returned to the design of transonic swept wings. Computerisation of mathematics into CFD finally brought together the analysis and design sides of aerodynamics in Lanchestrian symbiosis of theory and engineering. The figure above sketches seven decades of CFD development juxtaposed with the evolution of supercomputing.

The story begins in the late 1940s, before the first ‘knee’ in the S-shaped curve, when computers and numerical analysis were in their early days and progress was slow. What was not slow was the development of high-speed aircraft. With the cold war on, enormous resources were spent to reach air superiority by speed and altitude. Let’s take Saab development as an example, the J29 Tunnan (the barrel) was the first European swept wing fighter in service and made its maiden flight in 1948. Only seven years later the double-delta J35 Draken (the kite) flew at Mach 2, and most fighters in service today fly neither much faster nor higher. Then, the 1960s saw rapid development in numerical modelling fuelled by growing computer power to make the development curve turn abruptly upwards, enabling numerical simulation of airflow to provide predictions at all speeds. From the 1980s on, computer power and software could support not only flow prediction for a given shape, but also algorithmic shape optimisation.

Design with CFD predictions

During the past three decades, methods for Reynolds Averaged Navier-Stokes equations have become very effective CFD tools. Forces and moments are adequately predicted for cruise conditions when the flow is steady and the turbulent boundary layer remains attached over the aircraft surface, or when a vortex shed from a sharp slender wing remains concentrated over the vehicle. However, near the limits of the flight envelope, the stalling characteristics encountered as maximum lift is approached must be known, and CFD predictions become less reliable due to inadequate turbulence modelling. RANS simulations of separated flows apparently have reached a level of diminishing returns as regards capability and certainty, as indicated by the knee in the development curve after 2000. The ubiquitous challenge here is turbulence.

In view of this uncertainty, can CFD predictions of separated flow be used in design? The answer could be “yes”, if the predictions are put into the hands of an aerodynamicist, because the human drive is to figure out in human terms what the “flow physics” is doing. The designer strives for understanding and establishment of what Küchemann called “healthy” flows. Even “fuzzy” flow visualizations of boundary layers, shock waves and vortices, all interacting with each other, can spark new ideas and innovative aerodynamic design concepts.

The aerodynamic problems of the first-generation swept wings offer a good example of how CFD simulations near stall could be used. The design task was to mitigate the tendency for tip stall and pitch-up at high lift. Aided by wind-tunnel measurements and flight-test data, the Saab engineers found a simple cure for the swept-wing transonic fighters J29 and J32 − a stall fence. Today with forensic CFD, we can re-discover the aerodynamic motivations for their decisions by visualizing how a stall fence makes the flow healthier.

With its maiden flight 1952, the Saab J32 was a transonic fighter developed to replace the J29, see the figure below. The stall problems, ubiquitous for swept wings, are created by the movement of the leading-edge vortices as incidence increases. Called a vortex splitter by Saab engineers, the stall fence splits the vortex in two to better control the flow over the upper surface and improve the wing’s pitching moment. Shown are moment curves with and without fence for Mach 0.4 at sea level in typical flight conditions for vigorous manoeuvring. The fence clearly reduces the moment variation over the angle-of-attack range.

Could one apply near-stall CFD predictions in a mathematical shape optimization procedure? Here the answer would be “no” because the optimizer understands only numbers and the uncertainty in them due to physical modelling might lead to a false result. How to proceed then?

Turbulence and Machine Learning

Flow prediction at full scale Reynolds number by DNS (Direct Numerical Solution) of the unsteady Navier-Stokes equations requires enormous computer resources and will not be a practical tool for a long time to come. Progress past the upper knee will be dependent on new ideas and their correct implementation. Massive DNS data bases will become invaluable in building improved computable physical models for separated flows. Machine learning has the potential to suggest a fine-grained classification of flows with associated adapted turbulence models, and efforts are under way to accelerate development of physical modelling, but this is the subject for another blog.

Separated and vortical flow in aircraft aerodynamics: A CFD perspective. Rizzi, A. (2023).

This open access paper appears in Volume 127 – Issue 1313 – July 2023 of The Aeronautical Journal. 

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