Visualizing high-speed effects on turbulent structures by identifying regions with similar behavior

What is it about?

Turbulent flows are always around us and are essential to many aspects of our modern lifestyle. From driving to flying, turbulence is always present. Perhaps one synonym associated with turbulence is chaos or “randomness,” but turbulence is far more orderly than many could be led to believe. However, the intricate patterns and structures found in turbulence require attention since these structures are responsible for energy and mass transport within turbulent flows. Wall-bounded flows are of even greater engineering interest since these flows are observed in wings, cars, rockets, and a wide variety of applications. Flows that encounter a surface (such as a wing) exhibit a very thin layer of flow known as the boundary layer. This thin film is responsible for many physical phenomena of great engineering interest and many applications in both civil and military sectors. This publication focuses on high-speed boundary layers such as those seen in military planes, rockets, and future civilian planes. We leverage a computational approach known as direct numerical simulation (DNS), which numerically solves the famous (or infamous) Navier Stokes equations without incorporating additional models. DNS is computationally expensive but is often the closest alternative to experimental data. We emphasize flows at speeds above the speed of sound. Sound travels in small perturbations at speeds governed by the medium and its current state. The Mach number often characterizes high-speed flows, simply the ratio of the object or fluid’s speed studied to that of sound in the medium in which it is present. It has been proposed that structures in turbulent flows can be visualized by relating different regions of the flow and relating their changes. Although many techniques abound for such tasks, we leverage the two-point correlation. The operation entails precisely what the name suggests and correlates changes in two points in space. We fix one of these points (i.e., the reference point) and relate this point to every other point in the flow. Averaging this operation in time reveals patterns in the flow that can be visualized with high fidelity. Thus, one can qualitatively assess variations in structures dependent on Mach number. Humans are highly visual beings; consequently, visualizing turbulent structures and their dependency on other parameters can shed light on the physics of the boundary layer and suggest additional studies based on observations.

Featured Image

Photo by SpaceX on Unsplash

Photo by SpaceX on Unsplash

Why is it important?

We approach Mach number dependency effects from an angle not often considered. Compressibility phenomena is often studied through the lens of more engineering-focused parameters which often limits the creative thought and visual exploration of results that would be natural to humans. Studying turbulent structures visually could be a potential source of inspiration for both theoreticians and practitioners in the development of new engineering frameworks and theories regarding the turbulent transport of mass and energy. What’s more, it is a natural approach to qualitatively assessing turbulence and comparing multiple references. To further compound the relevance of the work, recent times have seen a renewed interest in high-speed flow due to both military and civilian interests. Military infrastructure is faced with many unknowns regarding high-speed aerothermodynamics whereas civilian infrastructure continues to chase the original goal of the Concorde of reducing flight times in a safe and economically viable manner.

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