Prandtl and Meyer

It would be difficult to create the right mood under the present circumstances, but perhaps by accident another beautiful differential equation will come along again, as it once did when I worked with you.

Letter from Meyer to Prandtl, May 5, 1918. Ref. no. GOAR:2647, DLR-Gottingen Archives

The prediction of cross-spectra from first mode instability waves within high-speed flow over sharp and blunt cones with plasma actuation

Abstract: Leading edge geometries, such as cones, moving at high-speed undergo intense loading due to the growth of instability waves and turbulent transition. These instability waves are highly spatially coherent. Aerodynamic loading related to instability waves and transition cause large-amplitude vibrations within the underlying structure, which may lead to flight-vehicle failure. We examine the effect of plasma actuation on the pressure fluctuations from first mode instability waves on the cone surface via theory with flow-fields predicted by computational fluid dynamics. We present predictions for a seven-degree half-angle cone at free-stream Mach 2.0, 3.5, and 5.0 with varying nose radii. Nose radii range from 0.038 to 38.1 mm and represent both sharp and large leading edge bluntness. For non-actuated flows, we observe that very small radii leading edges do not alter the maximum growth rates. Large radii cones have lower growth rates due to a thicker boundary layer. Spatial coherence of the instability waves decreases with increasing frequency. The growth rates are smaller at higher freestream Mach number. The effect of the simulated plasma actuator adds local heating to the flow-field. Increased nose radii lowers the relative temperature difference between the actuated and base flow-fields. The relative temperature differences are higher at higher freestream Mach number. We find that plasma actuation stabilizes the flow-field and spatial coherence becomes smaller.

  • Cheng, J. and Miller, S. A. E., “Cheng, J. and Miller, S. A. E., “The Prediction of Cross-Spectra from First Mode Instability Waves within High-Speed Flow Over Sharp and Blunt Cones with Plasma Actuation,” Aerospace Science and Technology, Vol. 130, No. 107870, 2022. pp. 1-21. DOI: 10.1016/j.ast.2022.107870 [Link via DOI][PDF Preprint]

On Challenges in Turbulent Flow Theory and Experiment

Research in macroscopic classical physics, such as fluid dynamics or aspects of condensed matter physics, continues to confront baffling challenges that are by no means less demanding than those at the post-Newtonian frontiers of physics that have been explored since the beginning of this century. This is so even though the basic equations of macroscopic classical physics are knownindeed, have been known for centuries in many cases. Chaos and nonlinear dynamics are examples of the topics that pose new challenges to our understanding of macroscopic classical systems. Turbulence, a phenomenon related to but distinct from chaos, and having strong roots in engineering, has been increasingly in the focus of physics research in recent years. Turbulence occurs in a very wide variety of flows, ranging from the mixing of cream in a coffee cup to the dispersal of pollutants in the atmosphere, from the formation of galaxies in the early universe to thermal convection in stars, from flows around automobiles, ships and aircraft to combusting flows in turbomachinery.

Uriel Frisch and Steven A. Orszag, DOI: 10.1063/1.881235

Syzygy

Would you like to know the best possible method for solving a Syzygy problem? It is this. Having ascertained from your doctor that you are in a state of health to bear, without risk, severe brainwork and keen intellectual excitement, from the most candid of your intimate friends that you are in a pleasant temper, and free from all morbid irritability; and from yourself that you are in the humour for the task seat yourself in an easy-chair, taking care that you have writing materials within reach, and that there are no dictionaries in the room; close your eyes, and paint the two given words on your mental retina.

Lewis Carroll

On the On-Set of Hypersonics

Almost everyone has their own definition of the term hypersonic. If we were to conduct something like a public opinion poll among those present, and asked everyone to name a Mach number above which the flow of a gas should properly be described as hypersonic there would be a majority of answers round about 5 or 6, but it would be quite possible for someone to advocate, and defend, numbers as small as 3, or as high as 12.

Philip Roe, verbal comment at von Karman Institute, 1970.