On the shape of bodies ablating in a supersonic gas stream

Kalashnik, V. N.; Killikh, B. E.; Petrov, G. I.; Polezhaev, Yu. V.; Смирнов, А. Н.; Chudetskii, Yu. V.

doi:10.1007/bf01094806

Cited by 3 publications

(3 citation statements)

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“…These effects can, however, arise in other applications. Thermal expansion becomes significant at near-sonic or supersonic flow speeds-for example, the air flows encountered by meteors ablating in the atmosphere [20,33]. Meanwhile, the contribution of surface tension to the free energy plays a role in nucleation and dendrite formation [21,47], where it has a stabilizing influence.…”

Section: Discussionmentioning

confidence: 99%

“…The specific heat of water is c p D 4:2 10 7 erg/(g ı C) (cgs units), and, consequently, Ec is very small in many laboratory experiments [25,27,42,50]. We will therefore neglect dissipative heating in the following, although we point out that this effect may be important in some natural examples, such as meteors ablating in the atmosphere [20,33].…”

Section: The Prandtl Flow Modelmentioning

confidence: 99%

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Riemann‐Hilbert Problems for the Shapes Formed by Bodies Dissolving, Melting, and Eroding in Fluid Flows

Moore¹

2017

Comm Pure Appl Math

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The classical Stefan problem involves the motion of boundaries during phase transition, but this process can be greatly complicated by the presence of a fluid flow. Here we consider a body undergoing material loss due to either dissolution (from molecular diffusion), melting (from thermodynamic phase change), or erosion (from fluid‐mechanical stresses) in a fast‐flowing fluid. In each case, the task of finding the shape formed by the shrinking body can be posed as a singular Riemann‐Hilbert problem. A class of exact solutions captures the rounded surfaces formed during dissolution/melting, as well as the angular features formed during erosion, thus unifying these different physical processes under a common framework. This study, which merges boundary‐layer theory, separated‐flow theory, and Riemann‐Hilbert analysis, represents a rare instance of an exactly solvable model for high‐speed fluid flows with free boundaries.© 2017 Wiley Periodicals, Inc.

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Section: Discussionmentioning

confidence: 99%

Section: The Prandtl Flow Modelmentioning

confidence: 99%

Riemann‐Hilbert Problems for the Shapes Formed by Bodies Dissolving, Melting, and Eroding in Fluid Flows

Moore¹

2017

Comm Pure Appl Math

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“…Much early work aimed to link the overall conical shape as well as surface features to the flows present (ref. 22 and references therein), and laboratory experiments on the ablation of plastic bodies fixed within supersonic airflow revealed the formation of a conical nose directed into the flow (32). This shape is thereafter retained as the windward face recedes.…”

mentioning

confidence: 94%

The role of shape-dependent flight stability in the origin of oriented meteorites

Amin

Huang

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

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The atmospheric ablation of meteoroids is a striking example of the reshaping of a solid object due to its motion through a fluid. Motivated by meteorite samples collected on Earth that suggest fixed orientation during flight—most notably the conical shape of so-called oriented meteorites—we hypothesize that such forms result from an aerodynamic stabilization of posture that may be achieved only by specific shapes. Here, we investigate this issue of flight stability in the parallel context of fluid mechanical erosion of clay bodies in flowing water, which yields shapes resembling oriented meteorites. We conduct laboratory experiments on conical objects freely moving through water and fixed within imposed flows to determine the dependence of orientational stability on shape. During free motion, slender cones undergo postural instabilities, such as inversion and tumbling, and broad or dull forms exhibit oscillatory modes, such as rocking and fluttering. Only intermediate shapes, including the stereotypical form carved by erosion, achieve stable orientation and straight flight with apex leading. We corroborate these findings with systematic measurements of torque and stability potentials across cones of varying apex angle, which furnish a complete map of equilibrium postures and their stability. By showing that the particular conical form carved in unidirectional flows is also posturally stable as a free body in flight, these results suggest a self-consistent picture for the origin of oriented meteorites.

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Sculpting of an erodible body by flowing water

Ristroph

Moore

Childress

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

112

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Erosion by flowing fluids carves striking landforms on Earth and also provides important clues to the past and present environments of other worlds. In these processes, solid boundaries both influence and are shaped by the surrounding fluid, but the emergence of morphology as a result of this interaction is not well understood. We study the coevolution of shape and flow in the context of erodible bodies molded from clay and immersed in a fast, unidirectional water flow. Although commonly viewed as a smoothing process, we find that erosion sculpts pointed and cornerlike features that persist as the solid shrinks. We explain these observations using flow visualization and a fluid mechanical model in which the surface shear stress dictates the rate of material removal. Experiments and simulations show that this interaction ultimately leads to selfsimilarly receding boundaries and a unique front surface characterized by nearly uniform shear stress. This tendency toward conformity of stress offers a principle for understanding erosion in more complex geometries and flows, such as those present in nature.R eflecting on his scientific discoveries, Isaac Newton compared himself to a boy on the seashore who marvels at having found a yet smoother stone (1). For pebbles and mountains alike, our curiosity about natural sculptures stems perhaps from the realization that these shapes reflect countless incremental events acting over eons. Morphology is often the only clue available as we attempt to reconstruct the physical history of the Earth as well as of our neighboring worlds (2-6). Recreating geologically inspired situations in the laboratory offers an opportunity to connect the development of structures to the underlying processes at work (7). This approach has been used to study phenomena across many scales, for example, the rounding of rocks by abrasion (8), the formation of rivers (9) and drainage channels (10), and the drift of continental plates driven by mantle convection (11).Rather than mimic a particular geological scenario, we conduct experiments that isolate a central aspect common to all erosive processes: the interdependent evolution of shape and flow (3). As described in Methods, we study the erosion of soft clay bodies by fast-flowing water, allowing us to witness what is an intractably slow process in nature. We consider unidirectional flow and canonical initial geometries-a thin flat bed of clay, a cylinder, and a sphere-with an eye toward informing mathematical models that intimately link the coevolving flow and shape (12, 13). Our experiments typically involve centimeter-scale bodies immersed in flows of 40-70 cm/s, yielding high Reynolds numbers of order 10 4 . Importantly, the solid boundaries recede at rates (approximately centimeters per hour) that are many orders slower than the flow speed, preserving the large separation of time-scales characteristic of natural erosion.Considering first the case of a 3D body, we form a clay sphere of diameter 4.9 cm and support it within a water tunnel with a cro...

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On the shape of bodies ablating in a supersonic gas stream

Cited by 3 publications

References 1 publication

Riemann‐Hilbert Problems for the Shapes Formed by Bodies Dissolving, Melting, and Eroding in Fluid Flows

Riemann‐Hilbert Problems for the Shapes Formed by Bodies Dissolving, Melting, and Eroding in Fluid Flows

The role of shape-dependent flight stability in the origin of oriented meteorites

Sculpting of an erodible body by flowing water

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