Planetesimal-Erosion: Difference between revisions
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A first step is to investigate the stresses acting on the surface of a stationary sphere flown around by a gas. In particular, the influence of the Mach number in the range \(0<\mathcal{M}<2\) on the shear and normal stress distribution is to be investigated in order to gain a basic understanding of the flow conditions relevant for erosion. | A first step is to investigate the stresses acting on the surface of a stationary sphere flown around by a gas. In particular, the influence of the Mach number in the range \(0<\mathcal{M}<2\) on the shear and normal stress distribution is to be investigated in order to gain a basic understanding of the flow conditions relevant for erosion. | ||
== Theoretical Framework == | |||
Required is the distribution of normal and shear stresses acting on the surface of a sphere at rest as a function of the Mach number \(\mathcal{M}\). The Mach number is defined as the ratio between the velocity \(\boldsymbol{v}\) of the flowing fluid (or an object moving through the fluid, depending on the chosen reference system) and the speed of sound \(c_S\) of the considered medium: | |||
\begin{align} | |||
\mathcal{M} = \frac{|\boldsymbol{v}|}{c_\mathrm{S}} | |||
\end{align} | |||
The normal stress describes the component of the mechanical stress acting perpendicular to the surface and contains in particular the contribution of the static pressure. Shear stress, on the other hand, acts tangentially to the surface and is closely linked to velocity gradients in the fluid. Both quantities are components of the stress tensor \(\boldsymbol{\sigma}\) and play a central role in the description of force transmissions between fluid and body, especially with regard to possible erosion processes on the object surface. | |||
Revision as of 10:29, 19 May 2025
Flow around a planetesimal
This project aims to investigate the flow around and erosion of a planetisimal by a viscous fluid under physical conditions that typically occur in protoplanetary discs. As a starting point, the erosion model presented in Cedenblad et al. (2021) will be numerically reproduced and systematically extended in perspective.
A first step is to investigate the stresses acting on the surface of a stationary sphere flown around by a gas. In particular, the influence of the Mach number in the range \(0<\mathcal{M}<2\) on the shear and normal stress distribution is to be investigated in order to gain a basic understanding of the flow conditions relevant for erosion.
Theoretical Framework
Required is the distribution of normal and shear stresses acting on the surface of a sphere at rest as a function of the Mach number \(\mathcal{M}\). The Mach number is defined as the ratio between the velocity \(\boldsymbol{v}\) of the flowing fluid (or an object moving through the fluid, depending on the chosen reference system) and the speed of sound \(c_S\) of the considered medium:
\begin{align} \mathcal{M} = \frac{|\boldsymbol{v}|}{c_\mathrm{S}} \end{align}
The normal stress describes the component of the mechanical stress acting perpendicular to the surface and contains in particular the contribution of the static pressure. Shear stress, on the other hand, acts tangentially to the surface and is closely linked to velocity gradients in the fluid. Both quantities are components of the stress tensor \(\boldsymbol{\sigma}\) and play a central role in the description of force transmissions between fluid and body, especially with regard to possible erosion processes on the object surface.