Nature of granular drag in microgravity

Abstract

The influence of gravity on the drag force acting on a projectile impacting granular media is investigated experimentally via embedded inertial measurement unit (IMU) sensor and numerically through discrete element method (DEM) simulations. As gravity approaches zero, inertial drag dominates, yielding qualitatively different scaling laws and cavity dynamics. Analogous to fluid dynamics, we define a dimensionless granular drag coefficient $C_{\rm gd}$, which is found to stay largely at a constant $\sim 1.2$ in microgravity while an additional term inversely proportional to impact velocity arises in the presence of gravity. The constant term can be understood from momentum transfer along the penetration direction while the additional term suggests the influence of internal stress built-up due to gravity. Similar discrepancy is also found for the initial peak of the drag force. This analogy provides novel insights into the nature of granular drag in microgravity and sheds light on future space missions.

Figures (5)

• Figure 1: (a) Droptower experimental Setup with the 3D printed spherical projectile with embedded IMU sensor highlighted. (b) Representative raw acceleration data collected from the IMU sensor during one capsule drop. Inset of (b) magnifies the onset of projectile impact on granular sample in microgravity. (c) A reconstructed trajectory of the projectile using the sensor data along with the projectile positions obtained from side view images, as illustrated in the inset.
• Figure 2: A comparison of vertical velocity $v$ vs penetration depth $z$ curves under micro- (left panels) and normal (right panels) gravity conditions. Spherical and triangle symbols correspond to experimental and numerical results. Solid curves denote fits to the data. See text for more details.
• Figure 3: Granular drag coefficient $C_{\rm gd} \equiv \gamma/(\rho_{\rm b} A)$ as a function of initial impact velocity $v_0$ for different $\tilde{g}$ and $\rho_{\rm b}$.
• Figure 4: Effective stress $F_{\rm d0}/A$ as a function of $\rho_{\rm b}v^2$ for all $\tilde{g}=0$ data. The dashed line corresponds to a linear fit to all the data. The insets show the simulation results of the packing density field $\phi$ of a granular sample ($\rho_{\rm b}=70$ kg/m$^3$) responding to the impact of the projectile with $v_0=2.5$ m/s in micro- (a) or normal gravity (b).
• Figure 5: Influence of gravity on the rescaled initial peak of $F_{\rm p}$ as a function of $v_0$ for the experimental results. Inset shows a sample drag force measured for $\rho_{\rm b} = \qty{70}{kg/m^3}$ and $\tilde{g}=1$. The solid curves correspond to power law fits of the data sets with exponents $1.3 \pm 0.1$ and $1.6\pm0.4$ in normal and microgravity, respectively.