Plume-surface interaction during lunar landing using a two-way coupled DSMC-DEM approach

In the present work, a numerical framework is developed for simulating gas-solid flows associated with interaction of a rocket plume on a planetary surface. For this investigation, a unique, two-way coupled, dusty-gas flow model has been developed in the coupled direct simulation Monte Carlo (DSMC)-discrete element method (DEM) framework, which has been applied for dust dispersion on lunar surface. In this model, the gas-gas collisions are modeled probabilistically, whereas grain-grain interactions are computed deterministically. Most importantly, a multiphase fluid-solid two-way coupling model is proposed where the fluid-particle interaction is modeled macroscopically by considering the momentum and energy exchange between the two phases. The use of the DEM approach allows us to model dense granular phase near a planetary regolith. Additionally, the framework allows us to calculate not only the particle trajectories, but also their temperatures. To make the framework efficient for dynamic calculation of drag and heat transfer from gas to grain phase, the same coefficients are precalculated (and used later as a look-up table) for gas flow over an isolated granular particle over a range of speed ratios for free molecular flow conditions. Using the developed framework, a comprehensive numerical study is performed to model dust dispersion associated with lunar landing. The influence of particle diameter on gas and grain phases and dust transportation has been analyzed in the coupled framework. Additionally, the impact of the two-way coupled gas-grain interaction model is analyzed and compared with one-way coupled model.

Figure 1

Illustration of the challenge of lunar landing that classifies distinct regions according to different criteria along with erosion schematic.

Figure 2

Gas and grain simulation methodology. (a) DSMC method flowchart; (b) flowchart of DEM used.

Figure 3

Normalized heat flux and coefficient of drag variations with speed ratio.

Figure 4

Verification parameters: (a) domain of verification, (b) horizontal velocity, (c) vertical velocity, and (d) temperature variation.

Figure 5

Flowchart representing the DSMC-DEM coupling algorithm.

Figure 6

Schematic view of plume impingement on a lunar surface.

Figure 7

(a) Schematic of a nozzle; (b) temperature and velocity contours of the flow field in the nozzle. $D_e$ and $R_e$ represent the diameter and radius of the nozzle exit, respectively.

Figure 8

Variation of flow properties at the nozzle exit. (a) Normalized vertical and horizontal velocities, and (b) normalized density and temperature.

Figure 9

Spatial distribution of temperature and vertical velocity with streamlines. $D_n$ represents the vertical distance from the nozzle exit, and $L_c$ denotes the distance from the nozzle centerline.

Figure 10

Spatial distribution of the horizontal velocity and overall temperature for the entire domain.

Figure 11

Contours representing the density flow field variation.

Figure 12

Contours representing the dynamic pressure responsible for erosion. Inset 1: Dynamic pressure variation at the depth of 3.5 m below nozzle exit. Inset 2: Erosion flux variation at the lunar surface.

Figure 13

Trajectories of lunar particles at different time instants.

Figure 14

Variation of (a) the vertical($V_v$) to horizontal($V_H$) velocity ratio and (b) inverse tangential of $V_v/V_H$ in degrees, at two depths from the nozzle exit.

Figure 15

Horizontal velocity contours of the gas and grain phase.

Figure 16

Horizontal velocity contours of lunar particles in the (a) absence and (b) presence of interparticle collisions.

Figure 17

Horizontal velocity comparison between nondissipative and dissipative grains at (a) two horizontal locations from the nozzle centerline and (b) two depths from the nozzle exit.

Figure 18

Spatial distribution of horizontal velocity and temperature for 1 mm diameter particles.

Figure 19

Spatial distribution of horizontal velocity and temperature for 100 $\mu \text{m}$ diameter particles.

Figure 20

Horizontal velocity and temperature variations at different far-field locations from the nozzle centerline. Legend for all plots are given in (a).

Figure 21

Horizontal velocity and temperature for two depths from the nozzle exit. Legend for all plots is given in (c).

Figure 22

Comparison of (a) horizontal velocity and (b) temperature, between one-way and two-way coupled models for various far-field distances from the nozzle centerline.

Figure 23

Comparison of (a) horizontal velocity and (b) temperature, between one-way and two-way coupled models for various depths below the nozzle exit.

Figure 24

Comparison of erosion profiles between one-way and two-way coupled models.

Figure 25

Contour showing volume fraction variation across the whole simulation domain for 1 mm diameter lunar particles.

Figure 26

Comparison of (a), (c) horizontal velocity and (b), (d) temperature, between one-way and two-way coupled models for 15 m far-field distance from nozzle centerline and 1.5 m depth below the nozzle exit.

Figure 27

Evolution of number of simulated gas particles in the domain.

Figure 28

Temporal variation of total kinetic energy of grains per unit mass.

Figure 29

Evolution of number of granular particles in the domain.