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Monte Carlo simulation of air resistance on an ellipsoid in motion : master thesis
Bukina, Veronika
The main goal of the master's thesis was the analysis of air resistance on the body in motion in a model that does not require solving the Navier-Stokes equations, but works on the basis of mechanics ...and statistical physics. The model was a Monte Carlo (MC) simulation of the motion of ideal gas molecules in a closed container in which a body was placed, moving along one of the axes. For the most part of calculations, the approach was used when the body was fixed in the middle of the simulation cell, and one of the components of the molecular velocity had an additional term that simulated the flow, as if the body was moving at this speed in the opposite direction. First of all, a linear dependence of the drag force on speed was found for low flow speed for a flat plate, which was predicted by linear drag law. For high molecular flow rates, the quadratic dependence predicted by the Bernoulli equation was clearly observed. The results of calculating the corresponding resistivity coefficients for the flat plate were in agreement with the analytical values for both regimes of speeds. By analogy, a simulation was made for a spherical body, which also demonstrated a strong quadratic dependence at high speeds and the drag coefficient value is approximately equal to the analytical one. In the following, we studied systematically ellipsoids with circular cross-section, where we varied the ratio between semiaxes in the direction of motion and perpendicular direction, respectively. The results for the ellipsoid showed that the drag coefficient value is maximum for a flat plate (a limiting case of an ellipsoid, when the semiaxis in the direction of motion tends to 0) and decreases with stretching of the body along the flow axis. When the Maxwell distribution of molecular speeds that was mainly used was replaced with uniform Root-Mean-Square (RMS) speed the results for drag coefficient were slightly different.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Maribor : [V. Bukina], 2021
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