Monte Carlo simulation of air resistance on an ellipsoid in motion

master thesis

Veronika Bukina (Author), Milan Ambrožič (Mentor)

Abstract

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.

Keywords

master theses;air resistance;drag force;quadratic drag law;drag coefficient;Monte Carlo (MC) simulation;Maxwell distribution;

Data

Language:	English
Year of publishing:	2021
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[V. Bukina]
UDC:	533.6.013.12(043.2)
COBISS:	76086275
Views:	254
Downloads:	19
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Monte Carlo simulacija zračnega upora na elipsoid v gibanju
Secondary abstract:	Glavni cilj magistrskega dela je analiza zračnega upora na telo v gibanju v modelu, ki ne zahteva reševanja Navier-Stokesovih enačb, ampak deluje na osnovi mehanike in statistične fizike. Model je Monte Carlo (MC) simulacija gibanja molekul idealnega plina v zaprti posodi, v kateri je telo, ki se je gibalo vzdolž ene od osi. Za večino izračunov je uporabljen pristop, ko je telo pritrjeno na sredini simulacijske celice in je imela ena od komponent molekularne hitrosti dodaten člen, ki je simuliral pretok, kot da bi se telo pri tem gibalo s hitrostjo v nasprotni smeri. Najprej je bila ugotovljena linearna odvisnost sile upora od hitrosti pri nizki hitrosti pretoka za ravno ploščo, kar je napovedano z linearnim zakonom upora. Pri visokih molekularnih pretokih je natančno opažena kvadratna odvisnost, predvidena z Bernoullijevo enačbo. Rezultati izračuna ustreznih koeficientov upora za ravno ploščo so se ujemali z analitičnimi vrednostmi za oba režima hitrosti. Po analogiji smo naredili simulacija za sferično telo, ki je prav tako pokazalo močno kvadratno odvisnost pri visokih hitrostih in je vrednost koeficienta upora približno enaka analitični. V nadaljevanju smo sistematično preučevali elipsoide s krožnim prerezom, kjer smo spreminjali razmerje med polosema v smeri gibanja oziroma v pravokotni smeri. Rezultati za elipsoid so pokazali, da je vrednost koeficienta zračnega upora največja za ravno ploščo (mejni primer elipsoida, ko se polos v smeri gibanja približa vrednosti 0) in zmanjšuje z raztezanjem telesa vzdolž osi toka. Ko je bila Maxwellova porazdelitev molekularnih hitrosti, ki je bila v glavnem uporabljena, nadomeščena z enakomerno hitrostjo povprečnega kvadratnega korena (RMS), so koeficienti zračnega upora nekoliko drugačni.
Secondary keywords:	magistrska dela;zračni upor;sila upora;kvadratni zakon upora;koeficient upora;simulacija Mone Carlo (MC);Maxwellova porazdelitev;Mehanika;Upor (Aerodinamika);Elipsa;Univerzitetna in visokošolska dela;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za fiziko
Pages:	VI, 36 f,
ID:	12406846