20.500.12556/DKUM-65048 Razvoj modela za tvorbo in razpad kolonij sferičnih alg v toku vode Development of a model for the formation and decomposition of spherical algae in water flow Do sedaj se je numerični model Vreteno DNS uporabljal zgolj za nežive delce. V magistrski nalogi pa smo se osredotočili na vedenje živih organizmov, alg. Prav tako Vreteno DNS do sedaj ni imelo vgrajenega modula za določanje trkov med delci. Ta raziskava je usmerjena v nadgradnjo sedanjega modela, da bo le-ta uporaben tudi za žive organizme ter bo upošteval trke, do katerih nedvomno prihaja v turbulentnem toku. Za izhodišče smo izbrali model trdih sfer, iz katerega smo pridobili enačbe za smer in hitrost, v_1 in v_2, ter kotni hitrosti, ω_1 in ω_2, alg po trku. Nato smo določili še smer in hitrost gibanja morebitne novonastale kolonije alg v_3, kakor tudi njeno kotno hitrost ω_3. Sedaj smo postavili pogoj, ki pogojuje trke z medsebojno razdaljo alg v času trkov. Razdaljo smo označili s črko B. Določili smo, da se bo trk zgodil, kadar bo B večji kot 0 in kadar bo manjši kot vsota polmerov obeh alg. V naslednjem koraku smo poiskali še ustrezen biološki parameter, ki določa, kdaj se alge med seboj odbijajo in kdaj prihaja do združevanja alg v kolonije. Ta parameter je stopnja hidrofobnosti ∆G. V primeru negativne stopnje hidrofobnosti prihaja do nastanka kolonij, medtem ko se v primeru pozitivne stopnje hidrofobnosti kolonije ne tvorijo, pač pa se alge med seboj odbijajo. Vse parametre in enačbe smo nato vstavili v program Scilab in nato še v model Vreteno DNS. Zagnali smo tri simulacije, in sicer simulacijo brez trkov, simulacijo s trki z odboji in še simulacijo, kjer se alge združujejo v kolonije. Podatke za simulacije smo pridobili iz magistrske naloge U. Žibert, ki je nastajala vzporedno s to nalogo. Rezultate smo nato med seboj grafično primerjali in ugotavljali vplive, ki jih imajo trki na vedenje alg. Ugotovili smo, da le-ti imajo nedvomen vpliv in jih model mora upoštevati, če se želimo kar se da približati naravnemu stanju. The model Vreteno DNS was until now only used on inanimate particles. In the following master thesis, we were focused on the behaviour of living organisms, algae. Until now Vreteno DNS also did not include a module for the determination of particle collisions. This thesis is aimed at upgrading the current model so it will be applicable for living organisms and so it will consider particle collisions which undoubtedly occur in turbulent flows. As a starting point we have chosen the hard sphere model from which we obtained the equations for determining the direction and the velocities of movement, v_1 and v_2, as the equation for determining the angular velocities, ω_1 and ω_2, after collision. Afterwards we determined the direction and velocity of movement for any possibly created algae colony v_3 and its angular velocity ω_3. At this point we have set a condition which considers the algae collisions on the distance between them at the time of impact. We marked the distance with the letter B. We determined that collisions will occur when B is larger than 0 and smaller than the sum of the two algal radii. In the next step we have searched for a suitable biological parameter, which determines when algae repulse of each other and when will they form a colony. The parameter is the degree of hydrophobicity ∆G. In the event of the degree of hydrophobicity being negative, the algae form colonies. In the event the degree of hydrophobicity being positive the algae repulse. All the parameters and equations were then inserted into the program Scilab and from there into the model Vreteno DNS. We then launched three simulations namely: the first without collisions, the second with collisions and repulsions and the third with the formation of colonies. Data for the simulations was obtained from the master’s thesis of U. Žibert that was being written parallel with ours. The results were graphically compared and the influence of collisions on algal behaviour were considered. We have determined that collisions undoubtedly have influence and have to be taken into account so that the model approaches the natural state. trki združevanje v kolonije alge Vreteno DNS model trdih sfer collisions colony formation algae Vreteno DNS hard sphere model true true false [A. Najžar] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2017-02-10 15:18:20 2017-03-23 11:26:05 2022-07-07 03:07:55 2019-07-11 15:05:45 2017 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.876.5:[582.263:532.517.4](043.2) 20524566 URN:SI:UM:DK:RCUCNDLW MAG_Najzar_Andraz_2017.pdf MAG_Najzar_Andraz_2017.pdf 1 30FF6CA412E6E9812C664AF29B74EC7F 871966102d48d97e3f126db0ece4c7840e9076d2894271356deac94266f0c4c8 02957112-7c0e-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=110064 Fakulteta za strojništvo 0 0 0