Matematično in fizično modeliranje toka v rekah s poplavnimi področji : doktorska disertacija

Bombač, Martin (author), Četina, Matjaž (mentor), Steinman, Franci (comentor)

V doktorski disertaciji so obravnavani različni pristopi k modeliranju toka v rekah s poplavnimi področji. Podatki, pridobljeni z meritvami na fizičnem hidravličnem modelu območja reke Save z izrazitimi poplavnimi področji, so služili za podrobno numerično analizo problematike izmenjave vode med tokom v glavni strugi in tokom na poplavnih področjih. Analizirani in dopolnjeni so bili modeli turbulence, vgrajeni v matematični model PCFLOW2D, ki ga že več kot dve desetletji razvijajo in dopolnjujejo na Katedri za mehaniko tekočin Fakultete za gradbeništvo in geodezijo Univerze v Ljubljani. Z analizo vpliva posameznega člena v dvodimenzijski dinamični časovno povprečeni Navier-Stokesovi (Reynoldsovi) enačbi, ki opisuje globinsko povprečen tok v rekah s poplavnimi področji, je bilo dokazano, da pri gibanju večjih vodnih mas po poplavnih področjih uporaba ustreznega modela turbelence ne igra bistvene vloge, saj je vpliv turbulence možno zadovoljivo zajeti preko trenjskega člena. Zato je bil v nadaljevanju obravnavan primer toka v ribji stezi, kjer je turbulenca zelo izrazita in ima njeno natančno modeliranje velik pomen. Na tem konkretnem primeru je bila opravljena občutljivostna analiza vgrajenega modela turbulence Smagorinsky. Analiza je pokazala, da je za dosego dobrega ujemanja numeričnih rezultatov z meritvami nujno umeriti koeficient Smagorinskega Cs, ki nastopa v modelu turbulence. To je novo dognanje, saj je v vseh nam znanih dosedanjih študijah ter drugih numeričnih programih priporočena vrednost koeficienta Cs enaka (oziroma spremenljiva znotraj zelo majhnega intervala) za vse vrste toka. Naša analiza je pokazala, da je vrednost koeficienta Cs zelo odvisna od uporabljene numerične mreže ter obravnavane vrste toka in lahko močno odstopa od do sedaj priporočenih vrednosti. Z detajlno občutljivostno analizo parametrov matematičnega modela je bil dosežen napredek pri razumevanju obravnavane problematike, kar v bodoče zagotavlja lažje in hitrejše umerjanje matematičnih modelov ter večje zaupanje v dobljene rezultate.

• Language: Slovenian
• Keywords: gradbeništvo, matematični model, disertacije, fizični model, poplavno področje, interakcija, turbolenca, ribja steza, PCFLOW2D, k - e model turbolence, model Smagorinsky, numerična difuzija
• Work type: Dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Place of publishing: Ljubljana
• Publisher: [M. Bombač]
• Year: 2014
• Number of pages: XXVII, 109 str., [62] pril.
• PID: 20.500.12556/RUL-32287
• UDC: 556.5:622.84:556.023(043.3)
• COBISS.SI-ID: 6621537
• Publication date in RUL: 10.07.2015

Secondary language

• Language: English
• Title: Mathematical and physical modeling of flow in rivers with floodplains

Abstract

This doctoral thesis discusses various approaches to modeling flow in rivers with floodplains. Measurements on a physical hydraulic model of the Sava River with distinctive floodplains provided noteworthy data which were used for a detailed numerical analysis of the flow interaction between the main channel and floodplains. Turbulence models incorporated into the mathematical model PCFLOW2D, which was developed more than two decades ago and is continuously being improved at the Chair of Fluid Mechanics with Laboratory, Faculty of Civil and Geodetic Engineering, University of Ljubljana, were precisely analyzed and modified. By analyzing the impact of a single term in a momentum two-dimensional time-averaged Navier-Stokes (Reynolds) equation, which describes the depth-averaged flow, it has been shown that in cases of flows in large water bodies, use of an appropriate turbulence model does not play an essential role because the influence of turbulence can be sufficiently covered through the friction term. Therefore the flow in a vertical slot fishway, where turbulence is very pronounced and its accurate modeling is of great importance was investigated. For this particular case, the sensitivity analysis was carried out for the recently integrated Smagorinsky turbulence model. Analysis has shown that, in order to achieve good agreement of numerical results with measurements, it is necessary to calibrate the Smagorinsky coefficient Cs. This is a new discovery, as to our knowledge all previous studies and other numerical programs recommended an equal value (or within a very small interval) of the coefficient Cs for all types of flow. Our analysis showed that the value of the coefficient Cs is highly dependent on the applied numerical grid and individual type of flow and can significantly deviate from the previous reference values. With the detailed sensitivity analysis of parameters of the mathematical model, progress has been made in understanding the issues addressed, which should in the future allow easier and faster calibration of mathematical models and greater confidence in the obtained results.

• Keywords: civil engineering, thesis, mathematical model, physical model, floodplain, interaction, turbulence, fishway, PCFLOW2D, k - e turbulence model, Smagorinsky model, numerical diffusion