Simulacije dvofaznih tokov s površinsko napetostjo z metodo hidrodinamike zglajenih delcev

Markelj, Eva (author), Tekavčič, Matej (comentor), Tiselj, Iztok (mentor)

Metoda SPH (Smoothed Particle Hydrodynamics), oziroma v slovenskem jeziku metoda hidrodinamike zglajenih delcev, je brezmrežna metoda, ki se uporablja za simuliranje problemov v računalniški dinamiki tekočin. Velja za alternativo tradicionalnim metodam, ki temeljijo na reševanju Navier-Stokesovih enačb na mrežah diskretnih točk. Tekočina je v metodi SPH predstavljena kot množica delcev, ki med seboj interagirajo. Približki vrednosti funkcij (hitrost, gostota, tlak) in njenih odvodov so določeni z uporabo funkcije glajenja, ki predstavlja utežno funkcijo delcev za računanje vrednosti teh funkcij v izbrani točki. Enačbe metode zglajenih delcev so Navier-Stokesove enačbe, zapisane za posamezni delec tekočine. Z metodo lahko simuliramo tudi večfazne tokove, pri katerih ima lahko velik vpliv površinska napetost. To magistrsko delo metodo predstavi ter vanjo vključi dva načina vključitve površinske napetosti. Predstavljena sta dva večfazna primera, ki prikazujeta vplive različnih parametrov metode, vpliv vključitve sil površinske napetosti ter zmogljivost metode SPH. Prvi primer je deformacija kvadratne kapljice, drugi pa je Rayleigh-Taylorjeva nestabilnost.

• Language: Slovenian
• Keywords: računalniška dinamika tekočin, metoda SPH, metoda hidrodinamike zglajenih delcev, površinska napetost, večfazni tok, Rayleigh-Taylorjeva nestabilnost
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-114840
• COBISS.SI-ID: 3415652
• Publication date in RUL: 19.03.2020

MARKELJ, Eva, 2020, Simulacije dvofaznih tokov s površinsko napetostjo z metodo hidrodinamike zglajenih delcev [online]. Master’s thesis. [Accessed 17 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=114840

Secondary language

• Language: English
• Title: Simulations of two-phase flows with surface tension using Smoothed Particle Hydrodynamics method

Abstract

The Smoothed Particle Hydrodynamics or SPH method is a meshless numerical method applicable to various problems in computational fluid dynamics (CFD). It is considered as an alternative to the traditional methods based on Navier-Stokes equations solved on meshes of discrete points. In the SPH method, the fluid is discretized with interacting particles. The SPH model consists of the aproximations of function values (velocity, density, pressure) and their derivatives using the smoothing function. Equations of SPH model are Navier-Stokes equations written for a specific particle. The method can also be used in simulations of multiphase flows where surface tension force can have a major impact. In this master thesis, a SPH method with surface tension force model is presented. Capabilities of the SPH method were demonstrated on two multiphase flow problems, where effects of surface tension force and other model parameters are presented. They also prove that SPH method is truly a powerful tool. First problem is deformation of a square droplet and the second one is famous Rayleigh-Taylor instability.

• Keywords: CFD, SPH method, smoothed particle hydrodynamics, surface tension, multiphase flow method, Rayleigh-Taylor instability