Modelling of isothermal separated gas-liquid flow in a vertical pipe

Tekavčič, Matej (author), Kljenak, Ivo (mentor)

Periodic liquid waves of large amplitude are one of distinctive phenomena observed in the churn flow regime of gas-liquid flow in vertical pipes, where the liquid flowing on the conduit wall is entrained upwards by the gas flow in the core. The basic mechanisms of churn flow can be related to the onset of the flooding phenomena (or the counter-current flow limitation) in vertical conduits. Flooding is of particular interest for safety analyses of the loss-of-coolant accident in pressurized water nuclear reactors, where part of the liquid coolant inventory evaporates due to the pressure loss caused by a leak in the primary system. The upward flow of steam in the central region of a vertical pipe can limit the downward flow of water film on the pipe wall. Flooding develops when the flow of liquid film reverses and cannot penetrate further into the primary system, which in turn limits the cooling of reactor components. Prediction of the onset of flooding in realistic geometries is very uncertain, indicating the need for more thorough understanding of its triggering mechanisms. New analytical model for the shape of a stationary liquid wave in vertical churn flow regime is proposed in the present thesis. The model is based on the hyperbolic secant function and offers more accurate description of the wave shape than the simpler hemispherical and sinusoidal models. The complexity of the proposed model is comparable to the existing Gaussian model and can be used in mechanistic models of wave motion in vertical churn flow. The present thesis deals primarily with the three-dimensional transient simulation of isothermal churn flow of air and water in a vertical pipe. Turbulent features in the air-water flow are modelled using the unsteady Reynolds Averaged Navier-Stokes approach with the k-$\omega$ SST (Shear Stress Transport) model. Interface sharpening with bounded compression was used to resolve the gas and liquid interface. The validity of the proposed modelling approach was confirmed by comparing the calculated results with the experimental results from the literature. Specifically, the present work investigates the frequency of large liquid waves, and how it is influenced by the liquid inlet model, with the final purpose to understand main mechanisms affecting the actual flow development. Namely, the existing simulations use a simple inlet boundary condition to model the perforated wall liquid inlet section, commonly used in experiments. Here, the magnitude of wall normal velocity is proposed as a modelling parameter, which is controlled by the boundary area at a given mass flow rate. The results show that wave frequencies are approximately proportional to the imposed wall normal velocity at the liquid inlet. Parametric study revealed that a suitable value for this parameter can be determined over a range of flow conditions, leading to a good agreement between the simulated and the measured wave frequencies. The main finding of the present thesis suggest, that the properties of large liquid waves in the churn flow do not depend solely on geometric and macroscopic flow conditions (such as, for instance pipe diameter and flow rates), but are also very much affected by the boundary conditions where liquid enters into the vertical pipe.

• Language: English
• Keywords: simulacija dvo-faznega toka, navpični raztrgan tok, omejitev proti-toka, frekvenca valov, model kapljevinskega vstopa
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2018
• PID: 20.500.12556/RUL-105912
• COBISS.SI-ID: 3286372
• Publication date in RUL: 23.12.2018

Secondary language

• Language: Slovenian
• Title: Modeliranje izotermnega ločenega toka plina in kapljevine v navpični cevi

Abstract

V dvofaznem navzgor usmerjenem raztrganem toku plin-kapljevina v navpični cevi kapljevina omoča steno cevi, medtem ko plin teče v osrednjem delu. Za raztrgan tok so značilni veliki poplavni valovi kapljevine, ki periodično potujejo navzgor v smeri toka plina. Raztrgan tok je tesno povezan z mehanizmi pojava poplavljanja oziroma omejitve protitoka. Pri izlivni nezgodi v tlačnovodnem jedrskem reaktorju, kjer pride do izgube tlaka v primarnem sistemu in se del hladila upari, je poplavljanje ali omejitev protitoka kapljevine eden od pomembnih pojavov z vidika varnosti. V navpični cevi lahko tok vodne pare, ki teče v osrednjem delu cevi, omejuje tok filma kapljevine, ki teče navzdol ob steni cevi in jo hladi. Do omejitve protitoka kapljevine pride v primeru zelo visoke hitrosti pare, ki povzroči vzbujanje in prekinjanje kapljevinskega filma ob steni: para lahko potiska kapljevino nazaj – se pravi, navzgor po cevi - in tako onemogoča hlajenje sten. Lokalna napoved pojava v poljubni geometriji in pri poljubnih pogojih zahteva razumevanje in poznavanje začetnih mehanizmov poplavljanja. Za analitičen popis oblike valov kapljevine v navpičnem raztrganem toku vode in zraka smo predlagali novi model, izpeljan na podlagi funkcije hiperboličnega sekansa. V primerjavi z enostavnejšimi polkrožnimi in sinusnimi modeli oblike, predlagani model bolje opiše izmerjeno obliko valov. Pri tem je novi model še vedno dovolj enostaven, saj je njegova zahtevnost primerljiva z obstoječim Gaussovim modelom oblike, in je primeren za uporabo v mehanističnih modelih gibanja valov v raztrganem toku. Opravili smo trirazsežne simulacije kapljevinskih valov v nestacionarnem izotermnem raztrganem režimu toka vode in zraka v navpični cevi. Turbulentni tok smo modelirali z metodo nestacionarnih Reynoldsovo povprečenih Navier-Stokesovih enačb in k-$\omega$ SST (ang. Shear Stress Transport) turbulentnim modelom. Za popis dvofaznega sistema zraka in vode smo uporabili model homogene mešanice z metodo ostrenja medfazne površine. Veljavnost predlaganega modeliranja smo potrdili s primerjavo izračunanih rezultatov z eksperimentalnimi rezultati iz literature. Ukvarjali smo se predvsem z vplivom modela kapljevinskega vstopa v cev in njegovim vplivom na simulirane frekvence valov. V tipičnem eksperimentu kapljevina vstopa v cev skozi porozno steno, ki jo v simulacijah obravnavamo poenostavljeno kot vstopni robni pogoj za kapljevino na kratkem odseku stene cevi. Pri podanem masnem pretoku kapljevine nam površina vstopne ploskve določa velikost komponente hitrosti kapljevine, ki je pravokotna na steno. Pokazali smo, da je frekvenca valov, določena na podlagi simulacij, sorazmerna s pravokotno komponento hitrosti kapljevine na vstopu. V doktorski tezi smo ugotovili, da lastnosti poplavnih valov kapljevine v navpičnem raztrganem toku niso odvisne le od same geometrije cevi ter makroskopskega pretoka kapljevine in plina, temveč v precejšnji meri tudi od robnih pogojev na samem vstopu tekočine v cev.

• Keywords: two-phase flow simulation, vertical churn flow, counter-current flow limitation, wave frequency, liquid inlet model