Publikacje

Streszczenie:

Artykuł dotyczy matematycznego modelowania w pełni rozwiniętego przepływu hydromieszaniny Binghama w przewodzie kołowym. Model matematyczny zbudowano na bazie równań Naviera-Stokesa z zastosowaniem koncepcji lepkości pozornej. Problem domknięcia układu równań, wynikający z dodatkowych składowych tensora naprężeń turbulentnych, rozwiązano poprzez użycie dwu równaniowego modelu turbulencji, w którym zastosowano zmodyfikowaną funkcję tłumiącą turbulencję przy ścianie. Ostateczna postać modelu matematycznego zawiera trzy nieliniowe równania różniczkowe cząstkowe. Głównym celem pracy jest przedstawienie wzmożonego tłumienia turbulencji w obszarze przyściennym, jako że współczynnik strat tarcia hydromieszaniny jest niższy w stosunku do wody. Artykuł przedstawia wyniki numerycznej symulacji współczynnika strat tarcia dla szlamu z niskim, umiarkowanym i wysokim progiem płynięcia. Obliczony jednostkowy spadek ciśnienia porównano z wynikami badań eksperymentalnych, uzyskując satysfakcjonującą dokładność. Wykazano, że jednostkowy spadek ciśnienia i współczynnik strat tarcia zależą istotnie od progu płynięcia. Wyniki numerycznej symulacji przedstawiono w postaci wykresów i wniosków oraz omówiono możliwe przyczyny wzmożonego zjawiska tłumienia turbulencji przy ścianie.

Abstract:

The paper deals with the mathematical modelling of fully developed turbulent flow of a Bingham hydromixture in a pipe. The mathematical model is based on time averaged Navier-Stokes equations and uses the apparent viscosity concept. The problem of closure of the turbulence stress tensor was solved by the two-equation turbulence model in which a modified turbulence damping function was taken into account. The final form of the mathematical model constitutes a set of three non-linear partial differential equations. The main aim of the paper is to demonstrate a significant decrease of turbulence near the pipe wall, as the friction factor is below that for a water flow. The paper presents results of numerical simulation of the frictional head loss and friction factor for slurry flows with low, moderate, and high yield stresses. Predicted frictional head losses have been compared with experimental data showing satisfying agreement. It is demonstrated that the frictional head loss and the friction factor substantially depend on the yield stress. The results of numerical simulation are presented as figures and conclusions. Possible causes of turbulence damping near the pipe wall are discussed.

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Simulation of the friction factor in a yield-stress slurry flow which exhibits turbulence damping near the pipe wall