THE THEORY OF NONLINEAR ELASTIC-PLASTIC-VISCOUS RIGID DEFORMATION OF EXTREMELY STRAINED SOILS IN BASES OF LOADED SINGLE PILES: MATHEMATICAL MODEL

Flow drag reduction induced by chemical additives, more commonly called drag-reducing agents (DRAs), has been studied for many years, but few studies can manifest the mechanism of this phenomenon. In this paper, a new mathematical model is proposed to predict the upper limit of drag reduction with polymer DRAs in a turbulent pipe flow. The model is based on the classic finitely extensible nonlinear elastic-Peterlin (FENE-P) theory, with the assumption that all vortex structures disappear in the turbulent flow, i.e., complete laminarization is achieved. With this model, the maximum drag reduction by a DRA at a given concentration can be predicted directly with several parameters, i.e., bulk velocity of the fluid, pipe size, and relaxation time of the DRA. Besides, this model indicates that both viscosity and elasticity contribute to the drag reduction: before a critical concentration, both viscosity and elasticity affect the drag reduction positively; after this critical concentration, elasticity still works as before but viscosity affects drag reduction negatively. This study also proposes a correlation format between drag reduction measured in a rheometer and that estimated in a pipeline. This provides a convenient way of pipeline drag reduction estimation with viscosity and modulus of the fluids that can be easily measured in a rheometer.

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A MATHEMATICAL MODEL AND SIMULATION RESULTS OF THE DYNAMIC SYSTEM RAILWAY VEHICLE WHEEL–TRACK WITH A WHEEL FLAT / DINAMINĖS SISTEMOS „GELEŽINKELIŲ VAGONO RATAS – KELIAS“ SU RATO IŠČIUOŽA MATEMATINIS MODELIS IR MODELIAVIMO REZULTATAI

Mokslas - Lietuvos ateitis ◽

10.3846/mla.2014.696 ◽

2014 ◽

Vol 6 (5) ◽

pp. 531-537 ◽

Cited By ~ 4

Author(s):

Rasa Žygienė ◽

Marijonas Bogdevičius ◽

Laima Dabulevičienė

Keyword(s):

Mathematical Model ◽

Dynamic System ◽

Vertical Plane ◽

Railway Vehicle ◽

Discrete Elements ◽

Model And Simulation ◽

Research Findings ◽

Wheel Flat ◽

Nonlinear Elastic ◽

Wheel Track

A mathematical model of the system Railway Vehicle Wheel–Track with a wheel flat of a wheelset has been made. The system Railway Vehicle Wheel–Track has been examined on the vertical plane. The mathematical model of the system Railway Vehicle Wheel–Track has employed linear, nonlinear, elastic and damping discrete elements. Rail dynamics haves been described using the finite element method. The unevenness of the rail and the wheel of the wheelset have been evaluated considering the contact between the rail and the wheel flat of the wheelset. The analysis of dynamic processes taking place in a railway vehicle wheel with the wheel flat moving at speed V = 60 km/h has been accomplished. The results of mathematical modelling of the above introduced dynamic system have been presented along with graphically displayed research findings of the conducted research. Sukurtas sistemos „Geležinkelių vagono ratas – kelias“ su aširačio rato iščiuoža matematinis modelis. Sistema „Geležinkelių vagono ratas – kelias“ nagrinėjama vertikalioje plokštumoje. Sistemos „Geležinkelių vagono ratas – kelias“ matematiniame modelyje yra panaudoti tiesiniai ir netiesiniai tamprieji ir slopinimo diskretiniai elementai. Bėgio dinamika aprašoma baigtinių elementų metodu. Kontakte tarp bėgio ir aširačio rato su iščiuoža įvertinti bėgio ir aširačio rato nelygumai. Atlikta geležinkelio vagono rato su iščiuoža, judančio greičiu V = 60 km/val., dinaminių procesų analizė. Pateikti šios dinaminės sistemos matematinio modeliavimo rezultatai. Tyrimų rezultatai pavaizduoti grafiškai ir pateiktos tyrimų išvados.

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