Abstract
A mathematical model of pulsating flow is proposed in the paper. The model includes more accurate description of energy dissipation, so it allows, for example, better stability analysis of water power plant control and more effective operation. Flow in a pipeline system is usually treated as a one-dimensional flow. This is also applied for more difficult cases of the Newtonian and non-Newtonian liquids simulations in the rigid or flexible pipes. Computational simulations of pressure pulsations in pipelines often predict lower damping than what the experimental results show. This discrepancy can be caused by neglecting one of the important damping mechanisms. The second viscosity describes the energy losses due to the compressibility of the liquid. Its existence and use in the computations specifies the real pulsations damping descriptions and predictions. A frequency dependent model of pressure pulsations including second viscosity is introduced. The second viscosity is determined from the system eigenvalue. The experiments were performed with water for low frequencies (from 0.1 to 1 kHz). This area is not fully covered by the current available research results.
Highlights
Fluid flow in pipeline systems is usually treated as a one-dimensional flow because one component of velocity is dominant; other components can be neglected
Considering the one-dimensional flow assumption, computational simulations of transient events, pressure pulsations or water hammer often suffer from inaccuracy of the mathematical description of the dissipation mechanism, which is usually derived from the energy loss of steady flow and is proportional to velocity squared
When we look for experimental data of second viscosity, we find out that they are very rare
Summary
Fluid flow in pipeline systems is usually treated as a one-dimensional flow because one component of velocity is dominant; other components can be neglected. Considering the one-dimensional flow assumption, computational simulations of transient events, pressure pulsations or water hammer often suffer from inaccuracy of the mathematical description of the dissipation mechanism, which is usually derived from the energy loss of steady flow and is proportional to velocity squared. Real energy dissipation is stronger than numerical models predict. This is obvious when the method of characteristic is used. Examination of the theoretical model of liquid was performed in [10], where authors noted the role of second viscosity in the spreading of wave fronts, dilatation and compression of fluid or attenuation of sound waves. A method of the second viscosity determination from the damping of pressure pulsations is described within this paper. The suggested procedure allows determining of the second viscosity at low frequencies
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