Motion of a body in a fluid with pressure dependent viscosity

Sláčík, Stanislav

A lot of technologically relevant incompressible fluids exhibit a substantial variaton of viscosity with the pressure;a falling cylinder viscometer is frequently used for the measurements, determining the viscosity indirectly from the time it takes the sinker to fall a given distance. The relation between the sinker fall velocity and the fluid viscosity is, however, derived under the constant viscosity assumption. The objective of the present thesis is to perform a numerical simulation of the viscometric experiment, assuming an explicit form of the pressure-viscosity dependence and realistic parameter values and to quantitatively assess the difference in body motion to the Navier- Stokes model. The computational method proposed, handling both the nonlinear constitutive relation and the body motion, was tested on simple problems with analytical solutions. The semianalytical relation for the Navier-Stokes model, also re-derived here, is compared to the computational results.The validity of the assumptions used in the theoretical derivation, based on the results of the numerical simulation, is discussed regarding the geometry of the viscometer. Powered by TCPDF (www.tcpdf.org)

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