AI Summary & Key Takeaways
AI InsightAs a result, the material parameters, sensitive and non-sensitive, were determined in each of the constitutive equations.
📌 3 Key Takeaways
Abstract
The effect of material parameters on three rate-type constitutive equations (White-Metzner, Oldroyd 3-constant and Kopaç-Arıkol) used successfully according to the literature was investigated. The flow along the symetry axis of a converging-diverging flow channel was considered. In order to determine the effect of material parameters appearing in constitutive equations, the tensorial expressions of the models were reduced to the axis of symmetry, using derivative operators of models and flow kinematics. Arıkol's values (1976, 1985) were used for the velocity and initial viscosity values appearing in reduced nonlinear ordinary differantial equations. The reduced constituve equations were solved numerically using the 4th order Runge-Kutta method. In these calculations, velocity and the 1st and 2nd derivatives of velocity were used as input in the equations. Solving the constitutive equations for 3 different values of the material parameters, the normal stress differences were determined along the axis of symmetry. The sum of squares between the calculated normal stress values and Arıkol's(1976, 1985) experimental values were determined. As a result, the material parameters, sensitive and non-sensitive, were determined in each of the constitutive equations.
Özet
The effect of material parameters on three rate-type constitutive equations (White-Metzner, Oldroyd 3-constant and Kopaç-Arıkol) used successfully according to the literature was investigated. The flow along the symetry axis of a converging-diverging flow channel was considered. In order to determine the effect of material parameters appearing in constitutive equations, the tensorial expressions of the models were reduced to the axis of symmetry, using derivative operators of models and flow kinematics. Arıkol's values (1976, 1985) were used for the velocity and initial viscosity values appearing in reduced nonlinear ordinary differantial equations. The reduced constituve equations were solved numerically using the 4th order Runge-Kutta method. In these calculations, velocity and the 1st and 2nd derivatives of velocity were used as input in the equations. Solving the constitutive equations for 3 different values of the material parameters, the normal stress differences were determined along the axis of symmetry. The sum of squares between the calculated normal stress values and Arıkol's(1976, 1985) experimental values were determined. As a result, the material parameters, sensitive and non-sensitive, were determined in each of the constitutive equations.