Identification of Non-Newtonian Rheological Parameter through an Inverse Formulation

In this work, we introduce an inverse formulation to be applied in the identification of a rheological parameter associated to non-Newtonian fluids. It is built upon a creeping flow through a 4 to 1 axisymmetric abrupt contraction. The fluid is modeled by the Generalized Newtonian Fluid constitutive equation. The viscosity function is based on the one proposed by Souza Mendes et al. (1995). It predicts an extensional elastic behavior, controlled by a theological parameter 0, which is the parameter determined via the proposed identification procedure. The numerical solution of the forward problem, needed in the iterative procedure introduced by the inverse formulation, is obtained through the finite volume method. A sensitivity analysis is also performed to evaluate the effect of the parameter theta on the dimensionless pressure drop through the contraction. The optimization algorithm is based on an iterative method to find the minimum of the cost function, which is given by the least square difference between numerical and experimental values of the dimensionless pressure drop. The gradient method was used to update the parameter theta, starting from the cost function gradient. The results obtained with the sensitivity analysis validated the adequacy of the proposed cost function, which is a key aspect on the identification formulation. Moreover, it shows that the method provides an attractive alternative for estimation of rheological properties.