Dimensionless Analysis of Non-Newtonian Power-Law Fluid Hammer

Abstract

The current study presents a mathematical model to simulate a power-law fluid hammer problem in pipelines. The flow is considered two-dimensional, isothermal, weakly compressible, and laminar. The governing equations consisting of mass and momentum balances are solved by the method of characteristics. The model results are compared to other numerical model values and validated against measured data found in the literature. The comparisons show that the two-dimensional model agrees better with experimental data than the one-dimensional approach. Two dimensionless parameters (a dissipative parameter and the power-law index) are identified to govern the phenomenon, and a sensitivity analysis with respect to these parameters is conducted. It can be anticipated that the first pressure overshoot due to line packing and pressure wave dissipation increase with the dissipative parameter and with the power-law index.