Non-Newtonian fluid hammer in elastic circular pipes: Shear-thinning and shear-thickening effects

• A model is developed for non-Newtonian fluid hammer in elastic pipes.
• The model is used to study pipe transients due to sudden valve closure.
• Shear-thickening effects result in more rapid attenuation of the transient.
• Excessive Richardson annular effect is associated with shear-thinning fluids.
• Shear-thickening fluids cause higher transient pressures due to line packing.

The present study aims to bridge the gap between water hammer theory and non-Newtonian fluid mechanics. To achieve this, a detailed numerical study is carried out to investigate the effect of sudden valve closure on the flow dynamics of power-law fluids in circular pipes. An unsteady two-dimensional pipe flow model is employed which takes into consideration both fluid compressibility and pipe elasticity. The present model is numerically integrated in time using the fourth-order accurate Runge–Kutta method while spatial terms are discretized using second-order accurate central difference expressions. Present results show that laminar pipe transients are significantly affected by the shear-thinning and shear-thickening behavior of the non-Newtonian fluid. Reported unsteady velocity profiles during the pipe transient show an excessive Richardson annular effect in the case of shear-thinning fluids, which is reduced significantly in the case of shear-thickening fluids. Present results also show that the shear-thickening behavior leads to more rapid attenuation of the fluid transient. Moreover, shear-thickening effects give rise to excessive pipeline packing which results in a pressure rise at the valve that could significantly exceed the theoretical maximum predicted by the inviscid Joukowsky pressure rise.