A numerical investigation on rheological turbulent flow through a 90° mixing elbow

Abstract Mixing elbows are widely used in various industrial processes to mix two different Newtonian or non-Newtonian fluids under turbulent flow conditions. This study numerically investigates the fluid flow and mixing characteristics in 90-degree elbows with different bend curvatures (curvature ratios of 3, 6, and 9) and Reynolds numbers ranging from 1 × 10 4 to 5 × 10 5 for both fluid types. The Reynolds-Averaged Navier–Stokes equations are solved using the turbulent k-epsilon model in ANSYS Fluent. Results show that the bend curvature creates an adverse pressure gradient that drives secondary flows, which become more pronounced with higher Reynolds numbers and lower curvature ratios. Higher Reynolds numbers improve mixing quality, as indicated by velocity and temperature variations quantified using standard deviations. For Reynolds numbers in the range of 10 4 , velocity fluctuations initially increase, but at higher values (~ 10 5 ), they decrease, even by up to 64% as the Reynolds number rises from 1 × 10 5 to 5 × 10 5 . Similarly, increasing the curvature ratio enhances mixing efficiency, with a 32% reduction in velocity fluctuations when the curvature ratio increases from 6 to 9. Furthermore, shear-thinning fluids ( $$n = 0.6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.6</mml:mn> </mml:mrow> </mml:math> ) exhibit superior mixing performance, with a standard deviation of velocity fluctuations at the outlet of 0.32, compared to 0.54 for shear-thickening fluids ( $$n = 1.4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.4</mml:mn> </mml:mrow> </mml:math> ). In terms of temperature fluctuations also, a similar trend is observed. These findings are valuable for optimizing mixing and fluid transport in industries such as chemical processing and food production, where effective mixing of complex fluids is critical. This study provides insights for improving the design of mixing systems that handle fluids with various rheological characteristics.