Parametric design and mechanical-hydraulic assessment of spherical in-pipe drag-based turbines

• Parametric framework for spherical in-pipe drag-based turbine design. • Dimensionless Ψ* metric integrates torque and pressure drop. • Geometry A improves Ψ* by up to 28% vs. reference designs. • CFD-based comparison of five spherical geometries. • Validated transient model predicts cyclic torque behavior. In-pipe drag-based hydrokinetic turbines represent a promising alternative for harnessing excess hydraulic energy within pressurized water distribution systems. Nonetheless, their implementation faces challenges related to low efficiency and pressure losses, which could potentially jeopardize system stability. This study assesses the influence of blade geometry on the mechanical and hydraulic performance of spherical in-pipe drag turbines operating under confined flow conditions. A systematic algebraic design methodology is utilized to establish offset spherical rotors with specified parameters, including blade diameter, overlap, and wall clearance, calibrated to a designated pipe diameter. Five configurations are examined, comprising two reference geometries (Semi-Elliptic and Bach) and three innovative designs (Geometries A, B, and C). The evaluation employs a validated transient Computational Fluid Dynamics (CFD) approach, based on the Reynolds-Averaged Navier-Stokes (RANS) equations coupled with the SST κ − ω turbulence model. Numerical validation against published benchmarks demonstrates substantial agreement in the prediction of cyclic torque and efficiency. The comparative assessment employs identical boundary conditions at the optimal flow coefficient ( ϕ = 1.5). In addition to conventional torque and efficiency metrics, a dimensionless mechanical-hydraulic effectiveness parameter (Ψ*) is introduced to quantify the trade-off between torque generation and pressure drop. The findings demonstrate that blade geometry significantly influences torque output, angular distribution, and hydraulic penalty. While Geometry C yields the highest average torque (0.4105 Nm), it also results in the greatest pressure drop (18.867 kPa). Geometry A provides the most advantageous balance, attaining the highest hydraulic efficiency (9.1%) and the maximum Ψ* value, thereby enhancing mechanical-hydraulic effectiveness by up to 28% in comparison to reference profiles. The proposed design methodology and performance metric establish a transferable approach for the geometry-driven optimization of in-pipe energy recovery systems.