Effect of Groove Spacing on the Characteristics of Steady Symmetric Wake

This numerical study investigates steady separated flow past a grooved circular cylinder within the Reynolds number range 7.5≤ReD≤30, comprising variations in groove depth (h) and spacing (β). The groove width (w) is kept constant, while h/w varies across four levels (0.5≤h/w≤2) and β across five angles (10°≤β≤45°). The results exhibit strong agreement with unbounded flow data, confirming blockage independence across the examined regime. Detailed analysis shows that β has a stronger influence than h/w on surface-pressure-dependent variables (Cp,0, Cp,b, CD, θsep) and wake-defining parameters (Lw, Ww, ξ, η), underscoring the dominant role of β in rectilinear groove aerodynamics. In this regard, a critical spacing of β=20° is observed, beyond which the sensitivity of the parameters toward the cylinder configuration decreases. Thus, significant flow control and drag reduction are attained for ReD=7.5 at the lowest spacing β=10°, regardless of the groove’s h/w. Among these, the streamwise-oriented variables, Cp,0, CD, Lw, ξ, and umin, exhibit monotonic trend with respect to β and are modeled using power-law relations. The models for Cp,0 and CD exhibit significant accuracy with R2≈0.999 across all β values considered, while it is 0.89–0.98 for Lw, ξ, and umin, depending on ReD. Transverse-oriented parameters (Ww and η) vary non-monotonically. In addition, it is found that the streamwise locations of maximum wake width (xw,max) and minimum velocity (xu,min) are unaffected by the grooved cylinder configuration.