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 $7.5\le R{e}_D\le 30$, comprising variations in groove depth ($h$) and spacing ($\beta$). The groove width ($w$) is kept constant, while h/w varies across four levels ($0.5\le h/w\le 2$) and $\beta$ across five angles ($10°\le \beta \le 45°$). The results exhibit strong agreement with unbounded flow data, confirming blockage independence across the examined regime. Detailed analysis shows that $\beta$ has a stronger influence than $h/w$ on surface-pressure-dependent variables ($C_{p,0}$, $C_{p,b}$, $C_D$, ${\theta }_{sep}$) and wake-defining parameters ($L_w$, $W_w$, $\xi$, $\eta$), underscoring the dominant role of $\beta$ in rectilinear groove aerodynamics. In this regard, a critical spacing of $\beta =20°$ is observed, beyond which the sensitivity of the parameters toward the cylinder configuration decreases. Thus, significant flow control and drag reduction are attained for $R{e}_D=7.5$ at the lowest spacing $\beta =10°$, regardless of the groove’s $h/w$. Among these, the streamwise-oriented variables, $C_{p,0}$, $C_D$, $L_w$, $\xi$, and $u_{min}$, exhibit monotonic trend with respect to $\beta$ and are modeled using power-law relations. The models for $C_{p,0}$ and $C_D$ exhibit significant accuracy with $R^2\approx 0.999$ across all $\beta$ values considered, while it is 0.89–0.98 for $L_w$, $\xi$, and $u_{min}$, depending on $R{e}_D$. Transverse-oriented parameters ($W_w\mathrm{a}\mathrm{n}\mathrm{d}\eta$) vary non-monotonically. In addition, it is found that the streamwise locations of maximum wake width ($x_{w,max}$) and minimum velocity ($x_{u,min}$) are unaffected by the grooved cylinder configuration.