The present study aims to solve the hydrodynamic stability problem through Direct Numerical Simulations(DNS) of the linearised 3D perturbation equations. The traditionally used schemes for stability analysis solve the stability equations as an Eigenvalue problem by assuming simplified forms for the perturbations. They also solve for only the spatial or the temporal evolution of a particular mode in the case of Local Stability Analysis or a group of modes in the case of Global Stability Analysis. DNS of the stability equations provides the simultaneous spatial and temporal evolution of all perturbations in the flow. This provides a better insight into the physics of the perturbation evolution than other methods of stability analysis used today. We have demonstrated the method using example problems of boundary layer flow over a porous laminated flat plate and flow past a square prism with slip surfaces. The above problems are solved using an in-house DNS code to generate the accurate base flow input required by the stability DNS code. In the case of porous laminated flat plate, it
was found that the porous lamination induces a slip velocity at the fluid-porous interface. This helps delay flow separation by maintaining a favourable stream-wise pressure gradient and positive shear stress at the interface. In the case of square prism, the slip velocity was applied on the surfaces of the prism using Maxwell’s slip model. Our analysis revealed that slip on the top and bottom surfaces of the prism is more effective in controlling vortex shedding than slip on the leading and trailing faces. A complete suppression of vortex shedding was observed for Re ≤ 60 in the former and negligible influence in the latter. The stability of the flow was analysed by solving the 3D linearised perturbation equations with perturbations added at the inlet. The perturbations developed into low frequency, large wavelength waves downstream of the cylinder. The temporal evolution of these perturbations pointed to the slip velocity acting as a inhibitor to the growth of the perturbations. The calculations of perturbation kinetic energy affirmed the suppressive nature of slip velocity. The stability
analysis using DNS of the perturbation equations provided data to analyse the absolute and convective instabilities in the flow simultaneously. The efficacy of slip velocity as a passive flow separation control technique was confirmed through stability analysis.