Articles written in Sadhana

    • Drag reduction by the introduction of shear-free surfaces in a turbulent channel flow


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      In this paper, a novel technique for drag reduction in turbulent flows is presented. The technique involves the modification of the large scales of turbulent flows and is a passive approach. The lateral transport of momentum, which is a dominant mechanism in turbulence, is attenuated by the introduction of moving shearfree surfaces (SFSes). This brings about a reduction in the drag. 2D simulations have been carried out for aturbulent channel flow using shear stress transport (SST) Reynolds-averaged Navier–Stokes (RANS) model and validated with the available experimental results. The interaction between the plates and the fluid is two way,and is enforced either by the use of a rigid body solver with moving mesh, or by considering the SFSes to befixed at particular locations and then updating the velocities of the plates at those locations. The latter is equivalent to solving a fully developed flow in the moving mesh case. The number, shape, size and placement of the SFSes strongly influence the amount of drag reduction. The phenomenon is confirmed to be governed by a

      ‘slow’ turbulent time scale. Further, the efficacy of the method is seen to depend on the ratio of two time scales – an advection time scale indicating the ‘resident time’ near an SFS, and the turbulent time scale. In addition, the effectiveness of the approach is improved by judicious placement of multiple SFSes in the flow.

    • Stability analysis of the carbuncle phenomenon and the sonic point glitch


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      Upwinding allows for accurate, non-oscillatory capturing of shocks waves; however, many Riemann solvers (both exact and approximate) suffer from some sort of numerical instability. One of the most mysterious and least understood of these is the carbuncle phenomenon. In the present study, we analyse theclosely allied ‘‘simplified carbuncle’’ problem, also known as the 2D shock stability problem or the 1.5D carbuncle problem. Motivated by the existence of some recently derived schemes that do not exhibit the instability, we perform a thorough stability analysis and extend previous studies by analysing the pseudo-spectra and hence the effects of non-normality in causing this instability. Our results establish that, contrary to previous indications in the literature, a non-linear mechanism is responsible for the instability. In order to understand thenature of this non-linear mechanism better, we perform a non-linear analysis of the sonic glitch, which shares some common features with the carbuncle. We provide two previously unknown results. Firstly, we show that even the ‘‘entropy-satisfying’’ Godunov scheme violates the entropy condition in the sonic glitch. Secondly, we provide a more accurate definition for the entropy condition for scalar conservation laws that supports the previous claim. We conjecture that a similar non-linear anti-dissipative mechanism might be responsible in triggering the carbuncle. This work is expected to lead to a better understanding of possible unphysical behaviour in Riemann solvers and thus help in the design of better solvers for high-Reynolds-number flows.

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