The present work numerically investigates vortex-induced vibrations (VIV) of a two-dimensional circular cylinder with an axisymmetric slit at Reynolds number 500. The study examines the effects of slit shape (i.e., converging, diverging, and parallel slits), the effect of slit-area ratios, slit width, and its angle with the freestream velocity on aerodynamic forces, vibration response, and associated flow characteristics. The results demonstrate that the addition of the slit assists the VIV suppression by adding an extra amount of flow to the main flow. It results in the stabilized wake with the pressure recovery downstream of the cylinder and causes a reduction in the lift force over the cylinder. Also, there exist different shedding patterns associated with different slit shapes. A proper orthogonal decomposition of the flow field suggests that among all the three slits, the parallel slit heavily modifies the flow behind the cylinder by distributing the amount of energy to a large number of modes as compared to other slits (converging slit and diverging slit), where the most of the energy is contained in a couple of modes. Further, increasing the slit angle (for parallel slit) with respect to the freestream increases the slit effectiveness up to a specific value of slit-angle and beyond that starts to affect the VIV suppression adversely. Observations for the effect of slit width are also reported from the perspective of suppression of VIV.
The present study investigates the passive flow control phenomena over a two-dimensional circular cylinder using numerical simulations in the laminar regime. The aim is to explore one of the passive control techniques, which involves the introduction of a slit to the geometry of the cylinder. The two parameters, slit width ratio S/D (slit width/diameter) and slit angle (measured with respect to the incoming flow direction), play an essential role in determining the trend of critical Reynolds number (Rec). Most of the analysis invokes flow visualization and saturation amplitude methods to obtain the critical Reynolds number (indicative of the onset of vortex shedding) for different cases. Further, Hopf bifurcation analysis using Stuart-Landau equation and global stability analysis confirm the accuracy and consistency in the predicted solutions. The additional amount of flow through slit increases the pressure downstream of the cylinder, which consequently leads to an increase in Rec of the modified cylinder. The critical Reynolds number increases with S/D of the modified cylinder at 0 slit angle (as an additional amount of flow grows with S/D). The critical Reynolds number shows an increasing trend with the slit angle in the range of S/D= 0.05-0.15 as the fluctuation intensity reduces with slit angle in this range. For S/D=0.15-0.25, the extra amount of flow through slit induces the instability in wake which causes a decrease in Rec with slit angle. A correlation is obtained that estimates the critical Reynolds number for a given S/D and slit angle.
Most of the turbulence models in practice are based on the assumption of a linear relation between Reynolds stresses and mean flow strain rates which generally provides a good approximation in case of attached and fully turbulent flows. However, this is seldom the need in most of the engineering problems; the majority of the engineering problems observe flow separation or flow transition. Recent developments in non-linear turbulence models have proven significant improvement in prediction of separated flow due to better resolution of anisotropy in modeled Reynolds stress. The domain of application of this improved RANS model can be extended to flow transitions as well, where the resolution of anisotropy in Reynolds stress is required. For a validation of such kind, a two-dimensional numerical study has been carried out over NACA 0021 with k- SST model with non-linear correction at Re = 120,000 for various angles of attack which experiences the formation of a Laminar Separation Bubble (LSB). A correct prediction of LSB requires an accurate resolution of anisotropy in Reynolds stresses. For comparison with other linear models, the simulations are also performed with k-kl- (a 3equation linear transition model), k- SST (a 2-equation linear model) and Spalart-Allmaras (a 1-equation model). The performance of these models is assessed through aerodynamic lift, drag, pressure and friction coefficients. It is found that the non-linear k- SST and kkl- transition model provide comparable quality of prediction in lift and drag coefficients (in spite of the fact that non-linear k- SST involves solving less number of transport equation than the transition model) as observed in the experiments whereas k- SST and SA models under predict the drag coefficient value at low angle of attack due to inability to capture the separation induced transition. It is also observed that the location of laminar separation bubble is captured accurately when non-linear or transition model is used as opposed to the SA or linear SST models, which lack in the ability to predict the same.
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