Shirzad Hosseinverdi

Direct numerical simulations of the effect of free-stream turbulence on 'long' laminar separation bubbles

Laminar separation bubbles on a flat plate boundary layer in the presence of freestream turbulence (FST) were investigated by means of Direct Numerical Simulations (DNS). A suction/blowing velocity distribution was applied along the free-stream boundary of the computational domain to induce separation on the flat plate. For numerically generating free-stream turbulence, isotropic grid turbulence, which is obtained from a superposition of eigenmodes from the continuous spectrum of OrrSommerfeld and Squire Equations, was introduced at the inflow boundary. The effect of the spanwise extent of the computational domain was investigated by carrying out computations with two different spanwise domain widths. The main characteristics of the separation bubble, such as the bubble length and the skin-friction distribution were very similar for both spanwise domain sizes. However, for the wider domain the 2-D “rollers” were modulated in the spanwise direction and broke up earlier than for the narrow domain. For the narrow domain counter-rotating streamwise vortices appeared (“braids”). Detailed numerical simulations were performed to investigate the effect of the free-stream turbulence energy spectrum. It was found that the transition location was essentially independent of the integral length scale of the free-stream turbulence. Also, the dependence of the separation length on the integral length scale was found to be very weak for the range of length scales considered in our studies. In contrast, the separation length was significantly reduced already for relatively low free-stream turbulence intensity (0.1%) when compared to the baseline case with zero FST. When the FST was increased further the length and height of the bubble continued to decrease. Instantaneous flow field visualizations revealed that the spanwise coherence of the dominant 2D structures was weakened with increasing FST intensity. In addition, proper orthogonal decomposition (POD) analyses of the instantaneous flow data revealed that streamwise “vortical” structures became dominant for high FST levels. Based on a detailed analysis of the time-dependent flow field and a comparison between DNS results and linear stability theory (LST) calculations, it was found that for freestream turbulence intensities up to 2%, transition in the bubble was still due to an inviscid (Kelvin-Helmholtz) instability of the inflectional velocity profile in the separated flow region, and not due to nonlinear bypass mechanisms.

Effect of Free-Stream Turbulence on the Structure and Dynamics of Laminar Separation Bubbles

Laminar separation is always associated with considerable unsteadiness. This unsteadiness is caused by large coherent structures that are a consequence of hydrodynamic instability mechanisms of the mean flow. The mean-flow topology and unsteady behavior of laminar separation bubbles (LSB) is in fact mainly governed by instability and transition. In this paper, laminar separation bubbles, which are generated on a flat plate by imposing a streamwise adverse pressure gradient, are investigated by means of Direct Numerical Simulations (DNS). The streamwise pressure gradient for the DNS is chosen such that the inviscid wall pressure distribution, as reported in the Gaster 1 experimental series I, case IV, is closely matched. This case was classified as a “short” laminar separation bubble. The timeaveraged flow field obtained from the DNS with no external disturbances introduced (no freestream turbulence), reveals that the bubble is longer than observed in the experiments. In fact, the bubble obtained in the simulations appeared to be a “long” bubble. This was confirmed by comparing the simulation results with the measurements by Gaster 1 for a long bubble. The discrepancy between the numerical simulations and experiments is possibly due to an earlier onset of transition in the experiments. In the present simulations, instead of forcing with random disturbances to promote transition, isotropic grid turbulence, which was modeled using a superposition of eigenmodes from the continuous spectrum of the Orr-Sommerfeld and Squire operators is introduced at the inflow boundary. It was observed that as the freestream turbulence (FST) intensity was increased, the bubble became smaller. The separation bubble was in fact shortened from both sides (separation and reattachment sides) in the presence of free-stream turbulence. Comparing the wall pressure distribution for 0.2% freestream turbulence with Gaster 1 experiment revealed that then the bubble could be classified as a “short” bubble. Based on the simulations performed, FST can change a separation bubbles form “long” to “short”. In order to investigate bubble “bursting”, the development of bubble, that had became short due to FST, was simulated after the FST was turned-off. The short bubble grew for a short period of time. Surprisingly however, it did not return to the original, state without FST.

Direct Numerical Simulations of transition to turbulence in two-dimensional laminar separation bubbles

Transition to turbulence in two-dimensional laminar separation bubbles on a flat plate is investigated by Direct Numerical Simulations (DNS). In laminar separation bubbles transition and separation are present simultaneously and interact in a physically complex manner. A set of numerical simulations has been carried out to investigate the transition process, and in particular to shed light on the development of large coherent structures, which arise during the transition. For the separation bubbles investigated, transition to turbulence appeared to be self-sustained, i.e., in contrast to zero pressure gradient boundary layers, no external forcing was required to initiate or sustain the transition process. The DNS results reveal that the streamwise vortices (‘braids’), which evolve between two neighboring spanwise coherent vortical structures, may be with a consequence of a similar instability mechanisms as observed in bluff-body wakes (mode B instability). The simulation results also suggest that the development of three-dimensional disturbances is due to an absolute secondary instability. High-amplitude 2D waves were introduced through a spanwise slot to control the separation. It was shown that strong 2D forcing significantly alters the flow filed. With large amplitude two-dimensional forcing the temporal growth of 3D disturbances inside the separated flow region can be suppressed and as a consequence, the secondary absolute instability can be prevented. Consequently, the flow remains laminar in almost the entire computational domain.

Very high-order accurate sharp immersed interface method: Application to direct numerical simulations of incompressible flows

Development of robust and very high-order accurate Immersed Interface Method (IIM) for solving the incompressible Navier-Stokes equations in the vorticity-velocity formulation on non-equidistant grids is presented. For computation of spatial derivatives on regular grid points, a seventh-order upwind Combined Compact Difference (CCD) scheme for firstderivative and sixth-order central CCD scheme for second derivative are employed. The coefficients of the CCD schemes are constructed for a non-equidistant grid instead of using a coordinate transformation. Corrections to the finite-difference schemes are used for irregular grid points near the interface of the immersed boundary to maintain high formal accuracy. For the interface points, the CCD schemes are tuned and adjusted accordingly to obtain numerically stable schemes and no jump correction will therefore be required. To demonstrate the numerical stability of the new IIM, both semiand fully-discrete eigenvalue problems are employed for the one-dimensional pure advection (inviscid) and the pure diffusion, and advection-diffusion equations. The new IIM satisfies both necessary and sufficient conditions for numerical stability. The new IIM was first applied to two-dimensional linear advection equation to demonstrate its stability. Then the development of a new, efficient and high-order sharp-interface method for the solution of the Poisson equation in irregular domains on non-equidistant grids is presented. The underlying approach for this is based on the combination of the fourth-order compact finite difference scheme and the Multiscale Multigrid (MSMG) method. The computational efficiency of the new solution strategy for the Poisson equation is demonstrated with regard to convergence rate and required computer time, which shows that the MSMG method is equally efficient for domains with immersed boundaries and for simple domains. To validate the application of IIM for incompressible flows, the results from the new method is compared with the benchmark solutions for the flow past a circular cylinder and the propagation of Tollmien–Schlichting wave in a boundary layer.

Numerical investigation of the interaction of active flow control and klebanoff modes

Highly resolved direct numerical simulations (DNS) are employed to investigate active flow control of laminar boundary-layer separation by means of two-dimensional harmonic blowing and suction through a narrow spanwise slot. The uncontrolled flow configurations are represented by laminar separation bubbles (LSBs) generated on a flat plate by an adverse pressure gradient according to earlier wind-tunnel experiments by Gaster.1 Active flow control is shown to significantly reduce the separation region. In agreement with our previous research the effectiveness of the flow control can be explained by the fact that the primary shear-layer instability is exploited. Furthermore, it is demonstrated that two-dimensional periodic forcing with a properly chosen frequency and amplitude can suppress the growth of three-dimensional disturbances and thus delays transition to turbulence, and even can relaminarize the flow. To investigate the effects of a realistic flow environment, very lowamplitude isotropic free-stream turbulence (FST) fluctuations are introduced at the inflow boundary. With FST the effectiveness of the flow control is not diminished and the extent of the separated flow region is reduced by the same amount as for the zero FST case. However, a striking difference is that in the presence of even very low FST, the flow transitions shortly downstream of the reattachment location of the bubble. It appears that this different behavior for even very small levels of FST is caused by an interaction between the high-amplitude 2D wave introduced by the forcing and the 3D Klebanoff modes caused by the FST. The streamwise streaks due to the Klebanoff modes cause a spanwise-periodic modulation of the primary 2D wave. The disturbances associated with this modulation exhibit strong growth and initiate transition via a continuous formation of Λ-vortices. Therefore, the relaminarization of the flow does not occur in a realistic environment, even for very low FST levels.

Effect of free-stream turbulence on control of laminar separation bubbles using pulsed vortex generator jets: Direct numerical simulations

Direct numerical simulations were employed to investigate the effects of free-stream turbulence on the control of laminar boundary-layer separation using pulsed vortex generator jets. Earlier research has shown that laminar separation can efficiently and effectively be controlled when an inviscid shear-layer instability is exploited. This paper addresses the question if such a control remains effective under free-flight conditions, which are characterized by free-stream turbulence. In the direct numerical simulations isotropic freestream turbulence was introduced at the inflow boundary. For low free-stream turbulence levels and a blowing ratio of 0.6 the pulsed jets showed the same effectiveness as observed in earlier research with zero free-stream turbulence. When the free-stream turbulence intensity was increased to 3% the effectiveness of the pulsed jets slowly diminished. A proper orthogonal decomposition of the time-dependent data revealed that the dominant flow structures are two-dimensional for low to moderate free-stream turbulence levels. For 3% turbulence intensity the dominant structures were streamwise- “streaky” structures. Additional simulations with higher blowing ratios were carried out for 3% free-stream turbulence. When the blowing ratio was increased to 1.5 the separation length was reduced. For larger blowing ratios the separation length remained constant. For a blowing ratio of 2.5 the most energetic flow structures were predominantly two-dimensional.

An efficient, high-order method for solving Poisson equation for immersed boundaries: Combination of compact difference and multiscale multigrid methods

Abstract A new efficient and high-order accurate sharp-interface method for solving the Poisson equation on irregular domains and non-uniform meshes is presented. The approach is based on a combination of a fourth-order compact finite difference scheme and a multiscale multigrid (MSMG) method. The key aspect of the new method is that the regular compact finite difference stencil is modified at the irregular grid points near the immersed boundary to obtain a sharp interface solution while maintaining the formal fourth-order accuracy. The MSMG method is designed based on the standard multigrid V-cycle technique to solve the system of equations derived from the fourth-order compact discretization, while the corresponding multigrid relaxation, restriction and prolongation operators are properly constructed for non-uniform grids with immersed boundaries. The contribution of the present work is the design of a fourth-order-accurate Poisson solver whose accuracy, efficiency and computational cost are independent of the complexity of the geometry and the presence or not of an immersed boundary. The new method is demonstrated and validated for a number of problems including smooth and jagged boundaries. The test cases confirm that the new method is fourth-order accurate in the maximum norm whether an immersed boundary is present or not and on uniform or non-uniform meshes. Furthermore, the computational efficiency of the new method is demonstrated with regard to convergence rate and run time, which shows that the MSMG method is equally efficient for domains with immersed boundaries as for simple domains. The new compact difference method is evaluated by comparison with the standard fourth-order (non-compact) finite difference approximation in terms of both accuracy and computational efficiency. The new compact difference scheme yields indeed more accurate numerical solutions. The striking difference between the two schemes is the much higher computational efficiency: The number of V-cycles needed to reach the discretization error is significantly lower for the new compact method compared to the standard difference scheme. As a result, the new compact scheme requires only a fraction of the computer time for convergence in comparison to the standard fourth-order difference scheme.