Session J32: Separated Flows: Simulations and Modeling

Resolvent analysis of separated flow around a NACA0012 airfoil: Reynolds number effects

Resolvent analysis provides great insights for understanding flow unsteadiness and designing flow control techniques. In this study, we employ bi-global resolvent analysis to investigate the effects of Reynolds numbers from Re=600 to 23000 on separated flow over a NACA0012 airfoil. The base flow is obtained by direct numerical simulations and wall resolved large eddy simulations with averaging performed in time and the spanwise direction. Particular emphasis is placed on uncovering the influence of the Reynolds number on the response and forcing modes as well as the energy gain associated with different frequencies and spanwise wavelengths. Comparisons are made between the results from resolvent analysis and the unsteady flow characteristics extracted from the numerical simulations. We will also discuss our efforts on studying Reynolds number effects for three-dimensional flows around finite wing with triglobal resolvent analysis.   

Modification of dynamic stall using broadcast mode analysis

The modification of dynamic stall on a pitching airfoil is studied using network analysis in conjunction with discrete vortex method that models the massively separated flow. This allows the discrete vortices to act as the nodes of the network and their interactions as the edges. Aiming to identify effective pathways for vortical perturbations to amplify, this study quantifies the vortical interactions using the Jacobian of the nonlinear function of induced velocity, instead of the induced velocity itself that is commonly used in previous studies. For the time-varying vortical network, we perform broadcast mode analysis to identify important stages during the process of dynamic stall that are receptive to perturbations and the vortices to seed effective perturbations. The analysis shows that the onset of dynamic stall, where the discrete vortices form a vortex sheet emanating from the leading edge, is the most important stage for perturbations to amplify for modifying the vortex dynamics. The vortex sheet remains as the most effective nodes to seed perturbations during the dynamic stall, but limited modification can be achieved when the discrete vortices are populated over the airfoil to form a large leading edge vortex. The present network analysis demonstrates potential for physics-based mitigation of dynamic stall.   

Understanding the interaction between unsteady streamwise vortices with a separated shear layer for novel flow control solutions.

Aircraft performance at high angles of attack, either during high-lift maneuvers or in gusty conditions is impacted by flow separation. Vortex generators have been widely used as a passive flow control solution to alleviate separation. Recent advances in active control provide opportunities for enhanced separation control, especially when the incoming boundary layer is unsteady or transitional. Understanding the interaction of unsteady disturbances with passive and active vortex generators, and the influence of the generated unsteady streamwise vortices with the dynamics of a separated shear layer and the separation bubble is key for advancing separation control. In this talk, we explore these questions in the well-studied setting of a backward-facing step. Large-eddy simulations are performed on a low to moderate Reynolds number inflow imposed with artificial disturbances representative of a transitional boundary layer and study their interaction, with passive and active vortex generators. The magnitude and frequency of forcing of the inflow and the active vortex generator are varied to generate different mean and the fluctuating components of the streamwise vorticity and the results are examined from a vorticity dynamics point of view.   

Analysis of the low-frequency unsteadiness of turbulent separated flows using vorticity variants

Separated flow regions often exhibit unsteadiness manifested by a low-frequency oscillation of characteristic variables. Such dynamics is often associated with an abrupt increase (or decrease) of friction drag, mixing, heat transfer, and aerodynamic noise, affecting the stability and robustness of the flow systems. Describing and predicting such events is not straightforward and dependent on heuristic and statistical approaches, lacking direct connection with the first principle from which they originate. Separated flows are inherently viscous and characterized by strong vortical motions, making vorticity a natural choice for describing their dynamics. In this study, a set of vorticity variants are investigated for several separated flows, including a turbulent wake flow behind a zero-thickness plate, a transitional supersonic flow over a backward-facing step, and a compressible turbulent boundary layer separated by an oblique impinging shock. The dynamic mode decomposition is applied to obtain the reduced-order representation of the low-frequency unsteadiness. Statistical analysis is conducted for the correlations of the vorticity variants with the integral quantities of the flows.   

Hysteresis and the hidden rhythm of flow separation and reattachment

Dynamic stall is an unsteady flow phenomenon characterized by the leading edge vortex formation. The formation of the vortex leads to a delay in the flow separation and reattachment and overshoots in aerodynamic forces. The separation delay of a pitching airfoil depends on the effective pitch rate at the critical stall angle, and the separation delay decreases with increasing pitch rate. The current work shows that the reattachment delay follows the same trend if the hysteresis effect is appropriately addressed. The critical reattachment angle should be considered as the reference for estimating the reattachment delay to account for the hysteresis effect. The time constants obtained from separation delay versus pitch rate have previously shown to generalize the Goman-Khrabrov dynamic stall model to predict the flow separation. Here, we test the Goman-Khrabrov model's generalizability for the reattachment stage using the time constants obtained for the reattachment delay.   

Collective Behavior of Free-Oscillating Cylinders in Cross-Flow

The collective behavior of progressively increasing numbers of free-oscillating cylinders is studied numerically using computational fluid dynamics. The 1-DOF cylinders are free to oscillate in the direction perpendicular to the direction of incoming flow with no structural damping and no stiffness. They are placed in a uniform cross-flow with a Reynolds number of 100, defined using the diameter of one of the identical cylinders. A fixed cylinder is positioned upstream as the leader, allowing a consistent upstream wake before each of the free-oscillating cylinders downstream. The patterns of vortex shedding as well as lift and drag are analyzed in each of the various configurations utilized in this study. Configurations include symmetric circular, triangular, and rectangular arrays as well as asymmetric arrangements. The comparisons between fixed and free-oscillating cylinder configurations serve to highlight the energy-saving reconfigurations present when there is no stiffness or damping of the structures.   

Simulations and experiments on the accelerating/decelerating flow on a square cylinder

We investigate the high-Reynolds accelerating/decelerating flow around a square cross-sectional cylinder. The square cross-section is a classic shape for wind-engineering applications, e.g. high-rise buildings and towers. The flow is characterized by shear-layer separation at the upstream edges. The separated shear layers undergo Kelvin-Helmholtz instability, but they do not lose coherence until they form the von Karman vortex street in the wake. The flow around a square cylinder has been well characterized when the inflow is steady. Much less is known when the inflow is accelerating or decelerating. These conditions are relevant, e.g., for civil structures in thunderstorms. This work may be considered a first step toward the characterization of the wind loads on buildings in variable wind conditions and to a better appraisal of the limits of the wind-load predictions obtained under the assumption of steady-wind conditions.

We perform high-fidelity Large-Eddy Simulations (LES) with the spectral-element code Nek5000 to investigate the effect of Gaussian-type inflow accelerations and decelerations in the Reynolds range Re=1.720x10^4–6.536x10^4 and an excellent agreement with the experiments in Brusco et al. (2022) is found. The flow exhibits discrete changes in the vortex-shedding frequency, with the presence of constant-frequency time cells. For the accelerating flow, the vortex-shedding Strouhal number witnesses a decrease within the time cells, followed by a sudden increase between the cells, pointing out the presence of discontinuities. The opposite for the decelerating flow. In addition, we perform a parametric study by considering different acceleration/deceleration intensities. Constant-frequency time cells are present for all the investigated cases. The increasing intensity of the flow variation reduces the time length of the time cells, and it decreases the vortex shedding Strouhal number inside each cell, but a similar behavior of St with Reynolds is found.   

The effect of rotation on flow separation behind a bump in turbulent channel flows

A spanwise-rotating turbulent channel with a bump on the bottom wall is studied via direct numerical simulation. The objective is to understand how the Coriolis force modulates the geometry-induced separation. The parabolic bump is 0.25H high. The mild curvature at the crest removes fixed point separation, allowing investigation of separation onset. Counter-clockwise (+) or clockwise (-) rotation is applied at rotation number Ro_b = 2ΩH/U_b of 0, ±0.42, and ±1.0. A constant mass flow rate is maintained among all cases corresponding to Re_b = HU_b/ν = 2500. Compared to the non-rotating flow, separation is delayed and reattachment occurs earlier when Ro_b > 0, reducing the mean recirculation region by up to 94% at the highest rotation rate. The delayed onset of separation is attributed to enhanced turbulence due to the Coriolis force, despite the mean momentum deficit at the crest of the bump is more significant than it in the non-rotating case. When Ro_b < 0 separation of the relaminarized flow occurs closer to the crest and the separated shear layer is stable until rolling into spanwise vortices approximately eight bump heights downstream. A lower form drag is correlated with reduced separation when Ro_b > 0, though not when Ro_b < 0. The total drag, including the friction drag over the flat walls, is lower for all rotation cases.