Session Q27: Focus Session: Modal Analysis Methods for Fluid Flows II

Use of biglobal stability and resolvent analyses for controlling cavity flows

Biglobal stability and resolvent analyses are used to numerically examine the three-dimensional characteristics of subsonic and supersonic flows over a rectangular cavity of aspect ratio 6 at a depth-based Reynolds number of 502. Direct numerical simulations are performed to characterize the unsteady flow features and to determine the base states (steady state and mean flows) for the stability and resolvent analyses. The present study finds preferential frequencies and wavenumbers for the intrinsic instabilities and flow response to continuously harmonic forcing, respectively. These insights from global stability and resolvent analyses are utilized to design active flow control strategies for suppressing adverse two-dimensional modes (Rossiter modes) that cause intense aerodynamic fluctuations. Flow control efforts are focused on triggering three-dimensional instability and resolvent modes that are sufficiently strong to induce spanwise mixing, modify the base state, and remove energy from the Rossiter modes. We assess the effectiveness of the proposed flow control designs in full direct numerical simulations.   

Comparison Between DNS Data and Resolvent Model Prediction of Opposition Control with a Phase Shift Between Sensor and Actuator

In a recent study, Luhar et al (J Fluid Mech, 2014) analyzed the opposition control scheme (Choi et al, J Fluid Mech, 1994) within the resolvent analysis framework (McKeon \& Sharma, J Fluid Mech, 2010) and demonstrated that their low-order model is able to qualitatively reproduce results from previous direct numerical simulation (DNS) studies. The model further predicts that introducing a phase shift between the sensor measurement and the actuator response strongly affects the attainable drag reduction and has the potential to improve the control effectiveness. The present study validates these predictions by means of a parametric DNS study and demonstrates that the response of the full nonlinear system to opposition control with various phase shifts between sensor and actuator very closely follows the low-order model. The good agreement between model prediction and DNS demonstrates for the first time the predictive capabilities of the resolvent analysis framework and suggests that it is a suitable low-order model to systematically design and optimize flow control schemes.   

Using resolvent analysis for the design of separation control on a NACA 0012 airfoil

A combined effort based on large-eddy simulation and resolvent analysis on the separated flow over a NACA 0012 airfoil is conducted to design active flow control for suppression of separation. This study considers the the airfoil at 6 deg. angle-of-attack and Reynolds number of 23000. The response mode obtained from the resolvent analysis about the baseline turbulent mean flow reveals modal structures that can be categorized into three families when sweeping through the resonant frequency: (1) von Karman wake structure for low frequency; (2) Kelvin--Helmholtz structure in the separation bubble for high frequency; (3) blended structure of (1) and (2) for the intermediate frequency. Leveraging the insights from resolvent analysis, unsteady thermal actuation is introduced to the flow near the leading-edge to examine the use of the frequencies from three families for separation control in LES. As indicated by the resolvent response modes, we find that the use of intermediate frequencies are most effective in suppressing the flow separation, since the shear layer over the separation bubble and the wake are both receptive to the perturbation at the these frequencies. The resolvent-analysis-based control strategy achieves 35% drag reduction and 9% lift increase with effective frequency.   

What a resolvent analysis for low speed cylinder flow reveals about turbulent flows

A resolvent analysis using global modes is performed for the mean wake around a circular cylinder at a Reynolds number of $Re$ = 100. Significant amplification resulting in a large resolvent norm occurs at a temporal frequency matching that of the vortex shedding. Moreover, the mode shapes identify the large-scale structures in the flow, which in this case is the vortex street. Rewriting the resolvent operator at this frequency as outer products of the forward and adjoint eigenvectors of the linear Navier-Stokes (LNS) operator reveals a close match between stability and resolvent modes. While resonance dominates the resolvent norm for the cylinder, high mean shear, which results in the LNS operator being non-normal, can also result in high amplification. In such cases a mean flow stability analysis does not identify the underlying structure at that temporal frequency and the perturbation energy is distributed in different velocity components for the optimal forcing and response modes. The implications of mean flow convection, which results in the non self-adjoint nature of the LNS operator, are discussed as well as extensions to canonical turbulence where wall-normal height influences whether stability outweighs non-normality.   

Modal analysis of non-homogeneous thermal fields in a turbulent pipe flow using extended proper orthogonal decomposition

We analyze a DNS database of fully developed flow and heat transfer in a pipe with non-homogeneous thermal forcing using a modal decomposition. The modal decomposition employed is based on an extended proper orthogonal decomposition, in which the temperature is decomposed using standard proper orthogonal decomposition while the velocity is decomposed using an extended proper orthogonal decomposition using the temperature basis. This method allows to discern which velocity fluctuations are correlated to the temperature fluctuations, obtaining insight on the physical mechanisms of convective heat transfer. Reconstructing the velocity fields using the extended modes it is possible to show that with only 40\% of the total turbulent kinetic energy we are able to reconstruct roughly 100\% of the turbulent heat flux, for the particular case under study.