WP4

Main Achievement

WP4 - Flow sensitivity and control

Objectives: To develop tools to obtain the sensitivity and receptivity of complex flows and their unsteady modes under external perturbations.

Description of Work

Flow sensitivity and control focus on identifying regions in a flow field where small perturbations significantly impact stability and performance. By analysing sensitivity to disturbances, effective control strategies, such as passive surface modifications or active flow actuations, can be implemented to delay transition, reduce drag, or suppress instabilities. WP4 will collect the information and development provided by WP2 and WP3 to define new strategies for flow control.

A more detailed description of the activities can be found in deliverables D4.1 to D4.3

T4.1 Algorithms to obtain the sensitivity of unsteady or even chaotic systems.

ESR8 conducted a receptivity and sensitivity analysis of the flow field related to the transonic buffet phenomenon to identify the most critical flow regions. Additionally, the discrete endogeneity field was examined to determine areas that either dampen or amplify the onset of transonic buffet.

Figure 1: Discrete endogeneity field highlighting damping (blue) and amplifying (red) regions near buffet onset (a, Mach 0.715) and deep within the buffet regime (b, Mach 0.735).

ESR8 performed sensitivity analyses to identify key flow regions driving linear instabilities and areas where modifications in the mean flow have the greatest impact on flow stability. These sensitivity formulations, based on adjoint equations, were applied to the configurations in T3.2, particularly concerning stall cells and low-frequency breathing linear modes. The findings provided insights into the origins of these instabilities and suggested possible physical mechanisms behind their onset. Furthermore, the mean-flow modification sensitivity field could be integrated into shape sensitivity algorithms (aligned with T4.3) to enable passive control of these phenomena

Figure 2: (a-b) Sensitivity ∇_u λ of stall cells mode’s eigenvalue λ to mean-velocity modifications. Streamwise components (a) 〖(∇_u)〗_R λ and (b) 〖(∇_u)〗_T λ, which account for modifications in the RANS momentum and turbulence model equations, respectively. (c) Difference in the streamwise velocity field 〖δu=u〗_d-u , with u_d being reference DNS data. (d) Local contribution to the induced eigenvalue variation, i.e. ∇_u λ∙δu

T4.2 Sensitivities of acoustic and structural output with respect to base-flow modifications

ESR14 analyzed the limitations of commonly used spatial mapping techniques for filtering unphysical pressure fluctuations in the solution of Linearized Navier-Stokes Equations (LNSE). The study compared different mapping strategies, identifying their advantages and disadvantages while proposing effective filtering techniques to enhance solver stability.

A dimensional analysis using Buckingham’s Π theorem was performed on a rectangular thin panel to assess the effectiveness of mapping techniques in filtering vorticity modes. Analytical pressure distributions were used as a reference to examine the influence of aerodynamic perturbations on the flow-acoustic discretization grid (DG). Pressure loads were transferred from the DG mesh to the finite element (FE) mesh using various mapping strategies. The study evaluated how well aerodynamic perturbations were filtered across different length scales, amplitude ratios, and Mach numbers.

Results showed that the force transfer approach produced lower errors than the pressure transfer approach, with the difference increasing as the length scale grew. Additionally, the low-resolution grid force transfer method (LRGAFT) demonstrated superior accuracy and was selected for further analysis. However, as Mach number and amplitude ratio increased, mapping effectiveness in filtering aerodynamic perturbations decreased.

An exponential filter was applied to smoothen the pressure profile. The study found that excessive dissipation increased displacement errors, suggesting optimal filter parameter values. While displacement errors were influenced by boundary conditions, force errors effectively assessed filter performance. The findings provide a framework for mitigating numerical instability in coupled LNSE solvers caused by under-resolved aerodynamic pressure fluctuations.

ESR15 analyzed the sensitivity of a swept-wing boundary layer on a wing with a surface modification, specifically a smooth hump. The study examined the effects of unsteady noise on the laminar boundary layer and developed tools to assess the impact of the hump on boundary-layer stability and laminar breakdown.

The findings demonstrate the potential of a smooth surface hump to significantly delay laminar-turbulent transition on swept wings. ESR15’s work provided new insights into the mechanisms responsible for this transition delay, contributing to the development of more efficient passive control devices in future aircraft designs. ESR15 also contributed to D4.2.

T4.3 Algorithms for shape sensitivity and actuators

Progress On Flow Actuation

ESR2 investigates the potential use of zero-net mass-flux (ZNMF) actuation under steady inflow conditions to reduce separation length and identify the key actuator parameters that lead to shorter recirculation. Fourteen cases are considered, varying in frequency, amplitude, spanwise spacing (λz), and spanwise size of the jet orifice (∆z). The longitudinal location and orientation of the jet actuation follow the Purdue experimental test setup, as shown in Fig. 6. Table 1 presents the simulated cases along with their jet actuation parameters and the corresponding reduction in separation length.

The study highlights that spanwise spacing (λz) and sizing (∆z) are both crucial and interdependent, suggesting that imposing a spanwise-dominant jet structure enhances actuation efficiency. The frequency of actuation, , also plays a significant role: at low mass-flow forcing, higher frequencies improve jet forcing efficiency, whereas at high absolute mass-flow forcing, the effect of frequency is reversed.

Among all the actuation cases studied, two distinct and effective strategies for reducing separation length are identified. The most efficient strategy involves energizing spanwise-dominant Kelvin-Helmholtz (KH) vortices. Since these vortices extract energy from the underlying flow as they grow, weak forcing is sufficient to generate strong vortices. The effectiveness of KH vortices in entraining and pulling fluid out of the recirculation region increases with their spanwise uniformity, making jet arrangements that promote more two-dimensional KH vortices preferable.

The most effective actuation strategy, which achieves the greatest reduction in separated flow length, promotes the formation of large vortex clusters similar to those produced by harmonic oscillations of the inflow. While this approach can reduce the mean separation length to half that of the most efficient strategy, it remains uncertain whether the higher actuation cost makes it the best option.

ESR6 formulated two optimization problems to address TC3. The first focuses on optimizing piezoelectric waveforms to cancel acoustic waves inside inkjet printheads. The second involves data assimilation of physics-based parameter models to characterize cross-talk effects between microchannels, as observed in Xaar’s experimental campaigns. In both cases, gradient-based optimization algorithms, accelerated using adjoint methods, were developed to solve the problems efficiently.

For illustration, Figures 6 present the main results for waveform optimization. The algorithm converges to an actuator motion that cancels reverberations while ensuring the desired droplet volume within the specified time interval between two droplet ejections. By inferring the parameters of the proposed physics-based model, the experimental outputs can be predicted with high accuracy. Additionally, a reduced-order model with only 10 parameters was developed, demonstrating a strong fit with the experimental dataset.

The integration of these two frameworks provides inkjet printhead manufacturers with a valuable starting point for waveform optimization, significantly reducing the time, costs, and resources typically required for extensive trial-and-error experimental campaigns

ESR15 developed a shape-optimization framework to determine the sensitivity of TS waves in compressible boundary layers to surface modifications. The framework is highly efficient and applicable to airfoil design at very high Reynolds numbers in the compressible flow regime. Sensitivities are computed using the adjoint method, which has been validated against the finite difference method.