Real-Time Adaptive Feedback Control of a Supersonic Dual-Stream Jet

This paper demonstrates that an online dynamic mode decomposition-based adaptive feedback control system effectively suppresses high-frequency resonant tones and shock trains in a supersonic dual-stream jet by stabilizing shear layer instabilities and mitigating intermittent low-pressure events, even under physical actuation constraints and varying sensor placements.

The Gist

Imagine a supersonic jet engine as a high-speed highway where two streams of air are merging: a fast "core" stream and a slightly slower "bypass" stream. When these two streams mix, they don't just blend smoothly; they create a chaotic, swirling dance of invisible whirlpools (vortices). This dance is so energetic that it screams a single, piercing, high-pitched note—like a whistle that never stops. This "screaming" is the noise problem the researchers are trying to fix.

Here is a simple breakdown of what the paper does and how it works:

1. The Problem: The Unwanted Whistle

The engine creates a specific, annoying tone (about 34,000 times per second) caused by these swirling whirlpools. This tone is linked to "low-pressure events"—moments where the air pressure drops sharply, creating a burst of energy that fuels the noise. The researchers wanted to stop this whistle without turning the whole engine into a different, less efficient machine.

2. The Solution: A "Smart" Control System

Instead of using a fixed, pre-programmed method to stop the noise (like a fan blowing constantly in one direction), the researchers built a smart, adaptive system.

• The "Ears" (Sensors): They placed tiny microphones (sensors) on the engine to listen to the air pressure in real-time.
• The "Brain" (Online DMD): They used a mathematical tool called "Online Dynamic Mode Decomposition." Think of this as a super-fast detective that looks at the last few seconds of data, figures out the pattern of the noise, and predicts what will happen next. It constantly updates its understanding of the flow, like a driver adjusting their steering wheel every second based on the road conditions.
• The "Hands" (Actuators): Based on what the "brain" predicts, it tells a tiny jet of air (an actuator) to blow or suck air at just the right moment to break up the swirling whirlpools before they can scream.

3. How It Works: The "Dance Partner" Analogy

Imagine the swirling air is a dancer spinning wildly.

• Old Method (Open-Loop): You try to stop the dancer by pushing them constantly in one direction. It works, but you have to push hard, and you might accidentally push the dancer off the stage (changing the engine's performance).
• New Method (Adaptive Control): You act like a dance partner who only steps in when the dancer starts to spin out of control. You give a tiny nudge to break their rhythm, then step back. You only use energy when absolutely necessary.

4. Key Findings

• Efficiency: The smart system used about 60% less energy than the old "constant pushing" method to achieve the same noise reduction.
• Precision: It successfully silenced the high-pitched whistle without messing up the engine's main airflow. The engine still flew the same way, just quieter.
• Flexibility: The system was surprisingly flexible. It didn't matter exactly where the "ears" (sensors) were placed; as long as the "hands" (actuators) were aimed at the right angle, the system worked.
• Real-World Limits: The researchers also tested what happens if the system is slower or weaker (simulating real-world hardware limits). Even with these limits, the system worked, though it made the shockwaves (pressure waves) in the engine wobble a bit more. However, it still successfully suppressed the noise-generating whirlpools.

5. The "Secret" of the Noise

By analyzing the data, the researchers discovered that the noise isn't caused by a steady hum, but by intermittent bursts—sudden, sharp drops in pressure.

• The smart controller is very good at spotting these specific "low-pressure bursts" and stopping them.
• It leaves the "high-pressure" parts of the flow alone, which is good because those parts make up the normal, healthy background noise of the engine.

Summary

The paper demonstrates a way to use a "smart" computer system to listen to a supersonic engine, predict its noisy moments, and gently nudge the airflow to stop the noise. It's like having a noise-canceling headphone for a jet engine that only activates when it hears a specific scream, saving energy and keeping the engine running smoothly.

Technical Summary

Technical Summary: Real-Time Adaptive Feedback Control of a Supersonic Dual-Stream Jet

Problem Statement
Modern supersonic engines, particularly those utilizing variable-cycle designs with independently modulated bypass streams, face persistent challenges regarding jet noise and flow instability. In the specific configuration studied—a supersonic dual-stream jet with a Mach 1.6 core and a Mach 1.0 bypass stream—the mixing of these streams generates a high-frequency resonant tone (approximately 34 kHz, or $St_{Dh} \approx 3.28$). This tone originates from vortex shedding at the splitter plate trailing edge and is associated with shock-boundary-layer interactions (SBLI) and shock-induced separation. While previous studies have utilized passive control (e.g., wavy splitter plates) or open-loop active control (steady micro-jet blowing) to mitigate these instabilities, such approaches often lack adaptability to off-design conditions, may alter the mean flow undesirably, or suffer from energy inefficiency. The objective of this work is to develop a data-driven, closed-loop adaptive feedback control system capable of suppressing the resonant tone and weakening the shock train while preserving the fundamental mean flow characteristics.

Methodology
The study employs two-dimensional direct numerical simulations (DNS) of a supersonic dual-stream jet using the CharLES solver. The flow configuration includes a single-sided expansion ramp (SERN) nozzle with a splitter plate. The control strategy relies on Online Dynamic Mode Decomposition (DMD), a data-driven modal decomposition technique that approximates system dynamics as a locally linear evolution.

• Online DMD Framework: Unlike traditional post-processing DMD, the algorithm operates in real-time. It utilizes a sliding window of sensor snapshots to construct state and shifted state matrices ($\mathbf{X}_k$ and $\mathbf{Y}_k$). The transition matrix $\mathbf{A}_k$ and control input matrix $\mathbf{B}_k$ are updated recursively using rank-1 updates (Sherman-Morrison-Woodbury lemma) as new data arrives. This allows the model to adapt to time-varying dynamics caused by external forcing.
• Feedback Control: A Linear Quadratic Regulator (LQR) is applied to the identified discrete-time linear model ($\mathbf{x}_{k+1} = \mathbf{A}\mathbf{x}_k + \mathbf{B}\mathbf{u}_k$). The control law is defined as $\mathbf{u}_k = -\mathbf{K}\mathbf{x}_k$, where $\mathbf{K}$ minimizes a cost function balancing state error and control effort.
• Actuation and Sensing: Control is applied via micro-jet actuators located on the vertical surface of the splitter plate trailing edge. The actuation angle ($\psi$) is tested at $0^\circ$ and $30^\circ$. Sensors measure instantaneous pressure fluctuations at various locations, including the splitter plate shear layer and the aft-deck surface.
• Constraints: To reflect physical limitations, the study investigates constrained scenarios where the controller frequency is reduced to $St_{Dh} = 0.16$ (1600 Hz), the model updates 10 times before a new input is applied, and actuation is limited to subsonic speeds ($|u_k/c_{ref}| \le 0.3$).
• Event Analysis: To understand the noise generation mechanism, the authors employ a signal reconstruction method based on intermittent low-pressure events, treating the noise source as a series of discrete bursts.

Key Results

1. Unconstrained Adaptive Control:

   • Flow Modification: Adaptive control effectively breaks down large-scale coherent vortex structures responsible for the resonant tone. Unlike steady open-loop control (OLC), which drastically alters the mean flow and shock positions, adaptive control suppresses the instability while preserving the baseline mean flow features and shock locations.
   • Efficiency: The adaptive approach introduces approximately 60% less momentum into the flow compared to steady-blowing OLC.
   • Spectral Impact: The resonant tone ($St_{Dh} = 3.28$) and its harmonics are eliminated in the pressure spectra. The broadband content is preserved, and local spectral spikes are "smoothed out."
   • Robustness: The control performance is found to be insensitive to sensor placement (across four tested configurations), suggesting that practical sensor layouts (e.g., on the aft-deck) are viable. However, the actuation angle is critical; $30^\circ$ blowing yields slightly better shock weakening than $0^\circ$.

2. Constrained Adaptive Control:

   • Sonic-Bounded ($|u_k/c_{ref}| \le 1.0$): At lower controller frequencies, the system exhibits transient behavior where the resonant tone re-emerges during suction phases. The shock train develops a large, irregular "breathing" pattern.
   • Subsonic-Bounded ($|u_k/c_{ref}| \le 0.3$): This configuration leads to repeated, irregular stabilization and destabilization of the shear layer. While the resonant tone is not as completely suppressed as in the unconstrained case, this mode yields greater vortex suppression and surface loading reduction than the sonic-bounded case due to the repeated transient stabilization.

3. Statistical Analysis of Events:

   • Signal reconstruction reveals that intermittent low-pressure events are the primary contributors to the resonant tone, accounting for approximately 80% of the signal amplitude. High-pressure events contribute mainly to low-frequency broadband noise.
   • Unconstrained adaptive control effectively suppresses these low-pressure events, eliminating the tone. Constrained controllers show a slight amplification of low-pressure events compared to the unconstrained case, resulting in partial tone attenuation.

Significance and Claims
The paper claims that the proposed online DMD framework offers a robust method for adaptive flow control in complex supersonic environments. Its primary significance lies in the ability to target specific high-frequency instabilities (the resonant tone) without disrupting the mean flow or shock structures, a limitation often found in open-loop or passive control methods. The study demonstrates that the control strategy is not sensitive to specific sensor locations, facilitating practical implementation where sensor placement is constrained by physical hardware. Furthermore, the work highlights that even with significant physical constraints (lower sampling rates and subsonic actuation), adaptive control can achieve substantial vortex suppression through the mechanism of repeated transitory stabilization. The findings suggest that future practical applications could benefit from placing actuators on the aft-deck and potentially utilizing multiple actuators to target different shear layers.