Data-driven Pressure Recovery in Diffusers

This paper investigates the application of a data-driven technique based on retrospective cost optimization to optimize the frequency of mass injection into an S-shaped diffuser, with the objective of maximizing the pressure recovery. Experimental data indicated that there is an optimal injection frequency between 100 Hz and 300 Hz with a mass flow rate of 1 percent of the free stream. High-fidelity numerical simulations using compressible unsteady Reynolds-Averaged Navier-Stokes (URANS) are conducted to investigate the mean and temporal features resulting from mass injection into an S-shaped diffuser with differing injection speeds and pulse frequencies. The results are compared with experiments to confirm the accuracy of the numerical solution. Overall, 2-D simulations are relatively in good agreement with the experiment, with 3-D simulations currently under investigation to benchmark the effect of spanwise instabilities. Simulation results with the proposed data-driven technique show improvements upon a baseline case by increasing pressure recovery and reducing the region of flow recirculation within the diffuser.

💡 Research Summary

This paper presents a data‑driven control methodology for improving pressure recovery in an S‑shaped diffuser by actively modulating the frequency of a small‑mass injection jet. The authors adopt Retrospective Cost Adaptive Control (RCAC), a model‑free, online optimization algorithm that updates controller gains based solely on measured performance, thereby avoiding the need for an accurate high‑fidelity flow model. The control objective is to maximize static pressure recovery at a downstream aerodynamic interface plane (AIP) while keeping the injected mass flow at only 1 % of the main stream.

Experimental investigations previously identified an optimal injection frequency range of roughly 100–300 Hz for this low‑mass‑flow actuation. To explore the underlying physics and to provide a testbed for the RCAC algorithm, the authors performed high‑fidelity unsteady Reynolds‑averaged Navier‑Stokes (URANS) simulations using the compressible rhoPimpleFoam solver in OpenFOAM. Turbulence is modeled with the Menter k‑ω SST formulation and standard wall functions, and a second‑order spatial discretization is employed on an unstructured mesh refined near the inlet lip and walls. A grid‑convergence study confirms that the pressure predictions are insensitive to further mesh refinement.

The injection jet is prescribed by a sinusoidal velocity profile:
 V(t) = L + A·sin(2π f t)·S,
where L is a constant offset, A the amplitude, f the frequency, and S a direction vector. Two amplitude levels are examined (high‑amplitude ≈110 m/s, low‑amplitude ≈57.5 m/s) at a nominal frequency of 200 Hz, as well as a baseline case with no actuation. The simulations reveal that a steady jet with 1 % mass flow already raises the pressure at the AIP modestly and slightly reduces the recirculation bubble. However, the high‑amplitude pulsed jet dramatically shrinks the separation region, leading to a pressure‑recovery increase of 5–7 % relative to the baseline. The low‑amplitude pulse produces negligible change, underscoring the sensitivity of the diffuser to both amplitude and frequency.

Spectral analysis of the axial velocity inside the separation bubble shows a dominant natural frequency near 200 Hz, which coincides with the imposed jet frequency. The RCAC algorithm therefore starts from this initial guess and iteratively adjusts f to minimize a cost function proportional to pressure loss. In the numerical experiments, RCAC converges to a frequency in the 150–250 Hz band, yielding the highest pressure recovery while maintaining the prescribed mass‑flow budget. The controller operates in a single‑input‑single‑output (SISO) configuration: the jet frequency is the sole control input, and the measured pressure recovery is the output.

Although the primary simulations are two‑dimensional, the authors acknowledge that the actual flow is inherently three‑dimensional, especially in the large separation zone where spanwise secondary structures can develop. Ongoing three‑dimensional URANS studies show the emergence of such structures, suggesting that the 2‑D model captures the dominant mechanisms but that full 3‑D analysis will be required for final design validation.

In summary, the study demonstrates that a data‑driven, model‑free adaptive controller can effectively tune a low‑energy actuation strategy to improve diffuser performance. The approach is robust to modeling uncertainties, leverages inexpensive 2‑D simulations for early‑stage controller tuning, and can be seamlessly transferred to higher‑fidelity 3‑D simulations or experimental hardware. Future work will focus on extending the RCAC framework to multi‑input‑multi‑output configurations, exploring a broader range of injection mass‑flow ratios, and implementing real‑time hardware‑in‑the‑loop tests on representative engine inlet geometries.