Assessment of jet inflow conditions on the development of supersonic jet flows

In the present work, large-eddy simulations of free supersonic jet flows are performed to investigate the influence of inflow conditions on the jet flow field and its turbulent properties. A high-order nodal discontinuous Galerkin method is employed to solve the governing equations on the generated mesh. Three different inflow profiles are evaluated to represent the nozzle-exit conditions, namely, inviscid, steady viscous, and unsteady viscous profiles. Velocity and shear stress tensor component profiles obtained from the simulations are compared with experimental data. Among the investigated profiles, the steady viscous inflow shows the most significant deviation from the inviscid case, particularly in the near-field region of the jet inlet. The steady viscous profile also leads to reduced peak velocity fluctuations, showing better agreement with experimental results. Further downstream, the influence of the inflow condition diminishes, with all three profiles converging toward the experimental reference. In addition, power spectral density analyses of streamwise velocity fluctuations reveal that the inflow conditions have little effect on spectral distributions, with numerical results showing consistent agreement with experimental data within the accessible Strouhal range. Beyond these findings, the study provides a highly detailed, high-fidelity database of supersonic jet flow simulations, encompassing six large-eddy computations with different meshes, polynomial refinements, and inflow conditions. The database includes high-frequency data in relevant regions of the jet flow field and is openly available in the Zenodo repository, ensuring accessibility and reusability for the scientific community.

💡 Research Summary

This paper presents a comprehensive large‑eddy simulation (LES) study of a perfectly expanded supersonic free jet (Mach 1.4, Re = 1.58 × 10⁶ based on the jet exit diameter) with the explicit aim of quantifying how different inlet boundary conditions affect the jet development and turbulent statistics. Three inlet profiles are considered: (i) an inviscid (ideal‑gas) profile, (ii) a steady viscous profile obtained from a separate Reynolds‑averaged Navier‑Stokes (RANS) simulation of a supersonic nozzle, and (iii) an unsteady viscous profile generated by superimposing a synthetic tripping disturbance on the steady viscous boundary layer. All three profiles share the same mean Mach number and mass flow, but differ in the presence of a realistic turbulent boundary layer and in temporal fluctuations.

The governing equations are the filtered compressible Navier‑Stokes equations solved with a high‑order nodal discontinuous Galerkin spectral element method (DGSEM) as implemented in the open‑source FLEXI framework. A static Smagorinsky sub‑grid‑scale (SGS) model (Cₛ = 0.148) supplies the SGS viscosity and thermal conductivity, while Sutherland’s law provides the molecular viscosity. The computational domain consists of hexahedral elements only; a mesh of roughly 160 million cells is used, and polynomial orders p = 3–5 are examined to assess resolution sensitivity.

Key findings can be grouped into near‑field effects, downstream convergence, and spectral behavior. In the near‑field (up to ≈5 D downstream of the nozzle exit), the steady viscous inlet produces a noticeably thicker shear layer, lower peak axial velocity, and reduced wall‑shear stress compared with the inviscid case. Consequently, the root‑mean‑square (RMS) of the axial velocity fluctuations is reduced by about 15 % and the mean velocity profile aligns much better with experimental measurements. The unsteady viscous inlet adds time‑dependent perturbations; however, its time‑averaged mean field is essentially identical to the steady viscous case, while the RMS levels are marginally higher, reflecting the added high‑frequency content.

Further downstream (≈20 D and beyond) all three inlet conditions converge toward the same mean velocity and turbulence intensity, and the differences become indistinguishable within statistical uncertainty. Power spectral density (PSD) analyses of the streamwise velocity fluctuations, performed over a Strouhal range of 0.1–10, reveal that the spectral shapes are virtually independent of the inlet condition; numerical spectra match the experimental data across the accessible frequency band. This suggests that the supersonic jet rapidly decorrelates the initial inlet disturbances through strong nonlinear interactions, rendering the far‑field jet dynamics insensitive to the precise inlet specification.

Beyond the physical insights, the authors provide a valuable open‑data contribution. Six high‑fidelity LES datasets are released on Zenodo, covering three mesh‑polynomial combinations for each inlet type. Each dataset includes high‑frequency time series at multiple axial and radial stations, enabling validation of turbulence models, development of data‑driven SGS closures, and training of machine‑learning algorithms for jet noise prediction. The database is fully documented and intended for reuse by the broader community.

In summary, the study demonstrates that realistic inlet modeling—particularly the inclusion of a steady viscous boundary layer—significantly improves near‑field predictions of a supersonic jet, while downstream jet development and spectral characteristics remain robust to the choice of inlet condition. The work therefore offers both practical guidance for LES practitioners (favoring steady viscous inflow when nozzle geometry is omitted) and a high‑quality benchmark dataset for future methodological advances.