Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1809.01439

Direct numerical simulation of conical shock wave/turbulent boundary layer interaction

Feng-Yuan Zuo·Antonio Memmolo·Guo-ping Huang·Sergio Pirozzoli
View original source ↗Read source document ↗Export metadata ↓

Abstract

Direct numerical simulation of the Navier-Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_\infty = 2.05$ and Reynolds number $Re_θ\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $θ_c = 25^\circ$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behavior is strongly affected by the imposed pressure gradient, with streaks which are locally suppressed in adverse pressure gradient (APG) zones, and which suddenly reform in the downstream region with favourable pressure gradient (FPG). Three-dimensional mean flow separation is only observed in the first APG region associated with formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical two-dimensional wedge-generated shock/boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to isotropic state in APG regions, and to a two-component anisotropic state in FPG.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Feng-Yuan Zuo, Antonio Memmolo, Guo-ping Huang, Sergio Pirozzoli. 2018-09-05. Direct numerical simulation of conical shock wave/turbulent boundary layer interaction. https://doi.org/10.1017/jfm.2019.558

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-similar Features in Secondary Breakup of a Droplet and Ligament Mediated Fragmentation under Extreme Conditions

Droplet formation is relevant in many applications spanning natural and artificial settings. A physical understanding of aerobreakup or air-assisted secondary atomization and predicting size distributions in these applications is non-trivial. We show that extreme airflow speeds induce catastrophic breakup, which, although chaotic and seemingly obscure, is not hopelessly unstructured. In the present study, through shockwave-induced breakups, we investigate the associated intermediate processes at smaller spatiotemporal scales at very high Weber numbers ($We \sim 10^3-10^4$). We show that microscale protrusions decorate the disintegrating droplet interface and eventually fragment, resulting in the generation of daughter droplets. We discover these undulations to follow breakup patterns (sub-secondary breakup) that resemble a scaled-down version of secondary atomization. The consistent topology across a vast range of scales $(10^{-6}m-10^{-2}m)$ suggests a self-similar mechanism bridged by local Weber number. The normalized size distribution of the resultant droplets exhibits universality and $We$ invariance within the investigated range of extreme conditions, including transient statistics for subsequent time periods. This conforms to a modified gamma distribution characterized by ligament shape factors, which tend toward the limiting behavior associated with the maximum corrugations physically possible. Scaling laws based on the $We$ are derived for the averaged diameter as $\sim {We}^{-1/3}$, using a high-energy aerodynamic breakup mechanism and subsequently used to derive a time-integrated distribution. These observations reinforce the idea of a self-similar mechanism for the catastrophic droplet breakups, encompassing multiscale deformation cascades, self-similar sub-secondary breakups, maximally corrugated ligaments, and universal droplet size distributions.

physics.flu-dyn↗
arXiv2026

Particle Trajectories Beneath Fully Nonlinear Waves Generated by Horizontal Seabed Motion

We investigate fully nonlinear water waves and fluid-particle dynamics generated by the horizontal motion of a seabed obstacle with prescribed time-dependent velocity. The governing equations are the full Euler equations, formulated in a time-dependent conformal domain that simultaneously maps the moving free surface and seabed onto fixed boundaries. The main contribution of this work is a Lagrangian formulation for computing particle trajectories in the resulting genuinely unsteady conformal domain. We derive a closed-form trajectory system in the canonical domain in which the time dependence of the conformal map is entirely represented by the real and imaginary parts of an analytic function that can be evaluated spectrally from the surface. We apply the formulation to waves generated by horizontal submarine landslide motion and characterize particle displacements throughout the fluid as functions of the initial particle position and Froude number. Our findings identify distinct regions in which particle motion is predominantly associated with the moving seabed, the generated wave, or the combined action of both. The results reveal a transition in the dominant mechanism driving particle motion: at low Froude numbers, particle displacements are primarily associated with the moving seabed, whereas at high Froude numbers the generated wave becomes increasingly dominant, particularly near the free surface and away from the obstacle path.The numerical predictions are benchmarked against laboratory data available in the literature, showing good agreement and providing a quantitative assessment of the model accuracy. Moreover, laboratory topographies beyond those considered here can be readily incorporated into the numerical framework through a Hermite interpolation procedure.

physics.flu-dyn↗
arXiv2026

Goal-Oriented Weighting of Reynolds-Stress Data for Learning Turbulence Models in Complex Flows

Data-driven turbulence models for the Reynolds-averaged Navier-Stokes (RANS) equations offer a promising route to improving predictions of complex flows. Such models, specifically the turbulence constitutive relations, can be learned efficiently from high-fidelity Reynolds-stress data without evaluating the RANS equations during training. However, conventional losses weight all tensor-component and spatial errors equally, although their influence on a quantity of interest (QoI) can differ significantly; reducing the aggregate stress error therefore does not necessarily lead to an improved QoI prediction. Training against flow-level observations accounts for this dependence but requires repeated, potentially expensive RANS solutions. In canonical shear flows, physical reasoning can identify the shear component as the only one relevant for the mean-flow prediction. Motivated by this example, we propose a goal-oriented method to select and weight Reynolds-stress training data for complex flows. For a specified QoI, a single offline adjoint evaluation quantifies its sensitivity to local perturbations of each Reynolds-stress component. These sensitivities are converted into fixed weights in the supervised loss, enabling training without further RANS solutions. We validate the weighting in square-duct and periodic-hill flows, then apply it to a film-cooling jet in crossflow, where it improves velocity and cooling-effectiveness predictions over uniformly weighted training despite using a velocity-only QoI. Beyond turbulence modelling, this work suggests a broader strategy for aligning supervised learning with downstream prediction goals while preserving training efficiency.

physics.flu-dyn↗