Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.33513

Six-Degree-of-Freedom Rotor-Load Cross-Spectral Density from Rotor-Plane Turbulence Cross-Spectra

Haoran Yang·Zhaolong Han
View original source ↗Read source document ↗Export metadata ↓

Abstract

A frequency-domain response analysis of a wind turbine rotor requires the complete hub-load spectrum, but the customary scalar thrust and torque spectra retain neither the four in-plane components nor the coupling between them. This paper derives the full six-degree-of-freedom (6-DOF) rotor-load cross-spectral-density (CSD) matrix from the IEC Kaimal turbulence model. By decoupling the spatial order of inflow coherence from the temporal Doppler shift, the formulation introduces a two-index rotational-sampling kernel. Rotor symmetry and azimuthal averaging constrain the observed Doppler carrier strictly to blade-passing harmonics $pBf_{\mathrm{rot}}$, while the azimuthal aerodynamic transfer shifts the spatial coherence order to $pB+s$. A convergence study of the retained azimuthal order $s$ shows that $\lvert s\rvert\le4$ suffices, the assembled CSD then deviating from the full-band result by less than $10^{-5}$ in relative norm. The formulation is compared with OpenFAST simulations of a rigid floating wind turbine over nine wind speeds: the six auto-spectral densities agree closely below 1~Hz, and the present theory over-predicts the spectra near the 6P and 9P rotational harmonics.

Explore related subjects

physics.flu-dynmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Haoran Yang, Zhaolong Han. 2026-10-24. Six-Degree-of-Freedom Rotor-Load Cross-Spectral Density from Rotor-Plane Turbulence Cross-Spectra. https://arxiv.org/abs/2610.33513

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

KEEP EXPLORING

Related papers

arXiv2026

Reservoir computing based predictive reduced order model for steel grade intermixing in an industrial continuous casting tundish

Continuous casting is a widely adopted process in the steel industry, where maintaining high steel quality is paramount. Efficient prediction of grade intermixing during ladle changeover operations is critical for maintaining steel quality and minimizing material losses in the continuous casting process. Among various factors influencing grade intermixing, operating parameters play a significant role, in addition to tundish geometry and flow control devices. In this study, three-dimensional, transient, two-phase turbulent flow simulations are conducted to investigate the ladle changeover operation. During this process, the molten steel level in the tundish typically varies over time, significantly affecting the grade intermixing phenomena. The influence of ladle change time on intermixing time has been presented. However, high-fidelity full-order simulations of such complex transient phenomena are computationally expensive and are impractical for real-time monitoring or design-space exploration in industrial-scale applications. To address this issue, a reduced order modelling approach based on proper orthogonal decomposition (POD) and reservoir computing (RC) is employed to efficiently predict intermixing time. The proposed reduced order model (ROM) demonstrates excellent predictive accuracy using limited training data while requiring significantly less computational resources and training time. The results demonstrate the potential of the proposed methodology as a fast, reliable tool for real-time process monitoring and optimization in industrial continuous casting operations.

physics.flu-dyn↗
arXiv2026

Physics-informed neural networks for shock capturing in inviscid flows around an airfoil

Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs). However, shock capturing remains challenging for PINNs, particularly in steady flows around an airfoil, where shocks may not even be captured. In this study, we point out that the steady Euler equations used to construct the loss function impose weak constraints, which make it difficult to correct the continuous function approximation preference of neural networks, causing gradient descent to converge to a smooth local optimum. Based on this insight, we propose to strengthen the physical constraints by reconstructing steady shock capturing as a temporal evolution process governed by the unsteady Euler equations. The temporal evolution law of the flow field guides gradient descent, thereby alleviating its tendency to converge to smooth local optima and ensuring shock formation. We introduce a PDE loss function incorporating a pseudo-time stepping mechanism to obtain the steady state solution without solving the unsteady Euler equations over a long time interval. In addition, we develop a simplified formulation of the Euler equations to reduce the complexity of the PDE loss function, thereby improving shock capturing accuracy. By solving four forward problems involving different flow conditions and geometries, we verify that the proposed method achieves high accuracy in shock capturing while reducing the wall time to one-seventh of that required by existing advanced methods. Moreover, the proposed method demonstrates its capability to solve a parametric problem involving the angle of attack and Mach number without relying on any labeled data.

physics.flu-dyn↗
arXiv2026

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear Partial Differential Equations

Physics-informed neural networks (PINNs) can solve forward and inverse PDE problems but may struggle with spectral bias and oscillatory, high-frequency, or phase-dependent solutions. We introduce a generalized split complex-valued PINN (SCV-PINN) framework with complex-valued parameters and latent representations. Split activations act separately on real and imaginary components while complex operations preserve their coupling, enabling amplitude--phase representations with practical optimization. Ablation studies evaluate split activation functions and collocation sampling strategies. Forward and inverse benchmarks include the Burgers, Allen--Cahn, Korteweg--de Vries, nonlinear Schrödinger, Helmholtz, and Poisson equations on regular and irregular domains; Kovasznay flow ($\mathrm{Re}=20$); lid-driven cavity flow ($\mathrm{Re}=100$); the Lorenz system; and inverse Burgers and Navier--Stokes problems ($\mathrm{Re}=100$). A three-dimensional Navier--Stokes Beltrami flow further demonstrates applicability to higher-dimensional nonlinear dynamics, with a relative $L_2$ error of $4.07\times10^{-5}$. Across these tests, SCV-PINN yields high-fidelity solutions and effective parameter identification, improving on real-valued PINNs and selected variants. The results suggest that split complex-valued representations can help address spectral-bias-related difficulties in nonlinear and oscillatory physical systems.

physics.flu-dyn↗