The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics

This paper treats 6j symbols or their orthonormal forms as a function of two variables spanning a square manifold which we call the "screen". We show that this approach gives important and interesting insight. This two dimensional perspective provides the most natural extension to exhibit the role of these discrete functions as matrix elements that appear at the very foundation of the modern theory of classical discrete orthogonal polynomials. Here we present 2D and 1D recursion relations that are useful for the direct computation of the orthonormal 6j, which we name U. We present a convention for the order of the arguments of the 6j that is based on their classical and Regge symmetries, and a detailed investigation of new geometrical aspects of the 6j symbols. Specifically we compare the geometric recursion analysis of Schulten and Gordon with the methods of this paper. The 1D recursion relation, written as a matrix diagonalization problem, permits an interpretation as a discrete Schr\"odinger-like equations and an asymptotic analysis illustrates semiclassical and classical limits in terms of Hamiltonian evolution.Comment: 14 pages,9 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio

The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior

The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.Comment: 14 pages, 8 figures, presented at ICCSA 2014, 14th International Conference on Computational Science and Application

Definition of a benchmark for low Reynolds number propeller aeroacoustics

Experimental and numerical results of a propeller of 0.3 m diameter operated at 5000 RPM and axial velocity ranging from 0 to 20 m/s and advance ratio ranging from 0 to 0.8 are presented as a preliminary step towards the definition of a benchmark configuration for low Reynolds number propeller aeroacoustics. The corresponding rotational tip Mach number is 0.23 and the Reynolds number based on the blade sectional chord and flow velocity varies from about 46000 to 106000 in the operational domain and in the 30% to 100% blade radial range. Force and noise measurements carried out in a low-speed semi-anechoic wind-tunnel are compared to scale-resolved CFD and low-fidelity numerical predictions. Results identify the experimental and numerical challenges of the benchmark and the relevance of fundamental research questions related to transition and other low Reynolds number effects

Towards the definition of a benchmark for low Reynolds number propeller aeroacoustics

Experimental and numerical results of a propeller of 0.3 m diameter operated in quiescent standard ambient conditions at 5000 RPM and axial velocity ranging from 0 to 20 m/s and advance ratio ranging from 0 to 0.8 are presented as a preliminary step towards the definition of a benchmark configuration for low Reynolds number propeller aeroacoustics. The corresponding rotational tip Mach number is 0.231 and the Reynolds number based on the blade sectional chord and flow velocity in the whole radial and operational domain ranges from about 54000 to 106000. Force and noise measurements carried out in a low-speed semi-anechoic windtunnel are compared with scale-resolved CFD and low-fidelity numerical results. Results identify the experimental and numerical challenges of the benchmark and the relevance of fundamental research questions related to transition and other low Reynolds number effects

PIV investigation of the 3D instantaneous flow organization behind a micro-ramp in a supersonic boundary layer

The flow field resulting from a single micro-ramp in a Ma=2.0 supersonic boundary layer is investigated using tomographic particle image velocimetry (Tomo-PIV). The measurements were carried out within two volumes behind the micro-ramp. Mean flow characteristics are analyzed, evidence of the streamwise vortex pair is given. In the instantaneous flow, a Kelvin-Helmholtz (K-H) instability developing in the wake of the element is revealed, and the K-H vortices are further identified. A conceptual model is provided to describe the instantaneous flow organization generated by a single micro-ramp

Low-order acoustic prediction tool for estimating noise emissions from distributed propeller configurations

A low-order numerical tool for estimating noise emissions from distributed propeller configurations is presented. The paper describes the tool’s computational framework, which uses Hanson’s near-field theory to calculate the thickness and loading noise components. The formulation assumes steady blade loading, but an unsteady case can be handled numerically by redefining the pressure distribution over the blade at each new time step. Two representative cases are analyzed to validate the tool: an isolated propeller operating in uniform flow and an array of three propellers in a side-by-side configuration under aerodynamic interference caused by adjacent propellers. The results obtained from the low-fidelity tool are compared to high-fidelity data to evaluate the accuracy and differences in predicting the noise of a distributed propeller system. The low-fidelity tool provides accurate results for both cases, with less than a 1.5 dB difference up to the fifth blade-passage frequency (BPF) when comparing tonal noise predictions at an observer located 10 diameters away and at the propeller plane. When analyzing the source directivity at the first BPF, there is a difference of approximately 0.5 dB at the propeller plane. However, this difference increases to 6 dB as the observer moves toward the inflow direction. This difference is due to the dominance of broadband noise near the propeller axis. The paper concludes with a noise analysis of the distributed propeller system, examining the relative importance of aerodynamic interference in the noise emitted by a propeller. In this case, the unsteady blade loading generated a tonal component of 40 dB at the first BPF in the propeller axis, while it had an insignificant effect at the rotor plan