Numerical Simulation of a Counter-Rotative Open Rotor Using Phase-Lagged Conditions: Initial Validation on a Single Rotor Case

This paper presents the large Eddy simulation (LES) of a propeller representative of the first rotor of a counter rotative open rotor (CROR) configuration based on a multiple frequency phase-lagged approach in conjunction with a proper orthogonal decomposition (POD) data storage. This method enables to perform unsteady simulations on multistage turbomachinery configurations including multiple frequency flows with a reduction of the computational domain composed of one single blade passage for each row. This approach is advantageous when no circumferential periodicity occurs in the blade rows of the configuration and a full 360 deg simulation would be required. The data storage method is based on a POD decomposition replacing the traditional Fourier series decomposition (FSD). The inherent limitation of phase-shifted periodicity assumption remains with POD data storage but this compression method alleviates some issues associated with the Fourier transform, especially spectrum issues. The paper is first dedicated to compare the flow field obtained with the LES with phase-lagged condition against full-matching URANS, LES simulations, and experimental data available around the blade and in the wake of the rotor. The study shows a close agreement of the phase-lagged LES simulation with other simulations performed and a thicker wake compared with the experiments with lower turbulent activity. The analysis of the losses generated in the configuration, based on an entropy formulation and a splitting between boundary layer and secondary flow structures, shows the strong contribution of the blade boundary layer in the losses generated.

Damage detection using wavelet entropy of acoustic emission waveforms in concrete under flexure

This work dives into the spectral realm of acoustic emission waveforms. The acoustic emission waveforms carry a footprint of source, its mechanism, and the information of the medium through which it travels. The idiosyncrasies of these waveforms cannot be visualized from the time-domain parameters. The complex fracture process of the heterogeneous composite, such as concrete, reflects in the spectral disorder of acoustic emission signals. The use of wavelet entropy is proposed to estimate the spectral disorder. To evaluate wavelet entropy, the relative energy distribution in frequency sub-bands is determined using the wavelet transform. The Shannon entropy formulation as a wavelet entropy is utilized for discriminating spatiotemporally distributed acoustic emission events according to their respective level of disorder. The possible twofold application of the wavelet entropy as a signal discriminator and a damage index is qualitatively demonstrated. The increase in the statistical variance of wavelet entropy distribution with the increase in stress level reveals the presence of multi-sources as well as multi-mechanistic fracture process.

An Entropy Formulation Based on the Generalized Liouville Fractional Derivative

This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also generalized and its variation with the fractional order is tested for the time series.

Some Notes on Maximum Entropy Utility

The maximum entropy principle is effective in solving decision problems, especially when it is not possible to obtain sufficient information to induce a decision. Among others, the concept of maximum entropy is successfully used to obtain the maximum entropy utility which assigns cardinal utilities to ordered prospects (consequences). In some cases, however, the maximum entropy principle fails to produce a satisfactory result representing a set of partial preferences properly. Such a case occurs when incorporating ordered utility increments or uncertain probability to the well-known maximum entropy formulation. To overcome such a shortcoming, we propose a distance-based solution, so-called the centralized utility increments which are obtained by minimizing the expected quadratic distance to the set of vertices that varies upon partial preferences. Therefore, the proposed method seeks to determine utility increments that are adjusted to the center of the vertices. Other partial preferences about the prospects and their corresponding centralized utility increments are derived and compared to the maximum entropy utility.

Delineating Loss Sources Within a Linear Cascade With Upstream Cavity and Purge Flow

Purge air is injected in cavities at the hub of axial turbines to prevent hot mainstream gas ingestion into interstage gaps. This process induces additional losses for the turbine due to an interaction between the purge and mainstream flow. This paper investigates the flow in a low-speed linear cascade rig with upstream hub cavity at a Reynolds number commonly observed in modern low-pressure turbine stages by the use of numerical simulation. Numerical predictions are validated by comparing against experimental data available. Three different purge mass flow rates are tested using three different rim seal geometries. Numerical simulations are performed using a large-eddy simulation (LES) solver on structured grids. An investigation of the different mechanisms associated with the turbine flow including cavity and purge air is intended through this simplified configuration. The underlying mechanisms of loss are tracked using an entropy formulation. Once described for a baseline case, the influence of purge flow and rim seal geometry on flow mechanisms and loss generation is described with the emphasis to obtain design parameters for losses reduction. The study quantifies loss generation due to the boundary layer on wetted surfaces and secondary vortices developing in the passage. The analysis shows different paths by which the purge flow and rim seal geometry can change loss generation including a modification of the shear layer between purge and mainstream, interaction with secondary vortices, and a modification of the flow behavior close to hub compared with a smooth configuration. The study shows the influence of purge flow rate and swirl on the strengthening of secondary vortices in the passage and the ability of axial overlapping rim seal to delay the development of secondary vortices compared with simple axial gaps.

Rigorous entropy formulation of the anelastic liquid equations in an ideal gas

The point of this short paper is to provide a useful set of equations governing stratified convection, expressed solely in terms of two thermodynamic variables, i.e. the pressure and the entropy, and the velocity field of the flow, free from any additional assumptions about the properties of turbulence. The pressure fluctuation is entirely eliminated from the energy equation and it appears only in the momentum balance, easily removable by taking its curl. This goal is achieved through the well-known anelastic approximation and an assumption of constant thermal diffusivity coefficient. The rigorously derived system of anelastic liquid equations constitutes a useful tool for modelling the dynamics of stellar interiors.