2D Cascade Research Articles

An Image Encryption Scheme Combining 2D Cascaded Logistic Map and Permutation-Substitution Operations

Confusion, diffusion, and encryption keys affect the quality of image encryption. This research proposes combining bit- and pixel-level permutation and substitution methods based on three advanced chaotic logistic map methods. The three chaotic methods are the 2D Logistic-adjusted-Sine map (2D-LASM), the 2D Logistic-sine-coupling map (2D-LSCM), and the 2D Logistic ICMIC cascade map (2D-LICM). The encryption method’s design consists of six stages of encryption, involving permutation operations based on chaotic order, substitution based on modulus and bitXOR, and hash functions. Hash functions are employed to enhance key space and key sensitivity quality. Several testing tools are utilized to assess encryption performance, including histogram and chi-square analysis, information entropy, correlation of adjacent pixels, differential analysis, key sensitivity and key space analysis, data loss and noise attacks, NIST randomness tests, and TestU01. Compared to using a single 2D logistic map, the amalgamation of bit-level and pixel-level encryption and the utilization of three 2D cascade logistic maps has improved encryption security performance. This method successfully passes the NIST, TestU01, and chi-square tests. Furthermore, it outperforms the previous method regarding correlation, information entropy, NPCR, and UACI tests.

1D and 2D Chaotic Time Series Prediction Using Hierarchical Reservoir Computing System

Reservoir Computing (RC) is a type of machine learning inspired by neural processes, which excels at handling complex and time-dependent data while maintaining low training costs. RC systems generate diverse reservoir states by extracting features from raw input and projecting them into a high-dimensional space. One key advantage of RC networks is that only the readout layer needs training, reducing overall training expenses. Memristors have gained popularity due to their similarities to biological synapses and compatibility with hardware implementation using various devices and systems. Chaotic events, which are highly sensitive to initial conditions, undergo drastic changes with minor adjustments. Cascade chaotic maps, in particular, possess greater chaotic properties, making them difficult to predict with memoryless devices. This study aims to predict 1D and 2D cascade chaotic time series using a memristor-based hierarchical RC system.

The New Chapter of Transonic Compressor Cascade Design at the DLR

Abstract The design of compressor blades has been transformed by the advent of optimization algorithms, allowing designers to focus on finding the best optimization strategy for a desired application. However, transonic flow conditions on compressor blades still present considerable modeling challenges, even for a 2D blade section. This paper then focuses on the design of a new state-of-the-art compressor cascade for future test campaigns at the DLR’s Transonic Cascade Wind Tunnel (TGK). For this purpose, a review of the cascades previously tested at the TGK was performed to select a main reference with good efficiency at high loading. The data gathered also informed the optimization strategy applied with the DLR’s optimizer, AutoOpti. The process chain was evaluated with Reynolds Averaged Navier–Stokes CFD simulations using the DLR’s solver, TRACE. The optimization was set to minimize two objective functions: the first one focused on the efficiency at the design point, and the second one focused on the efficiency over the working range. The result is a Pareto front of cascades with a wide variety of design features with an efficiency improvement over the working range of about 24%. This improvement was achieved with a comparable aerodynamic loading. Further analyses were performed to select the “best” cascade for future test campaigns. The significant improvement obtained with respect to the reference and the wide variety of designs observed demonstrates that there is still much to be learned about blade design through optimization; even for 2D cascades and specially in transonic flow.

LES prediction of transitional flows in LP turbine cascades: effects of blade loading, flow phenomena and numerical setup

This paper presents detailed validations of a Large Eddy Simulation (LES) methodology for various transitional phenomena in low pressure turbines. The results are discussed to identify key phenomena to be resolved accurately toward future industrial use of LES. Detailed comparisons between experimental and CFD results are made on three different 2D cascades with different blade loading. One is low-lift and fully laminar design, while the others are moderate- and high-lift designs with boundary layer transition. The experimental data are obtained in a low speed linear cascade at Iwate University. All computations are conducted by a carefully-designed overset LES code. For the high-load design with a distinct laminar separation on the suction side, the LES result shows satisfactory agreement with the test. However, although the peak of total pressure loss distribution is predicted quite accurately, integrated cascade losses are over-predicted in the other two cases. For the laminar blade, the LES result implies some differences can exist in the state of wake, while the transitional blade shows delay of transition in the boundary layer. The effects of inflow turbulence intensity, length scale, and stream tube contraction are discussed in detail to improve LES prediction.

Segmentation and differentiation of periventricular and deep white matter hyperintensities in 2D T2-FLAIR MRI based on a cascade U-net.

White matter hyperintensities (WMHs) are a subtype of cerebral small vessel disease and can be divided into periventricular WMHs (pvWMHs) and deep WMHs (dWMHs). pvWMHs and dWMHs were proved to be determined by different etiologies. This study aimed to develop a 2D Cascade U-net (Cascade U) for the segmentation and differentiation of pvWMHs and dWMHs on 2D T2-FLAIR images. A total of 253 subjects were recruited in the present study. All subjects underwent 2D T2-FLAIR scan on a 3.0 Tesla MR scanner. Both contours of pvWMHs and dWMHs were manually delineated by the observers and considered as the gold standard. Fazekas scale was used to evaluate the burdens of pvWMHs and dWMHs, respectively. Cascade U consisted of a segmentation U-net and a differentiation U-net and was trained with a combined loss function. The performance of Cascade U was compared with two other U-net models (Pipeline U and Separate U). Dice similarity coefficient (DSC), Matthews correlation coefficient (MCC), precision, and recall were used to evaluate the performances of all models. The linear correlations between WMHs volume (WMHV) measured by all models and the gold standard were also conducted. Compared with other models, Cascade U exhibited a better performance on WMHs segmentation and pvWMHs identification. Cascade U achieved DSC values of 0.605 ± 0.135, 0.517 ± 0.263, and 0.510 ± 0.241 and MCC values of 0.617 ± 0.122, 0.526 ± 0.263, and 0.522 ± 0.243 on the segmentation of total WMHs, pvWMHs, and dWMHs, respectively. Cascade U exhibited strong correlations with the gold standard on measuring WMHV (R2 = 0.954, p < 0.001), pvWMHV (R2 = 0.933, p < 0.001), and dWMHV (R2 = 0.918, p < 0.001). A significant correlation was found on lesion volume between Cascade U and gold standard (r > 0.510, p < 0.001). Cascade U showed competitive results in segmentation and differentiation of pvWMHs and dWMHs on 2D T2-FLAIR images, indicating potential feasibility in precisely evaluating the burdens of WMHs.

2D and Slab Turbulent Cascade Rates in the Inner Heliosphere

We present a theoretical and observational study of 2D and slab turbulence cascade (or heating) rates of transverse total turbulence energies, transverse cross helicity, transverse outward and inward Elsässer energy, transverse fluctuating magnetic energy density, and transverse fluctuating kinetic energy from the perihelion of the first Parker Solar Probe (PSP) orbit at ∼36.6 R ⊙ to Solar Orbiter (SolO) at ∼177 R ⊙. We use the Adhikari et al. (2021a) approach to calculate the observed transverse turbulence heating rate, and the nearly incompressible magnetohydrodynamic (NI MHD) turbulence transport theory to calculate the theoretical turbulence cascade rate. We find from the 1 day long PSP measurements at 66.5 R ⊙, and the SolO measurements at 176.3 R ⊙ that various transverse turbulent cascade rates increase with increasing angle, from 10° to 98°, between the mean solar wind speed and mean magnetic field (θ UB), indicating that the 2D heating rate is largest in the inner heliosphere. Similarly, we find from the theoretical and observed results that the 2D heating rate is larger than the slab heating rate as a function of heliocentric distance. We present a comparison between the theoretical and observed 2D and slab turbulence cascade rates as a function of heliocentric distance.

Effects of end-walls on flows in a highly loaded compressor cascade with double-circular-arc blades

A numerical study is carried out to understand the flows in a highly loaded compressor cascade made of double-circular-arc blades, which were measured by Zierke and Deutsch in the late 1980s. A two-dimensional (2D) cascade with periodic boundary conditions in both pitch-wise and span-wise directions and a three-dimensional (3D) cascade with two end-walls that are far away from each other are accounted for in the study. For the incidence angle α=−8.5°, the numerical results of the 2D-cascade flow are in excellent accordance with the experimental data. This not only validates the numerical method used in the study but also suggests that a 2D and periodic flow was successfully generated in the experiment for this incidence angle. However, the numerical results of 2D-cascade flows for α=−1.5° and 5° deviate from the experiment considerably because the strong effects of the end-walls on the wake are neglected in the simulation. By contrast, the simulation of 3D-cascade flows predicts an accurate pressure coefficient at the blade surface, the pressure increase coefficient, and the total pressure loss coefficient for all three incidence angles. This means that, to generate experimental data for validating numerical simulation, it is important to consider the effect of end-walls when the incidence angle is large. The numerical results also show that, for 2D-cascade flows with a low inlet turbulence intensity, the laminar-turbulent transition on the pressure surface is determined by the interaction of the Klebanoff distortions and T-S waves. The Klebanoff distortions are also clearly identified on the suction surface for α=−8.5°. The end-walls induce span-wise elongated disturbances, which suppress the stream-wise disturbances. The transition in 3D-cascade flows generally follows the mechanism of natural transition.

The incompressible energy cascade rate in anisotropic solar wind turbulence

Context. The presence of a magnetic guide field induces several types of anisotropy in solar wind turbulence. The energy cascade rate between scales in the inertial range depends strongly on the direction of this magnetic guide field, splitting the energy cascade according to the parallel and perpendicular directions with respect to magnetic guide field. Aims. Using more than two years of Parker Solar Probe (PSP) observations, the isotropy and anisotropy energy cascade rates are investigated. The variance and normalized fluctuation ratios, the kinetic and magnetic energies, and the normalized cross-helicity and residual energy are studied. The connection between the heliocentric distance, the local temperature of the plasma, and the energy cascade components is made. Methods. Using exact relations for fully developed incompressible magnetohydrodynamic (MHD) turbulence, the incompressible energy cascade rate is computed. In particular, using the isotropy and 2D and slab assumptions, the isotropic, perpendicular, and parallel energy cascade rate components are estimated. Results. The variance anisotropy ratios, for both velocity and magnetic fields, do not exhibit a dependence with respect to the heliocentric distance r between 0.2 and 0.8 au. While the velocity normalized fluctuation ratio shows a dependence with r, the magnetic normalized fluctuation ratio does not. A strong correlation between the isotropic and anisotropic energy cascade rates and the temperature is found. A clear dominance of the perpendicular cascades over the parallel cascades as PSP approaches the Sun is observed. A dominant 2D cascade and/or geometry over the slab component in slow solar wind turbulence in the largest MHD scales is observed.

Impact of three-dimensional turbulence modelling on rotor/stator interaction broadband noise

An accurate prediction of Fan/Outlet-Guide-Vane (OGV) interaction broadband noise (BBN) is fundamental to correctly characterise the noise footprint of high bypass ratio turbofan engines. A three-dimensional synthetic turbulence BBN prediction methodology, which accounts for cascade effects and the airfoil geometry using a frequency-domain Linearised Navier–Stokes Solver, is presented in this work. The methodology computes the BBN generated by an infinite three-dimensional (3D) linear cascade using a spectral representation in the spanwise direction. The 3D problem is reconstructed analytically using two-dimensional (2D) simulations, including additional source terms coming from the spanwise spatial derivatives, leading to a high computational efficiency compared to a standard 3D approach. The methodology has been applied to assess the impact of oblique gusts on a Fan/OGV and a low-pressure turbine airfoil, and the results are compared to a 2D methodology and a previously proposed quasi-3D (q3D) formulation. Differences of more than 10 dB arise when comparing the 3D results with a purely 2D approach caused by the over-estimation of the turbulent kinetic energy that can produce cut-on acoustic modes. The validity of a q3D correction to mitigate this 2D effect has been assessed, demonstrating differences smaller than 2 dB concerning the 3D formulation, and therefore, its use can be justified for rapid predictions. The 3D methodology removes the unphysical impact of the 2D cascade resonances that appear in the q3D approach. The differences between the 3D and q3D approaches have been assessed in detail using an azimuthal noise decomposition. Even though the acoustic response can be remarkably affected by changes in the spanwise wavenumber, the noise azimuthal decomposition and frequency spectra exhibit a similar shape because the acoustic response is relatively constant within a significant fraction of the spanwise wavenumbers that enable sound radiation.

Turbine tonal noise prediction using an improved quasi-3D linear model

This study presented a fast tonal noise prediction method for the turbine. The improved quasi-3D linear model was developed based on Hanson's coupled 2D cascade theory of blade row and Goldstein's duct aeroacoustics equation. The improved model can take into the influence of the radial modes account by applying the strip theory. Furthermore, a two-flat-plates assumption was used for the first time to account for the large turning angle of the turbine blade, and different wake velocity defect models with coefficient correction have been developed for each of the two-flat-plates. Briefly, firstly applying extended Hanson's theory to predict the unsteady load on blade surface and then using Goldstein equation to calculate cut-on modes and sound power level of interested frequencies. The present model was validated by URANS/Goldstein hybrid model by comparing the tonal noise radiation generated by the final stage of the GE E3 low pressure turbine at different rotational speeds and various stator-rotor spacings. The results showed that the present model generally agreed well with the hybrid model and can correctly capture the variations of the sound power level with the operating conditions, which indicated that the present model might be applied as an effective tool for turbine tonal noise prediction with less cost in early design phase of turbine blade.

Development and validation of a Riemann solver in OpenFOAM® for non-ideal compressible fluid dynamics

ABSTRACT Recently, there is an increased interest in supercritical CO2 and organic Rankine cycles (ORC) for their ability to achieve higher thermodynamic efficiency. However, the non-ideal gas thermodynamic in these cycles may affect the flow properties critically, necessitating the research of non-ideal compressible fluid dynamics (NICFD). Thus, simulation tools that can accurately predict fluid flows with NICFD are significant. This study presents a new approximation Riemann solver in OpenFOAM for NICFD. The new solver uses a real-gas (look-up table based) approximate Riemann flux calculator (modified from HLLC ALE flux calculator) through adding a new thermodynamic library tightly coupled with the OpenFOAM®. To validate the solver, three cases are presented, including a NASA transonic nozzle operating with air, to confirm the ability to correctly simulate the transonic flow phenomena and the shock waves; the VKI 2D cascade operated with MDM to assess the ability in simulating non-ideal gas flows typically to industrial applications; and the dense gas flow (MD4M) passing a backward ramp to illustrate the ability of the flux calculator and look-up table mechanism that can work well in the non-ideal region of fluid properties. This study can benefit future engineering applications of computational fluid mechanics of NICFD and the OpenFOAM community.

A New Loss Generation Body Force Model for Fan/Compressor Blade Rows: An Artificial-Neural-Network Based Methodology

Body force models of fans and compressors are widely employed for predicting performance due to the reduction in computational cost associated with their use, particularly in nonuniform inflows. Such models are generally divided into a portion responsible for flow turning and another for loss generation. Recently, accurate, uncalibrated turning force models have been developed, but accurate loss generation models have typically required calibration against higher fidelity computations (especially when flow separation occurs). In this paper, a blade profile loss model is introduced which requires the trailing edge boundary layer momentum thicknesses. To estimate the momentum thickness for a given blade section, an artificial neural network is trained using over 400,000 combinations of blade section shape and flow conditions. A blade-to-blade flow field solver is used to generate the training data. The model obtained depends only on blade geometry information and the local flow conditions, making its implementation in a typical computational fluid dynamics framework straightforward. We show good agreement in the prediction of profile loss for 2D cascades both on and off design in the defined ranges for the neural network training.

A novel 2D cascade modulation couple hyperchaotic mapping for randomized image encryption

In this paper, we design a novel two-dimensional hyperchaotic with two positive Lyapunov exponents and a phase distribution region close to uniform. Then, we propose a novel randomized hyperchaotic image encryption algorithm based on the proposed two-dimensional hyperchaotic mapping. The algorithm is designed in such a way that first adds randomization to the input image, and uses the SHA-256 value of the randomized image with the key for extracting required parameters. This randomization property is required for CPA-security. The security performance of the proposed encryption algorithm is illustrated by several experiments, including robustness against noise and data loss attacks, statistical, differential, and brute-force attacks. These experiments reveal acceptable security in comparison with several recent chaotic image encryption algorithms.

SnO2/2D-Bi2O2Se new hybrid electron transporting layer for efficient and stable perovskite solar cells

Interfacial engineering has been proved to be an effective way to enhance the performance of perovskite solar cells (PSCs) by reducing interfacial charge recombination. In this work, two-dimensional (2D) Bi2O2Se nanoflakes with high chargemobility are synthesized by facile composited molten salt method, and used as electron transport layer (ETL) of PSCs for the first time. The PSCs based on single 2D Bi2O2Se nanoflakes ETL exhibit power conversion efficiency (PCE) of 9.12%, which is 110% higher than those without ETL (4.32%). To fill pinholes and defects on the surface of SnO2 thin film, we also use the 2D Bi2O2Se nanoflakes to modify the surface of SnO2 thin film, and fabricate SnO2/2D-Bi2O2Se new hybrid ETL to effectively reduce recombination at hetero-interface. Owing to the high charge mobility of 2D Bi2O2Se nanoflakes and cascade band alignment between perovskite active layer and tin dioxide, more efficient electron transport in PSCs is obtained than the single SnO2 ETL. Moreover, novel hybrid ETL provides a smoother and more hydrophobic surface for larger perovskite crystal formation. Compared with PSCs with single SnO2 ETL, the PCE of PSCs based on SnO2/2D Bi2O2Se hybrid ETL is improved to 19.06% from 16.29% with suppressed hysteresis. More interesting, the stability of PSCs with the new hybrid ETLs is also improved due to the improved crystallinity of perovskite active layer. This work shows the 2D Bi2O2Se material has potential for applications in PSCs.

Turbine Cascades of Last Stage Blades for Wide Range of Operating Conditions

Recent trends in the electric energy market such as biomass, waste incineration or combined cycle power plants require innovative solutions in steam turbine design. Variable operating conditions cause significant changes in flow field surrounding the steam turbine last stage blades. Therefore, the enlargement of operating range for last stage blades presents new challenges in design of turbine cascades. Several turbine cascades were designed and analyzed by commercial and in-house software of CTU Prague. Selected profiles were experimentally validated in the high-speed wind tunnel for 2D cascade measurements of the Institute of Thermomechanics of the Czech Academy of Sciences which is equipped by an adjustable supersonic inlet nozzle, perforated inserts at side walls and adjustable perforated tailboard. Comparisons are presented of numerical results with optical and pneumatic measurements for a wide range of inlet and outlet Mach numbers for optimized hub and tip profile cascades.

Relative particle dispersion in two-dimensional and quasi-geostrophic turbulence

In this paper, phenomenological developments are used to explore relative particle dispersion (RPD) in two-dimensional (2D) and quasi-geostrophic (QG) fully-developed turbulence (FDT). The role played by the 2D and QG FDT cascade physics underlying this process is given special attention. Prevalence of spatial intermittency effects in 2D FDT enstrophy cascade, however small, is shown to lead to a structural change in the RPD growth law, more specifically the development of power-law scaling of RPD; this corroborates the difficulty in observing Lin’s (1972) exponential scaling law in laboratory experiments (Jullien (2003)). QG effects are found to lead to an enhanced RPD in the baroclinic regime of the energy cascade, which seems to be traceable to a negative eddy-viscosity characterizing the latter regime. They are also found to lead to particle clumping in the baroclinic regime of the enstrophy cascade (this aspect appears to be associated with the tendency of divorticity sheets to occur near the vortex nulls where particle clumping is known, as per numerical simulations and laboratory experiments, to be favored to occur). These results are developed from the established scaling relations for 2D and QG FDT and are validated further via alternative dimensional/scaling developments for 2D and QG FDT similar to the one given for 3D FDT by Batchelor and Townsend (1956). The feasibility of spatial intermittency effects is underscored via the nonlinear scaling dependence of RPD on the enstrophy (or energy) dissipation rate.

Analysis of classical flutter in steam turbine blades using reduced order aeroelastic model

In the present paper classical flutter phenomena in LP steam turbine rotor is studied . A reduced order aeroelastic model (ROAM) with acceptable accuracy and fast execution is developed for this purpose. The aerodynamics damping (AD) is estimated using Traveling wave mode (TWM) method. Flow field is modeled using Panel method. For the structural part ROM non-linear beam element method (BEM) based FEM structural solver is used. Partitioned based ( loose) coupling approach is adopted to perform aeroelastic (flutter) cosimulation. Both 2D cascade flow and 3D cascade are modeled.The estimated stability parameters are compared with experimental data. Moreover, present ROAM shows significant reduction in computational time.

Design strategies and numerical simulation of highly loaded aspirated compressor blades

Boundary layer suction can effectively eliminate flow separations and increase aerodynamic loading of axial compressors. The design methodology of highly loaded aspirated compressor blades was developed and illustrated in this study. In this work, Computational Fluid Dynamics (CFD) methods were first validated with existing data and then used to develop the design strategy of aspirated compressor blades. Design strategies for higher blade performances, including higher loading, larger stall margin and larger blade thickness near the suction slot of aspirated blades, were investigated through analyzing a series of highly loaded aspirated cascades with diffusion factors (DF) around 0.71. Results showed that the design methodology proposed in this paper was appropriate for designing highly loaded aspirated compressor blades. Under the condition of no boundary layer suction (BLS), severe flow separations of highly loaded blades were tailored at the aft part of suction surface by adopting the “ski-slope” velocity distribution, which almost remained unchanged within a large incidence range. The “ski-slope” velocity distribution was appropriate for removing flow separations and beneficial for obtaining thicker blade. High loading of aspirated blade was achieved by the postpositional suction peak and minimum velocity distribution on pressure surface. The stall margin of highly loaded aspirated cascades could be enlarged by designing the velocity distribution upstream of the suction slot and by selecting suction peak position and solidity. A three-dimensional (3D) highly loaded aspirated cascade was designed based on a two-dimensional (2D) cascade. Both the trailing edge separation and corner separation of the 3D highly loaded aspirated cascade were eliminated successfully with coupled suction surface and endwall suction.

Sensors: A Luminescent Inorganic/Organic Composite Ultrathin Film Based on a 2D Cascade FRET Process and Its Potential VOC Selective Sensing Properties (Adv. Funct. Mater. 37/2016)

Sensors: A Luminescent Inorganic/Organic Composite Ultrathin Film Based on a 2D Cascade FRET Process and Its Potential VOC Selective Sensing Properties (Adv. Funct. Mater. 37/2016)

Kriging-assisted design optimization of S-shape supersonic compressor cascades

In this paper, multi-objective design optimization of a supersonic compressor cascade was dealt with. The geometry considered was an S-shaped 2D cascade developed and tested at DLR (DLR-PAV-1.5), operating under unique incidence and inlet Mach number equal to 1.5 so as to develop approximately a static pressure ratio of 2. In such conditions, the cascade shows a strong lambda shock-boundary layer interaction. Methodology included the use of an in-house Kriging-assisted evolutionary algorithm driving an iterative loop which includes a parametric code for geometry representation and the ANSYS Fluent© solver for flow calculation. Cascade optimization was carried out by varying the shapes of both the suction and the pressure sides while maintaining the unique incidence condition using an iterative CFD-based procedure. The objectives were to minimize the cascade total pressure losses and to maximize the static pressure ratio using a Pareto ranking criterion. Results showed that loss coefficient could be reduced by 25% and the static pressure ratio could be improved by 6.5% as a results of a decrease in the pre-shock Mach number by virtue of an extended pre-compression mechanism that involves the entire suction surface upstream of the passage shock.