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19 pages, 6463 KiB  
Article
Biogeochemical Fe-Redox Cycling in Oligotrophic Deep-Sea Sediment
by Di Zhan, Qingyin Xia, Gaoyuan Li, Xinyu Li, Yang Li, Dafu Hu, Jinglong Hu, Ziqi Zhou and Yizhi Sheng
Water 2024, 16(19), 2740; https://doi.org/10.3390/w16192740 - 26 Sep 2024
Abstract
Biogeochemical redox cycling of iron (Fe) essentially governs various geochemical processes in nature. However, the mechanistic underpinnings of Fe-redox cycling in deep-sea sediments remain poorly understood, due to the limited access to the deep-sea environment. Here, abyssal sediment collected from a depth of [...] Read more.
Biogeochemical redox cycling of iron (Fe) essentially governs various geochemical processes in nature. However, the mechanistic underpinnings of Fe-redox cycling in deep-sea sediments remain poorly understood, due to the limited access to the deep-sea environment. Here, abyssal sediment collected from a depth of 5800 m in the Pacific Ocean was characterized for its elemental, mineralogical, and biological properties. The sedimentary environment was determined to be oligotrophic with limited nutrition, yet contained a considerable amount of trace elements. Fe-redox reactions in sediment progressed through an initial lag phase, followed by a fast Fe(II) reduction and an extended period of Fe(III) oxidation before achieving equilibrium after 58 days. The presence of an external H2 electron donor significantly increased the extent of Fe(III) bio-reduction by 7.73% relative to an amendment-free control under high pressure of 58 MPa. A similar enhancement of 11.20% was observed following lactate amendment under atmospheric pressure. Fe(II) bio-oxidation occurred after 16 days’ anaerobic culturing, coupled with nitrate reduction. During Fe bio-redox reactions, microbial community composition was significantly shaped by the presence/absence of an electron donor, while the hydrostatic pressure levels were the controlling factor. Shewanella spp. emerged as the primary Fe(III)-reducing microorganisms, and were stimulated by supplemented lactate. Marinobacter hydrocarbonoclasticus was the predominant Fe(II)-oxidizing microorganism across all conditions. Our findings illustrate continuous Fe-redox reactions occurring in the deep-sea environment, with coexisting Fe-redox microorganisms determining the oscillation of Fe valence states within the abyssal sediment. Full article
(This article belongs to the Special Issue Soil and Groundwater Quality and Resources Assessment)
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Figure 1

Figure 1
<p>XRD pattern of the untreated abyssal sediment.</p>
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<p>Fe-redox curves of the abyssal sediment over 58 days’ anaerobic culturing under atmospheric pressure or 58 MPa in the presence or absence of an external electron donor (H<sub>2</sub> or lactate).</p>
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<p>Nitrate-amended oxidation of the abyssal sediment over 45 days.</p>
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<p>(<b>a</b>) OTU number and (<b>b</b>) corresponding distribution; (<b>c</b>) principal component analysis; (<b>d</b>) sample clustering; relative abundance of (<b>e</b>) phylum and (<b>f</b>) genus in the 6 treated abyssal sediment cultures.</p>
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<p>Correlation heatmap indicating major microbial composition across the 6 treated abyssal sediment samples.</p>
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<p>(<b>a</b>) Redundancy analysis (RDA) among the 6 treated abyssal sediment samples and environmental factors (pressure, H<sub>2</sub> and lactate) and (<b>b</b>) the community functional prediction based on the FAPROTAX database.</p>
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<p>Phenotypic predictions of the dominant phyla within the 6 treated abyssal sediment samples based on BugBase: (<b>a</b>) aerobic, (<b>b</b>) anaerobic, (<b>c</b>) facultative anaerobic, (<b>d</b>) stress-tolerant, (<b>e</b>) Gram-negative, (<b>f</b>) Gram-positive, (<b>g</b>) containing mobile elements, and (<b>h</b>) forming biofilms.</p>
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<p>Scanning electron microscopic images of mineral–microbe interactions in A-Lactate.</p>
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31 pages, 21025 KiB  
Article
A Methodology to Optimize PMSM Driven Solar Water Pumps Using a Hybrid MPPT Approach in Partially Shaded Conditions
by Divya Shetty, Jayalakshmi N. Sabhahit and Ganesh Kudva
Clean Technol. 2024, 6(3), 1229-1259; https://doi.org/10.3390/cleantechnol6030060 - 18 Sep 2024
Abstract
Solar water pumps are crucial for farmers, significantly reducing energy costs and providing independence from conventional fuels. Their adoption is further incentivized by government subsidies, making them a practical choice that aligns with sustainable agricultural practices. However, the cost of the required solar [...] Read more.
Solar water pumps are crucial for farmers, significantly reducing energy costs and providing independence from conventional fuels. Their adoption is further incentivized by government subsidies, making them a practical choice that aligns with sustainable agricultural practices. However, the cost of the required solar panels for the chosen power makes it essential to optimize solar water pumping systems (SWPS) for economic viability. This study enhances the efficiency and reliability of permanent magnet synchronous motor (PMSM)-driven SWPS in rural areas using hybrid maximum power point tracking (MPPT) algorithms and voltage-to-frequency (V/f) control strategy. It investigates the sensorless scalar control method for PMSM-based water pumps and evaluates various MPPT algorithms, including grey wolf optimization (GWO), particle swarm optimization (PSO), perturb and observe (PO), and incremental conductance (INC), along with hybrid combinations. The study, conducted using MATLAB Simulink, assesses these algorithms on convergence time, MPPT accuracy, torque ripple, and system efficiency under different partial shading conditions. Findings reveal that INC-GWO excels, providing higher accuracy, faster convergence, and reduced steady-state oscillations, thus boosting system efficiency. The V/f control strategy simplifies control mechanisms and enhances performance. Considering system non-idealities and maximum duty cycle limitations, PMSM-based SWPS achieve superior efficiency and stability, making them viable for off-grid water pumping applications. Full article
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Figure 1

Figure 1
<p>Power versus voltage curves of PV system under uniform and partial shading.</p>
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<p>Block diagram of the PMSM driven SWPS.</p>
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<p>P-V and I-V curves of the PV system for PMSM based SWPS.</p>
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<p>Boost converter schematic.</p>
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<p>Operating range <span class="html-italic">A<sub>O</sub></span> of the converter under varying uniform shading.</p>
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<p>Operating range <span class="html-italic">A<sub>O</sub></span> of the converter under partial shading.</p>
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<p>DC Link control and V/f control of PMSM.</p>
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<p>The V/f profile.</p>
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<p>Classification of MPPT algorithms.</p>
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<p>INC−GWO MPPT flow chart.</p>
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<p>Variation in DC link voltage, stator frequency and duty ratio in the PMSM based SWPS with PO algorithm.</p>
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<p>Variation in motor torque, speed, and output power with PO algorithm.</p>
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<p>Partial shading patterns having GMPP in the left, center, and right of P-V curve.</p>
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<p>PV-voltage, current, and power under the different PSCs.</p>
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<p>DC link voltage, stator frequency, and duty with INC-GWO in PMSM based SWPS.</p>
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<p>PMSM torque, speed, and output power with INC-GWO.</p>
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<p>PV power, power tracked by INC-GWO MPPT, and PMSM output power.</p>
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<p>DC link voltage, stator frequency, and duty with PSO in PMSM based SWPS.</p>
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<p>PMSM torque, speed, and output power with PSO.</p>
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<p>DC link voltage, stator frequency, and duty with GWO in PMSM based SWPS.</p>
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<p>PMSM torque, speed, and output power with GWO.</p>
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<p>DC link voltage, stator frequency, and duty with PO-PSO in PMSM based SWPS.</p>
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<p>PMSM torque, speed, and output power with PO-PSO.</p>
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<p>DC link voltage, stator frequency, and duty with PO-GWO in PMSM based SWPS.</p>
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<p>PMSM torque, speed, and output power with PO-GWO.</p>
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<p>DC link voltage, stator frequency, and duty with Modified 0.8 V<sub>oc</sub> in PMSM based SWPS.</p>
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<p>PMSM torque, speed, and output power with Modified V<sub>oc</sub>.</p>
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<p>Comparison of parameters for different MPPT techniques for PS1.</p>
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<p>P-V curve with GMMP in the left region and local peak in the right region.</p>
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<p>Efficiency comparison with the MPP in the left and right regions of the P-V curve.</p>
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<p>THD of the inverter output voltage for PS1.</p>
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<p>THD of the inverter output voltage for PS2.</p>
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<p>THD of the inverter output voltage for PS3.</p>
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<p>THD of the inverter output voltage for PS4.</p>
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<p>Comparison of THD for various partial shading patterns.</p>
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<p>THD of the filtered inverter output voltage for PS4.</p>
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<p>THD of the filtered inverter output current for PS4.</p>
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<p>IM torque, speed, and output power with INC-GWO.</p>
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<p>PV power, power tracked by INC-GWO MPPT, and IM output power.</p>
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<p>Efficiency comparison between PMSM and IM based SWPS.</p>
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12 pages, 1035 KiB  
Article
A Methodology to Distribute On-Chip Voltage Regulators to Improve the Security of Hardware Masking
by Soner Seçkiner and Selçuk Köse
Information 2024, 15(8), 488; https://doi.org/10.3390/info15080488 - 16 Aug 2024
Viewed by 405
Abstract
Hardware masking is used to protect against side-channel attacks by splitting sensitive information into different parts, called hardware masking shares. Ideally, a side-channel attack would only work if all these parts were completely independent. But in real-world VLSI implementations, things are not perfect. [...] Read more.
Hardware masking is used to protect against side-channel attacks by splitting sensitive information into different parts, called hardware masking shares. Ideally, a side-channel attack would only work if all these parts were completely independent. But in real-world VLSI implementations, things are not perfect. Information from a hardware masking share can leak to another, making it possible for side-channel attacks to succeed without needing data from every hardware masking share. The theoretically supposed independence of these shares often does not hold up in practice. The effectiveness of hardware masking is reduced because of the parasitic impedance that stems from power delivery networks or the internal structure of the integrated circuit. When the coupling effect and noise spread among the hardware masking shares powered by the same power delivery network, side-channel attacks can be carried out with fewer measurements. To address this, we propose a new method of distributing on-chip voltage regulators to improve hardware masking security. The benefits of distributed on-chip voltage regulators are evident. Placing the regulators close to the load minimizes power loss due to resistive losses in the power delivery network. Localized regulation allows for more efficient adjustments to the varying power demands of different chip sections, improving overall power efficiency. Additionally, distributed regulators can quickly respond to power demand changes, maintaining stable voltage levels for high-performance circuits, leading to improved control over noise. We introduce a new DLDO voltage regulator that uses random clocking and randomizing limit cycle oscillations to enhance security. Our simulations show that with these distributed DLDO regulators, the t-test value can be as low as 2.019, and typically, a circuit with a t-test value below 4.5 is considered secure. Full article
(This article belongs to the Special Issue Hardware Security and Trust)
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Figure 1

Figure 1
<p>Simplified PDN model with masking shares and other circuitry where <span class="html-italic">R</span> is parasitic resistance, <math display="inline"><semantics> <msub> <mi>C</mi> <mrow> <mi>d</mi> <mi>e</mi> <mi>c</mi> <mi>a</mi> <mi>p</mi> </mrow> </msub> </semantics></math> is decoupling capacitor, and <span class="html-italic">C</span> is the parasitic capacitance.</p>
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<p>Proposed partition framework for the NxM grid power delivery network, where <span class="html-italic">t</span>-score is the <span class="html-italic">t</span>-test value.</p>
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<p>Power grid divided into four quadrants.</p>
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<p>Proposed DLDO.</p>
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<p>Schematic of bi-directional shift register [<a href="#B24-information-15-00488" class="html-bibr">24</a>,<a href="#B26-information-15-00488" class="html-bibr">26</a>].</p>
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<p>Activity of a bi-directional shift register [<a href="#B24-information-15-00488" class="html-bibr">24</a>].</p>
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<p>Description of the experiments and security analysis framework.</p>
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<p>The t-test scores at the location of voltage regulators and first-order hardware masking with two shares. The voltage regulators are colored orange with a circle, and hardware masking shares are colored blue with a star. (<b>a</b>) One ideal voltage regulator at the center and two hardware masking shares at the edges. (<b>b</b>) Four ideal voltage regulators at the center of the quadrants and two hardware masking shares at the edges. (<b>c</b>) Seven ideal voltage regulators at the center of the quadrants and two hardware masking shares at the edges.</p>
Full article ">Figure 9
<p>The <span class="html-italic">t</span>-test scores at the location of voltage regulators and first-order hardware masking with two shares. The voltage regulators are colored green with a circle and hardware masking shares are colored blue with a star. (<b>a</b>) One conventional DLDO at the center and two hardware masking shares at the edges of the power grid. (<b>b</b>) Four conventional DLDOs at the center of the quadrants and two hardware masking shares at the edges. (<b>c</b>) Seven conventional DLDOs at the center of the quadrants and two hardware masking shares at the edges.</p>
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<p>The <span class="html-italic">t</span>-test scores at the location of the proposed DLDO voltage regulators and first-order hardware masking with two shares. The voltage regulators are colored red with a circle, and hardware masking shares are colored blue with a star. (<b>a</b>) One proposed DLDO voltage regulator at the center and two hardware masking shares at the edges. (<b>b</b>) Four proposed DLDOs at the center of quadrants and two hardware masking shares at the edges.</p>
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<p>Seven conventional DLDOs are located according to different topologies. The conventional DLDO voltage regulators are colored green with a circle and hardware masking shares are colored blue with a star. (<b>a</b>) Seven conventional DLDOs at the center of the quadrants and two hardware masking shares at the edges of the power grid. (<b>b</b>) Seven conventional DLDOs according to the top–bottom topology. Two hardware masking shares at the edges of the power grid [<a href="#B27-information-15-00488" class="html-bibr">27</a>,<a href="#B28-information-15-00488" class="html-bibr">28</a>]. (<b>c</b>) Seven conventional DLDOs according to the daisy chain topology. Two hardware masking shares at the edges of the power grid [<a href="#B29-information-15-00488" class="html-bibr">29</a>].</p>
Full article ">
18 pages, 1128 KiB  
Article
Stability and Motion Patterns of Two Interactive Oscillating Agents
by Jyh-Ching Juang
Information 2024, 15(7), 388; https://doi.org/10.3390/info15070388 - 2 Jul 2024
Viewed by 548
Abstract
This paper investigates the stability and motion of two interactive oscillating agents. Multiple agents can be controlled in a centralized and/or distributed manner to form specific patterns in cooperative tracking, pursuit, and evasion games, as well as environmental exploration. This paper studies the [...] Read more.
This paper investigates the stability and motion of two interactive oscillating agents. Multiple agents can be controlled in a centralized and/or distributed manner to form specific patterns in cooperative tracking, pursuit, and evasion games, as well as environmental exploration. This paper studies the behavior of two oscillating agents due to their interaction. It shows that, through a combination of selecting oscillation centers and interaction gain, a variety of motions, including limit-cycles and stationary behavior, can be realized. Full article
(This article belongs to the Special Issue Intelligent Agent and Multi-Agent System)
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Figure 1

Figure 1
<p>Number of equilibrium points diagram in terms of <span class="html-italic">k</span> and <math display="inline"><semantics> <mrow> <mo>∥</mo> <mi mathvariant="bold">d</mi> <mo>∥</mo> </mrow> </semantics></math>.</p>
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<p>Stability diagram of <span class="html-italic">k</span> and <math display="inline"><semantics> <msub> <mi>l</mi> <mo>★</mo> </msub> </semantics></math>.</p>
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<p>Stability diagram of <span class="html-italic">k</span> and <math display="inline"><semantics> <mrow> <mo>∥</mo> <mi mathvariant="bold">d</mi> <mo>∥</mo> </mrow> </semantics></math>.</p>
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<p>Stability diagram of <span class="html-italic">k</span> and <math display="inline"><semantics> <mrow> <mo>∥</mo> <mi mathvariant="bold">d</mi> <mo>∥</mo> </mrow> </semantics></math>. The region is red contains two stable equilibrium points.</p>
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<p>Motions under identical oscillation centers. The red and blue curves are the trajectories of the agents. Note that a circular motion is formed and a consensus is reached when <span class="html-italic">k</span> is positive.</p>
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<p>The solution <math display="inline"><semantics> <msub> <mi>l</mi> <mo>★</mo> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold">q</mi> <mo>★</mo> </msub> </semantics></math> as <span class="html-italic">k</span> varies.</p>
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<p>Motions when <math display="inline"><semantics> <mrow> <mo>∥</mo> <mi mathvariant="bold">d</mi> <mo>∥</mo> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Distances when <math display="inline"><semantics> <mrow> <mo>∥</mo> <mi mathvariant="bold">d</mi> <mo>∥</mo> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> in Example 2.</p>
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<p>Change of <math display="inline"><semantics> <msub> <mi>l</mi> <mo>★</mo> </msub> </semantics></math> as a function of <span class="html-italic">k</span> in Example 3.</p>
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<p>Trajectories of agents under different interaction gains in Example 3.</p>
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<p>Distances when <math display="inline"><semantics> <mrow> <mrow> <mo>∥</mo> <mi mathvariant="bold">d</mi> <mo>∥</mo> </mrow> <mo>=</mo> <mn>2</mn> <msqrt> <mn>2</mn> </msqrt> </mrow> </semantics></math> in Example 3.</p>
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<p>Trajectories of agents under different initial conditions in Example 4.</p>
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19 pages, 12683 KiB  
Article
On the Lock-In Phenomena near the Transonic Buffet Onset of a Prescribed Pitching Airfoil
by Lianyi Wei, Guannan Zheng, Weishuang Lu, Yuchen Zhang and Guowei Yang
Appl. Sci. 2024, 14(13), 5463; https://doi.org/10.3390/app14135463 - 24 Jun 2024
Viewed by 454
Abstract
The limit cycle oscillation (LCO) in the transonic buffet on the fixed supercritical airfoil OAT15A under Ma = 0.73, AoA = 3.5° and Re3×106, is successfully simulated by means of the Reynolds Stress Model. Further, the [...] Read more.
The limit cycle oscillation (LCO) in the transonic buffet on the fixed supercritical airfoil OAT15A under Ma = 0.73, AoA = 3.5° and Re3×106, is successfully simulated by means of the Reynolds Stress Model. Further, the buffet lock-in phenomena under prescribed pitch conditions near the buffet onset are also studied by evaluating the modified energy exchange based on the pitching component of the moment coefficients as well as the normalized relative phase map between the pitching component of the moment coefficients and the airfoil’s angular velocity. The zero energy transfer branches in the modified energy map fail to indicate the lock-in boundaries, while the normalized phase map generally outlines the lock-in boundaries for small pitch amplitudes near the buffet onset, which suggests that the lock-in occurs where the moment is in phase with the angular velocity at small pitch amplitudes near the buffet onset. For pitch amplitudes larger than 0.4°, the lock-in onset deviates from the phase shift, possibly due to the fact the instantaneous angle of attack can be lower than the buffet onset where the buffet phenomena may vanish. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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Figure 1

Figure 1
<p>Lee’s self-sustained oscillation model.</p>
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<p>The aeroelastic structural system for a one degree-of-freedom (1-DOF) pitch.</p>
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<p>Computational domain of the test case: (<b>a</b>) the whole domain; (<b>b</b>) grids around the airfoil.</p>
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<p>(<b>a</b>) The mean pressure coefficient of simulations and the experiment; (<b>b</b>) the pressure RMSE of simulations and the experiment.</p>
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<p>Transient velocity contours and the streamlines around the airfoil in a complete buffet cycle.</p>
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<p><span class="html-italic">AoA</span> versus (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>l</mi> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>m</mi> </msub> </mrow> </semantics></math> for RSM simulation and AGARD CT5 case.</p>
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<p>The energy evolution <math display="inline"><semantics> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and the energy extraction <math display="inline"><semantics> <mrow> <msup> <mi>E</mi> <mo>*</mo> </msup> </mrow> </semantics></math> in each cycle of all cases at <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>θ</mi> </msub> <mo>=</mo> <mrow> <mn>0.3</mn> </mrow> <mo>°</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 7 Cont.
<p>The energy evolution <math display="inline"><semantics> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and the energy extraction <math display="inline"><semantics> <mrow> <msup> <mi>E</mi> <mo>*</mo> </msup> </mrow> </semantics></math> in each cycle of all cases at <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>θ</mi> </msub> <mo>=</mo> <mrow> <mn>0.3</mn> </mrow> <mo>°</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 7 Cont.
<p>The energy evolution <math display="inline"><semantics> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and the energy extraction <math display="inline"><semantics> <mrow> <msup> <mi>E</mi> <mo>*</mo> </msup> </mrow> </semantics></math> in each cycle of all cases at <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>θ</mi> </msub> <mo>=</mo> <mrow> <mn>0.3</mn> </mrow> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Frequency contents of all cases at <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>θ</mi> </msub> <mo>=</mo> <mrow> <mn>0.3</mn> </mrow> <mo>°</mo> </mrow> </semantics></math>. (Black solid: buffet frequency; black dashed: pitch frequency).</p>
Full article ">Figure 8 Cont.
<p>Frequency contents of all cases at <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>θ</mi> </msub> <mo>=</mo> <mrow> <mn>0.3</mn> </mrow> <mo>°</mo> </mrow> </semantics></math>. (Black solid: buffet frequency; black dashed: pitch frequency).</p>
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<p>Gain of the amplitude of the pitching component <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>m</mi> <mi>o</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> and the airfoil pitch amplitude <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>θ</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Relative phase <math display="inline"><semantics> <mi>Φ</mi> </semantics></math> between <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>m</mi> </msub> </mrow> </semantics></math> and the angular velocity <math display="inline"><semantics> <mover accent="true"> <mi>θ</mi> <mo>˙</mo> </mover> </semantics></math> versus frequency ratio <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>p</mi> </msub> <mo>/</mo> <msub> <mi>f</mi> <mi>b</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Modified energy map and the frequency response of the moment coefficient. Solid line: the flutter boundary at <math display="inline"><semantics> <mrow> <msup> <mi>E</mi> <mo>*</mo> </msup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
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<p>The normalized relative phase map and the frequency response of the moment coefficient. Solid line: phase shift at <math display="inline"><semantics> <mrow> <mi>Φ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
Full article ">
27 pages, 9307 KiB  
Article
Development and Verification of Coupled Fluid–Structure Interaction Solver
by Avery Schemmel, Seshendra Palakurthy, Anup Zope, Eric Collins and Shanti Bhushan
Computation 2024, 12(6), 129; https://doi.org/10.3390/computation12060129 - 20 Jun 2024
Viewed by 587
Abstract
Recent trends in aeroelastic analysis have shown a great interest in understanding the role of shock boundary layer interaction in predicting the dynamic instability of aircraft structural components at supersonic and hypersonic flows. The analysis of such complex dynamics requires a time-accurate fluid-structure [...] Read more.
Recent trends in aeroelastic analysis have shown a great interest in understanding the role of shock boundary layer interaction in predicting the dynamic instability of aircraft structural components at supersonic and hypersonic flows. The analysis of such complex dynamics requires a time-accurate fluid-structure interaction solver. This study focuses on the development of such a solver by coupling a finite-volume Navier-Stokes solver for fluid flow with a finite-element solver for structural dynamics. The coupled solver is then verified for the prediction of several panel instability cases in 2D and 3D uniform flows and in the presence of an impinging shock for a range of subsonic and supersonic Mach numbers, dynamic pressures, and shock strengths. The panel deflections and limit cycle oscillation amplitudes, frequencies, and bifurcation point predictions were compared within 10% of the benchmark results; thus, the solver was deemed verified. Future studies will focus on extending the solver to 3D turbulent flows and applying the solver to study the effect of turbulent load fluctuations and shock boundary layer interactions on the fluid-structure coupling and structural dynamics of 2D panels. Full article
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Figure 1

Figure 1
<p>(<b>a</b>–<b>c</b>) Schematics of FSI system with boundary conditions, (<b>d</b>) 2D fluid domain consisting of 70 K grid cells <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>200</mn> <mo>×</mo> <mn>350</mn> </mfenced> </semantics></math> with uniform spacing in the axial direction and hyperbolic tangent distribution in the wall-normal direction.</p>
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<p>Grid independence is shown through (<b>a</b>) displacement time history, (<b>b</b>) convergence ratio, (<b>c</b>) normalized pressure, and (<b>d</b>) coefficient of friction plots for a semi-infinite panel subjected to a supersonic laminar flow of <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math> at 3/4th chord location phase angles <math display="inline"><semantics> <mrow> <mo>Φ</mo> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>a</b>,<b>b</b>) show the convergence of the FSI solution, (<b>c</b>,<b>d</b>) show the convergence of the fluid solution.</p>
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<p>Time-step convergence is shown through (<b>a</b>) displacement time history, (<b>b</b>) convergence ratio, (<b>c</b>) normalized pressure, and (<b>d</b>) coefficient of friction plots for a semi-infinite panel subjected to a supersonic laminar flow of <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>875</mn> </mrow> </semantics></math> at 3/4th chord location phase angles <math display="inline"><semantics> <mrow> <mo>Φ</mo> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>a</b>,<b>b</b>) show the convergence of the FSI solution, (<b>c</b>,<b>d</b>) show the convergence of the fluid solution.</p>
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<p>(<b>a</b>) Fluid residual (<b>left</b>), Displacement time history (<b>right</b>) of the limit cycle solution (<b>b</b>) Structural residual of the FSI problem (<b>left</b>), and Panel deflection at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1.8945</mn> </mrow> </semantics></math> s (<b>right</b>), obtained for a panel exposed to a laminar flow at <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>875</mn> </mrow> </semantics></math>, with a shock strength of <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math> impinging at the center of the panel.</p>
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<p>(<b>a</b>) Non-dimensional dynamic pressure of bifurcation point obtained for inviscid solution for the Mach number range of <math display="inline"><semantics> <mrow> <mn>0.4</mn> <mo>&lt;</mo> <mi>M</mi> <mo>&lt;</mo> <mn>2.0</mn> </mrow> </semantics></math> compared with the benchmark results by reference [<a href="#B17-computation-12-00129" class="html-bibr">17</a>] and (<b>b</b>) zoomed-in view around <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
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<p>Bifurcation point analysis for the uniform transonic <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> inviscid flow over a flat panel compared with the benchmark results of reference [<a href="#B19-computation-12-00129" class="html-bibr">19</a>]. (<b>a</b>) The variation of mid-chord deflection with the increase in <math display="inline"><semantics> <mi>λ</mi> </semantics></math>. The bifurcation point is obtained at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>15.5</mn> </mrow> </semantics></math>. (<b>b</b>) panel deflection profiles for the range <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>105</mn> </mrow> </semantics></math> to 3500. (<b>c</b>,<b>d</b>) The time history of the panel deflection for <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>700</mn> </mrow> </semantics></math> and the resulting pressure contours. Results are shown for convex and concave deflections (<b>c</b>) and (<b>d</b>), respectively.</p>
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<p>Non-dimensional flutter frequency <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi mathvariant="normal">f</mi> </msub> <mo>)</mo> </mrow> </semantics></math> of the flat panel near bifurcation compared with the benchmark results by reference [<a href="#B17-computation-12-00129" class="html-bibr">17</a>]. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math>, two different bifurcation points were identified. The second circle indicates the non-dimensional frequency of the secondary bifurcation prediction.</p>
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<p>Panel flutter modes and corresponding pressure contours obtained for the inviscid solution for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> </mrow> </semantics></math> (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>1.2</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>1.414</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>1.6</mn> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>2.0</mn> </mrow> </semantics></math> close to the bifurcation location. The left panel shows panel structure at three different phases for a phase angle <math display="inline"><semantics> <mrow> <mo>Φ</mo> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <msup> <mn>90</mn> <mo>∘</mo> </msup> </semantics></math>, and <math display="inline"><semantics> <msup> <mn>180</mn> <mo>∘</mo> </msup> </semantics></math>.</p>
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<p>Bifurcation point analysis for the uniform supersonic <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> inviscid flow over a panel compared with the benchmark results by reference [<a href="#B19-computation-12-00129" class="html-bibr">19</a>]. (<b>a</b>) Variation of the 3/4th-chord location amplitude with the increase in <math display="inline"><semantics> <mi>λ</mi> </semantics></math>. Bifurcation point is obtained at <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>16.25</mn> </mrow> </semantics></math>. Time history of the 3/4th-chord deflection (<b>b</b>) for <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>15</mn> </mrow> </semantics></math>, which is slightly lower than the bifurcation point and (<b>c</b>) for <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math>, which is larger than the bifurcation point. (<b>d</b>) Variation of the FFT amplitude of the 3/4th-chord deflection time history and (<b>e</b>) dominant LCO frequency with increasing <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p>
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<p>FFT of the time history of the 3/4th-chord deflection for LCO predictions for inviscid flow. Predictions for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.414</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>75</mn> </mrow> </semantics></math> to 125, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.414</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>440</mn> </mrow> </semantics></math> to 560, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>185</mn> </mrow> </semantics></math> to 250, (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>640</mn> </mrow> </semantics></math> to 880, and (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>525</mn> </mrow> </semantics></math> to 1500.</p>
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<p>Panel deformation characteristics obtained for oblique shock impinging on a 2D semi-infinite panel for inviscid flow simulations over the range <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> to 900 at <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> compared with the benchmark results by reference [<a href="#B15-computation-12-00129" class="html-bibr">15</a>]. (<b>a</b>) Deformation amplitude (<b>b</b>) dominant frequency of the oscillations.</p>
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<p>Static panel deformation (<b>left panel</b>) and surface pressure (<b>right panel</b>) for steady-state equilibrium solutions for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> inviscid flow at different shock strengths. (<b>a</b>) Results for <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math> and 875 compared with benchmark results of Visbal [<a href="#B15-computation-12-00129" class="html-bibr">15</a>]. (<b>b</b>) Results for <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>875</mn> </mrow> </semantics></math> at two different phase angles of 3/4th-chord location compared with the benchmark results of Li et al. [<a href="#B23-computation-12-00129" class="html-bibr">23</a>]. (<b>c</b>) Results for <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>875</mn> </mrow> </semantics></math> at two different phase angles of 3/4th -chord location along with mean surface pressure verification with Visbal [<a href="#B39-computation-12-00129" class="html-bibr">39</a>].</p>
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<p>Instantaneous panel deflection (<b>left panel</b>) and surface pressures (<b>right panel</b>) of limit cycle solutions of laminar flow for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>875</mn> </mrow> </semantics></math> flow with a shock strength of <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math> and (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mi>LE</mi> </msub> <mo>=</mo> <mn>0.0156</mn> <mi>L</mi> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mi>LE</mi> </msub> <mo>=</mo> <mn>0.0262</mn> <mi>L</mi> </mrow> </semantics></math> for several phase angles. Dotted lines correspond with the benchmark of Li et al. [<a href="#B23-computation-12-00129" class="html-bibr">23</a>]. (<b>c</b>) Strouhal number for increasing boundary layer thickness for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> flow with a shock strength of <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>/</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math> shows primary and secondary frequencies with Li et al. [<a href="#B23-computation-12-00129" class="html-bibr">23</a>] benchmark predictions. (<b>d</b>) The instantaneous coefficient of friction is shown similar to panel deflection and surface pressure for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mi>LE</mi> </msub> <mo>=</mo> <mn>0.0156</mn> <mi>L</mi> </mrow> </semantics></math>.</p>
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<p>Panel deformation characteristics obtained for 3D uniform flow over a square panel at <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>700</mn> </mrow> </semantics></math> to 3000 compared with the benchmark results of Boyer et al. [<a href="#B18-computation-12-00129" class="html-bibr">18</a>] and Shinde et al. [<a href="#B26-computation-12-00129" class="html-bibr">26</a>]. (<b>a</b>) Deformation amplitude (<b>b</b>) dominant frequency of the oscillations.</p>
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<p>Force transfer from fluid to solid: Construction of scaffold element by projecting a fluid face onto a solid face.</p>
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<p>Displacement transfer from solid to fluid: Construction of scaffold element by projecting a fluid node onto a solid face.</p>
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<p>Scaffold element.</p>
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23 pages, 8853 KiB  
Article
Fluid–Structure Interactions between Oblique Shock Trains and Thin-Walled Structures in Isolators
by Xianzong Meng, Ruoshuai Zhao, Qiaochu Wang, Zebin Zhang and Junlei Wang
Aerospace 2024, 11(6), 482; https://doi.org/10.3390/aerospace11060482 - 18 Jun 2024
Viewed by 484
Abstract
Understanding aeroelastic issues related to isolators is pivotal for the structural design and flow control of scramjets. However, research on fluid–structure interactions (FSIs) between thin-walled structures and the isolator flow remains limited. This study delves into the FSIs between thin-walled panels and the [...] Read more.
Understanding aeroelastic issues related to isolators is pivotal for the structural design and flow control of scramjets. However, research on fluid–structure interactions (FSIs) between thin-walled structures and the isolator flow remains limited. This study delves into the FSIs between thin-walled panels and the isolator flow, as characterized by an oblique shock train, by quantitatively analyzing 11 flow parameters assessing the structural response, separation zones, shock structures, flow symmetry, and performance. The results reveal that an FSI triggers panel flutter under oblique shock train conditions, with the panel shapes exhibiting a combination of first- and second-mode responses, peaking at 0.75 of the panel length. Compared to rigid wall conditions, isolators with a flexible panel at the bottom wall experience downstream movement of the separation zones and shock structures, reduced flow symmetry, and minor changes in performance. Transient fluctuations occur due to the panel flutter. Two flexible panels at the top and bottom walls have a comparatively lesser influence on the averaged parameters but exhibit more violent transient fluctuations. Furthermore, the FSI effects under oblique shock train conditions are contrasted with those under normal shock train conditions. The flutter response under normal shock train conditions is more pronounced, with a larger amplitude and higher frequency, driven by the heightened participation of the first-mode response. The effects of FSIs under normal shock train conditions on the averaged parameters are the opposite (with a larger influence) to those under oblique shock train conditions, with significantly more drastic transient fluctuations. Overall, this study sheds light on the complex and substantial influence of FSIs on the isolator flow, emphasizing the necessity of considering FSIs in future isolator design and development endeavors. Full article
(This article belongs to the Special Issue Aeroelasticity, Volume IV)
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Figure 1
<p>Comparisons between experiments and simulations. (<b>a</b>) Flow field schlieren. (<b>b</b>) Wall pressure distribution on the bottom wall.</p>
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<p>Panel flutter in supersonic flow. (<b>a</b>) Structural response at 0.75<span class="html-italic">l</span> (centerline) under λ = 800. (<b>b</b>) Vibration amplitude at 0.75<span class="html-italic">l</span> (centerline) under different <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p>
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<p>Schematic of the computational configuration.</p>
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<p>Bottom wall pressure distributions of the different grids.</p>
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<p>The computational grid.</p>
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<p>The time-averaged flow structures of the oblique shock train under rigid wall conditions. (<b>a</b>) Mach contour. (<b>b</b>) Density gradient contour with streamlines.</p>
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<p>Mach number contours of two aeroelastic cases. (<b>a</b>) Case 1: One thin-walled panel at the bottom wall. (<b>b</b>) Case 2: Two thin-walled panels at the top and the bottom wall.</p>
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<p>Mach number contours of two aeroelastic cases. (<b>a</b>) Case 1: One thin-walled panel at the bottom wall. (<b>b</b>) Case 2: Two thin-walled panels at the top and the bottom wall.</p>
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<p>Dynamic responses of the structural and flow parameters for Case 1. (<b>a</b>) The transient response of structural displacement at different locations. (<b>b</b>) The transient response of the pressure recovery coefficient.</p>
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<p>Dynamic responses of the structural and flow parameters for Case 2. (<b>a</b>) The transient response of structural displacement. (<b>b</b>) The transient response of the pressure recovery coefficient.</p>
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<p>Schematic diagram of the monitored parameters.</p>
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<p>The influence of FSIs on panel structures. (<b>a</b>) Panel shapes (Case 1) during one LCO period. (<b>b</b>) Panel shapes of the panel at the bottom wall (Case 2) during one LCO period. (<b>c</b>) Panel shapes of the panel at the top wall (Case 2) during one LCO period. (<b>d</b>) The change in structural displacement at 0.75<span class="html-italic">l</span>.</p>
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<p>The influence of the FSI on the separation zones. (<b>a</b>) The locations of the separation zones. (<b>b</b>) The lengths of the separation zones at the top wall. (<b>c</b>) The lengths of the separation zones at the bottom wall.</p>
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<p>The influence of the FSI on the separation zones. (<b>a</b>) The locations of the separation zones. (<b>b</b>) The lengths of the separation zones at the top wall. (<b>c</b>) The lengths of the separation zones at the bottom wall.</p>
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<p>The influence of the FSI on the shock structures. (<b>a</b>) The location of the shock train front. (<b>b</b>) The distance between the first two shocks.</p>
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<p>The influence of the FSI on the flow symmetry level. (<b>a</b>) The local flow symmetry factor. (<b>b</b>) The lift coefficient.</p>
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<p>The influence of the FSI on the performance of the isolator. (<b>a</b>) The total pressure recovery coefficient. (<b>b</b>) The flow distortion index.</p>
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<p>Mach contours of two types of shock train under the influence of FSIs. (<b>a</b>) FSI between the thin-walled panel and the normal shock train at t = 0.5 s. (<b>b</b>) FSI between the thin-walled panel and the oblique shock train at t = 0.5 s.</p>
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<p>Mach contours of two types of shock train under the influence of FSIs. (<b>a</b>) FSI between the thin-walled panel and the normal shock train at t = 0.5 s. (<b>b</b>) FSI between the thin-walled panel and the oblique shock train at t = 0.5 s.</p>
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<p>Comparisons of the effect of FSIs on the structures under different shock train conditions. (<b>a</b>) Panel shapes (FSI of normal shock train) in one LCO period. (<b>b</b>) The change in structural displacement at 0.75<span class="html-italic">l</span>.</p>
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<p>Comparisons of the effect of FSIs on the separation zones under different shock train conditions. (<b>a</b>) The locations of the separation zones at the top wall. (<b>b</b>) The lengths of the separation zones at the top wall. (<b>c</b>) The locations of the separation zones at the bottom wall. (<b>d</b>) The lengths of the separation zones at the bottom wall.</p>
Full article ">Figure 18 Cont.
<p>Comparisons of the effect of FSIs on the separation zones under different shock train conditions. (<b>a</b>) The locations of the separation zones at the top wall. (<b>b</b>) The lengths of the separation zones at the top wall. (<b>c</b>) The locations of the separation zones at the bottom wall. (<b>d</b>) The lengths of the separation zones at the bottom wall.</p>
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<p>Comparisons of the effect of FSIs on the shock structures under different shock train conditions. (<b>a</b>) The location of the shock train front. (<b>b</b>) The distance between the first two shocks.</p>
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<p>Comparisons of the effect of FSIs on the shock structures under different shock train conditions. (<b>a</b>) The local flow symmetry. (<b>b</b>) The overall flow symmetry.</p>
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<p>Comparisons of the effect of FSIs on the performance under different shock train conditions. (<b>a</b>) The total pressure recovery coefficient. (<b>b</b>) The flow distortion index.</p>
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15 pages, 13798 KiB  
Article
Studies on the Evolution of Fatigue Strength of Aluminium Wires for Overhead Line Conductors
by Bartosz Jurkiewicz and Beata Smyrak
Materials 2024, 17(11), 2537; https://doi.org/10.3390/ma17112537 - 24 May 2024
Cited by 1 | Viewed by 535
Abstract
Traditional ACSR overhead wires, which consist of a high-strength steel core and several layers of aluminium wires, are currently the most popular overhead line conductor (OHL) design globally. Operating conditions, particularly operating under varying stresses from Karman vortices, lead to the fatigue cracking [...] Read more.
Traditional ACSR overhead wires, which consist of a high-strength steel core and several layers of aluminium wires, are currently the most popular overhead line conductor (OHL) design globally. Operating conditions, particularly operating under varying stresses from Karman vortices, lead to the fatigue cracking of wires of the outer layer, followed by wires of the inner layers. Karman vortices are formed by the detachment of a laminar wind stream flowing around the conductor, which causes vibrations in the conductor called wind or aeolian oscillations. Aluminium wires are manufactured using standard batch material drawing technology. Although the fatigue strength of such wires is not standardised, there are various criteria for evaluating this characteristic, as well as established limits on the number of cycles needed to break the first wires of the outer layer. Fatigue strength also strongly depends on the geometric structure of the wire and its operating conditions. The article analyses the influence of the mechanical condition of aluminium wires used in ACSR cables on their fatigue strength. We then present results from aluminium wire fatigue tests conducted on a specially constructed test rig. In addition, fatigue cracks were interpreted using scanning microscopy. Full article
(This article belongs to the Special Issue Study on Cyclic Mechanical Behaviors of Materials – 2nd Edition)
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Figure 1
<p>S–N curves for wires and cables on a logarithmic scale [<a href="#B17-materials-17-02537" class="html-bibr">17</a>].</p>
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<p>Diagram of the fatigue test stand.</p>
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<p>The methodology for analysing fatigue process results and constructing Wöhler curves.</p>
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<p>Wöhler curves of aluminium wire tested (red points on the left—test results; black, results in [<a href="#B23-materials-17-02537" class="html-bibr">23</a>], blue—tested in [<a href="#B29-materials-17-02537" class="html-bibr">29</a>]) along with SEM images of fatigue cracks of aluminium wire, magnification 100×.</p>
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<p>S–N curves of aluminium wires with different levels of strain hardening.</p>
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<p>SEM images of the fatigue cracks of aluminium wires tested in this paper (rows show images of cracks in the wires with different levels of the hardening state, while columns indicate stress values during the fatigue test).</p>
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<p>SEM image of aluminium (90% strain hardening) wire after fatigue tests (HCF), magnification 50×.</p>
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<p>SEM image of aluminium wires after fatigue tests (LCF), magnification 50×.</p>
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<p>SEM images of fatigue failures of aluminium wires (engineering strain—90%). The rows show stress values during the fatigue test; columns—SEM images at different magnifications.</p>
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<p>SEM images of the fatigue failures of aluminium wires (engineering strain—12%). The rows show stress values during the fatigue test; columns—SEM images at different magnifications.</p>
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14 pages, 1643 KiB  
Article
DFT and TD-DFT Investigations for the Limitations of Lengthening the Polyene Bridge between N,N-dimethylanilino Donor and Dicyanovinyl Acceptor Molecules as a D-π-A Dye-Sensitized Solar Cell
by Sharif Abu Alrub, Ahmed I. Ali, Rageh K. Hussein, Suzan K. Alghamdi and Sally A. Eladly
Int. J. Mol. Sci. 2024, 25(11), 5586; https://doi.org/10.3390/ijms25115586 - 21 May 2024
Cited by 1 | Viewed by 624
Abstract
One useful technique for increasing the efficiency of organic dye-sensitized solar cells (DSSCs) is to extend the π-conjugated bridges between the donor (D) and the acceptor (A) units. The present study used the DFT and TD–DFT techniques to investigate the effect of lengthening [...] Read more.
One useful technique for increasing the efficiency of organic dye-sensitized solar cells (DSSCs) is to extend the π-conjugated bridges between the donor (D) and the acceptor (A) units. The present study used the DFT and TD–DFT techniques to investigate the effect of lengthening the polyene bridge between the donor N, N-dimethyl-anilino and the acceptor dicyanovinyl. The results of the calculated key properties were not all in line with expectations. Planar structure was associated with increasing the π-conjugation linker, implying efficient electron transfer from the donor to the acceptor. A smaller energy gap, greater oscillator strength values, and red-shifted electronic absorption were also observed when the number of polyene units was increased. However, some results indicated that the potential of the stated dyes to operate as effective dye-sensitized solar cells is limited when the polyene bridge is extended. Increasing the polyene units causes the HOMO level to rise until it exceeds the redox potential of the electrolyte, which delays regeneration and impedes the electron transport cycle from being completed. As the number of conjugated units increases, the terminal lobes of HOMO and LUMO continue to shrink, which affects the ease of intramolecular charge transfer within the dyes. Smaller polyene chain lengths yielded the most favorable results when evaluating the efficiency of electron injection and regeneration. This means that the charge transfer mechanism between the conduction band of the semiconductor and the electrolyte is not improved by extending the polyene bridge. The open circuit voltage (VOC) was reduced from 1.23 to 0.70 V. Similarly, the excited-state duration (τ) decreased from 1.71 to 1.23 ns as the number of polyene units increased from n = 1 to n = 10. These findings are incompatible with the power conversion efficiency requirements of DSSCs. Therefore, the elongation of the polyene bridge in such D-π-A configurations rules out its application in solar cell devices. Full article
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Figure 1

Figure 1
<p>The dihedral angles for dye (n = 2) demonstrate the dihedral angle between the dye molecules’ planes.</p>
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<p>Diagram showing the HOMO and LUMO energy levels for dyes with n = 1 to n = 10.</p>
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<p>HOMO and LUMO frontier molecular orbital distribution of dyes n = 1 and n = 10.</p>
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<p>The absorption spectrum of dyes n = 1 to n = 10 simulated by the TD-CAM-B3LYP/6-311G (d, p) method in chloroform solvent.</p>
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<p>The studied molecule included a polyene bridge connecting the donor unit, DMA, to the acceptor unit, DCV, with n = 1, 2, ….</p>
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28 pages, 17751 KiB  
Article
An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction
by Tianchi Gong, Feng Wang and Yan Wang
Appl. Sci. 2024, 14(9), 3939; https://doi.org/10.3390/app14093939 - 5 May 2024
Viewed by 1045
Abstract
An arbitrary Lagrangian-Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with the mode superposition method is proposed in this work and applied to study two- and three-dimensional flutter phenomenon on dynamic unstructured meshes. The ALE-LBFS is applied to predict the flow field by using [...] Read more.
An arbitrary Lagrangian-Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with the mode superposition method is proposed in this work and applied to study two- and three-dimensional flutter phenomenon on dynamic unstructured meshes. The ALE-LBFS is applied to predict the flow field by using the vertex-centered finite volume method with an implicit dual time-stepping method. The convective fluxes are evaluated by using lattice Boltzmann solutions of the non-free D1Q4 lattice model and the viscous fluxes are obtained directly. Additional fluxes due to mesh motion are calculated directly by using local conservative variables and mesh velocity. The mode superposition method is used to solve for the dynamic response of solid structures. The exchange of aerodynamic forces and structural motions is achieved through interpolation with the radial basis function. The flow solver and the structural solver are tightly coupled so that the restriction on the physical time step can be removed. In addition, geometric conservation law (GCL) is also applied to guarantee conservation laws. The proposed method is tested through a series of simulations about moving boundaries and fluid–structure interaction problems in 2D and 3D. The present results show good consistency against the experiments and numerical simulations obtained from the literature. It is also shown that the proposed method not only can effectively predict the flutter boundaries in both 2D and 3D cases but can also accurately capture the transonic dip phenomenon. The tight coupling of the ALE-LBFS and the mode superposition method presents an effective and powerful tool for flutter prediction and can be applied to many essential aeronautical problems. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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Figure 1
<p>Schematic of an interface boundary where fluid (<math display="inline"><semantics> <mrow> <msub> <mo>Ω</mo> <mi>f</mi> </msub> </mrow> </semantics></math>) and solid domain (<math display="inline"><semantics> <mrow> <msub> <mo>Ω</mo> <mi>s</mi> </msub> </mrow> </semantics></math>) meet and their outward normal vectors <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>f</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>s</mi> </msub> </mrow> </semantics></math> point in opposite directions.</p>
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<p>Control volume of a median-dual cell-vertex scheme for (<b>left</b>) 2D and (<b>right</b>) 3D.</p>
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<p>Distribution of discrete lattice velocities in 1D model.</p>
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<p>Streaming process in the D1Q4 model.</p>
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<p>Computational flowchart for the tight-coupling method.</p>
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<p>Displacement and force transfer between fluid and structure solver.</p>
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<p>Flowchart of the solution process for the FSI problem.</p>
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<p>Comparison of <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi mathvariant="normal">m</mi> </msub> </mrow> </semantics></math> for NACA 0012 airfoil with the numerical and experimental results. (<b>a</b>) Coefficient of lift. (<b>b</b>) Coefficient of moment.</p>
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<p>Comparison of pressure coefficients distributed on NACA 0012 airfoil for four different snapshots in one pitch cycle. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>4.59</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>45</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>5.30</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>90</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>4.59</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>135</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>2.89</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>180</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Comparison of pressure coefficients distributed on NACA 0012 airfoil for four different snapshots in one pitch cycle. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>4.59</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>45</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>5.30</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>90</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>4.59</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>135</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mrow> <mn>2.89</mn> </mrow> <mo>∘</mo> </msup> <mo>,</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mrow> <mn>180</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Schematic diagram of the uCRM-13.5 wing.</p>
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<p>Distribution on the wing surface in a steady state. (<b>a</b>) Pressure coefficient contour. (<b>b</b>) Pressure coefficient distribution along <math display="inline"><semantics> <mrow> <mrow> <mi>y</mi> <mo>/</mo> <mi>b</mi> </mrow> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics></math>. (<b>c</b>) Pressure coefficient distribution along <math display="inline"><semantics> <mrow> <mrow> <mi>y</mi> <mo>/</mo> <mi>b</mi> </mrow> <mo>=</mo> <mn>0.89</mn> </mrow> </semantics></math>.</p>
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<p>Time-dependent <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> </semantics></math> for the wing at <math display="inline"><semantics> <mrow> <mrow> <mi>y</mi> <mo>/</mo> <mi>b</mi> </mrow> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics></math>. (<b>a</b>) Mode 1, frequency 0.505 Hz. (<b>b</b>) Mode 2, frequency 1.670 Hz. (<b>c</b>) Mode 3, frequency 2.733 Hz. (<b>d</b>) Mode 4, frequency 3.843 Hz.</p>
Full article ">Figure 12 Cont.
<p>Time-dependent <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> </semantics></math> for the wing at <math display="inline"><semantics> <mrow> <mrow> <mi>y</mi> <mo>/</mo> <mi>b</mi> </mrow> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics></math>. (<b>a</b>) Mode 1, frequency 0.505 Hz. (<b>b</b>) Mode 2, frequency 1.670 Hz. (<b>c</b>) Mode 3, frequency 2.733 Hz. (<b>d</b>) Mode 4, frequency 3.843 Hz.</p>
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<p>Time-dependent <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> </semantics></math> for the wing at <math display="inline"><semantics> <mrow> <mrow> <mi>y</mi> <mo>/</mo> <mi>b</mi> </mrow> <mo>=</mo> <mn>0.89</mn> </mrow> </semantics></math>. (<b>a</b>) Mode 1, frequency 0.505 Hz. (<b>b</b>) Mode 2, frequency 1.670 Hz. (<b>c</b>) Mode 3, frequency 2.733 Hz. (<b>d</b>) Mode 4, frequency 3.843 Hz.</p>
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<p>Pressure distribution on 3D pitching wing. (<b>a</b>) Mean pressure distribution. (<b>b</b>) Mean pressure coefficient at 60% wing span.</p>
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<p>The variation in terms of the amplitude and phase when the forced oscillation frequency f = 10 Hz. (<b>a</b>) Amplitude. (<b>b</b>) Phase.</p>
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<p>Schematic of (<b>a</b>) the typical section wing model and (<b>b</b>) AGARD 445.6 wing.</p>
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<p>Schematic of (<b>a</b>) the typical section wing model and (<b>b</b>) AGARD 445.6 wing.</p>
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<p>Flutter speed index <math display="inline"><semantics> <mrow> <msubsup> <mi>V</mi> <mi>f</mi> <mo>∗</mo> </msubsup> </mrow> </semantics></math> as a function of a free-stream Mach number for NACA 64A010.</p>
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<p>History of plunge and pitch for (<b>a</b>) damped response; (<b>b</b>) divergent response; (<b>c</b>) limit cycle oscillation (LCO).</p>
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<p>Pressure coefficient contours at four snapshots in a circle of LCO when Ma = 0.85. The red solid line represents the initial contour of the airfoil.</p>
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<p>Pressure coefficient contours at four snapshots in a circle of LCO when Ma = 0.85. The red solid line represents the initial contour of the airfoil.</p>
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<p>Geometry of AGARD 445.6 and its NACA 65A004 airfoil.</p>
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<p>Mesh for (<b>a</b>) shell model and (<b>b</b>) plate model with constant thickness.</p>
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<p>The contour of mode shape and deformation diagram for the first four mode frequencies. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>9.6224</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>40.925</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>49.863</mn> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>98.796</mn> </mrow> </semantics></math>.</p>
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<p>Generalized displacement for the first three modes for Ma = 0.96 and <math display="inline"><semantics> <mrow> <msubsup> <mi>V</mi> <mi>f</mi> <mo>∗</mo> </msubsup> <mo>=</mo> <mn>0.292</mn> </mrow> </semantics></math>.</p>
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<p>Displacement in x-, y-, z-directions at the probe of (<b>a</b>) the leading edge and (<b>b</b>) the trailing edge for Ma = 0.96 and <math display="inline"><semantics> <mrow> <msubsup> <mi>V</mi> <mi>f</mi> <mo>∗</mo> </msubsup> <mo>=</mo> <mn>0.292</mn> </mrow> </semantics></math>.</p>
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<p>Flutter speed index <math display="inline"><semantics> <mrow> <msubsup> <mi>V</mi> <mi>f</mi> <mo>∗</mo> </msubsup> </mrow> </semantics></math> as a function of a free-stream Mach number for AGARD 445.6 wing.</p>
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<p>Displacement in x-, y-, z-directions at the probe of (<b>a</b>) the leading edge and (<b>b</b>) the trailing edge for Ma = 0.499 and <math display="inline"><semantics> <mrow> <msubsup> <mi>V</mi> <mi>f</mi> <mo>∗</mo> </msubsup> <mo>=</mo> <mn>0.44</mn> </mrow> </semantics></math>.</p>
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23 pages, 10303 KiB  
Article
Acoustic Design Parameter Change of a Pressurized Combustor Leading to Limit Cycle Oscillations
by Mehmet Kapucu, Jim B. W. Kok and Artur K. Pozarlik
Energies 2024, 17(8), 1885; https://doi.org/10.3390/en17081885 - 15 Apr 2024
Viewed by 835
Abstract
When aiming to cut down on the emission of nitric oxides by gas turbine engines, it is advantageous to have them operate at low combustion temperatures. This is achieved by lean premixed combustion. Although lean premixed combustion is a proven and promising technology, [...] Read more.
When aiming to cut down on the emission of nitric oxides by gas turbine engines, it is advantageous to have them operate at low combustion temperatures. This is achieved by lean premixed combustion. Although lean premixed combustion is a proven and promising technology, it is also very sensitive to thermoacoustic instabilities. These instabilities occur due to a coupling between the unsteady heat release rate of the flame and the acoustic field inside the combustion chamber. In this paper, this coupling is investigated in detail. Two acoustic design parameters of a swirl-stabilized pressurized preheated air (300 °C)/natural gas combustor are varied, and the occurrence of thermoacoustic limit cycle oscillations is explored. The sensitivity of the acoustic field as a function of combustion chamber length (0.9 m to 1.8 m) and reflection coefficient (0.7 and 0.9) at the exit of the combustor is investigated first using a hybrid numerical and analytical approach. ANSYS CFX is used for Unsteady Reynolds Averaged Navier-Stokes (URANS) numerical simulations, and a one-dimensional acoustic network model is used for the analytical investigation. Subsequently, the effects of a change in the reflection coefficient are validated on a pressurized combustor test rig at 125 kW and 1.5 bar. With the change in reflection coefficient, the combustor switched to limit cycle oscillation as predicted, and reached a sound pressure level of 150 dB. Full article
(This article belongs to the Special Issue Heat Transfer and Advanced Combustion in Gas Turbines)
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Figure 1
<p>DESIRE experimental setup. (1) Fuel inlet, (2) Air inlet, (3) Cooling air inlet, (4) Swirler burner, (5) Combustion chamber, (6) Pressure sensor locations, (7) Exhaust.</p>
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<p>Pressure spectra of the combustor (measured acoustic oscillation amplitude as a function of frequency).</p>
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<p>Instability analysis. <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>−</mo> <mi>τ</mi> <mo>−</mo> <mi>σ</mi> </mrow> </semantics></math> model (◊), <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>−</mo> <mi>τ</mi> <mo>−</mo> <mi>σ</mi> </mrow> </semantics></math> model (low pass filter) (□), RTF (○).</p>
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<p>Flowchart for the methodology.</p>
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<p>1D acoustic network model representation of the experimental setup.</p>
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<p>Instability analysis for different length of the combustor. Light gray color represents the length of the combustor equal to 0.9 m, and black color represents the length of 1.8 m.</p>
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<p>Flow through a diaphragm [<a href="#B47-energies-17-01885" class="html-bibr">47</a>].</p>
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<p>Reflection coefficient calculations depending on the contraction diameter. Reflection coefficient magnitude (<b>top</b>) and phase (<b>bottom</b>) vs. frequency.</p>
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<p>Instability searches for different contraction diameter.</p>
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<p>Instability searches for different contraction diameter and length of the combustor. (■) represents the 38 mm contraction; (●) represents 75 mm.</p>
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<p>Computation domain. (1) Air inlet, (2) Plenum, (3) Swirler, (4) Fuel inlet, (5) Combustion chamber, (6) Exhaust (end contraction).</p>
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<p>Pressure spectrum for different contraction diameters (acoustic pressure amplitude as a function of frequency for two end conditions).</p>
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<p>End contraction: (<b>a</b>) 75 mm, seen from the downstream side, (<b>b</b>) 38 mm, seen from the upstream side.</p>
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<p>Quality of measured time signal. (<b>a</b>) 75 mm contraction, (<b>b</b>) 38 mm contraction, (<b>c</b>) zoomed in time signal for 75 mm contraction, (<b>d</b>) zoomed in signal for 38 mm contraction with sinusoidal fit (red dashed line).</p>
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<p>Quality of measured time signal. (<b>a</b>) 75 mm contraction, (<b>b</b>) 38 mm contraction, (<b>c</b>) zoomed in time signal for 75 mm contraction, (<b>d</b>) zoomed in signal for 38 mm contraction with sinusoidal fit (red dashed line).</p>
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<p>Measured pressure spectrum amplitude in sound pressure level (SPL) (dB ref. pressure 20 μPa) as a function of frequency.</p>
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<p>Pressure spectrum for contraction diameters 75 and 38 mm.</p>
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<p>Calibration of pressure transducers.</p>
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<p>The frequency response of the flame models. Measurement (o), <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>−</mo> <mi>τ</mi> <mo>−</mo> <mi>σ</mi> </mrow> </semantics></math> model (--), <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>−</mo> <mi>τ</mi> <mo>−</mo> <mi>σ</mi> </mrow> </semantics></math> model (-.), rational transfer function method (gray -), (PN = 5, PD = 6).</p>
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<p>Mesh of a computational domain.</p>
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<p>Pressure spectrum for 125 kW at 1.5 bar (15.7) and 250 kW at 3 bar (30.5) as a function of frequency.</p>
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<p>Failed and missing bolts of the liner window frame of the combustor after the 1.5 bar/125 kW test.</p>
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22 pages, 1754 KiB  
Article
Modelling the Dynamics of Outbreak Species: The Case of Ditrupa arietina (O.F. Müller), Gulf of Lions, NW Mediterranean Sea
by Jennifer Coston-Guarini, François Charles and Jean-Marc Guarini
J. Mar. Sci. Eng. 2024, 12(2), 350; https://doi.org/10.3390/jmse12020350 - 18 Feb 2024
Viewed by 1297
Abstract
An outbreak species exhibits extreme, rapid population fluctuations that can be qualified as discrete events within a continuous dynamic. When outbreaks occur they may appear novel and disconcerting because the limiting factors of their dynamics are not readily identifiable. We present the first [...] Read more.
An outbreak species exhibits extreme, rapid population fluctuations that can be qualified as discrete events within a continuous dynamic. When outbreaks occur they may appear novel and disconcerting because the limiting factors of their dynamics are not readily identifiable. We present the first population hybrid dynamic model that combines continuous and discrete processes, designed to simulate marine species outbreaks. The deterministic framework was tested using the case of an unexploited benthic invertebrate species: the small, serpulid polychaete Ditrupa arietina. This species is distributed throughout the northeast Atlantic Ocean and Mediterranean Sea; it has a life cycle characterised by a pelagic dispersive larval stage, while juveniles and adults are sedentary. Sporadic reports of extremely high, variable densities (from <10 to >10,000 ind.m2) have attracted attention from marine ecologists for a century. However, except for one decade-long field study from the Bay of Banyuls (France, Gulf of Lions, Mediterranean Sea), observations are sparse. Minimal formulations quantified the processes governing the population dynamics. Local population continuous dynamics were simulated from a size-structured model with a null immigration–emigration flux balance. The mathematical properties, based on the derived hybrid model, demonstrated the possibilities of reaching an equilibrium for the population using a single number of recruits per reproducer. Two extrapolations were made: (1) local population dynamics were simulated over 180 years using North Atlantic Oscillation indices to force recruitment variability and (2) steady-state population densities over the Gulf of Lions were calculated from a connectivity matrix in a metapopulation. The dynamics reach a macroscopic stability in both extrapolations, despite the absence of density regulating mechanisms. This ensures the persistence of D. arietina, even when strong, irregular oscillations characteristic of an outbreak species are observed. The hybrid model suggests that a macroscopic equilibrium for a population with variable recruitment conditions can only be characterised for time periods which contain several outbreak occurrences distributed over a regional scale. Full article
(This article belongs to the Section Marine Biology)
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<p>Study area in the context of the overall distribution of <span class="html-italic">D. arietina</span> occurrences along the northeastern Atlantic and Mediterranean coasts, post-1800. Data from: OBIS [<a href="#B10-jmse-12-00350" class="html-bibr">10</a>] (median year = 2006; 6696 instances in map area of 6765 total) and 20 additional locations from two new sources (Koehler [<a href="#B19-jmse-12-00350" class="html-bibr">19</a>], Hartley [<a href="#B8-jmse-12-00350" class="html-bibr">8</a>]). The violin plot shows the limited time range of the observations (&gt;99% are from the past 70 years) and most of these are from surveys in Norwegian waters (5365 instances between 1990 and 2021). Banyuls Bay is at the extreme western edge of the study area, near the French–Spanish border. No population genetics studies on this species have been reported in the region shown.</p>
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<p>The Bay of Banyuls-sur-Mer (Banyuls Bay) is located at the western edge of the Gulf of Lions (indicated by the star). <span class="html-italic">D. arietina</span> was studied in detail here for over a decade. Between 1996 and 2003, 78 stations (circles) were sampled yearly for abundances. One of the “SOLA” stations were sampled on a biweekly basis: 1994–1996 (square); 1997–2005 (diamond). The spatial domain used to characterise the structure of <span class="html-italic">D. arietina</span> abundance distributions is shown in orange.</p>
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<p>Numerical scheme for integrating Equation (<a href="#FD2-jmse-12-00350" class="html-disp-formula">2</a>). On the abscissa are the individual sizes, from <math display="inline"><semantics> <msub> <mi>s</mi> <mn>0</mn> </msub> </semantics></math>, the recruitment size, to <math display="inline"><semantics> <msub> <mi>s</mi> <mrow> <mi>l</mi> <mi>i</mi> <mi>m</mi> </mrow> </msub> </semantics></math>, the size limit reached by individuals. <math display="inline"><semantics> <msub> <mi>s</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> represents the average asymptotic size, as formulated in the von Bertalanffy equation. Above <math display="inline"><semantics> <msub> <mi>s</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math>, there is no growth per se, but a process of diffusion spreading the sizes across a range, to describe individual variability as it was observed. On the ordinate is time. The species’ abundance or density <math display="inline"><semantics> <msubsup> <mi>n</mi> <mi>s</mi> <mi>t</mi> </msubsup> </semantics></math> is shown here to be calculated by an implicit scheme from values of abundance or densities at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>+</mo> <mo>Δ</mo> <mi>t</mi> </mrow> </semantics></math>. The empty circles indicate the state variable nodes used.</p>
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<p>Dependence between probability density and depth, <span class="html-italic">z</span> (in <span class="html-italic">m</span>), in the Banyuls Bay spatial surveys as inferred from the kriging. Lines are the skew normal distributions fitted to the data (×).</p>
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<p>Number of recruits per reproducer (<math display="inline"><semantics> <msup> <mi>ρ</mi> <mo>★</mo> </msup> </semantics></math>), as a function of the period between two events (between 365 and <math display="inline"><semantics> <mrow> <mn>730</mn> <mspace width="4pt"/> <mi>d</mi> <mi>a</mi> <mi>y</mi> <mi>s</mi> </mrow> </semantics></math>) and as a function of the mortality rate value (between <math display="inline"><semantics> <mrow> <mn>0.002</mn> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mn>0.007</mn> <mspace width="4pt"/> <mi>d</mi> <mi>a</mi> <mi>y</mi> <msup> <mi>s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>). The function increases monotonously: when <span class="html-italic">T</span> increases and/or <math display="inline"><semantics> <mi>μ</mi> </semantics></math> increases as <math display="inline"><semantics> <msup> <mi>ρ</mi> <mo>★</mo> </msup> </semantics></math> increases.</p>
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<p>Short-term simulation of <span class="html-italic">D. arietina</span> population density (<math display="inline"><semantics> <mrow> <mi>i</mi> <mi>n</mi> <mi>d</mi> <mo>.</mo> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>) at the <math display="inline"><semantics> <mrow> <mn>27</mn> <mspace width="4pt"/> <mi>m</mi> </mrow> </semantics></math> SOLA station location, between 1994 and 2005. (<b>a</b>) Full simulation of the size-structure model where densities on natural log scale are shown as a function of time and size (<span class="html-italic">s</span>). On the right (<b>b</b>) each plot shows observed data (black symbols +, natural log of density, in <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>b</mi> <mspace width="4pt"/> <mi>i</mi> <mi>n</mi> <mi>d</mi> <mo>.</mo> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>; ×, mean individual size, <math display="inline"><semantics> <mrow> <mi>m</mi> <mi>m</mi> </mrow> </semantics></math>) and their corresponding simulations (blue lines). Light gray shaded intervals (91 days each) are the 5 recruitment events observed in the bay.</p>
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<p>Long-term trends simulated using the NAO proxy compared with short-term simulations of observations in Banyuls Bay. Three NAOi extrapolations shown: monthly NAOi integrated over a year (orange lines), NAOi integrated over the first six months of each year (gray, dotted lines), and the NAOi integrated over the 3 months of larval production (April, May, and June; gray solid lines). Upper plots (<b>a</b>,<b>b</b>) show population density variations (natural log of density, in <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>b</mi> <mspace width="4pt"/> <mi>i</mi> <mi>n</mi> <mi>d</mi> <mo>.</mo> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>). Years with maximum estimated population densities for each NAOi extrapolation are shown on (<b>a</b>). Lower plots (<b>c</b>,<b>d</b>) show the variation in mean individual tube lengths (in <math display="inline"><semantics> <mrow> <mi>m</mi> <mi>m</mi> </mrow> </semantics></math>). Plots (<b>a</b>,<b>c</b>) show the complete simulation period of 184 years; gray-shaded areas correspond to the expanded time intervals in plots (<b>b</b>,<b>d</b>) that show simulation trends when observations were made in Banyuls Bay. For comparison, short-term simulations from <a href="#jmse-12-00350-f006" class="html-fig">Figure 6</a>b (thick, pale blue lines) and observations (black + symbols, 1994–2004) are included.</p>
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<p>Metapopulation simulations of the open system and data at the scale of the Gulf of Lions. (<b>a</b>) 21 transects distributed along the coast of the Gulf of Lions were sampled in October 1998 (described in Labrune et al. [<a href="#B12-jmse-12-00350" class="html-bibr">12</a>]). The area treated by the metapopulation model is 3900 <math display="inline"><semantics> <mrow> <mi>k</mi> <msup> <mi>m</mi> <mn>2</mn> </msup> </mrow> </semantics></math>. Filled circles indicate stations where <span class="html-italic">D. arietina</span> individuals were found in samples, unfilled circles indicate no <span class="html-italic">D. arietina</span> individual was found in samples, and + symbols indicate the average geographic positions of the transect. On the right (<b>b</b>) is the steady-state simulations (orange line) and the observations (×) from Labrune et al. [<a href="#B12-jmse-12-00350" class="html-bibr">12</a>] for all transects from 1998. The simulation corresponds to a time sequence determined just after the recruitment event.</p>
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20 pages, 6966 KiB  
Article
Research on the Stability and Bifurcation Characteristics of a Landing Gear Shimming Dynamics System
by Shuang Ruan, Ming Zhang, Shaofei Yang, Xiaohang Hu and Hong Nie
Aerospace 2024, 11(2), 104; https://doi.org/10.3390/aerospace11020104 - 23 Jan 2024
Viewed by 1171
Abstract
A dynamic model is established to investigate the shimmy instability of a landing gear system, considering the influence of nonlinear damping. The stability criterion is utilized to determine the critical speed at which the landing gear system becomes unstable. The central manifold theorem [...] Read more.
A dynamic model is established to investigate the shimmy instability of a landing gear system, considering the influence of nonlinear damping. The stability criterion is utilized to determine the critical speed at which the landing gear system becomes unstable. The central manifold theorem and canonical method are employed to simplify the dynamic model of the landing gear. The first Lyapunov coefficient of the system is theoretically derived and verified using numerical simulation. Further investigation on the Hopf bifurcation characteristics and stability of the shimmy in the landing gear system is conducted. The results indicate that above a certain threshold speed, with a tire stability distance greater than half the tire length in contact with the ground plus the slack length, the aircraft remains stable during taxiing. At critical speeds, a shimmy system with higher-order nonlinear damping will undergo supercritical Hopf bifurcation. Quantitative analysis suggests an increase in the linear damping coefficient within a range that ensures a stability margin to mitigate undesired oscillation, while the nonlinear damping coefficient should be designed within a reasonable range to decrease the amplitude of the limit cycle. Full article
(This article belongs to the Section Aeronautics)
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<p>Schematic diagram of landing gear.</p>
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<p>Tire model.</p>
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<p>Time-domain curve near low-speed critical state.</p>
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<p>Time-domain curve near high-speed critical state.</p>
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<p>The relationship between speed and frequency.</p>
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<p>Stable area map.</p>
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<p>Critical velocity–damping coefficient curve.</p>
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<p>The variation curve of the maximum real part of the system eigenvalue.</p>
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<p>3D time-domain curve.</p>
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<p>Shimmy phase diagram.</p>
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<p>Hopf bifurcation diagram of sliding speed.</p>
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<p>Hopf bifurcation diagram of linear damping coefficient.</p>
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<p>Hopf bifurcation diagram of nonlinear damping coefficient.</p>
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<p>3D Hopf bifurcation diagram.</p>
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26 pages, 14115 KiB  
Article
Research on the Transient Characteristics of a Three-Stream Adaptive Cycle Engine
by Qiuxia Yu, Jun Hu, Weili Wang and Bin Gu
Energies 2023, 16(24), 8076; https://doi.org/10.3390/en16248076 - 15 Dec 2023
Viewed by 954
Abstract
Based on the transient-performance calculation model of a dual-spool mixed-flow turbofan engine, this article improves the dynamic algorithm of geometric adjustment mechanisms and establishes a transient-performance calculation model suitable for a three-stream adaptive cycle engine (three-stream ACE). Using this model, the transient characteristics [...] Read more.
Based on the transient-performance calculation model of a dual-spool mixed-flow turbofan engine, this article improves the dynamic algorithm of geometric adjustment mechanisms and establishes a transient-performance calculation model suitable for a three-stream adaptive cycle engine (three-stream ACE). Using this model, the transient characteristics of a three-stream ACE were analyzed. The results indicate that the delay in the area of the fan nozzle significantly reduces the surge margin of the front fan during deceleration, while the delay in the angle of the front-fan and aft-fan guide vanes significantly reduces the surge margin of the front fan during acceleration, therefore becoming a limitation of the transient performance of the engine. At the same time, to meet the demand for equal-thrust mode switching, this article also proposes a mode-switching control scheme that solves the problem of engine state oscillation during the mode-conversion process and achieves a smooth conversion with thrust fluctuations within 1%. The research results of this article can guide the optimization design of three-stream ACE transition-state control laws and the design of control system architecture, which has important engineering significance. Full article
(This article belongs to the Section I2: Energy and Combustion Science)
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<p>Schematic of the Structure of a Three-Stream Adaptive Cycle Engine.</p>
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<p>Physical Model of Three-Stream Adaptive Cycle Engine (own editing).</p>
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<p>Function Block Diagram of Adjustment Mechanisms Considering Delay.</p>
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<p>Fuel Calculation Logic.</p>
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<p>Relative Primary-Nozzle Throat Area vs. Time (own editing).</p>
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<p>Relative Corrected LP Rotor Speed vs. Relative Corrected HP Rotor Speed (own editing).</p>
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<p>Operating Line of Front Fan (own editing).</p>
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<p>Operating line of aft fan (own editing).</p>
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<p>Relative Thrust of Engine vs. Time (own editing).</p>
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<p>Comparison of Acceleration and Deceleration Times under Delayed Conditions of Geometric Adjustment Mechanisms (own editing).</p>
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<p>Comparison of Front-Fan Operating Line with α1 Delay and A18 Delay (own editing).</p>
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<p>Comparison of Front-Fan Operating Line with α3 Delay (own editing).</p>
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<p>Comparison of Front-Fan Operating Line with α2 Delay and A16 Delay (own editing).</p>
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<p>Comparison of Front-Fan Surge Margin with Geometric Adjustment Mechanism Delay (own editing).</p>
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<p>Comparison of Aft-Fan Operating Line with α1 Delay and A18 Delay (own editing).</p>
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<p>Comparison of Aft-Fan Operating Line with α3 Delay (own editing).</p>
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<p>Comparison of Aft-Fan Operating Line with α2 Delay and A16 Delay (own editing).</p>
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<p>Comparison of Aft-Fan Surge Margin with Geometric Adjustment Mechanism Delay (own editing).</p>
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<p>Comparison of HP Compressor Operating Line with α1 Delay and A18 Delay (own editing).</p>
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<p>Comparison of HP Compressor Operating Line with α3 Delay (own editing).</p>
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<p>Comparison of HP Compressor Operating Line with α2 Delay and A16 Delay (own editing).</p>
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<p>Comparison of HP Compressor Surge Margin with Geometric Adjustment Mechanism Delay (own editing).</p>
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<p>Relative Corrected LP Rotor Speed vs. Relative Thrust (own editing).</p>
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<p>Relative A18 vs. Relative Thrust (own editing).</p>
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<p>Relative Corrected HP Rotor Speed vs. Relative Thrust (own editing).</p>
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<p>Relative A16 vs. Relative Thrust (own editing).</p>
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<p>Rotor Speed Control Logic during Mode Switching (own editing).</p>
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<p>Relative Corrected HP Rotor Speed vs. Time (own editing).</p>
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<p>Relative Corrected LP Rotor Speed vs. Time (own editing).</p>
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<p>α2 vs. Time (own editing).</p>
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<p>Relative A18 vs. Time (own editing).</p>
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<p>Relative A16 vs. Time (own editing).</p>
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<p>Relative Thrust vs. Time (own editing).</p>
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26 pages, 2290 KiB  
Article
Modelling Predator–Prey Interactions: A Trade-Off between Seasonality and Wind Speed
by Dipesh Barman and Ranjit Kumar Upadhyay
Mathematics 2023, 11(23), 4863; https://doi.org/10.3390/math11234863 - 4 Dec 2023
Cited by 3 | Viewed by 1026
Abstract
Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind [...] Read more.
Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind speed along with seasonality on various parameters has been investigated. Here, we present two continuous-time models with specialist and generalist type predators incorporating the effect of wind and the seasonality on the model parameters. It has been observed that wind speed plays a significant role in controlling the system dynamics for both systems. It makes the systems stable for both of the seasonally unperturbed systems. However, it controls the chaotic dynamics that occur in case of no wind for the seasonally perturbed system with the predator as a specialist. On the other hand, for the seasonally perturbed system with a generalist predator, it controls period-four oscillations (which occur considering no wind speed) to simple limit-cycle oscillations. Furthermore, the wind parameter has a huge impact on the survival of predator species. The survival of predator species may be achieved by ensuring a suitable range of wind speeds in the ecosystem. Therefore, we observe that seasonality introduces chaos, but wind reduces it. These results may be very useful for adopting necessary management for the conservation of endangered species that are massively affected by wind speed in an ecosystem. Full article
(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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Figure 1
<p>Phase portrait plot for different levels of wind speed for System (<a href="#FD1-mathematics-11-04863" class="html-disp-formula">1</a>). Subfigure (<b>a</b>) and Subfigure (<b>b</b>), respectively, represent the unstable and stable behaviour of the corresponding system. The parameter values are taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of Hopf bifurcation diagram with respect to wind speed <span class="html-italic">W</span> for Model System (<a href="#FD1-mathematics-11-04863" class="html-disp-formula">1</a>) for <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.5</mn> <mo>]</mo> </mrow> </semantics></math>. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of population biomass with respect to wind speed <span class="html-italic">W</span> for Model System (<a href="#FD1-mathematics-11-04863" class="html-disp-formula">1</a>) for <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>∈</mo> <mo>[</mo> <mn>0.2</mn> <mo>,</mo> <mn>1.5</mn> <mo>]</mo> </mrow> </semantics></math>. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Considering no wind speed, the perturbed System (<a href="#FD5-mathematics-11-04863" class="html-disp-formula">5</a>) exhibits chaotic behaviour: (<b>a</b>) displays the phase plane projection of chaotic attractor, while (<b>b</b>,<b>c</b>) show the corresponding time-series solution of prey and predator species, respectively. The parameter set has been used from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of phase portraits and time evolution for prey species considering wind speed <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math> for the perturbed System (<a href="#FD5-mathematics-11-04863" class="html-disp-formula">5</a>). Here, the chaotic attractor disappears considering wind speed. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Time-series plot for <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> for the perturbed System (<a href="#FD5-mathematics-11-04863" class="html-disp-formula">5</a>). It shows that for a higher level of wind speed, the prey population oscillates in a particular region while the predator population goes very close to zero. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of bifurcation diagram with respect to the wind speed <span class="html-italic">W</span> for System (<a href="#FD5-mathematics-11-04863" class="html-disp-formula">5</a>). It exhibits that the prey population oscillates, while the predator population goes very close to zero with the rise in wind parameter value. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of Lyapunov exponents with respect to the wind speed <span class="html-italic">W</span> for System (<a href="#FD5-mathematics-11-04863" class="html-disp-formula">5</a>). It exhibits that the prey population shows chaotic behaviour while the predator population shows non-chaotic behaviour. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of phase portraits and time evolution for prey species considering no wind speed for System (<a href="#FD3-mathematics-11-04863" class="html-disp-formula">3</a>). The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of phase portraits and time evolution for prey species considering wind speed (<math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>) for System (<a href="#FD3-mathematics-11-04863" class="html-disp-formula">3</a>). The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of Hopf bifurcation diagram with respect to wind speed <span class="html-italic">W</span> for Model System (<a href="#FD3-mathematics-11-04863" class="html-disp-formula">3</a>) for <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.5</mn> <mo>]</mo> </mrow> </semantics></math>. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Plot of population density with respect to wind speed <span class="html-italic">W</span> for Model System (<a href="#FD3-mathematics-11-04863" class="html-disp-formula">3</a>) for <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>∈</mo> <mo>[</mo> <mn>0.35</mn> <mo>,</mo> <mn>20</mn> <mo>]</mo> </mrow> </semantics></math>. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Time-series and phase portrait plot of the perturbed System (<a href="#FD7-mathematics-11-04863" class="html-disp-formula">7</a>) considering no wind, which reveals the system undergoes period-four oscillations. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Time-series and phase portrait plot of the perturbed System (<a href="#FD7-mathematics-11-04863" class="html-disp-formula">7</a>) considering wind, <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, which reveals the system undergoes simple periodic oscillations. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Time-series plot of the perturbed System (<a href="#FD5-mathematics-11-04863" class="html-disp-formula">5</a>) considering different combinations between the wind speed <span class="html-italic">W</span> and strength of seasonality <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math>. The other parameter values have been taken from <a href="#mathematics-11-04863-t003" class="html-table">Table 3</a>.</p>
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<p>Time-series plot of the perturbed System (<a href="#FD25-mathematics-11-04863" class="html-disp-formula">25</a>) considering different values of the wind speed parameter <span class="html-italic">W</span>. The other parameter values have been mentioned in the text.</p>
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<p>Time-series plot of the perturbed System (<a href="#FD27-mathematics-11-04863" class="html-disp-formula">27</a>) considering different values of the wind speed parameter <span class="html-italic">W</span>. The other parameter values have been mentioned in the text.</p>
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