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Search Results (11,627)

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15 pages, 5267 KiB  
Article
Investigating the Energy Dissipation Mechanism of Piano Key Weir: An Integrated Approach Using Physical and Numerical Modeling
by Zixiang Li, Fan Yang, Changhai Han, Ziwu Fan, Kaiwen Yu, Kang Han and Jingxiu Wu
Water 2024, 16(18), 2620; https://doi.org/10.3390/w16182620 (registering DOI) - 15 Sep 2024
Abstract
The enormous energy carried by discharged water poses a serious threat to the Piano Key Weir (PKW) and its downstream hydraulic structures. However, previous research on energy dissipation in PKWs has mainly focused downstream effects, and the research methods have been largely limited [...] Read more.
The enormous energy carried by discharged water poses a serious threat to the Piano Key Weir (PKW) and its downstream hydraulic structures. However, previous research on energy dissipation in PKWs has mainly focused downstream effects, and the research methods have been largely limited to physical model experiments. To deeply investigate the discharge capacity and hydraulic characteristics of PKW, this study established a PKW model with universally applicable geometric parameters. By combining physical model experiments and numerical simulations, the flow pattern of the PKW, the discharge at the overflow edges, and the variation in the energy dissipation were revealed for different water heads. The results showed that the discharge of the side wall constitutes the majority of the total discharge at low water heads, resulting in a relatively high overall discharge efficiency. As the water head increases, the proportion of discharge from the inlet and outlet keys increases, while the proportion from the side wall decreases. This change results in less discharge from the side wall and a consequent reduction in the overall discharge efficiency. The PKW exhibits superior energy dissipation efficiency under low water heads. However, this efficiency exhibits an inverse relationship with an increasing water head. The overall energy dissipation efficiency can reach 40% to 70%. Additionally, the collision of the water flows inside the outlet chamber and the mixing of the overflow jet play a primary role in energy dissipation. The findings of this study have significant implications for hydraulic engineering construction and PKW operational safety. Full article
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Figure 1

Figure 1
<p>Schematics of the PKW and the laboratory equipment.</p>
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<p>The main geometric parameters of the Type A PKW.</p>
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<p>Overview of the simulation region and settings.</p>
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<p>Comparison between the simulated and measured values of the water surface profiles under three water head conditions.</p>
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<p>Experimental flow pattern of the PKW for (<b>a</b>) <span class="html-italic">H</span>/<span class="html-italic">P</span> = 0.09, (<b>b</b>) <span class="html-italic">H</span>/<span class="html-italic">P</span> = 0.20, and (<b>c</b>) <span class="html-italic">H</span>/<span class="html-italic">P</span> = 0.34.</p>
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<p>(<b>a</b>) Discharge proportion and (<b>b</b>) discharge efficiency of the three overflow edges.</p>
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<p>Relationship between (<b>a</b>) the energy and (<b>b</b>) the energy dissipation rate with the water head.</p>
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<p>Energy variation curves along the route.</p>
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<p>The vector in front of (<b>a</b>) the inlet key and (<b>b</b>) the outlet key of the PKW.</p>
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<p>Water overflows through the side wall for (<b>a</b>) the low water head and (<b>b</b>) the high water head.</p>
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<p>The turbulence dissipation (<b>a</b>) at the top of the PKW and (<b>b</b>) at the bottom of the PKW.</p>
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16 pages, 10922 KiB  
Article
Pressure Fluctuation Characteristics of a Pump-Turbine in the Hump Area under Different Flow Conditions
by Kai Zheng, Liu Chen, Shaocheng Ren, Wei Xiao, Yexiang Xiao, Anant Kumar Rai, Guangtai Shi and Zhengkai Hao
J. Mar. Sci. Eng. 2024, 12(9), 1654; https://doi.org/10.3390/jmse12091654 (registering DOI) - 14 Sep 2024
Viewed by 319
Abstract
During the operation of a reversible pump-turbine, a hump area can easily appear under the pump condition, which will greatly affect the performance of a storage unit, with pressure pulsation being the key factor for the stable operation of a pump-turbine. Therefore, in [...] Read more.
During the operation of a reversible pump-turbine, a hump area can easily appear under the pump condition, which will greatly affect the performance of a storage unit, with pressure pulsation being the key factor for the stable operation of a pump-turbine. Therefore, in order to explore the pressure pulsation characteristics of each flow component in the hump area, this paper first compared the full characteristics of the model test under different working conditions, and then it analyzed the pressure pulsation characteristics. By analyzing the pressure pulsation characteristics in the unit’s flow component under different flow rates in the hump area, the pulsation rule of a pump-turbine running in the hump area was revealed. It was found that the peak-to-peak value of the draft tube in the hump area was the smallest under the optimal flow condition, and the peak-to-peak value increased along the flow direction, with the rotor and stator interaction (RSI) effects being continuously enhanced. When away from the runner basin, the influence of RSI gradually weakened after leaving the runner. No low frequency was found in the optimal traffic. The peak-to-peak value of the low flow condition increased compared with the optimal flow condition, and the distribution was not uniform. The main frequency of the whole basin was relatively complex, indicating that the flow of water was unstable in the condition of partial load, resulting in the hump area during the unit operation. The research results can provide a theoretical reference for improving the stability of pump-turbines. Full article
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Figure 1

Figure 1
<p>Pump-turbine model diagram.</p>
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<p>Meshing.</p>
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<p>Y+ value distribution in the runner.</p>
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<p>Grid independence verification.</p>
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<p>Arrangement of the dynamic pressure recording points in the runner.</p>
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<p>Arrangement of the static pressure recording points in the whole flow channel.</p>
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<p>Full characteristic simulation—test results.</p>
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<p>The predicted and experimental <span class="html-italic">Q</span>-<span class="html-italic">H</span> and <span class="html-italic">Q</span>-<span class="html-italic">η</span> curves.</p>
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<p>Peak-to-peak value of dynamic point pulsation in each channel of the runner under Optimal Flow Conditions.</p>
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<p>Frequency domain diagram of the pressure fluctuation for the runner channel 1 points.</p>
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<p>Frequency domain diagram of pressure fluctuation at static recording points.</p>
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<p>Peak-to-peak pulsation values of the eight recording points in the whole flow channel.</p>
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<p>The pressure pulsation frequency domain diagram of the eight recording points and the propagation of the related frequencies in the flow channel.</p>
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<p>Flow characteristics of the flow components.</p>
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<p>Peak-to-peak value of dynamic point pulsation in each channel of the runner under Partial Load Conditions.</p>
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<p>Frequency spectrum analysis of rotating points in runner channel 1 and runner channel 5.</p>
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<p>Peak-to-peak values of the eight recording points.</p>
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<p>Flow situation of each component.</p>
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<p>The pressure fluctuation frequency domain diagram of eight recording points and the propagation of related frequencies in the flow channel.</p>
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22 pages, 3621 KiB  
Article
Estimating Non-Stationary Extreme-Value Probability Distribution Shifts and Their Parameters Under Climate Change Using L-Moments and L-Moment Ratio Diagrams: A Case Study of Hydrologic Drought in the Goat River Near Creston, British Columbia
by Isaac Dekker, Kristian L. Dubrawski, Pearce Jones and Ryan MacDonald
Hydrology 2024, 11(9), 154; https://doi.org/10.3390/hydrology11090154 (registering DOI) - 14 Sep 2024
Viewed by 168
Abstract
Here, we investigate the use of rolling-windowed L-moments (RWLMs) and L-moment ratio diagrams (LMRDs) combined with a Multiple Linear Regression (MLR) machine learning algorithm to model non-stationary low-flow hydrological extremes with the potential to simultaneously understand time-variant shape, scale, location, and probability distribution [...] Read more.
Here, we investigate the use of rolling-windowed L-moments (RWLMs) and L-moment ratio diagrams (LMRDs) combined with a Multiple Linear Regression (MLR) machine learning algorithm to model non-stationary low-flow hydrological extremes with the potential to simultaneously understand time-variant shape, scale, location, and probability distribution (PD) shifts under climate change. By employing LMRDs, we analyse changes in PDs and their parameters over time, identifying key environmental predictors such as lagged precipitation for September 5-day low-flows. Our findings indicate a significant relationship between total August precipitation L-moment ratios (LMRs) and September 5-day low-flow LMRs (τ2-Precipitation and τ2-Discharge: R2 = 0.675, p-values < 0.001; τ3-Precipitation and τ3-Discharge: R2 = 0.925, p-value for slope < 0.001, intercept not significant with p = 0.451, assuming α = 0.05 and a 31-year RWLM), which we later refine and use for prediction within our MLR algorithm. The methodology, applied to the Goat River near Creston, British Columbia, aids in understanding the implications of climate change on water resources, particularly for the yaqan nuʔkiy First Nation. We find that future low-flows under climate change will be outside the Natural Range of Variability (NROV) simulated from historical records (assuming a constant PD). This study provides insights that may help in adaptive water management strategies necessary to help preserve Indigenous cultural rights and practices and to help sustain fish and fish habitat into the future. Full article
(This article belongs to the Section Hydrological and Hydrodynamic Processes and Modelling)
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Figure 1

Figure 1
<p>L-moment ratio diagrams (LMRDs) for: (<b>a</b>) August total precipitation (mm) and (<b>b</b>) September 5-day low-flow (<math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">m</mi> <mn>3</mn> </msup> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>). Each panel includes the L-Coefficient of Variation (L-CV;<math display="inline"><semantics> <msub> <mi>τ</mi> <mn>2</mn> </msub> </semantics></math>) versus L-skewness (<math display="inline"><semantics> <msub> <mi>τ</mi> <mn>3</mn> </msub> </semantics></math>) and L-kurtosis versus L-skewness ratios.</p>
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<p>Relationship between L-moment ratios (LMRs) of August total precipitation (mm) and September 5-day low-flow (<math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">m</mi> <mn>3</mn> </msup> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>): (<b>a</b>) <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>2</mn> </msub> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>3</mn> </msub> </semantics></math>. <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>2</mn> </msub> </semantics></math>-Precipitation and <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>2</mn> </msub> </semantics></math>-Discharge: <span class="html-italic">p</span>-values &lt; 0.001; <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>3</mn> </msub> </semantics></math>-Precipitation and <math display="inline"><semantics> <msub> <mi>τ</mi> <mn>3</mn> </msub> </semantics></math>-Discharge: <span class="html-italic">p</span>-value for slope &lt; 0.001, intercept not significant with <span class="html-italic">p</span> = 0.451, assuming <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 0.05 and a 31-year rolling-windowed L-moments (RDLMs).</p>
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<p>Comparison of predicted and observed L-moments (LMs; testing during training) using a 31-year rolling-window. The plots display the predicted (green) and observed (blue) values for the first (<b>a</b>), second (<b>b</b>), third (<b>c</b>), and fourth (<b>d</b>) LMs. Each subplot includes the Overall Mean Squared Error (MSE) between the predicted and observed values computed by summing and averaging the best-fit model Squared Error (SE) for each step in the forward chaining process. The equations plotted alongside the model are derived from the final (best-fit) iteration (index 38), which demonstrated the lowest SE.</p>
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<p>Location, scale, and shape parameters estimated using [<a href="#B45-hydrology-11-00154" class="html-bibr">45</a>]’s method of L-moments (LMs) for the Generalized Extreme Value (GEV) probability distribution (PD) for the observed (blue) and predicted (testing during training; dashed red) LMs under a 31-year rolling-window.</p>
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<p>LMRDs using 31-year windows under two Representative Concentration Pathways (RCP) scenarios. Panels (<b>a</b>–<b>c</b>) correspond to the RCP 4.5 scenario, while panels (<b>d</b>–<b>f</b>) correspond to the RCP 8.5 scenario. Diagrams show: (<b>a</b>,<b>d</b>) L-CV/L-skewness, (<b>b</b>,<b>e</b>) L-kurtosis/L-skewness, with theoretical PDs described in [<a href="#B45-hydrology-11-00154" class="html-bibr">45</a>] (distributions include Generalized Logistic (GLO), Generalized Extreme Value (GEV), Generalized Pareto (GPA), Generalized Normal (GNO), Pearson Type III (PE3), Wakeby Lower Bound (WAK_LB), and All Distribution Lower Bound (ALL_LB)). Plots (<b>c</b>,<b>f</b>) show the distribution count for each window. The observed LMRs for the 5-day September low-flow at the Water Survey of Canada (WSC) Goat River Near Erikson Hydrometric Gauge Station (<a href="https://wateroffice.ec.gc.ca/report/data_availability_e.html?type=historical&amp;station=08NH004&amp;parameter_type=Flow&amp;wbdisable=true" target="_blank">08NH004</a>) are plotted alongside simulated future data derived from Multiple Linear Regression (MLR) driven with total August precipitation LMs. Future data are generated using a splice of six Coupled Model Intercomparison Project Phase 5 (CMIP5) series downscaled climate models (median of “ACCESS1-0”, “CanESM2”, “CCSM4”, “CNRM-CM5”, “HadGEM2-ES”, and “MPI-ESM-LR” from 2018 to 2100) downloaded using the single cell extraction tool from the Pacific Climate Impacts Consortium (<a href="https://pacificclimate.org/data/gridded-hydrologic-model-output" target="_blank">PCIC</a>). Historical climate data are downloaded from Historical Climate Data Online (HCDO) repository for the Creston station (Climate ID <a href="https://climate.weather.gc.ca/climate_data/daily_data_e.html?hlyRange=%7C&amp;dlyRange=1912-06-01%7C2017-12-31&amp;mlyRange=1912-01-01%7C2007-02-01&amp;StationID=1111&amp;Prov=BC&amp;urlExtension=_e.html&amp;searchType=stnName&amp;optLimit=yearRange&amp;StartYear=1840&amp;EndYear=2024&amp;selRowPerPage=25&amp;Line=0&amp;searchMethod=contains&amp;Month=12&amp;Day=2&amp;txtStationName=Creston&amp;timeframe=2&amp;Year=2017" target="_blank">1142160</a>; available from 1996 to 2017).</p>
Full article ">Figure 6
<p>Results of the L-moments (LMs) derived from Multiple Linear Regression (MLR) fit to a Generalized Extreme Value (GEV) probability distribution (PD) to produce shape, scale, and location parameters: (<b>a</b>) GEV parameters (shape, scale, and location) over 144 rolling windowed time units under Representative Concentration Pathway (RCP) 4.5 and (<b>b</b>) RCP 8.5.</p>
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<p>LMs derived from MLR fit to a GEV PD to produce shape, scale, and location parameters to derive median flows (<math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">m</mi> <mn>3</mn> </msup> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>) and confidence intervals (CIs) estimated from percentiles: (<b>a</b>) simulated September 5-day low-flows driven by MLR regression using August total precipitation LMs over a 31-year rolling time window under (<b>a</b>) RCP 4.5 and (<b>b</b>) RCP 8.5. The dashed red line denotes a flow of &lt;1 m<sup>3</sup>/s. Note: each simulation is based on <span class="html-italic">n</span> = 1000 iterations for both panels.</p>
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<p>Results of the LMs derived from MLR fit to the best-fit probability distribution (PD) (distributions described in [<a href="#B45-hydrology-11-00154" class="html-bibr">45</a>]) to produce shape, scale, and location parameters to derive median flows (<math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">m</mi> <mn>3</mn> </msup> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>) and confidence intervals (CIs) estimated numerically from percentiles: (<b>a</b>) simulated September 5-day low-flows driven by MLR regression using August total precipitation LMs over a 31-year moving window under RCP 4.5 and (<b>b</b>) RCP 8.5. The dashed red line denotes a flow of &lt;1 m<sup>3</sup>/s. Note: each simulation is based on <span class="html-italic">n</span> = 1000 iterations for both panels.</p>
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<p>Overall standardized Mean Square Error (MSE) across different window sizes during model training.</p>
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<p>Sensitivity of window size on location, scale, and shape parameters for September 5-day low-flow estimated using the method of LMs described in [<a href="#B45-hydrology-11-00154" class="html-bibr">45</a>] derived from MLR driven by total August precipitation LMs for six common distributions described in [<a href="#B45-hydrology-11-00154" class="html-bibr">45</a>] (Generalized Extreme Value (GEV; (<b>a</b>–<b>c</b>)), Generalized Logistic (GLO; (<b>d</b>–<b>f</b>)), Generalized Normal (GNO; (<b>g</b>–<b>i</b>)), Pearson Type III (PE3; (<b>j</b>–<b>l</b>)), and Generalized Pareto (GPA; (<b>m</b>–<b>o</b>)). The solid line displays data under the Representative Concentration Pathway (RCP) 4.5 emission scenario, while the dashed line displays the RCP 8.5 emissions scenario.</p>
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<p>Low-flow exceedance and cumulative exceedance probability for the Goat River near Erikson Gauge Station, showing values less than 2.7 cubic meters per second (<math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">m</mi> <mn>3</mn> </msup> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>) assuming <span class="html-italic">n</span> = 1000 simulations and a Generalized Extreme Value (GEV) probability distribution (PD). Future data assume a Representative Concentration Pathway (RCP) 4.5 emissions scenario.</p>
Full article ">
32 pages, 18298 KiB  
Article
CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures
by Robert Bayer, Petr Bača, Jiří Maxa, Pavla Šabacká, Tomáš Binar and Petr Vyroubal
Sensors 2024, 24(18), 5968; https://doi.org/10.3390/s24185968 (registering DOI) - 14 Sep 2024
Viewed by 192
Abstract
This paper deals with CFD analyses of the difference in the nature of the shock waves in supersonic flow under atmospheric pressure and pressure conditions at the boundary of continuum mechanics for electron microscopy. The first part describes the verification of the CFD [...] Read more.
This paper deals with CFD analyses of the difference in the nature of the shock waves in supersonic flow under atmospheric pressure and pressure conditions at the boundary of continuum mechanics for electron microscopy. The first part describes the verification of the CFD analyses in combination with the experimental chamber results and the initial analyses using optical methods at low pressures on the boundary of continuum mechanics that were performed. The second part describes the analyses on an underexpanded nozzle performed to analyze the characteristics of normal shock waves in a pressure range from atmospheric pressure to pressures at the boundary of continuum mechanics. The results obtained by CFD modeling are prepared as a basis for the design of the planned experimental sensing of density gradients using optical methods, and for validation, the expected pressure and temperature courses from selected locations suitable for the placement of temperature and pressure sensors are prepared from the CFD analyses. Full article
(This article belongs to the Section Physical Sensors)
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Figure 1

Figure 1
<p>Real experimental chamber (<b>a</b>), simplified 2D axisymmetric model of the experimental chamber (<b>b</b>), scheme of the ESEM (<b>c</b>), and scheme of the experimental chamber (<b>d</b>).</p>
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<p>Structured mesh for the CFD analysis (<b>a</b>), with the zoomed area showing the mesh refinement (<b>b</b>).</p>
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<p>Changes in the state variables across a normal shock wave.</p>
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<p>Used optical system.</p>
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<p>Two-dimensional axisymmetric model of the chambers for the CFD analysis, with labeled boundary conditions (<b>a</b>) and with the zoomed area showing its dimensions (mm) (<b>b</b>).</p>
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<p>Points of the pressure measurements on the nozzle wall in the experimental chamber.</p>
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<p>Mach number distribution.</p>
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<p>Static pressure distribution.</p>
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<p>Path along which selected state variables are plotted (blue line).</p>
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<p>Static pressure and Mach number layout on the path.</p>
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<p>Static temperature (<b>a</b>) and velocity (<b>b</b>) distribution on the path.</p>
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<p>Static temperature and density layout on the path.</p>
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<p>First velocity derivative imaging.</p>
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<p>Graphical density gradient distribution (<b>a</b>) and density gradient layout on the path (<b>b</b>).</p>
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<p>Locations for the <span class="html-italic">y+</span> verification.</p>
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<p>Points for the Reynolds number verification.</p>
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<p>Design of the shortened nozzle with its dimensions (mm) (<b>a</b>) with an emphasized nozzle outlet diameter (line) with the point for the values from the CFD simulations (<b>b</b>).</p>
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<p>Mach number layout of the shortened nozzle for each variant on the path (axis).</p>
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<p>Two-dimensional axisymmetric model of the underexpanded nozzle of the chambers for the CFD analysis with labeled boundary conditions (<b>a</b>) and with the zoomed area showing its dimensions (mm) (<b>b</b>).</p>
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<p>Mach number layout of each variant on the path (axis).</p>
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<p>Axis of the flow (blue line—path).</p>
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<p>Mach number layout of each variant on the path (axis) with the adjusted scale.</p>
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<p>Mach number layout of each variant on the path (axis) with another adjusted scale.</p>
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<p>Pressure layout of each variant on the path (axis).</p>
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<p>Pressure layout of each variant on the path (axis) with the adjusted scale.</p>
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<p>Pressure layout of each variant on the path (axis) with another adjusted scale.</p>
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<p>Pressure layout of each variant on the path (axis) with different adjusted scale.</p>
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<p>Density gradient layout of each variant on the path (axis).</p>
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<p>Examined nozzle surface (red line—nozzle wall).</p>
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<p>Pressure layout of each variant on the nozzle wall.</p>
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<p>Temperature layout of each variant on the nozzle wall.</p>
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<p>Points for the Reynolds number verification.</p>
Full article ">Figure A1
<p>Mach number distribution of each variant: 101,325 Pa (<b>a</b>), 50,000 Pa (<b>b</b>), 10,000 Pa (<b>c</b>), 5000 Pa (<b>d</b>), and 2000 Pa (<b>e</b>).</p>
Full article ">Figure A2
<p>Pressure distribution of each variant: 101,325 Pa (<b>a</b>), 50,000 Pa (<b>b</b>), 10,000 Pa (<b>c</b>), 5000 Pa (<b>d</b>), and 2000 Pa (<b>e</b>).</p>
Full article ">Figure A3
<p>Density gradient distribution of each variant: 101,325 Pa (<b>a</b>), 50,000 Pa (<b>b</b>), 10,000 Pa (<b>c</b>), 5000 Pa (<b>d</b>), and 2000 Pa (<b>e</b>).</p>
Full article ">
20 pages, 8018 KiB  
Article
Biomimetic Wings for Micro Air Vehicles
by Giorgio Moscato and Giovanni P. Romano
Biomimetics 2024, 9(9), 553; https://doi.org/10.3390/biomimetics9090553 (registering DOI) - 14 Sep 2024
Viewed by 139
Abstract
In this work, micro air vehicles (MAVs) equipped with bio-inspired wings are investigated experimentally in wind tunnel. The starting point is that insects such as dragonflies, butterflies and locusts have wings with rigid tubular elements (corrugation) connected by flexible parts (profiling). So far, [...] Read more.
In this work, micro air vehicles (MAVs) equipped with bio-inspired wings are investigated experimentally in wind tunnel. The starting point is that insects such as dragonflies, butterflies and locusts have wings with rigid tubular elements (corrugation) connected by flexible parts (profiling). So far, it is important to understand the specific aerodynamic effects of corrugation and profiling as applied to conventional wings for the optimization of low-Reynolds-number aerodynamics. The present study, in comparison to previous investigations on the topic, considers whole MAVs rather than isolated wings. A planform with a low aperture-to-chord ratio is employed in order to investigate the interaction between large tip vortices and the flow over the wing surface at large angles of incidence. Comparisons are made by measuring global aerodynamic loads using force balance, specifically drag and lift, and detailed local velocity fields over wing surfaces, by means of particle image velocimetry (PIV). This type of combined global–local investigation allows describing and relating overall MAV performance to detailed high-resolution flow fields. The results indicate that the combination of wing corrugation and profiling gives effective enhancements in performance, around 50%, in comparison to the classical flat-plate configuration. These results are particularly relevant in the framework of low-aspect-ratio MAVs, undergoing beneficial interactions between tip vortices and large-scale separation. Full article
(This article belongs to the Special Issue Biomechanics and Biomimetics for Insect-Inspired MAVs)
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Figure 1
<p>Details of MAV geometry and of six tested wing configurations.</p>
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<p>PIV set-up with laser arm, camera and MAV model in wind tunnel (<b>top</b>). Example of PIV-acquired images at full scale (large field of view) and reduced scale (small field of view, in red) with reference system (<b>bottom</b>).</p>
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<p>Lift and drag coefficients as functions of angle of attack for flat-plate MAV geometry. Present data are plotted for two Reynolds numbers and compared to data in [<a href="#B4-biomimetics-09-00553" class="html-bibr">4</a>,<a href="#B11-biomimetics-09-00553" class="html-bibr">11</a>].</p>
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<p>Lift and drag coefficients as functions of angle of attack for the corrugated and profiled MAV wing geometry. Present data are plotted for two Reynolds numbers and compared to data in [<a href="#B4-biomimetics-09-00553" class="html-bibr">4</a>,<a href="#B11-biomimetics-09-00553" class="html-bibr">11</a>].</p>
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<p>Lift and drag coefficients as functions of angle of attack for all tested MAV wing geometries for present large Reynolds number measurements.</p>
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<p>Lift-to-drag ratio and polar curve for all tested MAV wing geometries.</p>
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<p>The average absolute value of velocity and streamlines at an angle of attack of 15° for MAVs with the following wing configurations: flat (<b>a</b>), corrugated (<b>b</b>) and profiled (<b>c</b>). Large field of view. In the insets, detailed small-field-of-view plots are reported. Dashed lines indicate positions for velocity profiles.</p>
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<p>Average absolute value of velocity and streamlines at angle of attack of 30° for flat (<b>a</b>), corrugated (<b>b</b>) and profiled (<b>c</b>) MAV wing configurations. Large field of view. In the insets, detailed small-field-of-view plots are reported. Dashed lines indicate positions for velocity profiles.</p>
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<p>Average absolute value of velocity and streamlines at angle of attack of 36° for flat (<b>a</b>), corrugated (<b>b</b>) and profiled (<b>c</b>) MAV wing configurations. Large field of view. Dashed lines indicate positions for velocity profiles.</p>
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<p>Average (on the left) and instantaneous (on the right) vorticity for an angle of attack equal to 15°: flat-plate (row <b>a</b>), corrugated (row <b>b</b>) and profiled (row <b>c</b>) MAV configurations from top to bottom. Large field of view.</p>
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<p>Average (on the left) and instantaneous (on the right) vorticity for an angle of attack equal to 30°: flat-plate (row <b>a</b>), corrugated (row <b>b</b>) and profiled (row <b>c</b>) MAV configurations from top to bottom. Large field of view.</p>
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<p>Average <span class="html-italic">rms</span> of streamwise velocity component for angle of attack equal to 15°: flat-plate (<b>a</b>), corrugated (<b>b</b>) and profiled (<b>c</b>) MAV configurations. Large field of view. In insets, detailed small-field-of-view plots are reported. Dashed lines indicate positions for <span class="html-italic">rms</span> profiles.</p>
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<p>Average <span class="html-italic">rms</span> of streamwise velocity component for angle of attack equal to 30°: flat-plate (<b>a</b>), corrugated (<b>b</b>) and profiled (<b>c</b>) MAV configurations. Large field of view. In insets, detailed small-field-of-view plots are reported. Dashed lines indicate positions for <span class="html-italic">rms</span> profiles.</p>
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<p>Average <span class="html-italic">rms</span> of streamwise velocity component for angle of attack equal to 36°: flat-plate (<b>a</b>), corrugated (<b>b</b>) and profiled (<b>c</b>) MAV configurations. Large field of view. Dashed lines indicate positions for <span class="html-italic">rms</span> profiles.</p>
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<p>Vertical profiles of normalized streamwise velocity component at x/c = 0.3, for the three tested MAV configurations. Angles of incidence equal to 15° (<b>a</b>), 30° (<b>b</b>) and 36° (<b>c</b>).</p>
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<p>Vertical profiles of normalized streamwise velocity component at x/c = 0.6, for the three tested MAV configurations. Angles of incidence equal to 15° (<b>a</b>), 30° (<b>b</b>) and 36° (<b>c</b>).</p>
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<p>Vertical profiles of normalized <span class="html-italic">rms</span> streamwise component at x/c = 0.3, for the three tested MAV configurations. Angles of incidence equal to 15° (<b>a</b>), 30° (<b>b</b>) and 36° (<b>c</b>).</p>
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<p>Vertical profiles of normalized <span class="html-italic">rms</span> streamwise component at x/c = 0.6 for the three tested MAV configurations. Angles of incidence equal to 15° (<b>a</b>), 30° (<b>b</b>) and 36° (<b>c</b>).</p>
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15 pages, 7305 KiB  
Article
Contact Hole Shrinkage: Simulation Study of Resist Flow Process and Its Application to Block Copolymers
by Sang-Kon Kim
Micromachines 2024, 15(9), 1151; https://doi.org/10.3390/mi15091151 (registering DOI) - 13 Sep 2024
Viewed by 381
Abstract
For vertical interconnect access (VIA) in three-dimensional (3D) structure chips, including those with high bandwidth memory (HBM), shrinking contact holes (C/Hs) using the resist flow process (RFP) represents the most promising technology for low- [...] Read more.
For vertical interconnect access (VIA) in three-dimensional (3D) structure chips, including those with high bandwidth memory (HBM), shrinking contact holes (C/Hs) using the resist flow process (RFP) represents the most promising technology for low-k1 (where CD=k1λ/NA,CD is the critical dimension, λ is wavelength, and NA is the numerical aperture). This method offers a way to reduce dimensions without additional complex process steps and is independent of optical technologies. However, most empirical models are heuristic methods and use linear regression to predict the critical dimension of the reflowed structure but do not account for intermediate shapes. In this research, the resist flow process (RFP) was modeled using the evolution method, the finite-element method, machine learning, and deep learning under various reflow conditions to imitate experimental results. Deep learning and machine learning have proven to be useful for physical optimization problems without analytical solutions, particularly for regression and classification tasks. In this application, the self-assembly of cylinder-forming block copolymers (BCPs), confined in prepatterns of the resist reflow process (RFP) to produce small contact hole (C/H) dimensions, was described using the self-consistent field theory (SCFT). This research paves the way for the shrink modeling of the enhanced resist reflow process (RFP) for random contact holes (C/Hs) and the production of smaller contact holes. Full article
(This article belongs to the Special Issue Recent Advances in Micro/Nano-Fabrication)
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<p>Schematic representation of the resist flow process (RFP): (<b>a</b>) spin coating; (<b>b</b>) contact hole (C/H) patterns after development process; and (<b>c</b>) contact hole (C/H) patterns after thermal reflow. The structure consists of a silicon substrate and resist.</p>
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<p>(<b>a</b>) Scanning electron microscope (SEM) images of contact holes (C/Hs) and (<b>b</b>) a graph of critical dimension (CD) with a function of temperature and duty ratio after the thermal resist process. The upper labels of the images in <a href="#micromachines-15-01151-f002" class="html-fig">Figure 2</a>a represent the aspect ratio, which is the ratio between the contact hole size and the pitch size.</p>
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<p>Simulation results of Surface Evolver: (<b>a</b>) surface energy and surface area for one contact hole pattern and nine contact holes in terms of simulation times, one contact hole and nine contact holes (<b>b</b>,<b>e</b>) before the resist flow process (RFP), at surface areas of (<b>c</b>) 38.3685, (<b>d</b>) 32.9430, (<b>f</b>) 155.0468, and (<b>g</b>) 144.5697 after the resist flow process (RFP), respectively.</p>
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<p>Heat transfer analysis generated through MATLAB: (<b>a</b>) a block with the finite element mash displayed, (<b>b</b>) a temperature contour with constant thermal conductivity, and (<b>c</b>) a plot of simulated bake cycle profiles with constant thermal conductivity (or constant) and temperature-dependent thermal conductivity (or variable), respectively. Transfer time is 1 s.</p>
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<p>Static structural deformation of one contact hole (C/H) due to heat transfer, generated through ANSYS: (<b>a</b>) the structure of a <math display="inline"><semantics> <mrow> <mn>5</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>5</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>0.8</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo> </mo> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> </mrow> </semantics></math>, a <math display="inline"><semantics> <mrow> <mn>5</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>5</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>5.6</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> upper plate, and an emptied cylinder with a height of <math display="inline"><semantics> <mrow> <mn>5</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and a radius of <math display="inline"><semantics> <mrow> <mn>1.05</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, and plots of (<b>b</b>) mashing and deformation at (<b>c</b>) 0.5 s and (<b>d</b>) 1 s simulation times.</p>
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<p>Phase change of a contact hole (C/H) sidewall due to gravity from solid to liquid during thermal reflow, generated using the ANSYS Fluent (Student Edition 2024): melting boundaries at (<b>a</b>) 0 steps, (<b>b</b>) 1 step, (<b>c</b>) 30 steps, (<b>d</b>) 50 steps, (<b>e</b>) 100 steps, and (<b>f</b>) 150 steps.</p>
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<p>Experimental and simulation results for thermal reflow biases depending on temperatures and duty ratios in a 193-nm argon fluoride (ArF) chemically amplified resist (CAR): the results of (<b>a</b>) an orthogonal fitting function, linear regressions from (<b>b</b>) a Python program and (<b>c</b>) Scikit-Learn, and (<b>d</b>) a convolutional neural network (CNN). “Exp” and “Fit” represent the experimental results and simulation results, respectively.</p>
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<p>Classifications from a logistic regression in deep learning and a decision tree in machine learning: (<b>a</b>,<b>b</b>) are binary and multiple classifications from TensorFlow, respectively, (<b>c</b>,<b>d</b>) are the decision surfaces of a decision tree for the binary class with the max depth of two and the multiple class with a max depth of three, respectively, and (<b>e</b>) a decision tree for multiple classes with a max depth of four.</p>
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<p>Multi-class classification using a support vector machine (SVM): (<b>a</b>) support vector classification (SVC) with a linear kernel, (<b>b</b>) LinearSVC (linear kernel), (<b>c</b>) support vector classification (SVC) with a radial basis function (RBF) kernel, and (<b>d</b>) support vector classification (SVC) with a polynomial (degree 3) kernel.</p>
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<p>Classification of resist flow process (RFP) side images using a convolutional neural network (CNN). For the upper labels of the images, the first number represents the pattern type from experimental results, and the second number represents the predicted pattern type from a convolutional neural network (CNN).</p>
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<p>Schematic representation of the self-assembly of cylinder-forming block copolymers (BCPs) confined in cylindrical prepatterns: (<b>a</b>) contact hole (C/H) shrinkage patterns after thermal reflow (baking), (<b>b</b>) spin coating for PS-b-PMMA block copolymers (BCPs), (<b>c</b>) thermal annealing, and (<b>d</b>) wet development.</p>
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<p>Comparison of the simulation results (Sim.) using rectangular guiding patterns <math display="inline"><semantics> <mrow> <mo mathvariant="normal">(</mo> <msub> <mrow> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">D</mi> </mrow> <mrow> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> </mrow> </msub> <mo mathvariant="normal">)</mo> </mrow> </semantics></math> to the experimental results (Exp.) using cylindrical guiding patterns <math display="inline"><semantics> <mrow> <mo mathvariant="normal">(</mo> <msub> <mrow> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">D</mi> </mrow> <mrow> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">g</mi> </mrow> </msub> <mo mathvariant="normal">)</mo> </mrow> </semantics></math> from Reference [<a href="#B49-micromachines-15-01151" class="html-bibr">49</a>] for the resulting morphologies obtained after the directed self-assembly (DSA) of cylindrical PS-b-PMMA block copolymers (BCPs). <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> is a natural period of the block copolymer (BCP), which is directly correlated to the molecular weight of the block copolymer (BCP).</p>
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15 pages, 3878 KiB  
Article
Characteristics of Bacterial Community Structure and Function in Artificial Soil Prepared Using Red Mud and Phosphogypsum
by Yong Liu, Zhi Yang, Lishuai Zhang, Hefeng Wan, Fang Deng, Zhiqiang Zhao and Jingfu Wang
Microorganisms 2024, 12(9), 1886; https://doi.org/10.3390/microorganisms12091886 - 13 Sep 2024
Viewed by 214
Abstract
The preparation of artificial soil is a potential cooperative resource utilization scheme for red mud and phosphogypsum on a large scale, with a low cost and simple operation. The characteristics of the bacterial community structure and function in three artificial soils were systematically [...] Read more.
The preparation of artificial soil is a potential cooperative resource utilization scheme for red mud and phosphogypsum on a large scale, with a low cost and simple operation. The characteristics of the bacterial community structure and function in three artificial soils were systematically studied for the first time. Relatively rich bacterial communities were formed in the artificial soils, with relatively high abundances of bacterial phyla (e.g., Cyanobacteria, Proteobacteria, Actinobacteriota, and Chloroflexi) and bacterial genera (e.g., Microcoleus_PCC-7113, Rheinheimera, and Egicoccus), which can play key roles in various nutrient transformations, resistance to saline–alkali stress and pollutant toxicity, the enhancement of various soil enzyme activities, and the ecosystem construction of artificial soil. There were diverse bacterial functions (e.g., photoautotrophy, chemoheterotrophy, aromatic compound degradation, fermentation, nitrate reduction, cellulolysis, nitrogen fixation, etc.), indicating the possibility of various bacteria-dominated biochemical reactions in the artificial soil, which can significantly enrich the nutrient cycling and energy flow and enhance the fertility of the artificial soil and the activity of the soil life. The bacterial communities in the different artificial soils were generally correlated with major physicochemical factors (e.g., pH, OM, TN, AN, and AP), as well as enzyme activity factors (e.g., S-UE, S-SC, S-AKP, S-CAT, and S-AP), which comprehensively illustrates the complexity of the interaction between bacterial communities and environmental factors in artificial soils, and which may affect the succession direction of bacterial communities, the quality of the artificial soil environment, and the speed and direction of the development and maturity of the artificial soil. This study provides an important scientific basis for the synergistic soilization of two typical industrial solid wastes, red mud and phosphogypsum, specifically for the microbial mechanism, for the further evolution and development of artificial soil prepared using red mud and phosphogypsum. Full article
(This article belongs to the Special Issue Application of Microbes in Environmental Remediation)
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<p>Venn analysis of bacterial communities (OTUs (<b>a</b>), phyla (<b>b</b>), and genera (<b>c</b>)) in artificial soils.</p>
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<p>Composition of bacterial communities (at phylum level (<b>a</b>) and genus level (<b>b</b>)) in artificial soils.</p>
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<p>PCoA of beta diversity of bacterial communities (at phylum level (<b>a</b>) and genus level (<b>b</b>)) in artificial soils.</p>
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<p>Kruskal–Wallis H test analysis of bacterial communities (phyla (<b>a</b>) and genera (<b>b</b>)) in artificial soils.</p>
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<p>RDA/CCA of bacterial communities (at phylum level (<b>a</b>,<b>b</b>) and genus level (<b>c</b>,<b>d</b>)) in artificial soils.</p>
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<p>Spearman correlation heatmap analysis of bacterial communities (phyla (<b>a</b>) and genera (<b>b</b>)) in artificial soils. Note: * 0.01 &lt; <span class="html-italic">p</span> ≤ 0.05; ** 0.001&lt; <span class="html-italic">p</span> ≤ 0.01; *** <span class="html-italic">p</span> ≤ 0.001.</p>
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<p>FAPROTAX functional prediction analysis of bacterial communities in artificial soils.</p>
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17 pages, 3809 KiB  
Article
The Effect of Blood Flow Restriction during Low-Load Resistance Training Unit on Knee Flexor Muscle Fatigue in Recreational Athletes: A Randomized Double-Blinded Placebo-Controlled Pilot Study
by Aleksandra Królikowska, Maciej Daszkiewicz, Julia Kocel, George Mihai Avram, Łukasz Oleksy, Robert Prill, Jarosław Witkowski, Krzysztof Korolczuk, Anna Kołcz and Paweł Reichert
J. Clin. Med. 2024, 13(18), 5444; https://doi.org/10.3390/jcm13185444 - 13 Sep 2024
Viewed by 309
Abstract
Background/Objectives: Despite the growing popularity of training with a controlled form of vascular occlusion, known as blood flow restriction (BFR) training, in the rehabilitation of orthopedic patients and sports medicine, there remains ample space for understanding the basis of its mechanism. The pilot [...] Read more.
Background/Objectives: Despite the growing popularity of training with a controlled form of vascular occlusion, known as blood flow restriction (BFR) training, in the rehabilitation of orthopedic patients and sports medicine, there remains ample space for understanding the basis of its mechanism. The pilot study assessed the effect of BFR during a low-load resistance training unit on knee flexor muscle fatigue, intending to decide whether a larger trial is needed and feasible. Methods: The study used a prospective, randomized, parallel, double-blind, placebo-controlled design. Fifteen male healthy recreational athletes were randomly assigned to three equal groups: BFR Group, Placebo Group, and Control Group. The primary outcome was the change in the surface electromyography-based (sEMG-based) muscle fatigue index, which was determined by comparing the results obtained before and after the intervention. The intervention was the application of BFR during low-load resistance training for knee flexors. The occurrence of any adverse events was documented. Results: In all groups, the sEMG-based fatigue index for semitendinosus and biceps femoris muscles decreased after low-load resistance training, with the largest decrease in the BFR group. Although not statistically significant, BFR showed moderate and large effect sizes for the fatigue index of semitendinosus and biceps femoris, respectively. No adverse events were noted. Conclusions: The pilot study suggested that BFR during a low-load resistance training unit might affect knee flexor muscle fatigue, supporting the development of a larger randomized clinical trial. Full article
(This article belongs to the Section Orthopedics)
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<p>The starting position of the local knee flexors muscles fatigue assessment in the dominant lower limb using surface electromyography, performed during an isometric contraction against a hand-held dynamometer.</p>
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<p>The placement of the surface electromyography dual-electrode for recording the activity of the semitendinosus muscle in the examined dominant lower limb.</p>
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<p>The placement of the surface electromyography dual-electrode for recording the biceps femoris muscle activity in the examined dominant lower limb.</p>
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<p>The front view (<b>a</b>) and the side view from above (<b>b</b>) of the lower limb blood flow restriction cuff that was used for the present study purposes.</p>
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<p>Placement of the blood flow restriction cuff on the thigh of the dominant lower limb at the level of the largest circumference, directly under the inguinal fold.</p>
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<p>The starting position for the dominant limb low-load resistance training with blood flow restriction for knee flexors using an isokinetic dynamometer.</p>
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26 pages, 11662 KiB  
Article
Advanced Numerical Simulation of Scour around Bridge Piers: Effects of Pier Geometry and Debris on Scour Depth
by Muhanad Al-Jubouri, Richard P. Ray and Ethar H. Abbas
J. Mar. Sci. Eng. 2024, 12(9), 1637; https://doi.org/10.3390/jmse12091637 - 13 Sep 2024
Viewed by 226
Abstract
Investigating different pier shapes and debris Finteractions in scour patterns is vital for understanding the risks to bridge stability. This study investigates the impact of different shapes of pier and debris interactions on scour patterns using numerical simulations with flow-3D and controlled laboratory [...] Read more.
Investigating different pier shapes and debris Finteractions in scour patterns is vital for understanding the risks to bridge stability. This study investigates the impact of different shapes of pier and debris interactions on scour patterns using numerical simulations with flow-3D and controlled laboratory experiments. The model setup is rigorously calibrated against a physical flume experiment, incorporating a steady-state flow as the initial condition for sediment transport simulations. The Fractional Area/Volume Obstacle Representation (FAVOR) technique and the renormalized group (RNG) turbulence model enhance the simulation’s precision. The numerical results indicate that pier geometry is a critical factor influencing the scour depth. Among the tested shapes, square piers exhibit the most severe scour, with depths reaching 5.8 cm, while lenticular piers show the least scour, with a maximum depth of 2.5 cm. The study also highlights the role of horseshoe, wake, and shear layer vortices in determining scour locations, with varying impacts across different pier shapes. The Q-criterion study identified debris-induced vortex generation and intensification. The debris amount, thickness, and pier diameter (T/Y) significantly affect the scouring patterns. When dealing with high wedge (HW) debris, square piers have the largest scour depth at T/Y = 0.25, while lenticular piers exhibit a lower scour. When debris is present, the scour depth rises at T/Y = 0.5. Depending on the form of the debris, a significant fluctuation of up to 5 cm was reported. There are difficulties in precisely estimating the scour depth under complicated circumstances because of the disparity between numerical simulations and actual data, which varies from 6% for square piers with a debris relative thickness T/Y = 0.25 to 32% for cylindrical piers with T/Y = 0.5. The study demonstrates that while flow-3D simulations align reasonably well with the experimental data under a low debris impact, discrepancies increase with more complex debris interactions and higher submersion depths, particularly for cylindrical piers. The novelty of this work lies in its comprehensive approach to evaluating the effects of different pier shapes and debris interactions on scour patterns, offering new insights into the effectiveness of flow-3D simulations in predicting the scour patterns under varying conditions. Full article
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<p>Experimental flume for investigating turbulent characteristics and scour processes around varied pier geometries.</p>
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<p>Pier shapes are employed in experimental and numerical models including, (<b>A</b>) lenticular (LE), (<b>B</b>) ogival (OG), (<b>C</b>) rectangular (RE), (<b>D</b>) oblong (OB), (<b>E</b>) elliptical (EL), (<b>F</b>) octagonal (OC), (<b>G</b>) double-circular (DC), (<b>H</b>) Joukasaky (JO), (<b>I</b>) rectangular chamfered (REC), (<b>J</b>) diamond (DI) and square (S), and (<b>K</b>) polygonal (PO) shapes.</p>
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<p>Six uniform debris configurations were employed during the experiments, (<b>A</b>) rectangle, (<b>B</b>) tringle bow, (<b>C</b>) high wedge, (<b>D</b>) low wedge, (<b>E</b>) triangle yield, and (<b>F</b>) half circle.</p>
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<p>Detailed view of the computational domain with mesh representation: (<b>a</b>) top view, (<b>b</b>) side view, and (<b>c</b>) front view.</p>
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<p>The FAVOR technique in flow-3D meshing includes (<b>a</b>) square and cylindrical piers with six debris shapes and (<b>b</b>) various pier shapes without debris accumulations.</p>
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<p>The maximum relative scour depth (Z<sub>s</sub>/D) following encounters with debris for (<span class="html-italic">T</span>/<span class="html-italic">Y</span> = 0.25).</p>
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<p>The maximum relative scour depth (Z<sub>s</sub>/D) following encounters with debris for (<span class="html-italic">T</span>/<span class="html-italic">Y</span> = 0.5).</p>
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<p>The maximum relative scour depth (Z<sub>s</sub>/D) following encounters with debris for (<span class="html-italic">T</span>/<span class="html-italic">Y</span> = 1).</p>
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<p>Analysis of the shape factor for thirteen distinct pier geometries developed from [<a href="#B18-jmse-12-01637" class="html-bibr">18</a>].</p>
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<p>Standard deviation analysis of average scour depth for different pier shapes.</p>
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<p>Standard deviation analysis of average scour depth for different debris shapes.</p>
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<p>The local scour distribution around the different piers shapes includes (<b>a</b>) square, (<b>b</b>) rectangular, (<b>c</b>) rectangular chamfered, (<b>d</b>) diamond, (<b>e</b>) polygonal, (<b>f</b>) cylindrical, (<b>g</b>) octagonal, (<b>h</b>) double–circular, (<b>i</b>) Joukasaky, (<b>j</b>) elliptical, (<b>k</b>) ogival, (<b>l</b>) oblong, and (<b>m</b>) lenticular.</p>
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<p>The local scour distribution around the different piers shapes includes (<b>a</b>) square, (<b>b</b>) rectangular, (<b>c</b>) rectangular chamfered, (<b>d</b>) diamond, (<b>e</b>) polygonal, (<b>f</b>) cylindrical, (<b>g</b>) octagonal, (<b>h</b>) double–circular, (<b>i</b>) Joukasaky, (<b>j</b>) elliptical, (<b>k</b>) ogival, (<b>l</b>) oblong, and (<b>m</b>) lenticular.</p>
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<p>The flow velocity patterns around different pier shapes.</p>
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<p>Comparative scour depth value for square and cylindrical piers across various debris shapes when debris relative thickness (<span class="html-italic">T</span>/<span class="html-italic">Y</span>) cases equal to 0.25.</p>
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<p>Comparative scour depth value for square and cylindrical piers across various debris shapes when debris relative thickness (<span class="html-italic">T</span>/<span class="html-italic">Y</span>) cases equal to 0.5.</p>
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<p>Q–criterion flow visualization around a cylindrical pier includes (<b>a</b>) without debris, (<b>b</b>) 3 cm thick rectangular debris, and (<b>c</b>) 6 cm thick rectangular debris.</p>
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<p>Assessing flow-3D’s accuracy in predicting scour depths for cylindrical piers: a detailed examination at different (<span class="html-italic">T</span>/<span class="html-italic">Y</span>) ratios.</p>
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13 pages, 3677 KiB  
Article
Surface Topography Analysis of BK7 with Different Roughness Nozzles Using an Abrasive Water Jet
by Haihong Pan, Xuhong Chen, Lin Chen, Hui You and Xubin Liang
Materials 2024, 17(18), 4494; https://doi.org/10.3390/ma17184494 - 13 Sep 2024
Viewed by 223
Abstract
This study investigated the effect of abrasive water jet (AWJ) kinematic parameters, such as jet traverse speed and water pressure, abrasive mass flow rate, and standoff distance on the surface of BK7. Nozzle A reinforced with a 100 nm particle-sized coating of titanium [...] Read more.
This study investigated the effect of abrasive water jet (AWJ) kinematic parameters, such as jet traverse speed and water pressure, abrasive mass flow rate, and standoff distance on the surface of BK7. Nozzle A reinforced with a 100 nm particle-sized coating of titanium alloy has more wear resistance compared to Nozzle B coated with nothing. Through analysis of variance and measurement of BK7 surface quality, it is concluded that the grooving and plowing caused by abrasive particles and irregularities in the abrasive water jet machined surface with respect to traverse speed (3, 7.2, 7.8, and 9 mm/min), abrasive flow rate (7 L/min and 10 L/min, 80 mesh) and water pressure (2 and 3 MPa) were investigated using surface topography measurements. The surface roughness (15.734 nm) of BK7 results show that a nozzle coated with titanium alloy has more hardness, which protects BK7 undamaged and super-smooth. The values of selected surface roughness profile parameters—average roughness (Ra) and maximum height of PV (maximum depth of peak and valleys)—reveal a comparatively smooth BK7 surface in composites reinforced with 2% titanium alloy in the nozzle weight at a traverse speed of 7.8 mm/min. Moreover, abrasive water jet machining at high water pressure (3 MPa) produced better surface quality due to material removal and effective cleaning of lens fragmentation and abrasive particles from the polishing zone compared to a lower water pressure (2 MPa), low traverse speed (5 mm/min), and low abrasive mass flow rate (200 g/min). Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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<p>Physical image of nozzles.</p>
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<p>Surface roughness detection of nozzles (A and B).</p>
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<p>3D schematic diagram of AWJ.</p>
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<p>Polishing optical glass (BK7).</p>
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<p>Optical images of polished BK7 surfaces using Nozzle A and Nozzle B, respectively. (<b>a</b>) The surface condition of BK7 glass after 500 h of testing with Nozzle A. (<b>b</b>) The surface condition of BK7 glass after 500 h of testing with Nozzle B.</p>
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<p>Experiment Equipment of AWJ. (<b>a</b>) Diaphragm pump. (<b>b</b>) Abrasive mixing system. (<b>c</b>) Polishing system.</p>
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<p>SEM images of Nozzle A coated titanium alloy composite after 500 h tests: (<b>a</b>) the wear area at the Nozzle A exit position, magnification 100×; (<b>b</b>) the wear area at the Nozzle A exit position, magnification 3000×; and (<b>c</b>) the main metal contents of the Nozzle A outlet wear area.</p>
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<p>SEM images of Nozzle B without coating after 500 h tests: (<b>a</b>) the wear area at the Nozzle B exit position magnification 100×; (<b>b</b>) the wear area at the Nozzle B exit position magnification, magnification 3000×; and (<b>c</b>) the main metal contents of the Nozzle B outlet wear area.</p>
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<p>Optical quality of BK7 after Nozzle A polished: (<b>a</b>) 7.8 mm/min; 10 L/min; 500 nm grit size; hydraulic pressure 2 MPa; (<b>b</b>) optical quality of BK7 after polished: 7.4 mm/min; 20 L/min; 500 nm grit size; hydraulic pressure 3 MPa; (<b>c</b>) a graph in two orthogonal sections of BK7.</p>
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<p>Optical quality of BK7 after Nozzle B polished: (<b>a</b>) 7.8 mm/min; 10 L/min; 500 nm grit size; hydraulic pressure 2 MPa; (<b>b</b>) optical quality of BK7 after polished: 7.4 mm/min; 20 L/min; 500 nm grit size; hydraulic pressure 3 MPa; (<b>c</b>) a graph in two orthogonal sections of BK7.</p>
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18 pages, 10223 KiB  
Article
Flood Modeling of the June 2023 Flooding of Léogâne City by the Overflow of the Rouyonne River in Haiti
by Rotchild Louis, Yves Zech, Adermus Joseph, Nyankona Gonomy and Sandra Soares-Frazao
Water 2024, 16(18), 2594; https://doi.org/10.3390/w16182594 - 13 Sep 2024
Viewed by 516
Abstract
Evaluating flood risk though numerical simulations in areas where hydrometric and bathymetric data are scarcely available is a challenge. This is, however, of paramount importance, particularly in urban areas, where huge losses of human life and extensive damage can occur. This paper focuses [...] Read more.
Evaluating flood risk though numerical simulations in areas where hydrometric and bathymetric data are scarcely available is a challenge. This is, however, of paramount importance, particularly in urban areas, where huge losses of human life and extensive damage can occur. This paper focuses on the 2–3 June 2023 event at Léogâne in Haiti, where the Rouyonne River partly flooded the city. Water depths in the river have been recorded since April 2022, and a few discharges were measured manually, but these were not sufficient to produce a reliable rating curve. Using a uniform-flow assumption combined with the Bayesian rating curve (BaRatin) method, it was possible to extrapolate the existing data to higher discharges. From there, a rainfall–runoff relation was developed for the site using a distributed hydrological model, which allowed the discharge of the June 2023 event to be determined, which was estimated as twice the maximum conveying capacity of the river in the measurement section. Bathymetric data were obtained using drone-based photogrammetry, and two-dimensional simulations were carried out to represent the flooded area and the associated water depths. By comparing the water depths of 21 measured high-water marks with the simulation results, we obtained a Kling–Gupta Efficiency (KGE) and Nash–Sutcliffe Efficiency (NSE) values of 0.890 and 0.882, respectively. This allows us to conclude that even when only scarce official data are available, it is possible to use field data acquired by low-cost methodologies to build a model that is sufficiently accurate and that can be used by flood managers and decision makers to assess flood risk and vulnerability in Haiti. Full article
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<p>Study area: (<b>a</b>) Study site location in Haiti; (<b>b</b>) Rouyonne river channel and its upper watershed; (<b>c</b>) Altitude distribution in the upper watershed.</p>
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<p>Study area: (<b>a</b>) Study site location in Haiti; (<b>b</b>) Rouyonne river channel and its upper watershed; (<b>c</b>) Altitude distribution in the upper watershed.</p>
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<p>Illustration of image acquisition: (<b>a</b>) Aerial image of the river during the dry season; (<b>b</b>) DJI drone equipped with a GoPro camera (sensor type: 1/2.3” CMOS; camera type: sport/action camera; equivalent focal length: 16.41 mm; lens type: wide angle; aperture: f/2.8).</p>
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<p>Illustration of the morphological changes in the Rouyonne river channel: (<b>a</b>) Cross-section 54—54 of the Rouyonne River; (<b>b</b>) Bathymetric data comparison between UAV photogrammetry DTM (2022) and the manual survey (2022); (<b>c</b>) Evolution of morphological changes between 2014 and 2022 in cross-section 54—54.</p>
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<p>Illustration of the damage caused by the 3 June 2023 event: (<b>a</b>) Buildings destroyed by the flood in the town of Léogâne; (<b>b</b>) Pressure sensor broken by flood at the measuring section; (<b>c</b>) High-water mark measurement; (<b>d</b>) Spatial distribution of high-water marks measured for the 2–3 June 2023 event.</p>
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<p>Illustration of the damage caused by the 3 June 2023 event: (<b>a</b>) Buildings destroyed by the flood in the town of Léogâne; (<b>b</b>) Pressure sensor broken by flood at the measuring section; (<b>c</b>) High-water mark measurement; (<b>d</b>) Spatial distribution of high-water marks measured for the 2–3 June 2023 event.</p>
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<p>Illustration of the unstructured mesh of the study area.</p>
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<p>Cross-section at the limnimetric station with the equivalent rectangle (discontinuous black line) used in the BaRatin method.</p>
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<p>Relationships between water depth and discharge at the measurement section: comparison of the Bayesian rating curve with uncertainties and the uniform-flow assumption.</p>
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<p>Hydrological modeling: (<b>a</b>) Calibration (August 2022); (<b>b</b>) Validation (September 2022).</p>
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<p>Hydrological modeling applied to the event of 2–3 June 2023.</p>
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<p>Illustration of the 2–3 June 2023 event simulation.</p>
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<p>Model evaluation: Comparison between the observed and modeled water depths.</p>
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<p>Identification of the overflow points on the Rouyonne river: (<b>a</b>) Right bank overtopping to downtown Léogâne; (<b>b</b>) Left bank overtopping where the probe was installed.</p>
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15 pages, 2629 KiB  
Article
Wall Shear Stress (WSS) Analysis in Atherosclerosis in Partial Ligated Apolipoprotein E Knockout Mouse Model through Computational Fluid Dynamics (CFD)
by Minju Cho, Joon Seup Hwang, Kyeong Ryeol Kim and Jun Ki Kim
Int. J. Mol. Sci. 2024, 25(18), 9877; https://doi.org/10.3390/ijms25189877 (registering DOI) - 12 Sep 2024
Viewed by 287
Abstract
Atherosclerosis involves an inflammatory response due to plaque formation within the arteries, which can lead to ischemic stroke and heart disease. It is one of the leading causes of death worldwide, with various contributing factors such as hyperlipidemia, hypertension, obesity, diabetes, and smoking. [...] Read more.
Atherosclerosis involves an inflammatory response due to plaque formation within the arteries, which can lead to ischemic stroke and heart disease. It is one of the leading causes of death worldwide, with various contributing factors such as hyperlipidemia, hypertension, obesity, diabetes, and smoking. Wall shear stress (WSS) is also known as a contributing factor of the formation of atherosclerotic plaques. Since the causes of atherosclerosis cannot be attributed to a single factor, clearly understanding the mechanisms and causes of its occurrence is crucial for preventing the disease and developing effective treatment strategies. To better understand atherosclerosis and define the correlation between various contributing factors, computational fluid dynamics (CFD) analysis is primarily used. CFD simulates WSS, the frictional force caused by blood flow on the vessel wall with various hemodynamic changes. Using apolipoprotein E knockout (ApoE-KO) mice subjected to partial ligation and a high-fat diet at 1-week, 2-week, and 4-week intervals as an atherosclerosis model, CFD analysis was conducted along with the reconstruction of carotid artery blood flow via magnetic resonance imaging (MRI) and compared to the inflammatory factors and pathological staining. In this experiment, a comparative analysis of the effects of high WSS and low WSS was conducted by comparing the standard deviation of time-averaged wall shear stress (TAWSS) at each point within the vessel wall. As a novel approach, the standard deviation of TAWSS within the vessel was analyzed with the staining results and pathological features. Since the onset of atherosclerosis cannot be explained by a single factor, the aim was to find the correlation between the thickness of atherosclerotic plaques and inflammatory factors through standard deviation analysis. As a result, the gap between low WSS and high WSS widened as the interval between weeks in the atherosclerosis mouse model increased. This finding not only linked the occurrence of atherosclerosis to WSS differences but also provided a connection to the causes of vulnerable plaques. Full article
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<p>Scheme of WSS evaluation acquisition of ApoE-KO mice atherosclerosis model. (<b>A</b>) Partially ligated ApoE-KO mice fed a high-fat diet were developed as an atherosclerosis model. To confirm disrupted blood flow, (<b>B</b>) MRI images were acquired, along with (<b>C</b>) H&amp;E, Movat staining, and IF staining images. Based on these results, (<b>D</b>) a 3D reconstruction of the carotid artery was performed to evaluate WSS.</p>
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<p>Blood flow disrupt confirmation through MRI TOF mode and histological staining of carotid artery. (<b>A</b>) Cross-sectioned MRI image and lateral MRI image of 1- and 4-week partial ligated ApoE-KO mice. Partial ligated LCA are indicated as white arrows in MRI images. (<b>B</b>) The excised sample of 4-week mice and H&amp;E and MOVAT staining images of the cross-sectioned tissue at the partial ligation site (bifurcation), the midpoint, and the RCA without partial ligation as control. (<b>C</b>) H&amp;E staining results of 1-, 2-, and 4-week LCA. Pathological features are marked in the image.</p>
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<p>IF performed on the bifurcation part of the LCA. The samples were double-stained with VCAM-1 and NF-κB as one set, and CD31 and α-SMA as another set. (<b>A</b>–<b>C</b>) represent the 1-, 2-, and 4-week IF staining results for VCAM-1 (green) and NF-κB (red) in the LCA bifurcation. (<b>D</b>–<b>F</b>) show the staining results for CD31 (red) and α-SMA (green) in the LCA bifurcation, respectively. The arrows and dotted lines in the magnified images of each figure indicate the fluorescence biomarker. The arrows in Figures (<b>A</b>–<b>C</b>) represent NF-κB (red). The arrows in the magnified images of Figures (<b>D</b>–<b>F</b>) represent CD31 (red). For VCAM-1 (green), no significant observations were made, and α-SMA (green) was well visualized in Figures (<b>D</b>–<b>F</b>).</p>
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<p>A 3D construction of the left carotid artery from the midpoint of LCA to bifurcation of the partial ligation part with WSS evaluation. (<b>A</b>) 3D image of LCA with WSS distribution; the red part refers to high WSS, where the blue part refers to low WSS. (<b>B</b>–<b>E</b>) are maximum WSS graphs for 1-, 2-, and 4-week mice in all groups, respectively.</p>
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<p>Summary of (<b>A</b>) standard deviation of TAWSS, (<b>B</b>) area, (<b>C</b>) maximum WSS, and (<b>D</b>) fluorescence intensity for LCA and RCA (<span class="html-italic">p</span> value &lt; 0.01 ** and &lt;0.05 *).</p>
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16 pages, 5280 KiB  
Article
Simulation of Battery Thermal Management System for Large Maritime Electric Ship’s Battery Pack
by Fu Jia and Geesoo Lee
Energies 2024, 17(18), 4587; https://doi.org/10.3390/en17184587 - 12 Sep 2024
Viewed by 272
Abstract
In recent years, large power batteries have been widely used not only in automobiles and other vehicles but also in maritime vessels. The thermal uniformity of large marine battery packs significantly affects the performance, safety, and longevity of the electric ship. As a [...] Read more.
In recent years, large power batteries have been widely used not only in automobiles and other vehicles but also in maritime vessels. The thermal uniformity of large marine battery packs significantly affects the performance, safety, and longevity of the electric ship. As a result, the thermal management of large power batteries has become a crucial technical challenge with traditional battery management system (BMS) that cannot effectively solve the battery heating problem caused by electrochemical reactions and joule heating during operation. To address this gap, a battery thermal management system (BTMS) has been newly designed. This article presents the design of a large marine battery pack, which features a liquid cooling system integrated into both the bottom and side plates of each pack. The flow plate is constructed from five independent units, each connected by manifold structures at both ends. These connections ensure the formation of a stable and cohesive flow plate assembly. Although research on the BTMS is relatively advanced, there is a notable lack of studies examining the effects of liquid temperature, flow rate, and battery discharge rate on the temperature consistency and uniformity of large marine battery packs. This work seeks to design the cooling system for the battery pack and analyzes the impact of the temperature, flow rate, and battery discharge rate of the liquid fluid on the consistency and uniformity of the battery pack temperature on the overall structure of the battery pack. It was found that, in low discharge conditions, there was good temperature consistency between the battery packs and between the different batteries within the battery pack, and the temperature difference did not exceed 1 °C. However, under high discharge rates, a C-rate of 4C, there might have been a decrease in temperature consistency; the temperature rise rate even exceeded 50% compared to when the discharge rate was low. The flow rate in the liquid flow characteristics had little effect on the temperature consistency between the batteries and the temperature uniformity on the battery surface, and the temperature fluctuation was maintained within 1 °C. Conversely, the liquid flow temperature had little effect on the temperature distribution between the batteries, but it caused discrepancies in the surface temperature of the batteries. In addition, the liquid flow temperature could cause the overall temperature of the battery to increase or decrease, which also occurs under different discharge rates. Full article
(This article belongs to the Special Issue Battery Thermal Management)
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<p>Yara Birkeland, the first fully electric and autonomous container ship [<a href="#B3-energies-17-04587" class="html-bibr">3</a>].</p>
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<p>Schematic diagram of electric propulsion system.</p>
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<p>Schematic diagram of battery pack structure.</p>
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<p>Schematic diagram of the flow plate of a battery pack.</p>
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<p>Decomposition diagram of battery pack calculation domain.</p>
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<p>Computational grid system and overall temperature contour.</p>
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<p>Grid dependency test.</p>
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<p>Distribution of sampling points on the battery cell surface.</p>
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<p>Battery cell number index for module.</p>
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<p>Bar chart of surface center temperature for different groups of batteries. (<b>a</b>) Bar chart of surface center temperature for Group 1 (°C); (<b>b</b>) Bar chart of surface center temperature for Group 2 (°C); (<b>c</b>) Bar chart of surface center temperature for Group 3 (°C); (<b>d</b>) Bar chart of surface center temperature for Group 4 (°C); (<b>e</b>) Bar chart of surface center temperature for Group 5 (°C).</p>
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<p>Battery cell center temperature of different battery groups.</p>
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<p>The temperature distributions of the 3 groups.</p>
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<p>The temperatures distributions along the vertical direction on the battery surface (<b>a</b>) group 1; (<b>b</b>) group 3; (<b>c</b>) group 5.</p>
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<p>Schematic diagram of thermal conductivity process.</p>
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<p>Central temperature curve of battery group for varying flow rate.</p>
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<p>Temperature curve at the center of the battery group.</p>
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<p>Central temperature curve of battery group.</p>
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20 pages, 6955 KiB  
Article
Flow Performance Analysis of Non-Return Multi-Door Reflux Valve: Experimental Case Study
by Xolani Prince Hadebe, Bernard Xavier Tchomeni Kouejou, Alfayo Anyika Alugongo and Desejo Filipeson Sozinando
Fluids 2024, 9(9), 213; https://doi.org/10.3390/fluids9090213 - 12 Sep 2024
Viewed by 333
Abstract
Non-return multi-door reflux valves are essential in fluid control systems to prevent reverse flow and maintain system integrity. This study experimentally analyzes the flow performance of multi-door check valves under different operating conditions, focusing on pressure testing and evaluating their effectiveness in preventing [...] Read more.
Non-return multi-door reflux valves are essential in fluid control systems to prevent reverse flow and maintain system integrity. This study experimentally analyzes the flow performance of multi-door check valves under different operating conditions, focusing on pressure testing and evaluating their effectiveness in preventing backflow. A wide-ranging experimental setup was designed and implemented to simulate real-world scenarios, facilitating accurate measurement of flow rates, pressure differences, and valve response times. The collected experimental data were analyzed to evaluate the valve’s performance in terms of flow capacity, pressure drop, and hydraulic efficiency. Additionally, the effects of factors such as valve size, valve configuration, and fluid properties (water) on performance were considered. It was found that the non-return multi-door reflux valve has been proven effective and reliable in preserving system integrity and maintaining unidirectional flow at the same time during pressure testing. It exhibits no backflow, remains stable and constant across varied flow conditions, and demonstrates a low pressure drop and high flow capacity, making it suitable for critical pressure testing applications. The response curve revealed that valve opening takes longer to reach higher flow rates than closing, indicating pressure instability during transition periods. This non-linear relationship indicates possible irregularities in pressure drop response to flow rate changes, highlighting potential areas for further investigation. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics in Fluid Machinery)
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<p>Non-return multi-door reflux valve (<b>a</b>) schematic multi-door valve, (1)—inspection cover, (2)—door’s lever arm &amp; counterweights, (3)—outlet body, (4)—door’s main spindle, (<b>b</b>) physical valve (5)—inlet body.</p>
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<p>Valve design and operation, (<b>a</b>) hinged doors, (1)—upper door, (2)—center doors, (3)—lower door, (<b>b</b>) ductile iron materials.</p>
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<p>Experimental setup: (<b>a</b>)—1-inlet front view (<b>b</b>)—2-outlet valve side view.</p>
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<p>Test rig instrument: (<b>a</b>) motorized pump, (<b>b</b>) test plates (blank flanges), (<b>c</b>) tapped-hole air release plug.</p>
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<p>Pressure gauges: (<b>a</b>) pump gauge; (<b>b</b>) valve inlet gauge.</p>
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<p>Valve outlet test.</p>
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<p>Filling up the valve with water.</p>
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<p>Flow performance and pressure drop test results. (<b>a</b>)—flow rate vs. pressure; (<b>b</b>)—flow rate vs. pressure drop.</p>
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<p>Flow performance and cavitation test results.</p>
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<p>Flow performance and response time results. (<b>a</b>)—Time vs. flow rate; (<b>b</b>)—response time vs. pressure drop; (<b>c</b>) flow rate vs. pressure drop.</p>
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<p>Failure observed. (<b>a</b>) Door leak; (<b>b</b>) shaft bush leak; (<b>c</b>) high shaft bush leak.</p>
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<p>Stainless steel-to-stainless steel sealing surfaces: (<b>a</b>) body seat; (<b>b</b>) door seat.</p>
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<p>Failing shaft bush.</p>
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<p>Flow performance and pressure drop test results: (<b>a</b>)—flow rate vs. pressure; (<b>b</b>)—flow rate vs. pressure drop.</p>
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<p>Flow performance and cavitation test results.</p>
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<p>Flow performance and response time results: (<b>a</b>) time vs. flow rate; (<b>b</b>) response time vs. pressure drop; (<b>c</b>) flow rate vs. pressure drop.</p>
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17 pages, 3321 KiB  
Article
Sensitivity Analysis of Excited-State Population in Plasma Based on Relative Entropy
by Yosuke Shimada and Hiroshi Akatsuka
Entropy 2024, 26(9), 782; https://doi.org/10.3390/e26090782 - 12 Sep 2024
Viewed by 230
Abstract
A highly versatile evaluation method is proposed for transient plasmas based on statistical physics. It would be beneficial in various industrial sectors, including semiconductors and automobiles. Our research focused on low-energy plasmas in laboratory settings, and they were assessed via our proposed method, [...] Read more.
A highly versatile evaluation method is proposed for transient plasmas based on statistical physics. It would be beneficial in various industrial sectors, including semiconductors and automobiles. Our research focused on low-energy plasmas in laboratory settings, and they were assessed via our proposed method, which incorporates relative entropy and fractional Brownian motion, based on a revised collisional–radiative model. By introducing an indicator to evaluate how far a system is from its steady state, both the trend of entropy and the radiative process’ contribution to the lifetime of excited states were considered. The high statistical weight of some excited states may act as a bottleneck in the plasma’s energy relaxation throughout the system to a steady state. By deepening our understanding of how energy flows through plasmas, we anticipate potential contributions to resolving global environmental issues and fostering technological innovation in plasma-related industrial fields. Full article
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<p>Plots of non-adiabatic entropy weights in glow discharge plasma, calculated for each level using the revised model influenced by electron collisions. Dependency on the parameter FRC is illustrated (conditions: 1 Torr, 500 K, 1 eV, and 10<sup>9</sup> cm<sup>−3</sup>).</p>
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<p>Boltzmann plots illustrating the revised model due to electron collision and their dependency on the FRC parameter (conditions: 1 Torr, 500 K, 1 eV, and 10<sup>9</sup> cm<sup>−3</sup>).</p>
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<p>Plots of non-adiabatic entropy weights in glow discharge plasma, calculated for each level using the revised model, influenced by electron collisions. Dependency on the parameter FRC is shown (conditions: 0.1 Torr, 500 K, 1 eV, and 10<sup>9</sup> cm<sup>−3</sup>).</p>
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<p>Plots of non-adiabatic entropy weights in glow discharge plasma, calculated for each level using the revised model due to electron collisions. The dependency on the parameter FRC is depicted (conditions: 1 Torr, 1000 K, 1 eV, and 10<sup>9</sup> cm<sup>−3</sup>).</p>
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<p>Plots of non-adiabatic entropy weights in arc discharge plasma, calculated for each level using the revised model due to electron collisions. The dependency on the parameter FRC is demonstrated (conditions: 760 Torr, 500 K, 2 eV, and 10<sup>17</sup> cm<sup>−3</sup>).</p>
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<p>Plots of non-adiabatic entropy weights in recombining plasma, calculated for each level using the revised model influenced by electron collisions. The dependency on the parameter FRC is illustrated (conditions: 0.0075 Torr, 500 K, 0.2 eV, and 10<sup>13</sup> cm<sup>−3</sup>).</p>
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<p>Plots of non-adiabatic entropy weights in recombining plasma, calculated for each level using the revised model, influenced by electron collisions. Dependency on the parameter FRC is shown (conditions: 0.0075 Torr, 500 K, 0.2 eV, and 10<sup>9</sup> cm<sup>−3</sup>).</p>
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<p>Plots of non-adiabatic entropy weights in recombining plasma, calculated for each level using the revised model influenced by electron collisions. The plots illustrate the dependency on the parameter FRC (conditions: 0.0075 Torr, 500 K, 0.1 eV, and 10<sup>13</sup> cm<sup>−3</sup>).</p>
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<p>Plots of non-adiabatic entropy weights in glow discharge plasma, calculated using the revised model for each level affected by collisions with ground-state atoms. The dependency on the parameter FRC is shown (conditions: 1 Torr, 500 K, 1 eV, and 10<sup>9</sup> cm<sup>−3</sup>).</p>
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