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17 pages, 854 KiB  
Article
Non-Stationary Flow of a Viscous Incompressible Electrically Conductive Liquid on a Rotating Plate in the Presence of Media Injection (Suction), Considering Induction and Diffusion Effects
by Anatoly A. Gurchenkov and Ivan A. Matveev
Physics 2025, 7(1), 1; https://doi.org/10.3390/physics7010001 - 10 Jan 2025
Viewed by 512
Abstract
The branch of physics known as magnetohydrodynamics (MHD) emerged in the middle of the 20th century. MHD models, being substantially nonlinear, are quite challenging for theoretical study and allow nontrivial consideration only in particular limited cases. Thus, due to the exceptional growth of [...] Read more.
The branch of physics known as magnetohydrodynamics (MHD) emerged in the middle of the 20th century. MHD models, being substantially nonlinear, are quite challenging for theoretical study and allow nontrivial consideration only in particular limited cases. Thus, due to the exceptional growth of calculation power, research on MHD is now primarily concentrated on numerical modeling. The achievements are considerable; however, there is a possibility of overlooking some phenomena or missing an optimal approach to modeling and calculating that could be identified with theoretical guidance. The paper presents a theoretical study of a particular class of boundary and initial conditions. The flow of a viscous, electrically conductive fluid on a rotating plate in the presence of a magnetic field is considered. The fluid and the bounding plate rotate together with a constant angular velocity around an axis that is not perpendicular to the plane. The flow is induced by sudden longitudinal vibrations of the plate, injection (suction) of the medium through the plate, and an applied magnetic field directed normal to the plate. The full equation of magnetic induction is used, taking into account both the induction effect and energy dissipation due to the flow of electric currents. An analytical solution of three-dimensional magnetohydrodynamics equations in a half-space bounded by a plate is presented. The solution is given in the form of a superposition of plane waves propagating with certain wave numbers along the y-coordinate axis. For certain regions of system parameters, the vibration of the bounding plate does not cause waves in the media. Full article
(This article belongs to the Section Classical Physics)
Show Figures

Figure 1

Figure 1
<p>Schematic geometry of the problem. See text for details.</p>
Full article ">Figure 2
<p>Regions of solution on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane, where <span class="html-italic">Y</span> is a dimensionless frequency variable (<a href="#FD28-physics-07-00001" class="html-disp-formula">28</a>) and <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math> is a dimensionless injection velocity (<a href="#FD30-physics-07-00001" class="html-disp-formula">30</a>).</p>
Full article ">Figure 3
<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of injection. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines represent the intersection of the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> plane. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
Full article ">Figure 4
<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of injection. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines in <a href="#physics-07-00001-f004" class="html-fig">Figure 4</a> depict the intersection of the <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the region given by Equation (<a href="#FD31-physics-07-00001" class="html-disp-formula">31</a>). The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
Full article ">Figure 5
<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> </msub> </semantics></math>. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines represent the intersection of the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> plane. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
Full article ">Figure 6
<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> </msub> </semantics></math>. Pale red and pale blue lines on the (<span class="html-italic">Y</span>–<math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>)-plane indicate the boundaries of the regions in <a href="#physics-07-00001-f002" class="html-fig">Figure 2</a> shown with same colors. The upper pale blue line denotes the projection of the region drawn for clarity. The bright red and bright blue lines in <a href="#physics-07-00001-f004" class="html-fig">Figure 4</a> depict the intersection of the <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <mi>Y</mi> <mo>,</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> </semantics></math> surface with the region given by Equation (<a href="#FD31-physics-07-00001" class="html-disp-formula">31</a>). The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
Full article ">Figure 7
<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> </msub> </semantics></math>. See text for details. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
Full article ">Figure 8
<p>Wave surfaces of function <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>(</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </semantics></math>, case of suction for root <math display="inline"><semantics> <msub> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> </msub> </semantics></math>. See text for details. The bright green curves correspond to the lines of constant <span class="html-italic">Y</span> and the dark green curves represent the lines of constant <math display="inline"><semantics> <msup> <mi>U</mi> <mo>*</mo> </msup> </semantics></math>.</p>
Full article ">
6 pages, 3189 KiB  
Correction
Correction: Sachhin et al. Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection. Fluids 2024, 9, 94
by Sudha Mahanthesh Sachhin, Ulavathi Shettar Mahabaleshwar, David Laroze and Dimitris Drikakis
Fluids 2024, 9(10), 241; https://doi.org/10.3390/fluids9100241 - 17 Oct 2024
Viewed by 528
Abstract
Figures: In Section 5, we aligned Figures 14–18 by consistently adding all the modelling parameters inside the labels [...] Full article
Show Figures

Figure 14

Figure 14
<p>Temperature profiles for the dusty and fluid phases versus similarity variable for <span class="html-italic">S</span> = −2.</p>
Full article ">Figure 15
<p>Temperature profiles for the dusty and fluid phases versus similarity variable for <span class="html-italic">S</span> = 0.</p>
Full article ">Figure 16
<p>Temperature profiles for the dusty and fluid phases versus similarity variable for <span class="html-italic">S</span> = 2.</p>
Full article ">Figure 17
<p>Temperature profile versus similarity variable for a shrinking boundary.</p>
Full article ">Figure 18
<p>Velocity profile versus similarity variable variation in <math display="inline"><semantics> <mrow> <mi>D</mi> <msup> <mi>a</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
Full article ">
19 pages, 5575 KiB  
Article
Impact of Navier’s Slip and MHD on a Hybrid Nanofluid Flow over a Porous Stretching/Shrinking Sheet with Heat Transfer
by Thippaiah Maranna, Gadhigeppa Myacher Sachin, Ulavathi Shettar Mahabaleshwar, Laura M. Pérez and Igor V. Shevchuk
Fluids 2024, 9(8), 180; https://doi.org/10.3390/fluids9080180 - 10 Aug 2024
Cited by 4 | Viewed by 1449
Abstract
The main objective of this study is to explore the inventive conception of the magnetohydrodynamic flow of a hybrid nanofluid over-porous stretching/shrinking sheet with the effect of radiation and mass suction/injection. The hybrid nanofluid advances both the manufactured nanofluid of the current region [...] Read more.
The main objective of this study is to explore the inventive conception of the magnetohydrodynamic flow of a hybrid nanofluid over-porous stretching/shrinking sheet with the effect of radiation and mass suction/injection. The hybrid nanofluid advances both the manufactured nanofluid of the current region and the base fluid. For the current investigation, hybrid nanofluids comprising two different kinds of nanoparticles, aluminium oxide and ferrofluid, contained in water as a base fluid, are considered. A collection of highly nonlinear partial differential equations is used to model the whole physical problem. These equations are then transformed into highly nonlinear ordinary differential equations using an appropriate similarity technique. The transformed differential equations are nonlinear, and thus it is difficult to analytically solve considering temperature increases. Then, the outcome is described in incomplete gamma function form. The considered physical parameters namely, magnetic field, Inverse Darcy number, velocity slip, suction/injection, temperature jump effects on velocity, temperature, skin friction and Nusselt number profiles are reviewed using plots. The results reveal that magnetic field, and Inverse Darcy number values increase as the momentum boundary layer decreases. Moreover, higher values of heat sources and thermal radiation enhance the thermal boundary layer. The present problem has various applications in manufacturing and technological devices such as cooling systems, condensers, microelectronics, digital cooling, car radiators, nuclear power stations, nano-drag shipments, automobile production, and tumour treatments. Full article
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Figure 1

Figure 1
<p>Diagrammatic representation of fluid flow.</p>
Full article ">Figure 2
<p>The impact of velocity slip parameter on skin friction.</p>
Full article ">Figure 3
<p>The impact of magnetic field on skin friction.</p>
Full article ">Figure 4
<p>The impact of mass suction/injection on the radial velocity profile.</p>
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<p>The impact of mass suction/injection on the velocity profile.</p>
Full article ">Figure 6
<p>An impact of magnetic field on velocity profile.</p>
Full article ">Figure 7
<p>An impact of inverse Darcy number on velocity profile.</p>
Full article ">Figure 8
<p>The impact of velocity slip on velocity profile.</p>
Full article ">Figure 9
<p>The impact of mass suction/injection on temperature distribution.</p>
Full article ">Figure 10
<p>The impact of magnetic field on temperature distribution.</p>
Full article ">Figure 11
<p>The impact of inverse Darcy number on temperature distribution.</p>
Full article ">Figure 12
<p>The impact of velocity slip parameter on temperature distribution.</p>
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<p>The impact of temperature increase on temperature distribution.</p>
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<p>The impact of radiation on temperature distribution.</p>
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<p>The impact of magnetic field on Nusselt number.</p>
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<p>The impact of velocity slip on Nusselt number.</p>
Full article ">
29 pages, 11064 KiB  
Article
Water Injection for Cloud Cavitation Suppression: Analysis of the Effects of Injection Parameters
by Wei Wang, Zhijian Li, Xiang Ji, Yun Wang and Xiaofang Wang
J. Mar. Sci. Eng. 2024, 12(8), 1277; https://doi.org/10.3390/jmse12081277 - 29 Jul 2024
Cited by 3 | Viewed by 1025
Abstract
This study investigates cloud cavitation suppression around a model-scale NACA66 hydrofoil using active water injection and explores the effect of multiple injection parameters. Numerical simulations and a mixed-level orthogonal test method are employed to systematically analyze the impact of jet angle αjet [...] Read more.
This study investigates cloud cavitation suppression around a model-scale NACA66 hydrofoil using active water injection and explores the effect of multiple injection parameters. Numerical simulations and a mixed-level orthogonal test method are employed to systematically analyze the impact of jet angle αjet, jet location Ljet, and jet velocity Ujet on cavitation suppression efficiency and hydrofoil energy performance. The study reveals that jet location has the greatest influence on cavitation suppression, while jet angle has the greatest influence on hydrofoil energy performance. The optimal parameter combination (Ljet = 0.30C, αjet = +60 degrees, Ujet = 3.25 m/s) effectively balances energy performance and cavitation suppression, reducing cavitation volume by 49.34% and improving lift–drag ratio by 8.55%. The study found that the jet’s introduction not only enhances vapor condensation and reduces the intensity of the vapor–liquid exchange process but also disrupts the internal structure of cavitation clouds and elevates pressure on the hydrofoil suction surface, thereby effectively suppressing cavitation. Further analysis shows that positive-going horizontal jet components enhance the lift–drag ratio, while negative-going components have a detrimental effect. Jet arrangements near the trailing edge negatively impact both cavitation suppression and energy performance. These findings provide a valuable reference for selecting optimal injection parameters to achieve a balance between cavitation suppression and energy performance in hydrodynamic systems. Full article
(This article belongs to the Special Issue Cavitation Control in Marine Engineering: Modelling and Experiment)
Show Figures

Figure 1

Figure 1
<p>Schematic of hydrofoil with water injection: (<b>a</b>) Original hydrofoil for comparison. (<b>b</b>) Modified hydrofoil. (<b>c</b>) Details of the jet hole distance. (<b>d</b>) Diameter of the jet hole. (<b>e</b>) Graphical interpretation for the three variable parameters in this study.</p>
Full article ">Figure 2
<p>Computational domain and boundary conditions.</p>
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<p>Mesh distribution around the modified hydrofoil: (<b>a</b>) Jet hydrofoil with configuration of <span class="html-italic">L<sub>jet</sub></span> = 0.19<span class="html-italic">C</span> and <span class="html-italic">α<sub>jet</sub></span> = 0°. (<b>b</b>) Jet hydrofoil with configuration of <span class="html-italic">L<sub>jet</sub></span> = 0.45<span class="html-italic">C</span> and <span class="html-italic">α<sub>jet</sub></span> = 60°. (<b>c</b>) Grid distribution on the mid-section on hydrofoil. (<b>d</b>) Details of the hydrofoil trailing edge. (<b>e</b>) Details of mesh around the jet holes.</p>
Full article ">Figure 4
<p>Influence of spanwise nodes on the change trend of lift coefficient <span class="html-italic">C<sub>L</sub></span> and drag coefficient <span class="html-italic">C<sub>D</sub></span>.</p>
Full article ">Figure 5
<p>Schematic of velocity monitoring points for uncertainty analysis.</p>
Full article ">Figure 6
<p>Validation of cavitation cycle and patterns: (<b>a</b>) Monitored curves of non-dimensional cavitation area for experimental and numerical data, respectively. (<b>b</b>) Temporal evolution of vapor structures in one complete cavitation cycle (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83).</p>
Full article ">Figure 7
<p>Validation of cavitation cycle and patterns for jet hydrofoil: (<b>a</b>) Monitored curves of non-dimensional cavitation area for experimental and numerical data, respectively. (<b>b</b>) Temporal evolution of vapor structures, including top view and side view, in one complete cavitation cycle (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83, <span class="html-italic">U<sub>jet</sub></span> = 2.89 m/s).</p>
Full article ">Figure 8
<p>The performance of <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>η</mi> <mrow> <mi>c</mi> <mi>a</mi> <mi>v</mi> </mrow> </msub> </mrow> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>η</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>g</mi> </mrow> </msub> </mrow> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math> under the influence of three factors: (<b>a</b>) jet velocity, (<b>b</b>) jet location, and (<b>c</b>) jet angle, respectively.</p>
Full article ">Figure 9
<p>Monitored curves of non-dimensional cavitation area of H<sub>ori</sub>. and H<sub>opt</sub>, respectively.</p>
Full article ">Figure 10
<p>The cavitation dynamics and pressure features within one cavitation cycle of H<sub>ori</sub> and H<sub>opt</sub>, respectively.</p>
Full article ">Figure 11
<p>Contours of vapor volume fraction on the cut-planes along the chordwise direction: (<b>a</b>) 0.1<span class="html-italic">C</span>–0.5<span class="html-italic">C</span>. (<b>b</b>) 0.6<span class="html-italic">C</span>–1.0<span class="html-italic">C</span>. (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83).</p>
Full article ">Figure 12
<p>Contours of mass transferring on the hydrofoil’s mid-plane at moments of (<b>a</b>) attached cavitation developing, (<b>b</b>) max cavity volume, and (<b>c</b>) unstable scattered clouds shedding (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83).</p>
Full article ">Figure 13
<p><span class="html-italic">α<sub>v</sub></span> distribution near hydrofoil wall along the chordwise direction. (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83).</p>
Full article ">Figure 14
<p>Energy performance for the H<sub>ori</sub> and H<sub>opt</sub>, respectively: (<b>a</b>) lift coefficient, (<b>b</b>) drag coefficient, and (<b>c</b>) lift–drag ratio. (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83).</p>
Full article ">Figure 15
<p><span class="html-italic">x</span> velocity distribution near hydrofoil wall along the chordwise direction. (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83).</p>
Full article ">Figure 16
<p>Chordwise and temporal evolution of <span class="html-italic">C<sub>p</sub></span> gradient for (<b>a</b>) the original hydrofoil and (<b>b</b>) the jet hydrofoil, respectively. (Data extracted from the hydrofoil mid-section).</p>
Full article ">Figure 17
<p><span class="html-italic">C<sub>p</sub></span> distribution near hydrofoil wall along the chordwise direction. (<span class="html-italic">Re</span> = 5 × 10<sup>5</sup>, <span class="html-italic">σ</span> = 0.83).</p>
Full article ">Figure 18
<p>Schematic of interaction among the jet, mainstream, re-entrant jet, and cavitation: (<b>a</b>) The situation where the jet flows in the same direction as the mainstream. (<b>b</b>) The situation where the jet flows against the mainstream. (<b>c</b>) The situation where the jet is placed near the hydrofoil trailing edge.</p>
Full article ">
14 pages, 2795 KiB  
Article
Hybrid Nanofluid Flow over a Shrinking Rotating Disk: Response Surface Methodology
by Rusya Iryanti Yahaya, Norihan Md Arifin, Ioan Pop, Fadzilah Md Ali and Siti Suzilliana Putri Mohamed Isa
Computation 2024, 12(7), 141; https://doi.org/10.3390/computation12070141 - 10 Jul 2024
Viewed by 1066
Abstract
For efficient heating and cooling applications, minimum wall shear stress and maximum heat transfer rate are desired. The current study optimized the local skin friction coefficient and Nusselt number in Al2O3-Cu/water hybrid nanofluid flow over a permeable shrinking rotating [...] Read more.
For efficient heating and cooling applications, minimum wall shear stress and maximum heat transfer rate are desired. The current study optimized the local skin friction coefficient and Nusselt number in Al2O3-Cu/water hybrid nanofluid flow over a permeable shrinking rotating disk. First, the governing equations and boundary conditions are solved numerically using the bvp4c solver in MATLAB. Von Kármán’s transformations are used to reduce the partial differential equations into solvable non-linear ordinary differential equations. The augmentation of the mass transfer parameter is found to reduce the local skin friction coefficient and Nusselt number. Higher values of these physical quantities of interest are observed in the injection case than in the suction case. Meanwhile, the increase in the magnitude of the shrinking parameter improved and reduced the local skin friction coefficient and Nusselt number, respectively. Then, response surface methodology (RSM) is conducted to understand the interactive impacts of the controlling parameters in optimizing the physical quantities of interest. With a desirability of 66%, the local skin friction coefficient and Nusselt number are optimized at 1.528780016 and 0.888353037 when the shrinking parameter (λ) and mass transfer parameter (S) are −0.8 and −0.6, respectively. Full article
Show Figures

Figure 1

Figure 1
<p>Schematic diagram of the flow problem.</p>
Full article ">Figure 2
<p>Flowchart of the numerical and statistical procedures.</p>
Full article ">Figure 3
<p>The profiles of (<b>a</b>) radial velocity, (<b>b</b>) tangential velocity, (<b>c</b>) axial velocity, and (<b>d</b>) temperature with various values of <math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 3 Cont.
<p>The profiles of (<b>a</b>) radial velocity, (<b>b</b>) tangential velocity, (<b>c</b>) axial velocity, and (<b>d</b>) temperature with various values of <math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>The profiles of (<b>a</b>) local skin friction coefficient and (<b>b</b>) local Nusselt number with various values of <math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>Contour and surface plots for Response 1.</p>
Full article ">Figure 6
<p>Contour and surface plots for Response 2.</p>
Full article ">
21 pages, 4977 KiB  
Article
Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection
by Sudha Mahanthesh Sachhin, Ulavathi Shettar Mahabaleshwar, David Laroze and Dimitris Drikakis
Fluids 2024, 9(4), 94; https://doi.org/10.3390/fluids9040094 - 18 Apr 2024
Cited by 6 | Viewed by 1611 | Correction
Abstract
Understanding of dusty fluids for different Brinkman numbers in porous media is limited. This study examines the Darcy–Brinkman model for two-dimensional magneto-hydrodynamic fluid flow across permeable stretching/shrinking surfaces with heat transfer. Water was considered as a conventional base fluid in which the copper [...] Read more.
Understanding of dusty fluids for different Brinkman numbers in porous media is limited. This study examines the Darcy–Brinkman model for two-dimensional magneto-hydrodynamic fluid flow across permeable stretching/shrinking surfaces with heat transfer. Water was considered as a conventional base fluid in which the copper (Cu), silver (Ag), and titanium dioxide (TiO2) nanoparticles were submerged in a preparation of a ternary dusty nanofluid. The governing nonlinear partial differential equations are converted to ordinary differential equations through suitable similarity conversions. Under radiation and mass transpiration, analytical solutions for stretching sheets/shrinking sheets are obtained. Several parameters are investigated, including the magnetic field, Darcy–Brinkman model, solution domain, and inverse Darcy number. The outcomes of the present article reveal that increasing the Brinkman number and inverse Darcy number decreases the velocity of the fluid and dusty phase. Increasing the magnetic field decreases the momentum of the boundary layer. Ternary dusty nanofluids have significantly improved the heat transmission process for manufacturing with applications in engineering, and biological and physical sciences. The findings of this study demonstrate that the ternary nanofluid phase’s heat and mass transpiration performance is better than the dusty phase’s performance. Full article
(This article belongs to the Topic Advanced Heat and Mass Transfer Technologies)
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<p>Schematic diagram of the problem.</p>
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<p>Solution graph for stretching boundary with variation in <math display="inline"> <semantics> <mi>β</mi> </semantics> </math>. The results are obtained for stretching the boundary (<span class="html-italic">d</span> = 2).</p>
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<p>Solution graph for shrinking boundary with variation in <math display="inline"> <semantics> <mi>β</mi> </semantics> </math>. The results are obtained for shrinking the boundary (<span class="html-italic">d</span> = −1.4).</p>
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<p>Solution for stretching boundary for <math display="inline"> <semantics> <mrow> <mi>D</mi> <msup> <mi>a</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>10</mn> </mrow> </semantics> </math> with variation in <math display="inline"> <semantics> <mi>β</mi> </semantics> </math>.</p>
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<p>Solution for shrinking boundary for <math display="inline"> <semantics> <mrow> <mi>D</mi> <msup> <mi>a</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>10</mn> </mrow> </semantics> </math> with variation in <math display="inline"> <semantics> <mi>β</mi> </semantics> </math>.</p>
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<p>Solution for stretching boundary for <span class="html-italic">M</span> = 10 with variation in <math display="inline"> <semantics> <mi>β</mi> </semantics> </math>.</p>
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<p>Solution for shrinking boundary for <span class="html-italic">M</span> = 10 with variation in <math display="inline"> <semantics> <mi>β</mi> </semantics> </math>.</p>
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<p>Velocity profile with variation in <math display="inline"> <semantics> <mrow> <mi>D</mi> <msup> <mi>a</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics> </math>.</p>
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<p>Velocity profile versus similarity variable <span class="html-italic">M</span>.</p>
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<p>Velocity profile versus similarity variable <math display="inline"> <semantics> <mo mathvariant="normal">Λ</mo> </semantics> </math>.</p>
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<p>Axial momentum profile versus similarity variable.</p>
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<p>Axial momentum profile versus similarity variable.</p>
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<p>Axial momentum profile versus similarity variable for <math display="inline"> <semantics> <mo mathvariant="normal">Λ</mo> </semantics> </math>.</p>
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<p>Temperature profiles for the dusty and fluid phases versus similarity variable for <span class="html-italic">S</span> = −2.</p>
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<p>Temperature profiles for the dusty and fluid phases versus similarity variable for <span class="html-italic">S</span> = 0.</p>
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<p>Temperature profiles for the dusty and fluid phases versus similarity variable for <span class="html-italic">S</span> = 2.</p>
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<p>Temperature profile versus similarity variable for a shrinking boundary.</p>
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<p>Velocity profile versus similarity variable variation in <math display="inline"> <semantics> <mrow> <mi>D</mi> <msup> <mi>a</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics> </math>.</p>
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27 pages, 5143 KiB  
Article
Computational Fluid Dynamics Prediction of External Thermal Loads on Film-Cooled Gas Turbine Vanes: A Validation of Reynolds-Averaged Navier–Stokes Transition Models and Scale-Resolving Simulations for the VKI LS-94 Test Case
by Simone Sandrin, Lorenzo Mazzei, Riccardo Da Soghe and Fabrizio Fontaneto
Fluids 2024, 9(4), 91; https://doi.org/10.3390/fluids9040091 - 15 Apr 2024
Cited by 1 | Viewed by 1936
Abstract
Given the increasing role of computational fluid dynamics (CFD) simulations in the aerothermal design of gas turbine vanes and blades, their rigorous validation is becoming more and more important. This article exploits an experimental database obtained by the von Karman Institute (VKI) for [...] Read more.
Given the increasing role of computational fluid dynamics (CFD) simulations in the aerothermal design of gas turbine vanes and blades, their rigorous validation is becoming more and more important. This article exploits an experimental database obtained by the von Karman Institute (VKI) for Fluid Dynamics for the LS-94 test case. This represents a film-cooled transonic turbine vane, investigated in a five-vane linear cascade configuration under engine-like conditions in terms of the Reynolds number and Mach number. The experimental characterization included inlet freestream turbulence measured with hot-wire anemometry, aerodynamic performance assessed with a three-hole pressure probe in the downstream section, and vane convective heat transfer coefficient distribution determined with thin-film thermometers. The test matrix included cases without any film-cooling injection, pressure-side injection, and suction-side injection. The CFD simulations were carried out in Ansys Fluent, considering the impact of mesh sizing and steady-state Reynolds-Averaged Navier-Stokes (RANS) transition modelling, as well as more accurate transient scale-resolving simulations. This work provides insight into the advantages and drawbacks of such approaches for gas turbine hot-gas path designers. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics in Fluid Machinery)
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<p>Cascade geometrical parameters: nomenclature (reproduced from Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>]).</p>
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<p>LS-94 cross-sectional view (reproduced from Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>]).</p>
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<p>List of the features installed on the endwalls (reproduced from Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>]).</p>
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<p>Three-dimensional computational domain of the VKI LS-94 test case: (<b>a</b>) 3 mm thick reduced domain and (<b>b</b>) boundary conditions.</p>
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<p>Computational mesh of the reduced domain for the steady flow simulation of the LS-94 vane, featuring a volume global sizing of 1 mm, surface sizing of 0.31 mm, and 30 prismatic layers. The figure depicts detailed views of the leading-edge region and one film-cooling hole on the suction side.</p>
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<p>Mesh sensitivity results for the uncooled case using the fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS turbulence model, focusing on the surface sizing effect. Light-gray dashed lines indicate the positions of the film-cooling rows. Black dots represent the experimental results from Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars.</p>
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<p>Mesh sensitivity results for the PS injection case using the fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS turbulence model. Light-gray dashed lines indicate the positions of the film-cooling rows. Black dots represent the experimental results from Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars. (<b>a</b>) Surface sizing effect. (<b>b</b>) Prismatic layers effect.</p>
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<p>Mesh sensitivity results for the SS injection case using the fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS turbulence model. Light-gray dashed lines indicate the positions of the film-cooling rows. Black dots represent the experimental results from Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars. (<b>a</b>) Surface sizing effect. (<b>b</b>) Prismatic layers effect.</p>
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<p>Contours of the LES Resolution Quality and shielding function fields for the SBES quality assessment of the PS injection test case.</p>
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<p>Fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS Mach number (<b>left</b>), static pressure (<b>center</b>), and Schlieren (<b>right</b>) contours for the uncooled vane.</p>
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<p>RANS spanwise-averaged isentropic Mach number results for the uncooled vane plotted against the non-dimensional curvilinear abscissa. Light-gray dashed lines indicate the positions of the film-cooling rows.</p>
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<p>Experimental and RANS spanwise-averaged heat transfer coefficient results for the uncooled vane plotted against the non-dimensional curvilinear abscissa. Light-gray dashed lines indicate the positions of the film-cooling rows. Experimental data were obtained from thin-film thermometry measurements along the vane midspan by Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars.</p>
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<p>Decay of turbulence intensity from the inlet for the different turbulence transition models: fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST model (<b>left</b>), <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>−</mo> <mi>R</mi> <msub> <mi>e</mi> <mi>θ</mi> </msub> </mrow> </semantics></math> model (<b>center</b>), and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <msub> <mi>k</mi> <mi>l</mi> </msub> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> model (<b>right</b>). The <math display="inline"><semantics> <mi>γ</mi> </semantics></math> model is not depicted as it performed similarly to the <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>−</mo> <mi>R</mi> <msub> <mi>e</mi> <mi>θ</mi> </msub> </mrow> </semantics></math> model.</p>
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<p>Heat transfer coefficient (vane surface) and intermittency (perpendicular plane) contours for the uncooled case using the <math display="inline"><semantics> <mi>γ</mi> </semantics></math> transition model. On the suction side (SS), the model switches from a laminar (intermittency = 0) to a turbulent (intermittency = 1) boundary layer, whereas on the pressure side (PS), it does not.</p>
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<p>Heat transfer coefficient and temperature contours for the uncooled case underlining the mainstream hot gas ingestion and re-injection behavior.</p>
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<p>Experimental and RANS spanwise-averaged heat transfer coefficient results for the PS injection vane plotted against the non-dimensional curvilinear abscissa. Light-gray dashed lines indicate the positions of the film-cooling rows. Experimental data were obtained from thin-film thermometry measurements along the vane midspan by Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars.</p>
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<p>Heat transfer coefficient (<b>left</b>) and coolant concentration (<b>right</b>) contours for the PS injection case. The mainstream hot gas ingestion and re-injection phenomena are visible from the streamlines on the suction side and their effect on the HTC. The penetration of the coolant in the freestream and the poor coverage on the PS are visible from the coolant concentration contours.</p>
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<p>Experimental and RANS spanwise-averaged heat transfer coefficient results for the SS injection vane plotted against the non-dimensional curvilinear abscissa. Light-gray dashed lines indicate the positions of the film-cooling rows. Experimental data were obtained from thin-film thermometry measurements along the vane midspan by Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars.</p>
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<p>Heat transfer coefficient (<b>left</b>) and coolant concentration (<b>right</b>) contours for the SS injection case. The mainstream hot gas ingestion and re-injection phenomena are visible from the PS streamlines and their effect on the HTC. The limited penetration of the coolant and the good coverage close to the holes are visible from the coolant concentration contours.</p>
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<p>Spanwise-averaged isentropic Mach number results for the (<b>a</b>) PS injection and (<b>b</b>) SS injection cases plotted against the non-dimensional curvilinear abscissa. Light-gray dashed lines indicate the positions of the film-cooling rows.</p>
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<p>Vorticity magnitude for PS injection case for RANS (<b>left</b>) and SBES (<b>right</b>). A detailed view of the velocity curl in the Z-direction is provided for the SBES in the vicinity of the PS film-cooling holes.</p>
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<p>Experimental, fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>−</mo> <mi>R</mi> <msub> <mi>e</mi> <mi>θ</mi> </msub> </mrow> </semantics></math> transition model, and SBES heat transfer coefficient and coolant mass fraction results for the PS injection case plotted against the non-dimensional curvilinear abscissa. Light-gray dashed lines indicate the positions of the film-cooling rows. Experimental data were obtained from thin-film thermometry measurements along the vane midspan by Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars. (<b>a</b>) Heat transfer coefficient. (<b>b</b>) Coolant mass fraction.</p>
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<p>Heat transfer coefficient (<b>left</b>) and coolant mass fraction (<b>right</b>) contours for PS injection case for the different simulation approaches: steady-state fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS versus unsteady scale-resolving SBES modeling.</p>
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<p>Experimental, fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>−</mo> <mi>R</mi> <msub> <mi>e</mi> <mi>θ</mi> </msub> </mrow> </semantics></math> transition model, and SBES heat transfer coefficient and coolant mass fraction results for the SS injection vane plotted against the non-dimensional curvilinear abscissa. Light-gray dashed lines indicate the positions of the film-cooling rows. Experimental data were obtained from thin-film thermometry measurements along the vane midspan by Fontaneto [<a href="#B29-fluids-09-00091" class="html-bibr">29</a>], with corresponding 6.8% uncertainty level bars. (<b>a</b>) Heat transfer coefficient. (<b>b</b>) Coolant mass fraction.</p>
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<p>Heat transfer coefficient (<b>left</b>) and coolant mass fraction (<b>right</b>) contours for SS injection case for the different simulation approaches: steady-state fully turbulent <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ω</mi> </mrow> </semantics></math> SST RANS versus unsteady scale-resolving SBES modeling.</p>
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10 pages, 913 KiB  
Article
Development, Survival and Reproduction of Nezara viridula (Hemiptera: Pentatomidae) in Sesame Cultivars and Implications for the Management
by Adrielly Karoliny de Lima, José Janduí Soares, Marcus Alvarenga Soares, José Cola Zanuncio, Carla de Lima Bicho and Carlos Alberto Domingues da Silva
Plants 2024, 13(8), 1060; https://doi.org/10.3390/plants13081060 - 9 Apr 2024
Viewed by 1486
Abstract
Sesame, an oilseed plant with multiple applications, is susceptible to infestations by the stink bug Nezara viridula (Linnaeus, 1758) (Hemiptera: Pentatomidae). This pest suctions the seeds of this plant and injects toxins into them. Possible sources of resistance on sesame cultivars are important [...] Read more.
Sesame, an oilseed plant with multiple applications, is susceptible to infestations by the stink bug Nezara viridula (Linnaeus, 1758) (Hemiptera: Pentatomidae). This pest suctions the seeds of this plant and injects toxins into them. Possible sources of resistance on sesame cultivars are important to manage this bug. The objective of this study was to evaluate the biological aspects of N. viridula fed on three sesame cultivars aiming to select possible resistance sources for integrated pest management (IPM) programs of this stinkbug. The experimental design used randomized blocks with three treatments and four replications, each with newly emerged N. viridula nymphs fed with sesame capsules of the cultivars BRS Anahí (T1), BRS Morena (T2) and BRS Seda (T3). Two to three green sesame capsules were supplied every two days per group of ten N. viridula nymphs as one replication until the beginning of the adult stage. Adults of this stinkbug were fed in the same manner as its nymphs but with mature sesame capsules until the end of the observations. Survival during each of the five instars and of the nymph stage of N. viridula with green sesame capsules was similar between cultivars, but the duration of the nymph stage was shorter with green capsules of the BRS Morena than with those of the BRS Anahí. The oviposition period, number of egg masses and eggs per female, and the percentage of nymphs hatched were higher with mature capsules of the sesame cultivar BRS Anahí and lower with the others. Nymphs did not hatch from eggs deposited by females fed mature seed capsules of the sesame cultivar BRS Morena, which may indicate a source of resistance against this stinkbug in this cultivar. The worldwide importance of N. viridula to sesame cultivation makes these results useful for breeding programs of this plant aiming to develop genotypes resistant to this bug. In addition, the BRS Morena is a cultivar already commercially available and can be recommended in places where there is a history of incidence of N. viridula, aiming to manage the populations of this pest. Full article
(This article belongs to the Special Issue Integrated Pest Management and Plants Health)
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Graphical abstract

Graphical abstract
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<p>Water (<b>a</b>) and oil (<b>b</b>) content, respectively, of immature capsules and mature seeds of sesame (<span class="html-italic">Sesamum indicum</span> L.) cultivars BRS Anahi, BRS Morena and BRS Seda. Bars followed by the same lowercase letter per treatment do not differ according to the Tukey test at 5% probability. Campina Grande, Paraíba state, Brazil, 2023.</p>
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<p>Weight of <span class="html-italic">Nezara viridula</span> (Hemiptera: Pentatomidae) adults fed with immature sesame capsules (fruits) of the cultivars BRS Anahi, BRS Morena and BRS Seda per sex (a) and cultivar (<b>b</b>). Campina Grande, Paraíba state, Brazil, 2023.</p>
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27 pages, 853 KiB  
Article
Overlapping Grid-Based Spectral Collocation Technique for Bioconvective Flow of MHD Williamson Nanofluid over a Radiative Circular Cylindrical Body with Activation Energy
by Musawenkosi Patson Mkhatshwa
Computation 2024, 12(4), 75; https://doi.org/10.3390/computation12040075 - 5 Apr 2024
Cited by 4 | Viewed by 1398
Abstract
The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal [...] Read more.
The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal circular cylinder placed in a porous medium with nonlinear mixed convection and thermal radiation, heat sink/source, variable fluid properties, activation energy with chemical and microbial reactions, and Brownian motion for both nanoparticles and microbes. The flow analysis has also been considered subject to velocity slips, suction/injection, and heat convective and zero mass flux constraints at the boundary. The governing equations have been converted to a non-dimensional form using similarity variables, and the overlapping grid-based spectral collocation technique has been executed to procure solutions numerically. The graphical interpretation of various pertinent variables in the flow profiles and physical quantities of engineering attentiveness is provided and discussed. The results reveal that NF flow is accelerated by nonlinear thermal convection, velocity slip, magnetic fields, and variable viscosity parameters but decelerated by the Williamson fluid and suction parameters. The inclusion of nonlinear thermal radiation and variable thermal conductivity helps to enhance the fluid temperature and heat transfer rate. The concentration of both nanoparticles and motile microbes is promoted by the incorporation of activation energy in the flow system. The contribution of microbial Brownian motion along with microbial reactions on flow quantities justifies the importance of these features in the dynamics of motile microbes. Full article
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<p>Flow model and physical coordinate system.</p>
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<p>Dividing the time solution domain into <math display="inline"><semantics> <mi>ϖ</mi> </semantics></math> non-overlapping sub-intervals.</p>
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<p>Dividing the spatial solution domain into <math display="inline"><semantics> <mi>ς</mi> </semantics></math> overlapping sub-intervals.</p>
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<p>Comparison of solution errors <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>f</mi> </msub> <mo>,</mo> <msub> <mi>E</mi> <mi>θ</mi> </msub> <mo>,</mo> <msub> <mi>E</mi> <mi>ϕ</mi> </msub> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mi>χ</mi> </msub> <mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>ξ</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ϖ</mi> <mo>=</mo> <mn>20</mn> <mo>.</mo> </mrow> </semantics></math> (<b>a</b>) Solution errors against iterations for the MD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>N</mi> <mi>η</mi> </msub> <mo>=</mo> <mn>100</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) Solution errors against iterations for the OMD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>&gt;</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>N</mi> <mi>η</mi> </msub> <mo>=</mo> <mn>10</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of residual error approximations for the case of MD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and OMD-BSLLM <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ς</mi> <mo>&gt;</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>ξ</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ϖ</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> for different nodes (<math display="inline"><semantics> <mrow> <mrow> <mo>[</mo> <msub> <mi>N</mi> <mi>η</mi> </msub> <mo>,</mo> <mi>ς</mi> <mo>]</mo> </mrow> <mo>=</mo> <mrow> <mo>[</mo> <mn>100</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <mn>50</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <mn>20</mn> <mo>,</mo> <mn>5</mn> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <mn>10</mn> <mo>,</mo> <mn>10</mn> <mo>]</mo> </mrow> </mrow> </semantics></math>).</p>
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<p>Dimensionless velocity profiles.</p>
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<p>Dimensionless velocity profiles.</p>
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<p>Dimensionless velocity profiles.</p>
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<p>Dimensionless temperature profiles.</p>
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<p>Dimensionless temperature profiles.</p>
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<p>Dimensionless nanoparticle concentration profiles.</p>
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<p>Dimensionless density of the motile microbe profiles.</p>
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<p>Dimensionless density of the motile microbe profiles.</p>
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<p>Dimensionless surface drag coefficient.</p>
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<p>Dimensionless surface drag coefficient.</p>
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<p>Dimensionless surface drag coefficient.</p>
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<p>Dimensionless Nusselt number.</p>
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<p>Dimensionless Nusselt number.</p>
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<p>Dimensionless density number of the motile microbes.</p>
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<p>Dimensionless density number of the motile microbes.</p>
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15 pages, 4027 KiB  
Article
Distributed Fiber Optic Vibration Signal Logging Well Production Fluid Profile Interpretation Method Research
by Yanan Guo, Wenming Yang, Xueqiang Dong, Lei Zhang, Yue Zhang, Yi Wang, Bo Yang and Rui Deng
Processes 2024, 12(4), 721; https://doi.org/10.3390/pr12040721 - 2 Apr 2024
Cited by 1 | Viewed by 1389
Abstract
Traditional logging methods need a lot of data support such as suction profile information, reservoir geological information, and production information of injection and extraction wells to calculate oil and gas production, which is a tedious and complicated process with low interpretation accuracy. Distributed [...] Read more.
Traditional logging methods need a lot of data support such as suction profile information, reservoir geological information, and production information of injection and extraction wells to calculate oil and gas production, which is a tedious and complicated process with low interpretation accuracy. Distributed fiber optic vibration signal logging is a technology that uses fiber optics to sense the vibration signals returned from different formations or well walls to analyze the surrounding formation characteristics or downhole events, which has the advantages of strong real-time monitoring results and high reliability of interpretation results. However, the currently distributed fiber optic vibration signal logging also fails to fully utilize the technical advantages to form a systematic production calculation process. Therefore, this paper proposes to use the K-means++ algorithm to divide the vibration signal frequency bands to represent different downhole events and use the amplitude mean curve envelope area of the reservoir-related frequency bands to calculate the relative production of each production formation. The experimental results correspond well with the relative water absorption data interpreted by conventional production logging, and the accuracy of production interpretation is high, which fills the gap of a production calculation method in the field of distributed fiber optic vibration signal logging in China and strongly promotes the development of the intelligent construction of oil and gas fields. Full article
(This article belongs to the Special Issue Application of Chemical Smart Manufacturing in Industry 4.0)
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<p>Schematic diagram of distributed optical fiber vibration signal monitoring technology.</p>
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<p>Well A distributed fiber optic vibration signal spectrogram.</p>
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<p>Distributed fiber vibration signal spectrum diagram.</p>
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<p>K-means++ algorithm was used to cluster distributed fiber vibration signal data.</p>
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<p>Three frequency band vibration signal curves.</p>
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<p>Secondary clustering partition.</p>
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<p>Quadratic clustering vibration signal curve.</p>
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<p>The spectrum diagram of well A divides frequency bands.</p>
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<p>The spectrum diagram of well B divides frequency bands.</p>
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<p>Comparison of practical application of clustering methods.</p>
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<p>Vibration curve of reservoir fluid flow frequency band in well B.</p>
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13 pages, 1524 KiB  
Article
Performance Comparison of High-Temperature Heat Pumps with Different Vapor Refrigerant Injection Techniques
by Yuqiang Yang, Yu Wang, Zhaoyang Xu, Baojiang Xie, Yong Hu, Jiatao Yu, Yehong Chen, Ting Zhang, Zhenneng Lu and Yulie Gong
Processes 2024, 12(3), 566; https://doi.org/10.3390/pr12030566 - 13 Mar 2024
Cited by 2 | Viewed by 1757
Abstract
In order to develop a highly efficient and stable high-temperature heat pump to realize high-efficient electrification in the industrial sector, performance of high-temperature heat pumps with a flash tank vapor injection and sub-cooler vapor injection are compared under different evaporation temperatures, condensation temperatures, [...] Read more.
In order to develop a highly efficient and stable high-temperature heat pump to realize high-efficient electrification in the industrial sector, performance of high-temperature heat pumps with a flash tank vapor injection and sub-cooler vapor injection are compared under different evaporation temperatures, condensation temperatures, compressor suction superheat degrees, subcooling degrees and compressor isentropic efficiencies. The results show that the COP, injection mass flow ratio and VHC of the FTVC are higher than those of the SVIC-0, SVIC-5, SVIC-10 and SVIC-20 under the same working conditions, while the discharge temperature of the FTVC is approximately equal to that of the SVIC-0 and lower than those of the SVIC-5, SVIC-10 and SVIC-20. When the evaporation temperature, the condensation temperature and injection pressure are 55 °C, 125 °C and 921.4 kPa, respectively, the system COP of the FTVC is 4.49, which is approximately 6.7%, 7.3%, 7.8% and 8.9% higher than those of the SVIC-0, SVIC-5, SVIC-10, and SVIC-20, respectively. Full article
(This article belongs to the Special Issue Smart Wearable Technology: Thermal Management and Energy Applications)
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<p>Principle diagram of the vapor injection heat pump with flash tank.</p>
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<p>Principle diagram of the vapor injection heat pump with sub-cooler.</p>
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<p>Performance comparison under different evaporation temperatures.</p>
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<p>Performance comparison under different condensation temperatures.</p>
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<p>Performance comparison under different suction superheat degrees.</p>
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<p>Performance comparison under different subcooling degrees.</p>
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<p>Performance comparison under different isentropic efficiencies.</p>
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26 pages, 45915 KiB  
Article
Analysis of a Novel Fluidic Oscillator under Several Dimensional Modifications
by Kavoos Karimzadegan, Masoud Mirzaei and Josep M. Bergada
Appl. Sci. 2024, 14(5), 1690; https://doi.org/10.3390/app14051690 - 20 Feb 2024
Cited by 1 | Viewed by 1253
Abstract
To activate the boundary layer in Active Flow Control (AFC) applications, the use of pulsating flow has notable energy advantages over constant blowing/suction jet injections. For a given AFC application, five parameters, jet location and width, inclination angle, frequency of injection, and the [...] Read more.
To activate the boundary layer in Active Flow Control (AFC) applications, the use of pulsating flow has notable energy advantages over constant blowing/suction jet injections. For a given AFC application, five parameters, jet location and width, inclination angle, frequency of injection, and the momentum coefficient, need to be tuned. Presently, two main devices are capable of injecting pulsating flow with a momentum coefficient sufficient to delay the boundary layer separation: these are zero-net-mass-flow Actuators (ZNMFAs) and fluidic oscillators (FOs). In the present study, a novel FO configuration is analyzed for the first time at relatively high Reynolds numbers, and fluid is considered to be incompressible. After obtaining the typical linear correlation between the incoming Reynolds number and the outlet flow oscillating frequency, the effects of dimensional modifications on outlet width and mixing chamber wedge inclination angle are addressed. Modifications of the outlet width were observed to create large variations in FO performance. The origin of self-sustained oscillations is also analyzed in the present manuscript and greatly helps in clarifying the forces acting on the jet inside the mixing chamber. In fact, we can conclude by saying that the current FO configuration is pressure-driven, although the mass flow forces appear to be much more relevant than in previously studied FO configurations. Full article
(This article belongs to the Special Issue Advances in Active and Passive Techniques for Fluid Flow Manipulation)
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<p>Fluidic oscillator mixing chamber main parameters.</p>
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<p>Main view of the computational domain used in the present study. (<b>a</b>) Computational domain overall view. (<b>b</b>) Mesh in the central part of the fluidic oscillator, upper view. (<b>c</b>) Upper feedback channel inlet, zoomed view of the mesh.</p>
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<p>Fluidic oscillator performance at Reynolds number Re = 54,595 and for the four different mesh densities considered. Outlet mass flow frequency (<b>a</b>). Outlet mass flow (<b>b</b>). Lower feedback channel mass flow (<b>c</b>). Stagnation pressure measured at the mixing chamber downwards converging wall (<b>d</b>).</p>
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<p>Fluidic oscillator outlet mass flow (<b>a</b>) and feedback channel lower outlet mass flow (<b>b</b>) for three different turbulence intensities (<math display="inline"><semantics> <mrow> <mn>0.01</mn> <mo>%</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.1</mn> <mo>%</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>%</mo> </mrow> </semantics></math>) at the FO inlet. The standard (STD) Reynolds number 54,595 was used in all cases.</p>
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<p>Three-dimensional mesh in the fluidic oscillator mixing chamber (<b>a</b>). Zoomed view of the 3D mesh in the upper feedback channel (<b>b</b>).</p>
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<p>Fluidic oscillator outlet mass flow (<b>a</b>). Unsteady pressure at the lower feedback channel outlet (<b>b</b>). Fast Fourier transformation of the unsteady FO outlet mass flow (<b>c</b>). Comparison between 2D and 3D CFD simulations. The standard (STD) Reynolds number of 54,595 was used in all these cases.</p>
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<p>Fluidic oscillator outlet unsteady mass flow (<b>a</b>) and feedback channel mass flow (<b>b</b>) as a function of the Reynolds number.</p>
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<p>Unsteady stagnation pressure measured at the mixing chamber lower inclined wall (<b>a</b>), time-averaged values and peak-to-peak amplitudes (<b>b</b>). Pressure momentum terms measured at the FC lower outlet (<b>c</b>) and their respective average values and peak-to-peak amplitudes (<b>d</b>). Dynamic mass flow momentum terms measured at the FC lower outlet (<b>e</b>), and their respective average values and peak-to-peak amplitudes (<b>f</b>). Instantaneous net momentum obtained when considering pressure and mass flow momentum terms at both FC outlets (<b>g</b>), average values, and the peak-to-peak amplitudes (<b>h</b>). All graphs consider the four Reynolds numbers studied.</p>
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<p>Instantaneous net momentum pressure and mass flow terms measured at the feedback channels outlet sections and for the minimum and maximum Reynolds numbers studied. (<b>a</b>) Reynolds number 27,483. (<b>b</b>) Reynolds number 68,707.</p>
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<p>Pressure and mass flow peak-to-peak net momentum amplitude measured at the feedback channels for the four Reynolds numbers evaluated.</p>
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<p>Fluidic oscillator internal velocity magnitude field (<b>a</b>,<b>c</b>) and pressure field (<b>b</b>,<b>d</b>). Minimum Reynolds number <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> </mrow> </semantics></math> 27,483 (<b>a</b>,<b>b</b>), and maximum Reynolds number <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> </mrow> </semantics></math> 68,707 (<b>c</b>,<b>d</b>).</p>
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<p>Fluidic oscillator internal velocity magnitude field (<b>a</b>,<b>c</b>) and pressure field (<b>b</b>,<b>d</b>). Minimum Reynolds number <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> </mrow> </semantics></math> 27,483 (<b>a</b>,<b>b</b>), and maximum Reynolds number <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> </mrow> </semantics></math> 68,707 (<b>c</b>,<b>d</b>).</p>
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<p>Fluidic oscillator outlet unsteady mass flow (<b>a</b>) and feedback channel mass flow (<b>b</b>) for the smallest (outlet 1), largest (outlet 6) and standard (STD) outlet widths evaluated.</p>
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<p>Unsteady stagnation pressure measured at the mixing chamber lower inclined wall (<b>a</b>), time-averaged values and peak-to-peak amplitudes (<b>b</b>). Pressure momentum terms measured at the FC lower outlet (<b>c</b>) and their respective average values and peak-to-peak amplitudes (<b>d</b>). Dynamic mass flow momentum terms measured at the FC lower outlet (<b>e</b>) and the instantaneous net momentum obtained when considering pressure and mass flow momentum terms at both FC outlets (<b>f</b>). All graphs consider three different outlet widths, the smallest (outlet 1), the standard case (STD) = (outlet 3), and the largest one (outlet 6) studied in the present study.</p>
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<p>Instantaneous momentum pressure and mass flow terms measured at both feedback channels outlet sections and for the minimum and maximum outlet widths studied. (<b>a</b>) Minimum outlet width (outlet 1). (<b>b</b>) Maximum outlet width (outlet 6).</p>
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<p>Fluidic oscillator velocity magnitude (<b>a</b>,<b>c</b>,<b>e</b>) and pressure fields (<b>b</b>,<b>d</b>,<b>f</b>), for the minimum (outlet 1) (<b>a</b>,<b>b</b>), standard (<b>c</b>,<b>d</b>), and maximum (outlet6) (<b>e</b>,<b>f</b>) outlet widths evaluated. Reynolds number is kept constant at Re = 54,595.</p>
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<p>Fluidic oscillator outlet unsteady mass flow (<b>a</b>) and feedback channel mass flow (<b>b</b>), for the smallest mixing chamber internal angle (Angle 1), the largest MC internal angle (Angle 3), and the standard case (STD).</p>
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<p>Unsteady stagnation pressure measured at the mixing chamber lower inclined wall (<b>a</b>). Pressure momentum term measured at the FC lower outlet (<b>b</b>). Dynamic mass flow momentum term measured at the FC lower outlet (<b>c</b>) and the instantaneous net momentum obtained when considering pressure and mass flow momentum terms at both FC outlets (<b>d</b>). All graphs consider three different MC angles, the smallest (Angle 1), the standard case (STD) and the largest one (Angle 3) studied in the present study.</p>
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<p>Unsteady stagnation pressure measured at the mixing chamber lower inclined wall (<b>a</b>). Pressure momentum term measured at the FC lower outlet (<b>b</b>). Dynamic mass flow momentum term measured at the FC lower outlet (<b>c</b>) and the instantaneous net momentum obtained when considering pressure and mass flow momentum terms at both FC outlets (<b>d</b>). All graphs consider three different MC angles, the smallest (Angle 1), the standard case (STD) and the largest one (Angle 3) studied in the present study.</p>
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<p>Instantaneous mass flow and pressure forces measured at both feedback channels outlet sections and for the smallest MC angle (Angle 1), the standard case (STD), and the largest MC angle (Angle 3) studied. (<b>a</b>) Mass flow momentum. (<b>b</b>) Pressure momentum.</p>
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<p>Fluidic oscillator internal velocity magnitude field (<b>a</b>,<b>c</b>) and pressure field (<b>b</b>,<b>d</b>). Minimum MC inclined angle (Angle 1) (<b>a</b>,<b>b</b>), Maximum MC inclined angle (Angle 3) (<b>c</b>,<b>d</b>).</p>
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<p>Unsteady mass flow and pressure forces measured at both feedback channel outlets and the overall forces acting on the jet; about half of a cycle is presented here. Baseline case configuration (STD) at <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> </mrow> </semantics></math> 54,595.</p>
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<p>Velocity and pressure fields at different timesteps along a half oscillation period. Baseline case (STD) at Re = 54,595.</p>
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26 pages, 53961 KiB  
Article
Numerical and Experimental Characterization of a Coanda-Type Industrial Air Amplifier
by Miguel Chávez-Módena, Alejandro Martinez-Cava, Sergio Marín-Coca and Leo González
Appl. Sci. 2024, 14(4), 1524; https://doi.org/10.3390/app14041524 - 14 Feb 2024
Cited by 1 | Viewed by 1289
Abstract
The performance of an industrial air amplifier is assessed through experimental and numerical characterization, with a focus on examining the influence of various operating conditions (isolated, “blowing,” and “suction” modes) and direct geometric scaling of the device within the specified range of the [...] Read more.
The performance of an industrial air amplifier is assessed through experimental and numerical characterization, with a focus on examining the influence of various operating conditions (isolated, “blowing,” and “suction” modes) and direct geometric scaling of the device within the specified range of the injection gap (δ) and the inlet pressure characteristic values. The findings underscore the presence of a linear trend of the entrained mass flow and a nonlinear decay of the amplification factor, both with notable sensitivity to the gap width. Numerical RANS simulations validate the experimental data, characterize the asymmetric flow downstream from the device, and facilitate the exploration of more complex scenarios. In this regard, scaling the device’s dimensions reveals an optimal aspect ratio between the minimum diameter (Dm) and δ to maximize the entrained mass flow. This research provides valuable insights into the behavior of air amplifiers, offering guidance for their design and application across various industrial contexts. Full article
(This article belongs to the Special Issue Advances in Active and Passive Techniques for Fluid Flow Manipulation)
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<p>Sketch of the EXAIR Super Air Amplifier 120024 operation (<b>left</b>) and static pressure contours on an operating condition (<b>right</b>).</p>
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<p>Geometrical parameters air amplifier geometry (<b>left</b>) and detailed view of the compressed flow inner duct and the Coanda nozzle gap clearance (<b>right</b>).</p>
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<p>Air tank (<b>left</b>) and details of its outflow pressure regulation control (<b>right</b>).</p>
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<p>Main dimensions of the Venturi tube (in mm).</p>
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<p>Assembly of the Venturi tube parts and methacrylate tube.</p>
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<p>Detail of the CNC milled Venturi tube constriction (<b>left</b>) and the air amplifier fitting (<b>right</b>).</p>
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<p>Experimental configurations based on the air amplifier location with respect to the Venturi tube constriction. Blowing mode (<b>upper image</b>) and suction mode (<b>lower image</b>). The locations of the pressure taps are marked with red dots, and the blue arrow indicates the flow direction.</p>
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<p>Details of the pressure tap inserts inside the Venturi tube.</p>
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<p>Full experimental blowing setup for the mass flow measurement.</p>
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<p>Electronic pressure scanning module and pressure line array.</p>
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<p>Differential pressure transducers used on the Venturi tube constriction section.</p>
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<p>Hot wire measurement setup (<b>left</b>) and three-component probe close-up view (<b>right</b>).</p>
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<p>Sketch of the computational domain and boundary conditions considered for the isolated case.</p>
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<p>Three different levels of detail of the mesh <math display="inline"><semantics> <msub> <mi>h</mi> <mn>2</mn> </msub> </semantics></math> at section <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> m.</p>
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<p>Geometry comparison between 3D (<b>left</b>) and axisymmetric (<b>right</b>) model.</p>
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<p>Blowing mode. High-pressure line volumetric mass flow, <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>c</mi> </msub> </semantics></math>; entrained volumetric mass flow, <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>o</mi> </msub> </semantics></math>; and amplification factor <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mi>o</mi> </msub> <mo>/</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> </mrow> </semantics></math>, against the total pressure measured at the inlet of the air amplifier <math display="inline"><semantics> <msub> <mi>p</mi> <msub> <mi>c</mi> <mn>0</mn> </msub> </msub> </semantics></math>.</p>
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<p>Suction mode. High-pressure line volumetric mass flow, <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>c</mi> </msub> </semantics></math>; entrained volumetric mass flow, <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>o</mi> </msub> </semantics></math>; and amplification factor <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mi>o</mi> </msub> <mo>/</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> </mrow> </semantics></math>, against the total pressure measured at the inlet of the ESAA <math display="inline"><semantics> <msub> <mi>p</mi> <msub> <mi>c</mi> <mn>0</mn> </msub> </msub> </semantics></math>.</p>
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<p>Wake velocity profile at three downstream transversal sections (from left to right columns, <math display="inline"><semantics> <mrow> <mi>X</mi> <mo>=</mo> <mn>2.5</mn> <mi>D</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>X</mi> <mo>=</mo> <mn>3.5</mn> <mi>D</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>X</mi> <mo>=</mo> <mn>4.5</mn> <mi>D</mi> </mrow> </semantics></math>, respectively). Streamwise (<span class="html-italic">u</span>), crossed-vertical (<span class="html-italic">v</span>) and crossed-horizontal (<span class="html-italic">w</span>) velocities are plotted from numerical (■) and experimental (<span style="color: #FF0000"><math display="inline"><semantics> <mrow> <mo>−</mo> <mo>•</mo> <mo>−</mo> </mrow> </semantics></math></span>) tests, including experimental standard deviation.</p>
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<p>Comparison of numerical and refined experimental velocity profiles at downstream section <math display="inline"><semantics> <mrow> <mi>X</mi> <mo>=</mo> <mn>3.5</mn> <mi>D</mi> </mrow> </semantics></math>. Mean values of streamwise velocity are plotted from numerical (■) and experimental (<span style="color: #FF0000"><math display="inline"><semantics> <mrow> <mo>−</mo> <mo>•</mo> <mo>−</mo> </mrow> </semantics></math></span>) tests. Red lines depict the standard deviation of the experimental data.</p>
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<p>Velocity magnitude streamlines at section <math display="inline"><semantics> <mrow> <mi>Y</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> m (<b>top</b>) and <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> m (<b>bottom</b>).</p>
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<p>Line integral convolution colored by local Mach number values at sections <math display="inline"><semantics> <mrow> <mi>X</mi> <mo>=</mo> <mn>1.2</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math> m (<b>left</b>) and <math display="inline"><semantics> <mrow> <mi>X</mi> <mo>=</mo> <mn>1.7</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> m (<b>right</b>).</p>
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<p>Mach number contours depicting supersonic regime across the injection gap and the Coanda profile. Flow data from simulations performed for <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>0.55</mn> </mrow> </semantics></math> MPa.</p>
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<p>Primary volumetric flow <math display="inline"><semantics> <msub> <mi>Q</mi> <mi>c</mi> </msub> </semantics></math> (<b>left</b>) and non-dimensional mass flow (<b>right</b>) at different primary flow pressure <math display="inline"><semantics> <msub> <mi>p</mi> <mi>c</mi> </msub> </semantics></math>. Gap clearance of <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.23</mn> </mrow> </semantics></math> mm.</p>
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<p>Mach number at different primary flow pressure <math display="inline"><semantics> <msub> <mi>p</mi> <mi>c</mi> </msub> </semantics></math> when the clearance is <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.23</mn> </mrow> </semantics></math> mm.</p>
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<p>Variation in the outlet volumetric flow rate (<b>top-left</b>), outlet/primary flow rate ratio (<b>top-right</b>), primary volumetric flow rate (<b>bottom-left</b>), and non-dimensional mass flow (<b>bottom-right</b>) for different values of the clearance distance value <math display="inline"><semantics> <mi>δ</mi> </semantics></math>.</p>
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<p>Variation in the outlet volumetric flow rate (<b>top-left</b>), outlet/primary flow rate ratio (<b>top-right</b>), primary volumetric flow rate (<b>bottom-left</b>), and non-dimensional mass flow (<b>bottom-right</b>) for different values of the clearance distance <math display="inline"><semantics> <mi>δ</mi> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>0.55</mn> </mrow> </semantics></math> MPa.</p>
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<p>Comparison of the numerical results obtained for a 3D and an axisymmetric simulation with <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>0.45</mn> </mrow> </semantics></math> MPa and <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.23</mn> </mrow> </semantics></math> mm. Contours of flow Mach number are shown in the <b>left image</b> for both cases, together with streamwise velocity distributions in the <b>right image</b>. The experimental data include the standard deviation of the measured values.</p>
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<p>Variation in the total (injected+entrained) mass flow, <math display="inline"><semantics> <msub> <mover accent="true"> <mi>m</mi> <mo>˙</mo> </mover> <mi>o</mi> </msub> </semantics></math>, with the relation between the inlet diameter <math display="inline"><semantics> <msub> <mi>D</mi> <mi>m</mi> </msub> </semantics></math> and the gap width, <math display="inline"><semantics> <mi>δ</mi> </semantics></math>, for two different gap values at <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>0.45</mn> </mrow> </semantics></math> MPa.</p>
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21 pages, 7902 KiB  
Article
An Unsteady Reynolds–Averaged Navier–Stokes–Large Eddy Simulation Study of Propeller–Airframe Interaction in Distributed Electric Propulsion
by Omkar Walvekar and Satyanarayanan Chakravarthy
Aerospace 2024, 11(1), 17; https://doi.org/10.3390/aerospace11010017 - 24 Dec 2023
Cited by 1 | Viewed by 1502
Abstract
A conceptual framework is presented to determine the improvement in the aerodynamic performance of a canard aircraft fitted with distributed propellers along its main wing. A preliminary study is described with four airframe–propeller configurations predominantly studied in academic and commercial designs. The leading [...] Read more.
A conceptual framework is presented to determine the improvement in the aerodynamic performance of a canard aircraft fitted with distributed propellers along its main wing. A preliminary study is described with four airframe–propeller configurations predominantly studied in academic and commercial designs. The leading edge–based tractors and trailing edge–based pushers are identified as configurations of interest for the main study. Subsequently, a Navier–Stokes solver is used to simulate the flow using two numerical approaches–a modified steady-state actuator disk and an unsteady rotating propeller profile. Moving meshes with rotating sub-domains are used with a hybrid RANS-LES-based turbulence model while the actuator disks are modified to include viscous swirl effects. The preliminary study shows a local minimum in the change in CL and CD at 10 for the pusher and tractor configurations. The main study then demonstrates the outperformance of the pushers over tractors quantified using CL and CL/CD. There is a clear preference for the pushers as they increase the lifting capacity of the aircraft without disproportionately increasing the drag due to the flow smoothening by the suction of the pusher propellers over the main wing. The pushers also delay the separation of the boundary layer whereas the tractors are unable to prevent the formation of the separation bubble despite injecting momentum through their slipstreams into the flow. The results from the two numerical approaches are then compared for accuracy in designing DEP configurations for an airframe. Full article
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<p>Geometry of the UAV airframe.</p>
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<p>Geometric details of the propeller. (<b>a</b>) Propeller geometry. (<b>b</b>) Chord and pitch profile of the propeller.</p>
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<p>Mesh for the UAV airframe and propellers for the rotating propeller approach. (<b>a</b>) Mesh for the UAV wall. (<b>b</b>) Mesh for the propeller blades. (<b>c</b>) Mesh refinement for the body of the UAV airframe.</p>
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<p>Validation study of the numerical setup for propeller performance. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math> vs. <span class="html-italic">J</span>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>Q</mi> </msub> </semantics></math> vs. <span class="html-italic">J</span>. (<b>c</b>) <math display="inline"><semantics> <mi>η</mi> </semantics></math> vs. <span class="html-italic">J</span>.</p>
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<p>Baseline performance of the propeller for the main study. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math> vs. <span class="html-italic">J</span>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>Q</mi> </msub> </semantics></math> vs. <span class="html-italic">J</span>. (<b>c</b>) <math display="inline"><semantics> <mi>η</mi> </semantics></math> vs. <span class="html-italic">J</span>.</p>
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<p>DEP configurations tested in the preliminary study. (<b>a</b>) Pushers. (<b>b</b>) Tractors. (<b>c</b>) Tractors with a tail rotor. (<b>d</b>) Tractors with a tail rotor and two tip rotors.</p>
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<p><math display="inline"><semantics> <msub> <mi>C</mi> <mi>L</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>D</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <mo>/</mo> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> curves for all configurations for the preliminary study. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>L</mi> </msub> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>D</mi> </msub> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <mo>/</mo> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p><math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>C</mi> <mi>L</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> with and without swirl effects for the preliminary study using the modified actuator disk approach. (<b>a</b>) Pusher configuration. (<b>b</b>) Tractor configuration.</p>
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<p>DEP configurations for the main study. (<b>a</b>) Tractor configuration. (<b>b</b>) Pusher configuration.</p>
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<p>Domain cross–sectional view with velocity contours normal to the first propeller plane for tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 10<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math> using the rotating propeller approach. The cross–sections of the canard and main wings are visible in the image.</p>
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<p>Aerodynamic performance of the UAV airframe, UAV–tractor configuration, and UAV–pusher configuration using rotating propeller approach. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>L</mi> </msub> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>C</mi> <mi>L</mi> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>D</mi> </msub> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <mo>/</mo> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>C</mi> <mi>L</mi> </msub> <mo>/</mo> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Instantaneous velocity contours normal to the first propeller plane using the rotating propeller approach. (<b>a</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 8<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>b</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 8<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>c</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 10<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>d</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 10<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>e</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 12<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>f</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 12<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>g</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 14<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>h</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 14<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>.</p>
Full article ">Figure 12 Cont.
<p>Instantaneous velocity contours normal to the first propeller plane using the rotating propeller approach. (<b>a</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 8<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>b</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 8<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>c</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 10<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>d</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 10<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>e</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 12<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>f</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 12<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>g</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 14<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>h</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 14<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>.</p>
Full article ">Figure 13
<p>Instantaneous velocity contours normal to the second propeller plane using the rotating propeller approach. (<b>a</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 8<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>b</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 8<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>c</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 10<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>d</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 10<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>e</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 12<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>f</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 12<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>g</b>) Tractor configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 14<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. (<b>h</b>) Pusher configuration at <math display="inline"><semantics> <mi>α</mi> </semantics></math> = 14<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>.</p>
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<p>Instantaneous lift curves for both configurations for one rotation using the rotating propeller approach. (<b>a</b>) Tractor configuration. (<b>b</b>) Pusher configuration.</p>
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<p>Instantaneous propeller streamlines using rotating propeller approach. (<b>a</b>) Tractor configuration. (<b>b</b>) Pusher configuration.</p>
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<p>Comparing the <math display="inline"><semantics> <msub> <mi>C</mi> <mi>L</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>D</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <mo>/</mo> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> results from the modified actuator disk approach and rotating propeller approach. (<b>a</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>L</mi> </msub> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <msub> <mi>C</mi> <mi>D</mi> </msub> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>L</mi> </msub> <mo>/</mo> <msub> <mi>C</mi> <mi>D</mi> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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18 pages, 2433 KiB  
Article
The Effects of Thermal Memory on a Transient MHD Buoyancy-Driven Flow in a Rectangular Channel with Permeable Walls: A Free Convection Flow with a Fractional Thermal Flux
by Nehad Ali Shah, Bander Almutairi, Dumitru Vieru and Ahmed A. El-Deeb
Fractal Fract. 2023, 7(9), 664; https://doi.org/10.3390/fractalfract7090664 - 1 Sep 2023
Viewed by 1011
Abstract
This study investigates the effects of magnetic induction, ion slip and Hall current on the flow of linear viscous fluids in a rectangular buoyant channel. In a hydro-magnetic flow scenario with permeable and conducting walls, one wall has a temperature variation that changes [...] Read more.
This study investigates the effects of magnetic induction, ion slip and Hall current on the flow of linear viscous fluids in a rectangular buoyant channel. In a hydro-magnetic flow scenario with permeable and conducting walls, one wall has a temperature variation that changes over time, while the other wall keeps a constant temperature; the research focuses on this situation. Asymmetric wall heating and suction/injection effects are also examined in the study. Using the Laplace transform, analytical solutions in the Laplace domain for temperature, velocity and induced magnetic field have been determined. The Stehfest approach has been used to find numerical solutions in the real domain by reversing Laplace transforms. The generalized thermal process makes use of an original fractional constitutive equation, in which the thermal flux is influenced by the history of temperature gradients, which has an impact on both the thermal process and the fluid’s hydro-magnetic behavior. The influence of thermal memory on heat transfer, fluid movement and magnetic induction was highlighted by comparing the solutions of the fractional model with the classic one based on Fourier’s law. Full article
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Figure 1

Figure 1
<p>Schematic representation of the flow domain (dimensionless coordinates).</p>
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<p>Time-variation on <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mi>Pr</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <msub> <mi>v</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>.</p>
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<p>The influence of <math display="inline"><semantics> <mi>α</mi> </semantics></math> on <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>Combined effects of the thermal memory and injection/suction on the fluid temperature.</p>
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<p>Effects of the thermal memory and injection/suction on the fluid temperature.</p>
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<p>Profiles <math display="inline"><semantics> <mrow> <mi>u</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>w</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for different values of the thermal memory parameter <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Profiles <math display="inline"><semantics> <mrow> <mi>u</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>w</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Profiles of the induced magnetic field <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mi>x</mi> </msub> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mi>z</mi> </msub> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, and for different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Profiles of the induced magnetic field <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mi>x</mi> </msub> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mi>z</mi> </msub> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, and for different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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