[go: up one dir, main page]

 
 
Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (243)

Search Parameters:
Keywords = fully coupled numerical model

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
19 pages, 6733 KiB  
Article
Multidisciplinary Design Optimization of Alignment and Whirling Vibration Characteristics of a Submarine Propulsion Shafting Using Kriging Surrogate Model
by Zheng Gu and Jinlin Liu
J. Mar. Sci. Eng. 2024, 12(10), 1812; https://doi.org/10.3390/jmse12101812 - 11 Oct 2024
Viewed by 330
Abstract
To improve the performance indexes, such as safety, reliability and acoustic stealth, of a submarine, it is significant to optimize the dynamic characteristics of its propulsion shafting. The alignment state of a shafting has a coupling effect on its whirling vibration characteristics, and [...] Read more.
To improve the performance indexes, such as safety, reliability and acoustic stealth, of a submarine, it is significant to optimize the dynamic characteristics of its propulsion shafting. The alignment state of a shafting has a coupling effect on its whirling vibration characteristics, and the multidisciplinary design optimization (MDO) theory can fully consider the coupling relationships between different disciplines like this, which is a scientific and effective method to achieve the design optimization of shafting dynamics. However, the iterative calculation of high-precision numerical models greatly restricts the optimization efficiency of this method. Aiming at this problem, in this paper, an MDO model was established based on the coupling dynamic analysis of submarine propulsion shafting, and the Kriging surrogate model was used to predict the state variables within each subdiscipline. Along with the reduction of computational expense, the MDO of the alignment and whirling vibration characteristics of the shafting was achieved. The studied results can be applied to the design process of submarine propulsion shafting, which can provide technical and theoretical support for improving the optimization efficiency of its coupling dynamics. Full article
(This article belongs to the Section Ocean Engineering)
Show Figures

Figure 1

Figure 1
<p>Layout diagram of a submarine propulsion shafting.</p>
Full article ">Figure 2
<p>Finite-element analysis model of shafting.</p>
Full article ">Figure 3
<p>Deflection and bending stress distribution of shafting in straight-line alignment state. (<b>a</b>) Deflection distribution (mm); (<b>b</b>) bending stress distribution (MPa).</p>
Full article ">Figure 4
<p>Deflection and bending stress distribution of shafting in rational alignment state. (<b>a</b>) Deflection distribution (mm); (<b>b</b>) bending stress distribution (MPa).</p>
Full article ">Figure 5
<p>Campbell diagram.</p>
Full article ">Figure 6
<p>First three modal shapes of whirling vibration. (<b>a</b>) First order; (<b>b</b>) second order; and (<b>c</b>) third order.</p>
Full article ">Figure 6 Cont.
<p>First three modal shapes of whirling vibration. (<b>a</b>) First order; (<b>b</b>) second order; and (<b>c</b>) third order.</p>
Full article ">Figure 7
<p>Amplitude–frequency response curves of whirling vibration under different alignment states. (<b>a</b>) Straight-line alignment state; (<b>b</b>) rational alignment state.</p>
Full article ">Figure 8
<p>Coupling relationships between subdisciplines.</p>
Full article ">Figure 9
<p>MDO framework using Kriging model.</p>
Full article ">Figure 10
<p>Establishment process of surrogate model.</p>
Full article ">Figure 11
<p>Sample set obtained by LHS.</p>
Full article ">Figure 12
<p>Predicted results of state variables within alignment subdiscipline. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>|</mo> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mn>3</mn> </msub> </mrow> </semantics></math>; and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 12 Cont.
<p>Predicted results of state variables within alignment subdiscipline. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>|</mo> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mn>3</mn> </msub> </mrow> </semantics></math>; and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p>Predicted results of state variables within vibration and strength subdisciplines. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>a</mi> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>b</mi> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mn>1</mn> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math>; and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mn>2</mn> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 14
<p>Pareto fronts. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>a</mi> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>a</mi> </msub> <mo>−</mo> <mo>|</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>|</mo> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>b</mi> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>b</mi> </msub> <mo>−</mo> <mo>|</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>|</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 15
<p>Comparison of amplitude-frequency response of whirling vibration at monitoring points before and after MDO. (<b>a</b>) Point a; (<b>b</b>) Point b.</p>
Full article ">
20 pages, 14040 KiB  
Article
Shock Wave and Aeroelastic Coupling in Overexpanded Nozzle
by Haifeng Hu, Xinni Gao, Yushan Gao and Jianwen Yang
Aerospace 2024, 11(10), 818; https://doi.org/10.3390/aerospace11100818 - 7 Oct 2024
Viewed by 446
Abstract
The growing demand for increasing the engine power of a liquid rocket is driving the development of high-power De-Laval nozzles, which is primarily achieved by increasing the expansion ratio. A high-expansion-ratio for De-Laval nozzles can cause flow separation, resulting in unsteady, asymmetric forces [...] Read more.
The growing demand for increasing the engine power of a liquid rocket is driving the development of high-power De-Laval nozzles, which is primarily achieved by increasing the expansion ratio. A high-expansion-ratio for De-Laval nozzles can cause flow separation, resulting in unsteady, asymmetric forces that can limit nozzle life. To enhance nozzle performance, various separation control methods have been proposed, but no methods have been fully implemented thus far due to the uncertainties associated with simulating flow phenomena. A numerical study of a high-area-ratio rocket engine is performed to analyze the aeroelastic performance of its structure under flow separation conditions. Based on numerical methodology, the flow inside a rocket nozzle (the VOLVO S1) is analyzed, and different separation patterns are comprehensively discussed, including both free shock separation (FSS) and restricted shock separation (RSS). Since the location of the flow separation point strongly depends on the turbulence model, both the single transport equation and two-transport-equation turbulence models are simulated, and the findings are compared with the experimental results. Therefore, the Spalart–Allmaras (SA) turbulence model is the ideal choice for this rocket nozzle geometry. A wavelet is used to analyze the amplitude frequencies from 0 to 100 Hz under various pressure fluctuation conditions. Based on a clear understanding of the flow field, an aeroelastic coupling method is carried out with loosely coupled computational fluid dynamics (CFD)/computational structural dynamics (CSD). Some insights into the aeroelasticity of the nozzle under separated flow conditions are obtained. The simulation results show the significant impact of the structural response on the inherent pressure pulsation characteristics resulting from flow separation. Full article
(This article belongs to the Section Aeronautics)
Show Figures

Figure 1

Figure 1
<p>Sketch of the FSS/RSS flow separation patterns.</p>
Full article ">Figure 2
<p>Fluid computational domain with boundary conditions.</p>
Full article ">Figure 3
<p>Distributions of the pressure for different turbulence models.</p>
Full article ">Figure 4
<p>The contours of the velocity for different turbulence models.</p>
Full article ">Figure 5
<p>The nozzle wall pressure left the NPR =14 and right NPR = 16.</p>
Full article ">Figure 6
<p>Mach number contours of the FSS and RSS for VOLVO S1 nozzle (up NPR = 16, RSS; down NPR = 14, FSS).</p>
Full article ">Figure 7
<p>Calculated different velocity contours in the VOLVO S1 nozzle at different pressure ratios.</p>
Full article ">Figure 8
<p>The sketch of the FSS model inside the nozzle.</p>
Full article ">Figure 9
<p>Wall pressures during the different NPR of the FSS model.</p>
Full article ">Figure 10
<p>VOLVO S1 Mach number contour lines during the different NPR when the RSS model.</p>
Full article ">Figure 11
<p>Wall pressures during the different NPR of the RSS model.</p>
Full article ">Figure 12
<p>Lateral side-load force and pressure ratio NPR curve.</p>
Full article ">Figure 13
<p>The pressure variation curve over time at each monitoring point in the nozzle.</p>
Full article ">Figure 14
<p>Schematic diagram showing the monitoring point data’s wavelet analysis results.</p>
Full article ">Figure 15
<p>The grid of the nozzle.</p>
Full article ">Figure 16
<p>The frequency of the different model.</p>
Full article ">Figure 17
<p>Thirty modes shapes of the nozzle deformed model.</p>
Full article ">Figure 18
<p>The parameters were exchanged between two codes(CFD and CSD).</p>
Full article ">Figure 19
<p>Initial exchange and resulting coupling algorithms for two codes with “exchange before solution”.</p>
Full article ">Figure 20
<p>The flow chart of the loosed-coupled analysis.</p>
Full article ">Figure 21
<p>The deform of the nozzle during the different times.</p>
Full article ">Figure 22
<p>Point at the end of the deformation in the radial direction vs. time.</p>
Full article ">
17 pages, 13170 KiB  
Article
Continuous Casting Slab Mold: Key Role of Nozzle Immersion Depth
by Liang Chen, Xiqing Chen, Pu Wang and Jiaquan Zhang
Materials 2024, 17(19), 4888; https://doi.org/10.3390/ma17194888 - 5 Oct 2024
Viewed by 382
Abstract
Based on a physical water model with a scaling factor of 0.5 and a coupled flow–heat transfer–solidification numerical model, this study investigates the influence of the submerged entry nozzle (SEN) depth on the mold surface behavior, slag entrapment, internal flow field, temperature distribution, [...] Read more.
Based on a physical water model with a scaling factor of 0.5 and a coupled flow–heat transfer–solidification numerical model, this study investigates the influence of the submerged entry nozzle (SEN) depth on the mold surface behavior, slag entrapment, internal flow field, temperature distribution, and initial solidification behavior in slab casting. The results indicate that when the SEN depth is too shallow (80 mm), the slag layer on the narrow face is thin, leading to slag entrapment. Within a certain range of SEN depths (less than 170 mm), increasing the SEN depth reduces the impact on the mold walls, shortening the “plateau period” of stagnated growth on the narrow face shell. This allows the upper recirculation flow to develop more fully, resulting in an increase in the surface flow velocity and an expansion in the high-temperature region near the meniscus, which promotes uniform slag melting but also heightens the risk of slag entrainment due to shear stress at the liquid surface (with 110 mm being the most stable condition). As the SEN depth continues to increase, the surface flow velocity gradually decreases, and the maximum fluctuation in the liquid surface diminishes, while the full development of the upper recirculation zone leads to a higher and more uniform meniscus temperature. This suggests that in practical production, it is advisable to avoid this critical SEN depth. Instead, the immersion depth should be controlled at a slightly shallower position (around 110 mm) or a deeper position (around 190 mm). Full article
(This article belongs to the Special Issue Advanced Metallurgy Technologies: Physical and Numerical Modelling)
Show Figures

Figure 1

Figure 1
<p>Physical model experimental device: (<b>a</b>) schematic diagram; (<b>b</b>) physical map.</p>
Full article ">Figure 2
<p>Position diagram of liquid level fluctuation (1#–3#) and surface velocity measurement (4#–6#).</p>
Full article ">Figure 3
<p>Geometric model of mold calculation domain.</p>
Full article ">Figure 4
<p>Submerged entry nozzle and mold grid division diagram: (<b>a</b>) submerged entry nozzle; (<b>b</b>) mold calculation domain.</p>
Full article ">Figure 5
<p>Different SEN depths of molten steel flow trajectory tracer: (<b>a</b>) 80 mm; (<b>b</b>) 110 mm; and (<b>c</b>) 140 mm.</p>
Full article ">Figure 6
<p>Surface velocity distribution curves at different SEN depths.</p>
Full article ">Figure 7
<p>Effects of different SEN depths on liquid level fluctuation.</p>
Full article ">Figure 8
<p>Mold flux coverage at different SEN depths at casting speed of 1.1 m/min.</p>
Full article ">Figure 9
<p>Velocity distribution on line-up at different SEN depths.</p>
Full article ">Figure 10
<p>Velocity distribution and streamline diagram of characteristic surface X = 0 m: (<b>a</b>) SEN depth of 110 mm; (<b>b</b>) SEN depth of 130 mm; (<b>c</b>) SEN depth of 150 mm; (<b>d</b>) SEN depth of 170 mm; and (<b>e</b>) SEN depth of 190 mm.</p>
Full article ">Figure 11
<p>Velocity contour of free surface: (<b>a</b>) SEN depth of 110 mm; (<b>b</b>) SEN depth of 130 mm; (<b>c</b>) SEN depth of 150 mm; (<b>d</b>) SEN depth of 170 mm; and (<b>e</b>) SEN depth of 190 mm.</p>
Full article ">Figure 12
<p>Fluctuations in mold free surface: (<b>a</b>) SEN depth of 110 mm; (<b>b</b>) SEN depth of 130 mm; (<b>c</b>) SEN depth of 150 mm; (<b>d</b>) SEN depth of 170 mm; and (<b>e</b>) SEN depth of 190 mm.</p>
Full article ">Figure 13
<p>Temperature field distribution of free surface in mold: (<b>a</b>) SEN depth of 110 mm; (<b>b</b>) SEN depth of 130 mm; (<b>c</b>) SEN depth of 150 mm; (<b>d</b>) SEN depth of 170 mm; and (<b>e</b>) SEN depth of 190 mm.</p>
Full article ">Figure 14
<p>Distribution of shell thickness along casting direction on wide and narrow faces of mold at different SEN depths: (<b>a</b>) narrow face; (<b>b</b>) wide face.</p>
Full article ">
13 pages, 390 KiB  
Article
Magnetohydrodynamic Analysis and Fast Calculation for Fractional Maxwell Fluid with Adjusted Dynamic Viscosity
by Yi Liu and Mochen Jiang
Magnetochemistry 2024, 10(10), 72; https://doi.org/10.3390/magnetochemistry10100072 - 29 Sep 2024
Viewed by 343
Abstract
From the perspective of magnetohydrodynamics (MHD), the heat transfer properties of Maxwell fluids under MHD conditions with modified dynamic viscosity present complex challenges in numerical simulations. In this paper, we develop a time-fractional coupled model to characterize the heat transfer and MHD flow [...] Read more.
From the perspective of magnetohydrodynamics (MHD), the heat transfer properties of Maxwell fluids under MHD conditions with modified dynamic viscosity present complex challenges in numerical simulations. In this paper, we develop a time-fractional coupled model to characterize the heat transfer and MHD flow of Maxwell fluid with consideration of the Hall effect and Joule heating effect and incorporating a modified dynamic viscosity. The fractional coupled model is numerically solved based on the L1-algorithm and the spectral collocation method. We introduce a novel approach that integrates advanced algorithms with a fully discrete scheme, focusing particularly on the computational cost. Leveraging this approach, we aim to significantly enhance computational efficiency while ensuring accurate representation of the underlying physics. Through comprehensive numerical experiments, we explain the thermodynamic behavior in the MHD flow process and extensively examine the impact of various critical parameters on both MHD flow and heat transfer. We establish an analytical framework for the MHD flow and heat transfer processes, further investigate the influence of magnetic fields on heat transfer processes, and elucidate the mechanical behavior of fractional Maxwell fluids. Full article
(This article belongs to the Special Issue Advances in Multifunctional Magnetic Nanomaterial)
Show Figures

Figure 1

Figure 1
<p>Schematic diagram of the physical model.</p>
Full article ">Figure 2
<p>Computational times required by the direct method and fast method.</p>
Full article ">Figure 3
<p>Exact solutions and numerical solutions obtained with the direct method and fast method for velocity <span class="html-italic">v</span> (first row) and temperature <math display="inline"><semantics> <mi>θ</mi> </semantics></math> (second row).</p>
Full article ">Figure 4
<p>Effects of <math display="inline"><semantics> <msub> <mi>ϵ</mi> <mi>v</mi> </msub> </semantics></math> on the distributions of velocity <span class="html-italic">v</span> and temperature <math display="inline"><semantics> <mi>θ</mi> </semantics></math> at <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="false">¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>Effects of <math display="inline"><semantics> <msub> <mi>ϵ</mi> <mi>T</mi> </msub> </semantics></math> on the distributions of velocity <span class="html-italic">v</span> and temperature <math display="inline"><semantics> <mi>θ</mi> </semantics></math> at <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="false">¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>Effects of <span class="html-italic">m</span> on the distributions of velocity <span class="html-italic">v</span> and temperature <math display="inline"><semantics> <mi>θ</mi> </semantics></math> at <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>T</mi> <mo stretchy="false">¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">
15 pages, 1662 KiB  
Communication
A Fully Implicit Coupled Scheme for Mixed Elastohydrodynamic Problems on Co-Allocated Grids
by Sören Wettmarshausen and Hubert Schwarze
Lubricants 2024, 12(9), 322; https://doi.org/10.3390/lubricants12090322 - 19 Sep 2024
Viewed by 392
Abstract
In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme [...] Read more.
In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme uses finite-volume discretization and co-allocated grids for hydrodynamic pressure and elastic deformation. To provide strong coupling between pressure and deformation even in the highly loaded zone, a correction term that adds numerical diffusion is used. The resulting linear equation system of this scheme can be efficiently solved by Krylov subspace methods. This results in an improved accuracy and computational efficiency compared to the existing methods. This approach was validated and has been shown to be accurate. Full article
(This article belongs to the Special Issue Advances in Mixed Lubrication)
Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Spatial discretization on a co-allocated Cartesian grid.</p>
Full article ">Figure 2
<p>Sparsity pattern for a 8 × 8 grid: (<b>a</b>) smooth case; (<b>b</b>) rough case.</p>
Full article ">Figure 3
<p>(<b>a</b>) Surface height distribution of the generated surface; (<b>b</b>) flow factors and contact pressure for the rough case.</p>
Full article ">Figure 4
<p>Mesh study for the smooth case: (<b>a</b>) pressure; (<b>b</b>) minimum fill thickness; (<b>c</b>) maximum pressure.</p>
Full article ">Figure 5
<p>Central film thickness for various loads and viscosity–pressure coefficient combinations.</p>
Full article ">Figure 6
<p>Rough case results: (<b>a</b>) hydrodynamic pressure; (<b>b</b>) contact pressure; (<b>c</b>) gap height.</p>
Full article ">Figure 7
<p>Comparison of pressure and gap height for smooth and rough cases along x.</p>
Full article ">Figure 8
<p>Convergence history for the smooth test case.</p>
Full article ">
12 pages, 669 KiB  
Article
Predictions of the Effect of Non-Homogeneous Ocean Bubbles on Sound Propagation
by Yuezhu Cheng, Jie Shi, Yuan Cao and Haoyang Zhang
J. Mar. Sci. Eng. 2024, 12(9), 1510; https://doi.org/10.3390/jmse12091510 - 2 Sep 2024
Viewed by 580
Abstract
In the ocean, bubbles rarely appear alone and are often not evenly distributed, which makes it complicated to predict the effect of ocean bubbles on sound propagation. To solve this problem, researchers have tried to use approximations such as equivalent and multiple scattering [...] Read more.
In the ocean, bubbles rarely appear alone and are often not evenly distributed, which makes it complicated to predict the effect of ocean bubbles on sound propagation. To solve this problem, researchers have tried to use approximations such as equivalent and multiple scattering models, but these approximations are accompanied by large errors. Therefore, we propose a semi-numerical and semi-analytical calculation method for underwater sound fields containing non-homogeneous bubbles in this paper. Based on the attenuation cross section and scattering cross section of a single bubble, the non-homogeneous medium is divided into multiple layers of uniform medium. Each layer of the bubble group is regarded as a whole, which can fully reflect the influence of bubble group vibration and scattering on sound wave propagation and is conducive to faster calculation of the sound field of non-homogeneous bubbly liquids. Compared with the classic coupling model, the calculation process of this method is simpler and faster, which solves the problem of fast calculation of sound fields in bubbly liquids and simulation of distributed bubble groups containing non-homogeneous distributed bubbles. Full article
Show Figures

Figure 1

Figure 1
<p>Schematic diagram of the division of bubbly liquids.</p>
Full article ">Figure 2
<p>Simulation process of multiple bubble layer model.</p>
Full article ">Figure 3
<p>The comparison of sound pressure simulation results between the multiple bubble layer model and the coupling model.</p>
Full article ">Figure 4
<p>The attenuation coefficients of bubble layers.</p>
Full article ">Figure 5
<p>Sound pressure distributions where bubbles are homogeneous distributed in bubbly liquids (colors mean amplitudes), <math display="inline"><semantics> <msub> <mi>p</mi> <mn>0</mn> </msub> </semantics></math> = 10 kPa, <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math> = 60 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m, <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (pure water), (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>Sound pressure distributions where bubbles are distributed on a gradient in bubbly liquids. (<b>a</b>) Increasing distribution, (<b>b</b>) decreasing distribution.</p>
Full article ">Figure 7
<p>Numerical simulations with different distributions of bubbles in a bubbly liquid. (<b>a</b>) Same quantity distribution, (<b>b</b>) Gaussian distribution, (<b>c</b>) Power exponent distribution, and (<b>d</b>) the received backscattering sound pressure at the origin.</p>
Full article ">
17 pages, 8083 KiB  
Article
Prediction of Ground Subsidence Induced by Groundwater Mining Using Three-Dimensional Variable-Parameter Fully Coupled Simulation
by Jingjing Du, Yan Zhang, Zujiang Luo and Chenghang Zhang
Water 2024, 16(17), 2487; https://doi.org/10.3390/w16172487 - 1 Sep 2024
Viewed by 730
Abstract
In order to predict the ground settlement in a scientific, intuitive, and simple way, based on the theory of Bio-consolidation, a three-dimensional fluid-solid coupled numerical calculation programme FGS-3D for ground settlement was compiled by using the Fortran 95 language, and a front-end operation [...] Read more.
In order to predict the ground settlement in a scientific, intuitive, and simple way, based on the theory of Bio-consolidation, a three-dimensional fluid-solid coupled numerical calculation programme FGS-3D for ground settlement was compiled by using the Fortran 95 language, and a front-end operation platform was developed by using Microsoft VisualBasic, so that a three-dimensional variable-parameter fully coupled viscoelastic-plastic model of ground settlement was constructed using the city of Yancheng as an example, and the development of ground settlement and horizontal displacement changes from 2021 to 2030 were predicted. The results show that the three-dimensional fully coupled finite-element numerical model of building load, groundwater seepage, and soil deformation established by the above computer development program can directly create a hydrogeological conceptual model of groundwater mining and predict ground settlement, so as to achieve the visualisation of the three-dimensional seepage of groundwater and the fully coupled simulation of ground subsidence in the whole process of groundwater mining. Under the joint action of construction load and groundwater mining, the water level of the aquifer in Yancheng City rises by 1.26 m on average in the main groundwater mining area of the group III pressurised aquifer, forming two smaller landing funnels, and the lowest water level of the two landing funnels is −15 m. Full article
(This article belongs to the Special Issue Studies on Water Resource and Environmental Policies)
Show Figures

Figure 1

Figure 1
<p>Block diagram of the structure of the free surface iteration algorithm.</p>
Full article ">Figure 2
<p>Block diagram of the iterative algorithm for viscoplastic-elastic-plastic stress analysis.</p>
Full article ">Figure 3
<p>Block diagram of the fully coupled analysis procedure.</p>
Full article ">Figure 4
<p>Functions of software modules.</p>
Full article ">Figure 5
<p>Grid subdivision stereogram of the study area.</p>
Full article ">Figure 6
<p>Parameter zoning diagram of the third confined aquifer.</p>
Full article ">Figure 7
<p>Calculated flow field diagram of the third confined aquifer on 31 December 2016.</p>
Full article ">Figure 8
<p>Calculated flow field diagram of the third confined aquifer on 31 December 2018.</p>
Full article ">Figure 9
<p>Map of cumulative land subsidence from 2016 to 2018.</p>
Full article ">Figure 10
<p>Fitted map of ground subsidence at level observation points from 2016 to 2018.</p>
Full article ">Figure 11
<p>Isocontour map of forecasted water levels of the third confined aquifer on 31 December 2030 (m).</p>
Full article ">Figure 12
<p>Isocontour map of the compressive capacity prediction of the third confined aquifer on 31 December 2030 (mm).</p>
Full article ">Figure 13
<p>Projected horizontal displacement of the third confined aquifer on 31 December 2030 (m).</p>
Full article ">Figure 14
<p>Contour map of the predicted cumulative land subsidence from 2021 to 2030 (mm).</p>
Full article ">
37 pages, 8170 KiB  
Review
Review of Computational Fluid Dynamics in the Design of Floating Offshore Wind Turbines
by Rizwan Haider, Xin Li, Wei Shi, Zaibin Lin, Qing Xiao and Haisheng Zhao
Energies 2024, 17(17), 4269; https://doi.org/10.3390/en17174269 - 26 Aug 2024
Cited by 1 | Viewed by 1235
Abstract
The growing interest in renewable energy solutions for sustainable development has significantly advanced the design and analysis of floating offshore wind turbines (FOWTs). Modeling FOWTs presents challenges due to the considerable coupling between the turbine’s aerodynamics and the floating platform’s hydrodynamics. This review [...] Read more.
The growing interest in renewable energy solutions for sustainable development has significantly advanced the design and analysis of floating offshore wind turbines (FOWTs). Modeling FOWTs presents challenges due to the considerable coupling between the turbine’s aerodynamics and the floating platform’s hydrodynamics. This review paper highlights the critical role of computational fluid dynamics (CFD) in enhancing the design and performance evaluation of FOWTs. It thoroughly evaluates various CFD approaches, including uncoupled, partially coupled, and fully coupled models, to address the intricate interactions between aerodynamics, hydrodynamics, and structural dynamics within FOWTs. Additionally, this paper reviews a range of software tools for FOWT numerical analysis. The research emphasizes the need to focus on the coupled aero-hydro-elastic models of FOWTs, especially in response to expanding rotor diameters. Further research should focus on developing nonlinear eddy viscosity models, refining grid techniques, and enhancing simulations for realistic sea states and wake interactions in floating wind farms. The research aims to familiarize new researchers with essential aspects of CFD simulations for FOWTs and to provide recommendations for addressing challenges. Full article
Show Figures

Figure 1

Figure 1
<p>FOWT components [<a href="#B34-energies-17-04269" class="html-bibr">34</a>,<a href="#B35-energies-17-04269" class="html-bibr">35</a>].</p>
Full article ">Figure 2
<p>Coupling of FOWTs.</p>
Full article ">Figure 3
<p>Types of FOWT platforms [<a href="#B35-energies-17-04269" class="html-bibr">35</a>].</p>
Full article ">Figure 4
<p>Wind turbines: operational regions and control objectives. Reproduced with permission from [<a href="#B8-energies-17-04269" class="html-bibr">8</a>], Elsevier, 2022.</p>
Full article ">Figure 5
<p>Platform types [<a href="#B58-energies-17-04269" class="html-bibr">58</a>].</p>
Full article ">Figure 6
<p>FOWT platform stability triangle [<a href="#B62-energies-17-04269" class="html-bibr">62</a>].</p>
Full article ">Figure 7
<p>Quasi-static mooring model: (<b>a</b>) single line element, and (<b>b</b>) multi-segment line element.</p>
Full article ">Figure 8
<p>Dynamic mooring models: (<b>a</b>) lumped mass, and (<b>b</b>) finite element.</p>
Full article ">Figure 9
<p>FOWT numerical structure.</p>
Full article ">Figure 10
<p>Wind turbine actuator representations for aerodynamics: (<b>a</b>) wind turbine, (<b>b</b>) AD, (<b>c</b>) AL, and (<b>d</b>) AS. Note: In the figure, the symbol D represent diameter.</p>
Full article ">Figure 10 Cont.
<p>Wind turbine actuator representations for aerodynamics: (<b>a</b>) wind turbine, (<b>b</b>) AD, (<b>c</b>) AL, and (<b>d</b>) AS. Note: In the figure, the symbol D represent diameter.</p>
Full article ">Figure 11
<p>FOWT computational mesh. (<b>A</b>) Computational domain, (<b>B</b>) entire turbine model with overset region, and (<b>C</b>) close view of turbine parts and platform surface mesh. Adapted with permission from [<a href="#B24-energies-17-04269" class="html-bibr">24</a>], John Wiley and Sons, 2017.</p>
Full article ">Figure 12
<p>FOWT vorticity contours. Adapted with permission from [<a href="#B212-energies-17-04269" class="html-bibr">212</a>], Elsevier, 2016.</p>
Full article ">Figure 13
<p>(<b>a</b>) Sketch of FOWT domain and (<b>b</b>) computational grid for the domain. Adapted with permission from [<a href="#B224-energies-17-04269" class="html-bibr">224</a>], Elsevier, 2023.</p>
Full article ">Figure 14
<p>Flow field and vortex close to wind turbine: (<b>a</b>) T/6; (<b>b</b>) T/3; (<b>c</b>) T/2; (<b>d</b>) 2T/3; (<b>e</b>) 5T/6; and (<b>f</b>) T. Adapted with permission from [<a href="#B224-energies-17-04269" class="html-bibr">224</a>], Elsevier, 2023.</p>
Full article ">
21 pages, 6521 KiB  
Article
AI-Driven Model Prediction of Motions and Mooring Loads of a Spar Floating Wind Turbine in Waves and Wind
by Antonio Medina-Manuel, Rafael Molina Sánchez and Antonio Souto-Iglesias
J. Mar. Sci. Eng. 2024, 12(9), 1464; https://doi.org/10.3390/jmse12091464 - 23 Aug 2024
Viewed by 932
Abstract
This paper describes a Long Short-Term Memory (LSTM) neural network model used to simulate the dynamics of the OC3 reference design of a Floating Offshore Wind Turbine (FOWT) spar unit. It crafts an advanced neural network with an encoder–decoder architecture capable of predicting [...] Read more.
This paper describes a Long Short-Term Memory (LSTM) neural network model used to simulate the dynamics of the OC3 reference design of a Floating Offshore Wind Turbine (FOWT) spar unit. It crafts an advanced neural network with an encoder–decoder architecture capable of predicting the spar’s motion and fairlead tensions time series. These predictions are based on wind and wave excitations across various operational and extreme conditions. The LSTM network, trained on an extensive dataset from over 300 fully coupled simulation scenarios using OpenFAST, ensures a robust framework that captures the complex dynamics of a floating platform under diverse environmental scenarios. This framework’s effectiveness is further verified by thoroughly evaluating the model’s performance, leveraging comparative statistics and accuracy assessments to highlight its reliability. This methodology contributes to substantial reductions in computational time. While this research provides insights that facilitate the design process of offshore wind turbines, its primary aim is to introduce a new predictive approach, marking a step forward in the quest for more efficient and dependable renewable energy solutions. Full article
Show Figures

Figure 1

Figure 1
<p>Sketch of the NREL 5 MW wind turbine on the OC3-Hywind spar. Source: Jonkman and Musial [<a href="#B20-jmse-12-01464" class="html-bibr">20</a>].</p>
Full article ">Figure 2
<p>Database scatter based on WAM10 wave model for the grid at 56.45° N, 02.29° W [<a href="#B27-jmse-12-01464" class="html-bibr">27</a>]. The dataset provides data from 1 September 1957 to 31 December 2010, interpolated to 3 h intervals. This point corresponds to the closest grid point to the Inch Cape site.</p>
Full article ">Figure 3
<p>Surge platform motions in the numerical and NREL Report [<a href="#B20-jmse-12-01464" class="html-bibr">20</a>] decay tests.</p>
Full article ">Figure 4
<p>OC3-Hywind RAOs’ obtained with the present model simulation framework and validated with NREL Report [<a href="#B20-jmse-12-01464" class="html-bibr">20</a>].</p>
Full article ">Figure 5
<p>Diagram of the LSTM neural network architecture. Blue color in cells stands for linear (fully connected) neurons and orange for LSTM neurons.</p>
Full article ">Figure 6
<p>Validation loss after 20 epochs from the optimization of the hyperparameters using Ray Tune. Blue bars remain for the final hyperparameters employed in the NN model.</p>
Full article ">Figure 7
<p>Violin plots of the Root Mean Square of the input features from the training, validation, and tests subsets.</p>
Full article ">Figure 8
<p>Loss convergence curves for training and validation over the epochs while training heave motion.</p>
Full article ">Figure 9
<p>Predicted vs. actual motions of the OC3 FOWT under various sea states and wind conditions. Each subplot compares the predicted signal (blue) with the actual signal (gray) for surge, heave, and pitch motions.</p>
Full article ">Figure 9 Cont.
<p>Predicted vs. actual motions of the OC3 FOWT under various sea states and wind conditions. Each subplot compares the predicted signal (blue) with the actual signal (gray) for surge, heave, and pitch motions.</p>
Full article ">Figure 10
<p>Predicted vs. actual fairlead tensions of the OC3 FOWT under various sea states and wind conditions. Each subplot compares the predicted signal (blue) with the actual signal (gray) for <span class="html-italic">Fairlead 1</span>, <span class="html-italic">Fairlead 2</span>, and <span class="html-italic">Fairlead 3</span> tensions.</p>
Full article ">Figure 10 Cont.
<p>Predicted vs. actual fairlead tensions of the OC3 FOWT under various sea states and wind conditions. Each subplot compares the predicted signal (blue) with the actual signal (gray) for <span class="html-italic">Fairlead 1</span>, <span class="html-italic">Fairlead 2</span>, and <span class="html-italic">Fairlead 3</span> tensions.</p>
Full article ">Figure 11
<p><math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> scores and residual values for specified wave trains tested. (<b>a</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 2 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 8.5 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 12 m/s. (<b>b</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 0.5 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 4 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 6 m/s. (<b>c</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 2 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 21.5 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 12 m/s. (<b>d</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 9.5 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 17 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 26 m/s.</p>
Full article ">Figure 12
<p>Statistics (PDFs and CDFs) of the selected cases. (<b>a</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 2 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 8.5 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 12 m/s. (<b>b</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 0.5 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 4 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 6 m/s. (<b>c</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 2 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 21.5 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 12 m/s. (<b>d</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 9.5 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 17 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 26 m/s.</p>
Full article ">Figure 12 Cont.
<p>Statistics (PDFs and CDFs) of the selected cases. (<b>a</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 2 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 8.5 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 12 m/s. (<b>b</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 0.5 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 4 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 6 m/s. (<b>c</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 2 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 21.5 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 12 m/s. (<b>d</b>) Sea state with <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> 9.5 m, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>P</mi> </msub> </semantics></math> 17 s wave, and wind <math display="inline"><semantics> <msub> <mi>U</mi> <mn>90</mn> </msub> </semantics></math> 26 m/s.</p>
Full article ">Figure 13
<p>Distribution of the <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> for all the test cases.</p>
Full article ">Figure 14
<p><span class="html-italic">p</span>-value from the K–S Test for all the test cases. Significance level of the tests chosen was <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>.</p>
Full article ">
17 pages, 4720 KiB  
Article
Analysis of Production Laws of Hydrate Reservoirs via Combined Heat Injection and Depressurization Based on Local Thermal Non-Equilibrium
by Zhengfeng Shan, Boyu Zhou, Qingwen Kong, Xiansi Wang, Youqiang Liao, Zhiyuan Wang and Jianbo Zhang
J. Mar. Sci. Eng. 2024, 12(8), 1408; https://doi.org/10.3390/jmse12081408 - 16 Aug 2024
Viewed by 533
Abstract
Natural gas hydrate is a kind of low-carbon and clean new energy, so research on its efficient extraction in terms of theory and technology is particularly important. Combined thermal injection and depressurization is an effective method for extracting natural gas hydrate. In this [...] Read more.
Natural gas hydrate is a kind of low-carbon and clean new energy, so research on its efficient extraction in terms of theory and technology is particularly important. Combined thermal injection and depressurization is an effective method for extracting natural gas hydrate. In this study, the classical local heat equilibrium model was modified, and a pore-scale fully coupled unsteady heat transfer model for hydrate reservoirs was set up by considering multiple forms of heat flow accompanying hydrate’s decomposition and gas–liquid flow. Based on this model and the basic geological information of the X2 hydrate reservoir in the western Pacific Ocean, a numerical model of gas hydrate extraction using combined heat injection and depressurization was constructed to simulate the production performance of the hydrate reservoir. The results were fully compared with the results obtained by the depressurization method alone. The results indicated the hydrate extraction via a combined heat injection and depressurization would have a cumulative gas production of 31.609 million m3 and a cumulative water production of 1.5219 million m3, which are 72.57% higher and 31.75% lower than those obtained by depressurization alone, respectively. These study results can provide theoretical support for the industrial extraction of gas hydrate in seas. Full article
(This article belongs to the Special Issue Marine Gas Hydrates: Formation, Storage, Exploration and Exploitation)
Show Figures

Figure 1

Figure 1
<p>Schematics of the difference between the local thermal equilibrium model and the local thermal non-equilibrium model.</p>
Full article ">Figure 2
<p>Physical model and gridding of gas hydrate reservoir’s extraction via combined heat injection and depressurization in the western Pacific.</p>
Full article ">Figure 3
<p>Gas production rate and cumulative gas production in the hydrate extraction period.</p>
Full article ">Figure 4
<p>Water production rate and cumulative water production in the hydrate extraction period.</p>
Full article ">Figure 5
<p>Cloud maps of the temperature field distribution at the end of the 1st, 2nd, 4th and 8th year of hydrate extraction.</p>
Full article ">Figure 6
<p>Extended depth variation of isotherms with increasing hydrate extraction time.</p>
Full article ">Figure 7
<p>Cloud maps of the pressure field distribution at the end of the 1st, 2nd, 4th and 8th year of hydrate extraction.</p>
Full article ">Figure 8
<p>Variation of pressure distribution between heat injection and production wells with distance for different durations of hydrate extraction.</p>
Full article ">Figure 9
<p>Cloud maps of hydrate’s saturation distribution in the hydrate reservoir at the end of the 1st, 2nd, 4th and 8th year of hydrate extraction.</p>
Full article ">Figure 10
<p>Cloud maps of the gas saturation’s spatial distribution in the hydrate reservoir at the end of the 1st, 2nd, 4th and 8th year of hydrate extraction.</p>
Full article ">
21 pages, 5639 KiB  
Article
Study on Vibration and Noise of Railway Steel–Concrete Composite Box Girder Bridge Considering Vehicle–Bridge Coupling Effect
by Jinyan Si, Li Zhu, Weitao Ma, Bowen Meng, Huifeng Dong, Hongyang Ning and Guanyuan Zhao
Buildings 2024, 14(8), 2509; https://doi.org/10.3390/buildings14082509 - 14 Aug 2024
Viewed by 661
Abstract
A steel–concrete composite beam bridge fully exploits the mechanical advantages of the concrete structure and steel structure, and has the advantages of a fast construction speed and large stiffness. It is of certain research value to explore the application of this bridge type [...] Read more.
A steel–concrete composite beam bridge fully exploits the mechanical advantages of the concrete structure and steel structure, and has the advantages of a fast construction speed and large stiffness. It is of certain research value to explore the application of this bridge type in the field of railway bridges. However, with the rapid development of domestic high-speed railway construction, the problem of vibration and noise radiation of high-speed railway bridges caused by train loads is becoming more and more serious. A steel–concrete composite beam bridge combines the tensile characteristics of steel and the compressive characteristics of concrete perfectly. At the same time, it also has the characteristics of a steel bridge and concrete bridge in terms of vibration and noise radiation. This feature makes the study of the vibration and noise of the bridge type more complicated. Therefore, in this paper, the characteristics of vibration and noise radiation of a high-speed railway steel–concrete composite box girder bridge are studied in detail from two aspects: the theoretical basis and a numerical simulation. The main results obtained are as follows: Relying on the idea of vehicle–rail–bridge coupling dynamics, a structural dynamics analysis model of a steel–concrete combined girder bridge for a high-speed railroad was established, and numerical program simulation of the vibration of the vehicle–rail–bridge coupling system was carried out based on the parametric design language of ANSYS 18.0 and the language of MATLAB R2021a, and the structural vibration results were analyzed in both the time domain and frequency domain. By using different time-step loading for the vehicle–rail–bridge coupling vibration analysis, the computational efficiency can be effectively improved under the condition of guaranteeing the accuracy of the result analysis within 100 Hz. Based on the power flow equilibrium equation, a statistical energy method of calculating the high-frequency noise radiation is theoretically derived. Based on the theoretical basis of the statistical energy method, the high-frequency noise in the structure is numerically simulated in the VAONE 2021 software, and the average contribution of the concrete roof plate to the three acoustic field points constructed in this paper is as high as 50%, which is of great significance in the study of noise reduction in steel–concrete composite girders. Full article
(This article belongs to the Special Issue High-Performance Steel–Concrete Composite/Hybrid Structures)
Show Figures

Figure 1

Figure 1
<p>Vertical vehicle model.</p>
Full article ">Figure 2
<p>Slab ballastless track structure and mechanical vertical model.</p>
Full article ">Figure 3
<p>Bridge midspan cross-section (in dm).</p>
Full article ">Figure 4
<p>Spatial samples of left and right rail height irregularity. (<b>a</b>) Spatial samples of left rail height irregularity. (<b>b</b>) Spatial samples of right rail height irregularity.</p>
Full article ">Figure 5
<p>Train–track–bridge dynamics model.</p>
Full article ">Figure 6
<p>Flow chart of vehicle–rail–bridge coupling calculation.</p>
Full article ">Figure 7
<p>Results chart for different time stepping loading. (<b>a</b>) Time history of acceleration at midspan of beam. (<b>b</b>) Time history of vehicle acceleration. Note: Multiplier in the diagram represents multiplier for every different time stepping loading.</p>
Full article ">Figure 8
<p>Time history of vertical displacement of the first wheel set of the train.</p>
Full article ">Figure 9
<p>Vertical dynamic response of the train body. (<b>a</b>) Time history of vertical displacement of the vehicle body. (<b>b</b>) Time history of vertical acceleration of the vehicle body.</p>
Full article ">Figure 10
<p>Time history of vertical acceleration of the rail. (<b>a</b>) Vertical wheel–rail force. (<b>b</b>) Vertical acceleration of the rail.</p>
Full article ">Figure 11
<p>Time history of the dynamic response of the bridge structure. (<b>a</b>) Acceleration diagram of the bridge deck flange and midspan. (<b>b</b>) Comparison of acceleration of steel base plate and abdominal plate.</p>
Full article ">Figure 12
<p>Technology roadmap for statistical energy methods.</p>
Full article ">Figure 13
<p>Fastener force time history and frequency data results. (<b>a</b>) Time history of fastener force. (<b>b</b>) Spectrum of fastener forces.</p>
Full article ">Figure 14
<p>Time-domain diagram of fastener force after high-pass filtering.</p>
Full article ">Figure 15
<p>The modal number of bending modes of steel–concrete composite beam subsystem.</p>
Full article ">Figure 16
<p>Semi-infinite fluid subsystem. (The brown portion represents concrete and the purple portion represents steel.)</p>
Full article ">Figure 17
<p>Acoustic field point diagram (m).</p>
Full article ">Figure 18
<p>Simulation results of point noise radiation in medium- and high-frequency fields. (<b>a</b>) Radiation efficiency of each subsystem of bridge. (<b>b</b>) Radiation spectrum curve of medium- and high-frequency field point noise.</p>
Full article ">Figure 19
<p>Vibration simulation results of medium- and high-frequency plates. (<b>a</b>) Vibration velocity of medium- and high-frequency bridge plate. (<b>b</b>) The total vibration level of medium- and high-frequency bridge plate. Notes: TP, AP, DP, and BP represent top plate, abdominal plate, diaphragm plate, and base plate, respectively.</p>
Full article ">Figure 20
<p>Results of the contribution of the high-frequency bridge plate in three field points A, B, and C. (<b>a</b>) The contribution spectrum of high-frequency bridge plate in field point A. (<b>b</b>) The contribution spectrum of high-frequency bridge plate in field point B. (<b>c</b>) The contribution spectrum of high-frequency bridge plate in field point C. (<b>d</b>) Bar chart of the total sound pressure level contributed by the panels at the three points. Notes: TP, AP, DP, BP, and OSPL represent top plate, abdominal plate, diaphragm plate, base plate, and overall sound pressure level, respectively.</p>
Full article ">Figure 21
<p>Noise contribution of the plate at the medium–high-frequency field point.</p>
Full article ">Figure 22
<p>Overall sound pressure level at medium- and high-frequency field points.</p>
Full article ">
23 pages, 4283 KiB  
Article
Stochastic Optimal Bounded Parametric Control of Periodic Viscoelastomer Sandwich Plate with Supported Mass Based on Dynamical Programming Principle
by Zhi-Gang Ruan, Zu-Guang Ying, Zhao-Zhong Ying, Hua Lei, Wen Wang and Lei Xia
Buildings 2024, 14(8), 2309; https://doi.org/10.3390/buildings14082309 - 25 Jul 2024
Viewed by 612
Abstract
The sandwich plate (SP) with supported mass can model structural systems such as platform or floor with installed vibration-sensitive apparatus under random loading. The stochastic optimal control (in time domain) of periodic (in space) viscoelastomer (VE) SP with supported mass subjected to random [...] Read more.
The sandwich plate (SP) with supported mass can model structural systems such as platform or floor with installed vibration-sensitive apparatus under random loading. The stochastic optimal control (in time domain) of periodic (in space) viscoelastomer (VE) SP with supported mass subjected to random excitation is an important research subject, which can fully use VE controllability, but it is a challenging problem on optimal bounded parametric control (OBPC). In this paper, a stochastic OBPC for periodic VESP with supported mass subjected to random base loading is proposed according to the stochastic dynamical programming (SDP) principle. Response-reduction capability using the proposed OBPC is studied to demonstrate further control effectiveness of periodic SP via SDP. Controllable VE core modulus of SP is distributed periodically in space. Differential equations for coupling vibration of periodic SP with supported mass are derived and transformed into multi-dimensional system equations with parameters as nonlinear functions of bounded control. The OBPC problem is established by the system equations and performance index with bound constraint. Then, an SDP equation is derived according to the SDP principle. The OBPC law is obtained from the SDP equation under bound constraint. Optimally controlled responses are calculated and compared with passively controlled responses to evaluate control effectiveness. Numerical results on responses and statistics of SP via the proposed OBPC show further remarkable control effectiveness. Full article
(This article belongs to the Special Issue Structural Health Monitoring and Vibration Control)
Show Figures

Figure 1

Figure 1
<p>Diagram of VESP and supported mass.</p>
Full article ">Figure 2
<p>Sample of ND Gaussian white-noise excitation, (<math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mover accent="true"> <mi>w</mi> <mo>¯</mo> </mover> <mo>¨</mo> </mover> <mn>0</mn> </msub> </mrow> </semantics></math>).</p>
Full article ">Figure 3
<p>Optimally and passively controlled ND responses of SP with uniform parameters.</p>
Full article ">Figure 4
<p>Sample of OBPC of SP with uniform parameters.</p>
Full article ">Figure 5
<p>Optimally controlled ND responses of SP with uniform parameters for different control bounds (<span class="html-italic">e<sub>h</sub></span>).</p>
Full article ">Figure 6
<p>Optimally controlled ND response SD of SP with uniform parameters versus control bound <span class="html-italic">e<sub>h</sub></span> (<span class="html-italic">e<sub>l</sub></span> = 0.2 MPa).</p>
Full article ">Figure 7
<p>Relative reductions of optimally controlled response SD of SP with uniform parameters versus control bound <span class="html-italic">e<sub>h</sub></span> (<span class="html-italic">e<sub>l</sub></span> = 0.2 MPa).</p>
Full article ">Figure 8
<p>Mean optimal control (<span class="html-italic">e</span>*<span class="html-italic"><sub>a</sub></span><sub>1</sub>) versus control bound <span class="html-italic">e<sub>h</sub></span> for SP with uniform parameters.</p>
Full article ">Figure 9
<p>Optimally controlled ND response SD of SP with uniform parameters versus control bound <span class="html-italic">e<sub>l</sub></span> (<span class="html-italic">e<sub>h</sub></span> = 3.0 MPa).</p>
Full article ">Figure 10
<p>Relative reductions of optimally controlled response SD of SP with uniform parameters versus control bound <span class="html-italic">e<sub>l</sub></span> (<span class="html-italic">e<sub>h</sub></span> = 3.0 MPa).</p>
Full article ">Figure 11
<p>Optimal and passively controlled ND responses of SP with periodic parameters.</p>
Full article ">Figure 12
<p>Sample of OBPC of SP with periodic parameters.</p>
Full article ">Figure 13
<p>Optimally controlled ND responses of SP with periodic parameters for different control bounds (<span class="html-italic">e<sub>h</sub></span>).</p>
Full article ">Figure 14
<p>Optimally controlled ND response SD of SP with periodic parameters versus control bound <span class="html-italic">e<sub>h</sub></span> (<span class="html-italic">e<sub>l</sub></span> = 0.2 MPa).</p>
Full article ">Figure 15
<p>Relative reductions of optimally controlled response SD of SP with periodic parameters versus control bound <span class="html-italic">e<sub>h</sub></span> (<span class="html-italic">e<sub>l</sub></span> = 0.2 MPa).</p>
Full article ">Figure 16
<p>Mean optimal control (<span class="html-italic">e</span>*<span class="html-italic"><sub>a</sub></span><sub>1</sub>) versus control bound <span class="html-italic">e<sub>h</sub></span> for SP with periodic parameters.</p>
Full article ">Figure 17
<p>Optimally controlled ND response SD of SP with periodic parameters versus control bound <span class="html-italic">e<sub>l</sub></span> (<span class="html-italic">e<sub>h</sub></span> = 3.0 MPa).</p>
Full article ">Figure 18
<p>Relative reductions of optimally controlled response SD of SP with periodic parameters versus control bound <span class="html-italic">e<sub>l</sub></span> (<span class="html-italic">e<sub>h</sub></span> = 3.0 MPa).</p>
Full article ">
21 pages, 10668 KiB  
Article
Fully Coupled Hydrodynamic–Mooring–Motion Response Model for Semi-Submersible Tidal Stream Turbine Based on Actuation Line Method
by Guohui Wang, Jisheng Zhang, Xiangfeng Lin, Hao Chen, Fangyu Wang and Siyuan Liu
J. Mar. Sci. Eng. 2024, 12(7), 1046; https://doi.org/10.3390/jmse12071046 - 21 Jun 2024
Viewed by 602
Abstract
The modeling of floating tidal stream energy turbine (FTSET) systems demands significant computational resources, especially when incorporating fully coupled models that integrate hydrodynamics, mooring, motion response, and their interactions. In this study, a novel hybrid numerical model for FTSET systems has been developed, [...] Read more.
The modeling of floating tidal stream energy turbine (FTSET) systems demands significant computational resources, especially when incorporating fully coupled models that integrate hydrodynamics, mooring, motion response, and their interactions. In this study, a novel hybrid numerical model for FTSET systems has been developed, utilizing the open-source software OpenFOAM. The hydrodynamic characteristics of three-bladed vertical-axis turbines are simulated in steady, three-dimensional wave–current numerical tanks using an unsteady actuator line method (UALM). The interFoam two-phase Navier–Stokes solver within OpenFOAM is utilized to manage the kinematic characteristics of the floating platform. Mooring dynamics are addressed using the mass–spring–damper model (MoorDyn), and turbine wake dynamics are resolved using a buoyancy-modified RANS turbulence model. The comprehensive model can simulate wave, flow, mooring dynamics, platform motion, and the interactions between the turbine and platform within FTSET systems. To validate the model, several scenarios are analyzed, and experiments are conducted to validate the numerical results. The model accurately predicts platform motion responses and mooring line tensions, especially under wave–current conditions, capturing the interconnected effects of platform motion during turbine rotation. Additionally, the model extends predictions of turbine–platform wake development and interaction. Full article
(This article belongs to the Section Marine Energy)
Show Figures

Figure 1

Figure 1
<p>Schematic diagram of the computational domain.</p>
Full article ">Figure 2
<p>Flow chart of the FTSET fully coupled model.</p>
Full article ">Figure 3
<p>Diagram of mooring line facilities.</p>
Full article ">Figure 4
<p>Schematic diagram of the computational domain, (<b>a</b>) computational domain, (<b>b</b>) wake area meshing, (<b>c</b>) floating body meshing.</p>
Full article ">Figure 5
<p>Comparison of the platform motion response in regular wave case (WT = 1.4 s, Wh = 0.06 m).</p>
Full article ">Figure 6
<p>Comparison of the platform Response Amplitude Operators (RAOs) curves in a regular wave.</p>
Full article ">Figure 7
<p>Motion attitude and trajectory of the platform in wave–current case (WT = 1.4 s, Wh = 0.06 m).</p>
Full article ">Figure 8
<p>Comparison of mooring anchor tensions in the M1 and M3 lines in wave–current case (WT = 1.4 s, Wh = 0.06 m).</p>
Full article ">Figure 9
<p>Schematic diagram of instantaneous surface velocity and mooring tension in a wave period: (<b>a</b>) without turbine; (<b>b</b>) with turbine.</p>
Full article ">Figure 10
<p>The contours of velocity deficit on XY profile (WT = 1.4 s, Wh = 0.06 m).</p>
Full article ">Figure 11
<p>Lateral velocity distribution under crest, trough, and average conditions (WT = 1.4 s, Wh = 0.06 m).</p>
Full article ">Figure 12
<p>The contours of velocity deficit on the xz profile (WT = 1.4 s, Wh = 0.06 m).</p>
Full article ">Figure 13
<p>Vertical velocity distribution under crest, trough, and average conditions (WT = 1.4 s, Wh = 0.06 m).</p>
Full article ">
27 pages, 3642 KiB  
Article
Nonlinear Trajectory Tracking Controller for Underwater Vehicles with Shifted Center of Mass Model
by Przemyslaw Herman
Appl. Sci. 2024, 14(13), 5376; https://doi.org/10.3390/app14135376 - 21 Jun 2024
Viewed by 544
Abstract
This paper addresses the issue of trajectory tracking control for an autonomous underwater vehicle in the presence of parameter perturbations and disturbances in three-dimensional space. The control scheme is based on a combination of the backstepping method, the adaptive integral sliding mode control [...] Read more.
This paper addresses the issue of trajectory tracking control for an autonomous underwater vehicle in the presence of parameter perturbations and disturbances in three-dimensional space. The control scheme is based on a combination of the backstepping method, the adaptive integral sliding mode control scheme, and velocity transformation resulting from the decomposition of the inertia matrix, which is symmetric. In addition, adaptive laws were applied to eliminate the effects of parameter perturbations and external disturbances. The main feature of the proposed approach is that the vehicle model is not fully symmetric but contains quantities due to the shift of the center of mass. Another important feature of the control scheme is the ability to detect some of the consequences caused by reducing the vehicle model by neglecting dynamic couplings. Numerical results on the five degrees of freedom (DOF) vehicle model show the efficiency, effectiveness, and robustness of the developed controller. Full article
(This article belongs to the Special Issue Artificial Intelligence and Its Application in Robotics)
Show Figures

Figure 1

Figure 1
<p>Underactuated underwater vehicle model and frame coordinates.</p>
Full article ">Figure 2
<p>QV controller results, linear trajectory, and (<a href="#FD26-applsci-14-05376" class="html-disp-formula">26</a>): (<b>a</b>) trajectories: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>d</mi> </msub> </semantics></math>—desired, <span class="html-italic">p</span>—actual; (<b>b</b>) linear errors of position; (<b>c</b>) angular errors of position; (<b>d</b>) linear velocities; (<b>e</b>) angular velocities; (<b>f</b>) force and torque applied; (<b>g</b>) kinetic energy values; (<b>h</b>) errors of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>3</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>QV controller results, complex trajectory, and (<a href="#FD27-applsci-14-05376" class="html-disp-formula">27</a>): (<b>a</b>) trajectories: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>d</mi> </msub> </semantics></math>—desired, <span class="html-italic">p</span>—actual; (<b>b</b>) linear errors of position; (<b>c</b>) angular errors of position; (<b>d</b>) linear velocities; (<b>e</b>) angular velocities; (<b>f</b>) force and torque applied; (<b>g</b>) kinetic energy values; (<b>h</b>) errors of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>3</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Comparative CL controller results, linear trajectory, and (<a href="#FD26-applsci-14-05376" class="html-disp-formula">26</a>): (<b>a</b>) linear errors of position; (<b>b</b>) angular errors of position; (<b>c</b>) force and torque applied.</p>
Full article ">Figure 5
<p>Comparative CL controller results, linear trajectory, and (<a href="#FD28-applsci-14-05376" class="html-disp-formula">28</a>): (<b>a</b>) trajectories: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>d</mi> </msub> </semantics></math>—desired, <span class="html-italic">p</span>—actual; (<b>b</b>) linear errors of position; (<b>c</b>) angular errors of position; (<b>d</b>) linear velocities; (<b>e</b>) angular velocities; (<b>f</b>) force and torque applied.</p>
Full article ">Figure 6
<p>Comparative CL controller results and complex trajectory: (<b>a</b>) trajectories: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>d</mi> </msub> </semantics></math>—desired, <span class="html-italic">p</span>—actual; (<b>b</b>) linear errors of position; (<b>c</b>) angular errors of position; (<b>d</b>) linear velocities; (<b>e</b>) angular velocities; (<b>f</b>) force and torque applied.</p>
Full article ">Figure 7
<p>QV controller results, stronger couplings, complex trajectory, and (<a href="#FD27-applsci-14-05376" class="html-disp-formula">27</a>): (<b>a</b>) trajectories: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>d</mi> </msub> </semantics></math>—desired, <span class="html-italic">p</span>—actual; (<b>b</b>) linear errors of position; (<b>c</b>) angular errors of position; (<b>d</b>) linear velocities; (<b>e</b>) angular velocities; (<b>f</b>) force and torque applied; (<b>g</b>) kinetic energy values; (<b>h</b>) errors of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>Δ</mo> <msub> <mi>ζ</mi> <mn>3</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">
38 pages, 50304 KiB  
Article
Intracellular “In Silico Microscopes”—Comprehensive 3D Spatio-Temporal Virus Replication Model Simulations
by Markus M. Knodel, Arne Nägel, Eva Herrmann and Gabriel Wittum
Viruses 2024, 16(6), 840; https://doi.org/10.3390/v16060840 - 24 May 2024
Viewed by 982
Abstract
Despite their small and simple structure compared with their hosts, virus particles can cause severe harm and even mortality in highly evolved species such as humans. A comprehensive quantitative biophysical understanding of intracellular virus replication mechanisms could aid in preparing for future virus [...] Read more.
Despite their small and simple structure compared with their hosts, virus particles can cause severe harm and even mortality in highly evolved species such as humans. A comprehensive quantitative biophysical understanding of intracellular virus replication mechanisms could aid in preparing for future virus pandemics. By elucidating the relationship between the form and function of intracellular structures from the host cell and viral components, it is possible to identify possible targets for direct antiviral agents and potent vaccines. Biophysical investigations into the spatio-temporal dynamics of intracellular virus replication have thus far been limited. This study introduces a framework to enable simulations of these dynamics using partial differential equation (PDE) models, which are evaluated using advanced numerical mathematical methods on leading supercomputers. In particular, this study presents a model of the replication cycle of a specific RNA virus, the hepatitis C virus. The diffusion–reaction model mimics the interplay of the major components of the viral replication cycle, including non structural viral proteins, viral genomic RNA, and a generic host factor. Technically, surface partial differential equations (sufPDEs) are coupled on the 3D embedded 2D endoplasmic reticulum manifold with partial differential equations (PDEs) in the 3D membranous web and cytosol volume. The membranous web serves as a viral replication factory and is formed on the endoplasmic reticulum after infection and in the presence of nonstructural proteins. The coupled sufPDE/PDE model was evaluated using realistic cell geometries based on experimental data. The simulations incorporate the effects of non structural viral proteins, which are restricted to the endoplasmic reticulum surface, with effects appearing in the volume, such as host factor supply from the cytosol and membranous web dynamics. Because the spatial diffusion properties of genomic viral RNA are not yet fully understood, the model allows for viral RNA movement on the endoplasmic reticulum as well as within the cytosol. Visualizing the simulated intracellular viral replication dynamics provides insights similar to those obtained by microscopy, complementing data from in vitro/in vivo viral replication experiments. The output data demonstrate quantitative consistence with the experimental findings, prompting further advanced experimental studies to validate the model and refine our quantitative biophysical understanding. Full article
(This article belongs to the Section General Virology)
Show Figures

Figure 1

Figure 1
<p>Computational domain generation for the partial differential equation (PDE) model to be developed in the forthcoming sections, and definition of its subdomains. (<b>A</b>–<b>C</b>) Volume mesh generation based on a given surface geometry: (<b>A</b>) Reconstructed surface grid describing the ER and membranous web (MW)surfaces. (Screenshot published first in our previous study [<a href="#B31-viruses-16-00840" class="html-bibr">31</a>]. ER surface in dark blue, MW surfaces in red) (<b>B</b>) Enclosure of the surface grid by a rectangular hexahedron (green) to allow tetrahedralization. (<b>C</b>) Hexahedron opened by a clip plane. (ER surface in dark blue, MW surfaces in different colors to account for their assignment to different subdomains, as they are not connected spatially; each MW subdomain is marked with its own color). (<b>D</b>–<b>F</b>) Volume mesh subdomains after tetrahedralization: (<b>D</b>) ER surface with ribosomes (ER surface in dark blue, ribosomes with different colors, as spatially not connected, to account for different subdomains), (<b>E</b>) MW (membranous web) volume regions (different subdomains refer to the different spatially unconnected MW zones) and ER surface (dark blue), (<b>F</b>) volume mesh opened by a clip plane (colors as in (<b>E</b>), but with additional color for the now visible cytosol subdomain). (Perspectives of the screenshots differ from each other in most cases).</p>
Full article ">Figure 2
<p>This simplified graphical representation of the partial differential equation model illustrates the interaction of the main components. It shows the model compartments in the white rectangles (see also <a href="#viruses-16-00840-t002" class="html-table">Table 2</a>) in the respective regions. The main processes are shown by blue arrows and transitions between the surface and volume by gray arrows: viral RNA <math display="inline"><semantics> <msubsup> <mi>R</mi> <mi>R</mi> <mi>S</mi> </msubsup> </semantics></math> bounded at ribosome induces translation of viral polyprotein <math display="inline"><semantics> <msubsup> <mi>P</mi> <mi>R</mi> <mi>S</mi> </msubsup> </semantics></math>, which is cleaved in non-structural proteins <math display="inline"><semantics> <msubsup> <mi>W</mi> <mi>C</mi> <mi>S</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>N</mi> <mi>E</mi> <mi>S</mi> </msubsup> </semantics></math>. Non-structural proteins can detach from the ER surface and diffuse in the membranous web volume zone as <math display="inline"><semantics> <msubsup> <mi>W</mi> <mi>W</mi> <mi>V</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>N</mi> <mi>W</mi> <mi>V</mi> </msubsup> </semantics></math>. Replication complexes <math display="inline"><semantics> <msubsup> <mi>C</mi> <mi>W</mi> <mi>V</mi> </msubsup> </semantics></math> are formed, which produce polymerized viral RNA <math display="inline"><semantics> <msubsup> <mi>R</mi> <mi>P</mi> <mi>V</mi> </msubsup> </semantics></math>. Viral RNA can attach to the ER and form <math display="inline"><semantics> <msubsup> <mi>R</mi> <mi>E</mi> <mi>S</mi> </msubsup> </semantics></math>, which can again be bound to the ribosome to form new viral RNA <math display="inline"><semantics> <msubsup> <mi>R</mi> <mi>R</mi> <mi>S</mi> </msubsup> </semantics></math>. Further compartments are involved in these processes and these involvements are indicated by light green arrows. This is especially true for the generic host factor <math display="inline"><semantics> <msup> <mi>H</mi> <mi>V</mi> </msup> </semantics></math>, which is involved in several processes.</p>
Full article ">Figure 3
<p>Initial state of the simulation, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>: One vRNA (viral RNA) attached to one ribosomal region (<b>Panel A</b>); otherwise, the cell is healthy. All other viral components do not exist so far. In particular, so far, no “active” membranous web exists. The host factor is distributed homogeneously over throughout the cell. As in the following figures, high concentrations are indicated by dark-red color, low concentrations by dark-blue color.</p>
Full article ">Figure 4
<p>Simulation status at time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>127</mn> </mrow> </semantics></math> s <math display="inline"><semantics> <mrow> <mo>≈</mo> <mn>2</mn> </mrow> </semantics></math> min. The contamination of the cell by viral components starts, especially polyprotein translation followed by polyprotein cleavage. The web protein (WP) detaches from the ER surface and causes the growth of the first biophysically active membranous web zone, which is only weakly visible to date. The replication complex (RC) starts to emerge inside the membranous web as a combination of a previously ribosomally bound web protein and viral RNA (vRNA).</p>
Full article ">Figure 5
<p>Simulation status at simulated time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>639</mn> </mrow> </semantics></math> s <math display="inline"><semantics> <mrow> <mo>≈</mo> <mn>10</mn> </mrow> </semantics></math> min. Begin of vRNA (viral RNA) polymerization in the first MW (membranous web), viral RNA volume diffusion, and viral RNA attachment to ER surface, followed by surface diffusion.</p>
Full article ">Figure 6
<p>Simulation status at time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1185</mn> </mrow> </semantics></math> s <math display="inline"><semantics> <mrow> <mo>≈</mo> <mn>20</mn> </mrow> </semantics></math> min. We can observe the closing of the viral RNA cycle: Newly polymerized viral RNA attached to the ER diffuses to the second ribosomal zone. Surface-bound viral RNA is captured by the next ribosomal zone once it arrives. The newly attached ribosomal viral RNA translates polyproteins. The polyproteins cleave into web protein and NS5A. The host factor is slightly reduced in the first membranous web zone.</p>
Full article ">Figure 7
<p>Simulation status at the simulated time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2185</mn> </mrow> </semantics></math> s <math display="inline"><semantics> <mrow> <mo>≈</mo> <mn>40</mn> </mrow> </semantics></math> min. In the second ribosomal zone, the polyprotein is cleaved into the web protein (WP) and NS5A. The web proteins detach from the ribosomes, diffuse into the geometric membranous web (MW) subdomain volume, and induce further membranous web zone activation.</p>
Full article ">Figure 8
<p>Simulation status at the simulated time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3185</mn> </mrow> </semantics></math> s ≈ 50 min. The viral RNA begins to rush through the cell. More membranous web zones become active and the host factor becomes depleted, initially slowly, then increasingly faster. The host factor also starts to reduce in the second and even third membranous web zone because of the delivery of energy for viral RNA polymerization.</p>
Full article ">Figure 9
<p>Simulation status at the simulated time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>4185</mn> </mrow> </semantics></math> s ≈ 1 h 10 min. As viral RNA propagation, membranous web (MW) activation, and viral RNA polymerization continue, holes increasingly arise in the host factor, which still mirror the membranous webs but have already started to unify. While new spots arise where viral RNA is polymerized, former spots blur increasingly once the host factor is depleted and the surrounding cytosol is depleted as well. Replication complexes are entering more replication centers (active membranous web zones).</p>
Full article ">Figure 10
<p>Simulation status at the simulated time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>5185</mn> </mrow> </semantics></math> s ≈ 1 h 30 min. Membranous web activation continues. Most potential membranous web zones are activated and polymerize viral RNA. The membranous webs are the replication centers where the replication complexes polymerize viral RNA. Formerly active membranous webs increasingly encounter interruptions in viral RNA polymerization because of the lack of host factor.</p>
Full article ">Figure 11
<p>Simulation status at the simulated time <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>7186</mn> </mrow> </semantics></math> s ≈ 2 h. When viral RNA polymerization has stopped because of a lack of host factor, the membranous webs remain activated, but the viral RNA increasingly vanishes from the former active centers of replication because of diffusion and attachment to the ER surface. The host factor reduces globally, not only, but most strongly, in the replication centers. The last membranous web zone was activated and began to polymerize viral RNA.</p>
Full article ">Figure 12
<p>Simulation status at the simulated time t = 10,189 s ≈ 3 h. In addition, the last membranous web is now a viral RNA spot, while the host factor is so low that it starts to blur everywhere. All membranous web zones are now very strongly visible, but most of them have completed polymerizing viral RNA because of the lack of host factor.</p>
Full article ">Figure 13
<p>Simulation status at the simulated time t = 37,000 s = 7.5 h. The vast majority of the host factor is depleted, and most of the viral RNA is now located on the ER surface and within the replication complexes inside the membranous webs. Note that viral RNA is still everywhere in the cytosol volume and the membranous web zones, but is completely blurred compared with the initial state shown in <a href="#viruses-16-00840-f003" class="html-fig">Figure 3</a>.</p>
Full article ">Figure 14
<p>Long-term behavior of integrated compartmental concentrations in the complete computational domain (approximately 1% to 10% of a hepatoma cell) over time. Total simulated biophysical time approximately 7.5 hours. Results are computed at grid refinement level 4. (Note that those lines which are noted in the legends but not visible in the plots have such small values, that it effectively impossible to distinguish them from the x axis by blank eye vision.)</p>
Full article ">Figure 14 Cont.
<p>Long-term behavior of integrated compartmental concentrations in the complete computational domain (approximately 1% to 10% of a hepatoma cell) over time. Total simulated biophysical time approximately 7.5 hours. Results are computed at grid refinement level 4. (Note that those lines which are noted in the legends but not visible in the plots have such small values, that it effectively impossible to distinguish them from the x axis by blank eye vision.)</p>
Full article ">Figure A1
<p>Surface grid generation based on fluorescence z-stacks. Screenshots published first in our former paper [<a href="#B31-viruses-16-00840" class="html-bibr">31</a>].</p>
Full article ">
Back to TopTop