Solving Navier-Stokes Equations Research Articles

Optimal convergence analysis of two RPC-SAV schemes for the unsteady incompressible magnetohydrodynamics equations

Abstract In this paper, we present and analyze two linear and fully decoupled schemes for solving the unsteady incompressible magnetohydrodynamics equations. The rotational pressure-correction (RPC) approach is adopted to decouple the system, and the recently developed scalar auxiliary variable (SAV) method is used to treat the nonlinear terms explicitly and keep energy stability. One is the first-order RPC-SAV-Euler and the other one is generalized Crank–Nicolson-type scheme: GRPC-SAV-CN. For the RPC-SAV-Euler scheme, both unconditionally energy stability and optimal convergence are derived. The new GRPC-SAV-CN is constructed and can be regarded as a parameterized scheme, which includes PC-SAV-CN when the parameter $\beta =0$ and RPC-SAV-CN when $\beta \in (0,\frac {1}{2}]$; see Algorithm 3.2. However, Jiang and Yang (Jiang, N. & Yang, H. (2021) SIAM J. Sci. Comput., 43, A2869–A2896) point out that the SAV method has low accuracy by several commonly tested benchmark flow problem when solving Navier–Stokes equations. To improve the accuracy, we added two stabilization $-\alpha _{1}\varDelta t\nu \varDelta (\widetilde {\textbf {u}}^{n+1}-{\textbf {u}}^{n})$ and $\alpha _{2}\varDelta t\sigma ^{-1}\mbox {curl}\mbox {curl} (\textbf {H}^{n+1}-\textbf {H}^{n})$ in the GRPC-SAV-CN scheme, which play decisive roles in giving optimal error estimates. The unconditionally energy stability of the proposed scheme is given. We prove that the PC-SAV-CN scheme has second-order convergence speed, and the RPC-SAV-CN one has 1.5-order convergence rate. Finally, some numerical examples are presented to verify the validity and convergence of the numerical schemes.

Optimizing Infragravity Wave Attenuation to Improve Coral Reef Restoration Design for Coastal Defense

Coral reefs are effective natural flood barriers that protect adjacent coastal communities. As the need to adapt to rising sea levels, storms, and environmental changes increases, reef restoration may be one of the best tools available to mitigate coastal flooding along tropical coastlines, now and in the future. Reefs act as a barrier to incoming short-wave energy but can amplify low-frequency infragravity waves that, in turn, drive coastal flooding along low-lying tropical coastlines. Here, we investigate whether the spacing of reef restoration elements can be optimized to maximize infragravity wave energy dissipation while minimizing the number of elements—a key factor in the cost of a restoration project. With this goal, we model the hydrodynamics of infragravity wave dissipation over a coral restoration or artificial reef, represented by a canopy of idealized hemispherical roughness elements, using a three-dimensional Navier–Stokes equations solver (OpenFOAM). The results demonstrate that denser canopies of restoration elements produce greater wave dissipation under larger waves with longer periods. Wave dissipation is also frequency-dependent: dense canopies remove wave energy at the predominant wave frequency, whereas sparse canopies remove energy at higher frequencies, and hence are less efficient. We also identify an inflection point in the canopy density–energy dissipation curve that balances optimal energy losses with a minimum number of canopy elements. Through this work, we show that there are an ideal number of restoration elements per across-shore meter of coral reef flat that can be installed to dissipate infragravity wave energy for given incident heights and periods. These results have implications for designing coral reef restoration projects on reef flats that are effective both from a coastal defense and costing standpoint.

Enhancing wildfire propagation model predictions using aerial swarm-based real-time wind measurements: A conceptual framework

The dynamic behaviour of wildfires is mainly influenced by weather, fuel, and topography. Based on fundamental conservation laws involving numerous physical processes and large scales, atmospheric models require substantial computational resources. Therefore, coupling wildfire and atmospheric models is impractical for high resolutions. Instead, a static atmospheric wind field is typically input into the wildfire model, either as boundary conditions on the control surface or distributed over the control volume. Wildfire propagation models may be (i) data-driven; (ii)theoretical; or (iii)mechanistic surrogates. Data-driven models are beyond the scope of this paper. Theoretical models are based on conservation laws (species, energy, mass, momentum) and are, therefore, computationally intensive; e.g. the Fire Dynamics Simulator (FDS). Mechanistic surrogate models do not closely follow fire dynamics laws, but related laws observed to make predictions more efficiently with sufficient accuracy; e.g. FARSITE, and FDS with the Level Set model (FDS-LS). Whether theoretical or mechanistic surrogate, these wildfire models may be coupled with or decoupled from wind models (e.g. Navier-Stokes equations). Only coupled models account for the effect of the fire on the wind field. In this paper, a series of simulations of wildfire propagation on grassland are performed using FDS-LS to study the impact of the fire-induced wind on the fire propagation dynamics. Results show that coupling leads to higher Rates of Spread (RoS), closer to those reported from field experiments, with increasing wind speeds and higher terrain slopes strengthening this trend. Aiming to capture the fire–wind interaction without the hefty cost of solving Navier-Stokes equations, a conceptual framework is proposed: 1) a swarm of unmanned aerial vehicles measure wind velocities at flight height; 2) the wind field is constructed with the acquired data; 3) the high-altitude wind field is mapped to near-surface, and 4) the near-surface wind field is fed into the wildfire model periodically. A series of simulations are performed using an in-house decoupled physics-based reduced-order fire propagation model (FireProM-F) enhanced by wind field “measurements”. In this proof of concept, wind velocities are not measured but extracted from physics-based Large Eddy Simulations taken as ground truth. Unsurprisingly, higher measurement frequencies lead to more accurate and realistic predictions of the propagating fire front. An initial attempt is made to study the effect of wind measurement uncertainty on the model predictions by adding Gaussian noise. Preliminary results show that higher noise leads to the fire front displaying more irregular shapes and slower propagation.

Multi-objective aerodynamic optimization of expansion–deflection nozzle based on B-spline curves

An expansion–deflection nozzle (EDN) is an altitude-compensated nozzle that can accommodate a wide range of nozzle pressure ratio (NPR) variations. An EDN design with good thrust performance under both high- and low-NPR conditions can effectively improve the launch capability of the vehicle. In this study, a multi-objective aerodynamic optimization design is developed considering the performance of the EDN in both open and closed wake modes. The design method of the outer wall and pintle of the EDN is developed using B-spline curves. The design variables are the coordinates of the control points of the curves, and the objective functions are the thrust efficiencies of the EDN at NPRs of 30 and 400. The nozzle thrust is obtained using a Reynolds Averaged Navier–Stokes (RANS) equation solver and validated by experimental results. A radial basis function neural network and a non-dominated sorting genetic algorithm II (NSGA-II) are used to construct the surrogate model and search for the Pareto front, respectively. The relationship between the nozzle contour geometry and the nozzle thrust characteristics of the four optimised individuals on the Pareto front is discussed and analysed. The results demonstrate the effectiveness of the multi-objective optimization design for an EDN. One of the optimized designs improved the thrust efficiency at NPR = 30 by 3.5 % while improving the thrust efficiency at NPR = 400 by 0.6 %. Moreover, to ensure superior performance of the EDN in both operating modes, the nozzle length and pintle ending angle must be designed as a compromise, whereas a larger nozzle exit angle is favoured for both conditions. This study demonstrates the potential of the B-spline method for nozzle optimization design.

A high-order sharp-interface immersed boundary solver for high-speed flows

A sharp-interface immersed boundary (IB) solver for the three-dimensional compressible Navier-Stokes equations with shock discontinuities is presented. The IB method is based on high-order schemes and a ghost-cell method which uses Taylor polynomial interpolation and weighted least-squares error minimization to impose the boundary conditions on the immersed boundary. The results show that the method enables robust and accurate calculation of high-speed flow problems involving complex geometries, moving boundaries, and solid and membrane geometries. Third-order accuracy or higher is maintained even for supersonic conditions. The numerical framework is validated through several two-dimensional and three-dimensional benchmark problems at subsonic and supersonic speeds. Additionally, the method is demonstrated for airfoil dynamic stall and wing-store interaction investigations.

Stationary and Non-Stationary Periodic Flows Mathematical Modelling using Various Vortex Viscosity Models

Introduction. Mathematical modelling of currents is an urgent research topic in the field of hydrodynamics and oceanography. Despite ongoing research in the field of developing accurate and efficient numerical methods for solving Navier-Stokes equations that take into account vortex viscosity, the problems of accurate prediction and control of turbulence remain unresolved. The influence of nonlinear effects in vortex viscosity models on the accuracy of forecasts and their applicability to various flow conditions also remains relevant. The aim of the study is to study the influence of linearized and quadratic bottom friction and two turbulence models on the numerical solution of stationary and non-stationary periodic flows. Special emphasis is placed on comparing numerical results with analytical solutions within the framework of using various models of bottom friction.Materials and Methods. The computational models used in this study are based on a simplified two-dimensional wave model and full three-dimensional Navier-Stokes equations. The classical model of shallow water motion and the 2D model without taking into account dynamic changes in the geometry of the reservoir surface are derived from a system of equations for a spatially inhomogeneous three-dimensional mathematical model of wave hydrodynamics of a shallow reservoir. Analytical solutions were found by linearization of the equations, which obviously has its limitations. A distinction is made between two types of nonlinear effects – nonlinearities caused by higher-order terms in the equations of motion, i. e. terms of advective acceleration and friction, and nonlinear effects caused by geometric nonlinearities, this is due, for example, to different water depths and reservoir widths, which will be important when modelling a real sea.Results. The results of modeling stationary and non-stationary periodic flows in a schematized rectangular basin using linearized bottom friction are presented. The influence of linearization on the numerical solution is investigated in comparison with analytical profiles using models calculating bottom friction in a quadratic formulation. In combination with quadratic bottom friction, two turbulence models are studied: the constant vortex viscosity and the Prandtl mixing length model. The results obtained as a result of three-dimensional modelling are compared with the results of two-dimensional modeling and analytical solutions averaged in depth.Discussion and Conclusion. New approaches to modelling and studying flows with variable vortex viscosity are proposed, including analysis of the influence of linearization and the use of various turbulence models. For the linearized and quadratic formulations of bottom friction, it is proved that the numerical results for the case of stationary flow show great similarity with analytical solutions, since the surface height is much less than the water depth and advection can be neglected. The numerical results for the unsteady flow also show a good agreement with the theory. Unlike analytical solutions, numerical modelling has minor deviations in the long run. The study of flows, within the framework of using various turbulence models, will make it possible to take into account the influence of nonlinear effects in vortex viscosity models on the accuracy of forecasts and their applicability to various flow conditions. The results obtained make it possible to better understand and describe the physical processes occurring in shallow waters. This opens up new possibilities for applying mathematical modelling to predict and analyze the impact of human activities on the marine environment and to solve other problems in the field of oceanology and geophysics.

CFD study of active flow control around a wind turbine profile using synthetic jet

In this study, numerical simulations are performed to investigate the effect of the position and jet angle of the synthetic jet on the aerodynamic characteristics of a wind turbine blade profile. The study is applied to the NREL S809 profile with a 1m chord, set at an angle of attack of 15.2° in a flow at a Reynolds number Re=106. The synthetic jet is placed on the extrados of the profile and modeled by a sinusoidal function. The flow around the blade profile is simulated by solving Navier–Stokes equations using the commercial software ANSYS Fluent based on the finite volume method. Turbulence is simulated using the two-equation SST model. The results show that the considered jet parameters have a strong effect on the aerodynamic characteristics of the profile. Applying an optimal combination of synthetic jet parameters significantly improves the aerodynamic performance of the profile.

Dimensionless Moduli Governing Under-Rib Transport Phenomenon in Polymer Electrolyte Fuel Cell

Introduction The performance of polymer electrolyte fuel cell (PEFC) can be considerably improved by promoting the under-rib convection or cross flow between adjacent gas channels, e.g., applying the serpentine and staggered partially narrowed flow fields[1]. Although a lot of efforts have been devoted to analyze the under-rib transport phenomenon, an analytical model which quantitively demonstrates the dominant factors of the under-rib processes has not been established. In this study, a theoretical analysis of the relations between oxygen reduction reaction (ORR) and mass transfer capacity is carried out. The dimensionless moduli which combine physical properties, flow field dimensions and operating conditions are derived, which provides a theory for optimization of flow field and operating condition design for PEFC. Theoretical Analysis The water is assumed to only exist in vapor phase in a steady-state isothermal cell. The gas diffusion layer (GDL) is considered as uniform porous medium, in which Darcy’s law is applicable. The even velocity and oxygen mass fraction profiles in through-plane direction inside GDL is considered. The ORR was experimentally proven as a first order reaction of oxygen partial pressure according to our previous study,[2] and is regarded as a surface reaction, so that the oxygen consumption rate can be expressed as Eq. (1). The ORR rate constant, which is the function of the cathode overpotential or electromotive force, is assumed to be fixed across the rib.The theoretical model was derived from one-dimensioned mass balance of oxygen, which exhibits that the under-rib process is dominated by 3 dimensionless moduli, Péclet number Pe, Thiele number φ and the ratio of oxygen mass fractions θ at two sides of the under-rib GDL, which were defined by Eqs. (2)–(4). Péclet number represents the ratio of oxygen convection rate to oxygen diffusion rate, which is determined by the pressure difference between adjacent channels. Thiele number represents the ratio of oxygen diffusion resistance to reaction resistance. The average oxygen mass fraction can thus be calculated from Eq. (5). Results and Discussion The theoretical model was compared with the computational fluid dynamics (CFD) simulation in the computational domain shown in Fig. 1, where the GDL was placed between two parallel gas channels, instead of being laid under the gas channel, and the active area was only located under the rib. In the CFD simulation, the velocity and pressure distributions were calculated by solving Navier-Stokes equations, and the component distribution dependencies on density, diffusivity and viscosity were also considered. Fig. 2 shows the under-rib average current density at different geometries and operating conditions. The dimensionless moduli calculated from the inlet conditions offer an accurate current density prediction, which demonstrates these moduli dominate the under-rib transport phenomenon.The typical operating condition gives φ = 1.5 and Pe = 4, where the model provides the average current density with high confidence. The model provides lower oxygen mass fraction than the CFD results especially in case of θ = 1, which exists in the staggered partially narrowed flow field. The reason can be attributed to the interface between gas channel and GDL, where the low velocity cannot eliminate the mass transport resistance, so that the model overestimated the oxygen mass fraction at rib boundaries, as shown in Fig. 3.The effects of dimensionless moduli on the current density are exhibited in Fig. 4. In case of θ = 1, when Pe is lower than 5, the under-rib convection cannot obviously boost the under-rib oxygen concentration, which was also reported in our previous study[1]. On the other hand, in case of θ< 1 and Pe > 0, although little increase on Pe remarkably improves the under-rib mass transfer which explains the good performance of serpentine flow field, the benefits from the under-rib convection reduces when Pe is high. Additionally, since oxygen cannot be supplied sufficiently from the gas channel, higher φ gives lower under-rib oxygen concentration. Conclusions The theoretical model for describing the under-rib transport phenomenon was established and verified by CFD calculation, which was found to be dominated by 3 dimensionless moduli. The model demonstrates that the Péclet number is required to be large enough in partially narrowed flow fields to maximize the profits from the under-rib convection. Acknowledgment This work was supported by the FC-Platform Program: Development of design-for-purpose numerical simulators for attaining long life and high performance project (FY 2020–FY 2023) conducted by the New Energy and Industrial Technology Development Organization (NEDO), Japan. Reference [1] Y. Ma et al., ECS Trans., 109 (9), 171–197 (2022).[2] M. Kawase et al., ECS Trans., 75(14), 147–156 (2016). Figure 1

Solving Navier–Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes

Solving Navier–Stokes Equations with Stationary and Moving Interfaces on Unfitted Meshes

Mechanism of width effects on cavity-induced transitions at hypersonic speed using direct numerical simulation

Cavities on the surfaces of hypersonic vehicles cannot be avoided easily. Moreover, they can trigger boundary layer transition under certain conditions. However, little progress has been reported on boundary layer transitions induced by a three-dimensional (3-D) shallow cavity. In this study, transitions induced by six 3-D shallow cavities with the same length–depth ratios of 20 and different widths of 0.25, 0.5, 0.75, 1.0, and 1.5 times the baseline width (W), as well as infinite width, were investigated. A direct numerical simulation was conducted using the Roe scheme with 4th-order minimum dispersion and controllable dissipation, and weighted essentially non-oscillatory reconstruction, based on our in-house code: Unsteady NavIer–STokes equations solver. Cavity width was observed to have non-monotonic influences on transition. Both the 0.25 and 1.0 W cavities could induce transition constantly. Moreover, flow was maintained as laminar past the 1.5 W and InfW cavities. For the 0.5 and 0.75 W cavities, intermittent transition was observed with different intermittency factors. The intermittent transition phenomenon was determined to be caused by the periodic increase and decrease in the adverse pressure gradient (APG) in the front part of cavity. Notably, the recirculation with a synchronic size change was the origin of the APG oscillation.

Enhancing physics informed neural networks for solving Navier–Stokes equations

SummaryFluid mechanics is a critical field in both engineering and science. Understanding the behavior of fluids requires solving the Navier–Stokes equation (NSE). However, the NSE is a complex partial differential equation that can be challenging to solve, and classical numerical methods can be computationally expensive. In this paper, we propose enhancing physics‐informed neural networks (PINNs) by modifying the residual loss functions and incorporating new computational deep learning techniques. We present two enhanced models for solving the NSE. The first model involves developing the classical PINN for solving the NSE, based on a stream function approach to the velocity components. We have added the pressure training loss function to this model and integrated the new computational training techniques. Furthermore, we propose a second, more flexible model that directly approximates the solution of the NSE without making any assumptions. This model significantly reduces the training duration while maintaining high accuracy. Moreover, we have successfully applied this model to solve the three‐dimensional NSE. The results demonstrate the effectiveness of our approaches, offering several advantages, including high trainability, flexibility, and efficiency.

Physics-informed neural network combined with characteristic-based split for solving Navier–Stokes equations

This paper presents a novel approach for solving the shallow-water transport equation using a physics-informed neural network (PINN) combined with characteristic-based split (CBS). Our method separates the variables, so it is no need to consider the weight coefficients between different loss functions. As not all partial derivatives are involved in the gradient backpropagation, our method can save half of the memory occupation without losing accuracy, and resulting in a significant reduction in computation time compared to traditional PINN. We solving the progress of the dispersion of hot water under known flow fields. Furthermore, we propose a boundary condition that accounts for the second-order partial derivative term, which is more appropriate for solving the diffusion equation with open domains than the commonly used assumption of zero boundary values. Our numerical results demonstrate that this boundary condition leads to improved convergence of the network. In addition, we introduce a parameter estimation method to estimate the diffusion coefficient of hot water flow, which requires information from the field at only two different times. We observe that excessive participation of variables in gradient backpropagation can lead to neural networks getting trapped in local optima. We use PINN combined with CBS method to solve 3-D incompressible flow. As the number of variables involved in gradient backpropagation increases, the accuracy of the solution decreases, which can partially support our viewpoint. The source codes for the numerical examples in this work are available at https://github.com/double110/PINN-cbs-.git.

Numerical analyses of the flow past a short rotating cylinder

This work studies the three-dimensional flow dynamics around a rotating circular cylinder of finite length, whose axis is positioned perpendicular to the streamwise direction. Direct numerical simulations and global stability analyses are performed within a parameter range of Reynolds number $Re=DU_\infty /\nu &lt;500$ (based on cylinder diameter $D$ , uniform incoming flow velocity $U_\infty$ ), length-to-diameter ratio ${\small \text{AR}}=L/D\leq 2$ and dimensionless rotation rate $\alpha =D\varOmega /2U_\infty \leq 2$ (where $\varOmega$ is rotation rate). By solving Navier–Stokes equations, we investigated the wake patterns and explored the phase diagrams of the lift and drag coefficients. For a cylinder with ${\small \text{AR}}=1$ , we found that when the rotation effect is weak ( $0\leq \alpha \lesssim 0.3$ ), the wake pattern is similar to the unsteady wake past the non-rotating finite-length cylinder, but with a new linear unstable mode competing to dominate the saturation state of the wake. The flow becomes stable for $0.3\lesssim \alpha \lesssim 0.9$ when $Re&lt;360$ . When the rotation effect is strong ( $\alpha \gtrsim 0.9$ ), new low-frequency wake patterns with stronger oscillations emerge. Generally, the rotation effect first slightly decreases and then sharply increases the $Re$ threshold of the flow instability when $\alpha$ is relatively small, but significantly decreases the threshold at high $\alpha$ ( $0.9&lt;\alpha \leq 2$ ). Furthermore, the stability analyses based on the time-averaged flows and on the steady solutions demonstrate the existence of multiple unstable modes undergoing Hopf bifurcation, greatly influenced by the rotation effect. The shapes of these global eigenmodes are presented and compared, as well as their structural sensitivity, visualising the flow region important for the disturbance development with rotation. This research contributes to our understanding of the complex bluff-body wake dynamics past this critical configuration.

Abstract 18625: Mechano-Transcriptomic Interaction Mediates Spatial Variations in Early Vascular Fibrosis

Background: The spatiotemporal variations of wall shear stress (WSS) modulate vascular genomics and function. Despite the advances in imaging modalities and computational modeling, the link between local hemodynamics and genetic pathways underlying atherosclerosis development remains elusive. We hypothesized that differential WSS patterns in the aorta modulate fibroblast gene expression in response to high fat diet (HFD) leading to vascular stiffness. Methods: We performed ultrasound-based 4-D+time moving boundary computational fluid dynamics (CFD) on the aorta of Ldlr -/- mice fed a normal diet (ND) or HFD during 4 weeks. B-mode images (Vevo 3100) of the aortic arch were used to reconstruct a 3-D model of the lumen structure by revolving the vessel wall around the centerline in the aorta and the branches. Computational domain reconstruction was followed by image registration to generate a moving boundary model. WSS contours and velocity profiles were acquired by solving Navier-Stokes equations using svFSI code. The longitudinal strains along the outer curvature of the aortic arch over several cardiac cycles were measured, and the changes were compared with the effects of HFD. Mouse aortas were processed for single cell RNA sequencing and analyzed using the Scanpy package. Results and Conclusion: Our analysis of transcriptomics profiles revealed increased Acta2 and Postn expression in the myofibroblast subclusters, suggesting myofibroblast differentiation in response to HFD in the aortic arch. This was confirmed and localized to the lesser curvature of the aortic arch through Periostin immunostaining. We found that the increase in Postn and Acta2 is associated with reduced arterial strain or increased arterial stiffness measured in the aortic arch. In parallel, CFD analysis demonstrated that an elevated WSS along the outer curvature vs. low WSS and disturbed flow along the inner curvature in early diastole results in differential gene expression to regulate myofibroblast differentiation and modulates vascular stiffness.

Numerical Study on the Aerodynamic Heating Characteristics of the Cantilevered Injection System for Oblique Detonation Engine Inlets

This paper investigates the flowfield patterns and distributions of surface heat flux of the cantilevered injection system for oblique detonation engine inlets. Three-dimensional complex shock wave/boundary layer interaction and shock wave/shock wave interaction between injectors are studied by solving Navier–Stokes equations under laminar flow conditions. The results indicate that there are three possible positions of localized peak heat flux, i.e., the leading edge of the injector near the bottom, the inlet wall surface below the injector, and the downstream of the injector sidewall. All the regions of high heat flux are related to flow reattachment or stagnation. Three types of flow patterns are observed along the inlet surface, i.e., partial separation, completely regular separation, and completely nonregular separation, resulting in increasingly complex distributions of heat flux. The localized peak heat flux which appears at the leading edge and the sidewalls of the injectors can reach values dozens of times higher than the undisturbed region within the interaction region.

The acoustic streaming effects and transmission mechanisms of a micro-cavity acoustic black hole structure with an abrupt cross-section

This paper investigates the acoustic streaming effects (ASEs) and mechanisms behind the transmittance of sound in a metallic micro-cavity acoustic black hole (ABH) structure with an abrupt cross-section and examines the sound field flow characteristics inside the micro-cavity ABH under the sound excitation, such as the velocity, acceleration and pressure fields. And the sound transmission mechanisms are characterized by the ASEs which can be obtained by solving Navier–Stokes equations. The numerical results show that the sharp increase in the velocity and acceleration at the ABH tip position is the main reason for the focusing of the sound energy. And the dramatic increase in the tip cross-section reduces the acoustic streaming velocity, which is the main reason for the attenuation of the sound energy. Additionally, the thermoviscous effect of the acoustic boundary layer can also dissipate the low-frequency sound energy. The sound insulation experiment shows that the proposed micro-cavity ABH structure has a sound transmission loss (STL) of over 15[Formula: see text]dB in the low-frequency regime. This research reveals the mechanisms of the ASE’s work on the sound transmission properties of the micro-cavity ABH and provides new insight into low-frequency sound wave suppression. The ABH structure proposed in this paper has excellent strength, bearing capacity and long lifecycle, so it can be applied in the construction industry through its integrated design of structure and performance.

Applying Physics-Informed Neural Networks to Solve Navier–Stokes Equations for Laminar Flow around a Particle

In recent years, Physics-Informed Neural Networks (PINNs) have drawn great interest among researchers as a tool to solve computational physics problems. Unlike conventional neural networks, which are black-box models that “blindly” establish a correlation between input and output variables using a large quantity of labeled data, PINNs directly embed physical laws (primarily partial differential equations) within the loss function of neural networks. By minimizing the loss function, this approach allows the output variables to automatically satisfy physical equations without the need for labeled data. The Navier–Stokes equation is one of the most classic governing equations in thermal fluid engineering. This study constructs a PINN to solve the Navier–Stokes equations for a 2D incompressible laminar flow problem. Flows passing around a 2D circular particle are chosen as the benchmark case, and an elliptical particle is also examined to enrich the research. The velocity and pressure fields are predicted by the PINNs, and the results are compared with those derived from Computational Fluid Dynamics (CFD). Additionally, the particle drag force coefficient is calculated to quantify the discrepancy in the results of the PINNs as compared to CFD outcomes. The drag coefficient maintained an error within 10% across all test scenarios.

Effect of Gurney Flap on the Aerodynamic Performance of a Flapping Foil: Micro-Aerial Vehicle Application

Abstract Even with its small size, the Gurney flap (GF) can help considerably in increasing the lift of foils and wings. To exploit this feature, the objective of this research was to numerically study the effects of this flow control device on the aerodynamic performance of oscillating foils for micro-aerial vehicle (MAV) applications. Three sets of each important parameter were selected: the height (0.01c, 0.04c, and 0.16c), angle (45 deg, 90 deg, and 135 deg) and location from trailing edge (T.E, 0.05c and 0.1c). A two-dimensional laminar, incompressible Navier–Stokes equation solver was used to computationally investigate the effect of the Gurney flap on the aerodynamic performance of a flat plate (chord length = 10 mm and thickness = 0.03c). It was found that the best aerodynamic performance was obtained when the Gurney flap was installed at the trailing edge with a height of 0.04c and mount angle of 90 deg. The height of the Gurney flap had a major impact on aerodynamic performance. Results showed an increase of 23.5% in mean lift coefficient, 15.5% in maximum lift coefficient, and 5% in power economy as compared to flat plate, which is accredited to the increase in effective camber and the formation of counter-rotating vortices, decreasing the adverse pressure gradient. The weakening of counter-rotating vortices downstream of Gurney flap could also be the contributing factor to its good performance. The results suggest that the Gurney flap may be useful in enhancing the performance of wings for bio-inspired flapping wing MAVs.

Parameter Analysis of Active Flap Control for Rotor Aerodynamic Control and Design

Active rotor control of helicopters is the future development direction, and active flap control (AFC) is one of the most promising technologies. However, the numerical simulation of an AFC rotor is challenging. It is necessary to consider the fidelity of the local flow details while dealing with complex shapes and motions. Therefore, few simulations of the flow field and analyses of the influencing parameters have been conducted. In particular, there is a lack of aerodynamic design criteria and recommendations for the AFC rotor. Thus, a new overset assembly algorithm, an arbitrary multilevel moving grid transformation algorithm, and a solver for the unsteady Reynolds-averaged Navier-Stokes equations (URANS) are proposed to establish a suitable numerical method for AFC rotor simulation. The aerodynamic characteristics of the rotor and key influencing factors are systematically analyzed under different flow conditions and design and control parameters, and suggestions for the design of the AFC rotor are provided. The results show that the AFC significantly changes the load distribution of the rotor. The thrust loss of the rotor is approximately 1%, but the offset angle compensates for the loss. The control parameters show relatively consistent trends under different working conditions. The phase is the key control parameter, and the effect on the load is more pronounced when the control frequency is an integral multiple of the rotor’s natural load frequency. Increasing the chord length, span length, and deflection amplitude can also enhance the active control performance.

Hybrid numerical methods for modelling multi-physics mass transport in coal

It is a challenging task to predict and analyse the transient flow physics in unconventional complex geological formations such as coal seams. This is due to the multi-scale multi-physics nature of processes taking place in coal seam gas reservoirs. Therefore, numerical tools allowing the incorporation of various flow physics inherent to coal into the simulation routine are of particular importance. At the pore-scale, the rock images obtained by micro-computed tomography are frequently used for flow modelling in porous or fractured media by direct numerical simulations (Lattice Boltzman method or by solving Navier Stokes equations) or by utilising so-called pore-network modelling. Both methods have advantages and drawbacks, while their hybridisation may allow us avoid some of the major pitfalls. Due to a limited number of research dedicated to image-based pore-scale modelling in coal, we develop a hybrid numerical model that combines the Hagen-Poiseuille analytical solution and the volume of fluid advection scheme for fluid flow in fractures with the continuum Darcy flow in the coal matrix. The explicit coupling of fluid flow across the fracture-matrix domains is implemented via corresponding source terms in the governing equations. Besides, additional physics including sorption and matrix swelling-shrinkage phenomena are introduced into the numerical model. The hybrid solver is validated against analytical solutions and a previously developed Darcy-Brinkman-Stokes framework, which has similar functionality for modelling fluid flow in coal seams. To validate the developed model and show its capability to capture multi-scale multi-physics flow in coal, several illustrative simulations are conducted using synthetic and realistic digital images of coal. As a result, the accuracy of the hybrid solver was within 4% when compared to the Darcy-Brinkman-Stokes framework for flow simulation on realistic geometry. Besides, the non-parallelised hybrid model outperformed the parallelised direct numerical simulation, being more than 90 times faster in terms of computational time. The findings are beneficial for conducting larger core-scale simulations of multi-scale multi-physics flow in coal seams with potential applications to natural gas production, hydrogen storage, and carbon dioxide geosequestration.