Two-dimensional Flow Research Articles

Approximation of sea surface velocity field by fitting surrogate two-dimensional flow to scattered measurements

In this paper, a rapid approximation method is introduced to estimate the sea surface velocity field based on scattered measurements. The method uses a simplified two-dimensional flow model as a surrogate model, which mimics the real submesoscale flow. The proposed approach treats the interpolation of the flow velocities as an optimization problem, aiming to fit the flow model to the scattered measurements. To ensure consistency between the simulated velocity field and the measured values, the boundary conditions in the numerical simulations are adjusted during the optimization process. Additionally, the relevance of quantity and quality of the scattered measurements is assessed, emphasizing the importance of the measurement locations within the domain as well as explaining how these measurements contribute to the accuracy and reliability of the sea surface velocity field approximation. The proposed methodology has been successfully tested in both synthetic and real-world scenarios, leveraging measurements obtained from Global Positioning System (GPS) drifters and high-frequency (HF) radar systems. The adaptability of this approach for different domains, measurement types and conditions implies that it is suitable for real-world submesoscale scenarios where only an approximation of the sea surface velocity field is sufficient.

The influence of astronomical tide phases on urban flooding during rainstorms: Application to Macau

Study regionThe study area is the western part of the Macau Peninsula in China, with an area of 4.06 km2. Study focusThis study developed a coupled hydrological-hydraulic model that simulates the two-dimensional (2D) surface flow and one-dimensional (1D) drain pipe flow of compound inundation. The model was applied to Macau, China, as a study area, and the typhoon Mangkhut in 2018 was used as a case study to validate the model’s performance. Simulating compound inundation scenarios of extreme rainfall and astronomical tide and exploring the influence of astronomical tide on coastal urban inundation. New hydrological insights for the regionUrban flood disasters are profoundly influenced by tidal levels, albeit the height of tides alone does not solely exacerbate the phenomenon. Rather, the phase of astronomical tides during rainfall also plays a crucial role in determining the severity of urban flooding. This research has revealed that when rainfall synchronizes with the recession phase of the spring tide, urban flooding conditions become acute, 17.66 % increase in total surface water volume for the scenario with the highest tidal level impact compared to the scenario with the lowest tidal level impact. This paper presents the response of coastal cities to the flooding process under different combined rainstorm-astronomical tide scenarios, to provide scientific guidance for disaster preparedness planning in coastal areas, and to improve the resilience of disasters.

Unveiling air sparging analysis in flow cells through the continuum approach

We present various analytical solutions for a two-dimensional steady air source that demonstrate classical flow physics’ usefulness in air-sparging evaluation. These solutions capture different flow geometry and setup effects while offering accuracy, speed, and a deeper understanding of governing physics. Compared to empirical models, they excel with fewer physical parameters. We validate their accuracy by comparing these solutions to experimental air-sparging data from two-dimensional flow cells. This comparison underscores the applicability of the physical model and establishes a relationship between grain size and a key model parameter. Furthermore, this analysis enables predictive capabilities for scaled-up systems with diverse setup geometries.Plain Language Summary Air-sparging refers to the injection of air below the groundwater table, that is, to the water-saturated section of the aquifer. Air-sparging is used to facilitate the volatilization of organic pollutants (e.g., solvents, gasoline) and their extraction to the soil surface. However, evaluating and modeling the flow and distribution of air is limited by the complicated physics of unstable multiphase flow. These complexities drive researchers to search for empirical relations and rules of thumb to design air-sparging systems. In this research, we use previously published experimental data to demonstrate the capabilities and discuss the limitations of the classical physical solutions of steady single-phase flow to evaluate air flow through wet porous media such as aquifers.

Particle spacing and stability of initially staggered deformable particle trains migrating in a channel

Abstract We investigated the inertial migration of deformable particles in a two-dimensional channel flow. This study analyzes the effects of the channel Reynolds number ($Re$), channel blockage ratio ($k$), particle number ($N_p$) and reduced bending modulus ($E_b$) on the formation of staggered particle trains. The results show that the stable normalized distance $d_{p_{eq}} / H$ between two staggered particles is influenced by $Re$, $k$ and $E_b$, where $H$ is the channel width. As $k$ increases or $E_b$ decreases, $d_{p_{eq}} / H$ decreases. The value of $d_{p_{eq}} / H$ initially increases and then decreases with the increase of $Re$; when $E_b$ is large and $k$ is small, $d_{p_{eq}} / H$ continuously increases with increasing $Re$. With the increase of $N_p$, the closely arranged staggered particle trains evolve into five distinct migration Regimes. We explain the conditions for the formation of each Regime and explore the mechanisms of their interconversion. The findings of this study contribute to a better understanding of the self-organization process of deformable particles in channel flow.

Optimizing vortex-induced vibration suppression in π-shaped girders using wind tunnel testing and CFD analysis

This investigation meticulously explores the vortex-induced vibration (VIV) characteristics in Π-shaped girders within long-span cable-stayed bridges, presenting novel VIV mitigation techniques. Employing detailed wind tunnel evaluations of a 1:50 scale model alongside computational fluid dynamics (CFD) analyses to model the two-dimensional flow around the girder, this study reveals the formation and shedding of vortices behind the railings and main steel girder, which significantly contribute to VIV in such structures. The introduction of horizontal splitter plates, one m in width, in conjunction with two-m-wide V-shaped guide vanes, was found to substantially reduce the VIV amplitude of the Π-shaped girder, minimizing vortex generation on the deck’s sides and dramatically reducing the maximum vertical VIV amplitude from 208.75 mm to only 5.56 mm. CFD simulations confirm the effectiveness of these measures in suppressing Karman vortex street formation, thereby significantly improving downstream airflow characteristics. These findings offer pivotal insights for the advancement of bridge design and the proactive management of VIV, showcasing the potential of integrated aerodynamic modifications to enhance structural resilience and performance.

Thermal and irreversibility analysis of non-Newtonian fluid within trapezoidal cavity containing heated cylinder

In this article, the mixed convection transport of the Carreau fluid in the presence of a magnetic field and a heated circular cylinder within a trapezoidal cavity is examined. Finite element analysis is used via COMSOL Multiphysics software to simulate the two-dimensional flow. The heat equation is formulated by incorporating the effects of viscous dissipation and Joule heating. The upper and lower surfaces of the cavity are adiabatic, while the left and right sides are assumed to be cold. The temperature distribution and flow field within the cavity are visualized through the plotting of isotherms, streamlines, and total entropy generation. The graphical representations are performed to examine the impacts of physical parameters on temperature, flow field, and total entropy generation, including the Reynolds number , Weissenberg number ( 1.0 ≤ We ≤ 6.0 ) , Power law index ( 0.1 ≤ n ≤ 5.0 ) , Hartman number ( 1.0 ≤ M ≤ 50 ) , and Richardson number ( 0.2 ≤ Ri ≤ 5.0 ) and ( 0.2 ≤ Rc ≤ 0.8 ) . It is found that the Joule heating and Richardson number are the main reasons to increase the thermal performance within the cavity. The r ( 100 ≤ Re ≤ 500 ) ising values of power law index and Weissenberg numbers caused to reduce the velocity field, irreversible effects and circulation within cavity. While the entropy is augmented by elevating the Eckert and Hartmann numbers. Furthermore, heat transfer improved with the increased magnetic field and Eckert number.

Exact planetary waves and jet streams

We investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a $\beta$ -plane approximation at the equator, and the second to a $\gamma$ approximation, with the latter describing flow near the poles. We find exact wave solutions in the Lagrangian reference frame that cannot be written down in closed form in the Eulerian reference frame. The wave particle trajectories, contours of potential vorticity and Lagrangian mean velocity take relatively simple forms. The waves possess a non-trivial Lagrangian mean flow that depends on the amplitude of the waves and on a particle label that characterizes values of constant potential vorticity. The mean flow arises due to potential vorticity conservation on fluid particles. Solutions over the entire space are generated by assuming that the flow far from the origin is zonal and there is a region of uniform potential vorticity between this zonal flow and the waves. In the $\gamma$ approximation, a class of waves is found that, based on analogous solutions on the plane, we call Ptolemaic vortex waves. The mean flow of some of these waves, which we can describe in highly nonlinear scenarios due to the exact nature of the solutions, resembles polar jet streams. Several illustrative solutions are used as initial conditions in the fully spherical rotating Navier–Stokes equations, where integration is performed via the numerical scheme presented in Salmon & Pizzo (Atmosphere, vol. 14, issue 4, 2023, 747). The potential vorticity contours found from these numerical experiments vary between stable permanent progressive form and fully turbulent flows generated by wave breaking.

Long time behavior for the two-dimensional magnetohydrodynamic flows in a general domain

By utilizing spectral analysis methods and properties of fractional order operators, some new estimates have been established for the nonlinear terms appearing from the two-dimensional non-stationary magnetohydrodynamic flows in a general domain. Based on these, a series of energy decay properties are given. Furthermore, the large time decay behavior of the solution and that of its gradient have also been addressed in the L∞ and L2 spaces, respectively.

Decomposition of nonlinear collision operator in quantum Lattice Boltzmann algorithm

We propose a quantum algorithm to tackle the quadratic nonlinearity in the Lattice Boltzmann (LB) collision operator. The key idea is to build the quantum gates based on the particle distribution functions (PDF) within the coherence time for qubits. Thus, both the operator and a state vector are linear functions of PDFs, and upon quantum state evolution, the resulting PDFs will have quadraticity. To this end, we decompose the collision operator for a DmQn lattice model into a product of operators, where n is the number of lattice velocity directions. After decomposition, the operators with constant entries remain unchanged throughout the simulation, whereas the remaining will be built based on the statevector of the previous time step. Also, we show that such a decomposition is not unique. Compared to the second-order Carleman-linearized LB, the present approach reduces the circuit width by half and circuit depth by exponential order. The proposed algorithm has been verified through the one-dimensional flow discontinuity and two-dimensional Kolmogrov-like flow test cases.

Binary collision dynamics of immiscible Newtonian and non-Newtonian fluid droplets

This experimental and theoretical study is devoted to the investigation of head-on collisions of two immiscible Newtonian and non-Newtonian droplets. The density of the two droplets is similar, and the viscosity of 0.3% carboxymethyl cellulose droplet is slightly larger than 10 cSt silicone oil. The sizes and relative velocity of the colliding droplets close to the point of impact are measured by means of image processing. The deformed states after the impact and their evolution with time are studied by experimental visualization and the energy evolution with time are discussed by numerical results. The accuracy of the two-dimensional axisymmetric three-phase flow computational model is validated. We study the effects of collisions of non-Newtonian droplets with Newtonian droplets and the subsequent retraction kinetics. Droplet “cannibalization” is commonly observed: after collision and spreading, the droplet retracts rapidly, resulting in a Newtonian droplet wrapping around a non-Newtonian droplet. We show the whole process of droplet collision captured by a high-speed camera and obtain the cloud and velocity vector maps of the droplets by numerical simulation. The droplet wrapping phenomenon is produced by different three-phase interfacial tensions and viscosities. We delineate the different phases of the collision process and discuss the dominant forces in each phase. We calculate the energy evolution of the spreading phase and use it to derive a predictive model for the dimensionless maximum spreading diameter and spreading time.

Stiefel manifold interpolation for non-intrusive model reduction of parameterized fluid flow problems

Many engineering problems are parameterized. In order to minimize the computational cost necessary to evaluate a new operating point, the interpolation of singular matrices representing the data seems natural. Unfortunately, interpolating such data by conventional methods usually leads to unphysical solutions, as the data live on manifolds and not vector spaces. An alternative is to perform the interpolation in the tangent space to the Grassmann manifold to obtain interpolated spatial modes. Temporal modes are afterwards determined via the Galerkin projection of the high-fidelity model onto the interpolated spatial basis. This method, which is known for some fifteen years, is intrusive. Recently, Oulghelou and Allery (JCP, 2021) have proposed a non-intrusive approach (equation-free), but requiring the resolution of two low-dimensional optimization problems after interpolation. In this paper, a non-intrusive alternative based on Interpolation on the Tangent Space of the Stiefel Manifold (ITSSM) is presented. This approach has the advantage of not requiring a calibration phase after interpolation. To assess the method, we compare our results with those obtained using global POD on the one hand, and two methods based on Grassmann interpolation on the other. These comparisons are performed for two classical configurations encountered in fluid dynamics. The first corresponds to the one-dimensional non-linear Burgers' equation. The second example is the two-dimensional cylinder wake flow. We show that the proposed strategy can accurately reconstruct the physical quantities associated with a new operating point. Moreover, the estimation is fast enough to allow real-time computation.

A high-order generalised differential quadrature element method for simulating 2D and 3D incompressible flows on unstructured meshes

In this paper, a high-order generalised differential quadrature element method (GDQE) is proposed to simulate two-dimensional (2D) and three-dimensional (3D) incompressible flows on unstructured meshes. In this method, the computational domain is decomposed into unstructured elements. In each element, the high-order generalised differential quadrature (GDQ) discretisation is applied. Specifically, the GDQ method is utilised to approximate the partial derivatives of flow variables and fluxes with high-order accuracy inside each element. At the shared interfaces between different GDQ elements, the common flux is computed to account for the information exchange, which is achieved by the lattice Boltzmann flux solver (LBFS) in the present work. Since the solution in each GDQ element solely relies on information from itself and its direct neighbouring element, the developed method is authentically compact, and it is naturally suitable for parallel computing. Furthermore, by selecting the order of elemental GDQ discretisation, arbitrary accuracy orders can be achieved with ease. Representative incompressible flow problems, including 2D laminar flows as well as 3D turbulent simulations, are considered to evaluate the accuracy, efficiency, and robustness of the present method. Successful numerical simulations, especially for scale-resolving 3D turbulent flow problems, confirm that the present method is efficient and high-order accurate.

A Comprehensive Analysis on Thermally Enhanced Electro-Magneto-Hydrodynamic Micropolar Flow Mixture Comprising Water (70%) and Ethylene-Glycol (30%) with Alumina Nanoparticles over a Riga Plate

In this research paper, a two-dimensional flow of an electro-magneto-hydrodynamic water-ethylene glycol-based nanofluid over a Riga plate has been presented. The nanofluid mixture has micropolar and electrical behaviors. Furthermore, the effects of chemical reaction and activation energy are imposed in the present investigation. It is important to mention that the nanofluid mixture is composed of alumina nanoparticles (Al2O3) and base fluid as water-ethylene glycol (70:30). It is important to mention that the significance of this study lies in engineering cooling systems, drug delivery, and microfluidic devices. The main equations of problem have converted to dimension-free form using similarity variables. The transformed ODEs are then converted into first-order differential equations and solved numerically by executing the shooting method. The validation on the modeled equations is confirmed by validating the present analysis with the results available literature. From this analysis, it is obtained that the greater micropolar parameter and modified Hartmann number enhanced the streamwise velocity profile while reducing micro-rotational velocity. The greater micro-gyration constraint reduced streamwise velocity profile while enhancing micro-rotational velocity. The greater thermophoresis factor and thermal Biot number enhanced both thermal and concentration profiles. The greater activation energy factor enhanced the concentration distribution, and the greater Brownian motion factor and Schmit number reduced the concentration distribution. The higher thermophoresis factor reduced the heat transfer rate, and the higher heat source factor and thermal Biot number enhanced heat transfer rate.

Heat Transfer Characteristics of a Quiescent Fluid over a Moving Flat Surface

Optimizing thermal control methods and enhancing the efficiency of various engineering processes, such as the cooling of hot moving surfaces, is imperative. Therefore, it is crucial to investigate heat transfer and temperature distributions across moving surfaces in stationary fluids. In this study, the combined effects of viscous dissipation, temperature-dependent viscosity, and a moving surface in a quiescent fluid on the temperature and velocity profiles are investigated. A two-dimensional steady laminar boundary layer flow of an incompressible Newtonian fluid, driven by the movement of the surface where viscosity is an inverse function of temperature, is analyzed. The effects of flow parameters, including Reynolds number, Eckert number, Prandtl number, variable viscosity, and surface velocity on temperature and velocity profiles, are determined. The governing boundary layer partial differential equations are transformed into non-dimensional form and solved using the central finite difference numerical method, implemented in MATLAB software. The numerical results demonstrate that an increase in the Reynolds number and the variable viscosity parameter leads to an increase in the velocity profiles. Additionally, an increase in Reynolds number, Prandtl number, variable viscosity, and surface velocity leads to a decrease in temperature profiles. Finally, an increase in the Eckert number results in higher temperature profiles. Therefore, with suitable flow parameters, the temperature of the fluid can be regulated. These findings are useful in cooling hot sheets or metallic plates drawn over a quiescent fluid to obtain high-quality final products.

Observation of Two-Dimensional Dam Break Flow and a Gaseous Phase of Solitons in a Photon Fluid.

We report the observation of a two-dimensional (2D) dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to 2D nonlinear dynamics. We observe wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D soliton gas in integrable systems. We measure the statistical features of this gaslike phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.

Neural fields for rapid aircraft aerodynamics simulations

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains for different flow conditions, handle non-parametric 3D geometric variations, and generalize to unseen shapes at test time. The coordinate-based formulation naturally leads to robustness with respect to discretization, allowing an excellent trade-off between computational cost (memory footprint and training time) and accuracy. The method is demonstrated on two industrially relevant applications: a RANS dataset of the two-dimensional compressible flow over a transonic airfoil and a dataset of the surface pressure distribution over 3D wings, including shape, inflow condition, and control surface deflection variations. On the considered test cases, our approach achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures. Remarkably, the method can drastically accelerate high fidelity numerical solver, achieving a five order of magnitude speedup on the RANS transonic airfoil dataset.

Momentum, energy and vorticity balances in deep-water surface gravity waves

The particle trajectories in irrotational, incompressible and inviscid deep-water surface gravity waves are open, leading to a net drift in the direction of wave propagation commonly referred to as the Stokes drift, which is responsible for catalysing surface wave-induced mixing in the ocean and transporting marine debris. A balance between phase-averaged momentum density, kinetic energy density and vorticity for irrotational, monochromatic and spatially periodic two-dimensional water waves is derived by working directly within the Lagrangian reference frame, which tracks particle trajectories as a function of their labels and time. This balance should be expected as all three of these quantities are conserved following particles in this system. Vorticity in particular is always conserved along particles in two-dimensional inviscid flow, and as such even in its absence it is the value of the vorticity that fundamentally sets the drift, which in the Lagrangian frame is identified as the phase-averaged momentum density of the system. A relationship between the drift and the geometric mean water level of particles is found at the surface, which highlights connections between the geometry and dynamics. Finally, an example of an initially quiescent fluid driven by a wavelike pressure disturbance is considered, showing how the net momentum and energy from the surface pressure disturbance transfer to the wave field, and recognizing the source of the mean Lagrangian drift as the net momentum required to generate an irrotational surface wave by any conservative force.

Generative learning for forecasting the dynamics of high-dimensional complex systems

We introduce generative models for accelerating simulations of high-dimensional systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are down sampled to a lower dimensional manifold that is evolved through an auto-regressive attention mechanism. In turn, Bayesian diffusion models, that map this low-dimensional manifold onto its corresponding high-dimensional space, operate on batches of physics correlated, time sequences of data and capture the statistics of the system dynamics. We demonstrate the capabilities and drawbacks of G-LED in simulations of several benchmark systems, including the Kuramoto-Sivashinsky (KS) equation, two-dimensional high Reynolds number flow over a backward-facing step, and simulations of three-dimensional turbulent channel flow. The results demonstrate that generative learning offers new frontiers for the accurate forecasting of the statistical properties of high-dimensional systems at a reduced computational cost.

Shear wave elastography to evaluate the effect of serum uric acid levels on carotid artery elasticity in patients with high-normal blood pressure

Background: Populations with normal high blood pressure often already have elevated blood uric acid levels and a higher chance of developing atherosclerosis, which accelerates the process of cardiovascular disease. The risk of atherosclerosis increases with thickening of the carotid artery intima-media, and changes in carotid artery elasticity precede intima-media changes, so early monitoring of carotid artery elasticity is of great significance in the prevention of cardiovascular disease. Using shear wave elastography (SWE) to evaluate the effect of serum uric acid (SUA) levels on carotid artery elasticity in patients with high-normal blood pressure (BP). Methods: One hundred and fifteen patients with high-normal BP were selected, and then divided into tertiles according to the SUA levels. The left carotid intima-media thickness (IMT), peak systolic velocity (PSV) and diameter of common carotid artery were measured by two-dimensional ultrasound and Doppler flow imaging. Longitudinal elasticity of the left anterior carotid wall was measured by SWE, including the mean values of the minimum elastic modulus (MEmin), maximum elastic modulus (MEmax) and mean elastic modulus (MEmean). Results: IMT, MEmean, MEmin and MEmax were obviously higher in the 3rd tertile (all P < 0.05), while there were no obviously different between the 1st tertile and 2nd tertile. Pearson correlation analysis showed positive correlations between SUA and SWE-related parameters, while there was no correlation with IMT. Multiple linear regression analysis found that age, systolic BP, and SUA levels were independently associated with SWE-related parameters. Conclusion: SWE will be more helpful than IMT in monitoring the effect of blood uric acid levels on carotid artery elasticity in patients with high-normal BP.

Enhancing convergence speed with feature enforcing physics-informed neural networks using boundary conditions as prior knowledge

This research introduces an accelerated training approach for Vanilla Physics-Informed Neural Networks (PINNs) that addresses three factors affecting the loss function: the initial weight state of the neural network, the ratio of domain to boundary points, and the loss weighting factor. The proposed method involves two phases. In the initial phase, a unique loss function is created using a subset of boundary conditions and partial differential equation terms. Furthermore, we introduce preprocessing procedures that aim to decrease the variance during initialization and choose domain points according to the initial weight state of various neural networks. The second phase resembles Vanilla-PINN training, but a portion of the random weights are substituted with weights from the first phase. This implies that the neural network’s structure is designed to prioritize the boundary conditions, subsequently affecting the overall convergence. The study evaluates the method using three benchmarks: two-dimensional flow over a cylinder, an inverse problem of inlet velocity determination, and the Burger equation. Incorporating weights generated in the first training phase neutralizes imbalance effects. Notably, the proposed approach outperforms Vanilla-PINN in terms of speed, convergence likelihood and eliminates the need for hyperparameter tuning to balance the loss function.