Flow Method Research Articles

Observation-based quantification of aerosol transport using optical flow: A satellite perspective to characterize interregional transport of atmospheric pollution

Interregional transport plays a significant role in haze formation with varying and disputable contribution extent. Current research on quantitatively analyzing interregional atmospheric pollution transport has mainly relied on meteorological and chemical models. However, these models are typically affected by uncertainties due to the assumptions and simplifications inherent in the numerical simulations and source emission estimations. In this study, a comprehensive optical flow framework is developed to offer a new perspective on quantitative characterization of interregional transport of atmospheric pollution based on synergistic observations from geostationary and sun-synchronous satellites. In this framework, the high-frequency continuous aerosol observing images are regarded as video in computer vision, and an aerosol dynamic optical flow algorithm is proposed by incorporating aerosol-specific assumptions and constraints, overcoming the limitation that traditional optical flow methods are typically confined to rigid bodies. Results demonstrate that the developed optical flow framework could distinguish the aerosol transport process from other dynamic processes of aerosol development and accurately capture the fast-changing details of transport processes. Moreover, the satellite-based optical flow framework achieves aerosol transport results comparable to those of widely accepted model-based methods, demonstrating the physical interpretation of pixel-based optical flow results and highlighting its effectiveness in quantitative characterization of the atmospheric pollution transport process via the Aerosol Transport Index (ATI). Furthermore, a case analysis of long-term assessments of interregional transport of atmospheric pollution indicates that Beijing acts as a “sink” of atmospheric pollution, and a downward trend could be found from the annually averaged transported aerosol net loadings due to the emission reduction policy. Compared with model-based methods, the satellite-based optical flow framework is directly grounded in observations and does not rely on emission inventories that take years to update. Therefore, it not only helps improve understanding the patterns of atmospheric pollution interregional transport, but also provides a more efficient and economical way to assess the effectiveness of regional joint control policy.

Quantitative analysis of hydrogen leakage flow measurement and calculation in the on-board hydrogen system pipelines

The mass flow rate of hydrogen leakage directly affects hydrogen diffusion and concentration distribution. In this paper, a test platform was constructed to measure mass flow rates during hydrogen leakage in the supply pipelines of the on-board hydrogen system. Hydrogen leakage tests were conducted under two different conditions. Mass flow rates were measured for tube fittings with various loosening angles and hydrogen supply pressures. The data were then fitted to extrapolate mass flow rates of hydrogen leakage beyond the tested conditions. Additionally, mass flow rates were measured for hydrogen supply pipelines with small holes of different shapes and sizes. The effects of pipeline size, hydrogen supply pressure, hole shape, and size on the hydrogen leakage mass flow rate were analyzed. Hydrogen leakage flow coefficients were corrected, and the accuracy of three calculation methods for hydrogen leakage flow was compared and analyzed based on the test results. The results provide a foundation for future numerical simulation models of hydrogen leakage diffusion.

A priori and a posteriori error analysis of a mixed DG method for the three-field quasi-Newtonian Stokes flow

Abstract In this paper we propose and analyse a new mixed-type DG method for the three-field quasi-Newtonian Stokes flow. The scheme is based on the introduction of the stress and strain tensor as further unknowns as well as the elimination of the pressure variable by means of the incompressibility constraint. As such, the resulting system involves three unknowns: the stress, the strain tensor and the velocity. All these three unknowns are approximated using discontinuous piecewise polynomials, which offers flexibility for enforcing the symmetry of the stress and the strain tensor. The unique solvability and a comprehensive convergence error analysis for all the variables are performed. All the variables are proved to converge optimally. Adaptive mesh refinement guided by a posteriori error estimator is computationally efficient, especially for problems involving singularity. In line of this mechanism we derive a residual-type a posteriori error estimator, which constitutes the second main contribution of the paper. In particular, we employ the elliptic reconstruction in conjunction with the Helmholtz decomposition to derive the a posteriori error estimator, which avoids using the averaging operator. Several numerical experiments are carried out to verify the theoretical findings.

Adaptability analysis of flow and heat transfer multi-scale numerical method for printed circuit heat exchanger

The printed circuit heat exchanger (PCHE) is a high-efficiency and compact mini-channel heat exchanger. Due to the large number of fine channels, it is difficult to conduct the flow and heat transfer numerical simulation of the entire heat exchanger based on the actual channels, which requires a lot of computational resource and time. In this paper, a simplified multi-scale numerical method with a non-equilibrium porous media model (NOPM) is proposed to study the flow and heat transfer performance of PCHE at high temperature and pressure. The pressure field, velocity field and temperature field of NOPM and actual multi-channel model (MC) under different working conditions are compared to study the adaptability of NOPM for the PCHE. The results indicate that the NOPM can accurately predict the flow and heat transfer performance under PCHE configurations with a large number of channels. However, as the channel number decreases, the relative errors in the temperature and pressure prediction significantly increase due to the increased flow maldistribution. Similarly, the NOPM can well predict the overall temperature distribution of the PCHE solid when the channel number is numerous. This work could support accurate thermal design, and provide accurate temperature field for the thermal stress analysis of PCHE.

Efficiency high-order discontinuous Galerkin method for low speeds flows with time-derivative preconditioning

A local preconditioning high-order discontinuous Galerkin (DG) method is introduced to enhance the efficiency and accuracy of the density-based approach for low-speed flows. The method is based on the time-derivative preconditioning technique typically employed in finite volume methods. Traditional approximation methods that only precondition low-order derivatives lead to incompatibility of the equations. To extend the preconditioning technique to the DG method, we employ an analytic preconditioning mass matrix derived from the DG formulation of the preconditioned Navier–Stokes equations. Modified numerical flux functions and a self-adaptive local velocity truncation parameter are employed for DG systems with preconditioning. We demonstrate the efficiency and accuracy of the preconditioned DG method using explicit and implicit schemes for steady flows and a dual-time scheme for unsteady flows. The method has been implemented and used to compute a variety of flow problems, including inviscid and laminar flows, utilizing various degrees of polynomial approximations. Computations with and without preconditioning are performed to analyze the influence of spatial discretization on the accuracy and convergence of the DG solutions at low Mach numbers. Numerical results underscore the enhanced accuracy and convergence properties of the proposed method for low-speed flows, indicating significant performance improvements over traditional methods.

A coupled immersed boundary method and wall modelling framework for high-Reynolds number flows over complex terrain

We present the development and validation of an immersed boundary method (IBM) along with a wall model (WM) to simulate atmospheric boundary-layer flows over complex terrain. The framework presented here has two novel aspects over standard IBM implementations. First, the underlying schemes are global in nature and require specification of values throughout the solid region. Second, to enable high-Reynolds number simulations, a wall model is coupled to the IBM. The proposed numerical framework is shown to have second-order accuracy. The framework is validated by simulating flow over a 2D as well as 3D cosine-squared hill and comparing to previously published experimental results. The mean velocity and turbulence intensity are reproduced accurately by our LES. The flow over the Bolund hill, marked by steep slopes which makes this a challenging test case, is also simulated and results are compared to field observations showing good agreement. The framework also accurately reproduces the turbulent statistics in the wake of a turbine situated on a flat terrain, with the flat terrain modelled using the IBWM framework, thus demonstrating its applicability to high-Reynolds number atmospheric and wind farm flows over complex terrain.

Publisher's Note: “Prediction–correction projection immersed interface method for interfacial stress-induced flows and applications to electrohydrodynamics [Phys. Fluids 36, 092114 (2024)]

Publisher's Note: “Prediction–correction projection immersed interface method for interfacial stress-induced flows and applications to electrohydrodynamics [Phys. Fluids <b>36</b>, 092114 (2024)]

GPU parallel implementation of a finite volume lattice Boltzmann method for incompressible flows

This work presents a graphics processing units (GPU) parallel algorithm of a cell-centered finite volume lattice Boltzmann method (FVLBM) on unstructured meshes. In the present GPU parallel algorithm, the parallelization is performed in the physical space. To reduce the frequency of GPU memory accesses, this algorithm develops coalesced access to GPU memory. In addition, to avoid the race for resources leading to data anomalies, such as dirty read or phantom read etc., and the double counting for flux calculation, the efficient face-based data structure often used for flux calculation in cells in the central processing unit (CPU) version of FVLBM is modified into a face-based data structure used for the fluxes on all faces, followed by a cell-based loop for the final residuals in all cells. Therefore, the proposed GPU parallel algorithm does not need to use the resource lock and retains the high efficiency of the face-based data structure in the fluxes computation to enhance its’ parallel efficiency. Additionally, to demonstrate the computational efficiency of the proposed GPU parallel algorithm, various benchmark studies are performed in this work by the proposed parallel scheme on a double precision NVIDIA GeForce RTX 3090Ti GPU card, including (a) the lid-driven flow in a two-dimensional (2D) square cavity, (b) a 2D flow past a cylinder, and (c) the lid-driven flow in a three-dimensional (3D) cubic cavity. The numerical results show that the proposed GPU parallel algorithm can be as accurate as the original CPU serial scheme with 1 to 2 orders of speedup.

Uniform error analysis of an exponential IMEX-SAV method for the incompressible flows with large Reynolds number based on grad-div stabilization

Based on the grad-div stabilization and scalar auxiliary variable (SAV) methods, a first-order Euler implicit/explicit finite element scheme is studied for the Navier–Stokes equations with large Reynolds number. In the designing of numerical scheme, the nonlinear term is explicitly treated such that one only needs to solve a constant coefficient algebraic system at each time step. Meanwhile, the proposed scheme is unconditionally stable without any condition of the time step τ and mesh size h. In finite element discretization, we use the stable Taylor-Hood element for the approximation of the velocity and pressure. By a rigorous analysis, we derive an uniform L2 error estimate O(τ+h2) of the velocity in which the constant is independent of the viscosity coefficient. Finally, numerical experiments are given to support theoretical results and the efficiency of the proposed scheme.

Semi-implicit schemes for modeling water flow and solute transport in unsaturated soils

The coupled model of water flow and solute transport in unsaturated soils is addressed in this study. Building upon previous research findings by Keita, Beljadid, and Bourgault, we investigate a class of second-order time-stepping techniques where two free parameters are introduced, to identify the most stable and accurate scheme. The spatial discretization of the Richards equation is accomplished using the mixed finite element method. The proposed approach involves formulating noniterative schemes using an extrapolation formula and Taylor approximation in time to linearize nonlinear terms. Additionally, a specialized regularization technique is applied to ensure the convergence of the proposed numerical methods. Numerical simulations are conducted to determine the optimal scheme for solving the Richards equation, which is subsequently extended to the transport equation.Numerical simulations of water flow reveal the good accuracy of three schemes—SBDF, MSBDF, and Richards-M2 for homogeneous and heterogeneous soils. Notably, the SBDF scheme stands out for its computational efficiency and stability, especially when gravity forces dominate over capillary forces. Through numerical analysis of the coupled semi-implicit schemes, our results affirm the SBDF scheme’s superior robustness, establishing it as the optimal choice among the proposed numerical methods. Therefore, the SBDF scheme is employed to solve the coupled model of water flow and solute transport. We conducted various numerical experiments to solve the coupled model, addressing scenarios including single and multispecies nitrogen transport, pore water electrical conductivity, and nitrate transport. The SBDF scheme’s accuracy was rigorously verified through comparisons with reference solutions and experimental data. This establishes the SBDF scheme as an efficient alternative to traditional implicit methods for modeling water flow and solute transport in unsaturated soils.

An improved pressure gradient method for viscous incompressible flows

The pressure gradient method solves the viscous incompressible flow with the pressure gradients, rather than the pressure, as unknown variables. Two variants of the pressure gradient method have been developed in the past but have not received much attention due to their unsatisfactory performance or implementation complexity. Based on the artificial compressibility concept, this study proposes an improved pressure gradient method. One distinct feature of this method is that it requires no pressure/pressure gradient boundary condition or special treatment on wall boundaries. An auxiliary variable is introduced to represent the velocity dilatation, greatly simplifying the spatial discretization and computational procedure. The mathematical formulations are elaborated and compared with the previous pressure gradient methods, followed by discussions of compatibility relationships, boundary condition setup, and an extension to a pressure Poisson-like equation. Four validation examples are performed for various flow scenarios, and the solutions and domain solenoidity are examined for each case. The study also compares associated computational methods, different pressure boundary conditions, and flow characteristics, demonstrating the benefits of the present method.

Lattice Boltzmann simulations of unsteady Bingham fluid flows

Transient flows of viscoplastic fluids have very peculiar characteristics. The startup and cessation flows of viscoplastic materials have been subject to many theoretical and numerical investigations. The most challenging aspect of numerical solutions of viscoplastic fluids is the viscosity singularity during the transition from yielded to unyielded material. Hence, the proper representation of yield surfaces is the most critical aspect of numerical methods in viscoplastic fluid flow. In the present work, we use a lattice Boltzmann scheme to solve an ideal Bingham fluid’s startup and cessation flows. This numerical scheme advantage is that can represent infinite viscosity without noticeable numerical instabilities, producing yield surfaces with more accuracy and quality. Theoretical solutions for the startup flow are available in the literature. However, it is unclear which is more accurate and what their validity ranges are. Nonetheless, these solutions served as a reference for the present simulations. The overall aspect of the numerical solutions agreed with the theoretical models. The cessation flow of the Bingham fluid was also simulated. Unlike a Newtonian fluid, this type of flow is known to have a finite period until cessation. The simulations correctly reproduced this behavior. The transient yield surfaces matched very well with augmented Lagrangian solutions.

Marangoni flow-guided molecular accumulation for sensitive and rapid SERS detection of phthalates

Public attention has been emerging for the prevention and assessment of healthcare risks from phthalate esters (PAEs) in daily life. For the effective detection of small environmentally hazardous materials, we suggest two major points: i) the formation of high-density hotspots and ii) the delivery of molecules to the activated plasmonic regions. In this study, we developed a method for laser-induced Marangoni flow in cotton fabric (CF) nanopillars (NPs) deposited with Au (Au/CFNPs) for the detection of PAEs by surface-enhanced Raman spectroscopy (SERS). We optimized the performance of the Au/CFNP platforms by adjusting both the maskless plasma etching time and the Au deposition thickness. Narrow (∼8 nm) and populated hotspots were achieved at an Ar plasma treatment time of 30 s and a Au thickness of 150 nm. The molecular behaviors were observed via real-time monitoring of SERS signals. Under continuous laser illumination, Marangoni radial convection flow became predominant over the outward capillary force, resulting in molecular accumulation in the detection areas. For small probe dyes and PAEs, the maximum intensities were achieved within 80 s after the injection of analytes and their signal fluctuations were estimated to have a relative standard deviation of < 10 %, which indicated sensitive and reproducible sensing. The prediction of PAEs extracted from the actual samples was investigated on the basis of a model used to quantitatively fit reference samples and the results were compared with those obtained by high-performance liquid chromatography. The results demonstrated that the combination of densified hotspots on three-dimensional porous substrates and laser-induced Marangoni flow is highly desirable for on-site early screening assays for low-quantity harmful materials present in surrounding environments.

Slot coating of time-dependent structured materials: Effects of thixotropy on the flow dynamics and operating limits

Some of the most common liquid-like formulations rooted in the coating industry consist of rheologically complex structured materials such as inks, paints, and slurries. Yet, the impact of time-dependent structuring effects due to thixotropy on thin film coating applications remains elusive and still unclear. Here, we present a computational study of the effects of thixotropy on slot coating of time-dependent structured materials. By coupling a recent fluidity-based constitutive model for thixotropic materials with a well-established finite element/elliptic mesh generation method for free surface flows, we assess the role of thixotropy by comparing the predictions from the thixotropic model with those from a simple Generalized Newtonian Fluid model that uses the same flow curve for the material steady-state equilibrium viscosity. We find that thixotropy can indeed have a major impact on slot coating applications, potentially bringing strong implications not only to the flow dynamics but also to the operating limits of the process. In conclusion, the results and discussions we present in this study underscore the importance of accounting for thixotropy to genuinely model and fundamentally understand the behavior of time-dependent structured materials with complex rheology in processing flows like those ubiquitous across the broad fields of coating science and engineering.

Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media

Due to its non-intrusive nature and ease of implementation, the Non-Intrusive Reduced Basis (NIRB) two-grid method has gained significant popularity in numerical computational fluid dynamics simulations. The efficiency of the NIRB method hinges on separating the procedure into offline and online stages. In the offline stage, a set of high-fidelity computations is performed to construct the reduced basis functions, which is time-consuming but is only executed once. In contrast, the online stage adapts a coarse-grid model to retrieve the expansion coefficients of the reduced basis functions. Thus it is much less costly than directly solving a high-fidelity model. However, coarse grids in heterogeneous porous media of flow models are often accompanied by upscaled hydraulic parameters (e.g. hydraulic conductivity), thus introducing upscaling errors. In this work, we introduce the two-scale idea to the existing NIRB two-grid method: when dealing with coarse-grid models, we also employ upscaled model parameters. Both the discretization and upscaling errors are compensated by the rectification post-processing. The numerical examples involve flow and heat transport problems in heterogeneous hydraulic conductivity fields, which are generated by self-affine random fields. Our research findings indicate that the modified NIRB method can effectively capture the large-scale features of numerical solutions, including pressure, velocity, and temperature. However, accurately retrieving velocity fields with small-scale features remains highly challenging.

DZ-SLAM: A SAM-based SLAM algorithm oriented to dynamic environments

Precise localization is a fundamental prerequisite for the effective operation of Simultaneous Localization and Mapping (SLAM) systems. Traditional visual SLAM is based on static environments and therefore performs poorly in dynamic environments. While numerous visual SLAM methods have been proposed to address dynamic environments, these approaches are typically based on certain prior knowledge. This paper introduces DZ-SLAM, a dynamic SLAM algorithm that does not require any prior knowledge, based on ORB-SLAM3, to handle unknown dynamic elements in the scene. This work first introduces the FastSAM to enable comprehensive image segmentation. It then proposes an adaptive threshold-based dense optical flow approach to identify dynamic elements within the environment. Finally, combining FastSAM with optical flow method and embedding it into the SLAM framework to eliminate dynamic objects and improve positioning accuracy in dynamic environments. The experiment shows that compared with the original ORB-SLAM3 algorithm, the algorithm proposed in this paper reduces the absolute trajectory error by up to 96%; Compared to the most advanced algorithms currently available, the absolute trajectory error of our algorithm can be reduced by up to 46%. In summary, the proposed dynamic object segmentation method without prior knowledge can significantly reduce the positioning error of SLAM algorithm in various dynamic environments.

Hybrid Radial‐Axial Flow for Enhanced Thermal Performance in Packed Bed Energy Storage

ABSTRACTIn this work, a hybrid radial‐axial (HRA) system is used to store thermal energy in a packed bed. The heat transfer fluid (HTF) is delivered via a perforated radial pipe placed at the center of the packed bed along the axial length. Hot fluid flows from the center toward the wall through the holes (like other radial systems), but then leaves via the traditional axial flow exit, creating the HRA flow configuration. A computational fluid dynamics (CFD) model is used to analyze the thermal performance of the packed bed during the charging process utilizing the new HRA system. Alumina beads of 6 mm were filler materials and air was HTF with inlet temperature of 75°C for proof of concept. The present paper focuses on two aims: (1) utilizing CFD models to analyze flow and temperature profiles in the packed bed; (2) comparing the model results to experimental results published in a previous HRA flow study and to traditional axial flow. Two HRA configurations were considered based on previous experimental designs, one with uniform holes in the central pipe (R1) and one with gradients in the hole sizes to promote even flow from the central pipe into the bed (R2). The numerical results agree with the experimental results in both cases. The HRA system performance depends on the flow profile created by the hole designs, and it can perform better than the axial flow depending on the design of the radial pipe. Design R2, which promotes even flow from the central pipe into the bed, has higher charging efficiency than standard axial flow methods. For HRA design R2 at 0.0048 m3/s (7 SCFM, standard cubic feet per minute), numerical results for charging efficiency were 75.5% versus 73.8% for traditional axial flow. For HRA design R2 at 0.0061 m3/s (9 SCFM), numerical charging efficiency was 80.5% versus 78.1% for traditional axial flow. These results are consistent with experimental data.

Quantifying Uncertainty in Atmospheric Winds Retrieved from Optical Flow: Dependence on Weather Regime

Abstract This study explores the performance of a dense optical flow method in comparison to pattern-matching techniques for retrieving atmospheric motion vectors (AMVs) from water vapor images. Using high-resolution simulated datasets that represent various weather phenomena, we assess the performance of these methods across different weather regimes, time intervals, and pressure levels and quantify the uncertainties associated with retrieved winds. The optical flow algorithm consistently outperforms the feature matching approach. Notably, it produces wind speeds and AMVs that closely resemble the wind fields from the simulations, and unlike the feature matching algorithm, the optical flow algorithm exhibits consistent performance across different time intervals. In contrast, the feature matching approach yields vector fields that exhibit oversmoothing in certain areas and erratic behavior in others, while also producing less detailed, regionally constant speed maps. Furthermore, unlike feature matching, the optical flow method effectively calculates AMV near regions with missing data, generating a dense AMV field for every pixel in a pair of images. This superior performance and flexibility significantly influence the planning for future satellite missions aimed at retrieving atmospheric winds. As such, our work plays a critical role in determining the mission architecture and projected instrument performance for future atmospheric wind retrieval satellite missions. The study underscores the potential of the optical flow algorithm as a robust and efficient approach for atmospheric motion retrieval, thus contributing to advances in climate research and weather prediction. Significance Statement This research investigates the efficacy of two methods, optical flow and feature matching, for detecting atmospheric winds, referred to as atmospheric motion vectors, from satellite images of water vapor. Employing detailed simulated datasets that replicate real-world weather patterns, we found that optical flow consistently outperforms feature matching in various aspects. Notably, the optical flow method is not only more precise but also maintains its accuracy across different scenarios. These insights are critical for the design of future satellite missions focused on advancing our understanding of the atmosphere and enhancing weather predictions. This study contributes to advancements in climate research and supports improved weather forecasting, benefiting both scientific and societal needs.

Adjoint-based shape optimization for compressible flow based on volume penalization method

AbstractReducing the resistance of compressible flow around a blunt body is of great interest in engineering applications, while an efficient shape optimization method for compressible flows remains far from well established, especially for high Mach numbers. To this end, a volume penalization method for simulating compressible flows past a no-slip and isothermal solid is established by introducing an artificial body force and a heat sink into the governing equations. The level-set functions are introduced as design variables, and the cost functional is defined as the total drag acting on the solid. Then, a continuous adjoint-based shape optimization algorithm for drag reduction is developed by deriving the adjoint equations, the adjoint boundary conditions, and the shape update formula. Both the forward and adjoint simulations are verified by existing studies. The results show that the relative deviations of the drag coefficients obtained in the present study from those reported in the reference studies are around 5% at most, and also a comparable drag reduction rate and also optimal shapes can be reproduced by the present optimization scheme for benchmark problems at relatively low Mach numbers considered in previous studies. Finally, the present method is applied to shape optimization of an initially two-dimensional cylinder and also a three-dimensional sphere in the transonic regime of Ma∞ = 1.2. The drag reduction of over 20% is achieved for both two-dimensional and three-dimensional cases.

An improved detached eddy simulation method for cavitation multiphase flow

The evolution of cavitation flow involves intense transient characteristics and complex multi-scale motions, significantly increasing the difficulty and computational cost of solving in separation zones. This study proposes an Improved Detached Eddy Simulation (IDES) method, based on a single-equation eddy-viscosity model, aimed at enhancing the resolution of small-scale cavitation flows. By incorporating the broad-spectrum von Karman scale concept, the method effectively improves the resolution capability for small-scale flows in separated zones. The performance of the IDES model was validated through three computational cases, and the main conclusions are as follows: The results of the triangular cylinder flows show that the IDES model demonstrates a resolution capability for large-scale turbulence comparable to the Large Eddy Simulation (LES) model. The orifice flow results indicate that activating the LES method with insufficient grid resolution is highly discouraged, whereas the IDES model performs more robustly under such conditions. For hydrofoil flows, the IDES model more accurately captures the temporal evolution of cavitation, avoiding the premature cavity shedding predicted by LES under coarse grid conditions. The decomposition results of the vorticity transport equation show that both the dilatation term and viscous term are significant contributors in the vorticity transport process, with their average contributions to vorticity reaching 49.25% and 39.99%, respectively. Vortices can be considered the primary controllers of cavitation dynamics, while the dilatation term and viscous term can be regarded as the main controllers of vorticity. Overall, the energy compensation mechanism of the IDES model, based on local flow information, gives it unique advantages in handling small-scale turbulence and cavitation phenomena, providing both high computational efficiency and accuracy.