Droplet impact on solid surfaces is ubiquitous in agricultural, energy, and chemical engineering applications. Electrowetting-on-dielectric (EWOD) has been demonstrated to be an effective method for droplet manipulation, and its integration with spatial heterogeneity represents a promising direction. In this work, a locally addressable EWOD strategy is proposed by embedding multiple parallel electrodes within a hydrophobic substrate, where only the voltage-applied electrode region undergoes wettability switching. A validated diffuse interface method is adopted for interface capture. The effects of the activated electrode position, the Weber number, and the amplitude and duration of the applied voltage on droplet lateral motion are examined systematically. The numerical results reveal several scaling laws for the normalized lateral velocity. Moreover, the theoretical analysis based on unbalanced surface tension forces and momentum accumulation is conducted. A unified relationship between the droplet deflection and compound parameter ω (We−1S*U*Δt*) is obtained, which is well validated by all simulation data. This work establishes a prediction framework for controlled droplet rebound and offers a robust pathway toward active and precise droplet manipulation.

A three-dimensional (3D) high-order flux reconstruction lattice Boltzmann flux solver (FR-LBFS) is developed in this paper for accurate and efficient simulations of incompressible laminar and turbulent flows. The original lattice Boltzmann flux solver (LBFS) is a second-order finite volume method (FVM) which combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. But it is not convenient to construct high-order FVM, and the compactness is always a bottleneck. The present work separates LBFS from FVM and combines LBFS with high-order FR scheme. Thus, the FR-LBFS inherits the superiority of LBFS and FR and shares the following attractive features: (i) a fully-explicit arbitrary order compact method, (ii) weakly compressible (WC) model for unsteady incompressible flows and (iii) evaluating inviscid and viscous fluxes simultaneously and no particular technique requirement, such as local discontinuous Galerkin method (LDG), for viscous term discretization. To validate the current method, various 3D incompressible laminar isothermal and thermal numerical experiments are presented first. Good agreements are achieved between the current results and the previous experimental and numerical data whilst the present high-order solver adopt coarse meshes. Furthermore, the ability of the proposed method to perform accurate and stable computations of incompressible decaying homogeneous isotropic turbulent flows and turbulent channel flows with different mesh resolutions and accuracy orders are investigated. The results show that the present 3D FR-LBFS is a promising tool for under-resolved or implicit large eddy simulation (ILES) of incompressible turbulent flows.

A numerical method, which combines the high order flux reconstruction (FR) and the lattice Boltzmann flux solver (LBFS), has been developed to solve inviscid compressible flows in this article. Extensive research has shown that LBFS has absorbed the advantages of both finite volume method (FVM) and lattice Boltzmann method (LBM). On one hand, compared with FVM, FR can achieve arbitrary high order accuracy and is compact for parallel computing by avoiding wide stencils on meshes, which shows FR is a better choice than FVM. On the other hand, different from the discrete velocity Boltzmann equation based methods, the present method, that is, FR-LBFS, solves the Euler equations essentially, and then the calculation efficiency can be improved. In FR-LBFS, the common inviscid flux at the cell interface is evaluated by the local reconstruction of the lattice Boltzmann equation (LBE) solution from macroscopic flow variables at solution points. Unlike the traditional flux solution at the interface where the nonlinear convective terms have to be considered in the computation, the feature of linear convection term in LBE can make it easier to calculate flux in the current method. Furthermore, by considering real physical effects in LBM, the positive density and pressure can be achieved in the case of strong shocks and discontinuities. Some typical inviscid problems, including the advection of density perturbation, sod shock tube, Riemann problem for two-dimensional gas dynamics, supersonic flow in a convergent nozzle with a ramp, subsonic flow around a cylinder, and transonic flow over a NACA0012 airfoil, are simulated to demonstrate the accuracies and robustness of the proposed FR-LBFS.

In this paper, a high-order scheme based on the lattice Boltzmann flux solver (LBFS) is proposed to simulate viscous compressible flows. The flux reconstruction (FR) approach is adopted to implement the spatial discretization. The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables. Meanwhile, a switch function is used in LBFS to adjust the magnitude of the numerical viscosity. Thus, it is more beneficial to capture both strong shock waves and thin boundary layers. Moreover, the viscous flux is computed according to the local discontinuous Galerkin method. Some typical compressible viscous problems, including manufactured solution case, lid-driven cavity flow, supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil, are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.

In this paper, based on the double distribution function (DDF) model and the Boussinesq approximation, a high-order implicit-explicit flux reconstruction thermal lattice Boltzmann method (FRTLBM) is proposed for simulating nearly incompressible thermal flows. Two discrete velocity Boltzmann equations (DVBEs), one governing the flow field and the other governing the temperature field, are solved by using a high -order flux reconstruction scheme for spatial discretization and a second-order implicit-explicit Runge-Kutta scheme (IMEX RK) for time discretization in the generalized curvilinear coordinates with uniform and non-uniform grids. Numerical validations of the proposed method are implemented by simulating (a) porous plate problem, (b) natural convection in a square cavity, (c) Rayleigh-Benard convection, (d) natural convection in a concentric annulus and (e) mixed heat transfer from a heated circular cylinder. Numerical results demonstrate that the present method can achieve the high-order accuracy and it is stable and accurate even at the relatively high Rayleigh number (Ra = 10(7) and 10(8) ). The present method is efficient due to the small amount of mesh, the simple algorithm and the time step unlimited by the relaxation time. Since the rescontruction is conducted in a single cell, the present method is compact for parallel computing. Moreover, the present method has a good adaptability of complicated geometries. (c) 2022 Elsevier Ltd. All rights reserved.

This paper firstly reviews the development of the high-order off-lattice Boltzmann method (OLBM). Based on the high-order flux reconstruction scheme (FR), we develop a high-order flux reconstruction lattice Boltzmann method (FRLBM). Two numerical methods are adapted. One is to directly solve the discrete velocity Boltzmann equation with collision term treated implicitly (direct method) and the other is to sequencially implement collision step and the convection term (two-step method). Through the convergence study, the accuracy and stability of the two methods are compared. It is found that, when the time step is small, the errors of the two methods are in similar order, and the high-order accuracy can be obtained. However, when the time step is increased, the error of the direct method is almost unchanged, while the error of the two-step method increases significantly. The results indicate that the direct method can use a larger time step to obtain higher accuracy to abtain the reasonable accuracy in comparing with two step method. Meanwhile, the direct method also has better stability. Then, the ability of FRLBM to capture the details of the flow field is verified by simulating the lid-driven cavity flow. In addition, we compare the maximum Courant-Friedrichs-Lewy (CFL) numbers at different Reynolds numbers by semi-implicit time-marching scheme, first, second and third-order implicit-explicit (IMEX) Runge-Kutta schemes, respectively. The numerical results indicate the second-order IMEX performs best. Finally, the numerical simulation of the flow over a circular cylinder verifies the reliability of the FRLBM for calculation of the flow around the body with complex geometry.

In this paper, a high-order implicit-explicit flux reconstruction lattice Boltzmann method (FRLBM) is proposed for simulating viscous incompressible flows. The discrete velocity Boltzmann equation (DVBE) is solved by using a high-order flux reconstruction scheme (FR) for spatial discretization and a high-order implicit-explicit Runge-Kutta scheme (IMEX RK) for time discretization in the generalized curvilinear coordinates with uniform and non-uniform grids to obtain high simulation efficiency. Numerical validations of the proposed method are implemented by simulating (a) Taylor-Green vortex problem, (b) doubly periodic shear layer flow, (c) lid-driven cavity flow, (d) cylindrical Couette flow and (e) flow over a circular cylinder. Numerical results demonstrate that the present method is stable and accurate even at high Reynolds number. Compared with the existing high-order off-lattice Boltzmann methods, the present method is more efficient. In addition, the present method holds the compactness of the standard LBM for parallel computing, but greatly improves the adaptability of complicated geometries.

In this paper, a high-order solver combining the flux reconstruction (FR) method and the thermal lattice Boltzmann flux solver (FRTLBFS) is developed for accurately and efficiently simulating incompressible thermal flows. The conservative differential equations recovered from Chapman-Enskog analysis of the thermal lattice Boltzmann equation are solved by the high-order FR method. The thermal lattice Boltzmann method is only applied to reconstruct the local solution used for evaluating fluxes at the solution and flux points. Unlike the traditional Navier-Stokes-Boussinesq (NSB) solvers where the inviscid and viscous terms are treated separately, the inviscid and viscous fluxes in the current FRTLBFS are coupled and computed uniformly. In comparison with the recently developed high-order flux reconstruction thermal lattice Boltzmann method, the FRTLBFS holds advantages such as high-order accuracy, good stability, and compactness but is more efficient and low storage, since only macroscopic flow variables including density, velocity, and temperature are stored and evolved. In addition, the physical boundary conditions in FRTLBFS can be directly implemented by using the same method as in conventional NSB solvers. Numerical validations of the proposed method are implemented by simulating (a) the porous plate problem, (b) natural convection in a square cavity, (c) unsteady natural convection in a tall cavity, and (d) thermal lid-driven cavity flow. Numerical results demonstrate that the present solver is an attractive tool to simulate incompressible thermal flows due to its high-order accuracy, stability, and low memory cost.

In this article, a high order weighted essentially nonoscillatory finite difference‐based phase field lattice Boltzmann method (WENO‐PFLBM) is proposed for simulations of incompressible two‐phase flows with high density contrast. The weighted essentially nonoscillatory finite difference scheme is applied to discretize the convection term of the discrete Boltzmann equation for flow field. Moreover, the WENO scheme is also adopted to discretize the convection term of the modified Cahn–Hilliard equation for interface tracking. Numerical validations of the proposed WENO‐PFLBM are implemented by simulating stationary droplet, layered Poiseuille flow, Rayleigh–Taylor instability, bubble rising, and droplet impact on a thin film. Various numerical challenges like high density ratios (up to 1000), complex interfaces, and high Reynolds numbers are included in these examples, which demonstrate the robustness of the present method. In addition, the current method can achieve relatively small spurious velocity compared with the LB‐based model owing to the high order accuracy.

In this paper, a high order spectral difference-based phase field lattice Boltzmann method (SD-PFLBM) is proposed for simulating incompressible two-phase flows. The spectral difference method (SDM) is used to discretize the convection term and the gradient term of the discrete Boltzmann equation for obtaining the flow field. Moreover, the SDM is also adopted to discretize the convection term and the high order partial derivative term of the Cahn–Hilliard equation for interface tracking. The proposed method can overcome the drawback of the standard LBM such as tie-up between the time step and the mesh spacing. Meanwhile, the present method still holds the locality of the standard LBM because each cell only needs its own information to complete the discretization. Numerical validations of the proposed method are implemented by simulating rigid-body rotation of Zalesak’s disk, layered Poiseuille flows, bubble deformation in shear flow, Rayleigh–Taylor instability, and bubble merging. More satisfactory interface shapes and flow properties can be achieved as compared with the published data in the literature. In addition, the convergence studies are also given, which prove that the current SD-PFLBM can achieve high order accuracy by increasing the order of cell local polynomials.

An improved model for heat transfer process is established to study the ice accretion on airfoil, which takes into consideration the influence of conduction through ice and water film compared with the classical Messinger model. Incorporating the calculation of collection efficiency by the Eulerian two-phase theory, ice accretion in specific condition on a NACA0012 airfoil is simulated with the classical model and the improved model respectively. It is shown that the simulation result with the improved model agrees well with experiment data, and the model is demonstrated to be valid in ice shape prediction and complement the shortage of the Messinger model in the estimation of freezing fraction in glaze ice condition, especially in the initial stage of ice accretion.

For studying ice accretion on aircraft and helicopter airfoils, a modified model of the mass and heat transfer on icing surface was first proposed based on the classical Messinger model. Then an approach for predicting ice accretion on multi-element airfoils was set up through introducing the interpolation calculation of airflow field around the multi-element airfoils. Considering the equivalent thermal power from anti-ice system, a method of the prediction of ice accretion under anti-ice situation was proposed. In order to study the prediction of ice accretion on helicopter rotor, a numerical simulation method combining the computational fluid dynamics (CFD) technique with helicopter aerodynamics theory was set up. The agreement between the results of numerical simulation and the experimental data indicates that the model and methods proposed in this paper are feasible and effective, and that they can lay the foundation of the research on the dynamics in icing condition and design of anti/de-ice system.

The National Renewable Energy Laboratory (NREL) Phase II - IV wind turbine rotors [1] were used as the original research subjects in this article. In this paper, the numerical simulation method and business software FLUENT were used. The aerodynamic performances of different fixed-pitch, horizontal-axis wind turbine rotors were obtained through numerical computation. A rotational speed control model was given by direct calculation on the aerodynamic parameters of straight blades. As in the previous model, it required the wind turbine rotational speed be changed as little as possible in consideration of the life expectancy improvement and dynamo size reduction. Then, numerical simulation was used in one twisted wind turbine blade, three simple twist-oriented corrected models were acquired by flow-field analysis and simplified blade element theory application. Certain improvements in the wind turbine aerodynamic performances were obtained by contrasts of P-V curves and rotational speed model with original twisted wind turbine blade.

Fixed-pitch wind turbines commonly use stalled blades, and the ratio of lift coefficient to drag coefficient will rapidly decrease when the velocity of the wind exceeds the designed value, then the output of the power will be fixed under a safe value. As the main part to get power from the wind, Wind turbines' aerodynamic performance is very important and decides the power coefficient. How to evaluate the design of the wind turbine, and how to design a high performance wind turbine is important. First, the main methods to analyze the aerodynamic performance and the design methods of horizontal-axis wind turbines are introduced. Then the role of CFD technology in research of the wind turbines is explained. By using CFD software, a horizontal-axis wind turbine is studied. Through the analysis of the flow field and the pressure distribution on the blades, the deficit of the design will be found, which is helpful to improve the blades. At last, the feasibility of the combination of CFD and optimization techniques is discussed. The method relies on the interaction between a genetic algorithm, an artificial neural network, and a database of full three-dimensional computation results of fluid dynamic. On this foundation, users can generate various objectives and constraints for the optimization design of the geometric blade element shape parameters of the wind turbine.