Stokes Solver Research Articles

Collapse of a cohesive granular column

The collapse of a quasi-two-dimensional column of cohesive granular media is investigated experimentally and numerically in the framework of a continuum model. The configuration is an initial parallelepiped-shaped granular pile, which is suddenly released by opening a retaining door. The experiments rely on a model material developed by Gans et al. (Phys. Rev. E, vol. 101, 2020, 032904) made of silica particles coated with polyborosiloxane, for which the adhesive interparticle force can be tuned by controlling the thickness of the coating. Numerically, the collapse is simulated using a simple cohesive rheological model implemented in a two-dimensional Navier–Stokes solver. We investigate the role of cohesion on the stability of the column, the mode of failure, the flow dynamics and the geometry of the final deposit. Our results show that the continuum model captures the main features observed experimentally.

Semi-analytical load models describing the progressive immersion of a fixed vertical cylinder in a breaking wave

This paper is part of the DIMPACT (Design of floating wind turbines and impacts of energetic steep and breaking waves) project concerning slamming loads on floating offshore wind turbines. Two semi-analytical models accounting for the progressive immersion of a vertical cylinder in a breaking wave are presented. These models are based on the rate of change of the fluid momentum and the continuity of the added mass during immersion. The first model is based on the Generalized von Kármán Model where the real shape of the body and its added mass are accounted for. To account for the nonlinearity of the flow kinematics, the second-order terms of the momentum equation are considered in the inertia load. The total load is obtained by adding the drag force using a variable drag coefficient. To better predict the slamming load, a second model based on Wagner’s theory is presented. The Modified Logvinovich Model provides the pressure distribution at the first instants of impact. It is assumed that the flow does not separate from the structure. The load models are applied in a strip-theory approach under the Froude–Krylov assumption. For comparison, a Navier–Stokes solver is used to generate four phase-focused breaking waves. The resulting free surface shape and the ambient kinematics of the two-dimensional waves are used in the semi-analytical models. The present models are compared with existing slamming load formulations and a three-dimensional numerical simulation with an actual cylinder, where the load on four sections of the cylinder are considered. The force in the deeply immersed sections is in good agreement in all models considered. In the partially submerged section, the proposed load formulations and the three-dimensional simulation predict a similar load. Other standard engineering formulas predict a much lower force in this section. In the area impacted by the crest, the Froude–Krylov-based approaches predict a much higher force than that given by the Navier–Stokes result, likely due to the free surface being disturbed by the cylinder.

Prediction of biological development effects on drag forces of ceramic hull coating using Reynolds-averaged Navier–Stokes-based solver

Ships in service feature surfaces that exhibit biofouling, which alters the hydrodynamics of the vessels, thus affecting their normal displacement and significantly increasing their fuel consumption. The application of three types of ceramic coatings as ecological, effective and durable alternatives to commercial silicone-based marine coatings is investigated in this study. Three different ceramic glazes and two control commercial paints are analysed in an actual environment during 20 months of exposure to simulate the navigation conditions such that growth and roughness data can be obtained and then applied to computational fluid dynamics (CFD) software using an open-source Reynolds-averaged Navier–Stokes solver. The CFD results are validated under smooth hull conditions with a full-scale Kriso Container Ship (KCS) model and with different levels of hull roughness. The developed approach shows that the drag in hulls coated with conventional paint is 19% greater than that in hulls with ceramic coating.

A Review of Preconditioning and Artificial Compressibility Dual-Time Navier–Stokes Solvers for Multiphase Flows

This review paper aims to summarize recent advancements in time-marching schemes for solving Navier–Stokes (NS) equations in multiphase flow simulations. The focus is on dual-time stepping, local preconditioning, and artificial compressibility methods. These methods have proven to be effective in achieving high time accuracy in simulations, as well as converting the incompressible NS equations into a hyperbolic form that can be solved using compact schemes, thereby accelerating the solution convergence and allowing for the simulation of compressible flows at all Mach numbers. The literature on these methods continues to grow, providing a deeper understanding of the underlying physical processes and supporting technological advancements. This paper also highlights the imposition of dual-time stepping on both incompressible and compressible NS equations. This paper provides an updated overview of advanced methods for the CFD community to continue developing methods and select the most suitable two-phase flow solver for their respective applications.

Identification and Investigation of Extreme Events Using an Arbitrary Lagrangian–Eulerian Approach With a Laplace Equation Solver and Coupling to a Navier–Stokes Solver

AbstractIncreased deployment of offshore wind turbines is seen as an important pathway to increase green renewable energy production. Improved and rapid identification of extreme events and evaluation of hydrodynamic loads due to such events is essential to reduce the cost of energy production. Numerical modeling to pre-screen sea states and to identify the crucial events to prioritize model tests will make a major contribution to reduce design times and costs for such structures. In this effort, a highly efficient and nonlinear numerical model based on the Laplace equations is used to generate undisturbed wave kinematics. Such a simulation is used to identify extreme wave events in a sea state realization, and further, the wave loading due to such events are evaluated using Morison formula. Events screened in this manner can then be transferred to a high-resolution model such as a Navier–Stokes equation-based solver to investigate the hydrodynamics in detail. The implementation and application of such an approach in the open-source hydrodynamic model REEF3D is presented in this work.

Micro-nozzle flow and thrust prediction with high-density ratio using DSMC selection limiter

Introduction:A Direct Simulation Monte Carlo (DSMC) solver with a modified collisional routine is used to investigate an argon gas flow through a millimeter-scaled thruster nozzle with high-density ratios.Method:The limiter scheme, denoted as the constant selection limiter (CSL), limits the possible number of selected collisional pairs to a constant value in accordance with the present simulation particles in the cell.Results:Results of the CSL scheme are compared with the experimental and numerical results of a compressible Navier–Stokes solver and discussed in comparison with baseline DSMC simulations. The influence of collision limitation by the CSL is discussed on the stagnation pressure of the thruster and on thrust and specific impulse prediction. The application of the limiter scheme makes the prediction of stagnation pressure challenging in some cases.Discussion:In contrast, thrust and specific impulse are predicted well, and their study remains valid. Investigated mass flow rates are 0.178 mg/s ≤m.≤ 71.360 mg/s, and flow Knudsen numbers below Kn = 0.01 and over Kn = 10 are present. Near atmospheric conditions are reached inside the thruster, generating pressure ratios up to 3,741 along the nozzle. The computational performance of the scheme is also discussed, and speed-up factors up to 0.51 are achieved.

Stratified Taylor–Green vortex by lattice Boltzmann methods: Influence of stencils, forcing schemes, and collision models

Stably stratified Taylor–Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier–Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.

Adjoint-Based High-Fidelity Concurrent Aerodynamic Design Optimization of Wind Turbine

To evaluate novel turbine designs, the wind energy sector extensively depends on computational fluid dynamics (CFD). To use CFD in the design optimization process, where lower-fidelity approaches such as blade element momentum (BEM) are more popular, new tools to increase the accuracy must be developed as the latest wind turbines are larger and the aerodynamics and structural dynamics become more complex. In the present study, a new concurrent aerodynamic shape optimization approach towards multidisciplinary design optimization (MDO) that uses a Reynolds-averaged Navier–Stokes solver in conjunction with a numerical optimization methodology is introduced. A multidisciplinary design optimization tool called DAFoam is used for the NREL phase VI turbine as a baseline geometry. Aerodynamic design optimizations in terms of five different schemes, namely, cross-sectional shape, pitch angle, twist, chord length, and dihedral optimization are conducted. Pointwise, a commercial mesh generator is used to create the numerical meshes. As the adjoint approach is strongly reliant on the mesh quality, up to 17.8 million mesh cells were employed during the mesh convergence and result validation processes, whereas 2.65 million mesh cells were used throughout the design optimization due to the computational cost. The Sparse Nonlinear OPTimizer (SNOPT) is used for the optimization process in the adjoint solver. The torque in the tangential direction is the optimization’s merit function and excellent results are achieved, which shows the promising prospect of applying this approach for transient MDO. This work represents the first attempt to implement DAFoam for wind turbine aerodynamic design optimization.

Development of an overtopping wave absorption device for a wave-making circulating water channel

With the improvement of the stable flow generation function of circulating water channels (CWCs), CWCs are gradually developing toward multi-functionality. The wave test capability of a CWC is limited by its short test section; so, an efficient wave absorption device is required. This paper proposes the design concept of an overtopping wave absorption device (OWAD). An optimization design of the device by combining CFD and simulation-based design (SBD) is presented. The SBD system included optimal Latin hypercube design (Opt LHD), SVR, and particle swarm optimization (PSO). The reflection coefficient was used to estimate the wave absorption device performance. Numerical analysis was performed using the Unsteady Reynolds Averaged Navier–Stokes (URANS) solver and the boundary wave generation method, and was verified and validated via a procedure recommended by International Towing Tank Conference (ITTC). Under two wave conditions, four different OWAD design variables (slope angle, porosity, extension depth, and extension height) were optimized using the SBD system to minimize the reflection coefficient. Based on optimization results, the OWAD was assembled and its wave dissipation performance was confirmed experimentally. Installing an OWAD caused the reflection coefficient to be reduced from 0.161 to 0.089 for short-wave design conditions and from 0.528 to 0.128 for long-wave design conditions. A wave absorption test also showed that the wave absorption performance of the OWAD is significantly better than that of honeycomb and multiple porous plate wave absorption devices. The OWAD produces not only lower reflection coefficients but also smoother wave surfaces due to its two-dimensional structures.

Numerical investigation of aerodynamically efficient wing tip-mounted propeller configuration using coupled RANS–BEM approach

Purpose Recent interest in electric aircraft has opened avenues for exploring innovative concepts and designs. Because of its potential to increase wing aerodynamic efficiency, the idea of wing tip-mounted propellers is becoming more popular in the context of electric aircraft. This paper aims to address the question of which configuration, tractor or pusher at wing tip is more beneficial. Design/methodology/approach The interactions between the wing and tip-mounted propellers in tractor and pusher configurations have been studied computationally. In this study, the propeller is modeled as a disk, and the blade element method (BEM) coupled with the computational fluid dynamics (CFD)–Reynolds-averaged Navier–Stokes (RANS) solver is used to calculate propeller blade loading recursively. A direct comparison between the wing with tip-mounted propellers in tractor and pusher configurations is made by varying the direction of rotation and thrust. Findings Wing with tip-mounted propellers having inboard-up rotation is found to offer less drag in tractor and pusher configurations than those without propeller cases. Wing tip-mounted propeller in tractor configuration with inboard-up rotation offers higher wing aerodynamic efficiency than the other configurations. In tractor and pusher configurations with inboard-up rotating propellers, wing tip vortex attenuation is seen, whereas with outboard-up rotating propellers, the wing tip vortex amplification is observed. Originality/value SU2, an open-source CFD tool, is used in this study and BEM is coupled to perform RANS–BEM simulations. Both qualitative and quantitative comparisons were made between the tractor and pusher configurations, which may find its value when a question arises about the aerodynamically best propeller configuration at wing tips.

Experimental and numerical study on seakeeping performance of a benchmark ASD tug in head seas

Today’s modern ports are undergoing a wave of digital transformation to achieve higher efficiencies and better management of resources. The automation of harbour tugs are one example of concomitant developments for future-ready smart ports. Automating navigation and vessel operations implicitly requires a digital twin, which can be realized as a maneuvering model that incorporates the hydrodynamic behaviour and response of the tug. With the aim of building a maneuvering model, the present work investigates the seakeeping performance of a benchmark azimuthing-stern drive (ASD) tug using both experimental and numerical means. Experimental tests were performed in a towing tank using a 1:9.78 scale model at Fr = 0.378 and 0.165. Added resistance and hydrodynamic responses in head seas were measured in a captive setup. Some of the test cases were repeated in a free-sailing mode. Experiments provided validation data for numerical computational fluid dynamics (CFD) simulations, which were performed using a Reynolds-Averaged Navier–Stokes (RANS) solver, k-ω turbulence model, and a Volume of Fluid approach. Numerical results generally correlate well with experimental results. In addition to model-scale analysis, CFD simulations were also performed at full-scale to study scale effects.

A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers

In recent years, machine learning methods represented by deep neural networks (DNNs) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of high-fidelity data and the stability problem in the coupling process of turbulence models and the Reynolds-averaged Navier–Stokes (RANS) solvers. In this paper, we propose an improved ensemble Kalman inversion method as a unified approach of data assimilation and turbulence modeling for separated flows at high Reynolds numbers. A novel ensemble design method based on transfer learning and a regularizing strategy are proposed to improve the method. The trainable parameters of DNN are optimized according to the given experimental surface pressure coefficients in the framework of mutual coupling between the RANS solvers and DNN eddy viscosity models. In this way, data assimilation and model training are integrated into one step to get the high-fidelity turbulence models agree well with experiments directly. The effectiveness of the method is verified by cases of flows around S809 airfoil at high Reynolds numbers. Through assimilation of few experimental states, we can get turbulence models generalizing well to both attached and separated flows at different angles of attack, which also perform well in stability and robustness. The errors of lift coefficients at high angles of attack are significantly reduced by more than three times compared with the traditional Spalart–Allmaras model.

Modeling immiscible fluid flow in fractal pore medium by multiphase lattice Boltzmann flux solver

In this paper, the multiphase lattice Boltzmann flux solver (MLBFS), where the phase field model and the apparent liquid permeability model are built-in, is developed to simulate incompressible multiphase flows in fractal pore structure at the representative elementary volume scale. MLBFS takes advantage of the traditional Navier–Stokes solver (e.g., geometric flexibility and direct handling of complex boundary conditions) and lattice Boltzmann method (e.g., intrinsically kinetic nature, simplicity, and parallelism). It is easily applied to simulate multiphase flows transport in the porous medium with large density ratios and high Reynolds numbers. This study focuses on the fluid flow in fractal pore structures and provides an in-depth discussion of the effects of non-Newtonian index, fractal parameters, and density ratios on multiphase flow. The proposed model is validated with benchmark problems to test the applicability and reliability of the MLBFS in describing fluid flow in fractal pore structures with large density ratios and viscosity ratios. Simulation results show that the fractal parameters (i.e., fractal dimension, tortuous fractal dimension, porosity, and capillary radius ratio) can accurately characterize fractal pore structure and significantly affect the apparent liquid permeability. In addition, the flow rate increases with the fractal dimension and decreases with the tortuous fractal dimension, while both flow rate and apparent liquid permeability decrease as the capillary radius ratio. It is also noteworthy that the effect of nonlinear drag forces cannot be neglected for shear-thickened flows.

Experimental and numerical investigation of beer foam

The frothy foam on top of beer is produced by bubbles of gas, predominantly carbon dioxide, rising to the surface. The chemical components that produce the head are wort protein, yeast, and hop residue. This involves a large number of chemical components and numerous physical interactions. The beer foam and, especially, its stability is an essential quality characteristic of a beer. A consumer defines a beer's head by its stability, quantity, lacing (glass adhesion or cling), whiteness, creaminess, and strength. To achieve an accurate prediction of beer foam formation and collapse is challenging because complex numerical models are required to account for these nonlinear beer foam effects. To analyze a new design of a beer bottom-to-top pouring system for the startup company Einstein 1, we first set up the experimental tests of this pouring system. Afterward, we performed the associated repeatability studies to achieve stable working conditions. To study beer foam formation and its collapse, we employed a multiphase Reynolds-averaged Navier–Stokes solver that considered two inter-penetrating continua, which allowed accounting for multi-component phases and mass and heat transfer between these phases. We numerically and experimentally investigated beer foam patterns, beer heights, beer/foam ratio, foam height, foam stability, and foam volume fractions. We performed grid sensitivity studies and validated the numerical solver by comparing results against model test measurements. The results indicated that that the higher the temperature of the beer and the higher the tap pressure is, the greater the foam development and the associated foam height are but not necessarily the foam stability.

High-Order-Accurate Incompressible Flow Solver for High-Fidelity Numerical Simulations and Linear Stability Analysis

The development of high-fidelity versatile incompressible Navier–Stokes solver that is applicable for both direct numerical simulations (DNSs) and linear global stability investigations is presented and discussed. The solver is based on a vorticity–velocity formulation of the Navier–Stokes equations for orthogonal curvilinear grids. A rigorous and efficient approach is proposed that guarantees the divergence-free condition for the velocity and vorticity fields. The code incorporates advanced numerical algorithms including compact finite differences in combination with a pseudo-spectral method, together with an efficient and high-order-accurate Poisson solver. Linear stability modules based on the linearized Navier–Stokes equations (LNSEs) tailored for primary and secondary instability analyses are developed and incorporated into the code, such that the solver can switch from DNS to LNSE in a consistent manner by turning off the nonlinear terms and vice versa. The linear framework includes all the nonparallel effects with respect to the steady/unsteady baseflow and the form of disturbances, and because it is formulated as an initial value problem, both convective and absolute/global instability mechanisms can be investigated. An additional significant advantage of the linear module is that, for the secondary stability analysis, time-periodic assumption is not required and/or the unsteady baseflow does not have to be computed a priori. In the present paper, results obtained with the new Navier–Stokes solver are compared with benchmark solutions for the flow past a static and oscillating circular cylinder. The new code then was employed for a three-dimensional DNS of the flow for a wing section with a modified NACA 6 series airfoil at a chord Reynolds number of . Furthermore, the capability of the linear stability modules was demonstrated by investigating the primary and secondary (convective and absolute) instability mechanisms for boundary layers and the flow past a circular cylinder.

Influence of the canal width and depth on the resistance of 750 DWT Perintis ship using CFD simulation

Investigation of hydrodynamic interaction between the vessel and the seabed when entering shallow water is considered one of the most critical considerations of inland waterway transport. There are many investigations into the behavior of ships in restricted waters, such as ships traveling in different forms of canal cross-sections. The present study aims to evaluate the hydrodynamic interaction of the 750 DWT Perintis Ship moving through the different canal types to determine the relative effects of limiting the width and depth cross section on the ship's resistance. Two different canals with different cross sections, including canal bank and rectangular canal, were evaluated to investigate the influence of canal width (Wb), depth ratio (hw/T), and blockage ratio function (As/Ac). The Computational Fluid Dynamic (CFD) method with Reynolds-averaged Navier–Stokes (RANS) solver and turbulent model 𝑘−𝜀 were used to predict the total resistance of the ship. The proposed numerical simulation was initially validated with an experimental towing tank test in the error range of 0.11-7.74%. The results indicated similar phenomena were found both in rectangular and canal banks. The case with a shallower (lower hw/T) and a narrower (lower Bc/Bs) canal dimension has a higher resistance value. Backflow and subsidence of free surface became significant around the ship's hull in more restricted water, changing the ship's hydrodynamic characteristics and increasing resistance. It can be found that the higher the blockage ratio (mb), the higher the total resistance value in both canal types, which proved that ships with higher speeds were more sensitive to changes in waterway restrictions.

Physics and Accuracy of Dual-Solver Simulations of Rotors in Ground Effect

To characterize the interactions between rotorcraft and ground obstacles when tackling modern and emerging problems such as shipboard landings and urban air mobility, first-principles computational models offer the ability to perform design and analytical studies while resolving detailed flow features. However, the cost of Navier–Stokes methods with very high resolution is, for the most part, only tractable for research use cases. Conversely, midfidelity potential-based methods are cost-effective but may not capture important physics that occur near the rotor blades. Hybrid approaches that couple Navier–Stokes and potential solvers have recently been developed, which provide the ability to resolve complex physics with a Navier–Stokes solution while employing a potential solver to resolve far-wake effects for which it is well-suited. This research discusses the impact of new improvements to and best practices for the hybrid Navier–Stokes/free-wake solver OVERFLOW-CHARM applied to rotors in ground effect. Predictions of rotor performance and flow features are compared with experimental data for microscale and subscale rotors. Rotor performance is predicted within 6% of a conventional computational fluid dynamics simulation at approximately 20% of the computational cost and predicted flow features correlate well to experimental flow visualization.

Computational Characterization of Unsteadiness and Turbulence in Rotor Hub Wakes

Reynolds stresses and turbulent kinetic energy are studied in the wakes of several helicopter rotor hub geometries in forward flight. Computational fluid dynamics simulations are performed using NASA's OVERFLOW 2.2n Reynoldsaveraged Navier–Stokes solver. The simulations impose flow conditions based on previous and current experimental and numerical studies. Discrete Fourier transforms are used to examine velocity harmonics for several frequencies and compared against available experimental results. Components of the Reynolds stress tensor are computed and examined. Production and transport of the turbulent kinetic energy are examined through the rotor hub wakes at six streamwise coordinates. It was found that the scissor arms, previously found to have a significant effect on rotor hub force harmonics, also had a significant effect on the magnitudes of Reynolds stresses and turbulent kinetic energy. Integrated values of turbulent kinetic energy flux indicate that drag-reducing designs have a direct effect on turbulent kinetic energy levels in the wake.

Lattice Boltzmann method with nonreflective boundary conditions for low Mach number combustion

The paper presents a lattice Boltzmann (LB) method for premixed and nonpremixed combustion simulations with nonreflective boundary conditions, in contrast to Navier–Stokes solvers or hybrid schemes. The current approach employs different sets of distribution functions for flow, temperature and species fields, which are fully coupled. The discrete equilibrium density distributions are obtained from the Hermite expansions thus thermal compressibility is included. The coupling among the momentum, energy and species transport enables the model to be applicable for reactive flows with chemical heat release. The characteristic boundary conditions are incorporated into the LB scheme to avoid numerical reflections. The multi-relaxation-time collision schemes are applied to all the LB solution procedures to improve numerical stability. With detailed thermodynamics and chemical mechanisms for hydrogen-air, the LB modelling framework is validated against both premixed flame propagation and nonpremixed counterflow diffusion flame benchmarks. Simulations of circular expanding premixed flames further demonstrate the capability of the new reactive LB method. The developed LB methodology retains the advantages of classic LB methods and extends the LB capability to low Mach number combustion with potential applications in mesoscale and microscale combustors, catalysis, fuel cells, batteries and so on.

A hybrid numerical model for simulating aero-elastic-hydro-mooring-wake dynamic responses of floating offshore wind turbine

It demands many computational resources to model the coupled responses of a floating offshore wind turbine (FOWT), especially for its aero-elastic-hydro-mooring-wake dynamics and their interaction. In this paper, a new hybrid numerical model for FOWT systems is developed, which is based on the hybrid potential-viscous flow model called qaleFOAM. In this model, the aerodynamics of wind turbine are solved by the unsteady actuator line method (UALM); the elastic responses of the turbine blade are calculated by the Legendre spectral finite element model (BeamDyn); the hydrodynamics of the floating platform are dealt with by the combination of the fully nonlinear potential solver and a two-phase Navier–Stokes solver; the mooring dynamics are considered with the Lumped Mass Mooring Model (MoorDyn), and the turbine wake is solved with the large eddy simulation (LES) model. This newly formulated model can deal with wind, wave, mooring dynamics, platform motions, and turbine structural dynamics involved in the FOWT system. To demonstrate the capability of the present model, various cases with different complexities are investigated and compared with the experimental data and other numerical results. Then, the model is applied to simulation of a semi-submersible FOWT system, subjected to a regular wave and a uniform wind. The prediction of the aerodynamic performance, blade tip deflection, platform motion responses, and mooring line tension loads show good agreements with the results from other methods. In addition, the phenomenon of the coupled effects between the dynamic responses of platform, blade deformation and wake flow are captured reasonably well.