Fluid Flow Solver Research Articles

Current advancements in fluid-flow Problems: A brief review

This specific article is a compilation of a few current studies on fluid flow issues. This article provides an overview of current research on the experimental and theoretical analysis of various nanofluids' thermal conductivity. The current study examines a number of variables that have a significant impact on a nanofluid's ability to transfer heat, including temperature, solid volume fraction, type, size, shape, magnetic field, pH, ultrasonic time, and surfactant. In addition, some plausible and appealing theories that enhance the thermal conductivity of nanofluids are mentioned. The final important heat transmission mechanisms that play a significant part in improving thermal conductivity are Brownian motion, thermophoresis, nanoclustering, interfacial nano-layer, and osmophoresis. Thus, consideration is given to the heat transmission properties of nanofluids. And also discussed some Numerical method to solve fluid flow problems.

Fluid resonance in narrow gaps formed by three-box system with sharp and round edge profiles under irregular wave actions

Fluid resonance within narrow gaps in multiple-box systems with sharp and round edge profiles under irregular wave actions are investigated by using a viscous fluid flow solver based on OpenFOAM® package. In difference to the two-peak behavior under regular wave actions, the variation of free surface amplitudes in narrow gaps with incident spectral peak frequencies show the single-peak behavior, including the sharp and round edge profiles. Spectral analysis indicates that the wave spectrums of fluid oscillations in narrow gaps mainly around the first- and/or second-order resonant frequencies. The second-order fluid resonance is easier to be aroused for round edge profiles than that for sharp edge profiles. Furthermore, the statistical and histogram results indicate the significant periods are always around the resonant frequencies; while the corresponding standard deviations approach to cover the region between two resonant frequencies. The above results confirm that the wave responses in narrow gaps mainly oscillate with two resonant frequencies under irregular wave actions.

Enhancing CFD solver with Machine Learning techniques

This study addresses the computational challenges in fluid flow simulations arising from demanding computational grids, required to capture the temporal and length scales involved. Our approach focuses on the pressure solver, as this is a resource-intensive component in Computational Fluid Dynamics (CFD) solvers. We achieve this by integrating a Machine Learning (ML) surrogate model with an incompressible fluid flow solver. We created two variants of an ML-enhanced CFD solver which were able to reduce the number of iterations required by the CFD pressure solver during unsteady flow simulations. Consequently, the simulations yielded comparable drag coefficients and Strouhal numbers, accompanied by an eightfold decrease in execution time. The performance enhancements are attributed to reduced computational effort per temporal iteration and early-stage forcing on the simulation dynamical behavior when using the ML-based surrogate models. This research introduces an approach to enhance the computational efficiency of fluid flow analyses by incorporating surrogate models to aid the pressure solver in CFD simulations. We propose a Hybrid CFD solver, ie. a physics-informed solver enhanced with data-driven surrogate models.

The Design and Investigation of Hybrid a Microfluidic Micromixer

Today, microfluidics has become a revolutionary interdisciplinary topic with considerable attention in a wide range of biotechnology applications. In this research work, a numerical investigation of a microfluidic micromixer is carried out using a hybrid actuation approach with different micropillar shapes and gaps. For this purpose, COMSOL Multiphysics v.5.2. is used with three different physics, such as thermoviscous acoustic physics to solve acoustic governing equations, laminar physics to solve fluid flow governing equations, and diluted transport species to solve mixing governing equations. The simulations were carried out at different Reynolds numbers such as 2, 4, 6, 8, 10, and 12 with an oscillation frequency of 15 kHz. The results were in the form of acoustic characteristics such as acoustic pressure, acoustic velocity, acoustic stream, mixing index, and fluid flow behaviour at various Reynolds numbers. The results revealed that the inclusion of micropillars improved the mixing performance and strength of the acoustic field, resulting in an improvement of the mixing performance compared to the case without micropillars. In addition, the mixing performance is also investigated at different Reynolds numbers, and a higher mixing index is investigated at lower Reynolds numbers. Moreover, it was also investigated that blade-shaped micropillars with 0.150 mm gaps deliver the best results compared to the other cases, and the maximum and minimum values of the mixing index are 0.97 and 0.72, respectively, at Reynolds number 2. The main reason behind this larger mixing index at low Reynolds numbers is due to the inclusion of micropillars that enhance the diffusion rate and contact area, leading to the homogenisation of the heterogeneous fluids in the microchamber. The obtained results can be extremely helpful for the design and modifications of a hybrid microfluidics micromixer.

Application of machine learning to model the pressure poisson equation for fluid flow on generic geometries

This study addresses the importance of enhancing traditional fluid-flow solvers by introducing a Machine Learning procedure to model pressure fields computed by standard fluid-flow solvers. The conventional approach involves enforcing pressure–velocity coupling through a Poisson equation, combining the Navier–Stokes and continuity equations. The solution to this Poisson equation constitutes a substantial percentage of the overall computational cost in fluid flow simulations, therefore improving its efficiency can yield significant gains in computational speed. The study aims to create a versatile method applicable to any geometry, ultimately providing a more efficient alternative to the conventional pressure solver. Machine Learning models were trained with flow fields generated by a Computational Fluid Dynamics solver applied to the confined flow over multiple geometries, namely wall-bounded cylinders with circular, rectangular, triangular, and plate cross-sections. To achieve applicability to any geometry, a method was developed to estimate pressure fields in fixed-shape blocks sampled from the flow domain and subsequently assemble them to reconstruct the entire physical domain. The model relies on multilayer perceptron neural networks combined with Principal Component Analysis transformations. The developed Machine Learning models achieved acceptable accuracy with errors of around 3%. Furthermore, the model demonstrated enhanced computational efficiency, outperforming the classical PISO algorithm by up to 30 times.

A modified cell-centered nodal integral scheme for the convection-diffusion equation

The nodal integral methods (NIMs) are very efficient and accurate coarse-mesh methods for solving partial differential equations. The cell-centered NIM (CCNIM) is a simplified variant of the NIMs that has recently shown its efficiency in solving fluid flow problems but has been hampered by issues such as inapplicability to one-dimensional problems, complexities in handling Neumann boundary conditions and the formulation of a system of differential-algebraic equations (DAEs) for discrete unknowns. Here, we present a modified version of the CCNIM designed to overcome the challenges associated with its previous version. Our novel development retains the essence of CCNIM while resolving these issues. The proposed scheme, grounded in the nodal framework, achieves second-order accuracy in both spatial and temporal dimensions. Unlike its precursor, the proposed method formulates algebraic equations for discrete variables per node, eliminating the cumbersome DAE system. Neumann boundary conditions are seamlessly incorporated through a straightforward flux definition, and applicability to one-dimensional problems is now feasible. We successfully apply our approach to one and two-dimensional convection-diffusion problems with known analytical solutions to validate our approach. The simplicity and robustness of the approach lay the foundation for its seamless extension to more complex fluid flow problems.

Dissipative Non-Slip MHD Nanofluid Flow with Variable Viscousity and Thermal Conductivity in the Presence of Arrhenius Chemical Reaction

This research investigates the intricate dynamics of dissipative non-slip magnetohydrodynamic (MHD) nanofluid flow, characterized by variable viscosity and thermal conductivity, under the influence of an Arrhenius chemical reaction. The inclusion of the Arrhenius chemical reaction adds complexity through heat generation or absorption, impacting temperature and concentration gradients. The study is motivated by the extensive applications of nanofluids in engineering and industrial processes, where precise control of heat and mass transfer is critical. We develop a comprehensive mathematical model that incorporates the variable properties of the nanofluid, the effects of the Lorentz force due to the applied magnetic field, and the temperature-dependent reaction rates dictated by the Arrhenius equation. The formulated governing equations were non-dimensionalised to identify the flow governing parameters. Finite Element Method (FEM), grid generation, solution algorithms, and post-processing to analyse velocity, temperature, and concentration distributions were used to obtain the numerical methods to solve fluid flow problems based on the Navier-Stokes equations, involving concepts of discretization. pdsolve subpackage in Maple 2023 was used to numerically solve PDEs with specific initial and boundary conditions, incorporating the plot and display commands for graphical analysis, and the results are presented and discussed. The findings reveal that the interplay between parameters like Hartmann number, Darcy parameter, and heat generation or absorption profoundly influences flow behaviour and thermal characteristics. The reactivity parameter is crucial, dictating the rate of chemical reactions and affecting system dynamics. This research enhances understanding of the interdependencies among fluid properties, chemical reactions, and external parameters in nanofluid flows.

A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning.An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation.The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used.The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes.

Rigorous benchmarking of an iterative IBM solver by comparison to body-fitted mesh results

This study addresses the validation challenges of Immersed Boundary Method (IBM) solvers by proposing a consistent benchmarking approach. A temporally second-order Arbitrary Lagrangian–Eulerian (ALE) solver implemented in OpenFOAM is verified against lid-driven cavity flow and flow past static and oscillating cylinders. It then serves as the underlying fluid flow solver for a fully implicit diffusive direct forcing IBM solver that achieves temporal second-order accuracy, verified by the static and oscillating cylinder cases. Leveraging the shared numerical framework, the IBM solver is rigorously validated against ALE using identical settings, parameters, and nearly identical grids across twenty test cases, including stationary cylinder flow (Re = 40, 100, 185), oscillating cylinder in quiescent flow (Re = 100, KC = 5), and transversely oscillating cylinders with varying amplitudes and frequencies (16 cases in total). The IBM solver demonstrates robustness (CFL up to 8) and accuracy over a wide Reynolds number range, with relative drag coefficient errors below 7% for all considered cases. Incorporating body force correction, which reduces slip errors at negligible added computational cost, drastically improves accuracy. Proper Rhie–Chow momentum interpolation, including body forces, is critical in the adopted collocated finite volume method. For unsteady problems, the computational cost is greatly reduced without compromising accuracy by using CFL≈1.5−2 with only two outer iterations. The proposed benchmarking framework can be easily used for validation of other IBM approaches and thus potentially help to advance the state of IBM.

Potential of physics-informed neural networks for solving fluid flow problems with parametric boundary conditions

Fluid flows are present in various fields of science and engineering, so their mathematical description and modeling is of high practical importance. However, utilizing classical numerical methods to model fluid flows is often time consuming and a new simulation is needed for each modification of the domain, boundary conditions, or fluid properties. As a result, these methods have limited utility when it comes to conducting extensive parameter studies or optimizing fluid systems. By utilizing recently proposed physics-informed neural networks (PINNs), these limitations can be addressed. PINNs approximate the solution of a single or system of partial differential equations (PDEs) by artificial neural networks (ANNs). The residuals of the PDEs are used as the loss function of the ANN, while the boundary condition is imposed in a supervised manner. Hence, PDEs are solved by performing a nonconvex optimization during the training of the ANN instead of solving a system of equations. Although this relatively new method cannot yet compete with classical numerical methods in terms of accuracy for complex problems, this approach shows promising potential as it is mesh-free and suitable for parametric solution of PDE problems. This is achieved without relying on simulation data or measurement information. This study focuses on the impact of parametric boundary conditions, specifically a variable inlet velocity profile, on the flow calculations. For the first time, a physics-based penalty term to avoid the suboptimal solution along with an efficient way of imposing parametric boundary conditions within PINNs is presented.

Nodal integral method to solve the two-dimensional, time-dependent, incompressible Navier-Stokes equations in curvilinear coordinates

The numerical solution of the two–dimensional, time–dependent, incompressible Navier–Stokes equations (NSE) in curvilinear coordinates using the nodal integral method (NIM) is presented in this paper. The developed numerical scheme is applied to solve fluid flow problems in domains discretized using quadrilateral cells. Three test problems are numerically solved to assess the accuracy and efficiency of the method. The scheme is second-order accurate in space for all considered deformation levels and Re numbers. The results of the current scheme are compared with the other numerical results in the literature, and good agreement is obtained for all considered cases. The NIM demonstrates superior accuracy per cell compared to other second–order finite–volume schemes considered in this work. New benchmark results obtained from the solution on fine meshes are presented.

Current advancements in fluid-flow Problems: A brief review

This specific article is a compilation of a few current studies on fluid flow issues. This article provides an overview of current research on the experimental and theoretical analysis of various nanofluids' thermal conductivity. The current study examines a number of variables that have a significant impact on a nanofluid's ability to transfer heat, including temperature, solid volume fraction, type, size, shape, magnetic field, pH, ultrasonic time, and surfactant. In addition, some plausible and appealing theories that enhance the thermal conductivity of nanofluids are mentioned. The final important heat transmission mechanisms that play a significant part in improving thermal conductivity are Brownian motion, thermophoresis, nanoclustering, interfacial nano-layer, and osmophoresis. Thus, consideration is given to the heat transmission properties of nanofluids. And also discussed some Numerical method to solve fluid flow problems.

Collision of two drops moving in the same direction

The collision dynamics of two drops of the same liquid moving in the same direction has been studied numerically. A wide range of radius ratios of trailing drop and leading drop (Rr) and the velocity ratios (Ur) have been deployed to understand the collision outcomes. A volume of fluid based open-source fluid flow solver, Basilisk, has been used with its adaptive mesh refinement feature to capture the nuances of the interface morphology. The simulations are analyzed for the evolving time instances. Different collision outcomes, such as coalescence and reflexive separation with and without the formation of satellite drops, have been observed for various combinations of Ur and Rr. The study analyzes the evolution of kinetic energy and surface energy before and after the collision for plausible outcomes. The collision outcomes are depicted on a regime map with Ur−Rr space, highlighting distinct regimes formed due to variations in relevant governing parameters.

Implementation of a level-set-based volume penalization method for solving fluid flows around bluff bodies

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an open source field operation and manipulation (OpenFOAM), a computational fluid dynamics solver. The immersed boundary method offers the advantage of inserting a complex solid object inside a Cartesian grid system, and therefore, the governing equations can be applied to such a simpler grid arrangement. For capturing the fluid–solid interface more accurately, the grid is refined near the solid surface using topoSetDict and refineMeshDict utilities in OpenFOAM. In order to avoid any numerical oscillation and to compute the gradients accurately near the interface, the present volume penalization method (VPM) is integrated with a signed distance function, which is also referred to as a level-set function. Benchmark problems, such as flows around a cylinder and a sphere, are considered and thoroughly validated with the results available in the literature. For the flow over a stationary cylinder, the Reynolds number is varied so that it covers from a steady two-dimensional flow to an unsteady three-dimensional flow. The capability of the present solver has been further verified by considering the flow past a vibrating cylinder in the cross-stream direction. In addition, a flow over a sphere, which is inherently three-dimensional due to its geometrical shape, is validated in both steady and unsteady regimes. The results obtained by the present VPM show good agreement with those obtained by a body-fitted grid using the same numerical scheme as that of the VPM, and also with those reported in the literature. The present results indicate that the VPM-based immersed boundary technique can be widely applicable to scientific and engineering problems involving flow past stationary and moving bluff bodies of arbitrary geometry.

Solving 2D damped Kuramoto-Sivashinsky with multiple relaxation time lattice Boltzmann method

Lattice Boltzmann method (LBM) is a powerful fluid flow solver. Using this method to solve other PDEs might be a difficult task. The first challenge is to find a suitable local equilibrium distribution function (EDF) capable of recovering the desired PDE. The next difficulty arises from the explicit nature of LBM. The conditional stability of the LBM algorithm affects the numerical solution accuracy. Damped Kuramoto–Sivashinsky (DKS) equation is a fourth–order PDE that recently challenged many numerical methods' abilities. This equation is highly sensitive to a parameter that causes three states of solutions in a small interval of freedom. In this paper, we challenged LBM to solve the two–dimensional DKS equation by finding EDF using the Chapman–Enskog analysis up to the fourth–order. Also, the von Neumann analysis and a simple genetic algorithm are applied to find reliable values for the free parameters. Furthermore, a modification on image-based ghost node method is proposed for implementation of the boundary conditions in the complex geometries.

Matlab Implementation using Holtrop and Mennen Method of Bare Hull Resistance Prediction for Surface Combatant Ship Coupled with CFD

Holtop’s & Mennen’s method is one of the most widely used technique in resistance and powering prediction for tankers, general cargo ships, container ships and combatant surface ships. Holtrop’s Statistical Analysis method is utilized, as in comparison to the other options, more complete and closer to the actual results. The main purpose of this paper is to develop a Matlab application using Holtop’s & Mennen’s method for studying and research the total resistance of DTMB 5415 combatant ship. The solid modelling is developed using Maxsurf. The computational fluid dynamic (CFD) technique is applied to analyze the hydrodynamic behaviour of hull form and predict the total resistance (Rt) to provide a description of the other prediction methods. The simulation process was executed using ANSYS software based on fluid flow (STAR-CCM+) solver. The variation of computational grid used in computation is SST (Shear Stress Transport) coarse and fine mesh size for hull speed up to 32 kn. RT resulted from CFD computation is validated with results from Holtrop that has been developed by Matlab implementation. The larger the grid meshing size, the better the validation of the results. The CFD technique demonstrated good agreement with Holtrop formulae in predicting the (RT) of DTMB 5415

Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

AbstractAn accurate numerical tool is presented in this work to investigate the stationary incompressible Navier–Stokes equations. The proposed approach is based on a pseudo‐spectral method for discretizing the differential equations and the asymptotic numerical method to convert nonlinear systems into linear algebraic equations. The coupling of the spectral method with the asymptotic numerical method is considered as an efficient algorithm to solve any nonlinear differential equations. Their efficiency and robustness are examined here on the flow fluid in different canal with different geometries. These computational efficiency and performance have been analysed via several numerical and benchmark examples of incompressible fluid flow in lid‐driven cavity and vortex shedding over L‐Shaped cavity and fluid flow around a square obstacle. The validation of the proposed approach is made by comparison between the obtained results and those calculated using a finite element method or Ansys commercial code. This validation asserts that the presented numerical tool can be promise for solving fluid flow problems with high accuracy.

Three-dimensional sharp and conservative VOF method for the simulation of binary solidification

We present a 3D adaptive octree based numerical method for the simulation of binary solidification, with the temperature and the concentration fields being strongly coupled at the solidification front. The volume of fluid approach (VOF) is used to advance the front, which is geometrically reconstructed as a sharp interface separating the liquid and the solid domains. On basis of this, the embedded boundary method (EBM), together with the finite volume method, is employed to discretize the temperature and concentration fields at two sides of the interface in a sharp manner. The major novelty of the present study is displayed in several aspects: It is the first attempt to develop fully sharp schemes for the simulation of binary solidification in the VOF framework, while previous VOF-type methods consider the jump conditions at the interface as source terms; second the geometrically reconstructed interface and the EBM enable us to capture those discontinuities accurately without any artificial smearing, and particularly, we will show how to construct a second-order scheme for the flux jump condition of the temperature field across the interface; finally compared to other sharp schemes, we will show that the present method has natural advantages to adapt with the fluid flow solvers, because the hybrid VOF-EBM method guarantees good performance in solving the complex solid-fluid coupling problems based on the finite volume framework. Owing to all these advantages, we will show that regardless of pure substance or binary solution, all the numerical results agree well with the benchmark results. In particular, we apply the numerical method to model the solidification of a Ni-Cu alloy, which is thought to be very challenging owing to the high Lewis number. Besides, coupling to the fluid flow solver, we demonstrate that this method can predict the solidification/melting of an ice cylinder/sphere accurately in a salted solution under forced convection, by which the fluid, temperature and concentration equations are all solved sharply.

Applications of finite difference‐based physics‐informed neural networks to steady incompressible isothermal and thermal flows

AbstractPhysics‐informed neural networks (PINNs) have aroused an upsurge in scientific machine/deep learning community, especially in research areas involving solving partial differential equations. In this work, based on the multilayer perceptron neural network and finite difference (FD) method, we apply the finite difference‐based PINNs (FD‐PINNs) to simulate the steady incompressible flows. The spatial derivatives in nonlinear governing equations are discretized by the central FD scheme, and the physical boundary conditions can be exactly satisfied in a similar way to conventional fluid flow solvers. Compared to original PINNs using automatic differentiation (AD) to discretize the governing equations, FD‐PINNs hold three‐fold potential advantages in decoupling the predictive accuracy of derivatives from the network's approximating accuracy, fulfilling the physical boundary conditions, and saving computational costs when large‐size networks or meshes are used. We first attempt to make relatively fair comparisons between AD‐PINNs, FD‐PINNs and conventional flow solvers using a benchmark flow problem—steady incompressible laminar isothermal lid‐driven cavity flow across a wide range of Reynolds numbers (Re). Our results indicate that FD‐PINNs are superior to AD‐PINNs in both predictive precision, computational efficiency and training convergence. Moreover, FD‐PINNs exhibit higher accuracy than flow solvers when insufficient mesh points are used to solve high‐Re cavity flow. Even at Re = 10,000, with only 10 internal samples, FD‐PINNs can still precisely recover the flow details on a uniform mesh of size 51 × 51. Besides, the time consumption of FD‐PINNs grows much slower than that of conventional flow solvers. We also investigate the robustness of FD‐PINNs w.r.t. the noise level of samples and the effects of pressure boundary condition imposed on solid cavity walls. Furthermore, FD‐PINNs are extensively applied to predict the incompressible thermal flows: natural convective flows in a square cavity and in a concentric annulus, where the effects of governing equations on the predictive accuracy are discovered and discussed for the first time.

Numerical simulation of the grouting penetration process by developing a temperature‐dependent spatial–temporal rheological model

AbstractThis study aims to investigate the grout penetration process in rock fracture using a self‐developed grouting simulator, in which the spatial–temporal characteristics of the grout properties are adequately considered. To this end, time‐dependent Bingham models as rheological equations, which consider the time‐dependent characteristics of the cement‐sodium silicate grout properties induced by grout hydration, were proposed first by the experimental method. Then, the new grouting simulator was developed by integrating the time‐dependent Bingham model, modified stepwise algorithm, and fluid flow solver. To verify the developed model, two benchmark tests were conducted. Finally, to further explore the influences of the injection rates, ratios of cement to sodium silicate (C/S ratios) and temperatures on the grouting process, a series of numerical grouting examples were systematically conducted. The results indicate that the developed simulator can accurately model the penetration process of the grout with temperature‐dependent spatial–temporal rheological characteristics, especially the grouting pressure distribution in the grouted zone. With the increase of the C/S ratios and temperatures, the grout pressure in the grouted zone increases. The grout pressure distribution is greatly dependent on the injection rates and C/S ratios but is relatively less affected by the temperatures.