Incompressible Research Articles

Geometrically Parametrised Reduced Order Models for Studying the Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behavior of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution.The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behavior in a phase space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI.While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

Mixing in Incompressible Flows: Transport, Dissipation, and Their Interplay

Mixing in Incompressible Flows: Transport, Dissipation, and Their Interplay

Coupling SPH-DEM method for simulating the dynamic response of breakwater structures under severe free surface flow

This paper introduces a novel smoothed particle hydrodynamics (SPH) - discrete element method (DEM) to enhance our understanding of the impact of free-surface flow on breakwater structures. SPH is employed to simulate incompressible fluids, while DEM is utilized to track the trajectories of solid particles. Advanced strategies including polyhedral particle modeling and contact model are adopted to enhance the model's capability in solving the dynamic behavior of irregular particle. Several cases are analyzed to validate the accuracy of coupling model, showing a high level of agreement. Additionally, the impact of wave flow on coastal breakwaters composed of irregular rocks is simulated. This work reveals that the coupling model effectively provides extensive information about the flow field and dynamic response of multi-particle systems, such as velocity, fluid force and force chain distribution. This model exhibits significant potential for analyzing the dynamic response of severe free surface flow on the multi-block structures.

Wavelet Potentials: An Efficient Potential Recovery Technique for Pointwise Incompressible Fluids

AbstractWe introduce an efficient technique for recovering the vector potential in wavelet space to simulate pointwise incompressible fluids. This technique ensures that fluid velocities remain divergence‐free at any point within the fluid domain and preserves local volume during the simulation. Divergence‐free wavelets are utilized to calculate the wavelet coefficients of the vector potential, resulting in a smooth vector potential with enhanced accuracy, even when the input velocities exhibit some degree of divergence. This enhanced accuracy eliminates the need for additional computational time to achieve a specific accuracy threshold, as fewer iterations are required for the pressure Poisson solver. Additionally, in 3D, since the wavelet transform is taken in‐place, only the memory for storing the vector potential is required. These two features make the method remarkably efficient for recovering vector potential for fluid simulation. Furthermore, the method can handle various boundary conditions during the wavelet transform, making it adaptable for simulating fluids with Neumann and Dirichlet boundary conditions. Our approach is highly parallelizable and features a time complexity of O(n), allowing for seamless deployment on GPUs and yielding remarkable computational efficiency. Experiments demonstrate that, taking into account the time consumed by the pressure Poisson solver, the method achieves an approximate 2x speedup on GPUs compared to state‐of‐the‐art vector potential recovery techniques while maintaining a precision level of 10−6 when single float precision is employed. The source code of ‘Wavelet Potentials’ can be found in https://github.com/yours321dog/WaveletPotentials.

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

High-Order Bound-Preserving Local Discontinuous Galerkin Methods for Incompressible and Immiscible Two-Phase Flows in Porous Media

High-Order Bound-Preserving Local Discontinuous Galerkin Methods for Incompressible and Immiscible Two-Phase Flows in Porous Media

Quantum-inspired framework for computational fluid dynamics

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. However, the simulation of turbulent flows in complex geometries is a compute-power intensive task due to the vast vector dimensions required by discretized meshes. We present a complete and self-consistent full-stack method to solve incompressible fluids with memory and run time scaling logarithmically in the mesh size. Our framework is based on matrix-product states, a compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without passing through the expensive dense-vector representation. This framework lays the foundation for a generation of more efficient solvers of real-life fluid problems.

Free vibration analysis of soil-beam-fluid interaction with variable Winkler backfill using DTM

This study aims to analyze the free vibrations of the Euler-Bernoulli beam vibrating in the vicinity of an inviscid, irrotational, and incompressible fluid, as well as Winkler soil, using the differential transformation method. To show the robustness of the proposed formulation, it is used in different numerical tests in which the free vibration of different soil-beam-fluid systems is assessed. The differences between these systems are rooted in their supports and the soil characteristics. Furthermore, the results achieved from the proposed method are compared with those of the finite element strategy. It is emphasized that the differential transformation method employed in this study showcases sufficient precision and reliability throughout the analysis process.

Numerical analysis of velocity slip and magnetic Soret effect on dissipative Maxwell liquid motion about a stretching wall with heat source/sink

The main aim of present numerical analysis is to explore the effects of viscous dissipation and velocity slip on the two-dimensional steady-state viscous incompressible flow of Maxwell fluid over a stretching sheet under the infleunce of magnetic field. Novel collective effects of heat source/sink and Soret impacts have been included in the governing equations to explore the salient features of heat and mass transport mechanism. Further, the velocity slip is introduced into the boundary conditions to depict the momentum transport behavior in the flow region. A typical Maxwell fluid model is deployed to separate the non-Newtonian flow behavior from that of classical Newtonian fluids. However, the visco-elastic Maxwell fluid finds its abundant applications in various fields of engineering and medicine such as plastic sheet drawing, metallurgy, polymer sheet extrusion, chemical engineering, electronic cooling, injection molding and nuclear cooling and many others. Inspired by these applications, authors have made an attempt to disclose the magneto-thermo salient features of slip flow of Maxwell fluid over stretching wall under Soret effect. The current physical situation results the highly nonlinear coupled two-dimensional steady-state partial differential equations and which are not amenable to any of the direct techniques. Due to this, the suitable similarity transformations are deployed to reduce the dimensional complexity of the constructed partial differential equations. A robust Matlab-based bvp4c scheme is utilized as a basic tool to produce the similarity solutions of the governing equations. The computer generated numerical data is presented in view of flow, temperature and concentration profiles including physical quantities of interest like skin-friction coefficient, heat and mass transport rates for the various values of physical parameters range such as, 0 ≤ M ≤ 1 , 0 ≤ β ≤ 1 , − 0.3 ≤ λ ≤ 0.6 , − 0.2 ≤ Q ≤ 0.2 , 0 ≤ Ec ≤ 2.2 , 1.2 ≤ Pr ≤ 2.2 , 0 ≤ Sr ≤ 0.5 and 1.2 ≤ Sc ≤ 2.2 . Accordingly, it is noticed that, enhancing magnetic parameter decreases the Maxwell fluid flow and amplifies the temperature and concentration fields. Enlarging Maxwell fluid parameter decreases the velocity field and increases the temperature and concentration profiles. Amplified slip parameter diminished the Maxwell flow inside the flow regime. Increasing heat source/sink parameter amplifies the temperature field. Further, magnifying Soret number amplifies the concentration field. Magnitude of skin-friction coeffiecient enlarged with amplified magnetic and Maxwell fluid parameters. Heat and mass transport rates decayed with enhancement in heat source/sink and Soret parameters. Finally, it is described that, the present similarity solutions showing good agreement with the previously reported solutions in the literature and this fact confirms the accurateness of the used numerical method and the generated similarity solutions.

Magneto Hydrodynamic Effects on Unsteady Free Convection Casson Fluid Flow Past on Parabolic Accelerated Vertical Plate with Thermal Diffusion

The free convection MHD flow of a viscous, chemically reactive, electrically conducted, incompressible, and Casson fluid past a parabolically accelerated vertical plate was examined in the present article along with the transfer of the heat & mass in the incidence of thermal radiation. The inverse Laplace method is used to resolve the dimensionless equations. The concentration and temperature fields, axial and transverse velocity are examined for distinct parameters like the (Casson fluid), Sc (Schmidt number), Gr (thermal Grashof number), Pr (Prandtl number), and Gm (mass Grashof number). Utilizing the temperature of fluid and concentration of species as a solution is also proposed. Graphical representations of the fluctuations in temperature of fluid and velocity along species concentration are provided for several values of relevant flow parameters.

Validation of helicity-corrected Spalart-Allmaras model for corner separation prediction in incompressible flow with OpenFOAM

Steady Reynolds-averaged Navier-Stokes (RANS) computations save significant computational resources compared to unsteady RANS and large eddy simulation (LES). However, the ability of most RANS models to accurately predict flow separation in compressor/fan blade rows is limited. Recent research focused on reducing the computational cost of predicting compressor/fan stall points with steady computations has shown that the helicity-corrected Spalart-Allmaras (SA) turbulence model is able to avoid over-predicting corner separations and thus lead to converged RANS up to the actual stall point. To date, this model has mostly been implemented in in-house codes or in commercial codes as a user add-on, where the source code is not available. In a recent paper, the authors implemented the helicity-corrected SA model in OpenFOAM, an open-source CFD package. In this paper, the differences in the flow field for RANS solutions with the original SA model, the helicity-corrected SA model, and Menter’s shear stress transport (SST) model are highlighted for a linear cascade with incompressible flow. A NACA 65-1810 cascade is used, and computational results are compared to experimental data.

Arbitrary-order sensitivities of the incompressible base flow and its eigenproblem

First-order sensitivities and adjoint analysis are used widely to control the linear stability of unstable flows. Second-order sensitivities have recently helped to increase accuracy. In this paper, a method is presented to calculate arbitrary high-order sensitivities based on Taylor expansions of the incompressible base flow and its eigenproblem around a scalar parameter. For the incompressible Navier–Stokes equations, general expressions for the sensitivities are derived, into which parameter-specific information can be inserted. The computational costs are low since, for all orders, a linear equation system has to be solved, of which the left-hand-side matrix stays constant and thus its preconditioning can be exploited. Two flow scenarios are examined. First, the cylinder flow equations are expanded around the inverse of the Reynolds number, enabling the prediction of the two-dimensional cylinder base flow and its leading eigenvalue as a function of the Reynolds number. This approach computes accurately the base flow and eigenvalue even in the unstable regime, providing, when executed subsequently, a mean to calculate unstable base flows. This case gives a clear introduction into the method and allows us to discuss its constraints regarding convergence behaviour. Second, a small control cylinder is introduced into the domain of the cylinder flow for stabilization. Higher-order sensitivity maps are calculated by modelling the small cylinder with a steady forcing. These maps help to identify stabilizing areas of the flow field for Reynolds numbers within the laminar vortex shedding regime, with the required number of orders increasing as the Reynolds number rises. The results obtained through the proposed method align well with numerically calculated eigenvalues that incorporate the cylinder directly into the grid.

A non-overlapping optimization-based domain decomposition approach to component-based model reduction of incompressible flows

We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain decomposition technique to determine the control variable that minimizes jumps across the interfaces between sub-domains. To solve the resulting constrained optimization problem, we propose both Gauss-Newton and sequential quadratic programming methods, which effectively transform the constrained problem into an unconstrained formulation. Furthermore, we integrate model order reduction techniques into the optimization framework, to speed up computations. In particular, we incorporate localized training and adaptive enrichment to reduce the burden associated with the training of the local reduced-order models. Numerical results are presented to demonstrate the validity and effectiveness of the overall methodology.

Incompressible versus compressible fluid flow models: A case study on furnace tap-hole lancing

Pyrometallurgical furnaces, essential for metal extraction, operate at temperatures exceeding 1600°C and represent complex multiphase systems that challenge direct industrial research. Multiphysics models play a key role in shedding light on their intricate behaviours, supporting the refinement of design and operational strategies. Integral to the operation are the tap-holes, which facilitate the removal of molten products and are routinely opened by lancing, a process comparable to the use of a cutting torch, where high temperatures result from oxygen reacting with an iron lance. When the lance pierces the clay, oxygen gas enters the furnace, which could influence the behaviour of the molten material inside. In this work, a multiphase fluid flow model was used to investigate bulk flow dynamics, with a focus on the effects of the lancing process on the inside of the furnace, immediately behind the tap-hole. Incompressible and compressible multiphase fluid solvers were used and compared with respect their performance - the intention was to assess whether using a compressible solver would yield a different solution to the incompressible one. It was concluded that there are negligible disparities in bulk fluid flow behaviour between the solvers for the case studies examined, indicating that solver selection might be less consequential for certain aspects of oxygen lancing.

A generalized differential quadrature approach to the modelling of heat transfer in non-similar flow with nonlinear convection

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers.

Flow analysis of Williamson model over a moving surface with nonlinear convection/diffusion and variable thermal conductivity

This article analyses the flow across a moving surface using the magnetohydrodynamic (MHD) Williamson fluid model in detail, accounting for the effects of diffusion, nonlinear convection, and variable thermal conductivity. The heat transmission within the system is impacted by the changing thermal conductivity, which can also significantly alter the flow behavior. The effects of the moving surface on flow forms in porous media are explained here using the Darcy model. The similarity transformations are used to convert the underlying nonlinear partial differential equations into a collection of ordinary differential equations. The work uses a numerical RK4 technique to examine the complex incompressible fluid flow behavior on a moving surface. The study’s conclusions provide insight into the intricate flow patterns and shear layer forms brought on by the interaction of fluid and surface motion while taking varied thermal conductivity into account. The findings give important information for the design and optimization of engineering applications involving changeable thermal characteristics and advance our understanding of fluid dynamics in geophysical and atmospheric systems. Physical descriptions are used to depict how flow parameters behave in relation to velocity, temperature, and concentration distributions.

Numerical simulations of third-grade fluid flow with exothermic reactions in porous media-saturated vertical microchannels

The aim of this article is to analyze the electro-osmotic flow behavior of a third-grade (TG) incompressible fluid flowing in a vertical microchannel saturated with porous material. The electro-osmotic flow is regarded as an essential part of many scientific and engineering applications used in microfluidic devices. The flow is subjected to joule heating, exothermic reactions, and asymmetrical convective cooling. The viscosity which is assumed temperature dependent via a Naham-type law and the convective heat transfer rates governing the asymmetric convective cooling at the microchannel walls are modeled via Newton’s law of cooling. The governing system of nonlinear partial differential equations is solved computationally using an efficient and reliable finite difference method. The spatial and temporal convergence of the numerical scheme is showcased graphically. Our study findings reveal that the combination of exothermic reactions and Joule heating significantly influences the electroosmotic flow. Higher values of variable viscosity parameter (α), Brinkman number (Br), and Buoyancy parameter (Gr) result an enhancement in the flow variables. Conversely, a reverse trend is observed when augmenting the Prandtl number (Pr), non-Newtonian parameter (γ), and porous media parameters (Ω2). Numerical results for temperature and velocity are also discussed qualitatively and validated with the data previously published.

Interactive Airfoil Optimization Using Parsec Parametrization and Adjoint Method

In the development of interactive aerodynamic optimization tools, the need to reduce the computational complexity of flow calculations has arisen. Computational complexity can be reduced by estimating the flow variables using machine learning, but that approach has a number of hindrances. Avoiding these hindrances through lowering the computational complexity by stating the assumptions of inviscid incompressible potential flow is the focus of this article. The assumptions used restrict the applicability of this approach to only specific cases, but in engineering practice, these cases are quite widespread. The assumptions allowed the coupling of the adjoint method with parsec parametrization and the panel method, yielding a highly computationally efficient and robust tool for optimizing an airfoil’s lift coefficient (Cy). The optimization of the NREL S809 airfoil was carried out, and the results were verified using the Xfoil 6.99 software. The Xfoil verification showed that by making minimal changes to the airfoil’s shape, the Cy and lift-to-drag ratios were significantly improved. The improvement magnitude was over 94% for a 0 deg angle of attack (AoA) and over 16% for 6.2 deg AoA. This indicates an improvement in performance that is similar to that of some genetic algorithms, but with computational costs that are many orders of magnitude lower.

Characteristics and evolution of ground vortex under heaving ground conditions: Insights from large eddy simulation (LES) analysis

When an aircraft engine operates near the ground, the ambient vortices generated by the freestream velocity boundary layer and engine suction will gather and lift, forming ground vortices which may result in intake distortion, consequently affecting the engine operation stability. To develop a shipborne test platform, this study conducted large eddy simulation calculations using the ANSYS Fluent and based on the assumption of incompressible flow. The 3-D unsteady Navier-Stokes (N-S) equations were solved using the WALE sub-grid model. The analysis focused on the characteristics and evolution of ground vortices under heaving ground conditions within 1 s. The results indicate that the ground vortex exhibits strong unsteady characteristics. During the descending phase of the platform, the quantity of vortex formed beneath the intake duct would decrease while the trailing vortex becomes more pronounced. However, the structure of the inlet vortex remains relatively unchanged at each time step. The intensity of the vortex and pressure distortion coefficient exhibit significant fluctuations over time, and their temporal variations approximately follow a sinusoidal function, which is also the heaving motion of the platform. Generally, when the velocity of the platform reaches its maximum downward vertical value, the average vortex intensity of the ground vortex tends to be minimal while the pressure distortion coefficient approaches its maximum value. Conversely, when the velocity of the platform reaches its maximum upward vertical value, the opposite trend can be observed.

Numerical heat and mass transfer in magnetized Williamson liquid motion over a sensor wall engulfed in a micro-cantilever system: An application to thin-film fluidic cells

Central focus of this numerical analysis is to investigate the influence of magnetic body force and thermal radiation on the time-dependent electrically conducting two-dimensional viscous incompressible boundary layer flow of non-Newtonian Williamson fluid over a microcantilever sensor surface suspended in a squeezed regime numerically. A novel heat source/sink and Soret effects are included in the respective governing equations. The constructed time-dependent nonlinear coupled partial differential equations are solved by using a bobust RK-4 technique. Increasing magnetic number increases the velocity distribution and decreases the temperature and concentration profiles in the flow regime.Enhancing Soret number increases the mass diffusion profile. Increasing magnetic number suppress the skin-friction coefficient. Heat transport rate booted with rising radiation number and Sherwood number decreased with enlarged Schmidt number in the channel regime. Finally, the numerical accuracy of the present similarity solutions and used numerical method is validated with existing results and observed a remarkable agreement.