Incompressible Fluid Dynamics 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 behaviour 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 behaviour 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.

Predicting unsteady incompressible fluid dynamics with finite volume informed neural network

The rapid development of deep learning has significant implications for the advancement of computational fluid dynamics. Currently, most pixel-grid-based deep learning methods for flow field prediction exhibit significantly reduced accuracy in predicting boundary layer flows and poor adaptability to geometric shapes. Although graph neural network models for unstructured grid-based unsteady flow prediction have better geometric adaptability, these models suffer from error accumulation in long-term predictions of unsteady flows. More importantly, fully data-driven models often require extensive training time, greatly limiting the rapid update and iteration speed of deep learning models when facing more complex unsteady flows. Therefore, this paper aims to balance the demands for training overhead and prediction accuracy by integrating physical constraints based on the finite volume method into the loss function of the graph neural network. Additionally, it incorporates a twice-message aggregation mechanism inspired by the extended stencil method to enhance the unsteady flow prediction accuracy and geometric shape generalization ability of the graph neural network model on unstructured grids. We focus particularly on the model's predictive accuracy within the boundary layer. Compared to fully data-driven methods, our model achieves better predictive accuracy and geometric shape generalization ability in a shorter training time.

Exploring plasma phenomena with the Nizhnik–Novikov–Veselov formula: Analyzing ion-acoustic waves, solitons, and shocks

This paper delves into the intricacies of the ([Formula: see text])-dimensional asymmetric Nizhnik–Novikov–Veselov ([Formula: see text]) model, a nonlinear partial differential equation governing ion-acoustic wave propagation in plasma. By employing advanced analytical and numerical approaches, the study explores innovative solitary wave solutions, particularly focusing on the dynamics of isochoric flow. Isochoric flow analysis is crucial for unraveling the complex behaviors exhibited by incompressible fluids like elastomers and bio-elastomers, which maintain a constant density. The derivation of the ([Formula: see text])-dimensional [Formula: see text] equation stems from fluid equations governing plasma dynamics. This model serves as a valuable tool for simulating experimental observations of plasma waves. The computational methodology applied in this research demonstrates a commendable level of precision and consistency, yielding novel solitary wave solutions previously unreported in the [Formula: see text] model. These results underscore the study’s importance and novelty. The outcomes not only contribute to our understanding of incompressible fluid dynamics, but also lay the groundwork for future investigations in this domain. The revealed solitary wave solutions have the potential to inform the development of more accurate models for predicting fluid dynamics, thereby advancing the field.

Remarks on some unidirectional flows of Maxwell fluids through a rectangular channel filled with porous medium

AbstractExact solutions for the dynamics of incompressible fluids showing rate‐type behavior have mostly been found in circumstances where the boundary velocities are given in the body of existing research. This phenomenon results from the constitutive equation of the corresponding extra‐stress tensor, which specifies the natural relationship between velocity and shear stress. In this paper, we focus on a unique observation of the magnetohydrodynamic (MHD) movements of incompressible Maxwell fluids, and the governing equations regulating velocity and shear stress. We focus our analysis on the case of an infinite plate submerged in a porous substance. Within this framework, we do an analytical analysis of a motion issue with a boundary that has a predetermined shear stress. We can easily ascertain the shear stress associated with the motion brought on by a flat plate in order to be more exact. The fluid is subjected to a shear stress by this plate that changes over time. The velocity field from a boundary motion with a predetermined velocity is used to achieve this. We give two graphical representations of individual solutions for the sake of clarity and result verification. Last but not least, we use graphical depiction to highlight how a magnetic field and a porous media affect the fluid's flow resistance. The results show that the flow resistance of the fluid increases in the presence of a porous media and decreases when a magnetic field is present.

On the existence of energy‐variational solutions in the context of multidimensional incompressible fluid dynamics

We define the concept of energy‐variational solutions for the Navier–Stokes and Euler equations and prove their existence in any space dimension. It is shown that the concept of energy‐variational solutions enjoys several desirable properties. Energy‐variational solutions are not only known to exist and coincide with local strong solutions, but the operator, mapping the data to the set of energy‐variational solutions, is additionally continuous and all restrictions and all concatenations of energy‐variational solutions are energy‐variational solutions again. Finally, different selection criteria for these solutions are discussed.

Insight into Functional Boiti–Leon–Mana–Pempinelli Equation and Error Control: Approximate Similarity Solutions

The Boiti–Leon–Mana–Pempinelli Equation (BLMPE) is an essential mathematical model describing wave propagation in incompressible fluid dynamics. In the present manuscript, a novel generalization of the BLMPE is introduced, called herein the functional BLMPE (F-BLMPE), which involves different functions, including exponential, logarithmic and monomaniacal functions. In these cases, the F-BLMPE reduces to an explicit form in the dependent variable. In addition to this, it is worth deriving approximate similarity solutions of the F-BLMPE with constant coefficients using the extended unified method (EUM). In this method, nonlinear partial differential equation (NLPDE) solutions are expressed in polynomial and rational forms through an auxiliary function (AF) with adequate auxiliary equations. Exact solutions are estimated using formal solutions substituted into the NLPDEs, and the coefficients of the AF of all powers are set equal to zero. This approach is valid when the NLPDE is integrable. However, this technique is not valid for non-integrable equations, and only approximate solutions can be found. The maximum error can be controlled by an adequate choice of the parameters in the residue terms (RTs). Multiple similarity solutions are derived, and the ME is depicted in various examples within this work. The results found here confirm that the EUM is an efficient method for solving NLPDEs of the F-BLMPE type.

Forest density is more effective than tree rigidity at reducing the onshore energy flux of tsunamis

Communities around the world are increasingly interested in nature-based solutions to the mitigation of coastal risks by coastal forests, but it remains unclear how much protective benefits vegetation provides, particularly in the limit of highly energetic flows after tsunami impact. The current study, using a three-dimensional incompressible computational fluid dynamics model with a fluid–structure interaction approach, aims to quantify how energy reflection and dissipation vary with different degrees of rigidity and vegetation density of a coastal forest. We represent tree trunks as cylinders and use the elastic modulus of hardwood trees such as pine or oak to characterize the rigidity of these cylinders. The numerical results show that energy reflection increases with rigidity only for a single cylinder. In the presence of multiple cylinders, the difference in energy reflection created by varying rigidity diminishes as the number of cylinders increases. Instead of rigidity, we find that the blockage area created by the presence of multiple tree trunks dominates energy reflection. As tree trunks are deformed by the hydrodynamic forces, they alter the flow field around them, causing turbulent kinetic energy generation in the wake region. As a consequence, trees dissipate flow energy, highlighting coastal forests reducing the onshore energy flux of tsunamis by means of both reflection and dissipation.

CFD simulations of a semi-transverse ventilation system in a long tunnel

In the present work, a semi-transverse ventilation system in a long tunnel with a length of 4.9 km, as a complex case study, is numerically studied by performing a set of three-dimensional steady incompressible computational fluid dynamics (CFD) simulations. The ventilation system consisted of a ceiling duct connected to two axial fans at the ending portals, and a series of jet fans in the main tunnel for supporting airflow in the desired direction. To focus on what can and cannot be achieved in commissioning tests, the ventilation system’s performance in various scenarios is numerically evaluated with two different tunnel states; empty tunnel and complete traffic congestion with 1176 stationary vehicles – which is almost impossible to evaluate during a commissioning test. By considering two hypothetical locations for the extraction zone from the main tunnel (in a distance of 450 and 1000 m from one portal), it is shown that the required number of jet fans in a traffic condition drops from 57 for the first extraction location to 43 (25% decrease) when the ventilation system extracts from the second zone. We show that if only the close axial fan to the extraction zone is activated, the required number of jet fans reduces by 56% and 72% for the first and second extraction locations, respectively. This finding can provide a cheaper and easier controlling scenario for emergency ventilation.

Effect of Shear Modulus on the Inflation Deformation of Parachutes Based on Fluid-Structure Interaction Simulation

Parachutes and other inflatable aerodynamic decelerators usually use flexible fabrics due to their lightweight and high load-carrying capacity. The behavior of fabrics during complex deformations is mainly influenced by their shear properties. The shear properties of fabric can be explained by the shear stiffness or shear modulus. The design optimization of these inflatable structures relies on a detailed knowledge of the mechanical properties of the fabric material. To investigate the effect of shear modulus on the inflatable shapes of parachute canopies, an arbitrary Lagrangian–Eulerian coupling method based on the incompressible computational fluid dynamics solver and structural solver LS-DYNA is proposed. Finite element methods are used to describe continuous materials such as fabrics and airflow fields. The effects of the shear modulus on the inflated parachute shapes are investigated from the macroscopic and microscopic scales. A comparison analysis reveals that different shear moduli have little effect on the overall shape and in-plane shear strain of the parachute, while they have significant effects on the in-plane stress distribution and wrinkles of the parachute. The methods and conclusions of this paper can provide some reference for the materials design of parachutes in preforming stage.

Incompressible versus compressible large eddy simulation for the identification of premixed flame dynamics

The present work compares the respective advantages and disadvantages of compressible and incompressible computational fluid dynamics (CFD) formulations when used for the estimation of the acoustic flame response. The flame transfer function of a turbulent premixed swirl-stabilized burner is determined by applying system identification (SI) to time series data extracted from large eddy simulation (LES). By analyzing the quality of the results, the present study shows that incompressible simulations exhibit several advantages over their compressible counterpart with equal prediction of the flame dynamics. On the one hand, the forcing signals can be designed in such a way that desired statistical properties can be enhanced, while maintaining optimal values in the amplitude. On the other hand, computational costs are reduced and the implementation is fundamentally simpler due to the absence of acoustic wave propagation and corresponding resonances in the flame response or even self-excited acoustic oscillations. Such an increase in efficiency makes the incompressible CFD/SI modeling approach very appealing for the study of a wide variety of systems that rely on premixed combustion. In conclusion, the present study reveals that both methodologies predict the same flame dynamics, which confirms that incompressible simulation can be used for thermoacoustic analyses of acoustically compact velocity-sensitive flames.

Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs

For a nonlinear operator T satisfying certain structural assumptions, our main theorem states that the following claims are equivalent: i) T is surjective, ii) T is open at zero, and iii) T has a bounded right inverse. The theorem applies to numerous scale-invariant PDEs in regularity regimes where the equations are stable under weak⁎ convergence. Two particular examples we explore are the Jacobian equation and the equations of incompressible fluid flow.For the Jacobian, it is a long standing open problem to decide whether it is onto between the critical Sobolev space and the Hardy space. Towards a negative answer, we show that, if the Jacobian is onto, then it suffices to rule out the existence of surprisingly well-behaved solutions.For the incompressible Euler equations, we show that, for any p<∞, the set of initial data for which there are dissipative weak solutions in LtpLx2 is meagre in the space of solenoidal L2 fields. Similar results hold for other equations of incompressible fluid dynamics.

From the Nash–Kuiper theorem of isometric embeddings to the Euler equations for steady fluid motions: Analogues, examples, and extensions

Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface (M, g) isometrically embedded in R3, we construct a mapping that sends the second fundamental form of the embedding to the density, velocity, and pressure of steady fluid flows on (M, g). From a Partial Differential Equations perspective, this mapping sends solutions to the Gauss–Codazzi equations to the steady Euler equations. Several families of special solutions of physical or geometrical significance are studied in detail, including the Chaplygin gas on standard and flat tori as well as the irregular isometric embeddings of the flat torus. We also discuss tentative extensions to multiple dimensions.

Dimensional investigation of solar chimney power plant based on numerical and experimental results

• Construction of prototype solar chimney and recording air flow temperature and velocity data under different solar radiation. • 3D numerical simulation of the base case using FLUENT software and validation of the results with the experimental results obtained in this study and also validation with other researcher's numerical and experimental results. • Investigation of the fluid behavior pattern inside the solar chimney and system performance based on the simulation results under different geometric parameters. In this study, a pilot solar chimney power plant (SCPP) with a chimney height of 4 m and a collector diameter of 5 m was constructed. Main purpose of this research is identification and optimization of the system based on regional climatic experimental data which recorded from constructed solar chimney with new dimensions to utilize in our future studies. So that future studies can be conducted based on a suitable platform. Performance evaluation of solar chimney was simulated under different geometric configurations through a 3D axisymmetric incompressible steady computational fluid dynamics solver by applying k - ε turbulence model. For a better performance comparison of the SCPP between different geometries, air velocity and system output power were calculated for all states. The results showed that a higher collector radius and chimney radius increased the ​​air outflow velocity in the collector, whereas a higher collector height had a negative effect. According to the results, configurations with collector height of 5 cm have the highest velocity values compared to the others and the maximum power value of 1.74 W can be achieved for the collector inlet height of 15 cm and the chimney radius of 0.4 m.

Sıkıştırılamaz Visko Elastik Kelvin-Voigt Sıvısında Ortaya Çıkan Oskolkov Denkleminin Gezici Dalga Çözümleri

In this manuscript, exact solutions of the Oskolkov equation, which describes the dynamics of incompressible viscoelastic Kelvin-Voigt fluid, are presented. The -expansion method is used to search for these solutions. The dynamics of the obtained exact solutions are analyzed with the help of appropriate parameters and presented with graphics. The applied method is efficient and reliable to search for fundamental nonlinear waves that enrich the various dynamical models seen in engineering fields. It is concluded that the analytical method used in the study of the Oskolkov equation is reliable, valid and useful tool for created traveling wave solutions.

Decoupled finite element scheme of the variable-density and viscosity phase-field model of a two-phase incompressible fluid flow system using the volume-conserved Allen–Cahn dynamics

We aim to develop a fully-discrete version numerical scheme in this article for solving a variable density and viscosity phase-field model involving a nonlinear coupling between the conserved Allen–Cahn equation and the incompressible fluid dynamics. The scheme uses the finite element method for spatial discretization and the linearly stabilized-explicit method for time discretization. The fully-decoupled structure is achieved by applying the “zero-energy-contribution” feature satisfied by coupled nonlinear terms that include the advection and the surface tension, where two nonlocal auxiliary variables are used. These nonlocal auxiliary variables, combined with the operator Strang-splitting method, play as the keys to obtaining an efficient numerical algorithm. At each time step, only a series of full decoupling elliptic equations need to be solved. We rigorously demonstrate the solvability and unconditional energy stability of the scheme, and verify its effectiveness through carrying out various numerical examples including 3D droplets rising simulations.

Multi-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics

The simulation of fluid dynamics, typically by numerically solving partial differential equations, is an essential tool in many areas of science and engineering. However, the high computational cost can limit application in practice and may prohibit exploring large parameter spaces. Recent deep-learning approaches have demonstrated the potential to yield surrogate models for the simulation of fluid dynamics. While such models exhibit lower accuracy in comparison, their low runtime makes them appealing for design-space exploration. We introduce two novel graph neural network (GNN) models, multi-scale (MuS)-GNN and rotation-equivariant (RE) MuS-GNN, for extrapolating the time evolution of the fluid flow. In both models, previous states are processed through multiple coarsening of the graph, which enables faster information propagation through the network and improves the capture and forecast of the system state, particularly in problems encompassing phenomena spanning a range of length scales. Additionally, REMuS-GNN is architecturally equivariant to rotations, which allows the network to learn the underlying physics more efficiently, leading to improved accuracy and generalization. We analyze these models using two canonical fluid models: advection and incompressible fluid dynamics. Our results show that the proposed GNN models can generalize from uniform advection fields to high-gradient fields on complex domains. The multi-scale graph architecture allows for inference of incompressible Navier–Stokes solutions, within a range of Reynolds numbers and design parameters, more effectively than a baseline single-scale GNN. Simulations obtained with MuS-GNN and REMuS-GNN are between two and four orders of magnitude faster than the numerical solutions on which they were trained.

Incompressible flow through choke valve: An experimental and computational investigation

The flow within a control valve is complex, particularly for choke types with multiple entries. Despite the abundant use of control valves in pressure-reduction applications across various fields, there is lack of understanding of fluid flow behavior within such valves. Failure associated with vortex shedding and Flow-Induced Vibration (FIV) remains as a long-standing issue with operation of control (choke) valves. This industry-academia collaborative study constitutes a coupled computational and experimental methodology to analyze the complex flow within a choke valve under laminar inflow conditions. The investigation is conducted on a control valve, currently used in industry, at four specific choke positions. Incompressible Computational Fluid Dynamics (CFD) simulations are performed using water as fluid and Detached Eddy Simulation (DES) as turbulence model under two different laminar inlet flow rate (equivalent Reynolds number, Re, approximately 100 and 500). Experiments are carried out under the same conditions using Particle Image Velocimetry (PIV). The instantaneous and time-averaged (mean) vorticity and velocity contours are presented on four selected planar cross sections providing complementary information on the flow physics. Despite the complex geometry of the choke valve in question as well as the fluid flow developing within it, close agreement is found between the computational and experimental results. Both the studies reveal that, at low valve openings, when only the small ports are engaged, there forms a four-lobed vortical structure which is established upon collision of the incoming jets. The vortical structure of the flow is much more complex at higher valve openings when both the small and large ports are engaged. The inherent unsteadiness associated with turbulent flow within the valve chamber leads to flipping motion of the formed jets and vortex shedding; mechanisms of which are explained in detail in the paper. The frequency spectrum of the fluid flow is correspondingly assessed using Fast Fourier Transform (FFT) examining the dominant vibration modes and corresponding Strouhal numbers. The dominant frequency peaks found in computational and experimental studies can result in FIV and resonance failure of control valves in practice. The autocorrelation analysis and continuous wavelet transform have furthermore been augmented in signal processing of the data to illuminate the oscillatory behavior of the flow due to vortex shedding.

Simultaneously developing flow and heat transfer in circular and parallel-plates microchannels with velocity slip and temperature jump

The entrance effect has an important influence on the heat transfer characteristics in microchannels. It is necessary to determine the influence to design microchannel heat sinks properly. In this work, the simultaneously developing flow and convective heat transfer were investigated numerically inside circular and parallel-plates microchannels. The effects of the Knudsen number (0–0.1) and Peclet number (25–1000) on the local Nusselt number were taken into consideration in the slip flow regime. The numerical results were calculated via an incompressible and steady computational fluid dynamics algorithm under the boundary conditions of the velocity slip and temperature jump. The user-defined functions were used to achieve the velocity slip boundary condition, and a thermal resistance model was first proposed to easily impose the temperature jump boundary condition. The numerical approach was verified using both the analytic solutions of the thermally developing flow and the exact solutions of the fully developed flow, which was then employed to obtain the influences of the axial heat conduction and the rarefaction on the local Nusselt number of the simultaneously developing flow. The results of the apparent friction factor and the heat transfer coefficient were graphically presented as functions of the Knudsen number, Reynolds number or Peclet number, and non-dimensional axial length. It was found that the effect of the axial heat conduction on the entrance effect can be ignored when Pe > 500. The heat transfer performance of the simultaneously developing flow can be predicted by the results of the thermally developing flow when the Knudsen number is large enough. General correlations were also proposed for the apparent friction coefficients, local Nusselt number in circular and parallel-plates microchannels.

Finite element hybrid and direct computational aeroacoustics at low Mach numbers in slow time-dependent domains

In this work, we address the finite element computation of flow noise in the presence of arbitrarily slowly moving rigid bodies at low Mach numbers, by means of hybrid and direct computational aeroacoustics (CAA) strategies. As regards the former, the problem could be dealt with by means of the Ffowcs Williams–Hawkings acoustic analogy. That reduces to Curle’s analogy for a static body, which is analogous to a problem of diffraction of sound waves generated by flow eddies in the vicinity of the body. Acoustic analogies in CAA first demand computing the flow motion to extract an acoustic source term from it and then use the latter to calculate the acoustic pressure field. However, in the case of low Mach number flows, the Ffowcs Williams–Hawkings and Curle analogies present a problem as they require knowing the total pressure distribution on the body’s boundary (i.e. the aerodynamic pressure plus the acoustic one). As incompressible computational fluid dynamics (CFD) simulations are usually performed to determine the flow motion, the acoustic pressure distribution on the body surface is unavoidably missing, which can yield acoustic analogies inaccurate. In a recent work, it was proposed to tackle that problem for static and rigid surfaces, by keeping the incompressible CFD and then splitting the acoustic pressure into direct and diffracted components. Two separate wave equations were solved for them, in the framework of the finite element method (FEM). In this article, we extend that work to compute the aerodynamic sound generated by a flow interacting with a slowly moving rigid body. The incompressible Navier–Stokes equations are first solved in an arbitrary Lagrangian–Eulerian (ALE) frame of reference to obtain the acoustic source term. Advantage is then taken from the same computational run to separately solve two acoustic ALE wave equations in mixed form for the incident and diffracted acoustic pressure components. For validation of the total acoustic pressure field, an ALE formulation of a direct CAA approach consisting of a unified solver for a compressible isentropic flow in primitive variables is considered. The performance of the exposed methods is illustrated for the aeroacoustics of flow past a slowly oscillating two-dimensional NACA airfoil and for flow exiting a duct with a moving teeth-shaped obstacle at its termination.

An application of Gaussian process modeling for high-order accurate adaptive mesh refinement prolongation

We present a new polynomial-free prolongation scheme for Adaptive Mesh Refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the GP methods introduced by A. Reyes et al. (A New Class of High-Order Methods for Fluid Dynamics Simulation using Gaussian Process Modeling, Journal of Scientific Computing, 76 (2017), 443-480; A variable high-order shock-capturing finite difference method with GP-WENO, Journal of Computational Physics, 381 (2019), 189-217). In this paper, we extend the previous GP interpolations and reconstructions to a new GP-based AMR prolongation method that delivers a high-order accurate prolongation of data from coarse to fine grids on AMR grid hierarchies. In compressible flow simulations special care is necessary to handle shocks and discontinuities in a stable manner. To meet this, we utilize the shock handling strategy using the GP-based smoothness indicators developed in the previous GP work by A. Reyes et al. We demonstrate the efficacy of the GP-AMR method in a series of testsuite problems using the AMReX library, in which the GP-AMR method has been implemented.