Incompressible Flow Model Research Articles

THE COOLING CAPACITY OF NATURAL GASES FOR CIRCULAR/RECTANGULAR GEOMETRIES BY IMPINGING JET

In this work, influences of the variety of parameters on the heat-transfer forced convection of two confined impinging jets, such as inlet geometry and mass-flow rate, have been investigated numerically. Simulations were done using a 3D k - ε model for incompressible flow on two jet exit geometries comprising rectangular and circular jets at the dimensionless jet-to-plate distance of 2. A finite-volume method was employed to discretize the equations. Local Nusselt number was obtained for various mass-flow rates and geometries for air and pure gases of oxygen, nitrogen, argon, and carbon dioxide at a dimensionless jet-to-plate distance of 2. As the mass-flow rate increases, heat-transfer enhancement is obtained. The CO<sub>2</sub> gas has the highest level of the Nusselt number in comparison with others, and around 40% increases the rate of heat transfer compared to the air; thus, it could be beneficial in the cooling process rather than other gases. Also, this study revealed that the forced-convection heat transfer in the circular jet has a higher amount than the rectangular jet.

The error analysis for the Cahn-Hilliard phase field model of two-phase incompressible flows with variable density

<abstract><p>In this paper, we consider the numerical approximations of the Cahn-Hilliard phase field model for two-phase incompressible flows with variable density. First, a temporal semi-discrete numerical scheme is proposed by combining the fractional step method (for the momentum equation) and the convex-splitting method (for the free energy). Second, we prove that the scheme is unconditionally stable in energy. Then, the $ L^2 $ convergence rates for all variables are demonstrated through a series of rigorous error estimations. Finally, by applying the finite element method for spatial discretization, some numerical simulations were performed to demonstrate the convergence rates and energy dissipations.</p></abstract>

Thermo-rheological reduced order models for non-Newtonian fluid flows with power-law viscosity via the modal identification method

In the framework of melted polymer flows characterization, this study deals with the formulation, construction and validation of thermo-rheological Reduced Order Models (ROMs) for incompressible flows of pseudoplastic fluids. The dynamic viscosity is described by a shear rate power law defined by consistency index K and pseudoplastic index n. The flow dynamics are assumed to be quasi-static whereas the thermal state is unsteady. Viscous dissipation acts as a heat source term in the energy equation. ROMs are built through the Modal Identification Method (MIM). First, their general form is derived from governing local conservation equations and the viscosity power-law, with an original approach to handle the issues related to the pseudoplastic index n. Then ROMs are identified using Particle Swarm Optimization and Ordinary Least Squares, from simulations coming from a reference Full Order Model (FOM). The approach is applied to a polymer flow in an annular duct, corresponding to an experimental lab apparatus. ROMs allow computing temperature at chosen locations of interest whatever the applied inputs, here parameters K, n and inlet flowrate as well as a time-varying volumetric heat source power in the central axis. Compared to the reference Finite Elements FOM, computing time is considerably reduced with limited loss of accuracy.

Effect of 3D Shape of Pump-Turbine Runner Blade on Flow Characteristics in Turbine Mode

The effect of blade spatial profiling with the help of tangential blade lean of Francis pump-turbine runner with heads up to 200 m on the flow structure and energy characteristics was numerically investigated. A flow part model of Francis pump-turbine of the Dniester pumped storage plant was adopted as original version. Two new blade systems were designed, which differed from the original version by mutual position of cross-sections in tangential direction: with positive and negative lean, while the shape of the cross-sections themselves remained unchanged. Modeling of the viscous incompressible flow in calculation domain, which contains one channel of the guide vane and the runner, for three variants of flow parts, was performed using the IPMFlow software based on numerical integration of the Reynolds equations with an additional term containing artificial compressibility. To take into account the turbulent effects, the SST differential two-parameter turbulence model of Menter is applied. Numerical integration of the equations is carried out using an implicit quasi-monotonic Godunov scheme of second order accuracy in space and time. The study was carried out for models with runner diameter of 350 mm in a wide range of guide vane openings at reduced rotation frequencies corresponding to the minimal, design and maximal heads of the station. A comparison of pressure fields and velocity vectors in the runners, pressure graphs on runner blades, distribution of velocity components at inlet to a draft tube, and efficiency of three variants of flow parts are presented. It was concluded that calculation domain with the new RK5217M2 runner with negative tangential lean has the best characteristics. An experimental study of three runners on a hydrodynamic stand are planned

Resin infusion in porous preform in the presence of HPM considering complex geometry and gravity: Flow simulation and experimental validation

Present work demonstrates the complete numerical modeling and experimental validation of transient incompressible two-phase flow during vacuum infusion (VI) in the presence and absence of high permeability media (HPM) considering gravity effects. Coupled flow modeling based on continuity equations, Darcy’s law for porous media flow, including gravity effects with level set front tracking algorithm, has been developed on the multiblock-structured grid with higher-order finite-difference framework to predict the spatio-temporal preform saturation during infusion with/without HPM on the complex mold configurations. The model-predicted instantaneous change in pressure, thickness elevation, fill time, flow front positions, and influence of gravity have been validated with experiments for horizontal and vertical flat plates using pressure sensors and digital cameras. For the first time, the complete modeling and experimentation of transient VI in the presence or absence of HPM, including gravity, shows the ability to predict realistic preform saturation during VI in different mold geometry.

Application of deep learning neural networks for the analysis of fluid-particle dynamics in fibrous filters

A novel hybrid data-driven framework was introduced in this study for the prediction of fluid-particle dynamics of submicron particles under hydrodynamic and Brownian forces in fibrous filters. The distribution of flow parameters was predicted by a high-resolution flow surrogate model based on a deep convolutional neural network (CNN) coupled with a Lagrangian particle tracking method based on the discrete phase model (DPM). The CNN-DPM model was applied to a group of several nonuniformly distributed fibers to calculate filtration efficiency. For CNN training, ground-truth data were obtained using a two-dimensional computational fluid dynamics (CFD) model for laminar incompressible flow. A simulation speedup of three orders of magnitude was obtained by CNN for predicting the velocity components and static pressure distribution within an error range of ±10%. The generalizability of CNN model was also confirmed for overlapped irregular fiber shapes and porosities out of the range of the training dataset with deviations in a range of ±20% in comparison with CFD results. The collection efficiency by CNN-DPM for small particle diameters with dp≤0.3μm was overestimated by approximately 3 % while agreeing well with CFD-DPM for larger particles. The errors of flow velocity predictions by CNN near the fibers added more randomness to the particle motion which was combined with the random Brownian motion of particles, consequently increasing the probability of the small particle hit number and filtration efficiency. The overall acceptable accuracy of the CNN-DPM was confirmed, which is suitable for fibrous filter design and optimization purposes that require thousands of simulations.

Prediction of submicron particle dynamics in fibrous filter using deep convolutional neural networks

This study developed a data-driven model for the prediction of fluid–particle dynamics by coupling a flow surrogate model based on the deep convolutional neural network (CNN) and a Lagrangian particle tracking model based on the discrete phase model. The applicability of the model for the prediction of the single-fiber filtration efficiency (SFFE) for elliptical- and trilobal-shaped fibers was investigated. The ground-truth training data for the CNN flow surrogate model were obtained from a validated computational fluid dynamics (CFD) model for laminar incompressible flow. Details of fluid–particle dynamics parameters, including fluid and particle velocity vectors and contribution of Brownian and hydrodynamic forces, were examined to qualitatively and quantitatively evaluate the developed data-driven model. The CNN model with the U-net architecture provided highly accurate per-pixel predictions of velocity vectors and static pressure around the fibers with a speedup of more than three orders of magnitude compared with CFD simulations. Although SFFE was accurately predicted by the data-driven model, the uncertainties in the velocity predictions by the CNN flow surrogate model in low-velocity regions near the fibers resulted in deviations in the particle dynamics predictions. These flow uncertainties contributed to the random motion of particles due to Brownian diffusion and increased the probability of particles being captured by the fiber. The findings provide guidelines for the development of data science-based models for multiphysics fluid mechanics problems encountered in fibrous systems.

MHD-hybrid nanofluidic model on rotating plate with impact of thermal slip and heat absorption: a solution predictive neuro-computing approach

The main objective of this research is to design a numerical computational solver-based two-layers structure of Levenberg–Marquardt backpropagation neural networks, i.e. LMB-NNs for the analyses of the heat transfer phenomenon and velocities structure in the MHD incompressible hybrid nanofluidic flow (MHD-IHNF) model with thermal slip and heat absorption/generation over the rotating plate through varying involved parameters, including velocity slip parameter, thermal slip parameter, concentration of Al2O3 nanoparticles, heat generation parameter, Prandtl number, Hartman number, and thermophoresis for sundry scenarios. The MHD-IHNF model is mathematically formulated as a system of PDEs that are converted in the desired system of ODEs by means of suitable transformation. The data-sets are constructed by explicit Runge–Kutta numerical technique that is exploited as a target data-set for the learning of LMP-NNs based on the process of validation, training, and testing to determine the solution of MHD-IHNF model for sundry physical scenarios. The validation, convergence, stability, and verification of LMP-NNs for solution predictive strength of the MHD-IHNF problem are certified in terms of achieved accuracy, regression index measurements, and analysis of error histogram illustrations.

Assessment of an Implicit Discontinuous Galerkin Solver for Incompressible Flow Problems with Variable Density

Multi-component flow problems are typical of many technological and engineering applications. In this work, we propose an implicit high-order discontinuous Galerkin discretization of the variable density incompressible (VDI) flow model for the simulation of multi-component problems. Indeed, the peculiarity of the VDI model is that the density is treated as an advected property, which can be used to possibly track multiple (more than two) components. The interface between fluids is described by a smooth, but sharp, variation in the density field, thus not requiring any geometrical reconstruction. Godunov numerical fluxes, density positivity, mass conservation, and Gibbs-type phenomena at material interfaces are challenges that are considered during the numerical approach development. To avoid Courant-related time step restrictions, high-order single-step multi-stage implicit schemes are applied for the temporal integration. Several test cases with known analytical solutions are used to assess the current approach in terms of space, time, and mass conservation accuracy. As a challenging application, the simulation of a 2D droplet impinging on a thin liquid film is performed and shows the capabilities of the proposed DG approach when dealing with high-density (water–air) multi-component problems.

Three linear, unconditionally stable, second order decoupling methods for the Allen–Cahn–Navier–Stokes phase field model

Hydrodynamics coupled phase field models have intricate difficulties to solve numerically as they feature high nonlinearity and great complexity in coupling. In this paper, we propose three second order, linear, unconditionally stable decoupling methods based on the Crank–Nicolson leap-frog time discretization for solving the Allen–Cahn–Navier–Stokes (ACNS) phase field model of two-phase incompressible flows. The ACNS system is decoupled via the artificial compression method and a splitting approach by introducing an exponential scalar auxiliary variable. We prove all three algorithms are unconditionally long time stable. Numerical examples are provided to verify the convergence rate, unconditional stability, and computational efficiency.

Modeling and computation of nanofluid for thermo-dynamical analysis between vertical plates

It is well fact that the computational complexity of unsteady and viscoelastic nanofluid can be measured by mathematical modeling that allows the suitable performance for variations from specific to particular rheological parameters. This manuscript addresses the fractionalized mathematical modeling of an unsteady incompressible Maxwell transient free convection flow of nanofluids in the existence of radiation as well as damped thermal flux by using the Caputo time-fractional derivative. The integral transform technique is invoked on the fractionalized governing equations to find the exact solution. The numerical solution to the problem is also attained by utilizing Stehfest and Tzou algorithms. Finally, for the sake of graphical illustration, the comparative analysis for validating both algorithms on velocity and temperature profiles is performed numerically. The temperature and velocity curves are reduced by growing α for small time, and behavior is contrary for large time. By growing values of [Formula: see text] declines the velocity profiles. Velocity is linearly proportional to relaxation time λ, and the boundary layer difference is decreased by increasing the time. Our achieved solutions via two different numerical methods, that is, Stehfest and Tzou are equal.

A low-degree strictly conservative finite element method for incompressible flows on general triangulations

In this study, a new P 2 -P 1 finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn’s inequality hold for general triangulations. It yields strictly conservative velocity approximations when applied to models of incompressible flows. The convergence rate of the scheme can only be proved to be of suboptimal 𝒪(h) order, though, based on the property of strict conservation, the robust capacity of the pair for incompressible flows is verified theoretically and numerically.

Efficient IMEX and consistently energy-stable methods of diffuse-interface models for incompressible three-component flows

In this study, we consider the numerical approximation of incompressible three-component fluids, in which the fluid interfaces are captured by ternary Cahn–Hilliard equations and the fluid flows are governed by Navier–Stokes equations. This system includes not only nonlinear effects but also coupling among phase-field variables, velocities, and pressure. The ternary Cahn–Hilliard–Navier–Stokes system also satisfies the energy dissipation law, which is a basic physical property. For the appropriate treatment of the nonlinear and coupling terms and preservation of the energy dissipation law in a discrete version, we develop second-order time-accurate, linearly implicit-explicit (IMEX) methods using a variation of the scalar auxiliary variable (SAV) method. To improve the consistency between the original and modified energies, a simple and effective energy relaxation technique is considered. We analytically proved the unique solvability and the relaxed energy dissipation law. The proposed schemes are highly efficient for implementation because only linear elliptic equations need to be solved separately. Extensive computational experiments are performed to validate the accuracy, energy stability, and performance of the proposed method. To facilitate further study, we provide the C codes for the typical numerical simulations at http://github.com/yang521.

Application of Prandtl, von Kármán, and lattice Boltzmann methods to investigations of turbulent slip incompressible flow in a flat channel

The paper focuses on the modeling of turbulent slip incompressible flow in a flat channel. Slippage on the channel wall can be caused by two reasons. The first reason is microchannels when the mean free path of molecules exceeds a certain value, which is characterized by the Knudsen number. The second reason is hydrophobic surfaces, which are used to reduce hydraulic resistance. Two models of turbulence were used to derive analytical solutions of fully developed flow. The first model is the Prandtl model (model of mixing length). The second model is the von Kármán model (model of similarity of pulsation velocities). Analytical models were built in a two-layer approximation: a laminar sublayer and a turbulent core. Both models showed a good agreement with the lattice Boltzmann method. An increase in the Knudsen number leads to an increase in the flow rate and a decrease in shear stress on the walls, which reduces the friction factor. This is due to the weakening of the interaction between the flow and the wall, which also leads to a decrease in the shear stress on the walls. As the Reynolds number increases, this effect becomes more noticeable.

Augmented reduced order models for turbulence

The authors introduce an augmented-basis method (ABM) to stabilize reduced-order models (ROMs) of turbulent incompressible flows. The method begins with standard basis functions derived from proper orthogonal decomposition (POD) of snapshot sets taken from a full-order model. These are then augmented with divergence-free projections of a subset of the nonlinear interaction terms that constitute a significant fraction of the time-derivative of the solution. The augmenting bases, which are rich in localized high wavenumber content, are better able to dissipate turbulent kinetic energy than the standard POD bases. Several examples illustrate that the ABM significantly out-performs L2-, H1- and Leray-stabilized POD ROM approaches. The ABM yields accuracy that is comparable to constraint-based stabilization approaches yet is suitable for parametric model-order reduction in which one uses the ROM to evaluate quantities of interests at parameter values that differ from those used to generate the full-order model snapshots. Several numerical experiments point to the importance of localized high wavenumber content in the generation of stable, accurate, and efficient ROMs for turbulent flows.

Microparticle Brownian motion near an air-water interface governed by direction-dependent boundary conditions

HypothesisAlthough the dynamics of colloids in the vicinity of a solid interface has been widely characterized in the past, experimental studies of Brownian diffusion close to an air–water interface are rare and limited to particle-interface gap distances larger than the particle size. At the still unexplored lower distances, the dynamics is expected to be extremely sensitive to boundary conditions at the air–water interface. There, ad hoc experiments would provide a quantitative validation of predictions. ExperimentsUsing a specially designed dual wave interferometric setup, the 3D dynamics of 9 μm diameter particles at a few hundreds of nanometers from an air–water interface is here measured in thermal equilibrium. FindingsIntriguingly, while the measured dynamics parallel to the interface approaches expected predictions for slip boundary conditions, the Brownian motion normal to the interface is very close to the predictions for no-slip boundary conditions. These puzzling results are rationalized considering current models of incompressible interfacial flow and deepened developing an ad hoc model which considers the contribution of tiny concentrations of surface active particles at the interface. We argue that such condition governs the particle dynamics in a large spectrum of systems ranging from biofilm formation to flotation process.

Full and reduced order model consistency of the nonlinearity discretization in incompressible flows

We investigate both theoretically and numerically the consistency between the nonlinear discretization in full order models (FOMs) and reduced order models (ROMs) for incompressible flows. To this end, we consider two cases: (i) FOM–ROM consistency, i.e., when we use the same nonlinearity discretization in the FOM and ROM; and (ii) FOM–ROM inconsistency, i.e., when we use different nonlinearity discretizations in the FOM and ROM. Analytically, we prove that while the FOM–ROM consistency yields optimal error bounds, FOM–ROM inconsistency yields additional terms dependent on the FOM divergence error, which prevent the ROM from recovering the FOM as the number of modes increases. Computationally, we consider channel flow around a cylinder and Kelvin–Helmholtz instability, and show that FOM–ROM consistency yields significantly more accurate results than FOM–ROM inconsistency.

Evolution of water wave groups with wind action

A modified fully nonlinear model of an air–water system in deep water is presented in which the effect of wind in the air is simply represented by a direct link between the air–water interface pressure and the interface slope. The water system is a fully nonlinear Euler model of incompressible and irrotational fluid flow. Our main aim is to establish and compare with a reduced model represented by a forced nonlinear Schrödinger (FNLS) equation that describes wave groups in a weakly nonlinear asymptotic limit. Wave groups are described by the soliton and breather solutions generated by four cases of initial conditions in the relevant parameter regime. Numerical simulations of wave group formation in both models are compared, both with and without wind forcing. The FNLS model gives a good prediction to the modified fully nonlinear model when the wavenumber and wave frequency of the initial carrier waves are close to unity in dimensionless units based on typical carrier wavenumber and wave frequency. Wind forcing induces an exponential growth rate in the maximum amplitude wave. When the wave steepness becomes high in the fully nonlinear model some wave breaking is observed, but the FNLS model continues to predict large waves without breaking and there is then agreement only in the initial stage for the relevant initial conditions and parameter value ranges.

Variational Multiscale immersed boundary method for incompressible turbulent flows

This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on surfaces that are immersed in the stationary background discretizations. An interface stabilized form is developed by applying the Variational Multiscale Discontinuous Galerkin (VMDG) method at the immersed boundaries. The formulation is augmented with a variationally derived ghost-penalty type term. The weak form of the momentum balance equations is embedded with a residual-based turbulence model for incompressible turbulent flows. A significant contribution in this work is the variationally derived analytical expression for the Lagrange multiplier for weak enforcement of the Dirichlet boundary conditions at the immersed boundary. In addition, the analytical expression for the interfacial stabilization tensor emerges which accounts for the geometric aspects of the cut elements that are produced when the immersed surface geometry traverses the underlying mesh. A unique attribute of the fine-scale variational equation is that it also yields a posteriori error estimator that can evaluate the local error in weak enforcement of the essential boundary conditions at the embedded boundaries. The method is shown to work with meshes comprised of hexahedral and tetrahedral elements. Numerical experiments show that the norm of the stabilization tensor varies spatially and temporally as a function of the flow physics at the embedded boundary. Test cases with increasing levels of complexity are presented to validate the method on benchmark problems of flows around cylindrical and spherical geometric shapes, and turbulent features of the flows are analyzed.

Effect of upstream deflector utilization on H-Darrieus wind turbine performance: An optimization study

This paper aims to enhance the performance of H-Darrieus Vertical Axis Wind Turbine (VAWT) via introducing upstream deflectors. The impact of this addition has been investigated and discussed through different deflector configurations. The turbine performance before and after adding different wind rotor barriers was compared. A two dimensional, incompressible, transient, and turbulent flow model was built up in order to simulate the air flow around the turbine blades. Model verification and validation were performed through comparing the model solutions using different mesh sizes, time steps, turbulent models, and discretization schemes. Computational Fluid Dynamics (CFD) models were validated to provide novel insights on the effect of the deflectors on the aerodynamic characteristics of a VAWT blades. Results showed that the presence of a single deflector increases the highest value of the moment coefficient of the bare configuration by 24%, either increases the negative torque values, while two defectors increase the maximum value by 22% and the overall average value of the moment coefficient over the optimal range for the tip speed ratio.