3D Incompressible Flow Research Articles

A high-order implicit least square-based finite difference-finite volume method for incompressible flows on unstructured grids

In this study, a high-order implicit least squares-based finite difference-finite volume (ILSFD-FV) method with a lattice Boltzmann flux solver is presented for the simulation of two-dimensional incompressible flows on unstructured grids. In this method, a high-order polynomial based on Taylor series expansion is applied within each control cell, where the unknown spatial derivatives at each cell center are approximated by the least squares-based finite difference scheme. The volume integral of the high-order polynomial over the control cell results in a pre-multiplied coefficient matrix in the time-dependent term. This makes the high-order method be implicit in nature. With this feature, a high-order implicit Runge–Kutta time integration scheme, namely, the explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) scheme, is applied to obtain the time-accurate solutions for flow problems. The non-linear system of equations arising from each ESDIRK stage except for the first explicit stage is solved by a dual time stepping approach. A matrix-free lower-upper symmetric Gauss–Seidel solver is then used to efficiently march the solution in the pseudo time. The present high-order ILSFD-FV method is verified and validated by both steady and unsteady 2D incompressible flow problems. Numerical results indicate that the developed implicit method outperforms its explicit counterpart in terms of the convergence property and computational efficiency. The speedup ratio of the computational effort is about 3–22.

Aeroacoustic Sound Source Characterization of the Human Voice Production-Perturbed Convective Wave Equation

The flow-induced sound sources of human voice production are investigated based on a validated voice model. This analysis is performed using a hybrid aeroacoustic workflow based on the perturbed convective wave equation. In the first step, the validated 3D incompressible turbulent flow simulation is computed by the finite volume method using STARCCM+. In a second step, the aeroacoustic sources are evaluated and studied in detail. The formulation of the sound sources is compared to the simplification (neglecting the convective sources) systematically using time-domain and Fourier-space analysis. Additionally, the wave equation is solved with the finite element solver openCFS to obtain the 3D sound field in the acoustic far-field. During the detailed effect analysis, the far-field sound spectra are compared quantitatively, and the flow-induced sound sources are visualized within the larynx. In this contribution, it is shown that the convective part of the sources dominates locally near the vocal folds (VFs) while the local time derivative of the incompressible pressure is distributed in the whole supra-glottal area. Although the maximum amplitude of the time derivative is lower, the integral contribution dominates the sound spectrum. As a by-product of the detailed perturbed convective wave equation source study, we show that the convective source term can be neglected since it only reduces the validation error by 0.6%. Neglecting the convective part reduces the algorithmic complexity of the aeroacoustic source computation of the perturbed convective wave equation and the stored flow data. From the source visualization, we learned how the VF motion transforms into specific characteristics of the aeroacoustic sources. We found that if the VFs are fully closing, the aeroacoustic source terms yield the highest dynamical range. If the VFs are not fully closing, VFs motion does not provide as much source energy to the flow-induced sound sources as in the case of a healthy voice. As a consequence of not fully closing VFs, the cyclic pulsating velocity jet is not cut off entirely and therefore turbulent structures are permanently present inside the supraglottal region. These turbulent structures increase the broadband component of the voice signal, which supports research results of previous studies regarding glottis closure and insufficient voice production.

On the small rigid body limit in 3D incompressible flows

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the motion of the rigid body is described by the conservation law of linear and angular momentum. Under the assumption that the diameter of the rigid body tends to zero and that the density of the rigid body goes to infinity, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier-Stokes equations in the full space without rigid body.

Dynamics of multiple solutions of Darcy–Forchheimer saturated flow of Cross nanofluid by a vertical thin needle point

Nanofluids have exposed a significant promise in the thermal development of several industrial systems, and at the same time, the flow via needle has major applications in modern construction systems including microstructure electric gadgets and microscale cooling gadgets for thermal migration applications. According to these applications, the current investigation concentrates to deliberate on 2D steady, laminar and incompressible flow of magneto-Cross nanofluid towards the region of moving thin needle in the occurrence of Darcy–Forchheimer porous medium, Ohmic and viscous dissipation with chemical reaction and mixed convection. The new dimensionless similarity variables are introduced to convert the nonlinear expressions governing the flow and transfer of heat. The change in velocity, thermal and concentration profiles for various non-dimensional parameters is deliberated briefly and illustrated with the help of suitable plots. Further, analysis of skin friction and rate of heat transfer is done through graphs. The results obtained are validated by existing works and are found to have a good agreement. The result outcome reveals that advanced values of magnetic parameter and Weissenberg number slowdown the fluid velocity motion. Also, upshot in Brownian motion and thermophoresis parameters improves the thermal profile.

The convergence rate of a polygonal finite element for Stokes flows on different mesh families

This paper introduces an evaluation to consider the convergence rate of a polygonal finite element (PFE) to solve two-dimensional (2D) incompressible steady Stokes flows on different mesh families. For this purpose, a numerical example of 2D incompressible steady Stokes flows programmed and coded by MATLAB is deployed. Furthermore, the mixed equal-order PFE, i.e., Pe1Pe1, is utilised for this research. Additionally, five different mesh families, i.e., triangular, quadrilateral, hexagonal, random Voronoi, centroidal Voronoi meshes, are applied for this research. Moreover, an interesting evaluation of the CPU time for the performance of our proposed PFE in this research is employed as well. From these tests, differences in convergence rate, as well as CPU time of using Pe1Pe1 on different mesh families, are indicated.

3D incompressible flows with small viscosity around distant obstacles

In this paper, we analyze the behavior of three-dimensional incompressible flows, with small viscosities ν > 0, in the exterior of material obstacles ΩR = Ω0 + (R, 0, 0), where Ω0 belongs to a class of smooth bounded domains and R > 0 is sufficiently large. Applying techniques developed by Kato, we prove an explicit energy estimate which, in particular, indicates the limiting flow, when both ν → 0 and R → ∞, as that one governed by the Euler equations in the whole space. According to this approach, it is natural to contrast our main result to that one already known in the literature for families of viscous flows in expanding domains.

AERODYNAMIC PERFORMANCE ANALYSIS OF CO-FLOW JET AIRFOIL

The work in this paper aims to increase the maximum lift coefficient of the airfoil by implementing the co-flow jet concept on NACA 0018 airfoil and also to investigate the performance of co-flow jet (CFJ) airfoil. To conduct numerical solution, RANS equations have been solved for 2D incompressible and unsteady flow using the Spalart-Allmaras turbulence model. The suction surface of the airfoil is modified by placing the injection slot near the leading edge and the suction slot near the trailing edge. A small mass of air is withdrawn into the airfoil suction slot, pressurized by a pumping system located inside the airfoil, and re-injecting into the injection slot tangentially to the main stream flow. The CFJ airfoil is enhancing the aerodynamic lift coefficient significantly compare to the baseline airfoil. And also, the numerical analysis is carried out to investigate the effect of the location of injection and suction slot. And it is observed that the aerodynamic lift coefficient of CFJ airfoil is increasing with varying the injection slot away from the leading edge.

Numerical simulations of the 2D supersonic flow through the tip-section turbine blade cascade with a flat profile

Numerical simulations of 2D compressible flow through the tip-section turbine blade cascade with a flat profile and the supersonic inlet were carried out by the OpenFOAM code using the Favre-averaged Navier-Stokes equations completed by the γ-Re_θt bypass transition model with the SST turbulence model. Predictions completed for nominal regimes were concentrated particularly on the effect of the shock-wave/boundary layer interaction on the transition to turbulence. Further, the link between the inlet Mach number and the inlet flow angle i.e. the so called unique incidence rule was studied. Obtained numerical results were compared with experimental data covering optical and pressure measurements.

Nonlinear dissipative slip flow of Jeffrey nanomaterial towards a curved surface with entropy generation and activation energy

In this research work, mathematical modeling for steady magnetized two-dimensional (2D) incompressible flow of Jeffrey nanofluid is developed over a stretched curved surface with combined characteristics of activation energy, Brownian motion, viscous dissipation, nonlinear mixed convection, magnetohydrodynamics (MHD), Joule heating and thermophoresis diffusion. Velocity slip condition is further imposed on the curved stretched boundary. Total entropy generation rate which depends on the velocity, temperature and concentration fields is obtained via second law of thermodynamics. The dimensional differential equations are altered into dimensionless ordinary differential system by using appropriate similarity variables. The obtain system of dimensionless differential equations are solved numerically through Built-in-Shooting method. The influence of sundry flow variables associated with this problem like curvature parameter, velocity slip parameter, Deborah number, thermophoresis diffusion, Prandtl number, Brownian motion, chemical reaction, Brinkman number and activation energy are sketched for entropy generation rate, concentration, temperature and velocity field. Furthermore, Nusselt number and skin friction coefficient are calculated numerically in the presence of Deborah number, slip parameter, thermophoresis parameter, Eckert number and Brownian diffusion parameter. It is noted that velocity field is an increasing function of curvature parameter, while contrast impact is observed for Deborah number and velocity slip parameter. It is also seen that the magnitude of skin friction upsurges versus Deborah number while decays against relaxation time. Nusselt number is increased via larger Eckert number and declines against thermophoretic parameter.

Characteristic of Free-rolling Motion of Twodimensional Rectangular Body in the Regular Wave

his study investigated the characteristics of rolling motion of rectangular body for regular waves with a range of wave periods that are equal to and longer than its natural roll period. Using the volume of fluid (VOF) method based on the finite volume method with standard k-ε turbulence model, twodimensional (2D) incompressible viscous two-phase flow is simulated in a wave tank with the rectangular body. The present study introduces a wave period ratio (Tr=TW/TN) of an incident wave period (TW) to the roll natural period (TN) of body. The wide range of 1≤ Tr ≤2.5 is considered in this study. In the wave periods considered in this study, the roll motion shows two distinct patterns. One is the single oscillatory motion which appears in the period ratio of 1≤ Tr ≤1.7. The other is the double oscillatory motion in 1.8≤ Tr ≤2.5. In these two regimes, flow and the roll motion of the rectangular body, which are induced by the fluid flow-structure interaction for various wave periods, are carefully investigated to reveal the mechanism of two roll modes.

A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid

Abstract A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result proven in [M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations 32 2007, 7–9, 1345–1371], that the disk will never touch the boundary of the domain in finite time. Anisotropic, continuous piecewise linear finite elements are used for the space discretization, the Euler scheme for the time discretization. The adaptive criteria are based on a posteriori error estimates for simpler problems.

Modelling and simulation of oxygen transport during AlN crystal growth by the PVT method

The oxygen impurity exists mainly in the form of Al2O during the AlN crystal growth by the PVT method. In this paper, 2D incompressible flow and mass transport models are developed by the FEM method and by taking into account the effects of three-phase (Al/N/Al2O) Stefan flow, buoyancy and vapor diffusion during the PVT AlN crystal growth process. The effects of the growth conditions, viz. the temperature and atmospheric pressure, on the Al2O transport in a 2-in. AlN crystal growth chamber are investigated by a series of numerical simulations using the developed models. The simulation results show that Al2O transport is strongly affected by temperature and atmospheric pressure. A high temperature is unfavourable for AlN crystal growth but is beneficial for the removal of oxygen from the powder source. An increase in the atmospheric pressure can decrease the Al2O partial pressure in the growth chamber and therefore reduce the oxygen content in the growing AlN crystal.

Global regularity to the 2D non-isothermal inhomogeneous nematic liquid crystal flows

ABSTRACT In this paper, we prove the global strong solutions for the Cauchy problem of two-dimensional (2D) incompressible non-isothermal nematic liquid crystal flows, if the initial orientation satisfies a geometric condition. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states. When d is a constant vector and , we also extend the corresponding result in Wang Y. [Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier–Stokes flows with vacuum. Discrete Contin Dyn Syst B. doi:10.3934/dcdsb.2020099.] to the whole space , where the global strong solution of 2D inhomogeneous incompressible heat conducting Navier–Stokes flows is established on bounded domain.

Local well-posedness of solutions to the boundary layer equations for 2D compressible flow

In this paper, we give a new direct proof by energy method for the local well-posedness of the boundary layer equations for two-dimensional compressible isentropic flow with no-slip boundary condition. It requires less compatibility conditions than the previous result using Nash-Moser-Hörmander iteration scheme and linear energy estimates. It shows that maximum principle works for boundary layer equations so that the weighted L∞ estimates on the lower order terms can be obtained.

A wall boundary treatment using analytical volume integrations in a particle method

SummaryNumerical treatment of complicated wall geometry has been one of the most important challenges in particle methods for computational fluid dynamics. In this study, a novel wall boundary treatment using analytical volume integrations has been developed for two‐dimensional (2D) incompressible flow simulations with the moving particle semi‐implicit method. In our approach, wall geometry is represented by a set of line segments in 2D space. Thus, arbitrary‐shaped boundaries can easily be handled without auxiliary boundary particles. The wall's contributions to the spatial derivatives as well as the particle number density are formulated based on volume integrations over the solid domain. These volume integrations are analytically solved. Therefore, it does not entail an expensive calculation cost nor compromise accuracy. Numerical simulations have been carried out for several test cases including the plane Poiseuille flow, a hydrostatic pressure problem with complicated shape, a high viscous flow driven by a rotating screw, a free‐surface flow driven by a rotating cylinder and a dam break in a tank with a wedge. The results obtained using the proposed method agreed well with analytical solutions, experimental observations or calculation results obtained using finite volume method (FVM), which confirms that the proposed wall boundary treatment is accurate and robust.

The Algorithm of the Vortex Sheet Intensity Determining in 3D Incompressible Flow Simulation around a Body

An original algorithm is developed for vortex methods of computational fluid dynamics for determining the intensity of the vortex sheet on the surface of a body in the flow of an incompressible medium. Unlike the common in the vortex methods approach to satisfying the no-slip boundary condition on a streamlined surface, which is based on ensuring that the normal velocity component of the medium is zero, the proposed procedure is based on a mathematically equivalent condition of equality to zero of the tangent velocity component on the body surface. The unknown intensity of the vortex sheet is assumed to be piecewise constant on triangular panels that approximate the surface of the body. The resulting integral equation is approximated by a system of linear algebraic equations, which dimension is twice the number of panels. The coefficients of the system matrix are expressed through double integrals over the panels. An algorithm is proposed for calculating these integrals for the case of neighboring panels, when these integrals are improper. An additive singularity exclusion is performed and analytical expressions for the integrals of them are obtained. The smooth parts of integrands are integrated numerically using Gaussian quadrature formulae. The proposed algorithm makes it possible to improve significantly the accuracy of the vortex sheet intensity reconstruction when flow simulating around complex-shaped bodies by using vortex methods for arbitrary triangular surface meshes, including essentially non-uniform and having cells with high aspect ratio.

On Mixed Convection Squeezing Flow of Nanofluids

In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a highly nonlinear system of ordinary differential equations with aid of suitable similarity transforms. Then, the solution of a nonlinear system of ordinary differential equations is obtained numerically by using Runge–Kutta–Fehlberg (RKF) method. Furthermore, the surface drag force C f and the rate of heat transfer N u are portrayed numerically. The effects of different emerging physical parameters such as Hartmann number (M), Reynold’s number (Re), squeezing parameter ( β ), mixed convection parameter λ , and volume fraction ( φ ) are also incorporated graphically for γ — alumina. Due to the higher viscosity and thermal conductivity ethylene-based nanofluids, it is observed to be an effective common base fluid as compared to water. These observations portrayed the temperature of gamma-alumina ethylene-based nanofluids rising on gamma-alumina water based nanofluids.

Random attractors for 2D stochastic micropolar fluid flows on unbounded domains

<p style='text-indent:20px;'>The asymptotic behavior of a model for 2D incompressible stochastic micropolar fluid flows with rough noise on a Poincaré domain is investigated. First, the existence and uniqueness of solutions to an evolution equation arising from the underlying stochastic micropolar fluid model is established via the Galerkin method and energy method. Then the existence of a random attractor is studied by using the theory of random dynamical systems for which the noise is dealt with by appropriate reproducing kernel Hilbert space.

Study on the Performance Improvement of Axial Flow Pump’s Saddle Zone by Using a Double Inlet Nozzle

The operating range of axial flow pumps is often constrained by the onset of rotating stall. An improved method using a double inlet nozzle to stabilize the performance curve is presented in the current study; a single inlet nozzle and three kinds of double inlet nozzle with different rib gap widths at the inlet of axial flow pump impeller were designed. Three dimensional (3D) incompressible flow fields were simulated, and the distributions of turbulence kinetic energy and velocity at different flow rates located at the inlet section, as well as the pressure and streamline in the impeller, were obtained at the same time. The single inlet nozzle scheme and a double inlet nozzle scheme were studied; the experimental and numerical performance results show that although the cross section is partly blocked in the double inlet nozzle, the head and efficiency do not decline at stable operation flow rate. On small flow rate condition, the double inlet nozzle scheme effectively stabilized the head-flow performance, whereby the block induced by the backflow before the impeller was markedly improved by using a double inlet nozzle. It has also been found that the rib gap width impacts the efficiency curve of the axial flow pump.

Regularity of Desingularized Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach

SummaryWe establish the regularity of weak solutions for the vorticity equation associated to a family of desingularized models for vortex filament dynamics in 3D incompressible viscous flows. These generalize the classical model ‘of an allowance for the thickness of the vortices’ due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities in Sobolev spaces.