Navier-Stokes Equations For Incompressible Flow Research Articles

Effects of uniform injection and suction through perforated pentagonal cylinders on the flow and heat transfer

PurposeThe purpose of this paper is to study the effects of uniform injection and suction through a perforated pentagonal cylinder on the flow field and heat transfer.Design/methodology/approachThe finite-volume method has been used to solve the ensemble-averaged Navier-Stokes equations for incompressible flow at moderate Reynolds number (Re = 22,000) with the k-ɛ turbulence model equations.FindingsA computational fluid dynamics analysis of turbulent flow past a non-regular pentagonal cylinder with three different aspect ratios aspect ratios has been carried out to investigate the effects of uniform injection/suction through the front and all surfaces of the cylinder. It is found that flow field parameters such as drag coefficient, pressure coefficient and Nusselt number are affected considerably in some cases depend on injection/suction rate (Γ) and perforated wall position.Research limitations/implicationsTo optimize the efficiency of the injection and suction through a perforated surface, both wide-ranging and intensive further studies are required. Using various perforation ratios and injection/suction intensities are some possibilities.Practical implicationsControl of the vortex shedding and wake region behind bluff bodies is of vital interest in fluid dynamics. Therefore, applying uniform injection and suction from a perforated bluff body into the main flow can be used as a drag reduction mechanism, thermal protection and heat transfer enhancement.Originality/valueThis study provides unique insights into the active flow control method around pentagonal cylinders that can be useful for researchers in the field of fluid dynamics and aeronautics.

Forced Response of a Low-Pressure Turbine Blade using Spectral/hp Element Method: Direct Numerical Simulation

The Spectral/HP element method has been applied to perform Direct Numerical Simulations (DNS) over a single T106A turbine blade-row using the open source software Nektar++. The main goal of the current study is to perform preliminary investigations at modest Reynolds and Mach numbers, 8000 and 0.1 respectively, for uniform, steady flow past the aerofoil by employing Nektar++’s solver for the 2D Navier-Stokes equations for incompressible flow. The mesh was firstly validated against results obtained using the same software and for a similar set of parameter values. One dimensional, pitch-wise harmonic vibrations were subsequently imposed on the blade by means of a coordinate transformation. A parametric study in terms of the frequency and amplitude of the vibrations was carried out. The effects of the vibrations on entire domain, along the blade surface and in its wake were assessed. The pressure on the blade surface and the wake loss were each decomposed into components arising due to the mean flow and due to the vibrations. In each case the dominant components were then identified for the values of frequency and amplitude considered here.

Operator inference and physics-informed learning of low-dimensional models for incompressible flows

Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic Mode Decomposition and Operator Inference. With this work, we suggest a new approach to learning structured low-order models for incompressible flow from data that can be used for engineering studies such as control, optimization, and simulation. To that end, we utilize the intrinsic structure of the Navier-Stokes equations for incompressible flows and show that learning dynamics of the velocity and pressure can be decoupled, thus leading to an efficient operator inference approach for learning the underlying dynamics of incompressible flows. Furthermore, we show the operator inference performance in learning low-order models using two benchmark problems and compare with an intrusive method, namely proper orthogonal decomposition, and other data-driven approaches.

A structured adaptive mesh refinement strategy with a sharp interface direct-forcing immersed boundary method for moving boundary problems

We develop a versatile and accurate structured adaptive mesh refinement (S-AMR) strategy with a moving least square sharp-direct forcing immersed boundary method (IBM) for incompressible fluid-structure interaction (FSI) simulations. The computational grid consists of several nested blocks in different refinement levels. While blocks with the coarsest grid cover the entire computational domain, the computational domain is locally refined at the location of solid boundary (moving or fixed) by bisecting selected blocks in every coordinate direction. The grid topology and data structure is managed by an extended version of Afivo toolkit (Teunissen and Ebert, 2018), where a novel technique is introduced for conservative data transfer between the coarser and the finer blocks, particularly in velocity transformation for which the mass conservation plays a crucial role. In the present study, the continuity and Navier-Stokes equations for incompressible flows are spatially discretized with a second order central finite difference method using a collocated arrangement and are time-integrated using a semi-implicit second order fractional step method, although the proposed S-AMR strategy can be used with different discretization schemes. An IBM using a moving least square approach is utilized to impose boundary conditions. To handle FSI problems, all the governing equations for the dynamics of fluid and structure are simultaneously advanced in time by a predictor-corrector strategy. Several test cases of increasing complexity are solved in order to demonstrate the robustness and accuracy of the proposed method as well as its capability in simulation-driven mesh adaptivity.

Numerical Simulation of Ocean Currents with Hermite IFinite Elements

The article deals with the numerical simulations for equations of geophysical fluids. These physical phenomena are modeled by the Navier-Stokes equations which describe the motion of the fluid, the ocean currents, the flow of water in a pipe and many other fluid flow phenomenon.These equations are very useful because of there utility. The Navier-Stokes equations for incompressible flow are nonlinear partial differential equations that drive the motion of fluids in the approximation of continuous media. The existence of general solutions to the Navier Stokes equations have already proven but in this paper we have interested to the numerical solution of the incompressible Navier-Stokes equations. We get an optimal discretization of the Navier-Stokes equations and numerical approximations of the solution are also given. The convergence and the stabilityof the approximated system are proven. The numerical resolution is based on Hermite finite elements. The numerical system was expressed in matrix form for computation of velocity and the pression fieldsapproach using MATLAB software. Numerical results for velocity field in two dimensional space of the velocity u(x,y) and pression p(x,y,) are given. And finally we give physical interpretation of the results obtained.

Overset meshes for incompressible flows: On preserving accuracy of underlying discretizations

This study on overset meshes for incompressible-flow simulations is motivated by accurate prediction of wind farm aerodynamics involving large motions and deformations of components with complex geometry. Using first-order hyperbolic and elliptic equation proxies for the incompressible Navier-Stokes (NS) equations, we investigate the influence of information exchange between overset meshes on numerical performance where the underlying discretization is second-order accurate. The first aspect of information exchange surrounds interpolation of solution where we examine Lagrange and point-cloud-based interpolation for creating constraint equations between overset meshes. To maintain overall second-order accuracy, higher-order interpolation is required for elliptic problems, but linear interpolation is sufficient for hyperbolic problems in first-order form. Higher-order point-cloud-based interpolation provides a pathway to maintaining accuracy in unstructured meshes, but at higher complexity. The second aspect of information exchange focuses on comparing the approaches of overset single system (OSS) and overset Additive Schwarz (OAS) for coupling the linear systems of the overlapping meshes. While the former involves a single linear system, in the latter the discrete linear systems are solved separately, and solving the global system is accomplished through outer iterations and sequential information exchange in a Jacobi fashion. For the test cases studied, accuracy for hyperbolic problems is maintained by performing two outer iterations, whereas many outer iterations are required for elliptic systems. The order-of-accuracy studies explored here are critical for verifying the overset-mesh coupling algorithms used in engineering simulations. Accuracy of these simulations themselves is, however, quantified using engineering quantities of interest such as drag, power, etc. Consequently, we conclude with numerical experiments using NS equations for incompressible flows where we show that linear interpolation and few outer iterations are sufficient for achieving asymptotic convergence of engineering quantities of interest.

Unsteady numerical investigation of the full geometry of a horizontal axis wind turbine: Flow through the rotor and wake

Aerodynamics of the Mexico wind turbine was investigated using CFD techniques. The complete wind turbine was modelled. In order to accomplish this goal, the computational domain was discretized with a multi-block structured hexahedron grid, which was generated manually to ensure a good quality mesh and optimize the number of cells. Furthermore, a sliding mesh technique was applied to the moving mesh zone to calculate in detail the flow around the blades. All the relevant operating conditions were considered: turbulent wake state, nominal condition and stall state. The simulations were performed using the unsteady Reynolds-Averaged Navier-Stokes equations for incompressible flow and the SST k-ω turbulence model to close the governing equations. The CFD predictions were compared with the experimental data available from the MEXICO experiment: global forces and torques, pressure distributions around the blades and velocity distributions along the radial and axial traverses were all in a good agreement. The flow through the rotor, the interaction between the blades and the tower, and the development of the wake were then investigated. The CFD simulations have provided more accurate results, contributing to a deeper understanding of the wind turbine aerodynamics.

Numerical simulation of flow over stationary and rotating golf ball on Cartesian grid

Abstract Wake patterns behind a golf ball with and without back-spin (ωD/2U=0.1 where ω is the angular velocity, D is the diameter of the golf ball, and U is the freestream velocity) were investigated at ReD=1.1×105. To simulate wake regions, the in-house Cartesian mesh-based incompressible flow solver, namely ULSAN3D-Cart, was utilized. Navier-Stokes equations for incompressible flows are solved by the standard projection method with the unconditionally stable semi-Lagrangian scheme. The pressure Poisson equation is solved by the geometric multigrid method. The computational domain was set to [−4D,28D]×[−8D,8D]2. The number of grid cells was set to 4,096×2,0482(≅17.2×109). By using hybrid MPI/OpenMP parallelization, this large-scale flow was simulated on the KISTI Nurion supercomputer. For the flow simulation, total 32,768 cores of Intel Xeon Phi 7250 processors are utilized. For the visualization of the wake field, in-situ parallel processing was conducted on the Nurion machine using 17,408 CPU cores utilizing the open-source visualization software, Paraview. By the comparison of the stationary and the back-spinning golf balls, the differences in the wake patterns are clearly observable. For the stationary case, wake stretches in a symmetric manner with respect to the horizontal center line. On the other hands, for the back-spinning case, the wake bends downward direction, which indicates the generation of the upward lift.

Wind Turbine Design Using Thin Airfoil SD2030

This paper presents the performance of a horizontal axis wind turbine of diameter 0.6 m designed to operate at low Reynolds number. In this design work, the SD2030 thin airfoil was selected as a profile section for the turbine blades. The taper ratio, section twist angle and blade angle were optimized using the Blade Element Momentum (BEM) theory. In a numerical investigation, the aerodynamic flow field was computed using the two-dimensional Reynolds Averaged Navier-Stokes equations for incompressible flow to predict the performance of the airfoil at the Reynolds number of 1 x 105. The numerical results obtained were in accordance with the wind tunnel test’s result and thus validating this Computational Fluid Dynamics (CFD) works. Results depict that this new turbine design with the airfoil of SD2030 can rotate at a low start-up wind speed of 2.4 m/s, testifying that the design is successful, and that the turbine is capable to operate at low Reynolds number such as 1 x 105 with the desired output.

Properties at potential blow-up times for Navier-Stokes

In this paper we consider the Cauchy problem for the 3D navier-Stokes equations for incompressible flows. The initial data are assume d to be smooth and rapidly decaying at infinity. A famous open problem is whether classical solution can develop singularities in finite time. Assuming the maximal interval of existence to be finite, we give a unified discussion of various known solution properties as time approaches the blow-up time.

Impacts of wave and tidal forcing on 3D nearshore processes on natural beaches. Part II: Sediment transport

This is the second of two papers on the 3D numerical modeling of nearshore hydro- and morphodynamics. In Part I, the focus was on surf and swash zone hydrodynamics in the cross-shore and longshore directions. Here, we consider nearshore processes with an emphasis on the effects of oceanic forcing and beach characteristics on sediment transport in the cross- and longshore directions, as well as on foreshore bathymetry changes. The Delft3D and XBeach models were used with four turbulence closures (viz., k-e, k-L, ATM and H-LES) to solve the 3D Navier-Stokes equations for incompressible flow as well as the beach morphology. The sediment transport module simulates both bed load and suspended load transport of non-cohesive sediments. Twenty sets of numerical experiments combining nine control parameters under a range of bed characteristics and incident wave and tidal conditions were simulated. For each case, the general morphological response in shore-normal and shore-parallel directions was presented. Numerical results showed that the k-e and H-LES closure models yield similar results that are in better agreement with existing morphodynamic observations than the results of the other turbulence models. The simulations showed that wave forcing drives a sediment circulation pattern that results in bar and berm formation. However, together with wave forcing, tides modulate the predicted nearshore sediment dynamics. The combination of tides and wave action has a notable effect on longshore suspended sediment transport fluxes, relative to wave action alone. The model’s ability to predict sediment transport under propagation of obliquely incident wave conditions underscores its potential for understanding the evolution of beach morphology at field scale. For example, the results of the model confirmed that the wave characteristics have a considerable effect on the cumulative erosion/deposition, cross-shore distribution of longshore sediment transport and transport rate across and along the beach face. In addition, for the same type of oceanic forcing, the beach morphology exhibits different erosive characteristics depending on grain size (e.g., foreshore profile evolution is erosive or accretive on fine or coarse sand beaches, respectively). Decreasing wave height increases the proportion of onshore to offshore fluxes, almost reaching a neutral net balance.

Numerical modelling for evaluating the TMD performance in an industrial chimney

A numerical technique for fluid-structure interaction, which is based on the finite element method (FEM) and computational fluid dynamics (CFD), was developed for application to an industrial chimney equipped with a pendulum tuned mass damper (TMD). In order to solve the structural problem, a one-dimensional beam model (Navier-Bernoulli) was considered and, for the dynamical problem, the standard second-order Newmark method was used. Navier-Stokes equations for incompressible flow are solved in several horizontal planes to determine the pressure in the boundary of the corresponding cross-section of the chimney. Forces per unit length were obtained by integrating the pressure and are introduced in the structure using standard FEM interpolation techniques. For the fluid problem, a fractional step scheme based on a second order pressure splitting has been used. In each fluid plane, the displacements have been taken into account considering an Arbitrary Lagrangian Eulerian approach. The stabilization of convection and diffusion terms is achieved by means of quasi-static orthogonal subscales. For each period of time, the fluid problem was solved and the geometry of the mesh of each fluid plane is updated according to the structure displacements. Using this technique, along-wind and across-wind effects have been properly explained. The method was applied to an industrial chimney in three scenarios (with or without TMD and for different damping values) and for two wind speeds, showing different responses.

Simulation of two-dimensional high reynolds number wake flows with the use of filtered lagrangian navier-stokes equations

This work presents a method for numerical simulation of viscous fluid flows based on the use of filtered Lagrangian Navier-Stokes equations. It is based on the hypothesis that the small scale motions are responsible for the homogenization of the physical properties in infinitesimal fluid parcels through a mixing process, mathematically expressed as a spatial filter, which implicitly works as an averaging operator. When the filter was applied to the Navier-Stokes equations for incompressible flows, in the Lagrangian frame of reference, the functional form of the resulting equations was preserved, and the number of unknowns remained the same as the number of available equations, therefore circumventing the need of an explicit subgrid scale model. The method was validated by performing two-dimensional simulations of high Reynolds number wake flows. It was verified that the main large scale characteristics of the flows were properly replicated.

난류 경계층에 놓인 공동 내부유동에 관한 수치해석적 연구

본 논문은 공동 주위 난류유동특성을 LES 기법으로 수치해석을 수행하여 알아보았다. 본 연구에 적용된 레이놀즈수는 공동 깊이만큼의 높이 h 에서의 유속을 기준으로 1.0×105 이며 3 차원 공동에서의 유동특성을 알아보았다. 적절한 비압축성 Filtered Navier-Stokes 방정식을 적용하기 위해, 계산격자를 공동 표면 근처에는 조밀하게 멀어질수록 성기게 생성하였으며, 이는 계산시간을 단축시키며 빠른 수렴을 도와준다. 또한, Boussinesq 가설을 subgrid-scale 난류모델에 적용하였고, Subgrid-scale 난류점성을 얻기 위해 smagorinsky-Lilly SGS 모델을 적용하였으며, 그 때의 CFL 수는 1.0 이다. 또한, 본 논문은 서로 다른 4 가지 형상의 공동의 및 입구조건의 변화에 따른 유동 특성도 함께 연구되었다.

Justification of Asymptotic Two-dimensional Model for Steady Navier-Stokes Equations for Incompressible Flow

We study the asymptotic behavior of solutions to steady Navier-Stokes equations for incompressible flow in thin three-dimensional deformed cylinders. We prove that a sequence of the solutions converges strongly to a solution of a corresponding two-dimensional asymptotic model if the thickness of the cylinders converges to zero.

Numerical Simulation of Turbulent Flow Around a Square Cylinder with Uniform Injection or Suction and Heat Transfer

In the present study, the turbulent flow around a square cylinder with uniform injection or suction through various surfaces has been numerically studied. The wall functions of the viscous sublayer and log-law layer for velocity and temperature on the cylinder have been modified to allow for the effect of the injection or suction through the cylinder. The finite-volume method has been used for solving the ensemble averaged Navier-Stokes equations for incompressible flow in conjunction with the k − ϵ turbulence model equations that include the Kato-Launder's modification. A nonuniform staggered grid arrangement has been used. The results show that the parameters taken into account such as drag coefficient, and Strouhal and Nusselt numbers have been influenced by the uniform injection and suction through certain surfaces of the square cylinder, as well as the flow field parameters.

Effect of vertically logarithmic steady currents on shallow surface waves

The combined wave-current flow has been solved by researchers by assuming wave over either depthwise constant or linear current profile. Some complicated nonlinear current profiles have also been considered to simulate various shear currents. We consider a nonlinear current vertically logarithmic in nature and examine its interaction with a periodic surface wave. The Navier-Stokes equations for incompressible flow are solved for the current part and by using periodic boundary conditions. The effect of logarithmic current on wave components is assessed. The corresponding celerity and dispersion equation yields a close-form solution for the shallow-wave approximation. Several comparative trends between wave-only, wave with log current, and wave with constant current for the wave following/opposing these currents have been discussed. The flow properties of the first order are presented which can be applicable to the real inland and coastal flows, where progressive waves are ubiquitous over a depthwise logarithmic current. The work is further extended to the second-order semiempirical wave component by using past experimental data on the wave spectrum of combined flow.

ESTUDIO COMPARATIVO DE MODELOS NUMÉRICOS PARA EL SEGUIMIENTO DE INTERFACES MÓVILES: ESTUDIO DEL DERRAME DE UNA COLUMNA DE LÍQUIDO

The simulation of the collapse of a liquid column problem is presented in this work. The numerical analysis is done using a finite volume technique, where the well-known VOF technique is applied to describe the free surface motion. The adopted mathematical model is given by the Navier-Stokes equations for incompressible flows. These equations are solved in the whole domain occupied by both fluids (liquid and air) together with the interface motion equation. The study focuses on the analysis of two liquids with different viscosities. The response is assessed by considering various spatial discretizations when a turbulent model is applied. The computed numerical results are compared with those obtained using a fixed-mesh finite element technique and with experimental measurements reported in the literature.

Numerical simulation of sediment transport near sea bed under waves

The sediment transport near sea bed under waves is simulated using a three-dimensional (3D) numerical model that solves Navier-Stokes equations for incompressible flow, the sediment transport equation and the bed morphology equation. The numerical model consists of two basic modules, the 3D hydrodynamic module (HD) and sediment transport module (ST). The sigma-coordinate is used to convert the wavy flow-field into a cube leading to the easier realization of flow-field and boundary conditions. The model is able to simulate the dynamic change of suspended sediment concentration and bed morphology under various flow conditions. The case where the initial flow-field is full of evenly distributed suspended sediment subjected to a linear wave train is simulated. The results on sediment concentration distributions in the horizontal and vertical directions and resulting bed morphology are verified by the analytical solutions developed in this study. The good agreements between the numerical and analytical results show that the present numerical model is reliable in predicting sediment transport in coastal areas under waves.

Numerical solution of the Navier-Stokes equations for incompressible flow in porous media with free surface boundary

The paper presents numerical solution of the three dimensional Navier-Stokes equations for complex flow domains consisting of fluid and porous regions with free surface boundary. Flow in both regions is described by single set of conservation equations, extending the momentum equation for porous regions by additional viscous drag term according Darcy law. Free surface kinematics is “tracked” by Volume of Fluid method. Firstly the model is verified by comparision with numerical solution of Laplace equation for simple free surface flow through vertical dam. Good result agreements are observed. Application on realistic problems is presented on two cases. First case considers problem of pressure redistribution process around a deep tunnel excavation in low-conductivity porous media and second considers flow under and through porous, partially submerged bridge.