scholarly journals Four free surface algorithms for the 3D Navier–Stokes equations

2015 ◽  
Vol 17 (6) ◽  
pp. 845-856 ◽  
Author(s):  
Nils Reidar B. Olsen
Keyword(s):  
Wave Equation ◽  
Numerical Methods ◽  
Water Surface ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Free Water ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Free Water Surface

Four algorithms are described for computing a steady free water surface with the solution of the three-dimensional (3D) Navier–Stokes equations. The numerical methods are used in hydraulic engineering cases, typically spillways and river modelling. The algorithms were tested against a laboratory experiment of a v-shaped broad-crested weir. The complex geometry of the weir introduced three-dimensional effects, which the numerical methods handled with varying degrees of success. One of the methods tested was the classical volume of fluid (VOF) approach, implemented in the OpenFOAM software with a fixed grid. The other three algorithms used an adaptive grid that followed the free water surface. These methods were coded in the SSIIM 2 program and were based on water continuity, pressure differences and an implicit solution of the diffusive wave equation. The VOF method gave the best results compared with the experiments. However, this method requires a very short time step. Two of the investigated methods compute the water surface location implicitly and can therefore use a much longer time step. The method based on the diffusive wave equation has the disadvantage that the results depend on a calibrated friction factor. All four methods predicted the water depth over the weir with an average accuracy below 14%.

Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 727-750 ◽  
Author(s):  
Gareth P. Williams
Keyword(s):  
Poisson Equation ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Wave Flow ◽  
Trigonometric Interpolation ◽  
Time Step ◽  
Navier Stokes Equations ◽  
The Poisson Equation

A method of numerically integrating the Navier-Stokes equations for certain three-dimensional incompressible flows is described. The technique is presented through application to the particular problem of describing thermal convection in a rotating annulus. The equations, in cylindrical polar co-ordinate form, are integrated with respect to time by a marching process, together with the solving of a Poisson equation for the pressure. A suitable form of the finite difference equations gives a computationally-stable long-term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow.Trigonometric interpolation techniques provide accurate (discretely exact) solutions to the Poisson equation. By using an auxiliary algorithm for rapid evaluation of trigonometric transforms, the proportion of computation needed to solve the Poisson equation can be reduced to less than 25% of the total time needed to’ advance one time step. Computing on a UNIVAC 1108 machine, the flow can be advanced one time-step in 2 sec for a 14 × 14 × 14 grid upward to 96 sec for a 60 × 34 × 34 grid.As an example of the method, some features of a solution for steady wave flow in annulus convection are presented. The resemblance of this flow to the classical Eady wave is noted.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Strongly Coupled Fluid-Structure Interactions via a New Navier-Stokes Method for Prediction of Vortex-Induced Vibrations

2005 ◽  
Author(s):  
Yannis Kallinderis ◽  
Hyung Taek Ahn
Keyword(s):  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Design Tool ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibrations ◽  
Offshore Industry

Numerical prediction of vortex-induced vibrations requires employment of the unsteady Navier-Stokes equations. Current Navier-Stokes solvers are quite expensive for three-dimensional flow-structure applications. Acceptance of Computational Fluid Dynamics as a design tool for the offshore industry requires improvements to current CFD methods in order to address the following important issues: (i) stability and computation cost of the numerical simulation process, (ii) restriction on the size of the allowable time-step due to the coupling of the flow and structure solution processes, (iii) excessive number of computational elements for 3-D applications, and (iv) accuracy and computational cost of turbulence models used for high Reynolds number flow. The above four problems are addressed via a new numerical method which employs strong coupling between the flow and the structure solutions. Special coupling is also employed between the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. An element-type independent spatial discretization scheme is also presented which can handle general hybrid meshes consisting of hexahedra, prisms, pyramids, and tetrahedral.

Evaluation of numerical diffusion of the finite volume method when modelling surface waves

2019 ◽  
pp. 106-119
Author(s):  
Елена Сергеевна Тятюшкина ◽  
Андрей Сергеевич Козелков ◽  
Андрей Александрович Куркин ◽  
Вадим Викторович Курулин ◽  
Валентин Робертович Ефремов ◽  
...  
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Calculation Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Numerical Diffusion ◽  
Volume Method

Обсуждается применение метода конечных объемов при решении уравнений Навье-Стокса для моделирования поверхностных волн. Сформулирована задача о распространении поверхностных волн, которая используется для оценки численной диффузии в решении уравнений Навье-Стокса. Предлагается методика оценки численной диффузии, выражаемой коэффициентом уменьшения амплитуды волны при прохождении ею одной своей длины (коэффициентом затухания). Дана оценка размеров сетки и шага по времени, выраженных в безразмерных величинах относительно параметров волны, необходимых для обеспечения приемлемого значения коэффициента затухания. Показана степень влияния каждого из сеточных параметров на увеличение коэффициента затухания. The application of numerical simulation methods based on the solution of the full three-dimensional Navier-Stokes equations for modelling of wave propagation on the water surface requires the construction of a grid model containing countable nodes throughout the entire volume of water medium. Insufficient grid resolution leads to insufficient detailing of the fields of velocity and pressure, as well as volume fraction of the liquid, which increases the numerical diffusion of the method and, ultimately, leads to an underestimation of oscillation amplitudes of the medium. A large time step also results in a “blurring” of the solution and significantly reduces its stability, especially when using the schemes which compress the front of the media interface. This paper presents the results of an assessment of acceptable grid sizes and time steps expressed in dimensionless parameters with respect to the wave parameters necessary to ensure accuracy of the solution sufficient for geophysical applications. The estimate is given for the method of calculating three-dimensional multiphase flows with a free surface based on solving the Navier-Stokes equations in a one-velocity approximation based on a completely implicit connection between velocity and pressure using the finite volume method. The finite volume method for the numerical solution of the Navier-Stokes equations is implemented for use on arbitrary unstructured grids. The methodology for estimation of numerical diffusion of the calculation method is proposed. This estimation is expressed as a percentage of the wave amplitude decrease at the distance equal to the one wavelength. In turn the methodology is based on the parameters entered to estimate the acceptable grid sizes and time step for the calculation method. Based on the described methodology, the results of the estimation of the grid resolution in the horizontal and vertical directions, the estimation of the time step, and the evaluation of the influence of the discretization scheme of the convective term are presented.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

The inlet flow structure of a conceptual open-nose supersonic drone

2021 ◽  
pp. 095441002098304
Author(s):  
Eiman B Saheby ◽  
Xing Shen ◽  
Anthony P Hays ◽  
Zhang Jun
Keyword(s):  
Flow Structure ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Computational Fluid Dynamic Simulation ◽  
Navier Stokes ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Aerodynamic Efficiency ◽  
Performance Effects

This study describes the aerodynamic efficiency of a forebody–inlet configuration and computational investigation of a drone system, capable of sustainable supersonic cruising at Mach 1.60. Because the whole drone configuration is formed around the induction system and the design is highly interrelated to the flow structure of forebody and inlet efficiency, analysis of this section and understanding its flow pattern is necessary before any progress in design phases. The compression surface is designed analytically using oblique shock patterns, which results in a low drag forebody. To study the concept, two inlet–forebody geometries are considered for Computational Fluid Dynamic simulation using ANSYS Fluent code. The supersonic and subsonic performance, effects of angle of attack, sideslip, and duct geometries on the propulsive efficiency of the concept are studied by solving the three-dimensional Navier–Stokes equations in structured cell domains. Comparing the results with the available data from other sources indicates that the aerodynamic efficiency of the concept is acceptable at supersonic and transonic regimes.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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