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.

scholarly journals Numerical simulation of complex 3D compressible viscous flows through rotating blade passage

2003 ◽  
pp. 55-82
Author(s):  
M. Despotovic ◽  
Milun Babic ◽  
D. Milovanovic ◽  
Vanja Sustersic
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Convergence Acceleration ◽  
Design Tool ◽  
Navier Stokes ◽  
Internal Flows ◽  
Navier Stokes Equations ◽  
Rotating Blade ◽  
Compressible Viscous Flows

This paper describes a three-dimensional compressible Navier-Stokes code, which has been developed for analysis of turbocompressor blade rows and other internal flows. Despite numerous numerical techniques and statement that Computational Fluid Dynamics has reached state of the art, issues related to successful simulations represent valuable database of how particular tech?nique behave for a specifie problem. This paper deals with rapid numerical method accurate enough to be used as a design tool. The mathematical model is based on System of Favre averaged Navier-Stokes equations that are written in relative frame of reference, which rotates with constant angular velocity around axis of rotation. The governing equations are solved using finite vol?ume method applied on structured grids. The numerical procedure is based on the explicit multistage Runge-Kutta scheme that is coupled with modem numerical procedures for convergence acceleration. To demonstrate the accuracy of the described numer?ical method developed software is applied to numerical analysis of flow through impeller of axial turbocompressor, and obtained results are compared with available experimental data.

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.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

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.

Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part II—Applications

1997 ◽  
Vol 119 (4) ◽  
pp. 900-905 ◽  
Author(s):  
X. Zheng ◽  
C. Liao ◽  
C. Liu ◽  
C. H. Sung ◽  
T. T. Huang
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Grid Algorithm ◽  
High Reynolds

In this paper, computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency. It was found that the calculated body drag, lift, side force coefficients and moments at various angles of attack or angles of drift are in excellent agreement with experimental data. Fast convergence has been achieved for all the cases with large angles of attack and with modest drift angles.

scholarly journals RUBBLE MOUND BREAKWATER OVERTOPPING: ESTIMATION OF THE RELIABILITY OF A 3D NUMERICAL SIMULATION

2012 ◽  
Vol 1 (33) ◽  
pp. 8 ◽  
Author(s):  
Luca Cavallaro ◽  
Fabio Dentale ◽  
Giovanna Donnarumma ◽  
Enrico Foti ◽  
Rosaria E. Musumeci ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Fluid Dynamic ◽  
Complete Solution ◽  
Three Dimensional ◽  
Design Tool ◽  
Physical Models ◽  
Navier Stokes ◽  
Free Boundaries ◽  
Navier Stokes Equations

Until recently, physical models were the only way to investigate into the details of breakwaters behavior under wave attack. From the numerical point of view, the complexity of the fluid dynamic processes involved has so far hindered the direct application of Navier-Stokes equations within the armour blocks, due to the complex geometry and the presence of strongly non stationary flows, free boundaries and turbulence. In the present work the most recent CFD technology is used to provide a new and more reliable approach to the design analysis of breakwaters, especially in connection with run-up and overtopping. The solid structure is simulated within the numerical domain by overlapping individual virtual elements to form the empty spaces delimited by the blocks. Thus, by defining a fine computational grid, an adequate number of nodes is located within the interstices and a complete solution of the full hydrodynamic equations is carried out. In the work presented here the numerical simulations are carried out by integrating the three-dimensional Reynolds Average Navier-Stokes Equations coupled with the RNG turbulence model and a Volume of Fluid Method used to handle the dynamics of the free surface. The aim of the present work is to investigate the reliability of this approach as a design tool. Two different breakwaters are considered, both located in Southern Sicily: one a typical quarry stone breakwater, another a more complex design incorporating a spill basin and an armoured layer made up by Coreloc® blocks.

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.

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%.

A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids

2017 ◽  
Vol 21 (5) ◽  
pp. 1231-1257 ◽  
Author(s):  
Jian Cheng ◽  
Xiaodong Liu ◽  
Tiegang Liu ◽  
Hong Luo
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
High Order ◽  
Navier Stokes ◽  
Attractive Alternative ◽  
Order Of Accuracy ◽  
Navier Stokes Equations ◽  
Hybrid Grids

AbstractA parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailed studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.

Vortex-Induced Vibration of Two Side-by-Side Cylinders With a Small Gap in Uniform Flow

2017 ◽  
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu
Keyword(s):  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Ratio ◽  
Vortex Induced Vibrations ◽  
Lock In

Vortex-induced vibrations of two elastically mounted and rigidly coupled circular cylinders in side-by-side arrangement in steady flow are investigated numerically. The vibration of the cylinders is limited to the cross-flow direction only. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin Finite element method and the equation of motion is solved using the fourth order Runge Kutta method. It is well known that when the gap between two stationary side-by-side cylinders is very small, the flow between the two cylinders is biased towards one cylinder and the lift force on each cylinder is significantly smaller than that of an isolated single cylinder. The aim of this study is to investigate the effect of a small gap ratio of 0.5 between the two cylinders on the lock-in regime and the amplitude of the vibration of two side-by-side cylinders in a fluid flow. Simulations are carried out for a constant mass ratio of 2, a constant Reynolds number of 1000 and a range of reduced velocities. It is found that in the lock-in range of the reduced velocity, the two cylinders vibrate about their balance position with high amplitudes. Outside the lock-in regime the flow from the gap becomes biased towards one cylinder, which is similar to that from the gap between stationary cylinders.

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