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.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

Self-similar behaviour of a rotor wake vortex core

2014 ◽  
Vol 740 ◽  
Author(s):  
Mohamed Ali ◽  
Malek Abid
Keyword(s):  
Vortex Core ◽  
Scaling Laws ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Azimuthal Velocity ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotating Blade ◽  
Self Similar

AbstractWe report a self-similar behaviour of solutions (obtained numerically) of the Navier–Stokes equations behind a single-blade rotor. That is, the helical vortex core in the wake of a rotating blade is self-similar as a function of its age. Profiles of vorticity and azimuthal velocity in the vortex core are characterized, their similarity variables are identified and scaling laws of these variables are given. Solutions of incompressible three-dimensional Navier–Stokes equations for Reynolds numbers up to $Re= 2000$ are considered.

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 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.

Development of Numerical Code to Predict Three-Dimensional Sand Erosion Phenomena

2003 ◽  
Author(s):  
Kuki Junichi ◽  
Kazuyuki Toda ◽  
Makoto Yamamoto
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Suspended Particle ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Code ◽  
Particle Collision ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Sand Erosion

This paper presents a numerical procedure to predict a three-dimensional sand erosion phenomenon and the interaction between the flow field and the eroded surface. To simulate this phenomenon, the turbulent flow field, the particle trajectory and the amount of erosion on the eroded wall are calculated repeatedly. In computations of the flow field, compressible Navier-Stokes equations and low-Reynolds-number type k–ε turbulence model are adopted. Assuming that the concentration of suspended particle is dilute, particle-particle collision and the influence of particle motions on the flow field are neglected. The Neilson-Gilchrist erosion model is used to estimate the weight loss due to erosion. To verify the developed code, two types of 90-degree bends are computed. The results show that the present procedure can reasonably reproduce the sand erosion process and the temporal change of both the flow field and the wall surface qualitatively.

A Semi-Staggered Numerical Procedure for the Incompressible Navier-Stokes Equations on Curvilinear Grids

2011 ◽  
Author(s):  
Hessam Babaee ◽  
Sumanta Acharya
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Second Order ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Curvilinear Grids

An accurate and efficient finite difference method for solving the three dimensional incompressible Navier-Stokes equations on curvilinear grids is developed. The semi-staggered grid layout has been used in which all three components of velocity are stored on the corner vertices of the cell facilitating a consistent discretization of the momentum equations as the boundaries are approached. Pressure is stored at the cell-center, resulting in the exact satisfaction the discrete continuity. The diffusive terms are discretized using a second-order central finite difference. A third-order biased upwind scheme is used to discretize the convective terms. The momentum equations are integrated in time using a semi-implicit fractional step methodology. The convective and diffusive terms are advanced in time using the second-order Adams-Bashforth method and Crank-Nicolson method respectively. The Pressure-Poisson is discretized in a similar approach to the staggered gird layout and thus leading to the elimination of the spurious pressure eigen-modes. The validity of the method is demonstrated by two standard benchmark problems. The flow in driven cavity is used to show the second-order spatial convergence on an intentionally distorted grid. Finally, the results for flow past a cylinder for several Reynolds numbers in the range of 50–150 are compared with the existing experimental data in the literature.

A Computational Study of Tip Desensitization in Axial Flow Turbines: Part 1 — Baseline Turbine Computations and Comparisons With Measurement

2004 ◽  
Author(s):  
James A. Tallman
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Computational Study ◽  
Three Dimensional ◽  
Axial Flow ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Penn State ◽  
High Pressure Stage

This study used Computational Fluid Dynamics (CFD) to investigate modified turbine blade tip shapes as a means of reducing the leakage flow and vortex. The subject of this study was the single-stage experimental turbine facility at Penn State University, with scaled three-dimensional geometry representative of a modern high-pressure stage. To validate the numerical procedure, the rotor flowfield was first computed with no modification to the tip, and the results compared with measurements of the flowfield. The flow was then predicted for a variety of different tip shapes: first with coarse grids for screening purposes and then with more refined grids for final verification of preferred tip geometries. Part 1 of this two-part paper focuses on the turbine case description, numerical procedure, baseline flat-tip computations, and comparison of the baseline results with measurement. A Runge-Kutta time-marching CFD solver (ADPAC) was used to solve the Reynolds-Averaged Navier-Stokes equations. Two-equation turbulence modeling with low Reynolds number adjustments was used for closure. The baseline rotor flowfield was computed twice: with a moderately sized mesh (720,000 nodes) and also with a much more refined mesh (7.2 million nodes). Both solutions showed good agreement with previously taken measurements of the rotor flowfield, including five-hole probe measurements of the velocity and total pressure inside the passage, as well as pressure measurements on the blade and casing surfaces.

Viscous Flow Analysis as a Design Tool for Hydraulic Turbine Components

1990 ◽  
Vol 112 (1) ◽  
pp. 5-11 ◽  
Author(s):  
T. C. Vu ◽  
W. Shyy
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Hydraulic Turbine ◽  
Design Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Alternative Designs

Viscous flow analysis based on the full Reynolds-averaged Navier-Stokes equations is being applied to successfully predict turbulent flow characteristics and energy losses in different hydraulic turbine components. It allows the designer to evaluate the hydraulic performance of alternative designs before proceeding with laboratory testing or to perform elaborate parametric study to optimize the hydraulic design. In this paper, the applications of three-dimensional viscous flow analysis as an analytical design tool for elbow draft tube and spiral casing are presented and their impact on engineering design assessed.

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