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.

Numerical Investigation on Wavy Streak Formation Due to Sand Erosion

2005 ◽  
Author(s):  
Masaya Suzuki ◽  
Kazuyuki Toda ◽  
Makoto Yamamoto
Keyword(s):  
Flow Field ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Particle Collision ◽  
Navier Stokes ◽  
Two Phase ◽  
Sand Erosion ◽  
Wall Deformation ◽  
Turbulent Flow Field

It is well known that sand erosion is a typical multi-physic problem, that is, the interactions among flow field, particle motions and wall deformation are important. To simulate this phenomenon, turbulent flow field, particle trajectories and amount of erosion on an eroded wall are calculated repeatedly. In the 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 particles 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. Based on this numerical procedure, the gas-particle two-phase turbulent flow field in 90-degree bend with a square cross-section is simulated, in order to clarify erosion pattern formation by fluid/particle/wall interaction.

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.

scholarly journals Numerical and Analytical Study of Fluid Dynamic Forces in Seals and Bearings

1988 ◽  
Vol 110 (3) ◽  
pp. 315-325 ◽  
Author(s):  
L. T. Tam ◽  
A. J. Przekwas ◽  
A. Muszynska ◽  
R. C. Hendricks ◽  
M. J. Braun ◽  
...  
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Circumferential Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Lumped Model ◽  
Destabilizing Factors ◽  
Recirculation Zones

A numerical model based on a transformed, conservative form of the three-dimensional Navier-Stokes equations and an analytical model based on “lumped” fluid parameters are presented and compared with studies of modeled rotor/bearing/seal systems. The rotor destabilizing factors are related to the rotative character of the flow field. It is shown that these destabilizing factors can be reduced through a descrease in the fluid average circumferential velocity. However, the rotative character of the flow field is a complex three-dimensional system with bifurcated secondary flow patterns that significantly alter the fluid circumferential velocity. By transforming the Navier-Stokes equations to those for a rotating observer and using the numerical code PHOENICS-84 with a nonorthogonal body fitted grid, several numerical experiments were carried out to demonstrate the character of this complex flow field. In general, fluid injection and/or preswirl of the flow field opposing the shaft rotation significantly intensified these secondary recirculation zones and thus reduced the average circumferential velocity, while injection or preswirl in the direction of rotation significantly weakened these zones. A decrease in average circumferential velocity was related to an increase in the strength of the recirculation zones and thereby promoted stability. The influence of the axial flow was analyzed. The lumped model of fluid dynamic force based on the average circumferential velocity ratio (as opposed to the bearing/seal coefficient model) well described the obtained results for relatively large but limited ranges of parameters. This lumped model is extremely useful in rotor/bearing/seal system dynamic analysis and should be widely recommended. Fluid dynamic forces and leakage rates were calculated and compared with seal data where the working fluid was bromotrifluoromethane (CBrF3). The radial and tangential force predictions were in reasonable agreement with selected experimental data. Nonsynchronous perturbation provided meaningful information for system lumped parameter identification from numerical experiment data.

scholarly journals Dynamic Measurements with the Bicone Interfacial Shear Rheometer: Numerical Bench-Marking of Flow Field Based Data Processing

2018 ◽  
Author(s):  
Pablo Sánchez-Puga ◽  
Javier Tajuelo Rodríguez ◽  
Juan Manuel Pastor ◽  
Miguel Ángel Rubio
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Amplitude Ratio ◽  
Numerical Procedure ◽  
Complex Viscosity ◽  
Detailed Comparison ◽  
Interfacial Shear ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Air Water Interface

Flow field based methods are becoming increasingly popular for the analysis of interfacial shear rheology data. Such methods take properly into account the subphase drag by solving the Navier-Stokes equations for the bulk phases flows, together with the Boussinesq-Scriven boundary condition at the fluid-fluid interface, and the probe equation of motion. Such methods have been successfully implemented at the double wall-ring (DWR), the magnetic rod (MR), and the bicone interfacial shear rheometers. However, a study of the errors introduced directly by the numerical processing is still lacking. Here we report on a study of the errors introduced exclusively by the numerical procedure corresponding to the bicone geometry at an air-water interface. In our study we directly input a preset the value of the complex interfacial viscosity and we numerically obtain the corresponding flow field and the complex amplitude ratio for the probe motion. Then we use the standard iterative procedure to obtain the calculated complex viscosity value. A detailed comparison of the set and calculated complex viscosity values is made upon changing different parameters such as real and imaginary parts of the complex interfacial viscosity and frequency. The observed discrepancies yield a detailed landscape of the numerically introduced errors.

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.

Calculations of Two and Three-Dimensional Transonic Cascade Flow Fields Using the Navier-Stokes Equations

1986 ◽  
Vol 108 (1) ◽  
pp. 93-102 ◽  
Author(s):  
B. C. Weinberg ◽  
R.-J. Yang ◽  
H. McDonald ◽  
S. J. Shamroth
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Solid Surfaces ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Cascade Calculation ◽  
Transonic Cascade ◽  
Good Agreement

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and no-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive ‘O’-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (∼ 80–150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.

Numerical Simulation of Three-Dimensional Cathode Flow Field of ECM for Inner-Wall Rectangle Weight-Reduction Blind Groove

2010 ◽  
Vol 102-104 ◽  
pp. 321-325 ◽  
Author(s):  
Jian Min Wu
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Electrochemical Machining ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Workpiece Surface ◽  
Flow Passage

In order to design the flow field of the NC-Electrochemical Machining (NC-ECM), a three-dimensional physical model of the flow passage is constructed based on the characteristic of the fluid flow, and three-dimensional flow field simulation is conducted with the applications of the Reynolds time-averaged Navier-Stokes equations and standard k- turbulence numerical model, velocity vectors on workpiece surface are calculated respectively based upon the three cathode outlet slots under the steady electrochemical machining condition. The present analysis show that electrolyte insufficiency appeared on workpiece surface for initial cathode flow field, and the experiment results verified the correctness of numerical simulation.

scholarly journals NUMERICAL SIMULATIONS OF BREAKING SOLITARY WAVES

2012 ◽  
Vol 1 (33) ◽  
pp. 59 ◽  
Author(s):  
Pierre Lubin ◽  
Stéphane Glockner
Keyword(s):  
Experimental Data ◽  
Solitary Waves ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Point Of View ◽  
Numerical Code ◽  
Scale Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Description

This paper presents the application of a parallel numerical code to breaking solitary waves impacting a seawall structure. The three-dimensional Navier-Stokes equations are solved in air and water, coupled with a subgrid-scale model to take turbulence into account. We compared three numerical methods for the free-surface description, using the classical VOF-PLIC and VOF-TVD methods, and an original VOF-SM method recently developed in our numerical tool (Vincent et al., 2010). Some experimental data for solitary waves impinging and overtopping coastal structures are available in literature (Hsiao et al., 2010). Solitary waves are often used to model tsunami behaviors because of their hydrodynamic similarities. From a numerical point of view, it allows shorter CPU time simulations, as only one wave breaks. Here we apply the model to simulate three-dimensional solitary waves and compare qualitatively our results with the experimental data. We investigate three configurations of solitary waves impinging and overtopping an impermeable seawall on a 1:20 sloping beach.

Predicting Unsteady Flow Parameters in a Subsonic Air Diffuser Using MacCormack’s Explicit Method

2019 ◽  
Vol 7 (1) ◽  
pp. 1-10
Author(s):  
Tawfeeq Wasmi M. Salih
Keyword(s):  
Stokes Equations ◽  
Flow Characteristics ◽  
Numerical Procedure ◽  
Vertical Direction ◽  
Steady State Solution ◽  
Numerical Code ◽  
Navier Stokes ◽  
Explicit Method ◽  
Navier Stokes Equations ◽  
Subsonic Diffuser

A numerical procedure is presented to predict the flow characteristics inside a subsonic diffuser by solving Navier-Stokes' equations, using MacCormack’s explicit method. The flow is assumed to be viscous, compressible, unsteady and two-dimensional. The grid model suggested for the diffuser has 20 points in the horizontal direction and 30 points in the vertical direction. The numerical solution has shown reasonable results with a 2D variation of flow properties inside the diffuser and the steady state solution can be satisfied by 600-900 loops only. The obtained results of the present study are compared with those obtained by using a numerical code of National Project for Application-oriented Research in CFD (NPARC) as well as those obtained from a previous experimental study and give an acceptable range of errors (about ± 15%).

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