Flow Studies in Canine Artery Bifurcations Using a Numerical Simulation Method

1992 ◽  
Vol 114 (4) ◽  
pp. 504-511 ◽  
Author(s):  
X. Y. Xu ◽  
M. W. Collins ◽  
C. J. H. Jones
Keyword(s):  
Newtonian Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Simulation Method ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Element Mesh ◽  
Finite Volume Approach

Three-dimensional flows through canine femoral bifurcation models were predicted under physiological flow conditions by solving numerically the time-dependent threedimensional Navier-stokes equations. In the calculations, two models were assumed for the blood, those of (a) a Newtonian fluid, and (b) a non-Newtonian fluid obeying the power law. The blood vessel wall was assumed to be rigid this being the only approximation to the prediction model. The numerical procedure utilized a finite volume approach on a finite element mesh to discretize the equations, and the code used (ASTEC) incorporated the SIMPLE velocity-pressure algorithm in performing the calculations. The predicted velocity profiles were in good qualitative agreement with the in vivo measurements recently obtained by Jones et al. [1]. The non-Newtonian effects on the bifurcation flow field were also investigated, and no great differences in velocity profiles were observed. This indicated that the non-Newtonian characteristics of the blood might not be an important factor in determining the general flow patterns for these bifurcations, but could have local significance. Current work involves modeling wall distensibility in an empirically valid manner. Predictions accommodating these will permit a true quantitative comparison with experiment.

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.

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.

scholarly journals A Geometrical Regularity Criterion in Terms of Velocity Profiles for the Three-Dimensional Navier–Stokes Equations

2019 ◽  
Vol 72 (4) ◽  
pp. 545-562 ◽  
Author(s):  
C V Tran ◽  
X Yu
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Velocity Profiles ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Velocity ◽  
Whole Space ◽  
Velocity Region

Summary In this article, we present a new kind of regularity criteria for the global well-posedness problem of the three-dimensional Navier–Stokes equations in the whole space. The novelty of the new results is that they involve only the profiles of the magnitude of the velocity. One particular consequence of our theorem is as follows. If for every fixed $t\in (0,T)$, the ‘large velocity’ region $\Omega:=\{(x,t)\mid |u(x,t)|>C(q)\left|\mkern-2mu\left|{u}\right|\mkern-2mu\right|_{L^{3q-6}}\}$, for some $C(q)$ appropriately defined, shrinks fast enough as $q\nearrow \infty$, then the solution remains regular beyond $T$. We examine and discuss velocity profiles satisfying our criterion. It remains to be seen whether these profiles are typical of general Navier–Stokes flows.

Viscous Simulation Method for Unsteady Flows Past Multicomponent Configurations

1992 ◽  
Vol 114 (2) ◽  
pp. 161-169 ◽  
Author(s):  
Kamran Fouladi ◽  
Oktay Baysal
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Simulation Method ◽  
Parent Body ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Navier Stokes Equations ◽  
Time Period ◽  
Cavity Opening ◽  
Averaging Time

An algorithm is developed to obtain numerical simulations of flows about complex configurations composed of multiple and nonsimilar components with arbitrary geometries. The algorithm uses a hybridization of the domain decomposition techniques for grid generation and to reduce the computer memory requirement. Three-dimensional Reynolds-averaged, unsteady, compressible, and full Navier-Stokes equations are solved on each of the subdomains by a fully vectorized, finite-volume, upwind-biased, approximately factored, and multigrid method. The effect of Reynolds stresses is incorporated through an algebraic turbulence model with several modifications for interference flows. The algorithm is applied to simulate supersonic flows past an ogive-nose-cylinder near or inside a cavity. The cylinder is attached to an offset L-shaped sting when placed above the cavity opening. The unsteady nature of these flowfields and the interaction of the cavity shear layer with the cylinder are simulated. These cases illustrate two significantly different and important interference characteristics for an internally carried store separating from its parent body. Unsteadiness of the cavity flow has a more pronounced effect on the normal forces acting on the cylinder when the cylinder is placed inside the cavity. The time averaged surface pressures compare favorably with the wind tunnel data, despite the averaging time period for the computations being three orders of magnitude smaller than that of the experimental measurements.

Development of a CFD Simulation Method for Extreme Wave and Structure Interactions

2005 ◽  
Author(s):  
Chi Yang ◽  
Rainald Lo¨hner ◽  
Solomon C. Yim
Keyword(s):  
Cfd Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Simulation Method ◽  
Computer Code ◽  
Dam Break ◽  
Navier Stokes ◽  
Extreme Waves ◽  
Cfd Method ◽  
Incompressible Euler

A robust Volume of Fluid (VOF) technique is presented together with an incompressible Euler/Navier Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The incompressible Euler/Navier Stokes equations are solved using projection schemes and a finite element method. The classic dam-break problem has been used to validate the computer code developed based on the method described above. The numerical simulations of a three dimensional dam-break wave interacting with a single cylinder and a cylinder array have been carried out. Computational results have demonstrated that the present CFD method is capable of simulating the interactions of extreme waves and three-dimensional structures, which are of great importance for the comprehension of many natural phenomena in marine, coastal and marine engineering.

Three-Dimensional Steady Flow Through A Bifurcation

1990 ◽  
Vol 112 (2) ◽  
pp. 189-197 ◽  
Author(s):  
Chain-Nan Yung ◽  
Kenneth J. De Witt ◽  
Theo G. Keith
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Steady Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Simple Algorithm ◽  
Outer Wall ◽  
Navier Stokes

Steady flow of an incompressible, Newtonian fluid through a symmetric bifurcated rigid channel was numerically analyzed by solving the three-dimensional Navier-Stokes equations. The upstream Reynolds number ranged from 100 to 1500. The bifurcation was symmetrical with a branch angle of 60 deg and the area ratio of the daughter to the mother vessel was 2.0. The numerical procedure utilized a coordinate transformation and a control volume approach to discretize the equations to finite difference form and incorporated the SIMPLE algorithm in performing the calculation. The predicted velocity pattern was in qualitative agreement with experimental measurements available in the literature. The results also showed the effect of secondary flow which can not be predicted using previous two-dimensional simulations. A region of reversed flow was observed near the outer wall of the branch except for the case of the lowest Reynolds number. Particle trajectory was examined and it was found that no fluid particles remained within the recirculation zone. The shear stress was calculated on both the inner and the outer wall of the branch. The largest wall shear stress, located in the vicinity of the apex of the branch, was of the same order of magnitude as the level that can cause damage to the vessel wall as reported in a recent study.

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.

scholarly journals Viscous Flows in Centrifugal Compressor Diffusers at Transonic Mach Numbers

1992 ◽  
Author(s):  
I. Teipel ◽  
A. Wiedermann ◽  
W. Evers
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Flow Fields ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Accelerate Convergence ◽  
Mach Numbers

A numerical investigation of steady two- and three-dimensional flow fields in vaned diffusers of highly-loaded centrifugal compressors is described. The explicit MacCormack scheme was used to calculate inviscid and viscous effects because of the possibility of vectorization. Transonic Mach numbers are reached in the entrance of the diffuser and therefore time-dependent equations are solved. Two methods are employed to accelerate convergence of this explicit scheme. These techniques are (1) local time stepping and (2) applying a multigrid scheme. For the turbulent case an improved Baldwin-Lomax model given by Granville has been used. The numerical procedure has been used to compute two-dimensional transonic flow fields of a centrifugal compressor diffuser at different impeller speeds. It is shown that the predicted pressure field is in reasonable agreement with experimental data. Different approaches for the evaluation of global loss figures have been compared with each other. In addition, an evaluation of the complete three-dimensional Navier-Stokes equations is presented. The vanes in the diffuser are twisted such that the flow field contains a strong three-dimensional effect. Again a comparison with experiments is carried out and the agreement is fairly good.

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