A numerical technique for the solution of the Navier–Stokes equations of unsteady flow

2006 ◽  
Vol 195 (7-8) ◽  
pp. 534-550 ◽  
Author(s):  
Vassilios C. Loukopoulos
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Navier Stokes ◽  
Navier Stokes Equations

A 3D Unsteady Flow Analysis in a Doubly Constricted Tube

2000 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
T. Yamaguchi ◽  
H. Liu ◽  
R. Himeno
Keyword(s):  
Pressure Drop ◽  
Unsteady Flow ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
In Series ◽  
3D Unsteady Flow

Abstract Unsteady flow dynamics in a doubly constricted vessel is analyzed by using a time accurate Finite Volume solution of three dimensional incompressible Navier-Stokes equations. Computational experiments are carried out for various values of Reynolds number in order to assess the criticality of multiple mild constrictions in series and also to bring out the subtle 3D features like vortex formation. Studies reveal that pressure drop across a series of mild constrictions can get physiologically critical. Further this pressure drop is found to be sensitive to the spacing between the constrictions and also to the oscillatory nature of the inflow profile.

scholarly journals Unsteady flow around a two-dimensional section of a vertical axis turbine for tidal stream energy conversion

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Hyun Ju Jung ◽  
Ju Hyun Lee ◽  
Shin Hyung Rliee ◽  
Museok Song ◽  
Beom-Soo Hyun
Keyword(s):  
Unsteady Flow ◽  
Energy Conversion ◽  
Stokes Equations ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Tidal Stream ◽  
Tidal Stream Energy ◽  
Vertical Axis Turbine

ABSTRACTThe two-dimensional unsteady flow around a vertical axis turbine for tidal stream energy' conversion was investigated using a computational fluid dynamics tool solving the Reynolds-Averaged Navier-Stokes equations. The geometry' of the turbine blade section was NACA653-01S airfoil. The computational analysis was done at several different angles of attack and the results were compared with the corresponding experimental data for validation and calibration. Simulations were then carried out for the two-dimensional cross section of a vertical axis turbine. The simulation results demonstrated the usefulness of the method for the typical unsteady flows around vertical axis turbines. The optimum turbine efficiency was achieved for carefully selected combinations of the number of blades and tip speed ratios.

Symmetry-breaking bifurcations in spherical Couette flow

1996 ◽  
Vol 310 ◽  
pp. 293-324 ◽  
Author(s):  
Oleg Yu. Zikanov
Keyword(s):  
Symmetry Breaking ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Basic Equilibrium ◽  
Spherical Couette ◽  
Pseudo Spectral

The solutions of the nonlinear and linearized Navier-Stokes equations are computed to investigate the instabilities and the secondary two- and three-dimensional regimes in the flow of an incompressible viscous fluid in a thin gap between two concentric differentially rotating spheres. The numerical technique is finite difference in the radial direction, spectral in the azimuthal direction, and pseudo-spectral in the meridional direction. The study follows the experiments by Yavorskaya, Belyaev and co-workers in which a variety of steady axisymmetric and three-dimensional travelling wave secondary regimes was observed in the case of a thin layer and both boundary spheres rotating. In agreement with the experimental results three different types of symmetry-breaking primary bifurcations of the basic equilibrium are detected in the parameter range under consideration.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

scholarly journals A Numerical Model of the Onset of Stall Flutter in Cascades

1995 ◽  
Author(s):  
William S. Clark ◽  
Kenneth C. Hall
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Computational Fluid Dynamic Model ◽  
Navier Stokes ◽  
Aeroelastic Stability ◽  
Blade Vibration ◽  
Navier Stokes Equations ◽  
The Mean ◽  
Stall Flutter

In this paper, we present a computational fluid dynamic model of the unsteady flow associated with the onset of stall flutter in turbomachinery cascades. The unsteady flow is modeled using the laminar Navier-Stokes equations. We assume that the unsteadiness in the flow is a small harmonic disturbance about the mean or steady flow. Therefore, the unsteady flow is governed by a small-disturbance form of the Navier-Stokes equations. These linear variable coefficient equations are discretized on a deforming computational grid and solved efficiently using a multiple-grid Lax-Wendroff scheme. A number of numerical examples are presented which demonstrate the destabilizing influence of viscosity on the aeroelastic stability of airfoils in cascade, especially for torsional modes of blade vibration.

scholarly journals NUMERICAL CALCULATION OF WAVE FORCES ON STRUCTURES

1976 ◽  
Vol 1 (15) ◽  
pp. 131
Author(s):  
B.D. Nichols ◽  
C.W. Hirt
Keyword(s):  
Stokes Equations ◽  
Numerical Technique ◽  
Ocean Waves ◽  
Navier Stokes ◽  
Wave Forces ◽  
Transient Wave ◽  
Dynamic Interactions ◽  
Navier Stokes Equations ◽  
Calculational Method ◽  
Moving Bodies

A finite-difference technique for solving the Navier-Stokes equations for an incompressible fluid is used to calculate transient wave forces experienced by fixed and moving bodies. The numerical technique is based on the Marker-and-Cell (MAC) method developed by Harlow and Welch (1965). This new technique uses an especially simple solution algorithm that is designed for persons with little or no experience in numerical fluid dynamics. Originally conceived as an instructional tool, it has proven to be an extremely useful and versatile calculational method. Many useful calculations are possible with the publicly available code, SOLA-SURF, which is briefly described in Sec. II; however, the outstanding feature of this numerical scheme is the ease with which it can be modified to handle more complex problems. Reported here, in Sec. Ill, are examples to illustrate the utility of this new calculational tool for investigating the dynamic interactions between ocean waves and coastal structures.

scholarly journals Numerical simulation of unsteady flow of a viscous incompressible liquid in flat channels of arbitrary shape of heat exchangers

2020 ◽  
Vol 34 ◽  
pp. 41-55
Author(s):  
Y. Chоvniuk ◽  
V. Kravchuk ◽  
A. Moskvitina ◽  
I. Pefteva
Keyword(s):  
Numerical Simulation ◽  
Fluid Flow ◽  
Unsteady Flow ◽  
Heat Exchangers ◽  
Arbitrary Shape ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Navier Stokes Equations

Reasonable development and creation of any device in which there is an interaction between the fluid flow and the elements of the flow parts (for example, heat exchangers, transport and power machines, main pipelines), is impossible without detailed information about the characteristics of the flow, about the forces on the surfaces that are around, about vibroacoustic phenomena, etc. Among the various methods of obtaining information about the characteristics of the flow, about the forces on surfaces that are flown around, about vibroacoustic phenomena, an important role is played by theoretical methods that rely on the equation of hydrodynamics and numerous ways to solve them. In this case, the main efforts are aimed at solving the system of Navier-Stokes equations. In this paper, a general method is described for the numerical solution of the problem of unsteady flow of a viscous incompressible fluid in flat channels of an arbitrary shape of heat exchangers. An effective solution to the problem is achieved by using adaptive networks. The mathematical model of the flow is based on the two-dimensional Navier-Stokes equations in the variables "flow function - vortex" and the Poissonequation for pressure, which are solved on the basis of the finite-difference method. A numerical simulation of the fluid flow in a flat curvilinear elbow is carried out at the Reynolds number Re = 1000. This form reflects the most characteristic features of the flow paths of various hydraulic machines, heat exchangers, hydraulic and pipeline systems. The presentation of the numerical results was carried out on the basis of the VISSIM graphic processing package. One of the main problems (difficulties) in the numerical solution of problems of mathematical physics is the representation of boundary conditions for regions of arbitrary shape. The implementation of various artificial methods that are now used in the approximation of both the curvilinear boundaries themselves and the boundary conditions on them can lead to significant losses in the accuracy of the solution. This is especially evident in problems in which solutions in the boundary region have maximum gradients. An effective method for solving this problem is the use of adapted grids for the computational domain. The essence of this method lies in the fact that such a coordinate system, not necessarily orthogonal, is found in which the boundary lines (surfaces) of the region coincide with the coordinate lines (surfaces). In the flat case, the computational domain is transformed into a rectangular one, and the limit curve is displayed on the sides of the rectangle. In practice, the problem of constructing an adapted mesh is reduced to finding functions that describe the mappings of the canonical (rectangular) region onto the region for which the problem was originally formulated, that is, for the two-dimensional case, the functions x (ξ, η), y (ξ, η) are determined.

A Theoretical and Experimental Study of Confined Vortex Flow

1969 ◽  
Vol 36 (4) ◽  
pp. 687-692 ◽  
Author(s):  
G. J. Farris ◽  
G. J. Kidd ◽  
D. W. Lick ◽  
R. E. Textor
Keyword(s):  
Flow Field ◽  
Radial Flow ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
General Validity ◽  
Wide Range

The interaction of a vortex with a stationary surface was studied both theoretically and experimentally. The flow field examined was that produced by radially inward flow through a pair of concentric rotating porous cylinders that were perpendicular to, and in contact with, a stationary flat plane. The complete Navier-Stokes equations were solved over a range of tangential Reynolds numbers from 0–300 and a range of radial Reynolds numbers from 0 to −13, the minus sign indicating radially inward flow. In order to facilitate the solution, the original equations were recast in terms of a dimensionless stream function, vorticity, and third variable related to the tangential velocity. The general validity of the numerical technique was demonstrated by the agreement between the theoretical and experimental results. Examination of the numerical results over a wide range of parameters showed that the entire flow field is very sensitive to the amount of radial flow, especially at the transition from zero radial flow to some finite value.

Prediction of Cascade Performance Using an Incompressible Navier-Stokes Technique

1990 ◽  
Author(s):  
G. V. Hobson ◽  
B. Lakshminarayana
Keyword(s):  
Stokes Equations ◽  
Control Volume ◽  
Numerical Technique ◽  
Skin Friction Coefficient ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Distribution Boundary ◽  
Turbulence Effects ◽  
Good Agreement

A fully elliptic, control volume solution of the two-dimensional incompressible Navier-Stokes equations for the prediction of cascade performance over a wide incidence range is presented in this paper. The numerical technique is based on a new pressure substitution method. A Poisson equation is derived from the pressure weighted substitution of the full momentum equations into the continuity equation. The analysis of a double circular arc compressor cascade is presented, and the results are compared with the available experimental data at various incidence angles. Good agreement is obtained for the blade pressure distribution, boundary layer and wake profiles, skin friction coefficient, losses and outlet angles. Turbulence effects are simulated by the Low-Reynolds-Number version of the k-ε turbulence model.

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