Simulation of Flow Around Circular Cylinder Using a Collocation Spectral Method

2005 ◽  
Author(s):  
Johnny J. M. Rizales ◽  
Paulo T. T. Esperanc¸a ◽  
Andre´ Belfort Bueno
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Spectral Method ◽  
Stokes Equations ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Implicit Time ◽  
Integration Scheme ◽  
Navier Stokes Equations ◽  
Collocation Spectral Method

The purpose of this paper is to develop a Fourier-Chebyshev collocation spectral method for computing unsteady two-dimensional viscous incompressible flow past a circular cylinder for low Reynolds numbers. The incompressible Navier-Stokes equations (INSE) are formulated in terms of the primitive variables, velocity and pressure. The incompressible Navier-Stokes equations in curvilinear coordinates are spectrally discretized and time integrated by a second-order mixed explicit/implicit time integration scheme. This scheme is a combination of the Crank-Nicolson scheme operating on the diffusive term and Adams-Bashforth scheme acting on the convective term. The projection method is used to split the solution of the INSE to the solution of two decoupled problems: the diffusion-convection equation (Burgers equation) to predict an intermediate velocity field and the Poisson equation for the pressure, it is used to correct the velocity field and satisfy the continuity equation. Finally, the numerical results obtained for the drag and lift coefficients around the circular cylinder are compared with results previously published.

Numerical Simulation of Flow Around a Circular Cylinder Using a Fourier-Chebyshev Collocation Spectral Method

2003 ◽  
Author(s):  
Johnny J. Marti´nez R. ◽  
Paulo T. T. Esperanc¸a
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Spectral Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Design Stage ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Chebyshev Collocation ◽  
Collocation Spectral Method

Vortex-induced vibrations (VIV) of slender structural elements (marine cables, pipes and risers) are very important aspects to be considered in the design stage of many offshore structures, because the fatigue life of risers installed in deep water are often dominated by VIV effects. Despite the relatively fundamental nature of the problem, a small amount is known about the nature of the fluid-structure interaction. The purpose of this paper is to develop a Fourier-Chebyshev collocation spectral method for computing unsteady two-dimensional viscous incompressible flow past a circular cylinder for moderate Reynolds numbers. The incompressible Navier-Stokes equations (INSE) are formulated in terms of the primitive variables, velocity and pressure. The incompressible Navier-Stokes equations in curvilinear coordinates are spectrally discretized and time integrated by a second-order mixed explicit/implicit time integration scheme. This scheme is a combination of the Crank-Nicolson scheme operating on the diffusive term and Adams-Bashforth scheme acting on the convective term. The projection method is used to split the solution of the INSE to the solution of two decoupled problems: the diffusion-convection equation (Burgers equation) to predict an intermediate velocity field and the Poisson equation for the pressure, it is used to correct the velocity field and satisfy the continuity equation. Finally, the numerical results obtained for the drag and lift coefficients around the circular cylinder are compared with results previously published.

scholarly journals Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

1997 ◽  
Author(s):  
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto
Keyword(s):  
Gas Turbine ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Implicit Time ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Turbine Cascades ◽  
Annular Cascade

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

Steady Flow in the Transition Length of a Straight Tube

1942 ◽  
Vol 9 (2) ◽  
pp. A55-A58 ◽  
Author(s):  
Henry L. Langhaar
Keyword(s):  
Velocity Field ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Straight Tube ◽  
Pressure Function ◽  
Navier Stokes Equations ◽  
Dimensionless Constant ◽  
The Family ◽  
Transition Length

Abstract By means of a linearizing approximation, the Navier-Stokes equations are solved for the case of steady flow in the transition length of a straight tube. The family of velocity profiles is defined by Bessel functions, and the parameter of this family is tabulated against the axial co-ordinate in a dimensionless form. Hence, the length of transition is obtained. The curves give a comparison of the author’s calculations of the velocity field with those of other investigators, and with the experimental data of Nikuradse. The pressure function is derived from the computed velocity field by means of the energy equation, and the pressure drop in the transition length is defined by a dimensionless constant m, which is computed to be 2.28. A discussion of this constant is given in the conclusions.

On the limitation of imposed velocity field strategy for Coulomb-driven electroconvection flow simulations

2013 ◽  
Vol 727 ◽  
Author(s):  
Philippe Traoré ◽  
Jian Wu
Keyword(s):  
Velocity Field ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Simulations ◽  
Mobility Parameter ◽  
The Rich ◽  
Strong Injection ◽  
Unipolar Injection

AbstractThis study refers to the article of Chicón, Castellanos & Martion (J. Fluid Mech., vol. 344, 1997, pp. 43–66), who presented a numerical study of electroconvection in a layer of dielectric liquid induced by unipolar injection. An important characteristic of the numerical strategy proposed by Chicón et al. lies in the fact that the Navier–Stokes equations are never solved to obtain the velocity field, which is subsequently needed in the charge density transport equation. Instead, the velocity field is explicitly provided by an expression obtained with some assumptions about the flow structure and related to the electric field (the imposed velocity field approach; IVF). The validity of the above simplification is examined through a direct comparison of the solutions obtained by solving the Navier–Stokes equations (the Navier–Stokes computation approach; NSC). It is clearly demonstrated that, even in the strong injection regime ($C= 10$), the results look very similar for a given range of the mobility parameter $M$; however, in the weak injection regime ($C= 0. 1$), significant discrepancies are observed. The rich flow structures obtained with the NSC approach invalidate the use of the IVF approach in the weak injection regime.

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