Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder

1985 ◽  
Vol 158 ◽  
pp. 447-488 ◽  
Author(s):  
H. M. Badr ◽  
S. C. R. Dennis
Keyword(s):  
Circular Cylinder ◽  
Differential Equations ◽  
Numerical Study ◽  
Separated Flow ◽  
Time Dependent ◽  
Initial Development ◽  
Rotation Rates ◽  
Finite Set ◽  
Small Times ◽  
Two Dimensional Flow

A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R [ges ] 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Kármán vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent.

Symmetrical flow past an accelerated circular cylinder

1996 ◽  
Vol 308 ◽  
pp. 97-110 ◽  
Author(s):  
H. M. Badr ◽  
S. C. R. Dennis ◽  
S. Kocabiyik
Keyword(s):  
Circular Cylinder ◽  
Series Solution ◽  
Viscous Incompressible Fluid ◽  
Time Integration ◽  
Reynolds Numbers ◽  
Perturbation Series ◽  
Implicit Time ◽  
Implicit Time Integration ◽  
Small Times ◽  
Two Dimensional Flow

The development of the two-dimensional flow of a viscous incompressible fluid around a circular cylinder which suddenly starts to move with the velocity U = U0 + U1t + U2t2 is studied. Equations for the flow in terms of the stream function and vorticity in boundary-layer coordinates are presented. A perturbation series solution for small times is developed. The flow for longer times is computed numerically using an accurate implicit time-integration procedure. The numerical method is checked for small times by comparison with the results of the analytical solution. Reynolds numbers R in the range 200 to 104 (based on the diameter of the cylinder) are considered. One particularly interesting result is that for certain values of U1 and U2 at R = 500 and R = 103 it is found that two co-rotating vortices and three co-rotating vortices develop with time in each half of the wake in the two respective cases.

scholarly journals A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method

1991 ◽  
Vol 233 ◽  
pp. 243-263 ◽  
Author(s):  
Chien-Cheng Chang ◽  
Ruey-Ling Chern
Keyword(s):  
Finite Difference ◽  
Circular Cylinder ◽  
Numerical Study ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Numerical Results ◽  
High Reynolds Numbers ◽  
Small Times ◽  
Axis Of Symmetry ◽  
High Reynolds

Impulsively started flow around a circular cylinder at various Reynolds numbers is studied by a deterministic hybrid vortex method. The key feature of the method consists in solving the viscous vorticity equation by interlacing a finite-difference method for diffusion and a vortex-in-cell method for convection. The vorticity is updated along the surface of the cylinder to satisfy the no-slip condition. The present method is basically different from previous applications of vortex methods, which are primarily in the context of random vortex algorithms. The Reynolds numbers of the flows under investigation range from 300 to 106. Numerical results are compared with analytical solutions at small times, and compared with finite-difference solutions and flow visualization results at relatively long times. Satisfactory agreement is found in the evolutions of the separation angles, wake lengths, surface pressure and drag coefficients, streamline patterns, and some velocities on the axis of symmetry behind the circular cylinder. The present hybrid vortex method is highly stable and suffers from little numerical diffusivity, yielding convincing numerical results for unsteady vortical flows at moderately high Reynolds numbers.

Instability and sensitivity of the flow around a rotating circular cylinder

2010 ◽  
Vol 650 ◽  
pp. 513-536 ◽  
Author(s):  
JAN O. PRALITS ◽  
LUCA BRANDT ◽  
FLAVIO GIANNETTI
Keyword(s):  
Circular Cylinder ◽  
Passive Control ◽  
Base Flow ◽  
Structural Sensitivity ◽  
Rotation Rates ◽  
Rotating Circular Cylinder ◽  
Flow Stagnation ◽  
Two Dimensional Flow ◽  
Classic Approach ◽  
Structural Sensitivity Analysis

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a role of ‘wavemaker’ in the excitation of the global instability is identified by considering the structural sensitivity of the unstable mode. This approach is compared with the analysis of the perturbation kinetic energy production, a classic approach in linear stability analysis. Multiple steady-state solutions are found at high rotation rates, explaining the quenching of the second shedding mode. Turning points in phase space are associated with the movement of the flow stagnation point. In addition, a method to examine which structural variation of the base flow has the largest impact on the instability features is proposed. This has relevant implications for the passive control of instabilities. Finally, numerical simulations of the flow are performed to verify that the structural sensitivity analysis is able to provide correct indications on where to position passive control devices, e.g. small obstacles, in order to suppress the shedding modes.

scholarly journals Secondary frequencies in the wake of a circular cylinder with vortex shedding

1991 ◽  
Vol 225 ◽  
pp. 557-574 ◽  
Author(s):  
Saul S. Abarbanel ◽  
Wai Sun Don ◽  
David Gottlieb ◽  
David H. Rudy ◽  
James C. Townsend
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Algorithms ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Two Dimensional Flow

A detailed numerical study of two-dimensional flow past a circular cylinder at moderately low Reynolds numbers has been conducted using three different numerical algorithms for solving the time-dependent compressible Navier–Stokes equations. It was found that if the algorithm and associated boundary conditions were consistent and stable, then the major features of the unsteady wake were well predicted. However, it was also found that even stable and consistent boundary conditions could introduce additional periodic phenomena reminiscent of the type seen in previous wind-tunnel experiments. However, these additional frequencies were eliminated by formulating the boundary conditions in terms of the characteristic variables. An analysis based on a simplified model provides an explanation for this behaviour.

Numerical Study of the Combined Free-Forced Convection and Mass Transfer Flow Past a Vertical Porous Plate in a Porous Medium with Heat Generation and Thermal Diffusion

2006 ◽  
Vol 11 (4) ◽  
pp. 331-343 ◽  
Author(s):  
M. S. Alam ◽  
M. M. Rahman ◽  
M. A. Samad
Keyword(s):  
Mass Transfer ◽  
Flow Field ◽  
Differential Equations ◽  
Forced Convection ◽  
Heat Generation ◽  
Numerical Study ◽  
Porous Plate ◽  
Integration Scheme ◽  
Suction Parameter ◽  
Transfer Flow

The problem of combined free-forced convection and mass transfer flow over a vertical porous flat plate, in presence of heat generation and thermaldiffusion, is studied numerically. The non-linear partial differential equations and their boundary conditions, describing the problem under consideration, are transformed into a system of ordinary differential equations by using usual similarity transformations. This system is solved numerically by applying Nachtsheim-Swigert shooting iteration technique together with Runge-Kutta sixth order integration scheme. The effects of suction parameter, heat generation parameter and Soret number are examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The analysis of the obtained results showed that the flow field is significantly influenced by these parameters.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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