Computing internal viscous flow problems for the circle by integral methods

1977 ◽  
Vol 79 (3) ◽  
pp. 609-624 ◽  
Author(s):  
R. D. Mills
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Integral Representation ◽  
Analytical Solutions ◽  
Reynolds Numbers ◽  
Cylinder Wall ◽  
Two Dimensional ◽  
Discontinuous Surface ◽  
Flow Problems ◽  
Integral Methods

Steady two-dimensional viscous motion within a circular cylinder generated by (a) the rotation of part of the cylinder wall and (b) fluid entering and leaving through slots in the wall is considered. Studied in particular are moving-surface problems with continuous and discontinuous surface speeds, simple inflow–outflow problems and the impinging-jet problem within a circle. The analytical solutions at zero Reynolds number are given for the last two types of problem. Numerical results are obtained at various Reynolds numbers from the integral representation of the solution. At zero Reynolds number this approach involves a quadrature around the circumference of the cylinder. At other Reynolds numbers it involves an iterative–integral technique based on the use of the ‘clamped-plate’ biharmonic Green's function.

Two-dimensional simulation of unsteady heat transfer from a circular cylinder in crossflow

2007 ◽  
Vol 570 ◽  
pp. 177-215 ◽  
Author(s):  
SALEM BOUHAIRIE ◽  
VINCENT H. CHU
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Length Scale ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Transfer Rates ◽  
Two Dimensional Model

The heat transfer from the surface of a circular cylinder into a crossflow has been computed using a two-dimensional model, for a range of Reynolds numbers from Re=200 to 15550. The boundary-layer separation, the local and overall heat-transfer rates, the eddy- and flare-detachment frequencies and the width of the flares were determined from the numerical simulations. In this range of Reynolds numbers, the heat-transfer process is unsteady and is characterized by a viscous length scale that is inversely proportional to the square root of the Reynolds number. To ensure uniform numerical accuracy for all Reynolds numbers, the dimensions of the computational mesh were selected in proportion to this viscous length scale. The small scales were resolved by at least three nodes within the boundary layers. The frequency of the heat flares increases, and the width of each flare decreases, with the Reynolds number, in proportion to the viscous time and length scales. Despite the presence of three-dimensional structures for the range of Reynolds numbers considered, the two-dimensional model captures the unsteady processes and produced results that were consistent with the available experimental data. It correctly simulated the overall, the front-stagnation and the back-to-total heat-transfer rates.

Active Control of the Profile Drag of Two-Dimensional Cylinders

2002 ◽  
Author(s):  
Hani H. Nigim ◽  
Hide S. Koyama ◽  
Kohta Shiino
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Active Control ◽  
Control Method ◽  
Sound Field ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Phase Lag ◽  
Two Dimensional ◽  
Field Velocity

The control of profile drag on a circular cylinder was studied experimentally at Reynolds numbers, ranging from 160 to 400, using an acoustic active control system. The investigation has been carried by, quantitatively, hot-wire to measure the mean and fluctuating velocities and, qualitatively, by using smoke-wire flow visualization technique to examine the formation of the flow field down-stream of the cylinder. The present active control method is able to influence the rate of entrainment from main flow into the wake flow. When the Reynolds number is relatively small, it is the size of the cylinder and the induced sound field velocity as well as Reynolds number which are the significant parameters in determining the controlling reverse and optimum phase lag angels. The reported control strategy is able to alter the profile drag of a two-dimensional circular cylinder. At optimum lag angle and low Reynolds number the profile drag was reduced by 9%.

scholarly journals Three-dimensional Floquet stability analysis of the wake of a circular cylinder

1996 ◽  
Vol 322 ◽  
pp. 215-241 ◽  
Author(s):  
Dwight Barkley ◽  
Ronald D. Henderson
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Numerical Stability Analysis ◽  
Mode A

Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300. The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 188.5±1.0. The critical spanwise wavelength is 3.96 ± 0.02 diameters and the critical Floquet mode corresponds to a ‘Mode A’ instability. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0.822 diameters at onset. Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300.

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.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

A Stability Investigation of Two-Dimensional Surface Waves on Evaporating, Isothermal or Condensing Liquid Films: Part II — A Universal Linear Stability Formulation

2004 ◽  
Author(s):  
Xuemin Ye ◽  
Weiping Yan ◽  
Chunxi Li
Keyword(s):  
Reynolds Number ◽  
Surface Waves ◽  
Isothermal Condition ◽  
Reynolds Numbers ◽  
Liquid Films ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Lower Reynolds Number ◽  
Liquid Property ◽  
Dimensional Surface

When liquid film is under evaporating or condensing conditions, the flow stability is clearly different to that under isothermal condition due to thermal non-equilibrium effect at interface, especially under lower Reynolds number. The universal linear temporal and spatial stability formulations of the two-dimensional surface waves on evaporating or isothermal or condensing liquid films are established in present paper with the collocation method based on the boundary layer theory and complete boundary conditions. The models include the effects of Reynolds number, thermocapillarity, inclination angle, liquid property, evaporation, isothermal or condensation. The effects of above factors are investigated with the neutral stability curves at different Reynolds numbers, and stabilities characteristics are fully indicated in theory for evaporating or condensing films.

Numerical Simulation of Vortex Shedding From a Circular Cylinder in the Presence of a Free Surface

2003 ◽  
Author(s):  
S. Nagaya ◽  
R. E. Baddour
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Free Surface ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Cfd Simulations ◽  
Induced Drag

CFD simulations of crossflows around a 2-D circular cylinder and the resulting vortex shedding from the cylinder are conducted in the present study. The capability of the CFD solver for vortex shedding simulation from a circular cylinder is validated in terms of the induced drag and lifting forces and associated Strouhal numbers computations. The validations are done for uniform horizontal fluid flows at various Reynolds numbers in the range 103 to 5×105. Crossflows around the circular cylinder beneath a free surface are also simulated in order to investigate the characteristics of the interaction between vortex shedding and a free surface at Reynolds number 5×105. The influence of the presence of the free surface on the vortex shedding due to the cylinder is discussed.

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

2011 ◽  
Vol 681 ◽  
pp. 411-433 ◽  
Author(s):  
HEMANT K. CHAURASIA ◽  
MARK C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Vortical Flow ◽  
Forced Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Dimensional Instability

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

Prediction of Unsteady Loading on a Circular Cylinder in High Reynolds Number Flows Using Large Eddy Simulation

2005 ◽  
Author(s):  
Sung-Eun Kim ◽  
L. Srinivasa Mohan
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Turbulent Viscosity ◽  
Reynolds Numbers ◽  
Unstructured Meshes ◽  
Navier Stokes ◽  
Step Method ◽  
Fractional Step Method ◽  
Eddy Simulation ◽  
Large Eddy

Large eddy simulations were carried out for the flow around a hydrodynamically smooth, fixed circular cylinder at two Reynolds numbers, one at a subcritical Reynolds number (Re = 1.4 × 105) and the other at a supercritical Reynolds number (Re = 1.0 × 106). The computations were made using a parallelized finite-volume Navier-Stokes solver based on a multidimensional linear reconstruction scheme that allows use of unstructured meshes. Central differencing was used for discretization of both convection and diffusion terms. Time-advancement scheme, based on an implicit, non-iterative fractional-step method, was adopted in conjunction with a three-level, backward second-order temporal discretization. Subgrid-scale turbulent viscosity was modeled by a dynamic Smagorinsky model adapted to arbitrary unstructured meshes with the aid of a test-filter applicable to arbitrary unstructured meshes. The present LES results closely reproduced the flow features observed in experiments at both Reynolds numbers. The time-averaged mean drag coefficient, root-mean-square force coefficients and the frequency content of fluctuating forces (vortex-shedding frequency) are predicted with a commendable accuracy.

Two-Dimensional Unsteady Viscous Flows

2017 ◽  
Author(s):  
Jian-Jun Shu
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Hydrodynamic Force ◽  
Viscous Flows ◽  
Reynolds Numbers ◽  
Fundamental Solutions ◽  
Time Dependent ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Rotational Motions

A number of new closed-form fundamental solutions for the two-dimensional generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. As an example of application, the hydrodynamic force acting on a circular cylinder translating in an unsteady flow field at low Reynolds numbers is calculated using the new generalized fundamental solutions.

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