Fluid Forces on a Moving Body at Low Amplitude in Fluid at Rest: Part 2 — Analytical and Numerical Study for an Accelerated Circular Cylinder

2006 ◽  
Author(s):  
Vincent Melot ◽  
Jean Franc¸ois Sigrist ◽  
Christian Laine ◽  
Bruno Auvity ◽  
Hassan Peerhossaini
Keyword(s):  
Fourier Transform ◽  
Circular Cylinder ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Sine Wave ◽  
Small Displacement ◽  
Fluid Forces ◽  
Temporal Space ◽  
Ale Formulation ◽  
Starting Point

The present paper deals with the study of fluid forces in an incompressible viscous fluid at rest around an accelerated rigid circular cylinder. The movement subjected to the cylinder is an impulsive motion represented by a only one period of a sinusoidal acceleration. After this period, the cylinder is stopped. This study is performed for small displacement of the cylinder, i.e. for low KEULEGAN-CARPENTER numbers, and for various STOKES numbers. An analytical formulation of fluid forces exerted on a cylinder subjected to any motion is first proposed. The starting point of the analytical approach is the solution of fluid forces in steady state harmonic motion. A Fourier transform is applied on the harmonic solution to capture the wide frequency spectrum composing the transient motion. Then an inverse Fourier transform is applied on the expression to achieve the solution in the temporal space. A numerical simulation is then carried out with a CFD code using finite volume method with moving mesh technique in ALE formulation. The analytical and numerical solutions are exposed and discussed in the case of a cylinder subjected to a sine wave acceleration. The competition between the viscous diffusion time and the wave duration time is studied and highlights the history effect on pressure forces and shear forces.

scholarly journals Fluid Forces on a Circular Cylinder Subjected to a Transient Motion at Low Amplitude: Infinite Medium and Cylindrical Confinement

2006 ◽  
Author(s):  
Vincent Melot ◽  
Ce´dric Leblond ◽  
Jean-Franc¸ois Sigrist ◽  
Christian Laine ◽  
Bruno Auvity ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Circular Cylinder ◽  
Two Dimensional ◽  
Infinite Domain ◽  
Transient Motion ◽  
Fluid Forces ◽  
History Effects ◽  
Temporal Space ◽  
Moving Cylinder ◽  
Starting Point

The present paper deals with the fluid forces induced by a rapidly moving rigid circular cylinder in an incompressible fluid initially at rest. The cylinder is subjected to an impulsive motion which corresponds to unique sinusoidal period of acceleration and is then stopped. Two fluid domains are considered: infinite and cylindrically confined. This study focuses on small displacements of the cylinder in regards to its radius, i.e. for low Keulegan-Carpenter numbers. In a first part, the flow is assumed potential. Only the inner cylinder is displaced and the outer one, in the confined case, is at rest. The problem, formulated as a two-dimensional boundary-perturbation problem, is solved thanks to a regular expansion. A non-linear analytical formulation of the fluid forces experienced by the moving cylinder is then proposed. Its range of validity is discussed with regards to the inner cylinder displacement. The results are confronted to numerical simulations with a CFD code based on a finite volume discretization on a moving mesh. In a second part, a two-dimensional viscous flow is considered. Analytical formulations of the fluid forces experienced by the cylinder subjected to arbitrary motions are proposed. The starting point of the analytical approach is the fluid forces expressions obtained with harmonic motion. These expressions come from the Rosenhead model for the infinite fluid domain. A Fourier transform is applied on the harmonic solutions to capture the wide frequency spectrum composing the transient motion. An inverse Fourier transform is then applied on the resulting expressions to derive the solutions in the temporal space. The analytical solutions are discussed and compared to numerical simulation results obtained in an infinite domain for various Stokes numbers. The competition between the viscous diffusion time and the wave duration time is studied which allows to underline history effects on the force.

Stability bounds on turbulent Poiseuille flow

1988 ◽  
Vol 187 ◽  
pp. 435-449 ◽  
Author(s):  
G. R. Ierley ◽  
W. V. R. Malkus
Keyword(s):  
Reynolds Number ◽  
Reynolds Stress ◽  
Poiseuille Flow ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Linear Instability ◽  
Mean Flow ◽  
Starting Point ◽  
The Mean ◽  
The Stability

For steady-state turbulent flows with unique mean properties, we determine a sense in which the mean velocity is linearly supercritical. The shear-turbulence literature on this point is ambiguous. As an example, we reassess the stability of mean profiles in turbulent Poiseuille flow. The Reynolds & Tiederman (1967) numerical study is used as a starting point. They had constructed a class of one-dimensional flows which included, within experimental error, the observed profile. Their numerical solutions of the resulting Orr-Sommerfeld problems led them to conclude that the Reynolds number for neutral infinitesimal disturbances was twenty-five times the Reynolds number characterizing the observed mean flow. They found also that the first nonlinear corrections were stabilizing. In the realized flow, this latter conclusion appears incompatible with the former. Hence, we have sought a more complete set of velocity profiles which could exhibit linear instability, retaining the requirement that the observed velocity profile is included in the set. We have added two dynamically generated modifications of the mean. The first addition is a fluctuation in the curvature of the mean flow generated by a Reynolds stress whose form is determined by the neutrally stable Orr-Sommerfeld solution. We find that this can reduce the stability of the observed flow by as much as a factor of two. The second addition is the zero-average downstream wave associated with the above Reynolds stress. The three-dimensional linear instability of this modification can even render the observed flow unstable. Those wave amplitudes that just barely will ensure instability of the observed flow are determined. The relation of these particular amplitudes to the limiting conditions admitted by an absolute stability criterion for disturbances on the mean flow is found. These quantitative results from stability theory lie in the observationally determined Reynolds-Tiederman similarity scheme, and hence are insensitive to changes in Reynolds number.

scholarly journals A numerical study of steady viscous flow past a circular cylinder

1980 ◽  
Vol 98 (4) ◽  
pp. 819-855 ◽  
Author(s):  
Bengt Fornberg
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Viscous Flow ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Iteration Scheme ◽  
The Body ◽  
Flow Past ◽  
A New Technique

Numerical solutions have been obtained for steady viscous flow past a circular cylinder at Reynolds numbers up to 300. A new technique is proposed for the boundary condition at large distances and an iteration scheme has been developed, based on Newton's method, which circumvents the numerical difficulties previously encountered around and beyond a Reynolds number of 100. Some new trends are observed in the solution shortly before a Reynolds number of 300. As vorticity starts to recirculate back from the end of the wake region, this region becomes wider and shorter. Other flow quantities like position of separation point, drag, pressure and vorticity distributions on the body surface appear to be quite unaffected by this reversal of trends.

scholarly journals NUMERICAL STUDY OF FLUID FORCES ACTING ON A CIRCULAR CYLINDER IN ASYMMETRIC OSCILLATORY FLOW

2005 ◽  
Vol 49 ◽  
pp. 847-852
Author(s):  
Toshiharu MAGAI ◽  
Shinya UMEDA ◽  
Masatoshi YUHI ◽  
Hajime ISHIDA
Keyword(s):  
Circular Cylinder ◽  
Oscillatory Flow ◽  
Numerical Study ◽  
Fluid Forces

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

A Numerical and Experimental Investigation of Turbulent Heat Transport Downstream From an Abrupt Pipe Expansion

1983 ◽  
Vol 105 (4) ◽  
pp. 862-869 ◽  
Author(s):  
R. S. Amano ◽  
M. K. Jensen ◽  
P. Goel
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Expansion

An experimental and numerical study is reported on heat transfer in the separated flow region created by an abrupt circular pipe expansion. Heat transfer coefficients were measured along the pipe wall downstream from an expansion for three different expansion ratios of d/D = 0.195, 0.391, and 0.586 for Reynolds numbers ranging from 104 to 1.5 × 105. The results are compared with the numerical solutions obtained with the k ∼ ε turbulence model. In this computation a new finite difference scheme is developed which shows several advantages over the ordinary hybrid scheme. The study also covers the derivation of a new wall function model. Generally good agreement between the measured and the computed results is shown.

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