Computational study of unsteady viscous flow around a transversely and longitudinally oscillating circular cylinder in a uniform flow at high reynolls numbers

A finite difference simulation method for the time dependent viscous incompressible flow around a transversely and longitudinally oscillating circular cylinder at Reynolds numbers of Re=4×10³ and 4×10⁴ is presented. The Navier-Stokes equations in finite difference form are solved on a moving grid system, based on a time dependent coordinate transformation. Solution of the vortex street development behind the cylinder is obtained when the cylinder remains stationary and also when it is oscillating. Time eholution of the flow configuration is studied by means of stream lines, pressure contours and vorticity contours. The computer results predict the lock-in phenomenon which occurs when the oscillation frequency is close to the vortex shedding frequency in the transverse mode or around double the vortex shedding frequency in the longitudinal mode. The time dependent lift and drag coefficients are obtained by the integration of the pressure and shear forces around the body. The drag, lift and the displacement relations are also discussed.     

Steady viscous flow past a tapered cylinder

The three-dimensional nature of the viscous flow past a linearly tapered circular cylinder is examined at low Reynolds numbers. The numerical solution of the unsteady Navier–Stokes equations converges to a steady state. The primary flow in planes perpendicular to the cylinder axis is practically indistinguishable from the two-dimensional flow past a uniform cylinder. A secondary spanwise flow is observed in the stagnation zone going from the wide end towards the narrow end, whereas a secondary motion on the rear side goes in the opposite direction. In spite of this secondary flow, the length of the separation zone varies linearly with the local Reynolds number.     

Stability of viscous flow past a circular cylinder

A spectral method which employs trigonometric functions and Chebyshev polynomials is used to compute the steady, incompressible laminar flow past a circular cylinder. Linear stability methods are used to formulate a pair of decoupled generalized eigenvalue problems for the growth of symmetric and asymmetric (about the dividing streamline) perturbations. We show that, while the symmetric disturbances are stable, the asymmetric perturbations become unstable at a Reynolds number about 40 with a Strouhal number about 0.12. The critical conditions are found to depend on the size of the computational domain in a manner similar to that observed in the laboratory.     

Numerical simulation of unsteady viscous flow around a circular cylinder

A finite difference solution is obtained for the time-dependent viscous incompressible 2-dimensional flow past a circular cylinder by direct integration of the Navier-Stokes equations expressed in a general curvilinear coordinate system. The solution describes the development of the vortex street developed behind the cylinder. Evolution of flow configuration is studied by means of streamlines, pressure contours, and vorticity contours for different Reynolds numbers. The time-dependent lift and drag coefficients are also obtained.     

Ultrasonic scattering by a fluid cylinder of elliptic cross section, including viscous effects

This paper analyzes acoustic scattering by a viscous compressible fluid cylinder of elliptic cross section submerged in an unbounded viscous nonheat-conducting compressible fluid medium. The classical method of eigenfunction expansion along with the appropriate wave field expansions and the pertinent boundary conditions are used to develop a solution in the form of infinite series involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with the appearance of additional angular-dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A multiprecision code was developed for computing the Mathieu functions of complex argument in terms of complex Fourier coefficients that are themselves calculated by numerically solving appropriate sets of eigen-systems. The numerical results point to the imperative influence of fluid viscosity in notable reduction of pressure amplitudes at intermediate and high frequencies. They also reveal the central role of the cross sectional ellipticity in conjunction with the angle of incidence in altering the pressure directivities. Limiting cases are considered, and fair agreements with well-known solutions are obtained.     

Separation in a two-dimensional Stokes flow inside an elliptic cylinder

The two-dimensional Stokes flow due to a line rotlet inside a fixed elliptic cylinder is investigated, where it is assumed that the line rotlet intersects the major axis of each elliptical cross-section of the cylinder. For the case in which the line rotlet coincides with the centre-line of the elliptic cylinder, it is shown that the number of eddies in the flow increases in a roughly linear way with the ratio of length to width of a cross-section of the cylinder. Moreover, results obtained by varying the rotlet position for several different fixed boundary shapes suggest that the aforementioned ratio, and not the rotlet position, is the principal determinant of the number of eddies.     

Steady flow past an elliptic cylinder inclined to the stream

The properties of steady two-dimensional flow past an elliptic cylinder inclined to the oncoming stream are investigated for small to moderate values of the Reynolds number for which good accuracy can be assured. The solutions are based on a numerical method of solution of the Navier-Stokes equations for incompressible fluids which ensures that all the correct conditions of the problem are satisfied. In particular, the solution is carried out in such a way that the vorticity decays rapidly enough at large distances from the cylinder for the lift and drag on the cylinder to be finite. Results are presented for the variation of lift, drag and streamline patterns with inclination and Reynolds number. Two elliptic cylinders (based on their minor-to-major axes ratio) are considered. For an elliptic cylinder with minor-to-major axes ratio 1:5, results are obtained for Reynolds numbers up to 40 and inclination varying from zero to 90°. Streamline plots for these results show a development of the solution from asymmetric flow at zero inclination (with no separation), through asymmetric flows with increasing inclination (with either no separation, separation with a single recirculating region, or separation with two recirculatory regions) to the symmetric flow at 90° incidence (with two counter rotating vortices). Of interest are asymmetric steady-state results which contain two recirculatory regions trailing the cylinder, one attached and one unattached to the cylinder. Results are also obtained for a second elliptic cylinder with minor-to-major axes ratio 1:10 at Reynolds numbers 15 and 30, inclination 45°. These results are found to be in good agreement with corresponding unsteady results taken to long times (which are tending to a steady state).     

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t=0) steady and then at t>0 it becomes unsteady. The semi-similar solution of the unsteady Navier–Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier–Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier–Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time.     

Numerical simulation of a viscous separation flow around a rotating circular cylinder

Results of numerical solution of Navier-Stokes equations in stream function-vortex variables for a nonstationary laminar flow around a circular cylinder with a rotational degree of freedom are presented. The cases of definite, free, and inertial rotation of the indicated cylinder were considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 3, pp. 75–81, May–June, 2006.     

Oscillating cylinder in viscous fluid: calculation of flow patterns and forces

Laminar and large-eddy-simulation (LES) calculations with the dynamic Smagorinsky model evaluate the flow and force on an oscillating cylinder of diameter D = 2R in otherwise calm fluid, for β = D ²/νT in the range 197–61400 and Keulegan–Carpenter number K = U _m T/D in the range 0.5–8 (ν kinematic viscosity, T oscillation period, U _m maximal velocity). Calculations resolving the streakline patterns of the Honji instability exemplify the local flow structures in the cylinder boundary layer (β ~ 197–300, K ~ 2) but show that the drag and inertia force are not affected by the instability. The present force calculations conform with the classical Stokes–Wang solution for all cases below flow separation corresponding to K < 2 (with β < 61400). The LES calculations of flow separation and vortical flow resolve the flow physics containing a large range of motion scales; it is shown that the energy in the temporal turbulent fluctuations (in fixed points) are resolved. Accurate calculation of the flow separation occurring for K > 2 has strong implication for the force on the cylinder. Present calculations of the force coefficients for K up to 4 and β = 11240 are in agreement with experiments by Otter (Appl Ocean Res 12:153–155, 1990). Drag coeffients when flow separation occurs are smaller than found in U-tube experiments. Inertia coefficients show strong decline for large K (up to 8) and moderate β = 1035 but is close to unity for K = 4 and β = 11240. The finest grid has 2.2 × 10⁶ cells, finest radial Δr/R = 0.0002, number of points along the cylinder circumference of 180, Δz/R = 0.044 and a time step of 0.0005T.     

A proportional-integral-differential control of flow over a circular cylinder

In the present study, we apply proportional (P), proportional-integral (PI) and proportional-differential (PD) feedback controls to flow over a circular cylinder at Re=60 and 100 for suppression of vortex shedding in the wake. The transverse velocity at a centreline location in the wake is measured and used for the feedback control. The actuation (blowing/suction) is provided to the flow at the upper and lower slots on the cylinder surface near the separation point based on the P, PI or PD control. The sensing location is varied from 1d to 4d from the centre of the cylinder. Given each sensing location, the optimal proportional gain in the sense of minimizing the sensing velocity fluctuations is obtained for the P control. The addition of I and D controls to the P control certainly increases the control performance and broadens the effective sensing location. The P, PI and PD controls successfully reduce the velocity fluctuations at sensing locations and attenuate vortex shedding in the wake, resulting in reductions in the mean drag and lift fluctuations. Finally, P controls with phase shift are constructed from successful PI controls. These phase-shifted P controls also reduce the strength of vortex shedding, but their results are not as good as those from the corresponding PI controls.     

Hypersonic flow of a viscous radiating gas over blunted cones

Employing the equations describing the dynamics of a viscous radiating gas, we examine the hypersonic flow over blunted cones under conditions of re-entry into the earth's atmosphere. The problem is solved by means of numerical methods.     

Three‐dimensional viscous flow over rotating periodic structures

The three‐dimensional Stokes flow in a periodic domain is examined in this study. The problem corresponds closely to the flow inside internal mixers, where the flow is driven by the movement of a rotating screw; the outer barrel remaining at rest. A hybrid spectral/finite‐difference approach is proposed for the general expansion of the flow field and the solution of the expansion coefficients. The method is used to determine the flow field between the screw and barrel. The regions of elongation and shear are closely examined. These are the two mechanisms responsible for mixing. Besides its practical importance, the study also allows the assessment of the validity of the various assumptions usually adopted in mixing and lubrication problems. Copyright © 2003 John Wiley & Sons, Ltd.     

Nonlinear instability of mixed convection flow over a horizontal cylinder

Vortex shedding and instability of the mixed convection flow over a horizontal cylinder have been studied numerically for different flow directions with respect to the direction of buoyancy—with emphasis on assisting and opposing flows. Nonlinear instability and vortex shedding have been investigated with the help of the Landau equation—that is modified to identify critical Reynolds and Richardson numbers. Effects of flow direction are studied for a representative Richardson number. The average Nusselt number is estimated for all the cases to represent average heat transfer.     

Convective heat transfer in transverse gas flow over a cylinder

A method is described for studying convective heat transfer in transverse flow over a wire, from the temperature dependence of the heat transfer coefficients. A formula has been obtained for calculating convective heat transfer in gas flow over a. wire, for temperature differences up to 1000°C and Re values from 0.14 to 2.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 78–83, July, 1971.     

Modeling flow of a viscous liquid over a blunt plane plate

A calculation technique and results are presented for characteristics of detached flow on the lateral surface of a blunted planar plate, based on the Navier-Stokes equation and a two-parameter turbulence model.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 1, pp. 7–12, July, 1989.     

Unsteady viscous flow in the vicinity of an axisymmetric stagnation point on a circular cylinder

An analysis is presented to investigate the unsteady fluid dynamic characteristics of an axisymmetric stagnation flow on a circular cylinder performing a harmonic motion in its own plane. Different solutions are presented for the small and high values of the reduced frequency of oscillation. The range of Reynolds numbers considered was from 0.01 to 100. Numerical solutions for the velocity functions are presented and the wall values of the velocity gradients are tabulated.     

Laminar boundary-layer separation over a circular cylinder in uniform shear flow

Summary By appealing to the classical boundary-layer theory, the present paper investigates the effect of the freestream shear on the separation of the laminar boundary layer around a circular cylinder. It is shown that on the side of the cylinder with faster freestream velocity the location of the separation point (point of vanishing wall shear) is virtually unaffected by the freestream shear, while on the other side of the cylinder a critical shear rate is observed. Below this critical value, separation occurs typically at the rear surface of the cylinder and is found to shift towards the downstream direction with increasing freestream shear. Above the critical shear rate, the boundary layer separates from the windward side of the cylinder. Further increase of the freestream shear then causes the separation point to move towards the upstream direction. The present findings may have important implication on the issue regarding to the orientation of the lift force exerting on the cylinder.