Cylinder In Viscous Fluid Research Articles

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.

Radiation Hydrodynamics of Floating Vertical Cylinder in Viscous Fluid

Fully nonlinear axisymmetric viscous flow due to heave oscillation of a surface-piercing vertical cylinder is analyzed using a finite-difference method based on curvilinear coordinates. Of significance to numerical modeling is the present finding that the free-slip condition used to model the movement of the contact line affects neither the overall flow nor the hydrodynamic pressure force acting on vertical cylinder. The viscous-flow results are compared with fully nonlinear inviscid-flow results, which are obtained using a mixed Eulerian-Lagrangian formulation, to contrast the effects of viscosity on the flow field, hydrodynamic force, and radiating surface waves. New results are presented for a range of parameters to illustrate physical mechanisms of the inception and evolution of vertical structures due to body motion in a free surface and their effects on the hydrodynamic force.

Structural scaling and functional design of the cercal wind-receptor hairs of cricket

We have estimated the intrinsic mechanical parameters of cricket cercal wind-receptor hairs. The hairs were modeled as an inverted pendulum, and mechanical parameters of the equation of motion were determined from data given by a systematic measurement of mobility by the least-square error method. The theoretical torque which turns the hair shaft is given by the drag force due to the moving air. The drag force is given by the method of Stokes' mechanical impedance of an oscillating cylinder in viscous fluid. The effect of the boundary layer in which air is stagnating on the substrate surface is also taken into account. The moment of inertia of a hair shaft shows a clear length dependency to the power of 4.32 of the hair length. The torsional resistance within the hair base and the stiffness of hair-supporting spring also show clear length dependencies to the power of 2.77 and 1.67, respectively. The torsional resistance within the hair base is so large that the hair is a strongly damped non-oscillatory second-order system. The large resistance within the hair base represents an efficient energy absorption by the sensory cell. The resistance seems to match with the source impedance, i.e., the frictional resistance at the site of air-hair contact. The impedance matching provides the condition of maximum power transmission from the moving air to the sensory cell. Structural scaling is discussed in relation to the functional scaling of the frequency-range fractionation of the mechanical filter array with a common biological design.

Application of Bipolar Coordinates to the Two-Dimensional Creeping Motion of a Liquid. II. Some Problems for Two Circular Cylinders in Viscous Fluid

The bipolar coordinate solution of the two-dimensional Stokes equations is applied to flows around two circular cylinders. It is proved that there are three cases which this kind of solutions can describe. Solutions are presented for a cylinder revolving eccentrically in a cylindrical frame, a cylinder in the neighborhood of a plane wall and two cylinders in rotary motion as a pair.

Charts and Tables for Flow produced by Circular Motion of Circular Cylinder in Viscous Fluid

Charts and Tables for Flow produced by Circular Motion of Circular Cylinder in Viscous Fluid

Charts and Tables for Flow produced by Steady Rotations of Elliptic Cylinder in Viscous Fluid

Charts and Tables for Flow produced by Steady Rotations of Elliptic Cylinder in Viscous Fluid

On the Uniform Circular Motion of the Center Line of Rotating Circular Cylinder in Viscous Fluid

On the Uniform Circular Motion of the Center Line of Rotating Circular Cylinder in Viscous Fluid

On the Slow Steady Rotation of Cylinder in Viscous Fluid, Part III

On the Slow Steady Rotation of Cylinder in Viscous Fluid, Part III

The Discussion of Steady Eccentric Rotation of Circular Cylinder in Viscous Fluid

The Discussion of Steady Eccentric Rotation of Circular Cylinder in Viscous Fluid