Divergence-driven oscillations in a flexible-channel flow with fixed upstream flux

We consider flow in a finite-length channel, one wall of which contains a membrane under longitudinal tension. The upstream flux and downstream pressure are prescribed and an external linear pressure distribution is applied to the membrane such that the system admits uniform Poiseuille flow as a steady solution. The system is described using a one-dimensional model that accounts for viscous and inertial effects. A linear stability analysis reveals that the uniform state is unstable to static (or divergent) and oscillatory instabilities. Asymptotic analysis in the neighbourhood of a Takens–Bogdanov bifurcation point shows how, when the downstream rigid section of the channel is not substantially longer than the membrane, an oscillatory mode arises through an interaction between two static eigenmodes. Perturbations to the uniform state exhibit the dynamics of a weakly dissipative Hamiltonian system for which low-frequency self-excited oscillations are forced by the divergent instability of two nearby steady solutions, before ultimately growing to large amplitudes. Simulations show that the subsequent dynamics can involve slamming motion in which the membrane briefly comes into near-contact with the opposite rigid wall over short length scales.

Theoretical Analysis of the Sole Plate of Semi-Rigid Light Steel Column Footings on the Basis of Winkler Model of Elastic Foundation Beam

To obtain the pressure distribution model on the sole plate of semi-rigid light steel column footing, the deflection formulas of beams with free ends on elastic foundation subjected to arbitrarily concentrated load and arbitrarily trapezoidal load were developed by applying the Winkler model of elastic foundation beam and initiate-parameter expressions of deformation and internal force by presetting boundary condition and calculating with Maple software. The sole plate of semi-rigid square steel tube column footing was converted into elastic foundation beam which is supported by concrete foundation, the mechanical model of the sole plate subjected to eccentric load was obtained, and the theoretical solution of pressure distribution on the sole plate was presented. Then the theoretical solution was compared with the numerical solution via an example. The results show that the two solutions meet well with each other, and there is much great difference between the pressure distribution on sole plate of semi-rigid light steel column footing and the linear pressure distribution model in common use. As a result, the semi-rigid column footing stiffness would be overestimated by using linear pressure distribution model. The fruits presented in this paper are useful and convenient to the design of semi-rigid light steel column footing.

Statistical Modeling of Rarefied Gas Channel Flows

Lattice Boltzmann method (LBM) and direct simulation Monte Carlo (DSMC) method are used for analysis of moderate Knudsen number phenomena. Simulation results are presented for pressure-driven isothermal rarefied channel flow at various pressure ratios. Analytical equations for non-linear pressure distribution and velocity profiles along the channel axis are used to verify the present LBM and DSMC results. We conclude that the LBM method can be used as an alternative model to DSMC simulations.

Theoretical Calculations of the Flow Around a Rotating Circular Cylinder Placed in a Uniform Flow

The rotation of a circular cylinder placed in a uniform flow is assumed to add a circulation to the flow around the cylinder proportional to the product of the angular velocity of the cylinder and the front area between upper and lower separation points. Adding the velocity due to this induced circulation to the base velocity distribution of the non-rotating cylinder the new velocity distribution on the rotating cylinder is formed. Thwaites’ method is then used to calculate the laminar boundary layer on the upper and on the lower sides of the cylinder. The stagnation point, and the upper and lower separation points are also calculated at different values of rotational speed. The calculated lift and drag coefficients using a linear pressure distribution on the wake part of the cylinder with the calculated pressure dstribution on the front part between the two separation points show the same trend as the measured values. The torque coefficient is also calculated to estimate the necessary power required to rotate the cylinder to produce the needed lift.