Simulation of Sphere’s Motion Induced by Shock Waves

Simulations of experimental results appearing in Jourdan et al. (2007, “Drag Coefficient of a Sphere in a Non-Stationary Flow: New Results,”Proc. R. Soc. London, Ser. A, 463, pp. 3323–3345) regarding acceleration of a sphere by the postshock flow were conducted in order to find the contribution of the various parameters affecting the sphere drag force. Based on the good agreement found between present simulations and experimental findings, it is concluded that the proposed simulation scheme could safely be used for evaluating the sphere’s motion in the postshock flow.

Generalized analytic functions in magnetohydrodynamics

An approach of generalized analytic functions to the magnetohydrodynamic (MHD) problem of an electrically conducting viscous incompressible flow past a solid non-magnetic body of revolution is presented. In this problem, the magnetic field and the body’s axis of revolution are aligned with the flow at infinity, and the fluid and body are assumed to have the same magnetic permeability. For the linearized MHD equations with non-zero Hartmann, Reynolds and magnetic Reynolds numbers ( M , Re and Re m , respectively), the fluid velocity, pressure and magnetic fields in the fluid and body are represented by four generalized analytic functions from two classes: r -analytic and H -analytic. The number of the involved functions from each class depends on whether the Cowling number S= M 2 /( Re m Re ) is 1 or is not 1. This corresponds to the well-known peculiarity of the case S=1. The MHD problem is proved to have a unique solution and is reduced to boundary integral equations based on the Cauchy integral formula for generalized analytic functions. The approach is tested in the MHD problem for a sphere and is demonstrated in finding the minimum-drag spheroids subject to a volume constraint for S<1, S=1 and S>1. The analysis shows that as a function of S, the drag of the minimum-drag spheroids has a minimum at S=1, but with respect to the equal-volume sphere, drag reduction is smallest for S=1 and becomes more significant for S≫1.

Drag coefficient of a sphere in a non-stationary flow: new results

The drag coefficient of a sphere placed in a non-stationary flow is studied experimentally over a wide range of Reynolds numbers in subsonic and supersonic flows. Experiments were conducted in a shock tube where the investigated balls were suspended, far from all the tube walls, on a very thin wire taken from a spider web. During each experiment, many shadowgraph photos were taken to enable an accurate construction of the sphere's trajectory. Based on the sphere's trajectory, its drag coefficient was evaluated. It was shown that a large difference exists between the sphere drag coefficient in steady and non-steady flows. In the investigated range of Reynolds numbers, the difference exceeds 50%. Based on the obtained results, a correlation for the non-stationary drag coefficient of a sphere is given. This correlation can be used safely in simulating two-phase flows composed of small spherical particles immersed in a gaseous medium.

Fluid Slip of Flow Past a Hydrophobic Wall Sphere

The possibility of fluid slip has received considerable attention in recent years. Laminar drag reduction is achieved by using a hydrophobic wall with fluid slip. Fluid slip is closely related to the gas-liquid interface formed at a solid surface with many fine grooves. The friction generated by the solid boundary is modified considerably because the gas-liquid interface provides a zero-shear stress boundary condition. The purpose of this study is to experimentally clarify the flow characteristics and drag reduction of a hydrophobic wall sphere by visualizing flow and by measuring the drag. In addition, the flow patterns were numerically analyzed by applying a wet boundary condition for fluid slip. The flow visualization results showed that the Vortex Loop was not exist at Re &lt; 400 in the hydrophobic wall sphere and the separation point moved downstream compared with that of a conventionally smooth sphere. Drag reduction occurred in the flow and the maximum drag reduction ratio was 14.6% at Re=93.2. In this simulation, the flow patterns for the numerical simulation results agreed with those of the flow visualization results.