On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation

Modern engineering technology often involves the physical application of heat and mass transfer. These processes are associated with the creeping motion of a relatively homogeneous swarm of small particles, where the spheroidal geometry represents the shape of the embedded particles within such aggregates. Here, the steady Stokes flow of an incompressible, viscous fluid through an assemblage of particles, at low Reynolds numbers, is studied by employing a particle-in-cell model. The mathematical formulation adopts the Kuwabara-type assumption, according to which each spheroidal particle is stationary and it is surrounded by a confocal spheroid that creates a fluid envelope, in which the Newtonian fluid moves with a constant velocity of arbitrary orientation. The boundary value problem in the fluid envelope is solved by imposing non-slip conditions on the surface of the spheroid, which is also considered as non-penetrable, while zero vorticity is assumed on the fictitious spheroidal boundary along with a uniform approaching velocity. The three-dimensional flow fields are calculated analytically for the first time, in the spheroidal geometry, by virtue of the Papkovich–Neuber representation. Through this, the velocity and the total pressure fields are provided in terms of a vector and the scalar spheroidal harmonic potentials, which enables the thorough study of the relevant physical characteristics of the flow fields. The newly obtained analytical expressions generalize to any direction with the existing results holding for the asymmetrical case, which were obtained with the aid of a stream function. These can be employed for the calculation of quantities of physical or engineering interest. Numerical implementation reveals the flow behavior within the fluid envelope for different geometrical cell characteristics and for the arbitrarily-assumed velocity field, thus reflecting the different flow/porous media situations. Sample calculations show the excellent agreement of the obtained results with those available for special geometrical cases. All of these findings demonstrate the usefulness of the proposed method and the powerfulness of the obtained analytical expansions.

Inversion method for measuring multi-hole probe surface pressure distribution of supersonic compressible atmospheric flow field

The conventional method of measuring a multi-hole probe is based on Bernoulli’s equation and suffers from certain model errors. A computational fluid dynamics (CFD)-based method was used in this study to reduce the theoretical error and establish a parametric model of the surface pressure of a spherical multi-hole pressure probe for measuring compressible flow fields at supersonic velocities. A flow field inversion method based on the parametric model is proposed herein. Numerical simulations were conducted to validate the proposed method. The experiment results show that in the compressible atmospheric flow field within Mach 1.2–1.7, the measurement errors of the inversion method were 1.3% and 2.35% for velocity and angle, respectively, thus verifying the feasibility of the method. Thus, a new method of measuring multi-hole pressure probe atmospheric flow fields was demonstrated.

On the behavior of nonlinear hydrodynamic coefficients of a submerged cylinder beneath the water surface

This study aims at numerically exploring the behavior of flow fields and nonlinear hydrodynamic coefficients of a horizontal cylinder beneath the free surface flow considering the effects of nonlinear surface waves and various cylinder shapes. The computational model is based on two-dimensional incompressible Navier-Stokes solvers along with the treatment of the free surface flow using the volume of fluid method. The effect of the turbulent flow is also considered by using the shear stress transport turbulence model. The simulation result of a benchmark case study of the submerged cylinder is first validated with available experiment data, where a mesh convergence analysis is also performed. Afterward, the flow fields and hydrodynamic force coefficients around the cylinder surface are analyzed, and the influences of various cylinder shapes and Reynolds numbers on the hydrodynamic coefficients are investigated. A state diagram representing the hydrodynamic behavior including stable and unstable stages is finally proposed; this is an important criterion for the practice design of submerged civil structures under the free surface flow.