Stationary solutions of incompressible viscous flow in a wall-driven semi-circular cavity

Stationary numerical solutions of incompressible viscous flow inside a wall-driven semicircular cavity are presented. After a conformal mapping of the geometry, using a body-fitted mesh, the Navier-Stokes equations are solved numerically. The stationary solutions of the flow in a wall-driven semi-circular cavity are computed up to Re = 24000. The present results are in good agreement with the published results found in the literature. Our results show that as the Reynolds number increases, the sizes of the secondary and tertiary vortices increase, whereas the size of the primary vortex decreases. At large Reynolds numbers, the vorticity at the primary vortex centre increases almost linearly stating that Batchelor’s mean-square law is not valid for wall-driven semi-circular cavity flow. Detailed results are presented and also tabulated for future references and benchmark purposes.

CFD Simulation for Estimating Efficiency of PBCF Installed on a 176K Bulk Carrier under Both POW and Self-Propulsion Conditions

In this paper, the efficiency of Propeller Boss Cap Fins (PBCF) installed at the bulk carrier was estimated under both Propeller Open Water (POW) and self-propulsion conditions. For this estimation, virtual model-basin tests (resistance, POW, and self-propulsion tests) were conducted through Computational Fluid Dynamics (CFDs) simulation. In the resistance test, the total resistance and the wake distribution according to ship speed were investigated. In the POW test, changes of thrust, torque coefficient, and open water efficiency on the propeller according to PBCF installation were investigated. Finally, the International Towing Tank Conference (ITTC) 1978 method was used to predict the effect of PBCF installation on self-propulsive coefficient and brake horsepower. For analyzing incompressible viscous flow field, the Reynolds-Averaged Navier–Stokes (RANS) equation with SST k-ω turbulence model was calculated using Star-CCM+ 11.06.010-R8. All simulation results were validated by comparing the results of model tests conducted at the Korea Research Institute of Ships and Ocean Engineering (KRISO). Consequently, for the self-propulsion test with the PBCF, a 1.5% reduction of brake horsepower was estimated in the simulation and a 0.5% reduction of the brake horsepower was estimated in the experiment.

Effects of the Advance Ratio on the Evolution of Propeller Wake

This study numerically carried out the propeller open water test (POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the Κ-ω SST model. Numerical simulations were performed at wide range of advance ratios. A great difference of velocity magnitude between the inner region and the outer region of the slipstream tube forms the thick and large velocity gradient which originates from the propeller tip and develops along the downstream. Eventually, the strong shear layer appears and plays the role of the slipstream boundary. As the advance ratio increases, the vortical structures originated from the propeller tips quickly decay. The contraction of the vortices trace is considerable with decreasing the advance ratio.

A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid

A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result proven in [M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations 32 2007, 7–9, 1345–1371], that the disk will never touch the boundary of the domain in finite time. Anisotropic, continuous piecewise linear finite elements are used for the space discretization, the Euler scheme for the time discretization. The adaptive criteria are based on a posteriori error estimates for simpler problems.

Global Stability Analysis on the Spiral-Vortex Mode in the Confined Cavity Flow Between Rotating and Stationary Disks

Global stability analysis (GSA) is applied to a 3D confined cavity flow between rotating and stationary disks (viz., rotor and stator). The Arnoldi method extended for incompressible viscous flow is used together with the eigenvalue spectrum conversion to solve the eigenvalue problem of the GSA. As a first step, the GSA is conducted in an axisymmetric flow, and circular vortices are obtained as eigen modes. Then, the GSA is applied to a flow with circular vortex at a higher Reynolds number, and eigen vectors of spiral vortex are obtained. The result suggests that the GSA shows unstable flows after transition of the baseflow. However, it is necessary to reconsider the convergence of the eigenvalues for the parameters of Arnoldi method.

Grid-Free Modelling Based on the Finite Particle Method for Incompressible Viscous Flow Problems

In this paper, we present a grid-free modelling based on the finite particle method for the numerical simulation of incompressible viscous flows. Numerical methods of interest are meshless Lagrangian finite point scheme by the application of the projection method for the incompressibility of the Navier–Stokes flow equations. The moving least squares method is introduced for approximating spatial derivatives in a meshless context. The pressure Poisson equation with Neumann boundary condition is solved by the finite particle method in which the fluid domain is discretized by a finite number of particles. Also, a continuous particle management has to be done to prevent particles from moving into configurations problematic for a numerical approximation. With the proposed finite particle technique, problems associated with the viscous free surface flow which contains the study on the liquid sloshing in tanks with low volumetric fluid type, solitary waves movement, and interaction with a vertical wall in numerical flume as well as the vortex patterns of the ship rolling damping are circumvented. These numerical models are investigated to validate the presented grid-free methodology. The results have revealed the efficiency and stability of the finite particle method which could be well handled with the incompressible viscous flow problems.