A Viscous Velocity Potential/Stream Function

The motion of fluids presents interesting phenomena including flow separation, wakes, turbulence etc. The physics of these are enshrined in the continuity equation and the NSE. Therefore, their studies are important in mathematics and physics. They also have engineering applications. These studies can either be carried out experimentally, numerically, or theoretically. Theoretical studies using classical potential theory (CPT) have some gaps when compared to experiments. The present publication is part of a series introducing refined potential (RPT) that bridges these gaps. It leverages experimental observations, physical deductions and the match between CPT and experimentally observed flows in the theoretical development. It analytically imitates the numerical source/vortex panel method to describe how wall bounded eddies in a three-dimensional cylinder crossflow are linked to the detached wake eddies. Unlike discrete and arbitrary vortices/sources on the cylinder surface whose strengths are numerically determined in the panel method, the vortices/sources/sinks in RPT are mutually concentric and continuously distributed on the cylinder surface. Their strengths are analytically determined from CPT using physical deductions starting from Reynolds number dependence. This study results in the incompressible Kwasu function which is a Eulerian velocity potential/stream function that captures vorticity, boundary layer, shed wake vortices, three-dimensional effects, and turbulence. This Eulerian Kwasu function also theorizes streaklines. The Lagrangian form of the function is further exploited to obtain flow pathlines.

NON-UNIFORM RATIONAL B-SPLINE BASED ISO-GEOMETRIC ANALYSIS FOR A CLASS OF HYDRODYNAMIC PROBLEMS

Herein, we present the design and development of a ‘Non-uniform Rational B-spline (NURBS)’ based iso-geometric approach for the analysis of a number of ‘Boundary Value Problems (BVPs)’ relevant in hydrodynamics. We propose a ‘Potential Function’ based ‘Boundary Element Method (BEM)’ and show that it holds the advantage of being computationally efficient over the other known numerical methods for a wide range of external flow problems. The use of NURBS is consistent, as inspired by the ‘iso-geometric analysis’, from geometric formulation for the body surface to the potential function representation to interpolation. The control parameters of NURBS are utilised and they have been explored to arrive at some preferable values and parameters for parameterization and the knot vector selection. Also, the present paper investigates the variational strength panel method, and its computational performance is analyzed in comparison with the constant strength panel method. The two variations have been considered, e.g. linear and quadratic. Finally, to illustrate the effectiveness and efficiency of the proposed NURBS based iso-geometric approach for the analysis of boundary value problems, five different problems (i.e. flow over a sphere, effect of the knot vector selection on analysis, flow over a rectangular wing section of NACA 0012 aerofoil section, performance of DTMB 4119 propeller (un-skewed), performance of DTNSDRC 4382 propeller (skewed)) are considered. The results show that in the absence of predominant viscous effects, a ‘Potential Function’ based BEM with NURBS representation performs well with very good computational efficiency and with less complexity as compared to the results available from the existing approaches and commercial software programs, i.e. low maximum errors close to 110−3 , faster convergence with even up to 75 % reduction in the number of panels and improvements in the computational efficiency up to 32.5 % even with low number of panels.

Application of Various Spectral Fatigue Analysis Methods for Ship Structures

The Spectral Fatigue Analysis (SFA) is a comprehensive fatigue life assessment method. The SFA is performed by following a systematic process at the onset of hydrodynamic analysis, structural analysis, and spectral analysis. Hydrodynamic analysis and finite element based structural analysis are numerically intense stages, and require a substantial amount of computational time and resources. In the present paper, some simplifications are imposed on individual stages to perform the SFA analysis in a practical time scale but not compromising on the underlying theoretical assumptions. Three distinct methods (semi-analytical formulation, 2D strip method, and 3D panel method) have been used to compute the wave-induced loads while the structural responses are obtained using the beam theory based formulations (in case of semi-analytical and 2D strip method) and finite element analysis (in case of 3D panel method). Fatigue damages are calculated using these methods at the selected locations of a bulk carrier and results are compared with each other. It has been shown that the first two methods (semi-analytical and 2D strip based methods) are quick and efficient and can be used in initial design assessment or identifying the fatigue prone locations. The third method is realistic and accurate and can be used in case of a comprehensive assessment of the design.

Stability Study Using Numerical Analysis for the Panel Method Applied to the Weathered Rock Section below the National Highway

In sections with poor ground conditions, it is difficult to apply the commonly used NATM tunnel method; thus, applications of the non-open cut tunneling method are increasing. This section is a tunnel crossing area under the national road in which the Panel method is to be applied to the section where a deeply buried layer and a loose weathered soil layer are distributed. Therefore, the stability of the upper road, the amount of settlement, and the stability of the tunnel structure were reviewed for each construction stage by using MIDAS GTX. Through the installation of measuring instruments in the tunnel area, the results of the numerical analysis were reviewed and the stability during and after construction was evaluated. Therefore, it is likely that the Panel method is an appropriate countermeasure in the downtown area and in areas with soft ground sections where the application of the general tunnel excavation method is difficult.

Pengaruh Jumlah Unit Usaha, Investasi Dan Output UMKM Terhadap Kemiskinan

This study aims to analyzed the effect of the number of business units, investment and output of MSMEs on poverty in West Sumatra. The object of this research is the Regency / City in West Sumatra Province. This study uses the Least Square Panel method to see the effect of independent variables on the dependent variable as seen from the Regency / City of West Sumatra Province from 2014 to 2017 which was collected through documentation from related government agencies. This study uses a Random Effect Model (REM) approach. The results of this study indicate that (1) the number of business units, investment and output of MSMEs does not have a significant effect together on poverty in West Sumatra Province. (2) The number of business units does not have a significant effect on poverty in West Sumatra. (3) Investment does not have a significant effect on poverty in West Sumatra. (4) UMKM output has a significant effect on poverty in West Sumatra. From the results of the study, it is suggested that all subjects pay more attention to these factors to alleviate poverty and improve community welfare, be aware of the akak of poverty.Keywords : business unit, investment, umkm output, poverty