• Journal of computational fluids engineering
• /
• v.10 no.1
• /
• pp.45-50
• /
• 2005

A fundamental understanding of the flow around the wind turbine is important to investigate the performance of new type of wind turbine. This study presents the simulation of three dimensional flow fields around the Darius wind turbine as an example. Incompressible Navier-Stokes equations are used for this simulation. The rotating coordinate system that rotates in the same speed of the turbine is used in order to simplify the boundary condition on the blades. Additionally, the boundary fitted coordinate system is employed in order to express the shape of the blades precisely. Fractional step method is used to solve the basic equations. Third order upwind scheme is chosen for the approximation of the non-linear terms since it can compute the flow field stably even at high Reynolds number without any turbulence models. The flow fields obtained in this study are highly complex due to the three dimensionality and are visualized effectively by using the technique of the computer graphics.

• 한국전산유체공학회:학술대회논문집
• /
• 2003.10a
• /
• pp.230-231
• /
• 2003

Two and three-dimensional flows around a cross-flow wind turbine are investigated by the numerical simulation. The turbine studied in this paper has cylindrical shape with many small blades along its periphery. Incompressible Navier-Stokes equation is used for this simulation. A rotating coordinate system, which rotates at the same speed of the turbine, is used in order to simplify the boundary conditions on the blades of the turbine. Additionally, a boundary fitted coordinate system is employed in order to express the shape of the blades precisely. A third order upwind scheme is chosen for the approximation of the non-linear terms. When the number of blades is about 10, the highest torque is obtained.

• Communications of Mathematical Education
• /
• v.23 no.3
• /
• pp.625-642
• /
• 2009

In the school mathematics the concept of tangent is introduced in several steps in suitable contexts. Students are required to reflect and revise their concepts of tangent in order to apply the improved concept to wider range of contexts. In this paper we consider the tangent as the optimal linear approximation to a curve at a given point and make three discussions on pedagogical aspects of it. First, it provides a method of finding roots of real numbers which can be used as an application of tangent. This may help students improve their affective variables such as interest, attitude, motivation about the learning of tangent. Second, this concept reflects the modern point of view of tangent, the linear approximation of nonlinear problems. Third, it gives precise meaning of two tangent lines appearing two sides of a cusp point of a curve.

• Communications of the Korean Institute of Information Scientists and Engineers
• /
• v.1 no.1
• /
• pp.72-74
• /
• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• Smart Structures and Systems
• /
• v.16 no.1
• /
• pp.1-26
• /
• 2015

Minimizing construction cost and reducing seismic damage are two conflicting objectives in the design of any new structure. In the present work, we try to develop a framework in order to solve the optimum performance-based design problem considering the construction cost and the seismic damage of steel moment-frame structures. The Park-Ang damage index is selected as the seismic damage measure because it is one of the most realistic measures of structural damage. The non-dominated sorting genetic algorithm (NSGA-II) is employed as the optimization algorithm to search the Pareto optimal solutions. To improve the time efficiency of the proposed framework, three simplifying strategies are adopted: first, simplified nonlinear modeling investigating minimum level of structural modeling sophistication; second, fitness approximation decreasing the number of fitness function evaluations; third, wavelet decomposition of earthquake record decreasing the number of acceleration points involved in time-history loading. The constraints of the optimization problem are considered in accordance with Federal Emergency Management Agency's (FEMA) recommended seismic design specifications. The results from numerical application of the proposed framework demonstrate the efficiency of the framework in solving the present multi-objective optimization problem.

• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.1007-1011
• /
• 2003

In this paper, a design of I-PDA controller by CDM to control a flow process whose structure is first order lag plus a dead time is introduced. The factor of dead time of the process is approximated by second order Pade approximation in order to get a third order system. The simulations show that both of the transient and steady state specifications can be fulfilled. However, the transient response of the I-PDA control system still has long rise time. Then, a feedforward controller (FFC) with two adjustable parameters and one derivative time is introduced into I-PDA control system for improving the speed of the system response. It is shown, from the simulation results, that the performance of the I-PDA control system with suitable FFC has shorter rise time and no overshoot, while settling time remains almost the same. The performance comparison of the proposed control system with the PI control system with and without FFC is also made.

• The Korean Journal of Rheology
• /
• v.10 no.4
• /
• pp.202-216
• /
• 1998

Improved version of previous 'Orthotropic' closure approximation, termed 'ORW' has been numerically developed using new homogeneous flow data. Previous 'Orthotropic' closure approximation, i.e., ORF or ORL showed non-physical oscillation for interaction coefficient $C_1$<0.001 at simple shear flow. It also shows non-physcial oscillation and under-prediction compared with 'Distribution Function Calculation' at non-homogeneous flow of center-gated disk. These phenomena are mainly due to the flow data of 'Distribution Function Calculation' which were used for least-square optimization. ORW obtained by fitting flow data of low interaction coefficient does not show non-physical oscillation and results in reasonably good behaviors at non-homogeneous flows as well as homogeneous flows. Fitting function forms have not been found to improve overall behaviors. It has been found that considering all the eigenvalues of orientation tensor (including the third eigenvalues) might end up with a better closure approximation than just considering the first and second eigenvalues. It is, however, very important and yet difficult to select appropriate function forms of eigenvalues. Numerical simulation including coupling and in-plane velocity gradient effects were performed for injection mold filing process with a film-gated strip and a center-gated disk using ORW and various other closure approximations for comparisons. Although ORW is in excellent agreement with 'Distribution Function Calculation', the predicted results seem to have consistent error in comparison with experimental data. The diffusivity term with constant interaction coefficient might have to be further investigated in order to accurately describe orientation states.

• Ocean Systems Engineering
• /
• v.2 no.3
• /
• pp.229-238
• /
• 2012

We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

• Coupled systems mechanics
• /
• v.1 no.2
• /
• pp.155-163
• /
• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.6 no.3
• /
• pp.12-23
• /
• 1969

In this paper, the current distribution on a 6 points fed linear antenna is theoretically introduced. The antenna that we call the 6 points fed linear antenna is an antenna which are fed by emf E1 at the first two points, emf E2 at the second two points, and emf E3 at the third two points. symmetrical with respect to the center. In this analysis, Hallens theory has been extended with the approximation in the same order.