• Journal of Ocean Engineering and Technology
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• v.25 no.5
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• pp.9-14
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• 2011

The divergence-free finite elements introduced in this paper are derived from Hermite functions, which interpolate stream functions. Velocity bases are derived from the curl of the Hermite functions. These velocity basis functions constitute a solenoidal function space, and the gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into its solenoidal and irrotational parts, and the decoupled Navier-Stokes equations are then projected onto their corresponding spaces to form appropriate variational formulations. The degrees of the Hermite functions we introduce in this paper are bi-cubis, quartic, and quintic. To verify the accuracy and convergence of the present method, three well-known benchmark problems are chosen. These are lid-driven cavity flow, flow over a backward facing step, and buoyancy-driven flow within a square enclosure. The numerical results show good agreement with the previously published results in all cases.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.111-116
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• 2004

An experiment was carried out to confirm the validity of time series evaluation of supersonic mixing condition by using catalytic reaction on a platinum wire. Geseous hydrogen was injected parallel to supersonic freestream (M$\infty$ $\approx$ 1.81) from a slit injector, which was located at backward facing step. Time series condition of supersonic mixing was evaluated by using W-type probe which has a platinum wire and reference wire (nickel wire). The evaluation was by simultaneously measuring each electric circuit which kept the temperature of wire constant. Investigations were also conducted for helium, air and no secondary injectant cases to compare with the hydrogen injectant case. The results indicated that it was possible to measure the time series behavior of air and hydrogen supersonic mixing layer or coherent motion of turbulence by using this evaluation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.3
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• pp.1015-1027
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• 1996

In this paper, a numerical procedure for the calculation of the incompressible Navier-Stokes equations in a generalized nonorthogonal body fitted coordinate system is proposed and is validated through three test problems. Present numerical procedure derives the pressure equation by using the pressure substitution method on the regular grid system, and discretized momentum equations are based on the covariant velocity components. Cavity flow, backward facing step flow, and two dimensional channel flow with a sinusoidal wavy wall are chosen as three test problems. Numerical solutions obtained by present procedure shows a good agreement with previous numerical and/or experimental results. Convergence rate is also satisfactory.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.4
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• pp.578-586
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• 2002

Flow structures around a rectangular prism have been investigated by using a PIV(Particle Image Velocimetry) technique. A thick turbulent boundary layer was generated by using spires arid roughness elements. The boundary layer thickness, displacement thickness and momentum thickness were 650mm, 117.4mm and 78mm, respectively. The ratio between the model height(40mm) and the boundary layer thickness H/$\delta$, was 0.06. The Reynolds number based on the free stream velocity and the height of the model was 7.9$\times$10$^3$. The PIV measurements were performed at three different wall normal planes. Three recirculation regions at forward facing step, top of the roof and backward facing step are clearly seen and show three dimensional features. Dramatic changes of flow patterns are observed in the wake regions in the different spanwise wall normal planes. Instead of reattachment and recirculation zone, rising streamlines are depicted at the normal planes near the side wall due to the interaction with a rising horse shoe vortex. The peak of turbulent kinetic energy occurs at the separation bubble on top of the roof and the magnitude is 2.5 times higher compared with that of the wake region.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.3
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• pp.467-476
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• 2000

An unsteady numerical simulation was performed for locally-forced separated and reattaching flow over a backward-facing step. The local forcing was given to the separated and reattaching flow by means of a sinusoidally oscillating jet from a separation line. A version of the $k-{\varepsilon}-f_{\mu}$ model was employed, in which the near-wall behavior without reference to distance and the nonequilibrium effect in the recirculation region were incorporated. The Reynolds number based on the step height (H) was fixed at $Re_H=33000$, and the forcing frequency was varied in the range $0{\leq}St_H{\leq}2$. The predicted results were compared and validated with the experimental data of Chun and Sung. It was shown that the unsteady locally-forced separated and reattaching flows are predicted reasonably well with the $k-{\varepsilon}-f_{\mu}$ model. To characterize the large-scale vortex evolution due to the local forcing, numerical flow visualizations were carried out.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.8
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• pp.1104-1111
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• 2000

Erosion-corrosion in a pipe system often occurs at fittings, valves, and weld beads where flow separation and reattachment yield high turbulence intensity. Thus identifying their correlations would be the first step towards resolving the erosion-corrosion problems associated with industrial applications. Bremhorst of the Univ. of Queensland, Australia, proposed that a rotating cylinder with surface roughness (two backward-facing steps periodically mounted on a circular cylinder) be an economical and tractable tool which can generate extreme flow conditions for erosion-corrosion study. In this work, DNS has been carried out for turbulent flows around the same rotating cylinder as his experimental apparatus. Our result shows that a region of intense turbulence intensity and high wall-shear stress fluctuation is formed along the cylinder surface in the recirculating region behind the step, where high mass-transfer capacity is also experimentally observed. Since corrosion is mass-transfer controlled, our finding sheds light on the direction of future corrosion research.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.2
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• pp.446-455
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• 1994

An experimental study is conducted for the turbulent recirculating flow behind a backward-facing step when the oscillating jet is issued sinusoidally through a thin slit at the separation edge. Two key parameters are dealt with in the present experiment, i.e., the amplitude of forcing and the forcing frequency. The Reynolds number based on the step height is varied from 25,000 to 35,000. In order to investigate the effect of local forcing, turbulent structures are scrutinized for both the flow of forcing and the flow of no forcing. The growth of shear layer with a local forcing is larger than that of no forcing. The influence of a local forcing brings forth the decrease of reattachment length and the particular frequency gives a minimum reattachment length. The most effective frequency depends on the non-dimensional frequency, St/sub .theta./, based on the momentum thickness at the separation point. A comparative study leads to the conclusion that the large-scale vortical structure is strongly associated with the forcing frequency and the natural flow instability.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.12
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• pp.1087-1092
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• 2010

A micro 3D-PTV system has been constructed using a single camera system. Two viewing holes were created behind the object lens of the microscopic system to construct a stereoscopic viewing image. A hybrid recursive PTV algorithm was used. A concept of epipolar line was adopted to eliminate many spurious candidates. Three-dimensional velocity vector fields were obtained by calculating the three-dimensional displacements of particles that were identified as being identical. The system consists of a laser light source (Ar-ion, 500 mW), one high-definition camera ($1028{\times}1024$ pixels, 500 fps), a circular plate with two viewing holes, and a host computer. The performance of the developed algorithm was tested using artificial images. The characteristic of the vector recovery ratio was investigated for the particle numbers. A micro backward-facing step channel ($H{\times}h{\times}W:\;36{\mu}m{\times}70{\mu}m{\times}3000{\mu}m$) was measured using the developed measurement system. The results were in good qualitative agreement with other results.