• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.35-42
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• 1998

Time marching algorithms applied to compressible Navier-Stokes equation have a convergence problem at low Mach number. It is mainly due to the eigenvalue stiffness and pressure singularity as Mach number approaches to zero. Among the several methods to overcome the shortcomings of time marching scheme, time derivative preconditioning method have been used successfully. In this numerical analysis, we adopted a preconditioner of K.H. Chen and developed a two-dimensional, axisymmetric Navier-Stokes program. The steady state driven cavity flow and backward facing step flow problems were computed to confirm the accuracy and the robustness of preconditioned algorithm for low Mach number flows. And the transonic and supersonic flows insice the JPL axisymmetric nozzle internal flow is exampled to investigate the effects of preconditioning at high Mach number flow regime. Test results showed excellent agreement with the experimental data.

• 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.340-340
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• 2016

불연속 지형을 지나는 천수 흐름의 해석에서 흐름률을 정확하게 계산하기 위하여 계단에 의한 흐름 저항이 지배적인 계단 전면과 그 영향이 비교적 덜한 계단의 윗부분을 구분하여 접근하는 새로운 기법이 제안되었다(Hwang, 2015). 이 기법에 의한 모의 결과는 정확해, 가상의 문제에 대한 3차원 모의 결과, 그리고 실험 결과와 비교하여 대체로 만족스런 일치를 보인 바 있으나, 그 기법의 개선을 위해 보다 다양한 문제에 대해 검토할 필요가 있다. 이 연구에서는 높이 0.01 m인 계단의 전면 및 후면을 지나는 댐 붕괴 흐름에 대한 실험(Kim et al., 2014)에 대해 Hwang (2015)의 새로운 기법을 적용하고 그 결과를 비교하였다. 기존 모형(SGMS)의 결과에 비해 새로운 기법에 의한 결과(STP-TH)는 전면 계단의 앞(P2)과 뒤(P3) 그리고 후면 계단의 앞(P4)과 뒤(P5)에서 상류 저수지의 수심이 0.1 m인 실험 경우에 의한 수위와 더 잘 일치하였다.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1023-1032
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• 2003

The effect of local forcing on the separated flow over a backward-facing step is investigated through hot-wire measurements and flow visualization with multi-smoke wires. The boundary layer upstream of the separation point is laminar and the Reynolds number based on the free stream velocity and the step height is 13800. The local forcing is given from a slit located at the step edge and the forcing signal is always defined when the wind tunnel is in operation. In case of single frequency forcing, the streamwise velocity and the reattachment length are measured under forcing with various forcing frequencies. For the range of 0.010〈S $t_{\theta}$〈0.013, the forcing frequency component of the streamwise velocity fluctuation grows exponentially and is saturated at x/h = 0.75 , while its subharmonic component grows following the fundamental and is saturated at x/h = 2.0. However, the saturated value of the subharmonic is much lower than that of the fundamental. It is observed that the vortex formation is inhibited by the forcing at S $t_{\theta}$ = 0.019 . For double frequency forcing, natural instability frequency is adopted as a fundamental frequency and its subharmonic is superposed on it. The fundamental frequency component of the streamwise velocity grows exponentially and is saturated at 0.5 < x/ｈ < 0.75, while its subharmonic component grows following the fundamental and is saturated at x/ｈ= 1.5 . Furthermore, the saturated value of the subharmonic component is much higher than that for the single frequency forcing and is nearly the same or higher than that of the fundamental. It is observed that the subharmonic component does not grow for the narrow range of the initial phase difference. This means that there is a range of the initial phase difference where the vortex parring cannot be enhanced or amplified by double frequency forcing. In addition, this effect of the initial phase difference on the development of the shear layer and the distribution of the reattachment length shows a similar trend. From these observations, it can be inferred that the development of the shear layer and the reattachment length are closely related to the vortex paring.

• 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.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.48-54
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• 2004

The effects of injector spacing s and injector diameter d on mixing are numerically investigated in supersonic combustor with perpendicular injection behind a backward-facing step. Simulations are reported for airstream Mach number of 2.4. Parameters are changed on following 4 cases to investigate the effects of injector configuration on mixing efficiency $\eta_m$. In the case of varying d or s, dynamic pressure ratio $Rq(=(pu^2)_j/(pu^2)_a)$ is also varied to keep bulk equivalence ratio $\Phi({\oe})Rq.d^2/s)$ constant. (l) Injector spacing s is varied at constant $\Phi$=0.5, 1, 2 for injector diameter d=6mm. In the case of $\Phi$=1, $\eta_m$ has its maximum value at s=24mm. The reason is that increase of $\eta_m$. , by widening spacing at Rq=constant competes with decrease of $\eta_m$ by increasing Rq at s=constant. When spacing is narrow, the flow field of vicinity of injector becomes two-dimensional because adjacent jets interferes each other. By widening spacing, air is easily entrained by three-dimensional effect. This mechanism also appears in the case of $\Phi$=0.5, 2 for d=6mm, and $\eta_m$. reaches its maximum value at s=24mm for $\Phi$=0.5 and at s=42mm for $\Phi$=2. (2) In the case of injector diameter d varied at $\Phi$=1 for s=30mm, $\eta_m$. has its maximum value at d=3mm. The reason is that decrease of $\eta_m$ by increasing injector diameter competes with increase of $\eta_m$ by decreasing Rq at d=constant.(3) In the case of s varied at $\Phi$=0.5, 1,2 for d=3mm, the injector spacing at which mixing efficiency has its maximum value is s= 18mm for $\Phi$=0.5, s=24mm for $\Phi$=1, s=24mm for $\Phi$=2. Therefore it is found that d=3mm and s=24mm can be optimum configuration over a range of $\Phi$=0.5~2.(4) The effect of h on the optimum spacing is investigated. s is varied for d=6mm at step height h=4, 6, 8mm. The simulation results do not show significant change on the step height.

• 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.