The compressible laminar and turbulent viscous flow on a slender body in supersonic speed as well as subsonic speed has been numerically simulated at high angle of attack. The steady and time-accurate compressible thin-layer Navier-Stokes code based on an implicit upwind-biased LU-SGS algorithm has been developed and specifically applied at angles of attack of 20, 30, 40 deg, respectively. The modified eddy-viscosity turbulence model suggested by Degani and Schiff was used to simulate the case of turbulent flow. Any geometric asymmetry and numerical perturbation have not been intentionally or artificially imposed in the process of computation. The purely numerical results for laminar and turbulent cases, however, show clear asymmetric formation of vortices which were observed experimentally. Contrary to the subsonic results, the supersonic case shows the symmetric formation of vortices as indicated by the earlier experiments.

CFD techniques are widely used for the design and development of turbomachinery. The design and performance prediction, evaluation of performace and analysis are all important for the successful development of the machinery. The characteristics of the sturcture and performace of the centrifugal compressor are reviewed for the effective application of CFD techniques. The examples of flow calculations through an impeller and a channel diffuser are presented and phenomenological aspects are discussed. The future research topics of CFD area are also suggested.

비유선형의 물체 주위의 유동은 정체유동, 경계층 박리 및 주기적 와열 생성 등의 복잡한 유동현상이 공존한다. 본 연구에서는 비교적 단순한 형상인 정사각주 주위의 비정상 난류 유동을 2-방정식 와점성 난류모델인 표준 $k-{\varepsilon}$ 모델과 RNG $k-{\varepsilon}$ 모델을 이용하여 예측할 수 있는지를 검증하였다. 정교하게 수행된 최근의 실험과 대와류모사(LES)의 결과를 검증을 위한 비교의 자료로 삼았다. 적절한 난류모델의 선정과 더불어 시간 정확도, 공간 정확도 및 대류항 처리법 등이 해석결과에 미치는 영향도 살펴보았다. 기존의 표준 $k-{\varepsilon}$모델은 정체점 부근에서 난류 운동에너지를 과도하게 생성하는 근본적인 문제점 때문에 실험 및 LES의 결과를 제대로 예측할 수 없었다. 난류운동에너지의 초과 예측에 따른 운동량의 과도한 혼합으로 인해, 항력계수 및 양력계수의 비정상성 뿐 아니라 평균 항력계수도 부정확하게 예측하였다. RNG $k-{\varepsilon}$ 모델을 사용한 경우에는 정체점 주위 유동현상의 예측이 상당히 향상되어 항력계수 및 양력계수의 평균치, 진폭 및 비정상성의 주기 등을 정확하게 예측하는 것이 가능하였다. 그러나 이 경우에도 예측의 정확도가 시간 증분과 격자의 크기 및 대류항 처리법등에 영향을 받으며, 특별히 대류항 처리법에 상당히 민감하게 변하는 것을 알 수 있었다. 향상된 유동예측은 RNG $k-{\varepsilon}$ 모델의 난류에너지 소산율 방정식의 개선된 항이 과도하게 생성된 난류에너지를 정체점 부근에서 제거하기 때문에 가능하다는 것을 알 수 있었다.의 20세 이하 골절 및 탈구가$30.3\%까지 감소하게되어 년도가 증가함에 따라 청장년 층에 비하여 소아골절 및 탈구가 전체적으로 감소하는 경향을 보였다. 스키골절의 부위별 발생빈도는 1990년 이전까지 하지골절 및 탈구가 많았으나 이후 점차 상지의 골절 탈구가 증가하였다 하지에서 가장 많은 골절은 경골 골절이었으며, 경골골절은 회전력에 의한 나선형골절이 $76.5\%로 가장 많았고 년도에 따른 변화는 보이지 않았다. 스키손상의 발생빈도는 초기에 비하여 점차 감소하는 경향을 보였으며, 손상의 특성도 부위별, 연령별로 다양한 변화를 나타내었다.해가능성을 가진 균이 상당수 검출되므로 원료의 수송, 김치의 제조 및 유통과정에서 병원균에 대한 오염방지에 유의하여야 할 것이다. 확인할 수 있었다. 이상의 결과에 의하면 고농도의 유기물이 함유된 음식물쓰레기는 Hybrid Anaerobic Reactor (HAR)를 이용하여 HRT 30일 정도에서 충분히 직접 혐기성처리가 가능하며, 이때 발생된 $CH_{4}$를 회수하여 이용하면 대체에너지원으로 활용 가치가 높은 것으로 판단된다./207), $99.2\%$(238/240), $98.5\%$(133/135) 및 $100\%$ (313)였다. 각각 두 개의 요골동맥과 우내흉동맥에서 부분협착이나 경쟁혈류가 관찰되었다. 결론: 동맥 도관만을 이용한 Off pump CABG를 시행하여 감염의 위험성을 증가시키지 않으면서 영구적인 신경학적 합병증을 일으키지 않았고 좋은 혈관 개존율을 보여주었다. 따라서 동맥 도관을 이용한 Off pump CABG는 관상동맥의 협착의 정도에 따라 효율적으로 시행

In the present study, an improved version of 4-equation low-Reynolds-number 4-equation model is proposed. The equations of the temperature variance ($k_{\theta}$) and its dissipation rate(${\varepsilon}_{\theta}$) are solved, in concert with the equations of the turbulent kinetic energy(k) and its dissipation rate(${\varepsilon}$). In the present model, the near-wall effect and the non-equilibrium effect are fully taken into consideration. The validation of the model is then applied to the turbulent flow behind a backward-facing step and the flow over a blunt body. The predicted results of the present model are compared and evaluated with the relevant experiments.

A numerical computation is carried out to analyse characteristics of flow fields around Air Supported Ships having arbitrary form. The computations are performed in a rectangular grid system with MAC(Marker And Cell) method. The governing equations are represented in a Finite Difference form by forward differencing in time and centered differencing in space except for convection terms. For validation of this numerical analysis method, the computation of flow fields around Catamaran and ACV(Air Cushion Vehicle) with pressure distribution on free surface are done, and that around Surface Effect Ship is also carried out. The results of the computations are compared with the those of existed numerical computation and experimental results with the same condition.

A numerical analysis on the effect of the front shape on the aerodynamic characteristics of HST model is made, using FVM based general purpose 3D Navier-Stokes eq. solver, TURBO-3D program. Numerical solutions are compared with each case of different front shape for HST model. The result shows a good quantitative aerodynamic characteristic tendencies for variation of front shape of HST. Thus it may be used as a basis in the design of the shape of real HST.

The flow field around a high-speed train including cross-wind effects has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations in the inertial frame using the iterative time marching scheme. The governing equations are differenced with 1st-order accurate backward difference scheme for the time derivatives, 3th-order accurate QUICK scheme for the convective terms and 2nd-order accurate central difference scheme for the viscous terms. The Marker-and-Cell concept was applied to efficiently solve continuity equation, which is differenced with 2nd-order accurate central difference scheme. The 4th-order artificial damping is added to the continuity equation for numerical stability. A C-H type of elliptic grid system is generated around a high-speed train including ground. The Baldwin-Lomax turbulent model was implemented to simulate the turbulent flows. To validate the present procedure, the flow around a high speed train at constant yaw angle of $45^{\circ}\;and\;90^{\circ}$ has been simulated. The simulation shows 3-D vortex generation in the lee corner. The flow separation is also observed around the rear of the train. It has concluded that the results of present study properly agree with physical flow phenomena.

A computer code for solving the Reynolds averaged full Navier-Stokes equations has bent developed for analysis of gas and steam turbine cascade flows with the option of using one of two types of turbulence model. One is the Baldwin-Lomax model and the other is standard $k-{\varepsilon}$ model. The numerical integration is based on the explicit four stage Runge-Kutta scheme and finite volume method. To be verified, the resulting code is applied to VKI turbine cascade and compared with the previous experimental results. Finally, the flowfield around a steam turbine cascade is analyzed. Comparisons with experimental data show that present numerical scheme is an accurate Navier-Stokes solver and can give very good predictions for both gas and steam turbine cascade flow.

Recently, for the thermal system design in an engine room, the importance of the numerical analysis on the heat and fluid flow has been recognized. In the present study, the flow inside an engine room with complex geometry was analysed by use of TURBO-3D program being developed in KIST. Radiator and Cooling fan were simulated by porous media and momentum sources, and the result shows a good agreement with our expectation.

A numerical procedure for the analysis of transient behavior in a monolithic catalytic converter is presented. The thermal behavior of a monolithic catalytic converter is fully coupled with mass transfer and exothermic reaction between exhaust gases and the catalytic converter. In the present study, all these processes are solved simultaneously. The heat transfer process is approximated by combinging one dimensional convection and conduction and the chemical reaction is also simply modelled by using the concepts of reaction rate and reaction heat. All the partial diffenrential equations for the heat transfer, mass transfer and chemical reactions are appximated by using finite volume method. Resulting algebraic equations are solved using the Newton's method. To see the workability of present numerical method, two well known problems, say step increase and step decrease in the gas inlet temperature, have been calculated. Comparion of present solutions with previous solutions shows a good agreement.

In the present paper, a method of nearly orthogonal grid generation in an arbitrary simply-connected 3D domain will be presented. The method is a new direct and non-iterative scheme based on the concept of the decomposition of the global orthogonal transformation into consecutive mapping of a conformal mapping and an auxiliary orthogonal mapping, which was suggested by King and Leal [4]. In our numerical scheme. Kang and Leal's method is extended from 2D problems to 3D problems while the advantage of the non-iterative algorithm is maintained. The essence of the present mapping method is that an iterative scheme can be avoided by introducing a preliminary step. This preliminary step corresponds to a conformal map and is based on the boundary element method(BEM). This scheme is applied to generate several nearly-orthogonal grid systems which are orthogonal at boundaries.

최근 전산 유체 역학은 Navier-Stokes 방정식을 보다 복잡한 유동장 형상에 대해 풀 수 있을 만큼 발달해 왔으나 아직도 유동장 형상이 복잡할 때는 많은 애로를 느끼고 있다. 특히 격자 구성 문제에 있어서 많은 시간과 노력을 기울이고 있으며 심지어 격자 구성 문제를 해결하지 못해 유동해석을 하지 못하는 경우가 많은 실정이다. 따라서 본 연구에서는 주로 내부 유동인 변형 도관를 예로 유동장 형상에 따라 격자구성이 어떻게 달라지는가를 살펴 보았다.

This study examines effect of various interpolations of interior control function for analytic methods such as Thomas-Middlecoff and Sorenson methods. Laplace interpolation is developed and compared among linear interpolation and exponential interpolation systematically.

Viscous analysis on incompressible flows is performed using unstructured triangular meshes. A two-dimensional and axisymmetric incompressible Navier-Stokes equations are solved in time-marching form by artificial compressibility method. The governing equations are discretized by a cell-centered based finite-volume method. and a centered scheme is used for inviscid and viscous fluxes with fourth order artificial dissipation. An explicit multi-stage Runge-Kutta method is used for the time integration with local time stepping and implicit residual smoothing. Convergence properties are examined and solution accuracies are also validated with benchmark solution and experiment.

This paper presents the result of a computational study on the wake characteristics of two tanker models. i.e HSVA and DYNE hull forms. The focus of the study is on the distributions of axial. radial and tangential velocities of the two hull forms in way of the propeller, especially over the propeller disk. The effect of bilge vortices on the velocity distribution is also concerned. For the computation of stern and wake flows of the two hull forms. the incompressible Reynolds-Averaged Navier-Stokes(RANS) equations are numerically solved by the use of a second order finite difference method, which employs a four stage Runge-Kutta scheme with a residual averaging technique and the Baldwin-Lomax model. The calculated pressure distributions on the hull surface and the axial. radial and tangential velocity distributions over the propeller disk are presented for the two hull forms. Finally, the result of wake analysis for the computed wake distribution over the propeller disk is given in comparison with those for the experimental wake distribution for the both hull forms.

In this paper we study steady capillary-gravity waves in a two-layer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction, Two critical speeds for the waves are obtained. Near the smaller critical speed, the derivation of the usual forced KdV equation (FKdV) fails when the coefficient of the nonlinear term in the FKdV vanishes. To overcome this difficulty, a new equation called a forced extended KdV equation (FEKdV) governing interfacial wave forms is obtained by a refined asymptotic method. Various solutions and numerical results of this equation are presented.

Numerical analysis is conducted on the deformation of free surface of magnetic fluid. Steady magnetic fields are induced by a circular current loop. Governing equations of magnetic fields are solved by using the concept of vector potential. The free surface of magnetic fluid is formed by the balance of surface force, gravity, pressure difference, magnetic normal pressure and magnetic body force. The deformations of free surface of magnetic fluid are qualitatively clarified. And, the patterns of steady non-uniform magnetic fields induced by a circular current loop are quantitatively presented.

The boundary conditions for the free-surface including the important meaning for both scientific and engineering purposes are described together with the numerical techniques to implement the conditions. Two kinds of numerical method based on MAC method are introduced. One is applied to the problem of 2D solitary wave propagation and the other is applied to the problem of 3D bow wave breaking.

Three dimensional turbulent flow fields around ships are simulated by a numerical method. Reynolds Averaged Navier-Stokes equations are used where Reynolds stresses are approximated by Baldwin-Lomax and Sub-Grid Scale(SGS) turbulence models. Body-fitted coordinate system is introduced to conform three dimensional ship geometries. The governing equations are discretized by a finite volume method. Temporal derivatives are approximated by the forward differencing and the convection terms are approximated by the QUICK or Kawamura scheme. The 2nd-order centered differencing is used for other spatial derivatives. Pressure and velocity fields are simultaneously iterated by the Highly Simplified Marker-And-Cell method. To verity the numerical method and turbulence models, flow fields around ships are simulated and compared to the experiments.

Numerical optimization technique with Navier-Stokes code has been used to reduce the drag of conventional ogival nose. Forebody optimizations are performed for supersonic laminar and turbulent flow conditions. To alleviate the computing time of aerodynamic drag calculation, axisymmetric boundary condition is implemented in the 3-dimensional Navier-Stokes code. The automated optimization procedure with gradient based method results in a drag reduction of $4\;\%$.

This paper describes computational efforts on the various energy and environmental problems using Patankar's SIMPLE method. The specific problems included in this study are : pollutant and flammable material dispersions in open and confined areas, aerator-induced flow in a lake for DO(dissolved oxygen) concentration, primary clarifier for water and waste water treatment, hood ventilation in workplace, cyclone and LNG combustors and Dow chlorination reactor. A control-volume based finite-difference method is employed together with the power-law scheme. The pressure-velocity coupling is resolved by the use of the revised version of SIMPLE, says SIMPLER and SIMPLEC. The Reynolds stresses are closed using the standard or the RNG $k-{\varepsilon}$ models. Turbulent reaction is modeled using two fast chemistry methods such as eddy breakup and conserved scalar models. Further, a nonequilibrium model is developed for the application of the chlorination process in the Dow reactor. Other important empirical models and physical insights appeared in this study are presented and discussed in a brief note. The computational method developed in this study is considered, in general, as a viable tool for the design and determination of the optimal condition of various engineering system of interest.

A finite element scheme using the concept of PISO method has been developed to solve the viscous flow problems in all speed range. In this study, new pressure equation is proposed such that both the hyperbolic term related with the density variations and elliptic term reflecting the incompressibility constraint are included. Present method has been applied to incompressible flow in two-dimensional driven cavity(Re=100, 400 and 1,000), and its computed results are compared with other's. Also, Carter plate problem(M=3 and Re=1,000) is computed and the comparison is made with Carter's results. Finally, we simulate a shock-boundary layer interaction problem(M=2 and $Re=2.96{\times}10^5$) to illustrate the shock capturing capability of the present solution algorithm.

Three-Dimensional Euler equations are solved numerically for the analysis of contraction flows in wind or water tunnels. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. In order to speed up the convergence, the local time stepping and the implicit residual-averaging schemes are introduced. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. For the evaluation of the present Euler solver, numerical computations are carried out for the various contraction geometries, one of which was adopted in the Large Cavitation Channel for the U.S. Navy. The comparison of the computational results with the available experimental data shows good agreements.

The present paper explains some advancement made by the authors for the compressible flow computation of the Euler equations based on the unstructured grid and vertex- centered finite volume method. Accurate solutions to the unsteady axisymmetric shock wave propagation problems and three-dimensional airplane flows have been obtained by a high-order upwind TVD and FCT schemes. Unstructured grid adaption is made for the unsteady shock wave problems by the dynamic h-refinement/unrefinement procedure and for the three-dimensional steady flows by the Delaunay point-insertion method to generate three-dimensional tetrahedral mesh enrichment. Some physics of the shock wave diffraction phenomena and three-dimensional airplane flow are discussed.

Incompressible developing entry flows through square ducts with 90 degree bends are studied numerically by using an efficient implicit SMAC scheme with different boundary conditions. This study eventually aimed at passage flow analysis of turbomachinery elements with a strong curvature such as centrifugal impeller or draft tube. The generalized implicit scheme used in the present study has been developted to solve the three-dimensional Navier-Stokes equations by the author. Numerical results for some different numerical conditions are obtained and compared with each other

비정상(unsteady) 압축성(compressible) 유동에 의한 공력음향(aeroacoustics)을 모사하여 공력소음원을 해석하기 위해서는 고차(high order)의 정확도와 높은 해상도(resolution)를 가지며, 상대적으로 계산시간을 많이 필요로 하지 않는 외재적(explicit) 유한차분법이 필수적으로 요구된다. 이것은 주어진 차분방식과 격자계로써 공간과 시간상에 존재하는 미소크기의 파동성분들을 충분히 구현하여야 만족할 만한 수치해를 얻을 수 있기 때문이다. 본 연구에서는, 그러한 유한차분법 중 최근에 관심의 대상이 되고있는 삼각(tridiagonal)또는 오각(pentadiagonal) 집적유한차분법(compact finite difference scheme)이 최대의 해상도를 갖도록 하는 수학적인 방법을 개발하고, 이 방법으로써 새롭게 집적유한차분법을 최적화하였다. 개발된 최적화 방법은, 푸리에 해석법(Fourier analysis)을 통하여 파동수(wavenumber) 영역에서 수학적으로 계산된 위상오차(phase error)를 최소화하는 것이며, 이러한 개념과 방법은 본 연구에서 처음으로 집적유한차분법에 적용되었다. 여러가지 절단정확도(truncation order)에 대해서 최적화 된 집적유한차분법들이 실제 공간과 시간상에서 보여주는 정확도와 오차특성을 알아보기 위하여, 이 방법들을 1차원 선형파동방정식에 적용하였고, 이 결과를 통하여 가장 정확하고 효과적인 절단정확도의 집적유한차분법을 선별하였다. 특히, 오각(pentadiagonal)법에 비해 더욱 효율적인 6차 삼각(tridiagonal)법을 1차원 Euler방정식에 적용하여, 비선형 파동에 대한 모사를 수행할 수 있었다.

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone($5^{\circ}$) geometry. The effective gamma($\bar{r}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30Km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about $3\sim5$ percent. The skin friction coefficient and heat transfer coefficient were also calculated.

마하수 4일때 초음속 풍동의 벽면과 모델지지부의 간섭에 관해 연구하였다. 특히 모델지지부 주위에서의 충격파 형성과 sting, strut 그리고 second throat에서의 반사 충격파의 상호 작용에 연구의 촛점을 두었다. 수치 기법은 내재적 플럭스 차분 분할기법 (implicit flux-difference splitting technique)을 사용하였다. 2차원과 3차원 유동해석 결과로부터 모델지지부 후류의 유동에 미치는 diffuser 출구 경계조건의 영향을 알아보았다.

The adaptive wall test section has distinct advantage over the other devices for reduction of wall interference in the wind tunnel testing. For two-dimensional steady flows the wall adaption strategy has been well established and, in some extent, has been effectively applied to three-dimensional steady flows. For unsteady testing, the wall adaptation is conceptually possible but has never been realized in the wind tunnel experiment. In this study, relatively simple adaptive wall models have been proposed and evaluated through numerical tests. The effect of Mach number, frequency, and amplitude of pitching oscillation on the wall interference reduction has been also studied.

터빈익렬내부의 유동해석을 위해 비압축성 점성유동해석을 이용한 수치 해석 프로그램을 개발하였다. 지배방정식으로는 2차원의 비정상 비압축성 Navier-Stokes 방정식을 일반화된 곡선좌표계로 전환하여 암시적으로(implicitly) 반복적인 시간진행방법을 이용하여 유동해석을 하였다. 지배방정식의 각항들은 시간에 대해 1차의 정확도 그리고 영역에 대해서는 2차의 정확도, 대류항에 대해서는 3차의 정확도를 가지는 Upwind기법을 적용하였다. 특히, 실험적 접근이 매우 어려운 터빈의 정익과 회전하고 있는 동익과의 상호운동을 멀티블럭기법과 데이터 interface를 통해 보다 쉽게 해석할 수 있었다. 본 연구결과는 정익만을 계산한 타 연구자의 결과와의 비교시 매우 일치하였으며 물리적인 유동을 잘 파악할 수 있었다. 난류유동 해석을 위해서 Baldwin-Lomax 모델을 적용하였다.

The paper describes hypersonic rarefied flow of helium and nitrogen over a flat plate by the direct simulation Monte Carlo (DSMC) method. The effect of incomplete accommodation and plate thickness are analyzed and the computational results are compared with wind tunnel test data. Also computational aspects of the method are outlined.

This paper presents the studies on the variation of shape and thickness of a normal shock wave with Mach number and density by using the most useful numerical technique in rarefied gas regime, DSMC(Direct Simulation Monte Carlo). Calculations are peformed for the three different Mach numbers and for one Mach number with different densities. From the obtained results, we find that the shock thickness is decreasing with increasing Mach number, and there are much variations in thickness and shape with decreasing density. Also, there is a noticeable overshoot of the translational temperature near the shock center in the case of a large Mach number.

The transient incompressible flow behind the bluffbody is numerically simulated using the random vortex method(RVM). Based on the vorticity formulation of the unsteady Navier-Stokes equations, the Lagrangian approach with the random walk technique is employed to account for the transport processes of the vortex elements. The random walk procedure for the diffusion process has been validated against the exact solutions. The present simulation focuses on the transition flow regime where the recirculation zone behind the bluffbody becomes highly unsteady and large-scale vortex eddies are shed from the bluffbody wake. The unsteady flow structures and the mixing characteristics behind the bluffbody are discussed in details.