Unsteady natural convection of an enclosed fluid has been one of the fundamental thermo-fluid problems, of which dynamic relevance is found in many engineering applications. Together with the inherent coupling between the boundary layers and the interior core, and strong interaction between flow and temperature fields, the unsteadiness poses serious hurdles for analytical and experimental approaches. With the recent development of computers and solution algorithms, computational fluid dynamics has become the prevailing tool to tackle the underlying problems. In this presentation, a few examples of numerical studies are introduced. The usefulness and potential of numerical simulations in investigating unsteady natural convection are elaborated.

The performances of the CRAYT3E and CRAYC90 were compared in the point of aerodynamics. The CRAYC90 with and without the highest vector option was run, respectively. The CRAYT3E was run with various processors (from 1pe to 32pes). The communication utilities of MPI and SHMEM were used to inform the boundary data to the other processors. The DADI Euler solver, which is implicit scheme and use central difference method, was used. The domain decomposition method was also used. As the result, the CRAYC90 with the highest vector option is 5.7 times faster than the CRAYT3E with 1 processor. However, because of the scalability of the CRAYT3E, the CRAYT3E with more than 6 processors is faster than CRAYC90. In case that 32 processors used, the CRAYT3E is 6 times faster than CRAYC90 with the highest vector option.

A parallel implementation is made of a two-dimensional finite volume model based on the SIMPLER. The solution domain is decomposed into several subdomains and the solution at each subdomain is acquired by parallel use of multiple processors. Communications between processors are accomplished by using the standard MPI and the Cray-specific SHMEM. The parallelization method for the overall solution procedure to the Navier-Stokes equations is described in detail, The parallel implementation is validated on the Cray T3E system for a benchmark problem of natural convection in a sidewall-heated cavity. The parallel performance is assessed and the issues encountered in achieving a high-performance parallel model are elaborated.

An implicit viscous turbulent flow solver is developed for two-dimensional geometries on unstructured triangular meshes. The flux terms are discretized based on a cell-centered finite-volume formulation with the Roe's flux-difference splitting. The solution is advanced in time using an implicit backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with the Gauss-Seidel relaxation scheme. The effect of turbulence effects is approximated with a standard $k-{\varepsilon}$ two-equation model which is solved separately from the mean flow equations using the same backward-Euler time integration scheme. The triangular meshes are generated using an advancing-front/layer technique. Validations are made for flows over the NACA0012 airfoil and the Douglas 3-element airfoil. Good agreements are obtained between the numerical results and the experiment.

A multiblock grid generation has been applied to a Navier-Stokes design procedure of a axial-flow compressors. A multiblock structure simplifies the creation of structured H-grids about complex turbomachinery geometries and facilitate the creation of a grid in the tip flow region. The numerical algorithm adopts the combination of the algebraic and elliptic method to create the internal grids efficiently and quickly. The input module is made of the results of the preliminary design, i.e., flow-path, aerodynamic conditions along the spanwise direction, and the blade profile data. The final grids generated from each module of the system are used as the preprocessor for the performance prediction of the sectional blade, the blade-stacking process and the three-dimensional flow simulation inside the blade passage. Application to the blade design of the LP compressor was demonstrated to be very reliable and practical in support of design activities. This customized system are coupled strongly with the design procedure of the turbomachinery cascades using the Navier-Stokes technique.

When computing the flow around complex three dimensional aircraft configurations, the generation of the grid is the most time consuming part. This paper presents a survey of the grid generation technique. The technique for treating problems arising in surface grid generation for complex geometries is addressed. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries.

Rice's monotone streamline upwind finite element method, which was proposed to treat convection-dominated flows, is applied to the linear triangular element. An alignment technique of unstructured grids with given velocity fields is used to prevent the interpolation error produced in evaluating the convection term in the upwind method. The alignment of grids is accomplished by optimizing a target function defined with the inner-product of a properly chosen side vector in the element with the velocity field. Two pure advection problems are considered to demonstrate the superiorities of the present approach in solving the convection-dominated flow on the unstructured grid. Solutions obtained with aligned grids are much closer to the exact solutions than those with initial regular grids. The capability of the present approach in predicting the appearance of the secondary vortex in the laminar confined jet impingement is shown by comparing streamlines to those produced by SIMPLE on a highly stretched grid toward the impingement plate.

An unstructured finite volume method is presented for seeking steady and unsteady flow solutions of the two-dimensional incompressible viscous flows. In the present method, SMAC-type algorithm is implemented on unstructured triangular meshes, using second order upwind scheme for the convective fluxes. Validation tests are made for various steady and unsteady incompressible flows. Convergence characteristics are examined and accuracy comparisons are made with some benchmark solutions.

A two-dimensional airfoil under ground effect in subsonic turbulent flow is calculated by sieving the Navier-Stokes equation. Some numerical results for different NACA four-digit airfoils are presented. The numerical results show that the lift and drag coefficients are strongly influenced by the shape of the region between the lower surface of airfoil and the ground In general, the airfoil with large camber and small thickness is suitable for WIG vehicles

Circular-to-rectangular transition ducts are used as exhaust components of high performance fighter aircraft with vectored thrust nozzles. Three-dimensional incompressible Navier-Stokes solver is used to analyze the transition duct. Cross sections of transition duct are defined by superelliptic equation. The grid system is generated by Non-Uniform Rational B-Spline, after generating surface grid by blending the cross sections. Good agreement between the results of the computational simulation and the experimental data is observed.

Objective of the present study is to examine the convergence characteristics of the various multi-stage Runge-Kutta methods in solving the incompressible Navier-Stokes equations of a time-marching from casted by the artificial compressibility method. Convergence characteristics are examined over 2-stage, 4-stage and hybrid type (using 4-, 3-, 2-stages sequentially) Runge-Kutta methods for a laminar lid-driven cavity flow, and also for a turbulent bump channel flow using Chien's low-Reynolds number turbulence model. Efforts are made to establish a stable and fast convergent multi-stage Runge-Kutta method with minimal artificial dissipations.

The Computer code KAIST-ADD LUFUNS has been developed to solve 3D compressible turbluent flow. This method employs Harten-Yee's modified upwind scheme in the explicit part and Steger-Warming Splitting in the implicit part. Flow past RAE wing-body aircraft has been computed for three different flow conditions. The result have shown good comparision with the experimental data. Baldwin-Lomax turbluence model is used for this computer code.

This paper describes analysis of complex flow around Car-like body using Chimera grid technique. As a computational algorithm, Pullboat and Chaussee's Diagonal algorithm is selected to reduce computational time. Introducing hole points flag to this Diagonal algorithm, an algorithm for Chimera grid is generated easily. This study solves 3-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system using second-order accurate schemes for the time derivatives, and third/second-order scheme for the spatial derivatives. The Marker-and-Cell concept is applied to efficiently solve continuity equation. The fourth-order artificial damping is added to the continuity equation for numerical stability, It has concluded that the results of present study properly agree with physical flow phenomena.

A finite-difference method based on characteristic upwind flux difference splitting has been studied on the blowing effect on the wall heat transfer over blunt-bodies. As the blowing rates increased, the wall heat transfer rate decreased and the temperature gradient also decreased compared with no blowing case. The heat trasfer rate at Mach No. 20 was almost twice higher than that of Mach No. 15 at 50km altitude. The surface blowing can be an effective mechanism to reduce the surface heat transfer rate at hypersonic flight condition.

A finite-difference method based on conservative supra characteristic method type upwind flux difference splitting has been developed to study the nonequilibrium chemically reacting inviscid flow. For nonequilibrium air, NS-1 species equations were strongly coupled with flowfield equations through convection and species production terms. Inviscid nonequilibrium chemically reacting air mixture flows over Blunt-body were solved to demonstrate the capability of the current method. At low altitude flight conditions the nonequilibrium air models predicted almost the same temperature, density and pressure behind the shock as equilibrium flow: however, at high altitudes they showed substantial differences due to nonequilibrium chemistry effect. The new nonequilibrium chemically reacting upwind flux difference splitting mettled can be extended to viscous flow and multi-dimensional flow conditions.

The effects of radiative heat transfer are investigated in a turbulent combustion flow field with highly non-adiabatic flames. Turbulent combustion is modeled by the $k-{\varepsilon}-g$ model and a one step irreversible reaction scheme for the combustion chemistry. The radiative trasport equation is solved by the finite volume method considering the radiative transfer from $CO_2,\;H_{2}O$ and soot only. Gray gas is assumed to calculate the radiative properties of $CO_2\;and\;H_2O$. A two-equation soot formation model is applied to predict soot volume faction distribution. All equations are solved in a coupled manner and the numerical results are compared with available experimental data.

This paper addresses to the injection pressure effect on the diesel spray. The injection pressure is varied from 10MPa, in general system, upto 200MPa, in high pressured system in order to understand the effect. The gas phase is modelled in terms of the Eulerian continuum conservation equations of mass, momentum, energy and fuel vapour fraction. The liquid phase is modelled following the discrete droplet model approach in Lagrangian form. The droplet distributions, vapor fractions and gas flows are analyzed in various injection pressure cases.

In the present work the influence of various physical parameters on the two-phase flow behavior in a self-heated porous medium has been studied using a numerical model, that is, the effects of heat generation rate, of porosity, of particle size, and of system pressure on the dryout process. To analyze the effect of these parameters, the variation of both liquid volumetric fraction (i.e., liquid saturation) and liquid axial velocity is evaluated at the steady state or at the onset of a first boiled-out region. The analysis of computational results indicate that a qualitative tendency exists between the parameters such as heat generation rate, porosity, effective particle diameter and the temporal development of the liquid volumetric fraction field up to dryout. In addition to these parameters, a variation of fluid properties such as phase density, phase viscosity due to a change of system pressure can be used for gaining insight into the nature of two-phase flow behavior up to dryout.

A new and efficient method is presented for design optimization, which is based on a computational fluid dynamics (CFD). The method is applied to design an airfoil configuration. The Navier-Stokes equations are solved for the viscous analysis of the flow, which provides the object function. The CFD analysis is then coupled with the optimization procedure that used a conjugate gradient method. During the one-dimensional search of the optimization procedure, an approximate flow analysis based on a first-order Taylor series expansion is used to reduce the computational cost, (This study is supported by Korean Ministry of Education through Research Fund)

Effect of wall curvature on flow characteristics is studied for mildly and strongly curved duct flows. The ducts are S-shaped, and the flow is partially blocked at the rear of the downstream. The presence of blockage in combination with curvature generates secondary flows on the concave surface; the magnitude of the secondary flow being dependent on the degree of wall curvature. Objectives are to compare the flow structures for mild and strong cases and to illuminate the changes in flow structure as the flow turns. Sensitivity on numerical solutions due to different inflow boundary conditions is also examined.

The present study is aimed to investigate flow characteristics of confined jet flow within circular pipe. Numerical method based upon revised SOLA scheme which secures conservation form of convective terms on irregular grids by interpolating the variables appearing in staggered meshes is adopted on cylindrical coordinate formation. Computation was carried out for two kinds of Reynolds number, $10^5\;and\;1.5{\times}10^5$ defined by diameter of outer pipe and time-mean driving jet velocity. Results show that periodic vortex shedding from the jet mixing layer is profound and related unsteady flow characteristics prevail over the entire region. Spatial distribution of pressure and kinetic energy, fluctuation of static wall pressure, together with radial velocity components are examined in terms of instantaneous and time-mean point of views.

Differential pressure Venturi cone flowmeter is an advanced flowmeter which has many advantages such as wide range of measurement, high accuracy, excellent flow turndown ratio, low headless, and short installation pipe length requirement, etc. Like other differential pressure flowmeter, Venturi cone flowmeter uses the law of energy conservation, but its shape and position make it perform better than others. The cone acts as its own flow conditioner and mixer, fully conditioning and mixing the flow prior to measurement. For the analysis, we use Reynolds-averaged Navier-Stokes equations and $k-{\omega}$ turbulence model. The equations are fully trans-formed in the computational coordinates, the pressure-velocity coupling is made through SIMPLER algorithm, and the equations are discretized using analytic solutions of the linearized equations(Finite Analytic Method). At the end of the paper, using the result of analysis, We propose a new shape of cone with the hope of drag reduction and high performance.

Based on the full Navier-Stokes solutions, the thermohydrodynamic performance of a long journal bearing is investigated. A numerical method based on Galerkin's procedure and B-spline test functions has been presented for solving two-dimensional problems involving fluid flow and heat transfer. For numerical stability the artificial compressibility is employed to the conservation of mass. The discretized algebraic equations are solved by Newton's method. Effects of varying the speed of an inner cylinder to load carrying capacity are investigated. The results indicated that the increase of the speed of an inner cylinder has a significant effect on the temperature profile and ultimately on the performance.