• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1071-1084
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• 2023

We consider inviscid, incompressible homogeneous shear flows of variable cross section known as extended Rayleigh problem. For this extended Rayleigh problem, we derived instability region which intersect with semi-circle instability region under some condition. Also we derived condition for stability, upper bound for amplification factor and growth rate of an unstable mode.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.105-121
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• 2024

We consider incompressible, inviscid, stratified shear flows in β plane. First, we obtained an unbounded instability region intersect with semi-ellipse region. Second, we obtained a bounded instability regions depending on Coriolis, stratification parameters and basic velocity profile. Third, we obtained a criterion for wave stability. This has been illustrated with standard examples. Also, we obtained upper bound for growth rate.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1518-1526
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• 2001

In this paper, the mechanism of unsteady potential interaction and wake interaction in one stage axial turbine is numerically investigated at design point in two-dimensional viewpoint. The numerical technique used is the upwind scheme of Van-Leer's Flux Vector Splitting (FVS) and Cubic spline interpolation is applied on zonal interface between stator and rotor. The inviscid analysis is used to embody the influence of potential interaction only and viscous analysis is used to embody the influences of both potential interaction and wake interaction at the same time. The potential-flow disturbance from the stator into a rotor passage and the periodic blockage effect of rotor produce the unsteady pressure on the blade surface in inviscid analysis. After the wake is cut by rotor, two counterrotating votical patterns flanking the wake centerline in the passage are generated. So, these phenomena magnify the unsteady pressure in viscous analysis than that in inviscid analysis. The resulting unsteady forces on the rotor, generated by the combined interaction of the two effects by potential and wake interaction, are discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.2
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• pp.240-252
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• 1998

The purpose of this study is to develop a method for predicting the aerodynamic performance of the low speed airfoils in the 2-dimensional, steady and viscous flow. For this study, the airfoil geometry is specified by adopting the longest chord line system and by considering local surface curvature. In case of the inviscid incompressible flow, the analysis is accomplished by the linearly varying strength vortex panel method and the Karman-Tsien correction law is applied for the inviscid compressible flow analysis. The Goradia integral method is adopted for the boundary layer analysis of the laminar and turbulent flows. Viscous and inviscid solutions are converged by the Lockheed iterative calculating method using the equivalent airfoil geometry. The analysis of the separated flow is performed using the Dvorak and Maskew's method as the basic method. The wake effect is also considered by expressing its geometry using the formula of Summey and Smith when no separation occurs. The computational efficiency is verified by comparing the computational results with experimental data and by the shorter execution time.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2002.09a
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• pp.19.2-19
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• 2002

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.269-276
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• 2009

The local preconditioning method has both robust convergence and accurate solutions by using local flow properties for parameters in the preconditioning matrix. Preconditioning methods have been very effective to low speed inviscid flows. In the viscous and turbulent flows, deterioration of convergence should be overcame on the high aspect ratio grids to get better convergence and accuracy. In the present study, the local time stepping and min-CFL/max-VNN definitions are applied to compare the results and we propose the method that switches between two methods. The min-CFL definition is applied for inviscid flow problems and the min-CFL/max-VNN definition is implemented to viscous and turbulent flow problems.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.6
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• pp.765-771
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• 2002

This Paper presents numerical solutions of two-dimensional Euler equations for supersonic steady and unsteady flows with heat addition in a convergent-divergent duct, The Van Leer FVS (flux vector splitting) method in generalized coordinates is employed in order to calculate the inviscid strong shock waves caused by thermal choking. We discuss on transient characteristics, start and unstart phenomena caused by thermal choking, limit of equivalence ratio to avoid thermal choking and fluctuation of specific thrust caused by thermal choking. We prove that thermal choking is a serious problem in view of engine performance.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2000.04a
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• pp.140-145
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• 2000

The spectral method which is composed of an eigenfunction expansion of free modes in the wave number domain is used to produce two dimensional unsteady inviscid wave simulation such as progressive waves in a numerical pneumatic wave tank. A spatial and time dependent free surface elevation and the potential are calculated by integrating ODE derived from fully nonlinear kinematic and dynamic free surface boundary condition at each time step. The nonlinear characteristics in the waves by this method were notable as increasing wave steepness. This method is very useful and powerful in terms of saving computational time caused by rapid convergence exponentially with increasing number of nodes, even preserving accurate numerical results. Moreover, it will given us many possibilities to apply to naval and ocean engineering fields.

• 유체기계공업학회:학술대회논문집
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• 2000.12a
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• pp.158-162
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• 2000

Secondary flows in gas turbines, especially those associated tip clearance and labyrinth seals, have become a focus of interest for engine manufacturers. In the past, many analytical and experimental studies, which focused solely on the flows in either tip clearances or seals, have been conducted. This paper presents an analytical model that describes the flow response in a single stage turbine induced by a finite sealing gap at the turbine rotor. The flow is assumed to be axisymmetric and the analysis is done in the meridional plane. Upon going through the stage, the radially uniform upstream flow is assumed to split into two streams one associated with the seal and the other which has gone through the blades. The former is referred to as the leakage flow, and the latter is referred the as the passage flow. The passage flow is assumed to be inviscid and incompressible while the flow in the seal can be modeled as either inviscid or viscous. Thus, the model is capable of predicting the kinematic effects of labyrinth seals on the turbine flow field.

• Journal of computational fluids engineering
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• v.2 no.2
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• pp.51-58
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• 1997

A reliable computational solver has been developed for the analysis of three-dimensional inviscid compressible flows around a nacelle of a high bypass ratio turbofan engine, The numerical algorithm is based on the modified Godunov scheme to allow the second order accuracy for space variables, while keeping the monotone features. Two step time integration is used not only to remove time step limitation but also to provide the second order accuracy in a time variable. The multi-block approach is employed to calculate the complex flow field, using an algebraic, conformal, and elliptic method. The exact solution of Riemann problem is used to define boundary conditions. The accuracy of the developed solver is validated by comparing its results around the isolated nacelle in the cruise flight regime with the solution obtained using a commercial code "RAMPANT. "