• Journal of computational fluids engineering
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• v.21 no.1
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.32 no.6
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• pp.429-445
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• 2008

Two-phase compressible flow fields of air-water are investigated numerically in the fixed Eulerian grid framework. The phase interface is captured via volume fractions of each phase. A way to model two phase compressible flows as a single phase one is found based on an equivalent equation of states of Tait's type for a multiphase cell. The equivalent single phase field is discretized using the Roe‘s approximate Riemann solver. Two approaches are tried to suppress the pressure oscillation phenomena at the phase interface, a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. In discretizing the compressible form of volume fraction equation, phase interfaces are geometrically reconstructed to minimize the numerical diffusion of volume fraction and relevant variables. The motion of a projectile in a water-filled tube which is fired by the release of highly pressurized air is simulated presuming the flow field as a two dimensional one, and several design factors affecting the projectile movement are investigated.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1103-1119
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• 2007

We consider multiscale mortar mixed finite element discretizations for slightly compressible Darcy flows in porous media. This paper is an extension of the formulation introduced by Arbogast et al. for the incompressible problem [2]. In this method, flux continuity is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. Optimal fine scale convergence is obtained by an appropriate choice of mortar grid and polynomial degree of approximation. Parallel numerical simulations on some multiscale benchmark problems are given to show the efficiency and effectiveness of the method.

• 유체기계공업학회:학술대회논문집
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• 2002.12a
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• pp.331-336
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• 2002

Recently the critical nozzles with small diameter are being extensively used to measure mass flow in a variety of industrial fields and these have different configurations depending on operation condition and working gas. The curvature radius of the critical nozzle throat is one of the most important configuration factors promising a high reliability of the critical nozzle. In the present study, computations using the axisymmetric, compressible, Navier-Stokes equations are carried out to investigate the effect of the nozzle curvature on critical flows. The diameter of the critical nozzle employed is D=0.3mm and the radius of curvature of the critical nozzle throat is varied in the range from 1D to 3D. It is found that the discharge coefficient is very sensitive to the curvature radius(R) of critical nozzle, leading to the peak discharge coefficient at R = 2.0D and 2.5D, and that the critical pressure ratio increases with the curvature radius.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.178-183
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• 2000

An efficient Newton-GMRES algorithm is presented for computing two-dimensional steady compressible viscous flows on unstructured hybrid meshes. The scheme is designed on cell-centered finite volume method which accepts general polygonal meshes. Steady-state solution is obtained with pseudo-transient continuation strategy. The preconditioned, restarted general minimum residual(GMRES) method is employed in matrix-free form to solve the linear system arising at each Newton iteration. The incomplete LU fartorization is employed for the preconditioning of linear system. The Spalart-Allmars one equation turbulence model is fully coupled with the flow equations to simulate turbulence effect. The accuracy, efficiency and robustness of the presently developed method are demonstrated on various test problems including laminar and turbulent flows over flat plate and airfoils.

• Advances in aircraft and spacecraft science
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• v.2 no.1
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• pp.77-94
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• 2015

The paper focuses on the integration of a non-linear one-dimensional model of Synthetic Jet (SJ) actuator in a well-assessed numerical simulation method for turbulent compressible flows. The computational approach is intended to the implementation of a numerical tool suited for flow control simulations with affordable CPU resources. A strong compromise is sought between the use of boundary conditions or zero-dimensional models and the full simulation of the actuator cavity, in view of long-term simulation with multiple synthetic jet actuators. The model is integrated in a multi-domain numerical procedure where the controlled flow field is simulated by a standard CFD method for compressible RANS equations, while flow inside the actuator is reduced to a one-dimensional duct flow with a moving piston. The non-linear matching between the two systems, which ensures conservation of the mass, momentum and energy is explained. The numerical method is successfully tested against three typical test cases: the jet in quiescent air, the SJ in cross flow and the flow control on the NACA0015 airfoil.

• 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. "

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.98-111
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• 1996

The compressible laminar and turbulent viscous flows on a slender body in supersonic speed as well as subsonic speed have 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 and 40 dog, 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.11
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• pp.1521-1530
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• 2002

This article proposes a pressure based method for predicting flows at all speeds. The compressible SIMPLE algorithm is extended to unstructured grid framework. Convection terms are discretized using second-order scheme with deferred correction approach. Diffusion term discretization is based on structured grid analogy that can be easily adopted to hybrid unstructured grid solver. This method also uses node centered scheme with edge based data structure for memory and computing time efficiency of arbitrary grid types. Both incompressible and compressible benchmark problems are solved using the above methodology. The demonstration of this method is extended to slip flow problem that has low Reynolds number but compressibility effect. It is shown that the proposed method can improve efficiency in memory usage and computing time without losing any accuracy.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1966-1971
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• 2003

Matching inviscid and boundary layer methods are developed for hypersonic flow with thick boundray layer. The new equations match all the boundary layer properties with a variation in the inviscid solution near the edge, except for the normal velocity. Computational comparison are performed for incompressible and compressible flows over a flat plate. Results from the present method are compared with Navier-Stokes solutions. The present results are in good agreement with Navier-Stokes solutions. They show that the new technique can provide improved heating rates and skin friction predictions for preliminary design of vehicles where shear layers and entropy layer swallowing are important.