• International Journal of Aeronautical and Space Sciences
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• v.12 no.4
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• pp.318-330
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• 2011

This paper investigates the convergence characteristics of the modified artificial compressibility method proposed by Turkel. In particular, a focus is mode on the convergence characteristics due to variation of the preconditioning factor (${\alpha}_u$) and the artificial compressibility (${\beta}$) in conjunction with an upwind method. For the investigations, a code using the modified artificial compressibility is developed. The code solves the axisymmetric incompressible Reynolds averaged Navier-Stokes equations. The cell-centered finite volume method is used in conjunction with Roe's approximate Riemann solver for the inviscid flux, and the central difference discretization is used for the viscous flux. Time marching is accomplished by the approximated factorization-alternate direction implicit method. In addition, Menter's k-${\omega}$ shear stress transport turbulence model is adopted for analysis of turbulent flows. Inviscid, laminar, and turbulent flows are solved to investigate the accuracy of solutions and convergence behavior in the modified artificial compressibility method. The possible reason for loss of robustness of the modified artificial compressibility method with ${\alpha}_u$ >1.0 is given.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.2
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• pp.224-232
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• 2000

Four turbulent $k-{\varepsilon}$ models (i.e., standard model, modified models with streamline curvature modification and/or preferential dissipation modification) are applied in order to analyze the turbulent flow of wall-attaching offset jet. For numerical convergence, this paper develops a method of slowly increasing the convective effect induced by skew-velocity in skew-upwind scheme (hereafter called Partial Skewupwind Scheme). Even though the method was simple, it was efficient in view of convergent speed, computer memory storage, programming, etc. The numerical results of all models show good prediction in first order calculations (i.e., reattachment length, mean velocity, pressure), while they show some deviations in ·second order (i.e., kinetic energy and its dissipation rate). Like the previous results obtained by upwind scheme, the streamline curvature modification results in better prediction, while the preferential dissipation modification does not.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.3
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• pp.172-179
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• 2000

In this paper, the analysis of the arc-flow in the GCB is presented by using the modified FLIC method and the arc model. The modified FLIC method adopts the upwind scheme and requires short calculation time. The arc model used in this paper treats the arc as a energy source in the energy equation. The energy source is composed of the ohmic heating and the radiation energy transfer. At each step, the movement of electrode is simulated. From the simulation, reasonable results can be obtained.

• Proceedings of the KIEE Conference
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• 1999.07a
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• pp.366-368
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• 1999

In this paper, the analysis of the gas flow in the GCB is presented by using the modified FLIC method and the arc model. The modified FLIC method has two step calculation procedure. And it adopts the upwind scheme, which results in the stability.[1] The arc model used in this paper makes arc a heating source in the energy equation. The heating source is composed of ohmic heating and radiation energy transfer. And the type of the GCB in this paper is a auto-expansion type.[2]

• Journal of Advanced Marine Engineering and Technology
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• v.23 no.2
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• pp.216-225
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• 1999

Four turbulent $k-{varepsilon}$models(i.e standard model modified models with streamline curvature modification and/or preferential dissipation modification) are applied in order to analyze the tur-bulent flow of wall-attaching offset jet. The upwind numerical scheme was adopted in the present analyses. The streamline curvature modification results in slightly better prediction while the preferential dissipation modification does not. The obtained analytic results will be used as refer-ences for further study regarding Reynolds stress model. In addition this paper introduced a method of increasing nozzle outlet velocity gradually for numercal convergence. Even though the method was simple it was efficient in view of convergent speed CPU running time computer memory storage programming etc.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.9
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• pp.1148-1156
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• 2000

The QUICK scheme for convection terms is modified for unstructured finite volume method by using linear reconstruction technique and validated through the computation of two well defined laminar flows. It uses two upstream grid points and one downstream grid point in approximating the convection terms. The most upstream grid point is generated by considering both the direction of flow and local grid line. Its value is calculated from surrounding grid points by using a linear construction method. Numerical error by the modified QUICK scheme is shown to decrease about 2.5 times faster than first order upwind scheme as grid size decreases. Computations are also carried out to see effects of the skewness and irregularity of grid on numerical solution. All numerical solutions show that the modified QUICK scheme is insensitive to both the skewness and irregularity of grid in terms of the accuracy of solution.

• 유체기계공업학회:학술대회논문집
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• 1998.12a
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• pp.217-222
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• 1998

CSCM upwind flux difference splitting compressible Navier-Stokes method has been used to predict the transonic flows in centrifugal compressor diffuser. The modified cyclic TDMA and the mass flux boundary conditions were used as boundary conditions of the diffuser analysis. With the mass flux boundary condition and the $130{\times}80{\times}40$ grid, the compressible upwind Navier-Stokes method predicted the transonic diffuser flowfield successfully. Plow changes in the impeller exit region due to the strong interaction between impeller exit and vaned diffuser, broad flow separation on the suction surface near hub and shroud was observed from the results of the mass flow rates 6.0 and 6.2kg/s at 27000 rpm. The static pressure increased and the total pressure decreased through the flow passage of the channel diffuser, which were predicted better from the three-dimensional analysis than from the two-dimensional analysis due to the strong effect of the three-dimensional flow. The mass averaged loss coefficients and pressure coefficients were also studied.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.815-832
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• 1999

High-order weighted difference schemes with uniform meshes are considered for the convection-diffusion problem depending on Reynolds numbers. For small Reynolds numbers, a weighed cen-tral difference scheme is suggested since there is no boundary layer. For large Reynolds numbers, we propose a modified up wind method with an artificial diffusion in order to overcome nonphysical oscilla-tion of central schemes and obtain good accuracy in the boundary later. Existence and corresponding error estimates of the solution for the difference scheme have been shown. Numerical experiments are provided to back up the analysis.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.260-265
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• 2008

A numerical scheme for solid propellant rocket has been studied using preconditioning method to research unsteady combustion processes for the double-base propellant with a converging-diverging nozzle. The Navier-Stokes equation is solved by dualtime stepping method with finite volume method. The turbulence model uses a shear stress transport modeling. The species equation follows up the method of Xinping WI, Mridul Kumar and Kenneth K. Kuo. A preconditioned algorithm is applied to solve incompressible regime inside the combustor and compressible flow at nozzle. Mass flux was evaluated using modified advective upwind splitting method. The simulated result the comparison a fully coupled implicit method and a semi implicit method in terms of accuracy and efficiency. This report shows the result of solid rocket propellant combustion.

• The KSFM Journal of Fluid Machinery
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• v.2 no.1 s.2
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• pp.64-72
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• 1999

CSCM upwind flux difference splitting compressible Navier-Stokes method has been used to predict the transonic flows in a centrifugal compressor diffuser. The modified cyclic. TDMA and the mass flux boundary conditions were used as boundary conditions of the diffuser analysis. Broad flow separation on the suction surface near the hub and shroud was observed from the results of the mass flow rates 5.8, 6.0 and 6.2kg/s at 27000 rpm. The three-dimensional flow analysis predicted successfully that the static pressure increased and the total pressure decreased through the flow passage of the channel diffuser when compared to two-dimensional analysis due to the strong effect of the three-dimensional flow. The mass averaged loss coefficients and pressure coefficients were also studied.