• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.723-728
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• 2008

We performed numerical analysis of base drag phenomenon, when a projectile with backward step flies into atmosphere at supersonic speed. We compared with other researchers. From our previous studies that were 2-dimensional simulation, we found out from sophisticated simulations that need dense mesh points to compare base pressure and velocity profile after from base with experimental data. Therefore, we focus on high order spatial disceretization over 3rd order with TVD such as MUSCL TVD 3rd, 5th, and WENO 5th order, and Limiters such as minmod, Triad. Moreover, we enforce to flux averaging schemes such as Roe, RoeM, HLLE, AUSMDV. In present, one dimensional result of Euler tests, there are Sod, Lax, Shu-Osher and interacting blast wave problems. AUSMDV as a flux averaging scheme with MUSCL TVD 5th order as spatial resolution is good agreement with exact solutions than other combinations. We are carrying out the same approaches into 3-dimensional base flow only candidate flux schemes that are Roe, AUSMDV. Additionally, turbulence models are used in 3-dimensional flow, one is Menter s SST DES model and another is Sparlat-Allmaras DES/DDES model in Navier-Stokes equations.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.1B
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• pp.21-27
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• 2012

The HLLL scheme, proposed by T. Linde, determines all the wave speeds from the initial states because the middle wave is evaluated by the introduction of a generalized entropy function. The scheme is considered a genuine successor to the original HLL scheme because it is completely separated form the Roe's linearization scheme unlike the HLLE scheme and does not rely on the exact solution unlike the HLLC scheme. In this study, a numerical model was configured by the HLLL scheme with the total energy as a generalized entropy function to solve governing equations, which are the one-dimensional shallow water equations without source terms and with an additional conserved variable relating a concentration. Despite the limitations of the first order solutions, results to three cases with the exact solutions were generally accurate. The HLLL scheme appeared to be superior in comparison with the other HLL-type schemes. In particular, the scheme gave fairly accurate results in capturing the front of wetting and drying. However, it revealed shortcomings of more time-consuming calculations compared to the other schemes.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.8
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• pp.20-28
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• 2004

For the prediction on the onset of oblique shock wave-induced vortex breakdown, computational studies on the Oblique Shock wave/Vortex Interaction (OSVI) are conducted and compared with both experimental results and analytic mode1. A Shock-stable numerical scheme, the Roe scheme with Mach number-based function (RoeM), and a two-equation eddy viscosity-transport approach arc used for three-dimensional turbulent flow computations. The computational configuration is identical to available experiment, and we attempt to ascertain the effect of parameters such as a vortex strength, streamwise velocity deficit, and shock strength at a freestream Mach number of 2.49. Numerical simulations using the k-w SST turbulence model and suitably modeled vortex profiles are able to accurately reproduce many fine features through a direct comparison with experimental observations. The present computational approach to determine the criterion on the onset of oblique shock wave-induced vortex breakdown is found to be in good agreement with both the experimental result and the analytic prediction.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.115-122
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• 2008

The effects of characteristic condition number on the convergence of preconditioned Euler equations were investigated. The two-dimensional preconditioned Euler equations adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Euler equations are strongly affected by the characteristic condition number, and there is an optimal characteristic condition number for a problem. The optimal characteristic condition numbers for the Choi and Merkle's preconditioning and temperature preconditioning are different.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.123-130
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• 2008

The effects of characteristic condition number on the convergence of preconditioned Navier-Stokes equations were investigated. The two-dimensional preconditioned Navier-Stokes adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Navier-Stokes equations are strongly affected by the characteristic condition number. Also it is shown that the optimal characteristic condition numbers for viscous flows are larger than that in inviscid flows.

• Journal of the Korean Society of Propulsion Engineers
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• v.8 no.1
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• pp.16-26
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• 2004

The objective of this study is to apply preconditioning to Wavier-Stokes equations with a turbulence model. The concept of a pseudo sonic speed was adopted. Roe's FDS was used for spatial discretization, LU-SGS scheme was used for time integration. In order to test the algorithms, the low speed flows around NACA airfoils and the flows through supersonic nozzle were calculated. The algorithm developed in the present study shows good performance in the calculations of low speed viscous flows and supersonics flows.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.153-158
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• 2000

For the analysis of compressible flow with real gas effect, characteristic form of Roe's Riemann solver was derived again using real gas equation of state and variable specific heal and it was extended to multi component reactive system. From this study, it is known that some correction should be made for the use of existing numerical algorithm. 1) Sonic speed and characteristic variable should be corrected with real gas effect. 2) Roe's average was applicable only with the assumption of constant properties. 3) Artificial damping term and characteristic variables should be corrected but their influence may not be significant.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.05a
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• pp.332-335
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• 2008

The purpose of this study is analysis of flow field where is around of injector of supersonic combustor which is bluff-body stabilized flame and hyper-mixer type of supersonic combustor injector by using hydrogen or hydrocarbon fuel. Various schemes are evaluated to supersonic backward step flow filed with massive separation region in validation step. Compounded scheme of 5th-order TVD-MUSCL, Roe FDS, S-A DES/DDES has a good performance in base and base-bleed flow.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.38-44
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• 2001

An efficient Gauss-Seidel time integration scheme is developed for solving the Euler and Navier-Stokes equations on unstructured meshes. Roe's FDS is used for the explicit residual computations and van Leer's FVS for evaluating implicit flux Jacobian. To reduce the memory requirement to a minimum level, off-diagonal flux Jacobian contributions are repeatedly calculated during the Gauss-Seidel sub-iteration process. Computational results based on the present scheme show that approximately $15\%$ of CPU time reduction is achieved while maintaining the memory requirement level to $50-60\%$ of the original Gauss-Seidel scheme.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.6
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• pp.18-28
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• 2006

Numerical analysis of high Mach number flow over a blunt-body poses many difficulties and various numerical schemes have been suggested to overcome the problems. However, the new schemes were used in the limited fields of applications because of the lack of field experience compared to more than 20 years old numerical schemes and the intricacies of modifying the existing code for the special application. In this study, some tips to overcome the numerical difficulties in solving the 3D high-Mach number flows by using Roe's scheme, the most widely used for the past 25 years and adopted in many commercial codes, were examined without a correction of the algorithm or a modification of the CFD code. The well-known carbuncle phenomena of Riemann solvers could be remedied even for an extremely high Mach number by applying the entropy fixing function and a unphysical solution could be overcome by applying a simply modified initial condition regardless of the entropy fixing and grid configuration.