• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.30 no.2
• /
• pp.30-38
• /
• 2002

The monotonic characteristics of AUSM-type shemes are proven by mathmatics and numerics. Qualitatively well-known characteristics are quantified by mathematics and the magnitude of oscillatory behaviors of each schemes could be compared directly. Moreover, it is also studied how the sonic transition position affects the oscillation in capturing the shocks. Lastly M-AUSMPW+, the latest improved AUSM-type scheme, is shown to have monotonic characeristics though all shock conditions.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.38 no.1
• /
• pp.1-11
• /
• 2010

The definition of the speed of sound is reexamined since it is crucial in the numerical analysis of compressible real gas flows. The thermodynamic speed of sound (TSS), $a_{th}$, and the characteristic speed of sound (CSS), $a_{ch}$, are derived using generalized equation of state (EOS). It is found that the real gas EOS, for which pressure is not linearly dependent on density and temperature, results in slightly different TSS and CSS. in this formalism, Roe's approximate Riemann solver was derived again with corrections for real gases. The results show a little difference when the speeds of sound are applied to the Roe's scheme and Advection Upstream Splitting Method (AUSM) scheme, but a numerical instability is observed for a special case using AUSM scheme. It is considered reasonable to use of CSS for the mathematical consistency of the numerical schemes. The approach is applicable to multi-dimensional problems consistently.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.30 no.3
• /
• pp.27-36
• /
• 2002

Numerical stability is studied based on numerics and mathematics. It is frequently observed in the region where velocity is zero. In that region, the Euler equation have numerous solutions and, thus, it is impossible to determine a unique solution with only governing equations. However, a unique solution can be determined by additional outer flow conditions or outer numerical discontinuity calculation since the information or a unique solution under undisturbed conditions is lost by disturbances. In this reason, the numerical scheme comsistent with Euler equations cannot remove shock instability completely.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.9
• /
• pp.12-26
• /
• 2004

A new treatment of cell-interface flux in AUSM-type methods is introduced to reduce the numerical dissipation. Through analysis of TVD limiters, a criterion for the more accurate prediction of cell-interface state is found out and M-AUSMPW+ is developed by determining the transferred property newly and appropriately within the criterion. The superiority of M-AUSMPW+ is clearly revealed in multi-dimensional flow problems. It can eliminate numerical dissipation effectively in a non-flow aligned grid system. As a result, M-AUSMPW+ is shown to be much more accurate and effective than other previous schemes in multi-dimensional problems. Through a stationary contact discontinuity, a vortex flow, a shock wave/boundary layer interactions and viscous shock tube problems, it is verified that accuracy of M-AUSMPW+ is improved.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.30 no.2
• /
• pp.21-29
• /
• 2002

The M-AUSMPW+ scheme that can capture shock waves exactly with monotonic characteristic is developed by analyzing the cause of oscillation in shock regions. Firstly shock-capturing characteristics of general FVS including the AUSM-type schemes are investigated in detail, according to the different between a cell-interface and a sonic transition position. The cause of oscillation is the improper numerical dissipation that could not represent the real physics. The M-AUSMPW+ could capture shocks exactly without oscillatory behaviors in considering the sonic transition position and an cell-interface position

• 한국전산유체공학회:학술대회논문집
• /
• 2004.10a
• /
• pp.3-6
• /
• 2004

In order to reduce the excessive numerical dissipation which is induced when a grid system is not aligned with a discontinuity, a new spatial treatment of cell-interface fluxes is introduced. The M-AUSMPW+ in this paper has the formula that has an additional procedure of re-defining transferred properties at a cell-interface, based on AUSMPW+. The newly defined transferred property could eliminate numerical dissipation effectively in non-flow aligned grid system of multi-dimensional flows.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.30 no.8
• /
• pp.1-9
• /
• 2002

Axisymmetric separated flows in a converging-diverging conical nozzle are investigated through numerical simulations for various pressure ratios. We employ AUSM scheme for spatial derivatives and Pulliam's 2nd order subiteration time stepping scheme for implicit time integration. Numerical results indicate that the separated flow structures are very complex when compared to the simple quasi-one dimensional flow. Depending on the pressure ratio, the flow within the nozzle is either separated or non-separated. Various separated flow patterns with distinctive features are illustrated and discussed in detail.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.73-78
• /
• 1999

극초음속 유동장의 정확한 해석을 위해 AUSMPW+ 수치기법과 충격파 포착시 생기는 수치오차를 제거하기 위해 충격파 정렬 기법(Shock-Aligned Grid Technique)을 개발하였다. AUSMPW+ 수치기법은 자체 수치점성이 적은 수치기법으로 점성 경계층 계산시 정확한 계산결과를 보여주며 기존의 AUSM 계열이 가지는 문제점인 물성치의 진동 현상을 제거한 수치기법이다. 원통형과 무딘 물체 주위의 극초음속 유동장 해석을 통해 공력이 진동현상 없이 정확하게 계산됨을 확인하였다. 그리고 충격파 정렬 기법의 특성을 파악하기 위해 충격파 반사문제와 충격파-충격파 상호작용 문제를 해석하여 수치오차 없이 충격파를 포착할 수 있음을 보였다. 또한 화학적 평형 비평형 유동 영역까지 충격파 정렬 격자 기법을 확장하였다.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2008.05a
• /
• pp.175-178
• /
• 2008

A Numerical Simulation which uses preconditioning algorithm to examine unsteady combustion processes for the AP/HTPB propellant with a converging-diverging nozzle has been compared with experimental data for solid rocket motor. To analysis reacting flow of solid rocket motor, unsteady pressure, temperature contour was simulated by grid moving of propellant.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.29-34
• /
• 1999

A two-dimensional Navier-Stokes code based on AUSMPW+ scheme has been developed to simulate the hypersonic flowfield of hypersonic shock-shock interaction. AUSMPW+ scheme is a new hybrid flux splitting scheme, which is improved by introducing pressure-based weight functions to eliminate the typical drawbacks of AUSM-type schemes, such as non-monotone pressure solutions. To study the real gas effects, three different gas models are taken into account in this paper: perfect gas, equilibrium flow and nonequilibrium flow. It has been investigated how each gas model influences on the peak surface loading, such as wall pressure and wall heat transfer, and unsteady flowfield structure in the region of shock-shock interaction. With the results, the value of peak pressure is not sensitive to the real gas effects nor to the wall catalyticity. However, the value of peak heat transfer rates is affected by the real gas effects and the wall catalyticity. The structure of the flowfield also changes drastically in the presence of real gas effects.