• 한국전산유체공학회:학술대회논문집
• /
• 2001.10a
• /
• pp.20-30
• /
• 2001

A multigrid DADI method for low Mach number preconditioning method is presented. The eigenvalues of governing equations are modified by A low Mach number preconditioner developed by Choi & Merkle, and it results in an accurate solution and fast convergence In the low Mach number region. The convergence of numerical method is further accelerated by multigrid method. The efficient and accuracy of present method is shown by comparison with conventional solution method for the compressible flows.

• Bulletin of the Korean Chemical Society
• /
• v.17 no.4
• /
• pp.385-390
• /
• 1996

It has been well known that the Grad thirteen-moment equations have solutions only when the Mach number is less than a limiting value for the stationary plane shock-waves. The limit of Mach number has been re-examined by including successive terms in the series expansion of distribution function. The method employed is the linear analysis of moment equations near up-streaming and down-streaming flows. For the thirteen moment case, it has been confirmed that equations have solutions only when the Mach number is less than 1.6503, which is consistent with the literature value. For the case of twenty moments, the limit of Mach number is decreased to 1.3416.

• Journal of computational fluids engineering
• /
• v.15 no.2
• /
• pp.55-61
• /
• 2010

A dependence of weighting parameter in preconditioning method for solving low Mach number flow with incompressible flow nature is investigated. The present preconditioning method employs a finite-difference method applied Roe‘s flux difference splitting approximation with the MUSCL-TVD scheme and 4th-order Runge-Kutta method in curvilinear coordinates. From the computational results of benchmark flows through a 2-D backward-facing step duct it is confirmed that there exists a suitable value of the weighting parameter for accurate and stable computation. A useful method to determine the weighting parameter is introduced. With this method, high accuracy and stable computational results were obtained for the flow with low Mach number in the range of Mach number less than 0.3.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.35-42
• /
• 1998

Time marching algorithms applied to compressible Navier-Stokes equation have a convergence problem at low Mach number. It is mainly due to the eigenvalue stiffness and pressure singularity as Mach number approaches to zero. Among the several methods to overcome the shortcomings of time marching scheme, time derivative preconditioning method have been used successfully. In this numerical analysis, we adopted a preconditioner of K.H. Chen and developed a two-dimensional, axisymmetric Navier-Stokes program. The steady state driven cavity flow and backward facing step flow problems were computed to confirm the accuracy and the robustness of preconditioned algorithm for low Mach number flows. And the transonic and supersonic flows insice the JPL axisymmetric nozzle internal flow is exampled to investigate the effects of preconditioning at high Mach number flow regime. Test results showed excellent agreement with the experimental data.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.35 no.12
• /
• pp.1075-1081
• /
• 2007

The temperature preconditioning is applied to the Navier-Stokes equations. Also, a new concept of diffusion Mach numbers is introduced to modify the reference Mach number for the Navier-Stokes equations. Flows over a circular cylinder were calculated at different Reynolds numbers. It is shown that the temperature preconditioning improves the convergence characteristics of Navier-Stokes equations. Also, it is shown that the modified reference Mach number alleviates the convergence problems at locally low speed regions.

• 한국전산유체공학회:학술대회논문집
• /
• 1995.10a
• /
• pp.241-245
• /
• 1995

This paper presents the studies on the variation of shape and thickness of a normal shock wave with Mach number and density by using the most useful numerical technique in rarefied gas regime, DSMC(Direct Simulation Monte Carlo). Calculations are peformed for the three different Mach numbers and for one Mach number with different densities. From the obtained results, we find that the shock thickness is decreasing with increasing Mach number, and there are much variations in thickness and shape with decreasing density. Also, there is a noticeable overshoot of the translational temperature near the shock center in the case of a large Mach number.

• Journal of computational fluids engineering
• /
• v.17 no.4
• /
• pp.93-102
• /
• 2012

Once the condensation of water vapor in moist air around a thin airfoil occurs, liquid droplets nucleate. The condensation process releases heat to the surrounding gaseous components of moist air and significantly affects their thermodynamic and flow properties. As a results, variations in the aerodynamic performance of airfoils can be found. In the present work, the effects of upstream Mach number and thickness ratio of airfoil on the transonic flow of moist air around a thin airfoil are investigated by numerical analysis. The results shows that a significant condensation occurs as the upstream Mach number is increased at the fixed thickness ratio of airfoil($\epsilon$=0.12) and as the thickness ratio of airfoil is increased at the fixed upstream Mach number($M_{\infty}$=0.80). The condensate mass fraction is also increased and dispersed widely around an airfoil as the upstream Mach number and thickness ratio of airfoil are increased. The position of shock wave for moist air flow move toward the leading edge of airfoil when it is compared with the position of shock wave for dry air.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.9
• /
• pp.2283-2296
• /
• 1995

Experiments of normal shock wave/turbulent boundary layer interaction were conducted in a supersonic diffuser. The flow Mach number just upstream of the normal shock wave was in the range of 1.10 to 1.70 and Reynolds number based upon the turbulent boundary layer thickness was varied in the range of 2.2*10$^{[-994]}$ -4.4*10$^{[-994]}$ . The wall pressures in streamwise and spanwise directions were measured for two test cases, in which the turbulent boundary layer thickness incoming into the supersonic diffuser was changed. The results show that the interactions of normal shock wave with turbulent boundary layer in the supersonic diffuser can be divided into three patterns, i.e., transonic interaction, weak interaction and strong interaction, depending on Mach number. The weak interactions generate the post-shock expansion which its strength is strong as the Mach number increases and the strong interactions form the pseudo-shock waves. From the spanwise measurements of wall pressure, it is known that if the flow Mach number is low, the interacting flow fields essentially appear two-dimensional, but they have an apparent 3-dimensionality for the higher Mach numbers.

• Advances in aircraft and spacecraft science
• /
• v.9 no.2
• /
• pp.119-130
• /
• 2022

Supersonic projectiles like rockets, missiles, or aircraft find various applications in the field of defense. The shape of the wings is mainly designed as wedge shape or delta wings for supersonic vehicles. The study of supersonic flows over the wedges and flat plate delta wings around the large scale of incidence angle is considered in the supersonic projectile. In the present paper, the prime attention is to study the pressure at the nose of the plane wedge over the various Mach number and the various angles of incidence. Ghosh piston theory is used to obtain the pressure distribution analytically, and the results are compared with CFD analysis results. The wedge angle and Mach number are the parameters considered for the research work. The range of wedge angle is 50 to 250, and Mach number is 1.5 to 4.0 are considered for the current research work. The analytical results show excellent agreement with the CFD results. The results show that both the parameters wedge angle and Mach number are influential parameters to vary the static pressure. The static pressure increases with an increase in Mach number and wedge angle.

• 한국전산유체공학회:학술대회논문집
• /
• 1996.05a
• /
• pp.40-45
• /
• 1996

This paper discribes the viscous interaction of Hypersonic Wedge Flows using Roe FDS and AUSM+. For this purpose we developed the frozen and the equilibrium code and numerically simulated the viscous interaction by changing the surface temperature and the mach number. We used curve fitting data in NASA Reference Publication 1181, 1260 to calculate equilibrium properties. We compare the equilibrium flow with the frozen flow. We conclude that the mach number and the surface temperature are significant parameters, as the surface temperature and the mach number increase the viscous interaction becomes stronger, and we must consider high-temperature effects in hypersonic flow