• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.12
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• pp.1624-1634
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• 1997

A numerical study on two-dimensional unsteady transonic cascade flow has been performed by adopting dual time stepping and the k-.omega. turbulence model. An explicit 4 stage Runge-Kutta scheme for the compressible Navier-Stokes equations and an implicit Gauss-Seidel iteration scheme for the k-.omega. turbulence model are proposed for fictitious time stepping. This mixed time stepping scheme ensures the stability of numerical computation and exhibits a good convergence property with less computation time. Typical steady-state convergence accelerating schemes such as local time stepping, residual smoothing and multigrid combined with dual time stepping shows good convergence properties. Numerical results are presented for unsteady laminar flow past a cylinder and turbulent shock buffeting problem for bicircular arc cascade flow is discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.10
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• pp.1229-1239
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• 1999

A computational study on unsteady compressible flows has been performed by adopting a low Reynolds number $k-{\omega}$ turbulence model in conjunction with dual time stepping scheme. An explicit four-stage Runge-Kutta scheme for the Navier-Stokes equations and an approximate factorization scheme for the $k-{\omega}$ turbulence model equations are used. Computational results obtained for blade surface pressure distributions in the process of rotor-stator interaction in a turbine stage are in good agreement with extant experimental data. The effects of the wake from the stator on the boundary-layer transition over the rotor blade surface are discussed by showing that high intensity turbulence of the stator wake induces an early transition.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.59-62
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• 2002

In the present study, solution algorithms for the computation of unsteady flows on an unstructured mesh are presented. Dual time stepping is incorporated to achieve the 2-nd order temporal accuracy while reducing the linearization and the factorization errors associated with a linear solver. Hence, any time step can be used by only considering physical phenomena. Gauss-Seidel scheme is used to solve linear system of equations. Rigid motion and spring analogy method fur moving mesh are all considered and compared. Special treatments of spring analogy for high aspect ratio cells are presented. Finally, numerical results for oscillating wing are compared with experimental data.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.18-24
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• 2003

In the present study, solution algorithms for the connotation of unsteady flows on an unstructured mesh me presented Dual time stepping is incorporated to achieve the 2-nd order temporal accuracy while reducing the linearization and the factorization errors associated with a linear solver. Hence, any time step can be used by only considering physical phenomena. Gauss-Seidel scheme is used to solve linear system of equations. Rigid motion and suing analogy method for moving mesh are all considered and compared. Special treatments of suing analogy for high aspect ratio cells are presented. Finally, numerical results for oscillating ing are compared with experimental data.

• Journal of computational fluids engineering
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• v.9 no.2
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• pp.52-61
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• 2004

In the present study, a solution algorithm for the computation of unsteady flows on unstructured meshes is presented. Dual time stepping is incorporated to achieve the second-order temporal accuracy while reducing errors associated with linearization and factorization. This allows any time step size, which is suitable for considering physical phenomena of interest. The Gauss-Seidel scheme is used to solve the linear system of equations. A special treatment based on spring analogy is made to handle meshes with high aspect-ratio cells. The present method was validated by comparing the results with experimental data and those obtained from rigid motion.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.9
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• pp.34-40
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• 2005

In present study, a two dimensional unsteady Navier-Stokes solver has been developed using the Diagonalized ADI (DADI) method and implicit dual time stepping method. The jacobian matrices in steady state Navier-Stokes equations are introduced from inviscid flux terms. The implicit treatment of artificial dissipation terms results in a block penta-diagonal matrix system and it becomes a scalar penta-diagonal matrix by diagonalization. In steady state equations about fictitious time, a new residual including a real time derivative term is introduced. From a converged solution about fictitious time, a real time unsteady solution can be obtained, which is called 'implicit dual time stepping method'. For code validation, an oscillating flat plate, a regular Karman vortices past a circular cylinder and shock buffeting around a bicircular airfoil problems are numerically solved. And they are compared with a theoretical solution, experiments and other researcher's computations.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.181-182
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• 2003

A preconditioned numerical method for gas-liquid to-phase flow is applied to solve cavitating flow. The present method employs a density based finite-difference method of dual time-stepping integration procedure and Roe's flux difference splitting approximation with MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. The method permits simple treatment of the whole gas-liquid two-phase flow field including wave propagation, large density changes and incompressible flow characteristics at low Mach number. By this method, two-dimensional internal flows through a venturi tuve and decelerating cascades are computed and discussed.

• Journal of the Korean Society of Propulsion Engineers
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• v.6 no.2
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• pp.75-84
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• 2002

A numerical analysis of unsteady motion in solid rocket motors with a nozzle has been conducted. The numerical formulation including modified $\kappa$-$\varepsilon$ turbulence model treats the complete conservation equation for the gas phase and the one-dimensional equations in the radial direction for the condensed phase. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations. After obtaining a steady state solution, pulse and periodic oscillations of pressure are imposed at the head-end to simulate acoustic oscillations of a travelling-wave motion in the combustion chamber. Various steady and unsteady state features in the combustion chamber of a rocket motor has been analyzed as results of numerical calculations.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1903-1908
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• 2004

A preconditioned numerical method for gas-liquid two-phase flows is applied to solve cavitating flow. The present method employs a finite-difference dual time-stepping integration procedure and the MUSCLTVD scheme. A homogeneous equilibrium cavitation model is used. The present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation, large density changes and incompressible flow characteristics at low Mach number. Some internal flows such as convergent-divergent nozzles are computed using this method. Comparisons of predicted and experimental results are provided and discussed.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.90-95
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• 1998

The two-dimensional incompressible and compressible Navier-Stokes codes are developed for the computation of the viscous turbulent flow over high-lift airfoils. Incompressible code using pseudo-compressibility and dual-time stepping method involves a conventional upwind differencing scheme for the convective terms and LU-SGS scheme for time integration. Compressible code also adopts an FDS scheme and LU-SGS scheme. Several two-equation turbulence models (the standard $k-{\varepsilon}$ model, the $k-{\omega}$ model. and $k-{\omega}$ SST model) are evaluated by computing the flow over single and multi-element airfoils. The compressible and incompressible codes are validated by computing the flow around the transonic RAE2822 airfoil and the NACA4412 airfoil, respectively. Both the results show a good agreement with experimental surface pressure coefficients and velocity profiles in the boundary layers. Also, the GA(W)-1 single airfoil and the NLR7301 airfoil with a flap are computed using the two-equation turbulence models. The grid systems around two- and three-element airfoil are efficiently generated using Chimera grid scheme, one of the overlapping grid generation methods.