1990 Fiscal Year Final Research Report Summary
Finite-Difference Schemes for 3-D Incompressible Viscous Flows in Curvilinear Coordinate Systems
| Project/Area Number |
01550131
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Fluid engineering
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| Research Institution | Tohoku University |
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Principal Investigator |
IKOHAGI Toshiaki Tohoku Univ., Dept. Mech. Eng., Asso. prof., 工学部, 助教授 (90091652)
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| Co-Investigator(Kenkyū-buntansha) |
DAIGUJI Hisaaki Tohoku Univ., Dept. Mech. Eng., Prof., 工学部, 教授 (70005239)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Computational Fluid Dynamics / Incompressible Viscous Flow / Navier-Stokes Equation / Finite-Difference Method / General Curvilinear Coordinate Systems / Contravariant Velocity / Upstream-difference / High Reynolds Number Flow |
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| Research Abstract |
In order to analyze numerically the 3-D incompressible viscous flows with complex geometries, efficient finite-difference schemes and their computing programs have been developed.
Since the present scheme deals with the contravariant velocity as unknown variable in contrast with the conventional approach, in which the physical velocities are computed in a transformed space, it is possible to treat accurately the solid and cyclic boundary conditions, and to introduce easily a turbulence model into the scheme. First, the momentum equations of contravariant velocity components in curvilinear coordinate systems were newly derived from the Navier-Stokes equations. Second, an explicit time-marching finite-difference scheme extended to the curvilinear coordinate grid by using SMAC method or the fractional step method, was proposed. Employing a staggered grid in the transformed space in a similar manner to MAC method, the continuity condition can be satisfied identically and the occurrence of s
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purious error in pressure can be removed completely. Third, applying the trapezoidal rule, an implicit scheme was developed, in which the approximate factorization method and the partial consideration of viscous terms for the implicit portion are taken in order to enhance the stability of the scheme and to save the computational time. In the both explicit and implicit schemes, the momentum equations of contravariant velocities have been solved by discretising the convective term with QUICK scheme or thirdorder TVD scheme. Numerical simulations of stepped duct flows, cavity flow and rotor flow of axial-flow blower have shown the validity of the present schemes. Furthermore, the above-mentioned implicit scheme was also extended to an unsteady flow scheme by applying the Crank-Nicholson scheme and Newton iteration method. Direct numerical simulations were performed for the high Reynolds number flows in 2-D stepped duct and through a cascade. The evolution of shedding vortices into the wake from trailing-edge and the vortex behavior in the recirculating zone behind a step were able to be visualized. Less
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