Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

[1]  A. Dovgal,et al.  Flow instability in the laminar boundary layer separation zone created by a small roughness element , 1990 .

[2]  A. Dovgal,et al.  Hydrodynamic Instability and Receptivity of Small Scale Separation Regions , 1990 .

[3]  Victor V. Kozlov,et al.  Nonlinear development of a wave in a boundary layer , 1977 .

[4]  Ronald D. Joslin,et al.  Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate , 1992 .

[5]  D. J. Benney,et al.  On the Secondary Motion Induced by Oscillations in a Shear Flow , 1960 .

[6]  P S Klebanoff,et al.  MECHANISM BY WHICH A TWO-DIMENSIONAL ROUGHNESS ELEMENT INDUCES BOUNDARY-LAYER TRANSITION: ROUGHNESS INDUCED TRANSITION , 1972 .

[7]  Hermann F. Fasel,et al.  Numerical investigation of the three-dimensional development in boundary-layer transition , 1987 .

[8]  Hermann F. Fasel,et al.  NUMERICAL SIMULATION STUDIES OF TRANSITION PHENOMENA IN INCOMPRESSIBLE, TWO-DIMENSIONAL FLOWS. , 1977 .

[9]  W Tollmien The Production of Turbulence , 1931 .

[10]  Mehran Tadjfar,et al.  Velocity measurements within boundary layer roughness using index matching , 1985 .

[11]  Sedat Biringen,et al.  Final stages of transition to turbulence in plane channel flow , 1984, Journal of Fluid Mechanics.

[12]  T. Herbert Secondary Instability of Plane Channel Flow to Subharmonic Three-Dimensional Disturbances , 1983 .

[13]  Hermann F. Fasel,et al.  Non-parallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations , 1990, Journal of Fluid Mechanics.

[14]  G. B. Schubauer,et al.  Laminar-boundary-layer oscillations and transition on a flat plate , 1947 .

[15]  P. S. Klebanoff,et al.  The three-dimensional nature of boundary-layer instability , 1962, Journal of Fluid Mechanics.

[16]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[17]  P. J. Roache,et al.  A combined visual and hot-wire anemometer investigation of boundary-layer transition. , 1967 .

[18]  Craig L. Streett,et al.  Spectral multi-domain for large-scale fluid dynamic simulations , 1989 .

[19]  S. Biringen Three‐dimensional vortical structures of transition in plane channel flow , 1987 .

[20]  L. Kleiser,et al.  Numerical investigation of interactive transition control , 1985 .

[21]  T. Herbert Boundary-layer transition - Analysis and prediction revisited , 1991 .

[22]  G. Danabasoglu,et al.  Numerical simulation of spatially-evolving instability control in plane channel flow , 1990 .

[23]  Leonhard Kleiser,et al.  Numerical simulation of transition in wall-bounded shear flows , 1991 .

[24]  Hermann F. Fasel,et al.  Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations , 1976, Journal of Fluid Mechanics.

[25]  Steven A. Orszag,et al.  Instability mechanisms in shear-flow transition , 1988 .

[26]  S. McCormick,et al.  Multigrid methods for flow transition in a planar channel , 1991 .

[27]  M. Y. Hussaini,et al.  Numerical experiments in boundary-layer stability , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[28]  P. R. Spalart,et al.  Direct numerical study of leading-edge contamination , 1989 .

[29]  A. Craik,et al.  Non-linear resonant instability in boundary layers , 1971, Journal of Fluid Mechanics.