Data Reduction And Error Analysis For The Physical Sciences

Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

Effects of large computational time steps on the computed turbulence were investigated using a fully implicit method. In turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined. Turbulence fluctuations could not be sustained if the computational time step was near or larger than the Kolmogorov time scale.

Effects of the computational time step on numerical solutions for turbulent flow

Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.

Three-dimensional instability in flow over a backward-facing step

Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids

Backward-Facing Step (BFS) flow is one representative model for separation flows, which can be widely seen in aerodynamic flows (airfoil, spoiler, high attack angle process), engine flows, condensers, vehicles (cars, boat), heat transfer systems, and even the flow around buildings, etc. The flow separation after a simple stage will introduce separation bubble formation, evolution and re-attachment process, which is dependent on the BFS geometric design, the inlet and outlet conditions, turbulent intensity, as well as heat transfer conditions. In the past decades, it has been widely studied by various theoretical, experimental and numerical methods. Considering the importance of BFS flow in both theoretical and engineering aspects, this paper is focused on a review study of BFS flows from fundamental understandings to various experimental and numerical developments in a historical viewpoint. Basic models and the parameter-based after-step flow laws are summarized and categorized in this study. It is shown that the step size (duct expansion ratio) will define the basic re-circulation and re-attachment process, while the coupled effects of inflow parameters and the perturbation designs also help shape the flow behaviors after BFS. The review is also extended with model generalizations and the implications on system design, especially the heat transfer effects and the representative control designs are discussed in detail. Future trends and prospects in BFS studies are also included in this study.

A review of Backward-Facing Step (BFS) flow mechanisms, heat transfer and control

Short Note: ADI-SGS scheme on ideal magnetohydrodynamics

Large-eddy simulations have been conducted to investigate the mechanisms of separated-flow control using a dielectric barrier discharge plasma actuator at a low Reynolds number. In the present study, the mechanisms are classified according to the means of momentum injection to the boundary layer. The separated flow around the NACA 0015 airfoil at a Reynolds number of 63 000 is used as the base flow for separation control. Both normal and burst mode actuations are adopted in separation control. The burst frequency non-dimensionalized by the freestream velocity and the chord length (F+) is varied from 0.25 to 25, and we discuss the control mechanism through the comparison of the aerodynamic performance and controlled flow-fields in each normal and burst case. Lift and drag coefficients are significantly improved for the cases of F+ = 1, 5, and 15 due to flow reattachment associated with a laminar-separation bubble. Frequency and linear stability analyses indicate that the F+ = 5 and 15 cases effectively exc...

Taku Nonomura

Papers

Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids

A review of Backward-Facing Step (BFS) flow mechanisms, heat transfer and control

Short Note: ADI-SGS scheme on ideal magnetohydrodynamics

Mechanisms for laminar separated-flow control using dielectric-barrier-discharge plasma actuator at low Reynolds number

Effects of difference scheme type in high-order weighted compact nonlinear schemes