An improvement of the dynamic procedure of Park et al. [Phys. Fluids 18, 125109 (2006)] for closure of the subgrid-scale eddy-viscosity model developed by Vreman [Phys. Fluids 16, 3670 (2004)] is proposed. The model coefficient which is globally constant in space but varies in time is dynamically determined assuming the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation of which utilization was proposed by Park et al. Like the Vreman model with a fixed coefficient and the dynamic-coefficient model of Park et al., the present model predicts zero eddy-viscosity in regions where the vanishing eddy viscosity is theoretically expected. The present dynamic model is especially suitable for large-eddy simulation in complex geometries since it does not require any ad hoc spatial and temporal averaging or clipping of the model coefficient for numerical stabilization and more importantly, requires only a single-level test filter in contrast to the dynamic model of Park et al., which employs two-level test filters.

A large-eddy simulation methodology for high performance parallel computation of statistically fully inhomogeneous turbulent flows on structured grids is presented. Strategies and algorithms to improve the memory efficiency as well as the parallel performance of the subgrid-scale model, the factored scheme, and the Poisson solver on shared-memory parallel platforms are proposed and evaluated. A novel combination of one-dimensional red–black/line Gauss–Seidel and two-dimensional red–black/line Gauss–Seidel methods is shown to provide high efficiency and performance for multigrid relaxation of the Poisson equation. Parallel speedups are measured on various shared-distributed memory systems. Validations of the code are performed in large-eddy simulations of turbulent flows through a straight channel and a square duct. Results obtained from the present solver employing a Lagrangian dynamic subgrid-scale model show good agreements with other available data. The capability of the code for more complex flows is assessed by performing a large-eddy simulation of the tip-leakage flow in a linear cascade. Copyright © 2006 John Wiley & Sons, Ltd.

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

OVER the past several decades various active flow control concepts have been proposed and evaluated to improve the efficiency and stability of aero-/hydrodynamic systems such as turbomachines and road/flight vehicles. Many of these techniques involve continuous blowing or suction, which can produce effective control but is difficult to apply in real fluid systems. In recent years, control devices involving zero-net-mass-flux oscillatory jets or synthetic jets have shown feasibility for industrial applications and effectiveness in controlling flow separation [1–11]. An accurate prediction, not to mention control, of incipient flow separation at high Reynolds numbers is a challenging task for numerical simulations. Recently, a broad range of numerical techniques such as direct numerical simulation (DNS)[6], large-eddy simulation (LES)[7], implicit LES (ILES)[8], detached eddy simulation (DES)[9], and steady or unsteady …

The effects of tip-gap size on the tip-leakage vortical structures and velocity and pressure fields are investigated using large-eddy simulation, with the objective of providing guidelines for controlling tip-leakage cavitation and viscous losses associated with the tip-leakage flow. The effects of tip-gap size on the generation and evolution of the end-wall vortical structures are discussed by investigating their evolutionary trajectories and the mean velocity field. The tip-leakage jet and tip-leakage vortex are found to produce significant mean velocity gradients, leading to the production of vorticity and turbulent kinetic energy. Inside the cascade passage, the peak streamwise velocity deficit and magnitudes of vorticity and turbulent kinetic energy in the tip-leakage vortex are reduced as the tip-gap size decreases. The present analysis indicates that the mechanisms for the generation of vorticity and turbulent kinetic energy are mostly unchanged by the tip-gap size variation. However, larger tip-gap sizes are found to be more inductive to tip-leakage cavitation judged by the levels of negative mean pressure and pressure fluctuations.

A high-order alternating direction implicit (ADI) method for computations of unsteady convection–diffusion equations is proposed. By using fourth-order Padé schemes for spatial derivatives, the present scheme is fourth-order accurate in space and second-order accurate in time. The solution procedure consists of a number of tridiagonal matrix operations which make the computation cost effective. The method is unconditionally stable, and shows higher accuracy and better phase and amplitude error characteristics than the standard second-order ADI method [D.W. Peaceman, H.H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, Journal of the Society of Industrial and Applied Mathematics 3 (1959) 28–41] and the fourth-order ADI scheme of Karaa and Zhang [High order ADI method for solving unsteady convection–diffusion problem, Journal of Computational Physics 198 (2004) 1–9].

Numerical stability and accuracy of finite-difference schemes on a skewed non-uniform mesh are investigated to provide guidelines for mesh design and for devising appropriate solution methods when mesh skewness is unavoidable. In the current analysis, a linear advection–diffusion equation in a Cartesian coordinate system is transformed into a curvilinear one corresponding to a skewed mesh. A finite-difference approximation of the transformed equation leads to the leading-order error terms which are responsible for time-step restrictions and numerical instability. A truncation error analysis of central-difference approximation reveals the effects of mesh non-uniformity and skewness on the solution quality. In addition, a modified wavenumber analysis is performed for the central- and upwind-difference schemes coupled with time-integration methods, to examine the effects of mesh skewness angle and flow direction relative to the mesh angle on the numerical stability. In general, severe mesh skewness leads to restrictions on the allowable cell Peclet number and time-step size and also increases phase and amplitude errors.

A powerful computational technique, large-eddy simulation, helps researchers study the detailed flow dynamics in the tip-gap region of hydraulic turbomachines. LES also helps researchers investigate ways to mitigate undesirable effects, such as cavitation, which can lead to reduced performance, increased noise, and structural vibration and erosion.

THE existence of tip clearance between the rotor blade and cas-ing wall is a major source of performance deterioration for axial turbomachines. In a transonic compressor, the interaction between the passage shock and the tip-leakage vortex is implicated in degradation of efficiency as well as noise generation. 1 Also, the tip clearance is responsible for a significant portion of performance losses in turbines, and the blade tip is known to be susceptible to damage from excessive thermal loading. 2 These issues have motivated a number of experimental and computational investigations of the tip-leakage flow configuration. 1− 15 For liquid handling systems like axial pumps and ducted propellers (Fig. 1), the rotor tip clearance is also considered to be the cause for low-pressure fluctuations downstream of the rotor in the vicinity of the end wall. Experimental studies of the incompressible rotor-tip-clearance flow3− 5 …

Laminar vortex sheddings behind a circular cylinder with and without splitter plates attached to the cylinder base at the Reynolds numbers of 100 and 160 are simulated by solving the unsteady two-dimensional incompressible Navier–Stokes equations. The Strouhal number, lift, and drag rapidly change with the length of the splitter plate. Acoustic source functions are obtained from the computed near-field velocity and pressure using Curle's solution of the Lighthill acoustic analogy. In the case of no splitter plate, the volume quadrupole noise is small at low Mach number compared with the surface dipole noise from the cylinder. When a splitter plate is attached to the cylinder, there are significant modifications of the dipole and quadrupole sources. Changes in the noise sources at Re = 100 are very different from those at Re = 160, and their differences are closely related to the secondary vortex generated at the tip of the splitter plate. Scattering effects at the edge of the splitter plate are also considered.