An efficient second-order accurate finite-volume method is developed for a solution of the incompressible Navier–Stokes equations on complex multi-block structured curvilinear grids. Unlike in the finite-volume or finite-difference-based alternating-direction-implicit (ADI) methods, where factorization of the coordinate transformed governing equations is performed along generalized coordinate directions, in the proposed method, the discretized Cartesian form Navier–Stokes equations are factored along curvilinear grid lines. The new ADI finite-volume method is also extended for simulations on multi-block structured curvilinear grids with which complex geometries can be efficiently resolved. The numerical method is first developed for an unsteady convection–diffusion equation, then is extended for the incompressible Navier–Stokes equations. The order of accuracy and stability characteristics of the present method are analyzed in simulations of an unsteady convection–diffusion problem, decaying vortices, flow in a lid-driven cavity, flow over a circular cylinder, and turbulent flow through a planar channel. Numerical solutions predicted by the proposed ADI finite-volume method are found to be in good agreement with experimental and other numerical data, while the solutions are obtained at much lower computational cost than those required by other iterative methods without factorization. For a simulation on a grid with O(105) cells, the computational time required by the present ADI-based method for a solution of momentum equations is found to be less than 20% of that required by a method employing a biconjugate-gradient-stabilized scheme.

We conduct wind-tunnel experiments on three different uniform roughness arrays composed of sparsely distributed rectangular cylinders for the estimation of surface parameters. Roughness parameters such as the roughness length z 0 and zero-plane displacement d are extracted using a best-fit approximation of the measured wind velocity. We also perform a large-eddy simulation (LES) to confirm that four sampling points are sufficient to surrogate a space average above the canopy layer of the sparse roughness arrays. We propose a new morphological model from a systematic analysis of experimental data on the arrays. The friction velocity predicted by the proposed model agrees well with the peak value of the measured Reynolds shear stress. The proposed model is further validated in an additional wind-tunnel experiment conducted on a scaled configuration of a real urban area exposed to four wind directions. The proposed model is found to perform very well particularly in the estimation of the friction velocity, readily leading to a better estimation of turbulence, which is essential for an accurate prediction of pollutant dispersion.

The governing equations for large-eddy simulation are derived from the application of a low-pass filter to the Navier–Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter, causing results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operation, and hence the resolved turbulence, from the underlying mesh distribution alleviating some of the grid sensitivities. We investigate the use of explicit filtering in large-eddy simulation in order to obtain numerical solutions that are grid independent. The convergence of simulations using a fixed filter width with varying mesh resolutions to a true large-eddy simulation solution is analyzed for a turbulent channel flow at Re_tau = 180⁠, 395, and 640. By using explicit filtering, turbulent statistics and energy spectra are shown to be independent of the mesh resolution used.

A novel flow configuration devised for investigation of active control of separated airfoil flows using synthetic jets is presented. The configuration consists of a flat plate, with an elliptic leading edge and a blunt trailing edge, at zero incidence in a free stream. Flow separation is induced on the upper surface of the airfoil at the aft-chord location by applying suction and blowing on the top boundary of the computational domain. Typical separated airfoil flows are generally characterized by at least three distinct frequency scales corresponding to the shear layer instability, the unsteadiness of the separated region and the vortex shedding in the wake, and all these features are present in the current flow. Two-dimensional Navier–Stokes simulations of this flow at a chord Reynolds number of 6 × 104 have been carried out to examine the nonlinear dynamics in this flow and its implications for synthetic-jet-based separation control. The results show that there is a strong nonlinear coupling between the various features of the flow, and that the uncontrolled as well as the forced flow is characterized by a variety of ‘lock-on’ states that result from this nonlinear coupling. The most effective separation control is found to occur at the highest forcing frequency for which both the shear layer and the separated region lock on to the forcing frequency. The effects of the Reynolds number on the scaling of the characteristic frequencies of the separated flow and its subsequent control are studied by repeating some of the simulations at a higher Reynolds number of 1 × 10^5

The dynamic global-coefficient subgrid-scale eddy-viscosity model by You and Moin [Phys. Fluids 19, 065110 (2007)] is generalized for large-eddy simulation of turbulent flow with scalar transport. The model coefficient for subgrid-scale scalar flux which is constant in space but varies in time is dynamically determined based on the “global conservation” of the transport equation for scalar variance. Large-eddy simulations of turbulent flow with passive scalar transport through a channel and over a backward-facing step show that the present model has a similar predictive capability as the dynamic Smagorinsky model. The present dynamic model is especially suitable for large-eddy simulation of turbulent flow with scalar transport in complex geometries since it does not require any spatial and temporal averaging or clipping of the model coefficient for numerical stabilization and requires only a single-level test filter. The present model is not more complicated in implementation and not more expensive in terms of computational cost than the dynamic Smagorinsky model.

We perform large-eddy simulation of turbulent flow separation over an airfoil and evaluate the effectiveness of synthetic jets as a separation control technique. The flow configuration consists of flow over an NACA 0015 airfoil at Reynolds number of 896,000 based on the airfoil chord length and freestream velocity. A small slot across the entire span connected to a cavity inside the airfoil is employed to produce oscillatory synthetic jets. Detailed flow structures inside the synthetic-jet actuator and the synthetic-jet/cross-flow interaction are simulated using an unstructured-grid finite-volume large-eddy simulation solver. Simulation results are compared with the 2005 experimental data of Gilarranz et al., and qualitative and quantitative agreements are obtained for both uncontrolled and controlled cases. As in the experiment, the present large-eddy simulation confirms that synthetic-jet actuation effectively delays the onset of flow separation and causes a significant increase in the lift coefficient. Modification of the blade boundary layer due to oscillatory blowing and suction and its role in separation control is discussed.

An unstructured-grid large-eddy simulation (LES) technique is used to investigate the turbulent flow separation over an airfoil with and without synthetic-jet control. Numerical accuracy and stability on arbitrary shaped mesh elements at high Reynolds numbers are achieved using a finite-volume discretization of the incompressible Navier–Stokes equations based on higher-order conservation principles—i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithm. Two different stall configurations, which consist of flow over a NACA 0015 airfoil at and angles of attack, are simulated at Reynolds number of based on the airfoil chord length and freestream velocity. In the case of angle of attack where flow separates around a midchord location, LES results show excellent agreement with the experimental data for both uncontrolled and controlled cases. LES confirms the experimental finding that synthetic jets, which are produced through a slot across the entire span on suction surface at 12% chord location, effectively delay the onset of flow separation and cause a significant increase in the lift coefficient. In the case of angle of attack where flow separates near the leading edge, LES predicts reasonable results comparable to experimental data when grid resolution is sufficient to predict the separated shear layer. In this case, the synthetic-jet actuation at 12% chord location is found marginally effective in controlling leading-edge separation.

The tip-leakage flow in a turbomachinery cascade is studied using large-eddy simulation with particular emphasis on understanding the underlying mechanisms for viscous losses in the vicinity of the tip gap. Systematic and detailed analysis of the mean flow field and turbulence statistics has been made in a linear cascade with a moving endwall. Gross features of the tip-leakage vortex, tip-separation vortices, and blade wake have been revealed by investigating their revolutionary trajectories and mean velocity fields. The tip-leakage vortex is identified by regions of significant streamwise velocity deficit and high streamwise and pitchwise vorticity magnitudes. The tip-leakage vortex and the tip-leakage jet which is generated by the pressure difference between the pressure and suction sides of the blade tip are found to produce significant mean velocity gradients along the spanwise direction, leading to the production of vorticity and turbulent kinetic energy. The velocity gradients are the major causes for viscous losses in the cascade endwall region. The present analysis suggests that the endwall viscous losses can be alleviated by changing the direction of the tip-leakage flow such that the associated spanwise derivatives of the mean streamwise and pitchwise velocity components are reduced.

The tip-clearance flow in axial turbomachines is studied using large-eddy simulation with particular emphasis on understanding the unsteady characteristics of the tip-leakage vortical structures and the underlying mechanisms for cavitation-inducing low-pressure fluctuations. A systematic and detailed analysis of the velocity and pressure fields has been made in a linear cascade with a moving end-wall. The generation and evolution of the tip-leakage vortical structures have been investigated throughout the cascade using mean streamlines and contours. An analysis of the energy spectra and space-time correlations of the velocity fluctuations suggests that the tip-leakage vortex is subject to a pitchwise low frequency wandering motion. Detailed statistics of the pressure fields has been analyzed to draw inferences on cavitation. The regions of low pressure relative to the mean values coincide with regions of strong pressure fluctuations, and the regions are found to be highly correlated with the vortical structures in the tip-leakage flow, particularly in the tip-leakage and tip-separation vortices.

Effects of hydrophobic surfaces on the drag and lift of a circular cylinder at Reynolds numbers of 300 and 3900 are investigated using numerical simulations. A cylinder of which the entire surface is no-slip, a cylinder of which the entire surface is hydrophobic, and cylinders with alternating circumferential bands of slip and no-slip conditions are considered. The width of the alternating bands ranges from 0 to ⁠, where is a spanwise characteristic wavelength in the near wake. At Reynolds number 300, the hydrophobic surface consisting of alternating slip and no-slip bands of width is found to be most effective in enhancing wake instability, thereby decreasing the base suction, drag, and rms lift coefficients. At Reynolds number 3900, hydrophobic surface treatments are found to delay flow separation, thereby decreasing the drag and rms lift.