Among the important physical phenomena associated with the jet in crossflow is the formation and evolution of vortical structures in the flow field, in particular the counter-rotating vortex pair (CVP) associated with the jet cross-section. The present computational study focuses on the mechanisms for the dynamical generation and evolution of these vortical structures. Transient numerical simulations of the flow field are performed using three-dimensional vortex elements. Vortex ring rollup, interactions, tilting, and folding are observed in the near field, consistent with the ideas described in the experimental work of Kelso, Lim & Perry (1996), for example. The time-averaged effect of these jet shear layer vortices, even over a single period of their evolution, is seen to result in initiation of the CVP. Further insight into the topology of the flow field, the formation of wake vortices, the entrainment of crossflow, and the effect of upstream boundary layer thickness is also provided in this study.

We perform direct numerical simulations (DNS) of a turbulent channel flow over porous walls. In the fluid region the flow is governed by the incompressible Navier-Stokes (NS) equations, while in the porous layers the Volume-Averaged Navier-Stokes (VANS) equations are used, which are obtained by volume-averaging the microscopic flow field over a small volume that is larger than the typical dimensions of the pores. In this way the porous medium has a continuum description, and can be specified without the need of a detailed knowledge of the pore microstructure by indipendently assigning permeability and porosity. At the interface between the porous material and the fluid region, momentum-transfer conditions are applied, in which an available coefficient related to the unknown structure of the interface can be used as an error estimate. To set up the numerical problem, the velocity-vorticity formulation of the coupled NS and VANS equations is derived and implemented in a pseudo-spectral DNS solver. Most of the simulations are carried out at Re τ = 180 and consider low-permeability materials; a parameter study is used to describe the role played by permeability, porosity, thickness of the porous material, and the coefficient of the momentum-transfer interface conditions. Among them permeability, even when very small, is shown to play a major role in determining the response of the channel flow to the permeable wall. Turbulence statistics and instantaneous flow fields, in comparative form to the flow over a smooth impermeable wall, are used to understand the main changes introduced by the porous material. A simulations at higher Reynolds number is used to illustrate the main scaling quantities.

We present the three-dimensional linear stability analysis of a pressure-driven, incompressible, fully developed, laminar flow in a channel delimited by rigid, homogeneous, isotropic, porous layers. We consider porous materials of small permeability in which the maximum fluid velocity is small compared to the mean velocity in the channel region and for which inertial effects may be neglected. We analyse the linear stability of symmetric laminar velocity profiles in channels with two identical porous walls as well as skewed laminar velocity profiles in channels with only one porous wall. We solve the fully coupled linear stability problem, arising from the adjacent channel and porous flows, using a spectral collocation technique. We validate our results by recovering the linear stability results of a flow in a channel with impermeable walls as the permeabilities of the porous layers tend to zero. We also verify that our results are consistent with the assumption of negligible inertial effects in the porous regions. We characterize the stability of pressure-driven flows by performing a parametric study in which we vary the permeability, porosity, and height of the porous layers as well as an interface coefficient, τ, associated with the momentum transfer process at the interfaces between the channel and porous regions. We find that very small amounts of wall permeability significantly affect the Orr-Sommerfeld spectrum and can dramatically decrease the stability of the channel flow. Within our assumptions, in channels with two porous walls, permeability destabilizes up to two Orr-Sommerfeld wall modes and introduces two new damped wall modes on the left branch of the spectrum. In channels with only one porous wall, permeability destabilizes up to one wall mode and introduces one new damped wall mode on the left branch of the spectrum. In both cases, permeability also introduces a new class of damped modes associated with the porous regions. The size of the unstable region delimited by the neutral curve grows substantially, and the critical Reynolds number can decrease to only 10% of the corresponding value for a channel flow with impermeable walls. We conclude our study by considering two real materials: foametal and aloxite. We fit the porosity and interface coefficient τ to published data so that the porous materials we model behave like foametal and aloxite, and we compare our results with previously published numerical and experimental results. © 2008 Cambridge University Press

This study quantifies the dynamics of actuation for the temporally forced, round gas jet injected transversely into a crossflow, and incorporates these dynamics in developing a methodology for open loop jet control. A linear model for the dynamics of the forced jet actuation is used to develop a dynamic compensator for the actuator. When the compensator is applied, it allows the jet to be forced in a manner which results in a more precisely prescribed, temporally varying exit velocity, the RMS amplitude of perturbation of which can be made independent of the forcing frequency. Use of the compensator allows straightforward comparisons among different conditions for jet excitation. Clear identification can be made of specific excitation frequencies and characteristic temporal pulse widths which optimize transverse jet penetration and spread through the formation of distinct, deeply penetrating vortex structures.

A reduced-order linear feedback controller is designed and applied to turbulent channel flow for drag reduction. From the linearized two-dimensional Navier-Stokes equations a distributed feedback controller, which produces blowing/suction at the wall based on the measured turbulent streamwise wall-shear stress, is derived using model reduction techniques and linear-quadratic-quadratic-Gaussian/loop-transfer-recovery control synthesis. The quadratic cost criterion used for synthesis is composed of the streamwise wall-shear stress, which includes the control effort of blowing/suction. This distributed two-dimensional controller developed from a linear system theory is shown to reduce the skin friction by 10% in direct numerical simulations of a low-Reynolds number turbulent nonlinear channel flow. Spanwise shear-stress variation, not captured by the distributed two-dimensional controller, is suppressed by augmentation of a simple spanwise ad hoc control scheme. This augmented three-dimensional controller, which requires only the turbulent streamwise velocity gradient, results in a further reduction in the skin-friction drag. It is shown that the input power requirement is significantly less than the power saved by reduced drag. Other turbulence characteristics affected by these controllers are also discussed

Two-dimensional unsteady separated flow past a semi-infinite plate with transverse motion is considered. The rolling-up of the separated shear-layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A power-law starting flow is assumed along with a power law for the transverse motion. The effects of the motion of the plate on the starting vortex circulation and trajectory are presented. A suitable vortex shedding mechanism is introduced and a class of flows involving several vortices is presented. Finally, some possibilities for actively controlling the production of circulation by moving the plate are discussed

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We perform a three-dimensional linear stability analysis of a laminar flow in a channel delimited by rigid, homogeneous, isotropic, porous blocks sealed by impermeable walls. We consider porous materials with small permeability and neglect inertial effects in the porous flow. We solve the coupled linear stability problem, arising from the adjacent channel and porous flows, using a spectral collocation technique. We find that very small amounts of wall permeability can dramatically decrease the stability of the channel flow with respect to Poiseuille flow. We also observe two new wall modes and a new class of modes in the porous regions