A singular value analysis of boundary layer control

Lim, Junwoo; Kim, John

doi:doi:10.1063/1.1710522

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Effects of nonperfect thermal sources in turbulent thermal convection

The effects of the plates thermal properties on the heat transfer in turbulent thermal convection are investigated by direct numerical simulations of the Navier–Stokes equations with the Boussinesq approximation. It has been found that the governing parameter is the ratio of the thermal resistances of the fluid layer Rf and the plates Rp; when this ratio is smaller than a threshold value (Rf/Rp ≈ 300 arbitrarily defined by requiring that the actual heat transfer differs by less than 2% from its ...

Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall

The shear flow of a binary mixture of rarefied gases over a plane wall is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. This fundamental problem in rarefied gas dynamics is analyzed numerically by a finite-difference method, in which the complicated collision integrals are computed by the extension to the case of a gas mixture of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)]....

Several approaches for boundary-layer control are analyzed from a linear system point of view. The singular value decomposition (SVD) is applied to the linearized Navier–Stokes system in the presence of control. The performance of control is examined in terms of the largest singular values, which represent the maximum disturbance energy growth ratio attainable in the linear system under control. It is shown that the maximum growth ratio is less in controlled systems than in the uncontrolled system only when control parameters are within a certain range of values. With opposition control, for example, when the detection plane is located too far away from the wall, the maximum energy growth ratio is larger, consistent with the results observed in direct numerical simulations. The SVD analysis of other controls also shows a similarity between the trend observed in the SVD analysis (linear) and that observed in direct numerical simulations (nonlinear), thus reaffirming the importance of linear mechanisms in the near-wall dynamics of turbulent boundary layers. The present study illustrates that the SVD analysis can be used as a guideline for designing controllers for drag reduction in turbulent boundary layers. © 2004 American Institute of Physics.