Alireza Mohammadi

Groove optimization for drag reduction

Optimal shapes of laminar, drag reducing longitudinal grooves in a pressure driven flow have been determined. It has been shown that such shapes can be characterized using reduced geometry models involving only a few Fourier modes. Two classes of grooves have been studied, i.e., the equal-depth grooves, which have the same height and depth, and the unequal-depth grooves. It has been shown that the optimal shape in the former case can be approximated by a certain universal trapezoid. There exists an optimum depth in the latter case and this depth, combined with the corresponding groove shape, defines the optimal geometry; this shape is well-approximated by a Gaussian function. Drag reduction due to the use of the optimal grooves has been determined. The analysis has been extended to kinematically driven flows. It has been shown that in this case the longitudinal grooves always increase the flow resistance.

Mechanism of drag generation by surface corrugation

Drag generated by periodic corrugation has been determined analytically in the limit of long corrugation wavelength. Three physical mechanisms have been identified, i.e., the additional shear drag due to an increase of the wetted area and the re-arrangement of the shear stress distribution, the pressure form drag associated with the mean pressure gradient, and the pressure interaction drag associated with the phase difference between the surface geometry and the periodic part of the pressure field. The total drag increases rapidly with increase of the corrugation amplitude, with the form and interaction drags contributing up to 45% and 30% of this increase, respectively.

Spectrally-accurate immersed boundary conditions method for three-dimensional flows

A three-dimensional, spectrally accurate algorithm based on the immersed boundary conditions (IBC) concept has been developed for the analysis of flows in channels bounded by rough boundaries. The algorithm is based on the velocityvorticity formulation and uses a fixed computational domain with the flow domain immersed in its interior. The geometry of the boundaries is expressed in terms of double Fourier expansions and boundary conditions enter the algorithm in the form of constraints. The spatial discretization uses Fourier expansions in the stream-wise and span-wise directions and Chebyshev expansions in the wall-normal direction. The algorithm can use either the fixed-flow-rate constraint or the fixed-pressure-gradient constraint; a direct implementation of the former constraint is described. An efficient solver which takes advantage of the structure of the coefficient matrix has been developed. It is demonstrated that the applicability of the algorithm can be extended to more extreme geometries using the over-determined formulation. Various tests confirm the spectral accuracy of the algorithm.