Injection into boundary layers: solutions beyond the classical form

Richard Hewitt, Peter Duck, Anthony Williams

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    This theoretical and numerical study presents three-dimensional boundary-layer solutions for laminar incompressible flow adjacent to a semi-infinite flat plate, subject to a uniform free-stream speed and injection through the plate surface. The novelty in this case arises from a fully three-dimensional formulation, which also allows for slot injection over a spanwise lengthscale comparable to the boundary-layer thickness. This approach retains viscous effects in both the spanwise and transverse directions, and effectively results in a parabolised Navier–Stokes system (sometimes referred to as the ‘boundaryregion equations’). Any injection profile can be described in this approach, but we restrict attention to three-dimensional states driven by a finite-width slot aligned with the flow
    direction and self-similar in their downstreamdevelopment. The classical two-dimensional
    states are known to only exist up to a critical (‘blow off’) injection amplitude, but the
    three-dimensional solutions here appear possible for any injection velocity. These new
    states take the form of low-speed streamwise-aligned streaks whose geometry depends
    on the amplitude of injection and the spanwise width of the injection slot; intriguingly,
    although very low wall shear is typically obtained, streamwise flow reversal is not observed,
    however hard the blowing. Asymptotic descriptions are provided in the limit of
    increasing slot width and fixed injection velocity, which allows for classification of the
    solutions according to two bounding injection rates.
    Original languageEnglish
    JournalJournal of Fluid Mechanics
    Early online date7 Jun 2017
    Publication statusPublished - 31 Jul 2017


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