Theoretical breakthrough in the dynamics of a jet in a free-stream flow around a corner Articles uri icon

publication date

  • July 2022

start page

  • 127035-1

end page

  • 127035-12


  • 424

International Standard Serial Number (ISSN)

  • 0096-3003

Electronic International Standard Serial Number (EISSN)

  • 1873-5649


  • For the first time, the laminar jet in a free-stream flow around a corner with/without a
    moving wall condition (as it assists the flow) is studied theoretically. The corner may con-
    tract the streamlines or expand them depending on the angle of inclination. In the context
    of incompressibility, it is presented a composite non-similar transformation of the Navier-
    Stokes (N-S) equations in Cartesian space to approximately decipher the nature of the
    boundary layer flow over the entire physical domain; i.e. 0 ≤ x, y < ∞. The transformed
    Partial Differential Equations (PDEs) are then solved by an in-house MATLAB code, which
    employs an implicit algorithm of a tridiagonal form with quasi-linearization technique. For
    a stationary wall, as the negative angle of the corner meets Falkner-Skan (F-S) limitation
    and expands beyond, the predictive model starts to show a critical location, which reveals
    directly the flow separation point. This critical location moves toward the jet origin as
    the angle of inclination becomes more negative. Here, these locations are extracted as a
    function of the inclination parameter in order to manifest the suitability of a jet to de-
    lay boundary layer separation. A similar scenario also applies to the moving wall case. In
    this case, it was recorded that a moving wall condition delays separation for a consider-
    able distance. It should be pointed out that up to date, there is no theoretical investigation
    on this specific flow geometry despite the many associated applications; and the limited
    available reports on an analogous flow geometry are those from the Computational Fluid
    Dynamics (CFD) and on a case by case basis. More specifically, the present geometry is
    quite similar to the flow passing the way down to the trailing edge of an airfoil, with a jet
    generator mechanism such as Dielectric Barrier Discharge (DBD) plasma actuator to delay
    flow separation on the backside of the airfoil.
    Here, by the use of the theoretical non-similarity concept empowered by some recent
    advancements (see Jafarimoghaddam, 2020 and Jafarimoghaddam, 2021), the fundamental
    problem of a jet discharged in the lower boundary of a freestream flow over a wedge is
    successfully solved.
    This theoretical breakthrough suggests promising avenues for the future design of air-
    foils with moving parts/flaps as an innovative step forward to enhance maneuverability of
    the flying objects.


  • wall jet in a free stream flow, jet in a co-flow stream around a corner; wedge flow; impinging jet in falkner-skan flow; non-similarity