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Modelling the decay of finite-span starting and stopping wall jets in an external stream

Published online by Cambridge University Press:  08 November 2022

Ben Steinfurth Open the ORCID record for Ben Steinfurth [Opens in a new window]  and
Julien Weiss Open the ORCID record for Julien Weiss [Opens in a new window]
Ben Steinfurth*
Affiliation:
Institute of Aeronautics and Astronautics, Technische Universität Berlin, Marchstr. 12–14, 10587 Berlin, Germany
Julien Weiss
Affiliation:
Institute of Aeronautics and Astronautics, Technische Universität Berlin, Marchstr. 12–14, 10587 Berlin, Germany
*
†Email address for correspondence: ben.steinfurth@tu-berlin.de
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Abstract

The flow under consideration is a wall jet that results from an inclined jet in cross-flow emitted into a zero-pressure-gradient turbulent boundary layer from a slot-like outlet of width $b=0.5\,\mathrm {mm}$ and span $L=20\,\mathrm {mm}$. Despite the finite jet span, the velocity decay and wall-normal spreading rate in the symmetry plane can be described with power laws almost identical to those for the two-dimensional flow determined by Zhou & Wygnanski (AIAA J., vol. 31, 1993, pp. 848–853). This is explained by the lack of significant lateral spreading found in the present configuration due to a self-amplifying inward-directed fluid motion, fundamentally differing from conditions found in the absence of an external stream. Regions with ‘approximately self-similar’ properties also exist in the case of unsteady velocity programmes where the fluid is ejected in a pulsatile fashion. Here, the wall jet is enclosed by a leading vortex structure and a deceleration wave, for which the time-dependent locations can be predicted by means of empirical constants. This yields models for the major properties inside the advancing and diffusing wall jet that only require knowledge regarding the velocity ratio, the ejected momentum flux and the kinematic viscosity, representing an extension to scaling laws for steady wall jets in still ambience established by Narasimha et al. (Aeronaut. Q., vol. 77, 1973, pp. 355–359).

JFM classification

Boundary Layers: Boundary layer control Vortex Flows: Vortex dynamics Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 951 , 25 November 2022 , A28
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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Steinfurth and Weiss supplementary movie 1

Visualisation of the extraction of time-dependent propagation front location $x_p/b$; upper diagram: FTLE field with $x_p/b$ marked by red dashed vertical line, lower diagram: jet spreading rates for steady and starting wall jets with $x_p/b$ marked by red circle
Download Steinfurth and Weiss supplementary movie 1(Video)
Video 1.7 MB

Steinfurth and Weiss supplementary movie 2

Visualisation of the extraction of time-dependent deceleration wave location $x_d/b$; upper diagram: FTLE field with $x_d/b$ marked by red dashed vertical line, lower diagram: maximum jet velocities for steady and starting wall jets with $x_d/b$ marked by red circle

Download Steinfurth and Weiss supplementary movie 2(Video)
Video 759.5 KB