page_title: Coandă effect
section_title: Conditions of existence
hierarchical_section_title: Coandă effect / Conditions of existence
caption_attribution_description: English: Measuring surface pressure along a circular wall of radius r = 12 cm, deflecting a jet Reynolds number 106 of width h. The pressure begins to decrease due to the transverse gradient to an angle 9° along the wall, then remains constant if the h/r ratio of the width of the jet to the radius is less than 0.25 along an additional angle which is "true Coandă effect", and finally increases back to the ambient pressure again over another angle 9°. If the h/r ratio is more than 0.5, the local effects 2 x 9° only occur and there is "no true Coandă effect". Experiments made by the author and J. Liermann in the laboratory of the author, SNECMA, published in: Kadosch M., "Déviation d'un jet par adhérence à une paroi convexe" in: Journal de Physique et Le Radium, avril 1958, Paris, p.9A.
context_page_description: The Coandă effect is the tendency of a fluid jet to stay attached to a convex surface. It is named after Romanian inventor Henri Coandă, who described it as "the tendency of a jet of fluid emerging from an orifice to follow an adjacent flat or curved surface and to entrain fluid from the surroundings so that a region of lower pressure develops."
  Coandă was the first to recognize the practical application of the phenomenon in aircraft design.
context_section_description: Early sources provide information, both  theoretical and experimental, needed to derive by comparison a detailed explanation of the Coandă effect and its limits. Coandă effect may occur along a curved wall either in a free jet or a wall jet.
  On the left image of the preceding section: "The mechanism of Coanda effect", the effect as described, in the terms of T. Young as "the lateral pressure which eases the inflection of a current of air near an obstacle", represents a free jet emerging from an orifice and an obstacle in the surroundings. It includes the tendency of a free jet emerging from an orifice to entrain fluid from the surroundings confined with limited access, without developing any region of lower pressure when there is no obstacle  in the surroundings, as is the case on the opposite side where turbulent mixing occurs at ambient pressure.
  On the right image, the effect occurs along the curved wall as a wall jet. The image here on the right represents a two dimensional wall jet between two parallel plane walls, where the "obstacle" is a quarter cylindrical portion following the flat horizontal rectangular orifice, so that no fluid at all is entrained from the surroundings along the wall, but only on the opposite side in turbulent mixing with ambient air.
  1. Wall jet. To compare experiment with a theoretical model, we first refer to a two-dimensional plane wall jet of width h along a circular wall of radius r. A wall jet follows a flat horizontal wall, say of infinite radius, or rather  whose radius is the radius of the Earth without separation because the surface pressure as well as the external pressure in the mixing zone is everywhere equal to the atmospheric pressure and the boundary layer does not separate from the wall.
  With a much smaller radius (12 centimeters in the image on the right) a transverse difference arises between external and wall surface pressures of the jet, creating a pressure gradient depending upon h/r, the relative curvature. This pressure gradient can appear in a zone before and  after the origin of the jet where it gradually arises, and disappear at the point  where the jet boundary layer separates from the wall, where the wall pressure reaches atmospheric pressure (and the transverse gradient becomes zero).
  Experiments made in 1956 with turbulent air jets at a Reynolds number of 10⁶ at various  jet widths (h) show the pressures measured along a circularly curved wall (radius r) at a series of horizontal distance from the origin of the jet (see the diagram on the right).
  Above a critical h/r ratio of 0.5 only local effects at the origin of the jet are seen extending over a small angle of 18° along the curved wall. The jet then immediately separates from the curved wall. A Coandă effect is therefore not seen here but only a local attachment:  a pressure smaller than atmospheric pressure appears on the wall along a distance corresponding to a small angle of 9°, followed by an equal angle of 9° where this pressure increases up to atmospheric pressure at the separation of the boundary layer, subject to this positive longitudinal gradient. However, if the h/r ratio is smaller than the critical value of 0.5, the lower than ambient pressure measured on the wall seen at the origin of the jet continues along the wall (until the wall ends –; see diagram on the right). This is "a true Coandă effect" as the jet clings to the wall "at a nearly constant pressure" as in a conventional wall jet.
  A calculation made by Woods in 1954 of an inviscid flow along a circular wall shows that an inviscid solution exists with any curvature h/r and any given deflection angle up to a separation point on the wall, where a singular point appears with an infinite  slope of the surface pressure curve. 
  Introducing in the calculation  the angle at separation found in the preceding  experiments for each value of the relative curvature h/r, the image here was recently obtained, and shows inertial effects represented by the inviscid solution: the calculated  pressure field is similar to the experimental one described abov
caption: Measurements of surface pressure along a circularly curved wall of radius r = 12 cm, deflecting a turbulent jet of air (Reynolds number = 106) of width h. The pressure begins to fall before the origin of the jet, due to local effects at the point of exit of the air from the nozzle which creates the jet. If the h/r ratio (ratio of the width of the jet to the radius of curvature of the wall) is less than 0.5, a true Coandă effect is observed, with the wall pressures along the curved wall remaining at this low (sub-ambient pressure) level until the jet reaches the end of the wall (when the pressure rapidly returns to ambient pressure). If the h/r ratio is more than 0.5, only the local effects occur at the origin of the jet, after which the jet immediately separates from the wall, and there is no Coandă effect. Experiments by M. Kadosch and J. Liermann in  M. Kadosch's  laboratory, SNECMA.[12]
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