7.0 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Coandă effect | 2/5 | https://en.wikipedia.org/wiki/Coandă_effect | reference | science, encyclopedia | 2026-05-05T10:54:48.580764+00:00 | kb-cron |
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 above, outside the nozzle. The flow curvature is caused exclusively by the transverse pressure gradient, as described by T. Young. Then, viscosity only produces a boundary layer along the wall and turbulent mixing with ambient air as in a conventional wall jet—except that this boundary layer separates under the action of the difference between the finally ambient pressure and a smaller surface pressure along the wall. According to Van Dyke, as quoted in Lift, the derivation of his equation (4c) also shows that the contribution of viscous stress to flow turning is negligible. An alternative way would be to calculate the deflection angle at which the boundary layer subjected to the inviscid pressure field separates. A rough calculation has been tried that gives the separation angle as a function of h/r and the Reynolds number: The results are reported on the image, e.g., 54° calculated instead of 60° measured for h/r = 0.25. More experiments and a more accurate boundary layer calculation would be desirable. Other experiments made in 2004 with a wall jet along a circular wall show that Coandă effect does not occur in a laminar flow, and the critical h/r ratios for small Reynolds numbers are much smaller than those for turbulent flow. down to h/r = 0.14 with a Reynolds number of 500, and h/r = 0.05 for a Reynolds number of 100.
=== Free jet === L. C. Woods also made the calculation of the inviscid two-dimensional flow of a free jet of width h, deflected round a circularly cylindrical surface of radius r, between a first contact A and separation at B, including a deflection angle θ. Again a solution exists for any value of the relative curvature h/r and angle θ. Moreover, in the case of a free jet the equation can be solved in closed form, giving the distribution of velocity along the circular wall. The surface pressure distribution is then calculated using Bernoulli equation. Let us note the pressure (pa) and the velocity (va) along the free streamline at the ambient pressure, and γ the angle along the wall which is zero in A and θ in B. Then the velocity (v) is found to be:
v
v
a
=
exp
(
2
h
π
r
arctan
sinh
2
(
π
θ
r
4
h
)
−
cosh
2
(
π
θ
r
4
h
)
tanh
2
(
π
γ
r
4
h
)
)
{\displaystyle {\frac {v}{v_{\mathrm {a} }}}=\exp \left({\frac {2h}{\pi r}}\arctan {\sqrt {\sinh ^{2}\left({\frac {\pi \theta r}{4h}}\right)-\cosh ^{2}\left({\frac {\pi \theta r}{4h}}\right)\tanh ^{2}\left({\frac {\pi \gamma r}{4h}}\right)}}\,\right)}