The Coandă effect ( or ) is the tendency of a fluid jet to stay attached to a surface of any form.Tritton, D.J., Physical Fluid Dynamics, Van Nostrand Reinhold, 1977 (reprinted 1980), Section 22.7, The Coandă Effect. Merriam-Webster describes 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."
It is named after Romanian inventor Henri Coandă, who was the first to recognize the practical application of the phenomenon in aircraft design around 1910. It was first documented explicitly in two patents issued in 1936.
History A description of this phenomenon was provided by Thomas Young in a lecture to The Royal Society in 1800:
More than a hundred years later, Henri Coandă identified an application of the effect during experiments with his Coandă-1910 aircraft, which mounted an unusual engine he designed. The motor-driven turbine pushed hot air rearward, and Coandă noticed that the airflow was attracted to nearby surfaces. In 1934, Coandă obtained a patent in France for a "method and apparatus for deviation of a fluid into another fluid". The effect was described as the "deviation of a plain jet of a fluid that penetrates another fluid in the vicinity of a convex wall". The first official documents that explicitly mention the effect were his two 1936 patents.Coanda, H. US Patent# 2,052,869; "Device for Deflecting a Stream of Elastic Fluid Projected into an Elastic Fluid (1936)".Coanda H. (1936a), US Patent n. 3,261,162, Lifting Device Coanda Effect, USA This name was accepted by aerodynamicist Theodore von Kármán, who had a long scientific relationship with Coandă on aerodynamics problems.
Mechanism
A free jet of air entrains molecules of air from its immediate surroundings causing an axisymmetrical "tube" or "sleeve" of low pressure around the jet (see Diagram 1). The resultant forces from this low pressure tube end up balancing any perpendicular flow instability, which stabilises the jet in a straight line. However, if a solid surface is placed close, and approximately parallel to the jet (Diagram 2), then the entrainment (and therefore removal) of air from between the solid surface and the jet causes a reduction in air pressure on that side of the jet that cannot be balanced as rapidly as the low pressure region on the "open" side of the jet.
The pressure difference across the jet causes the jet to deviate towards the nearby surface, and then to adhere to it (Diagram 3).Coanda Effect Retrieved 17 November 2017 The jet adheres even better to curved surfaces (Diagram 4), because each (infinitesimally small) incremental change in direction of the surface brings renews the effect of the initial bending of the jet.Jeff Raskin: Coanda Effect: Understanding how wings work. Retrieved 17 November 2017 If the curvature is not too sharp, the jet can adhere to the surface even after flowing 180° around a cylindrically curved surface, and thus travel in the opposite direction. The forces that cause these changes cause an equal and opposite force on the surface along which the jet flows. These forces can be harnessed to cause lift and other forms of motion, depending on the orientation of the jet and the surface to which the jet adheres. A small surface "lip" at the point where the jet starts to flow over that surface (Diagram 5) increases the initial deviation of the jet flow direction. This results from the fact that a low pressure vortex forms behind the lip, promoting the dip towards the surface.
The Coandă effect can be induced in any fluid, and is therefore equally effective in water and air. A heated airfoil significantly reduces drag.
Existence conditions
Early sources provide theoretical and experimental information needed to derive a detailed explanation of the effect. The Coandă effect may occur along a curved wall either in a free- or wall-jet.
On the left image of the preceding section: "The mechanism of Coandă 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.
Wall jet To compare experiment with a theoretical model, a two-dimensional plane wall jet of width () along a circular wall of radius () is referred to. 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 , 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 () show the pressures measured along a circularly curved wall radius () at a series of horizontal distance from the origin of the jet (see the diagram on the right).
Above a critical 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 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 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 , 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 and the Reynolds number: The results are reported on the image, e.g., 54° calculated instead of 60° measured for = 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 ratios for small Reynolds numbers are much smaller than those for turbulent flow. down to = 0.14 with a Reynolds number of 500, and = 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 . Again a solution exists for any value of the relative curvature and angle . 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 () and the velocity () along the free streamline at the ambient pressure, and the angle along the wall which is zero in A and in B. Then the velocity () is found to be:
An image of the surface pressure distribution of the jet round the cylindrical surface using the same values of the relative curvature , and the same angle as those found for the wall jet reported in the image on the right side here has been established: it may be found in reference (15) p. 104 and both images are quite similar: the Coandă effect of a free jet is inertial, the same as Coandă effect of a wall jet. However, an experimental measurement of the corresponding surface pressure distribution is not known.
Experiments in 1959 by Bourque and Newmann concerning the reattachment of a two-dimensional turbulent jet to an offset parallel plate after enclosing a separation bubble where a low pressure vortex is confined (as in the image 5 in the preceding section) and also for a two-dimensional jet followed by a single flat plate inclined at an angle instead of the circularly curved wall in the diagram on the right here describing the experience of a wall jet: the jet separates from the plate, then curves towards the plate when the surrounding fluid is entrained and pressure lowered, and eventually reattaches to it, enclosing a separation bubble. The jet remains free if the angle is greater than 62°.
In this last case which is the geometry proposed by Coandă, the claim of the inventor is that the quantity of fluid entrained by the jet from the surroundings is increased when the jet is deflected, a feature exploited to improve the scavenging of internal combustion engines, and to increase the maximum lift coefficient of a wing, as indicated in the applications below.
The surface pressure distribution as well as the reattachment distance have been duly measured in both cases, and two approximate theories have been developed for the mean pressure within the separation bubble, the position of reattachment and the increase in volume flow from the orifice: the agreement with experiment was satisfactory.
Applications
Aircraft