The Coanda effect can be described by few main physical parameters.  Considering any two-dimensional Coanda flow and referring to Figure 1, the main geometric parameters are the angle of separation θ, the slot width b, radius of curvature a. Physical parameters are Reynolds number Re and the pressure differential ps−p∞, (where ps is the supply pressure).
Different fluid dynamic effects concur to create the so-called “Coanda effect” which was defined by Coanda in 1910 although still in an embryonic formulation .
Further, it was completely formulated in 1936 as the combination of three effects: the boundary layer effect, the tendency of a fluid jet approaching a curved surface to remain attached to the surface; the adhesion effect, the ability of a fluid jet to adhere to a nearby surface; the attraction effect, the tendency of jet flows over convex curved surfaces to attract surrounding fluid and increase more rapidly than that of plane wall jets.
The scientific studies about the Coanda effect are characterized by a fundamental landmark study by Newman. He investigated a two-dimensional, uncompressible  turbulent jet flowing around a circular cylinder (Figure 2-a). It can be demonstrated that Coanda adhesion to a curved surface is a consequence of the balance of the forces applied to the fluid. During adhesive motion on a curved wall, two forces are in equilibrium: centrifugal force and radial pressure.
The contact pressure with the Coanda surface is lower than ambient pressure because of the speed of the fluid and the viscous interaction between fluid and wall. This differential pressure is the main cause of the fluid movement in contact with curved wall surface.
The pressure along the curved wall rises and gradually equates the ambient pressure generated at the end a detachment of the jet from the curved wall.
Newman using this setup obtained a relation among detachment angle θ and main geometric parameters of the flow and dynamic quantities involved in the system schematized in Figure a.
Coanda effect applications classification
The main application of Coanda nozzles can be classified into the four main groups presented in Figure:
coanda effect
Single jet Coanda nozzle
This configuration has been used by Newman, Bradshaw, Patankar and others was fundamental for first studies about Coanda effect and its laws, it has been used especially for study reasons both in 2D and 3D mostly for experimental purposes and only some applications related to combustion and wings improvements are known;
Enhanced Coanda nozzles
this definition has been historically used by Smith, but is related to the research activity of Postma, Smith, Trent, and Juvet; it is based on the testing architecture developed both by Juvet (Figure b) and uses a mainstream with a great mass flow and one or more secondary jets with high speed, demonstrating that an axis symmetric apparatus is not influenced by the Coanda effect with no blowing through the secondary slot. The other important conclusion produced is that:
  • when blowing ratio is below 0.1 the primary jet has a low influence by Coanda surfaces and centreline  velocity  decreases due to entrainment of the secondary flow;
  • when blowing ratio is above 0.1 the main jet has vectored in a radial direction and it has not the behaviour of a free jet; if the blowing ratio increases the vectoring capability increases.

Some interesting patents have been also presented by Smith, forcing the typical Juvet architecture into three dimensional architectures.

Enhanced Coanda nozzles with moving surfaces
many authors, especially involved in aeronautic propulsion have developed Coanda deflection systems based on moving surfaces and on the pilot jet controlled applications with movable appendices. The first application has been developed by Wing, focused on two-dimensional thrust vectoring of a primary jet using a secondary jet deflected via a Coanda surface (Figure c), producing an unsatisfactory jet deflection about 36°. Wing concluded that the result was influenced by a lack of momentum in the primary jet and that the nozzle design would require a better optimization to produce larger vector angles.
Another aeronautic related study has been conducted by Mason, enhancing the experimental setup by Wings and analysing the possibility of thrust vectoring. Mason used geometry more accurate than Wings’ one and focused his attention on thrust force more than on a jet vector angle. The vector angles produced are larger than the results obtained by Wing. The largest angle achieved is still relatively small (35°).
Mason’s work is a direct reference for this project, because it is focused only on propulsion performances and constitutes the first attempt at creating a fully controllable Coanda jet.
Coanda effect based oscillators:
Coanda effect based fluidic oscillators has not used directly as nozzles because of their complex geometry but they are used both for anti-icing applications, drilling, and flow separation control. Even if not strictly related to this work oscillators (Figure d) are cited because they constitute the only Coanda effect application that could realize prior than H.O.M.E.R. nozzle an easy to control the dynamic deflection of a fluid jet really without any other moving part. In particular the fluidic oscillators can be used to produce pulsating fluid jets which can improve the effectiveness of active flow control.


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