(8-6) From Equation (8-5) this may be written
9. JET ATTACHMENT
AF16 Jet Attachment Apparatus
Introduction
In a previous experiment on the flow round a circular cylinder, the phenomenon of separation of flow from a surface had been observed. The present experiment deals with an effect which in some respects is the reverse, namely, the tendency for a plane jet to attach itself to an adjacent wall and to flow along it. Figure 9.1(a) shows a typical configuration. A plane jet emerges from the slit which discharges into the atmosphere alongside a wall. It is found to deflect sideways and to attach to the wall.
If the wall curves as shown, it will follow the curve and so may suffer a considerable change of direction. Exploitation of this phenomenon was proposed in the 1930’s by Henri Coanda, who made several inventions which used this form of jet deflection;
the phenomenon is therefore sometimes referred to as the “Coanda Effect”.
Figure 9.1 Mechanics of Jet Attachment to a Wall
A descriptive explanation of why a jet should exhibit this behaviour can be made along the following lines. It is known that a jet emerging from a tube or slit will entrain fluid from the surroundings as it mixes into the ambient fluid; in most cases of engineering importance the mixing is turbulent and entrainment is much more intense than if the process were laminar.
Consider now entrainment into the jet of Figure 9.1(a). In the first moment after starting, the jet is straight and entrainment takes place equally on both sides. The inflow from the surroundings into the jet is, however, restricted on one side due to the
presence of the wall and this restriction results in a reduction of pressure which bends the jet towards the wall.
This in turn further restricts the supply of fluid to this side of the jet, causing further reduction of pressure and further jet curvature until very soon the jet moves over to the wall as shown in the diagram. In the final condition shown, there is a zone of separated flow in which recirculation takes place. The rate at which fluid is entrained into the jet is balanced by the return flow into the separation zone from the region of jet attachment. The pressure in the separation zone is approximately constant, and is lower than in the atmosphere on the opposite side of the jet. Figure 9.1(b) shows the effect of opening a hole from the atmosphere into the separation zone. Fluid flowing through the hole is entrained into the jet; the entrainment rate now balances the sum of recirculation and inflow through the hole. The pressure in the separation zone rises somewhat, the jet curvature is reduced and the separation zone lengthens. If the inflow rate from the atmosphere is sufficiently high, the entrainment rate may be insufficient to maintain the balance, and the jet will detach from the wall.
Returning to Figure 9.1(a), we see that having attached to the wall, the flow tends to stick to it because separation would require a supply of fluid to the space between the surface and the separating jet. Separation is therefore unlikely to occur unless the curvature of the surface is unduly severe or if an adverse pressure gradient is encountered.
The previous explanations have assumed two-dimensional flow. This assumption will be valid if the jet is very wide in the direction normal to the plane of the diagram in comparison to its width. If this is not so, however, flow from the atmosphere round the ends of the jet into the separation zone will have considerable effect. Because of the importance of these end effects, the ratio of jet width (in the direction normal to the diagram) to jet thickness has acquired a specific description, known as the ‘aspect ratio’.
The principle of wall jet attachment has recently found an application in the technology of fluidics. Figure 9.2 shows a typical fluidic switch in which the supply jet S is directed to either outlet 01 or 02 depending on to which of the two walls the jet attaches. Suppose the outlet 01 is active. By introduction of fluid at control hole C1, the jet may be switched across to outlet 02, and it will remain there after the inflow at C1 has ceased. Further action at C1 will not have any effect; to switch the jet back to 01 requires a signal at C2.
The switch is a fluidic counterpart of an electronic ‘flip-flop’ and is called a fluidic flip-flop. Other switches or gates, such as AND and OR gates, may be constructed, and fluidic logic circuits may be developed by interconnection.
Figure 9.2 A Fluidic Flip-Flop
In the experiments which follow, the attachment of a jet to a single adjacent wall is first studied, and the behaviour of a flip-flop is then observed.
Description of Apparatus and Procedure
The essential features of the arrangement are shown in Figure 9.3. The equipment, which fixes to the outlet flange of the contraction section of the airflow bench, consists of a nozzle plate which houses a rectangular supply nozzle. The jet which emerges from this nozzle is contained between side plates that may be moved laterally so that the offset between the nozzle and the attachment wall be varied. The aspect ratio of the nozzle may be altered by removing one of the nozzle blocks and fitting a different sized block.
Figure 9.3 Details of Apparatus and Notation
For the single-wall tests, the left-hand attachment wall is fitted between the side plates. It is mounted on a spindle which terminates at a control used to rotate the attachment to any desired angle. For tests on the flip-flop, a further attachment wall and a splitter block are added. The space between the nozzle block and the attachment wall may be left open to atmosphere or may be sealed by closing a flexible seal as indicated.
The left-hand attachment wall is first fitted and the flexible seal attached. The second, larger control is used to lock the wall at any desired angle. The right-hand seal should be in its open position. The offset, dimensioned y in Figure 9.3, and the wall angle β are both set to zero. The wind speed is then brought up to a convenient value close to the maximum and is then held constant by maintaining a constant airbox pressure, throughout the tests. The wall angle β is now slowly increased until separation is observed at angle βs. This is most easily detected simply by holding the hand in the jet, some 150 mm downstream of the trailing edge of the wall so as not to interfere with the flow along it, and noting when the flow pattern suddenly changes.
The change is usually audible. The process should be repeated once or twice to ensure that the value of βs is established to within about 1°. Then, starting with a detached jet and reducing the wall angle, the value at which reattachment occurs βr, is established. The same procedure is repeated at several different values of offset y in the range from approximately −4 mm to 20 mm. Intervals of 2 mm are recommended, but smaller steps may be required where large changes in βs or βr are seen to take place. The whole test may then be repeated with the flexible seal removed.
Proceed now to construct a flip-flop by inserting the second attachment wall, and fixing the flexible seals to both walls. Centralise the assembly on the centreline of the nozzle. Starting with parallel walls, both set at zero wall angle, slowly increase the wall angles until the jet is clearly attached to one or the other of the walls. Then lock the walls in position. Try to switch the jet by prising open the seal on the ‘attached’
side. If this does not produce the desired switching, increase the angles in small steps until it does. It should then be possible to demonstrate flip-flop action, switching the jet back and forth at will by briefly prising open the seals. Further increase the angles to discover the upper limit at which a satisfactory flip-flop action is possible.
The central splitter may now be added. It will be observed that this enhances the bi-stability, as the range of wall angles which give satisfactory switching is considerably increased.
Flexible Seal Closed Flexible Seal Open
y mm βs (°) βr (°) y mm βs (°) βr (°) Table 9.1 Separation and Reattachment Angles at a Single Wall
Table 9.1 gives results obtained for separation and reattachment of the jet at a single wall, and the results are plotted on Figure 9.4.
The following observations were made when two walls were used.
Offset y to each wall = 13.5 mm Without splitter fitted:
β = 15° Jet attaches to one wall and will not separate when seal is lifted.
β = 20° - 30° Jet attaches to one wall and may be switched back and forth as a flip-flop.
β = 35° Jet attaches to one wall but when seal is fitted it moves to centre position instead of attaching to opposite wall.
With splitter fitted
β = 15° - 80° Jet attaches to one wall and emerges from the passage between the wall and splitter without spilling into the opposite passage.
Switches as a flip-flop.
Discussion
Figure 9.4 exhibits the way in which the jet may be deflected through very considerable angles, exceeding 90°, by the Coanda effect. When the wall projects into the jet, i.e. when y is negative, the behaviour is much the same with a seal fitted as when it is removed. There is some 17° hysteresis between detachment and reattachment in this range of y. As soon as the wall is moved out of the jet, however, the two conditions behave entirely differently. With the seal fitted, the separation angle and the reattachment angle both continue to grow until, at a value of y about 8 mm, the hysteresis range is suddenly increased by a sharp drop in the reattachment angle. There is some 50° of hysteresis at this condition. The separation angle continues to grow as y increases to 20 mm, reaching a maximum of about 110°.
When the wall is unsealed, as y increases from zero, both separation and reattachment angles decrease steadily and the hysteresis also decreases, diminishing to approximately 3° when y reaches 20 mm.
Figure 9.4 Detachment and Reattachment for a Single Wall
The behaviour with two attachment walls is in fair agreement with predictions that may be made from Figure 9.4. Consider the separation condition. At y = 13.5 mm (which is the value used in the experiment with two walls), Figure 9.4 shows that the jet will separate from the unsealed wall at βs = 26°. The experimental result observed when two walls were used is that for βs greater than 20°, the jet detaches when the seal is lifted. So separation occurs at a somewhat smaller angle when there is a further sealed wall on the other side of the jet. Again, at y = 13.5 mm, Figure 9.4 shows that the jet will reattach to a sealed wall at βr = 35°. This agrees exactly with the observed behaviour of flip-flop action up to 30°, but for β = 35° or more, the jet moves to the centre position when the seal is lifted instead of attaching to the opposite wall.
The presence of a splitter improves the bi-stability. It generates a recirculation, as indicated in Figure 9.2, which strengthens the attachment very considerably, thereby increasing the range of successful flip-flop action.
Conclusion
Tests on a single-wall configuration have shown that the wall attachment effect, or Coanda effect, may be used to divert a plane jet along a plane wall through angles up to 90° or more. Considerable hysteresis is found between the condition for jet separation and that for jet attachment. The effect of offset between the jet and the wall, and venting the space between the nozzle and the wall, have been investigated.
A fluidic flip-flop which exploits the phenomenon of wall attachment has been constructed and satisfactory switching has been observed.
Suggestions for Further Experiments
1. Investigate the effect of changing the aspect ratio of the jet on the single-wall detachment and reattachment characteristics. Change the nozzle width to, say, 8 mm and 5 mm in turn.
2. Determine the significance of the side plates on the single-wall results. Blank off, 20 mm at each end of the breadth of the nozzle with adhesive tape, leaving 40 mm clear in the middle, so that the jet is not in contact with the side plates when it emerges from the nozzle, and repeat the tests.
3. Consider the possibility of an asymmetric fluidic switch. Suppose it were desired to produce a switch which stayed ‘on’ until a control signal switched it
‘off’. Could this be done and if so, can such a switch be made from the parts described here?