Measurement of wall shear stress present in the boundary layer of a fluid as it flows over a surface is of fundamental importance to engineers and other fluid mechanics specialists concerned with research into, and design of, fluid dynamic systems. This is because wall shear stress defines the value of skin friction, which is the drag -axerted on an object due to relative movement between a surface of the object and a fluid in which it is immersed. For instance, in the fields of aircraft airframe and aeroengine nacelle design, a major concern of designers is to reduce drag due to the passage of the airframe and its engines through the air. Aeroengine designers are also anxious to reduce aerodynamic drag internally of the . engines due to flow of air and combustion gases through their internal ducts and over their internal components. Clearly, therefore, robust, accurate, conveniently useable and preferably inexpensive instrumentation for measuring wall shear stress and related quantities is required for these situations.

Determination of mean wall shear stress within the boundary layer is possible using a number of well-known instruments, e.g. spring balances, Preston tubes, Stanton tubes, surface fences, and so on. Unfortunately, such

instruments do not have sufficiently fast response times to be useful for determination of dynamic shear stress, and are also inconvenient or even impossible to provide on many aerodynamic components, such as rotating aerofoils. Consequently, hot film devices have been utilised in more recent years, involving the provision of thin electrically- heated metallic films on surfaces. This technique involves heat transfer measurements, which result in poor resolution of derived shear stress because the shear stress varies as the cube of the heat transfer rate. The above and other techniques are reviewed in "An Outline of the Techniques Available for the Measurement of Skin Friction in Turbulent Boundary Layers" by K.G. Winter, Prog. Aerospace Sci. 1977, Col. 8, pp.1-57, Pergamon Press. A further publication which should be consulted in respect of hot film devices is "Determination of Mean and Dynamic Skin Friction, Separation and Transition in Low Speed Flow with a Thin-Film Heated Element", by B. J. Bellhouse and D. L. Schultz, J. Fluid Mech (1966), Vol. 24, part 2, pp. 379-400.

It is an object of the present invention to enable simple, cheap and accurate measurement of wall shear stress and related quantities in both the dynamic and steady-state modes. According to the present invention in its broadest aspect, a transducer device for providing a measure of fluid shear stress and related quantities at a surface subject to fluid flow thereover, comprises flow disturbing means arranged to project above the surface to a height of between 10% and 70% of the expected thickness of the viscous sublayer of the boundary layer, and at least first and second pressure sensitive transducers disposed immediately adjacent the flow disturbing means on opposed sides thereof for registering the pressure difference across the flow disturbing means due to the disturbance.

the pressure sensitive regions of the transducers being arranged to be at least partly coextensive with the expected streamwise extent of the disturbance.

Also according to the present invention, a transducer device for providing a measure of fluid shear stress and related quantities at a surface subject to fluid flow thereover, comprises flow disturbing means arranged to project above the surface to a height of between 10% and 70% of the expected thickness of the viscous sublayer of the boundary layer, and at least first and second pressure sensitive transducers consisting of diodes disposed immediately adjacent the flow disturbing means on opposed sides thereof for registering the pressure difference across the flow disturbing means due to the disturbance, the pressure sensitive junction regions of the diodes being arranged to be at least partly coextensive with the expected streamwise extent of the disturbance.

For maximum sensitivity, the diodes may comprise tunnel diodes, and the diodes are preferably produced by an ion implantation process, although a diffusion process could be used instead. In use for measurements of fluid shear,etc., the diodes may be connected in an electrical circuit in parallel with a resistor for operation in an amplifier mode. Preferably, the diodes comprise thin films of semiconductor material arranged on the surface subject to fluid flow and also electrically isolated therefrom if necessary, e.g. because the surface is metallic.

In a first suggested embodiment, the surface may be that of a machine component in a fluid stream, such as a fan blade in a turbofan aeroengine, or the engine's air intake casing, the flow disturbing means being a discrete component which is affixed directly to the component's surface separately from the transducers.

In a second suggested embodiment, the transducers and the fluid flow disturbing means are arranged on a

substrate suitable for attachment to an object, such as a fluid flow machine component, to form the surface subject to fluid flow. Thus, the substrate may be a self-adherent or adhereable non-conducting plastic or ceramic film (e.g. "Kapton" [Trade Mark], alumina, or silicon nitride) on which the components of the transducer have been formed or to which they have been affixed, the film itself then being adhered to a machine component to instrument it. The second suggested embodiment is amenable to mass or batch production of the transducers at a site distant from that at which the testing is to occur. Plainly it is convenient if the flow disturbing means is an integral part of the non-conducting film, e.g. is formed as an embossment on it. In a third alternative embodiment, the fluid flow disturbing means and the transducers are integral with a semiconductor substrate suitable for fixing to an object to form the surface subject to fluid flow, as suggested for the previous embodiment. The flow disturbing means should preferably be arranged to project above the surface to a height of between 20% and 60%, preferably 50% to 60% of the expected thickness of the viscous sublayer of the boundary layer. Furthermore, the extent of the junction region of the diodes is arranged to be not substantially greater than the expected streamwise extent of the disturbance, and preferably substantially less.

In one embodiment, suitable for use in situations where the direction of fluid flow is predetermined, the flow disturbing means comprises a linear feature whose height extends parallel to the surface and whose length is intended to extend normal to the direction of fluid flow. Another embodiment provides both vector and scalar measurements of dynamic shear stress, for situations where the flow cannot be predicted to remain in one direction.

In this case the flow disturbing means comprises linear features having a common height relative to the surface and arranged mutually orthogonally to define a cross shape, a transducer being disposed in each of the four triangular areas defined between the four arms of the cross shape, the pressure sensitive regions of the transducers being adjacent the intersection of the linearly extending features.

The or each linear feature may comprise an abrupt ridge in the surface. For example, the ridge may comprise a step increase in height relative to the surface and a step decrease in height by the same amount as the step increase, with a narrow land between the two steps.

Alternatively, the or each linear feature may comprise a cylindrical form of small diameter, such as a wire fixed to and lying on the surface.

For situations where the flow cannot be predicted to remain in one direction but where scalar measurements are sufficient, the flow disturbing means may comprise a small protrusion from the surface, the pressure sensitive regions of the transducers being substantially semi-circular and arranged to encircle the protrusion.

Exemplary embodiments of the invention will now be described with reference to the accompanying drawings, in which:-

Figures IA and IB are respectively enlarged plan and sectional end elevation views of a basic transducer device according to the invention, suitable for scalar measurement of wall shear stress in unidirectional flow over a wall surface;

Figure 2 is a circuit-diagram showing a circuit for obtaining measurements from the transducer device;

Figure 3 is an enlarged view similar to Figure IB illustrating a more convenient version of the basic

device;

Figure 4 is a plan view of another embodiment of the invention, showing a transducer device suitable for vector measurement of wall shear stress; and Figure 5 is a plan view of a further embodiment of the invention, showing a transducer device suitable for scalar measurement of wall shear stress in multi¬ directional flow over a wall surface.

Referring first to Figures IA and IB, there is shown a metallic component 10 having a wall surface 11 over which fluid flows in the direction shown by the arrows 12. The component 10, could, for instance, be part of a gas turbine aeroengine, such as its air intake duct. The fluid flow 12 over the wall surface 11 will usually be turbulent in an aeroengine, but there will of course be a boundary layer associated with the surface, comprising a viscous sublayer 14 next to the wall surface 11 and an overlying turbulent sublayer 16 which grades off into the turbulent free stream 12.

Lying on the wall surface 11 is a short, small diameter length of round wire 18 which is firmly attached to the surface 11 by means of tack welds 20,22 made e.g., by resistance, argon arc or laser spot welding methods. The wire 18 is oriented to lie perpendicular to the known direction of fluid flow 12 over the wall surface, and is a component part of a transducer device 24 capable of providing a measure of, inter alia, fluid shear stress at the wall surface. The other main component parts of the transducer device 24 are two pressure sensitive transducers comprising tunnel diodes 26,26' formed by thin film techniques on the wall surface 11 immediately adjacent the wire 18 in the upstream and downstream directions. So far as possible the diodes 26,26' are identical, and each comprises a 'p'-type silicon film

28,28' which in a selected small area 30,30' has been heavily doped by an ion implantation process in order to change it to 'n'-type. The heavy doping enables the diodes 26,26' to function as tunnel diodes, which renders them highly sensitive to fluid pressure variations when utilised in the amplifier/oscillator mode.

The ion implantation step produces radiation damage in the semiconductor film, but this can be overcome by heat treatment, as known. In order to insulate the diodes 26,26' from electrical contact with the metallic wall surface 11, they are formed on respective thin (say 0.5mm or less) vitreous enamel layers 31,31', which have been previously painted onto the surface through a mask and then fired, leaving a strip 32 between them of bare metal surface in which the wire 18 is fixed after formation of the diodes.

Electrical connections to the diodes 26,26' must be such as to avoid any substantial interference with the flow of fluid in the boundary layer and therefore thin metallic printed circuit connections 34,36 and 34',36' are provided to areas 28,30 and 28',30' respectively by printing a known conductive metal ink onto the surface of the semiconductor film and firing it at an appropriate temperature to fuse the metal particles in the ink and evaporate off the organic vehicle. In the case of connections 36,36', contact between them and the semiconductor areas 28,28' is prevented by printing them onto thin films 38,38' of insulator material, e.g. silicon dioxide, which can be vacuum deposited beforehand onto the surfaces of semiconductor films 28,28' through appropriate masking.

Electrical leads (not shown) can be attached to the printed connections 34,36, and 34 ',36', in a way which avoids disturbing the fluid flow, by means of holes 40,42 and 40* ,42' drilled through the component 10, the leads

comprising thin insulated wires which extend through the holes and are exposed at their ends for attachment to the printed connections 34,36 and 34',36', e.g. by soldering. The device 24 functions as follows. The short length of round wire 18 forms a projection from the wall surface 11 which in order to adequately disturb the flow should protrude into the boundary layer to a height not less than about 50% of the expected (undisturbed) thickness of the viscous sublayer 14. The resulting disturbance in the flow 44 in the viscous sublayer 14 results in a pressure difference between the upstream and downstream sides of the wire 18; the upstream side is at a slightly higher pressure than the downstream side. As mentioned above, diodes 26,26' are highly sensitive to fluid pressure variations and so when operated in their amplifier mode by connection into a suitable circuit, the difference in the outputs of the two diodes will be a function of the pressure difference between the two sides, and therefore of the shear stress at the wall surface 11. In fact, the difference in diode outputs will be a linear function of surface shear stress when the disturbance caused by the wire 18 is within the viscous sublayer 14 of the boundary layer, as shown in Figure IB. If the disturbance protrudes beyond the viscous sublayer 14, the difference in diode outputs will be a repeatable but non-linear function of shear stress. In order that the diodes be sufficiently sensitive to the pressure differences associated with the disturbance produced in the viscous sublayer by the wire 18, the junction region of each diode should extend upstream or downstream from the wire by a distance not substantially greater than the streamwise extent of the disturbance, and preferably substantially less.

Figure 2 shows a simple circuit arrangement suitable for measuring the output voltages of the diodes shown in

Figure 1. The circuit arrangement comprises a D.C source 201, a current-limiting variable resistor 202, an ammeter 203, and parallel circuit branches 204, 205 and 206. Circuit branch 204 is only completed when connected to the leads from one of the diodes 26,26' of Figure 1, as shown in dashed lines. Branch 205 comprises a shunt resistor 207 whose purpose is to stabilise the diode connected into branch 204 so that it operates in the amplifier mode rather than the switching mode. Branch 206 comprises a digital voltmeter 208 whose purpose is to record the output voltage from the diode.

A suitable experimental method for obtaining measurements from the device 24 of Figure 1, using the circuit arrangement of Figure 2, is as follows. (1) Carry out a calibration of volts output versus pressure input from the diodes at a chosen convenient current by exposing the component 10 with its diodes to known pressures in a suitable pressure chamber while they are connected to the circuit arrangement of Figure 2. (2) Place the component 10 in its test situation and reconnect each diode as shown.

(3) Adjust the current limiting resistor 202 until the correct current is indicated on the ammeter 203 (this is the current at which the calibration in step (1) was carried out) .

(4) With the component and its diodes exposed to the fluid flow to be measured, record the output voltages on the digital voltmeter and find their difference.

This process could of course be readily automated if desired.

For further information on the use of tunnel diodes as pressure transducers the reader is referred to the article "Tunnel Diode Hydrostatic Pressure Transducer" by Sikorski and Andreatch, The Review of Scientific Instruments, Vol. 33, No. 2, February 1962, from which

Figure 2 is derived. In particular, it is noted from this article that the pressure range and the pressure sensitivity within a chosen large pressure interval can be varied easily by adjusting the value of the shunt resistor 207 and the current measured by ammeter 203.

Turning now to Figure 3, there is shown in a much enlarged cross-sectional elevation a device 300 which although functioning in the same way as the device 24 in Figure 1, is more convenient to use, and also cheaper to manufacture, because it is made by integrated circuit techniques essentially from a single piece of silicon, and can be adhered directly to any surface after detachment from its backing layer 302.

In more detail, the device 300 comprises a thin slice of n-type semiconductor material 303 whose original shape is shown by the dashed lines. After production of the n-type slice it is given a masking stripe of silicon dioxide 304 across its middle upper surface and the rest of the surface of the slice is anisotropically etched away to a depth 'd' on the (100) crystallographic surfaces using an etchant with a slow convex undercut rate. In this way a rectangular section ridge 306 is left projecting from the etched surface of the slice to fulfil the same function which the round-section wire 18 fulfilled in Figure 1. A tunnel diode is then formed on each side of the ridge 306 by producing small but heavily doped p-type semiconductor regions 308, 308' using an ion implantation or diffusion process. If necessary to prevent leakage currents between the diodes on opposite sides of the ridge 306, the ridge and the material under it may also be converted to an insulating 'p'-type barrier region produced by a diffusion process. The etched surface portions 310,310' are then coated with insulating layers 312,312' of silicon nitride (Si ₃ N ₄ ) except for small areas 314,314' directly over the middle of the

'p'-type regions 308,308', and similar small areas (not shown) over the 'n'-type regions closely adjacent the 'p'-type regions. Printed circuit techniques are then used to produce the connections 316,316' to the 'p'-type regions 308,308' and the other connections (not shown) to the 'n'-type regions. By fixing the device 300 in a shallow recess in the surface of the component to which it is to be attached so that the connections 316,316', etc., are flush or nearly flush to the component surface, electrical leads can be soldered or otherwise brought into electrical contact with the connections after being brought to them along shallow channels in the surface of the component, and disturbance of the boundary layer flow, otherwise then by ridge 306, can be avoided. The backing layer 302, to which the device 300 is adhesively attached, is a carrier member for this and other of the devices and is easily separable from them.

In a further alternative embodiment (not shown), again functioning in the same way as the previous two embodiments, it is contemplated that the diodes and their connections could be formed on a substrate of non-conducting plastic film using thin film, ion implantation and printed circuit techniques as described in connection with Figure 1, the plastic film replacing the enamel layer but being continuous and being suitable for adhesive bonding to any surface (assuming compatible temperatures). The protrusion into the boundary layer could be either a ridge formed integrally with the plastic film or a wire such as 18 in Figure 1 adhesively fixed to it. A suitable plastic film, already known for use in supporting thin film devices, has the trade name "Kapton" (Trade Mark) . This way of forming transducers would be particularly suitable for production of small batches on a continuous length of film, from which transducers could be cut as required.

An alternative to the use of plastic film would be known non-conducting ceramic films, such as alumina or silicon nitride.

The basic idea behind the above three embodiments lends itself to many variations. For example, in Figure 4 is shown a plan view of a transducer device 400 in which intersecting elongate flow disturbers 402,404 on a substrate surface 406 are arranged mutually orthogonally to define an "X"-shape. Again, flow disturbers 402,404 could, for example, be discrete intersecting wires fixed to the surface 406, or else ridges integral with the substrate as already described. In either case the triangular areas 408,409,410 and 411 between the arms of the x-shape include respective tunnel diodes which are electrically isolated from each other within the device and whose 'p'-type regions 412,413,414,415 are placed such that the pressure sensitive junction regions of the diodes are at the apices of the triangular areas, adjacent the intersection of the arms of the x-shape. The diodes may be produced using thin-film or integrated circuit technology as appropriate.

To appreciate the advantages of the Figure 4 embodiment as compared with the Figures 1 and 3 embodiments, it should be re-emphasised that for the latter two embodiments the obtaining of a correct measure of the wall shear stress requires the wire 18 or the ridge 306 to be oriented substantially at right angles to the direction of flow in the boundary layer. For such geometry, the absolute shear stress magnitude is resolved by the diodes in the direction perpendicular to the wire 18 or ridge 306, but if the wire 18 or the ridge 306 intercepts the flow at an angle other than 90°, only a component of the shear stress magnitude is resolved. This fact is exploited in Figure 4 in that the mutually orthogonally arranged ridges or wires 402,404 and the

corresponding pairs of diodes can be used to resolve both wall shear stress and direction. Hence, in the case of a fluid flow vector V, diode pair 412,415 on opposite sides of flow disturber 402 resolve a shear stress component t _χ in a reference direction x defined by disturber 404, while diode pair 412,413 resolve a shear stress component t in a reference direction y defined by disturber 402. From this the true magnitude and direction of the wall shear stress t can be determined relative to the orientation of the device 400 on the surface of a component to which it is attached. Hence, such a device, when adequately calibrated, is able to facilitate accurate measurements of shear stress no matter what the direction of flow over the wall surface in the boundary layer. As an alternative to Figure 4, Figure 5 shows an enlarged plan view of a directionally insensitive transducer device 500 constructed with a flow disturber comprising a central hemispherical protrusion 502 on a substrate surface 504. The device has two 'n'-type semiconductor regions 506,508 electrically separated from each other by a barrier region 510 within the device. Each 'n'-type region 506,508 is provided with a heavily doped semicircular 'p'-type region 512,514 arranged adjacent the protrusion 502 so that apart from the division caused by the barrier region 510, the 'p'-type regions encircle the protrusion. It will be readily seen that the Figure 5 embodiment is therefore capable of facilitating a correct scalar measurement of wall shear stress. Although the above embodiments refer to the diodes being tunnel diodes, it should be understood that any type of semiconductor diode could be used to perform the same function.