Measuring unsteady axial velocity of fibres and threads

Sensors and Actuators A 155 (2009) 89–97

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Measuring unsteady axial velocity of fibres and threads V. Tesaˇr ∗ Institute of Thermomechanics of the Academy of Sciences of the Czech Republic, v.v.i., Dolejskova 5, 182 00 Prague, Czech Republic

a r t i c l e

i n f o

Article history: Received 3 March 2009 Received in revised form 10 August 2009 Accepted 13 August 2009 Available online 22 August 2009 Keywords: Thread Fibre Fluidics Fluidic sensors Colliding jets

a b s t r a c t To measure – in fact even sense – axial motions of fibres and threads is difficult. Especially synthetic fibres may lack any distinguishable features on their surface, so that they seem to be motionless and optical sensing fails. The motion may be transferred by friction to a mechanical component (e.g., a pulley) the speed of which is measured, but this fails if the fibre motion is unsteady (periodic—a common situation in textile machinery). The unique solution by the described fluidic sensor was developed to measure velocity of the weft in shuttle-less looms. In the sensor, the weft passes axially through colliding air jets, accelerating one of them while the opposite jet is slowed down. Output signal is the pressure difference in collectors surrounding the stagnation point of the collision (and converted by a differential pressure sensor to the electric output). The design successfully tested is described in detail. Surprisingly, later performed computations discovered that the sensor actually operates in a manner not in complete agreement with the original idea upon which its design was based. © 2009 Elsevier B.V. All rights reserved.

1. Introduction If an extremely elongated (and usually flexible) object like a fibre or thread moves in the direction of its longitudinal axis, the motion is practically impossible to percept visually. Measuring its speed by optical methods is therefore difficult. Dye marks may be applied on the fibre surface but besides the operation increasing the costs the marks may be not acceptable for the final appearance of the final product made of the fibres. Correlation measurements or an application of the laser Doppler anemometer principle are possible if there are enough optically distinguishable natural irregularities on the fibre surface. These, however, are practically missing on synthetic fibres made by continuous processes. The optical methods (because of their complexity) tend to be expensive and, most importantly, fail if the velocity varies fast, since the detectable features may be not always present in sufficient numbers everywhere. If the motion is steady, the common solution is to measure the rotational speed of a pulley with which the fibre is in contact, as shown in Fig. 1. This ceases to be practicable, however, when the motion is unsteady – accelerated and decelerated. Because of its inertia, the pulley then slips and fails to follow the fibre motion. The slipping may be countered by increasing the contact angle ˛ (Fig. 1), but the forces needed to accelerate the pulley then may be in excess of the fibre tensile strength. Yet there are applications in which measuring the unsteady axial motion is not only useful but also quite important. Typical examples

∗ Tel.: +420 2 66052270. E-mail address: [email protected]. 0924-4247/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2009.08.011

are found in the weaving machinery (e.g. [1]) where, for example the thread or fibre weft in a shuttle-less loom is moved axially as it is inserted into the shed formed between the system of warp threads (Fig. 2). To increase productivity, present-day weaving is a very fast process. The weft is accelerated – and then decelerated – often more than 500 times per minute up to speeds around 50 m/s (though lower values, near to 15 m/s, are more typical, e.g. [2]). One reason for measuring the weft motion is the fact that even small departures form the proper acceleration and deceleration pattern in each weaving cycle are an important signal for the operational diagnostics system of the loom. This diagnostic application was the original impetus for the development of the discussed sensor. Another use for the developed sensor was then found in pneumatic shuttle-less looms in which the insertion nozzle action is assisted by relay nozzles placed along the weft path (Fig. 2). The sensor signal carrying information about weft speed may be used to evaluate, by integration, the instantaneous position of the “head” (front end) of the inserted weft. This makes possible control of the supplied compressed air into the individual nozzles in a manner approaching the optimum insertion: the weft is kept straight (suppressing its tendency to snaking and forming loops) and it is possible to save considerable amount of the expensive supplied compressed air otherwise admitted indiscriminately. 2. Colliding-jets fluidic sensor The fluidic solution of the seemingly impossible to solve problem of measuring the weft insertion speed and its variations during the operating cycle is simple and surprisingly inexpensive. It is

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Nomenclature b cP d P P PS PY PY1 PY2 Re s S S1 S2 u

v w1 V X Y Y1 Y2

nozzle slit width [m] pressure coefficient [dimensionless] diameter of hole in splitter plate [m] pressure [Pa] pressure difference [Pa] supply pressure difference between S and V [Pa] output pressure difference [Pa] pressure difference between Y1 and V [Pa] pressure difference between Y2 and V [Pa] nozzle exit Reynolds number [dimensionless] splitter plate thickness [m] supply terminal first supply terminal second supply terminal fibre or thread speed [m/s] specific volume [m3 /kg] time-mean axial velocity [m/s] vent Input output terminal first output terminal second output terminal

based on adapting [3] the principle of fluidic colliding-jets amplifiers as described e.g. in [4,5]. These use two jets issuing from mutually opposed nozzles – usually round ones with their axes coincident – impinging head-on upon one another. If the nozzle shapes, supply pressures, and other conditions are equal, a stagnation point is formed at the position halving the distance between the two nozzles. The colliding flow streamlines are bent there to a direction perpendicular to the common axis of the two nozzles and leave together, forming a radial jet. This behaves as if it were issuing radially from the stagnation point. In the sensor, as shown in Fig. 3, the cavity in which the radial jet is generated is divided by a radial splitter positioned so that it surrounds the stagnation point. The splitter divides the radial jet into two parts each leaving on one side of the splitter. In the basic balanced state the two parts are equal, each leaving through its output outlet located at one side of the splitter. The sensor uses the fact that the position of the stag-

Fig. 1. Classical solution of the problem of measuring the axial velocity of a fibre motion: measurement of the rotational speed of a pulley the circumference of which is in contact with the fibre. The idea fails if the fibre is accelerated: the pulley either slips or, if the contact angle ˛ is made large to increase the friction force, the fibre tends to tear.

Fig. 2. A typical example in which measuring axial fibre motion is useful: compressed air is supplied into the relay nozzles of a shuttle-less loom not continuously but modulated in dependence on the instantaneous position of the inserted thread. The position is computed by integrating the velocity signal from the weft speed sensor positioned net to the insertion nozzle.

Fig. 3. A fluidic solution of the fibre velocity measurement problem—an illustration from the original Patent [3]. This is a version with eccentric position of the splitter intended for detecting deviations from a pre-set fibre velocity.

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nation point – and the consequent distribution of the flows into the two outlets – is very sensitive to disturbances acting on the jets. In the fibre speed sensing application, the sensor is arranged so that the fibre is arranged to move through both opposed nozzles and through the jets issuing from them, passing through the common axis. While the fibre drags along one of the jets, increasing its momentum, its slows down the opposing one. This causes the stagnation point to move away from its balanced position. The resultant difference between the two output flows is sensed as the differential fluidic signal. In general, propagation of fluidic signals is slow and if they travel over a longer distance their amplitudes and waveshapes are deformed. The fluidic outputs are here therefore converted into the required electric signal by a pressure transducer located as near as possible to the fluidic sensor. Transducers reacting to pressure are preferred for the conversion though those sensing flow may be also used. The pressure transducers, as a rule, do not admit a fluid flow through them. A slightly different layout of the output than in Fig. 3 is thus advisable. The fluid from the colliding jets is left to leave the sensor body through vents V into the atmosphere—while the pressure output is generated by quite narrow collectors, positioned on the both sides of the splitter and connected to the fluidic output terminals Y1 and Y2 . The electric output signal generated by the transducer is proportional to the difference between the instantaneous pressure levels in the terminals Y1 and Y2 . In a design intended for practical use on a loom it would be practical to place the transducer inside the sensor body. For flexibility of the conditions in laboratory tests (different transducers and sensor versions), however, it was preferable to connect the transducer to the sensor collectors by short, small-diameter tubes. With their small fluidic capacitance [5,6], together with the small volume inside the collectors, the width of the fluidic signal frequency band was sufficiently wide for detecting all the details of interest in the acceleration and deceleration time histories. It should be noted that the sensor, with its two nozzles, two collectors, and the difference character of the output has certain features of a pneumatic Wheatstone bridge. In the balanced zerospeed state it is therefore insensitive to variations of temperature or supply pressure, which act simultaneously in both branches of the bridge and are eliminated when as the output signal is taken the difference between the two output terminals. Of course, the actually measured quantity is the degree of unbalancing so that the disturbing variations in actual operation are not eliminated completely—nevertheless even then there is some suppression of the disturbances. In case of applications in which the fibre does not slow down to zero during the cycle or where there is a certain velocity the deviations from which it is desirable to detect, the sensor may be easily made in an asymmetric version, as is the case shown in Fig. 3. An even less expensive alternative may use for the conversion into the electric output two thermistors, placed each on one side of the splitter [7,8]. Their frequency band may be increased by connecting them in a feedback loop, keeping them at a constant temperature. The problem of bringing the fibre into and out from the high pressure chambers upstream from the two nozzles is actually easy to solve. Experience shows no caulking or gaskets are necessary, the fibre is simply led through small-diameter gland channels. Some fluid is inevitably lost into the atmosphere through them, but the amounts are practically be negligible. In fact, the fibre motion in these channels causes a welcome positive (on one side) and negative (on the opposite side) pumping effect. This pumps some air into the left-hand side nozzle in Fig. 3 – the side on which the jet is to be promoted – and pumps some air out from the opposite sight-hand side nozzle in which it is desirable to decrease the momentum of the jet. The effect – especially with long channels – may be strong enough to be used as the sole pressure-difference generating action

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Fig. 4. Photograph of the tested version of the fluidic colliding-jets sensor.

in another sensor version [9]. It is also possible to generate eliminate the loss of air through the gland channels by generating a jet-pumping effect if the inlets into the nozzles are shaped to form a jet pump. Instead of losing some compressed air into the atmosphere through the sealing duct gland, the jet-pumping suction effect would actually cause some air from atmosphere to move into the sensor through these channels. 3. Experiments A sensor for laboratory tests based on the principles discussed in the previous part 2, operating with air and using the pressure transducer for the conversion into the electric output signal was designed by the author. Because of the feasibility study character of the tests and foreseen necessity of changes, the device was designed as composed of easily removable components, made by classical workshop methods—turned from steel on a lathe and stacked in a cylindrical cavity inside the body shown in Fig. 4. Supply inlets and output outlets were short brass ferrules passing through the slot on one side of the body. The section drawing in Fig. 5 provides

Fig. 5. Drawing of a section through the fluidic sensor test model from Fig. 4 in its original configuration.

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Fig. 6. Individual components of the original fluidic sensor test model.

an idea about the internal layout. Photograph of the components is presented in Fig. 6. The main design constraint was the requirement of the axial length – the horizontal overall length in Fig. 5 – short enough for the complete sensor fitting into an available relatively short free segment of the weft path on a loom upstream from the insertion nozzle. To make the overall length small, the nozzles in the sensor were configured so that the bodies containing the fibreinlet and fibre-outlet channel glands, shown at both ends in Fig. 3, were placed inside the upstream chambers of the nozzles. The air supplied into the jets leaves the body through the six axially oriented went holes V at both ends of the body. Noteworthy are the small internal volumes of the radial collector, designed to limit their fluidic capacitance [5] that might in principle decrease the achievable upper boundary frequency. Most fibre specimens available to the author for use in the tests were very thin, single-fibre polyester material, with very smooth glossy surface, certainly not very efficient for dragging along the surrounding air. The two opposed nozzles were chosen to be of 1.2 mm inner diameter, with their exits 12 mm (i.e. 10 diameters) apart axially. This means each jet had to travel a distance equal to ∼5 diameters from the exit to the stagnation point of the mutual impact. This is a distance where without the fibre the jet would still have its potential core. Even with the fibre present the jets could be expected to posses a rather high

kinetic energy utilised in generation of the radial jet captured by the collectors. The design was guided by the idea of the output signal – the variations of the output pressure differences – generated by axial translations of the stagnation point. The translation distance was expected to be rather short. It was assumed that because of the expected rather small air-dragging effect, the stagnation point would remain inside the central passage hole of the relatively thick – 2 mm thickness – radial splitter. The passage hole was of 3 mm diameter and had rounded inner surface (rounding diameter 1 mm, Fig. 5). Rough estimates of the changes in relative jet momentums led to expectation that the translation of the stagnation point due to the fibre motion would be within the range of about only 2 mm. Most of the initial feasibility tests and all later calibration of the sensor with a particular weft grade were made in steady states, at a constant fibre speed. The setup for this purpose, shown schematically in Fig. 7, compared the sensor output with the fibre velocity measured by the rotating pulley principle of Fig. 1 (acceptable in this case because of the steady motion). The pulley, driven at a varied speed, has actually also driven the fibre. The pulling force was increased by the fibre pushed towards the pulley by the rubber rim of a spring-loaded wheel. The pressure difference response was investigated for gradually varied fibre speed at a particular constant supply pressure that was kept constant. Initial experience has shown the sensitivity of the device to be too small. To obtain reasonably measurable output pressure differences, the supply pressure levels PS were to be of the order of 10 kPa and yet the sensor was producing outputs in only 1 Pa range, i.e. 10,000-times smaller. This unfavourable results necessitated the design to be adapted. The prime factor limiting the sensor performance was the short length at which the air-dragging action of the fibre could act on the two opposing jets. This was due to the original limitation of the overall sensor length in the direction of fibre motion. After discussions with the loom manufacturers, a possibility was found for increasing by small changes on the loom the overall sensor length by ∼15 mm. The distances to be travelled by the jets before their collision, were increased by this distance by means of the inserts shown in Fig. 8 so as to give the fibres more opportunity for the dragging action on the jets. Of course this, on the other hand, meant the jets would arrive towards the stagnation point with less kinetic energy. Because of the rather unfavourable experi-

Fig. 7. Schematic (not to scale) representation of the sensor calibration. Because the speed was steady, the differential output pressure signal could be compared with pulley rotation speed measurement according to Fig. 1.

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Fig. 8. Geometry of the later, improved fluidic sensor with longer jets and a thin splitter plate.

ence gained with the original thick, rounded-hole splitter (together with an effort to get additional length of the jets even by a small amount) the splitter was replaced with a very thin disk of thickness s = 0.3 mm. Several tests with various central hole diameters also indicated that it is possible to obtain better output pressure difference with smaller diameter d. Its size was finally chosen to be d = 2.2 mm. The mean lengths of the jet on which they were exposed to the dragging action of the fibre were thus increased to 12.55 mm, i.e. slightly more than to 10.5 nozzle exit diameters. The geometry of the resultant adapted configuration is presented in Fig. 8. The next Fig. 9 presents a typical example of measured pressure output signal as a function of the fibre velocity in steady-state regime obtained with the adapted sensor. The sensitivity was increased indeed. The output pressure levels were still rather low, but within the sensitivity range of the transducer. Typically the output pressure differences of ∼220 Pa were roughly 100-times lower than the 22 kPa supply pressure. An important favourable fact is the practically perfect linearity – throughout the whole range of the tested states – of the dependence of the output signal on the mea-

Fig. 9. An example of the calibration: dependence of the output pressure difference on the speed of a polyester fibre (of rather large, 100 den size) at a constant supply pressure obtained with the geometry shown in Fig. 7.

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Fig. 10. Internal cavities of the tested sensor, representing the computational domain of the performed numerical flowfield solutions. The basic idea was the output collectors are hit by the radial jet issuing from the stagnation point. If the fibre moves in the sense indicated here, the displacement of the stagnation point towards the “downstream” collector should produce PY2 > PY1 .

sured fibre speed. The two recognisable regions of slightly larger deviations R1 and R2 were found to be due to a resonance in the test rig. The linearity, of course, is of particular significance for proper measurements of unsteady changes. A strange situation arose during the tests. The pressure difference was found to be actually very opposite to what was expected. The displacement of the stagnation point towards the “downstream” collector Y2 was expected to produce a higher pressure in the output connected to it, i.e. PY2 > PY1 . What was actually found was the very opposite: the upstream collector pressure was higher than in the downstream one, PY1 > PY2 . Nevertheless the sensor worked and was successfully used. 4. Computational studies The sensor fulfilled the task of monitoring the weft acceleration and deceleration pattern during the loom working cycle in testing and development of the looms. For the use in large quantities (one sensor per loom) to control the air supply into the relay nozzles (according to Fig. 2) it was felt it had to be more robust and to exhibit, in particular, a higher sensitivity. At the time, the problem that limited the further development was insufficient understanding of the actual aerodynamic processes that take place inside the interaction cavity and therefore insufficient knowledge about the character of the desirable changes. The small dimensions and the axisymmetric layout, with the critical locations hidden inaccessibly inside the body, did not offer much opportunity for either inserting some velocity probes or for application of flow visualisation methods. There was still, as a “skeleton in the closet”, the opposite actual pressure difference effect, which remained unexplained. An opportunity for obtaining a better understanding came with the availability of modern computational software. The flowfields inside the body – in the computational domain shown in Fig. 10 – were computed using commercially available software FLUENT. With the exception of the six vent holes, the domain was axisymmetric. Since the vents were in locations where the air flow velocities were very small and had therefore little influence on the flowfield in the critical central part, no serious impairment resulted from replacing the vent holes by an equivalent annular space. The resultant axisymmetric domain could be then much faster solved using the two-dimensional variant of the software. The domain was discretised by an unstructured triangular grid which was adapted during the computational run by successive refinements in locations of high absolute velocity gradients. Typically, the refined grid possessed some 60,000 triangular elements. The computation was performed using standard two-equation model of turbulence with

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Fig. 12. Results of numerical flowfield computations: pathlines obtained for u = 12 m/s (i.e. at the speed below the change of the slope) for the conditions indicated in Fig. 11.

Fig. 11. A typical result of numerical flowfield computations. The output pressure difference is here much higher than in the experiments because of the large chosen fibre diameter. A surprising fact is the change in the slope of the dependence at larger fibre air-dragging action.

the low turbulence Reynolds number regions handled by the RNG approach. The numerical values of the turbulence model constants were retained as provided by the software supplier. The boundary conditions were (a) the atmospheric conditions in the outer space into which led the vents V, (b) equal supply pressure in both supply terminals leading into the nozzles, and (c) a constant horizontal velocity of the fibre surface. Fibres of various diameters could be used as alternative boundary conditions surrounding the symmetry axis. Initially, the interest concentrated on reproducing the experimentally determined characteristics—the output pressure difference as a function of fibre speed, as shown in the example in Fig. 9. The computed characteristics, indeed, were satisfactory in being also linear. The numerical solutions could be made even for conditions (very high fibre speed or size) outside of the range of experimental data. This has shown an effect which was not found in the experiments, namely the change of the slope of the characteristic obtained with extremely large fibre sizes, an example of which is presented in Fig. 11. That the characteristic remained linear beyond this change was, however, quite surprising: what could be expected was a saturation behaviour due to the stagnation point of jets collision having moved too far from the collectors. In the search for the explanation of this effect, closer studies were made of the internal flowfield inside the sensor. In particular, conditions corresponding to those indicated in Fig. 11 and differing the value of the fibre speed u are presented in Figs. 12 and 13. The illustrations present the computed pathlines – trajectories of imaginary particles – released from the two nozzle exits. In the first one (Fig. 12) the fibre speed was u = 12 m/s and the conditions correspond to the standard regimes as encountered in the experiments. In the other case (Fig. 13) the fibre speed was 3-times higher, u = 36 m/s, and the conditions correspond to the regime well above the “kink” in the characteristic.

Interesting additional information about these two regimes is provided by the following Fig. 14. It presents, for the same two cases differing in the value of the fibre speed, the axial distributions of the axial component of time-mean velocity obtained by the numerical computation in the immediate neighbourhood of the fibre surface (0.1 mm above the 0.4 mm thick fibre). Qualitatively, the two distributions in Fig. 14 are the same. Both exhibit an expected, immediately apparent asymmetry due to the fact that even at the extreme positive and negative axial locations outside from the sensor the air moves with considerable velocity as it is dragged along with the moving fibre. Of importance for the output signal are the locations of the zero-velocity stagnation points. The sensor design was guided by the idea of the stagnation point remaining very near to the midpoint between the two nozzles, translating axially only by the small distance sufficient for moving the generated radial jet towards the downstream collector. What the flowfield computations show, however, is a different situation. The most remarkable difference between the flowfields in Figs. 12 and 13 is the remarkable presence of the standing vortex E in the latter case. Such standing vortices tend to be rather unstable. The performed steady-state computations, of course, show them as stationary, but in reality they quite often tend to be shed and moved away with the flow, even if the walls are shaped so as to form a toroidal cavity keeping there the large captive vortex in the case studied by [10] (cf. also the discussion by [11,12] and also by [19], of the idea due to [13], based on Welzenbach’s 1930 observations of snow cornices [14]). Such cavity is not there in the present case and this makes the idea of their stationarity rather suspect. If this vortex E is indeed the only difference found in the flows for the conditions above the “kink”, then the absence of any such “kink” in the experimental characteristics may be not only due to their appearing only at extremely large translations of the stagnation point, but also due to their absence by being carried away with the flow in real flowfields. Yet another interesting view of the internal flowfield inside the sensor is presented by the computed example in Fig. 15. It is a grey-scale rendering of the original coloured contours of absolute velocity for the conditions below the “kink”. It is obvious there that the critical role is played by the small size of the passage hole in the splitter disk. It allows for only a percentage of the air of the

Fig. 13. Results of numerical flowfield computations: pathlines obtained for fibre speed u = 36 m/s at otherwise the same conditions as in Fig. 12. The lower slope of the line in Fig. 11 at the high speeds is explained by the formation of the stationary vortex E.

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Fig. 14. Results of numerical flowfield computations: distributions of the velocity of air flow in the close neighbourhood of the fibre surface for two different fibre speeds. Stagnation (zero velocity) points are much further away than expected from the central location between the nozzles.

“upstream”(i.e. left-hand) jet to pass through and interact with the opposite jet, as is also apparent from Fig. 12. A considerable amount of the “upstream” jet air is diverted along the upstream wall of the collector towards the upstream vent (i.e. it leaves the sensor on the left-hand side). The unexpected extreme downstream (i.e. right-hand side) position of the two stagnation points in the computed results presented in Figs. 12–15 obviously means that the small part of the upstream jet passing through the splitter hole is the energetically most powerful part—moreover accelerated, of course, by the air-dragging effect of the moving fibre also passing there. This is why it manages to translate the stagnation point so far downstream. For such very distant stagnation point locations it was not expected, according to the original idea of sensor operation, that there would be any pressure difference found between the two collectors Y1 and Y2 . An yet the computations not only

show the pressure difference to be there, but shows it to continue increasing in magnitude as the fibre translational speed u further increases. 5. Surprising phenomenon of “swapped outputs” Obviously, the sensor operation mechanism differs from the simple idea of axial translation of the radial jet virtually emanating from the stagnation point and thus acting with different intensities in the two collector entrances. The computed character of the output pressure generation is in variance with this original idea. It is most apparently reflected by the diagram in Fig. 16 The shifting of the stagnation point in the direction of the fibre motion should decrease the kinetic energy of the part of the radial jet entering the upstream collector Y1 (since only lower velocity outer part of the radial jet gets there) and increase what is captured by Y2 (since

Fig. 15. A typical example of the computed velocity field inside the sensor, u = 16 m/s. Higher velocity is represented by darker shade of grey colour (note the scale at right).

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Fig. 18. Schematic representation of the actual mechanism of generating the output pressure difference PY1 > PY2 . Impingement stagnation pressure acts in the upstream collector Y1 because the small passage hole in the splitter permits only a small fast jet getting to the downstream side, where it generates a jet-pumping effect in Y2 .

that it is the pumping by the jet passing through the central passage hole in the splitter plate. 6. Real mechanism of output generation

Fig. 16. Computed pressure differences between the two collectors and the surrounding atmosphere. Note that (according to Fig. 10) the collector Y1 is upstream (at left-hand side) and Y2 downstream.

it receives the higher velocity portion). In the experiments, however, the upstream collector pressure was found to be higher than in the downstream one, PY1 > PY2 . At that time, the effect was relegated as being probably due to accidentally swapped output tubes or perhaps output wires from the transducer. The computed values in Fig. 16 demonstrates that PY1 > PY2 is a real fact, the tubes were certainly not swapped. This is also documented by the example presented in Fig. 17, which shows grey-scale filled contours of computed pressure field for the conditions (u = 36 m/s, i.e. with the recirculation vortex E) same as the pathlines in Fig. 13. The high pressure PY1 in the collector Y1 is immediately apparent. Perhaps less apparent is the low pressure inside the “downstream” collector Y2 and yet Fig. 16 clearly demonstrates that it is this low downstream pressure and its steeper slope of faster decrease with increasing fibre speed u that is mainly responsible for the generation of the measured output pressure difference. Obviously, this low pressure (at high fibre speed actually lower than atmospheric) must be a consequence of some jet-pumping effect. Figs. 13 and 15 show quite convincingly

Fig. 17. Astounding explanation of the “swapped tubing”: the pressure in the upstream collector (note that higher pressure is here shown in the lighter shade of grey) is actually higher than that in the downstream collector, PY1 > PY2 . The sensor operates in a manner opposite to what its designer expected.

The results of the performed computations gave a clear picture of the actual mechanism that produces the output pressure difference. Schematically, the directions of the main flows are presented by the dark lines in Fig. 18. In addition, the light grey lines indicate the trend of the motion that would be present if the collector outputs were not blocked by the connected transducer and would permit some flow passing through them. This motion trends are indicative of the direction in which local pressure rises. The term “splitter” is in the present context obviously inappropriate. It does not split a radial jet. The pressure rise in the collector Y1 on the upstream, left-hand side of the splitter is in fact due to the impact pressure by the flow from the upstream nozzle. This flow is slowed down near the entrance into Y1 and divides there into the smaller (but more energetic) amount passing through the hole in the splitter and the larger amount bent to follow the outer wall of the collector body. On the other side of the splitter, the jetpumping action decreases the pressure PY2 in the “downstream” collector Y2 . Diagram Fig. 16 shows this jet-pumping to be quite

Fig. 19. Actual later version of the weft insertion speed sensor; the discussed colliding-jets principle is combined with the fluidic amplification [5,15]. The key problem in these designs is proper matching [18] of the sensor and amplifier properties.

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effective – it loses the effectiveness (Fig. 16) when the fibre speed reaches the level at which the computations predict the presence of the standing vortex E (Fig. 13).

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the research plan AV0Z20760514 are gratefully acknowledged. The sensor used in the experiments was made by Mr. E. Hokeˇs. References

7. Concluding remarks The described sensor performs a task which would be hardly executable by another known principle of the fibre or thread speed measurement – perhaps with the exception of the much more expensive, more sensitive, and less reliable optical correlation method. Especially on pneumatic shuttle-less looms, with their readily available source of compressed air, the solution offered by the described idea can be hardly beaten by another principle. Rather surprisingly, the sensor did operate even though it was built following a different (and wrong) idea of the acting mechanism, leading to the very opposite pressure difference than expected. The solution of the enigma by the performed numerical flowfield computations now provides paths to follow towards improving the efficiency—especially increasing the generated output pressure difference levels, which were rather low in the original device. Another readily applied possibility how to increase the output signal is to use a fluidic signal amplifier as presented as integrated into the sensor body in Fig. 19. The axisymmetric design of the model used in the tests may be – with several advantages – replaced by the planar layout, perhaps with the cavities fabricated by a photochemical method [16]. Whenever available space permits, the performance may be also increased by making the fibre-guiding channels long. Other alternatives, also already tested, described by [15], increase the generated output pressure difference by providing a jet directed perpendicularly to the fibre and deflected by its motion – an advantage of this layout is suppression of the turbulence noise of the colliding jets. Another interesting solution, according to [8], uses the an integrated fluidic high-frequency oscillator, the frequency of which is modulated by the motion of the fibre. Useful theoretical and numerical solution introduction into the problem of dragging the surrounding fluid by a fibre was presented in [17]. Acknowledgment Support by research grant IAA200760705 from the Grant Agency of the Academy of Sciences of the Czech Republic, by the grant 101/07/1499 from the Grant Agency of the Czech Republic, and by

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