05/008340

11/16/1971

02/03/1970

Download PDF 3620651       PDF help

Click for automatic bibliography generation

International Combustion
Limited, London

417/436

440/16, 416/81

B63H11/06; F04B43/02; B63H11/00; F04B19/00; B63H1/30; F03D5/06

417/436,437,476,475,479,481 416/79,80,81,82,83 115/28A

Robert, Walker M.

Hall & Houghton

1. A fluid flow apparatus comprising in combination a. means defining at least one fluid flow path, said means comprising at least one flexible sheet defining a sidewall of said path and another sidewall cooperating with said one flexible sheet, said flexible sheet having the capability of transmitting tension along its length without substantial increase therein, b. a plurality of discrete movable members disposed at intervals along the length of the said flexible sheet and connected thereto, c. means proximate to said members for constraining movement of the latter to impose a traveling wave motion on said flexible sheet, d. said plurality of discrete, movable members including some connected to said sheet at points separated by a distance equal to nλ/2 where n is an integer at least equal to 1 and λ is the wavelength of the traveling wave, said some members being free to move in a direction parallel to the longitudinal axis of the traveling wave, and, e. means interconnecting the ends of said sheet to form a loop for transmitting tension from one end of the sheet round the loop to the other end of the sheet.

2. Apparatus as claimed in claim 1 in which said other cooperating sidewall is a further flexible sheet, said apparatus further comprising f. means for imposing on said further flexible sheet a motion in contraflexing relationship with that of said first mentioned flexible sheet.

3. Apparatus as claimed in claim 1 in which said members comprise a first set of thrust rods each of which is connected, at one end, to the sheet and, at the other end, to the constraining means.

4. Apparatus as claimed in claim 3 and further comprising a plurality of weights distributed along the sheet.

5. Apparatus as claimed in claim 4 in which the weights are spaced uniformly along the length of the sheet.

6. Apparatus as claimed in claim 5 in which some of the weights are connected to thrust rods of the first set and in which the mass of each weight connected to a thrust rod together with the mass of its associated portion of the thrust rod is substantially equal to the mass of any one of the weights not connected to a thrust rod.

7. Apparatus as claimed in claim 1 in which the flexible sheet has a length equal to the surface length of one wavelength of the traveling wave.

8. Apparatus as claimed in claim 7 in which the thrust rods are disposed at each end of the sheet and at positions along the sheet spaced apart by one-quarter of a wavelength of the traveling wave.

9. Apparatus as claimed in claim 2 in which said members comprise a first set of thrust rods, and in which said means for imposing contraflexing relationship on said further sheet comprise a further set of thrust rods which pass through said first-mentioned sheet.

10. Apparatus as claimed in claim 9 in which the thrust rods of the further set are connected to said other sheet at the same positions along said other sheet as the first set of thrust rods connected to the first-mentioned flexible sheet, the sets of thrust rods being connected to said constraining means for movement 180° out of phase with each other.

11. Apparatus as claimed in claim 10 in which each thrust rod is displaceable by an eccentric, the eccentrics being rotated by a common shaft.

12. Apparatus as claimed in claim 1 in which the fluid flow path has an inlet and an exit and further comprising g. a fluid bypass from said inlet to said exit.

13. Apparatus as claimed in claim 12 in which the bypass has a nozzle so that fluid is fed from the said exit directly into said inlet end, in the direction of flow of the fluid stream in said fluid flow path.

14. Apparatus as claimed in claim 12 in which the bypass includes a fluid flow control valve.

15. Apparatus as claimed in claim 1 in which the flexible sheet is of a length greater than one wavelength of the traveling wave.

16. Apparatus as claimed in claim 15 in which the flexible sheet is of tapering width, being wider at the inlet to said fluid flow path than at the outlet thereof.

17. Apparatus as claimed in claim 15 in which the wavelength of the traveling wave reduces along the length of the flexible sheet, being greatest at the inlet of said fluid flow path.

This invention relates to fluid flow apparatus, and has particular, but not exclusive reference to fluid flow apparatus for use as fans.

Conventional fans employ a blade, or a series of blades which are rotated to drive the fluid being pumped from one position to another; this normally entails a fan having a circular section. The object of the present invention is to provide apparatus in which fluid may be pumped by a nonrotating impeller.

By the present invention, there is provided apparatus comprising a fluid flow path, at least one side of the fluid flow path being a flexible sheet, a plurality of members disposed along the length of the flexible sheet and connected to the flexible sheet, the members being constrained to have a sequential movement such that movement of the flexible sheet is constrained to the movement of a traveling transverse wave along the sheet. The members may be oscillatable members.

The ends of the flexible sheet may be operatively interconnected to form a loop capable, in use, of transferring tension from one end of the flexible sheet to the other end outside the sheet. The flexible sheet may be capable of transmitting tension along itself without substantial increase in the length of sheet.

The present invention also provides apparatus which comprises a fluid flow path, at least one side of the fluid flow path being a flexible sheet, a plurality of oscillatable members disposed along the length of the sheet and connected to the flexible sheet, the oscillatable members being constrained to have a sequential movement such that the movement of the flexible sheet is constrained to the movement of a traveling transverse wave along the sheet, the sides of the flexible sheet moving adjacent to, and in the plane of, sideplates.

The present invention also provides apparatus comprising a fluid flow path, which fluid flow path includes a pair of noninterconnected opposed sides, one at least of the opposed sides being a flexible sheet, there being a plurality of oscillatable members disposed along the length of the flexible sheet and operatively connected to the flexible sheet, the oscillatable members being constrained to have a sequential movement, such that movement of the flexible sheet is constrained to the movement of a traveling transverse wave along the sheet.

The oscillatable members may each comprise a thrust rod connected to the sheet at one end, and operatively connected to an eccentric at the other end.

The flexible sheet may have a plurality of weights distributed along the sheet, preferably uniformly along the sheet. The thrust rods may be hollow tubes. The mass of each weight connected to a thrust rod, together with the mass of its associated portion of thrust rod may be substantially equal to the mass of any one of the weights not connected to a thrust rod.

Thus in a particular case, if the mass of a weight not connected to a thrust rod is five units, and the mass of a thrust rod operating four sheets is eight units, the associated portion of the thrust rod will have a mass of 8/4, i.e., two units, each sheet takes one-fourth of the load, then the mass of the weight connected to the thrust rod will be three units, giving a total mass of 2+ 3= 5 units for the connected weight, which is equal to the mass of an unconnected weight.

The flexible sheet may be of a length equal to one wavelength of the traveling transverse wave, and opposite ends of the flexible sheet may be rigidly interconnected. In the arrangement in which the length of the sheet is equal to one wavelength of the traveling transverse wave, the thrust rods may be disposed at positions successively one-quarter of a wavelength from each other along the sheet. The end thrust rods may be constrained by the same eccentric.

The thrust rods may each include at least one universal joint along their length. The thrust rods may be supported in bearings which can be lubricated under pressure, preferably with a lubricant compatible with the fluid passed through the apparatus.

The eccentrics may all be mounted upon a common shaft. In one embodiment of the invention, bell cranks may be used to transmit motion from the eccentrics to the thrust rods.

There may be provided a fluid bypass from the exit end to the inlet end. The bypass may have a nozzle so that, in use, fluid is fed from the exit end directly into the inlet end, in the direction of flow. The bypass may include a fluid flow control valve.

In a further embodiment of the invention the flexible sheet may be of a length greater than one and one-half wavelengths of the traveling transverse wave and may have an operative portion of a length equal to one and one-half wavelengths of the traveling transverse wave and the ends of the sheet may be rigidly interconnected.

There may be provided a plurality of flexible sheets which can be arranged in pairs. Pairs of flexible sheets may be separated by a rigid plate. Alternatively, pairs of flexible sheets may be arranged in contraflexing relationship and may directly face each other.

There may be provided a compressor which comprises at least one flexible sheet having a length of greater than one wavelength of the traveling transverse wave, and of a tapering width, the flexible sheet being wider at the inlet than at the outlet.

A further form of compressor may comprise a flexible sheet having traveling transverse waves of successively reducing wavelength along the sheet in the direction of fluid flow.

The present invention further provides a method of inducing flow in a fluid, said method comprising constraining the fluid in a duct having at least one flexible wall and applying cyclic forces to the flexible wall so as to impose thereon a traveling transverse wave motion whereby the fluid is impelled to flow in the duct in the direction of the wave motion, the kinetic energy in the flexible wall being utilized as an energy reservoir, to spread the energy input from the cyclic forces to the wall to minimize fluctuations in energy input to the fluid from the wall along the length of the wall in the direction of fluid flow.

By the present invention there is also provided a method of generating mechanical energy from a fluid at a relatively high pressure which comprises constraining the fluid in a duct having at least one flexible sidewall, the latter being constrained so as to move in a traveling transverse wavelike motion, expanding the fluid at the relatively high pressure to a relatively low pressure by causing a portion of the traveling wave to move in the direction of the relatively low pressure.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a diagrammatic view of one arrangement of flexible sheets in a fluid flow path.

FIG. 2 is a development of a wave along one flexible sheet.

FIG. 3 is a graph illustrating thrust point loci on the flexible sheets.

FIG. 4 is a graph illustrating the relationship between thrust point displacement, total power, and power per thrust point.

FIG. 5 is a block schematic of a multifan unit.

FIG. 6 is a section through a bond between a sheet and a thrust rod.

FIG. 7 is a section through a bond between a weight and a sheet.

FIG. 8 is a section through a compressor pump embodying the invention.

FIG. 8a is a section along the line XIIA--XIIIA of FIG. 8.

FIG. 9 is a diagrammatic view of an alternative form of compressor.

FIG. 10 is a diagrammatic representation of alternative arrangements of the flexible sheets.

FIG. 11 is an elevation, partly in section of a second embodiment of the invention.

FIG. 12 is a sectional view along the lines XXIA, and XXIB of FIG. 11.

FIG. 13 is a schematic view of a single flexible sheet,

FIG. 14 illustrates a section of FIG. 13.

FIG. 15 is a seal between a flexible sheet and a sideplate.

FIG. 16 is a side elevation, partly in section of a further embodiment of the invention.

FIG. 17 is a plan view along the line XVII--XVII of FIG. 16.

FIG. 18 is a cross section along the line XVIII--XVIII of FIG. 16.

FIG. 19 is a detail of FIG. 16.

FIG. 20 is a cross section along the line XX--XX of FIG. 16.

FIG. 21 is a part view along the arrow XXI of FIG. 20.

FIG. 22 is a detail of a part of the embodiment.

FIG. 23 is an enlarged view of a sheet.

FIG. 24 is a cross section along the lines XXIV--XXIV of FIG. 23.

FIG. 25 is a plan view along the arrow XXV of FIG. 24.

FIG. 26 is a detail of an end joint of the sheet.

FIG. 27 is a cross section along the line XXVII--XXVII of FIG. 24, and

FIG. 28 is a graph of sheet displacement.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

One form of the invention is illustrated in FIG. 1 which shows four flexible sheets 1, 2, 3, and 4 between two walls 5 and 6. Each of the flexible sheets is capable of being vibrated to set up a traveling transverse wave, hereinafter referred to as a traveling wave in the sheet, which moves in the direction of the arrow 7. This will cause a fluid flow in the direction of the arrow 8. The length of each sheet, L, is equal to one wavelength of the traveling wave, and the distance between the walls 5 and 6 is equal to 8 y, where y is equal to the amplitude of the traveling wave in one direction.

Referring to FIG. 2, the advance of the position of maximum amplitude can be followed along the traveling wave. The FIG. shows nine positions of the flexible sheet, from zero to one cycle in steps of one-eighth of a cycle. The positions of maximum amplitude to the left of the flexible sheet (when seen in the drawing) are designated A1, and the positions of maximum amplitude to the right of the flexible sheet are designated A2. If a "lump" of fluid is imagined as being trapped between the position A1, and the tangent to the curve at A2, shown shaded in FIG. 2 it can be seen that the "lump" is moved from the top to the bottom of the diagram. Thus if a traveling wave is set up in a flexible sheet which is sealed off in a manner which will allow it to accept "lumps" of fluid, fluid will be transferred from the input to the output. This is, of course, a pumping action.

It can be seen that the distance along the convolutions of the flexible sheet is greater than the wavelength of the traveling wave in the sheet and is in fact equal to the surface length of the traveling wave. If the loci of a series of fixed points on a pair of contraflexing sheets are followed as the sheets fluctuate, different parts of the sheet will be seen to follow different loci. Considering the sheets illustrated by FIG. 3, the loci of the points E, B, C, D and E', B', C', D (E and E' occur twice as they are at the start of one wavelength and at the end of the adjacent wavelength) can be seen to be straight lines in the case of the points E and C, and figures of eight in the case of the points B and D. When the points B', B and D', D are 180° out of phase, their heights Z at any given point of time are the same.

The traveling wave is set up in the sheet by a series of thrust rods which are described in more detail below. These thrust rods are connected to the sheet at the points B, C, D, and E and cause the sheets to fluctuate. The points E and C have loci which move in straight lines, and thus a simple thrust rod can be used which can reciprocate in a straight line. However, the points B and D move in a figure of eight, and this means that the thrust rod must be capable of reciprocation and also of lateral movement.

FIG. 4 illustrates the relationship between, in the top graph, time and displacement for each of the points B, C, D, and E; in the lower graph, the power needed to be supplied to each thrust point to maintain fluctuation of the sheet; and in the middle graph the total power applied, being a summation of the power applied to each individual thrust point. The points B, C, D, and E correspond with those illustrated in FIG. 3, and the displacement X is in the direction shown in FIG. 3. The power which has to be applied to the thrust point is proportioned to the square of the velocity, i.e., it is a maximum whenever the graph of displacement crosses the central axis, and is zero whenever the graph of displacement indicates a maximum or a minimum.

To give a uniform power requirement, therefore, the flexible sheet has to be oscillated at five points, the input, the output, the center, and two intermediate points. With a sheet occupying one wavelength, however, it can be seen from the above description that the input and the output of the sheet move in step. Thus only four different displacement actions are required to fluctuate the sheet.

So far, a fluctuating sheet has been described which is one wavelength long, and has five bars down its length, which bars are oscillated by thrust rods. The details have been concerned with one particular form of the embodiment in which certain of the thrust rods have loci of movement which are figures of eight. There has been little description of the role of the flexible sheet. However, the sheet is very important, and its role will now be considered, both in respect of its actual motion, and to its part in the transfer of energy between the thrust rods. The sheet has to be flexible in a plane parallel to its longitudinal axis and normal to its surface. The sheet need not be flexible in the two other planes, namely the plane parallel to its transverse axis and normal to its surface, or the plane parallel to the surface of the sheet.

There is a further problem which can be solved by the sheet, and this is the question of the energy involved in accelerating the decelerating the sheet and also the thrust rods. If one rod is considered, it is first accelerated from the rest position at one extreme until it reaches the center, whence to the other extreme position it is decelerated and comes to rest at that other extreme position. Thus energy is imparted to the thrust rod in the accelerating period of movement and has to be dissipated in the decelerating period of movement. One way of doing this would be to connect the thrust rod to an energy storage system, for example a spring or springs. However, this would be an added complication. Referring again to FIG. 3 it can be seen that the points E and C are exactly out of phase, as are the points B and D. Thus the point E is being accelerated by a force which at any time is equal to the force required to decelerate the point C, and vice versa.

The overall power requirement of the system, should it be fluctuating in a vacuum, would therefore be zero. Thus if the thrust rods are considered to be a part of the sheet, the portions of the sheet which are slowing down generate tensions along the sheet that are just sufficient to overcome the inertia forces in the section of the sheet which are accelerating.

Referring to FIGS. 13 and 14, the flexible sheet is shown schematically. The sheet 220 is shown with its midpoint 221 about to make contact with a sideplate 222. The sheet will be under tension in both directions, the tensions being T1 and T2. Onto the enlarged view of FIG. 14 of the point of the sheet which is about to make contact with the sideplate, there has been superimposed a tension vector diagram. The tension vector T1 can be regarded as composed of two further vectors T3 and T4. Similarly the tension vector T2 can be resolved into the two components T5 and T6. It can be seen that the two vectors T3 and T5 cancel each other out, and the result of adding the two vectors T1 and T2 is equivalent to the vectors T4 and T6. Thus, a force applied to a thrust rod at the points 221 can be resolved into tensions along the sheet. Along a whole wavelength of the sheet, these tensions will cancel themselves out. The only points of the sheet which are different are the ends of the sheet. However, if the ends are interconnected by a member which is capable of carrying tensions, then the whole sheet will be in balance.

The thrust rods are heavier than the sheet, and with a plain sheet, the force required to accelerate the thrust rods is greater than the force available from the decelerating sheet. This problem is overcome by increasing the momentum of the sheet by adding weights to the sheet, and reducing the weight of the thrust rod system as much as possible. The sheet can, therefore, transfer energy from the decelerating thrust rods to the accelerating thrust rods.

Such a weighted sheet can also perform the two seemingly contradictory functions referred to above. The sheet can be flexible and yet the inertia forces caused by the weights' accelerating and slowing down generate tensions in the belt which enable it to resist pressure forces in the same way that an inflated balloon is able to resist deforming forces when it is under tension as a result of its internal pressure. This resistance stops the belt being pushed to one side by the fluid on the high-pressure side of the sheet when the sheet is being used as a pump.

To summarize the material requirements of the sheet, to accommodate the slight cyclic flexing of the sheet, the material should have:

1. Small fiber diameter or be of thin multiply sheet.

2. Good fatigue properties.

3. For high-temperature applications, good creep properties.

4. A low value of Young's modulus of elasticity.

5. In multilayer fiber or sheet configurations, good self-lubricating properties.

To accommodate the necessary tension, the material should have;

1. For high-temperature applications, good creep properties.

2. A high value of Young's modulus of elasticity, for minimum stretch, and/or

3. A low level of stress in the wall to ensure a minimum stretch.

Using a thick belt having a low value for its Young's modulus would give rise to the following problems:

1. Self-lubrication limitations.

2. Load sharing between fibers across the width will lead to eventual breakage on the outside of a radius and zero tensions on the inside of the radius.

3. The thicker the belt, the greater the overall cross section of a fan for a given working cross section.

4. With increasing thickness it becomes difficult to ensure adequate anchoring of fibers in the middle layer of the belt.

There is thus clearly a compromise to be made between the contradictory Young's modulus requirements; and the design choice will depend on the performance characteristics and operational environment of a particular embodiment.

One form of the invention is shown in FIGS. 11 and 12. There are four sheets 95, 96, 97, 98 which are reciprocated by the five eccentrics 99, 100, 101, 102, and 103. Considering the sheets 95 and 96, they are disposed one on each side of a center plate 104 and are anchored at each end between rubber buffers 105, 106; 107, 108; 109,110; 111, and 112. The buffers 106 and 111 define two sides of an entrance duct, and the buffers 108 and 109 define two sides of an exit duct.

The eccentric 99 is in the form of an inner circle 113 which is mounted eccentrically upon a shaft 114 and is prevented from rotating upon the shaft by the key 115. Surrounding the inner circle 113 is an outer circle 116, which is clamped between two collars 117 and 118. The upper of the collars, 118, has a hemispherical socket 119, which cooperates with a hemispherical socket 120 to clamp a ball 121 between and form a universal joint. The ball 121 is joined to a further ball 122 by a thrust rod 123, which ball 122 is a second pair of hemispherical sockets 124, 125, and forms a second universal joint.

The second universal joint is connected to a crosshead 126, and the first universal joint has a bearing housing restraint link 127 to counteract the torque developed when the eccentric is operating. The right-hand side of FIG. 12 illustrates the method by which the flexible sheets are secured to their supports. Extending from the crosshead 126a is a thrust rod 128 which carries a reinforcing bar 129. The flexible sheet 95 is riveted between the reinforcing bar 129 and a clamping bar 130 on one side, and the flexible sheet 96 is riveted between a clamping bar 131 and a reinforcing bar 132.

The flexible sheets are riveted at the top and the bottom to an end frame 133. The flexible sheets 97 and 98 are connected to their respective reinforcing and clamping bars. It can be seen that the flexible sheet is supported by the clamping bar on either side of the plate 104.

The shaft 114 is mounted in bearings 134 and 135, and is provided with two sets of balanced weights 136 and 137 each of which comprises a pair of individually variable bobs 138, 139, and 140, 141 which can be adjusted angularly to balance the shaft 114.

The four flexible sheets are provided with a series of weights 142, 143, 144, and 145, the function of which has been explained above.

The unit is operated by rotating the shaft 114, which in turn rotates the eccentrics, and causes the thrust rods to reciprocate the crossheads and the flexible sheets. The points 146 and 147, as seen in FIG. 11, will move laterally and this movement is taken up by the universal joints 148, 149 and 150, 151.

Referring to FIG. 6, the flexible sheet is protected by a pair of rubber cushions 153, 154 where it is joined to a thrust rod 155. A pair of plates 156, 157 is held against the cushions 153, 154 by circlips 158, 159. The cushions are bonded to the flexible sheet, and increase the radius of curvature about which the sheet bends, so reducing the tendency of the sheet to kink where it is joined to the thrust rod, and also reducing bending stresses in the sheet.

One form of seal between a flexible sheet 224 and a sideplate 255 is shown in FIG. 15. The seal 226 is substantially H-shaped in cross section, with the two upper arms, as seen in FIG. 15 splayed apart by contact with the sideplates. In some cases if leakage is not too great a problem, a very small gap can be left between the sidewalls and the edges of the sheets.

FIG. 7 illustrates the arrangement which is used to attach weights to the flexible sheet 152. Again, two annular cushions 160, 161 are bonded to the belt, and a pair of weights 162, 163 are attached to the belt by a rivet 164.

The arrangement illustrated in FIG. 5 shows five flow paths 176 to 180, each of which has one or more flexible sheets, and a motor 181 to 185 to drive the flexible sheet or sheets in its path. To control the unit, one or more of the motors is shut down, and a damper is placed in the flow path to prevent the fluid being pumped from seeping back past the stationary sheet.

One form of a compressor unit is illustrated diagrammatically in FIGS. 8 and 8a. The compressing action in this unit is obtained by causing the gas to pass at constant velocity along a duct of reducing cross-sectional area. This compressor comprises a tapering duct 186 which has four flexible sheets 187, 188, 189, and 190. The sheets are 12 wavelengths long but of a tapering height, i.e., the width of the sheet reduces. This taper is best seen in FIG. 8, and each of the gaps between the lines, e.g. 191, 192 of FIG. 8 indicate one compressor stage. The ninth stage is shown to have an intermediate takeoff duct 193. Each of the exit ducts, the intermediate duct 193, and the normal outlet duct 194, is equipped with a pair of butterfly closure valves 195, 196, and 197, 198, which can be used to control the output of the compressor. In the arrangement shown in FIG. 8 the intermediate duct valves are closed, and the normal outlet duct valves are open, this will give the maximum compression.

An alternative form of compressor is shown in FIG. 9. The compressing action in this unit is obtained by causing gas to pass at reducing velocity along a duct of constant cross-sectional area. This compressor utilizes the flexibility of the flexible sheet. The compressor comprises a fluid flow duct 199, in which there is a flexible sheet 200 which is driven by a series of thrust rods 201 which are reciprocated by the eccentrics 202 on the shaft 203. The shaft is shown to be supported in bearings 204 and 205 at either end. Five chambers can be distinguished, 206, 207, 208, 209, and 210. The two end chambers, 206 and 210 are shown to be open to the inlet and the outlet respectively. It can be seen that the chambers get progressively smaller as they go from the inlet to the outlet. The shape and size of the chambers change continuously as the shaft is rotated, and the chambers appear to move towards the exit and diminish in size. They are able to do this because one of their walls is the flexible sheet which can adopt any required angle and can form a wave which has different wavelengths along its length.

FIG. 9 illustrates a flexible sheet, the operational part of which is two wavelengths long, but the invention can be utilized by sheets of other than a multiple of wavelengths. FIG. 10 illustrates two arrangements using flexible sheets of one wavelength each. The upper arrangement shows a pulsing flow with a single flexible sheet 211 which is mounted at each end in the midpoint of a duct 212. The lower arrangement is different from the other units described above giving a smooth flow, instead of having two rigid walls and a single flexible sheet between them the lower arrangement utilizes two flexible sheets 213 and 214 which are separated by a single plate 215. The minimum length of the plate is one wavelength of the traveling wave, this means that at least one point on the flexible sheet is always in contact with the single plate, and there is no abnormal back passage of the fluid being pumped.

An alternative embodiment of the invention is shown in FIGS. 16 to 27. Referring to FIG. 16, this shows eight flexible sheets 200A to 200H. The four sheets 200A, C, E, and G are connected to move in unison, as are the four sheets 200B, D, F, and H. The sheets are mounted in a duct 201 which is defined by walls 202, 203, 204, and 205. Flanges 206 and 207 are fitted to the ends of the duct to facilitate its positioning in fluid-ducting arrangement. Connected to the sheets 200A, C, E, and G are five pairs of thrust rods 208, 209, 210, and 211. The two end rods 211 move in unison and are designated with the same reference numeral. Similarly, connected to the sheets 200B, D, F, and H are five pairs of thrust rods 212, 213, 214, and 215. The thrust rods of each pair are connected to a crosshead 216, 217, 218, 219, 220, 221, 222, 223, 224, and 225. The crossheads are connected by linkages to an eccentric shaft 226. Connected to the shaft are six eccentrics 227, 228, 229, 230, 231, and 232, which in turn are connected to six shafts 227A ... 232A by means of bearings 227B ... 232B.

It can be seen that the two bearings 228 and 231 are larger than the other four bearings. This is because there are four motions needed altogether, two of them are supplied by the large bearings, and the other two are each supplied by the other two bearings. Thus bearings 227 and 229 act in unison, as do bearings 230 and 232. By aligning the bearings as shown most clearly in FIG. 20, the bearings 227 and 229 balance the bearing 228, and the bearings 230 and 232 balance the bearing 231.

Connected to the shaft 227A are two cross-shafts 223B and 218B. The remainder of the shafts are connected in the following manner (for the sake of completeness, the first shaft has been included again). Shaft Connected Cross-shafts ____________________________________________________________ _____________ _ 227A 223B 218B 228A 222B 219B 229A 223B 218B 230A 217B 220B 225B 231A 224B 216B 232A 225B 220B 217B ____________________________________________________________ _____________ _

the cross-shafts are each supported at both ends by means of bearings. Only one set of these, 219C and 219D is illustrated for reasons of clarity, although each of the cross-shafts is so supported. Each of the cross-shafts forms a pivot bar for a bellcrank arrangement, one arm of the crank 216A ... 225A being connected through a shackle link 216E ... 225E to the crossheads 216 ... 225, and the other arm of the crank 216F ... 225F being connected to shafts 227A ... 232A.

The shafts and eccentrics are housed within the walls 240, which are joined to the main duct 201 through a felt antivibration washer 241, which is mounted between the bottom of the duct 202 and a flange 242 surrounding the walls 240.

The flexible sheet is shown in greater detail in FIGS. 23, 24, 25, 26, and 27. As can be clearly seen in FIG. 23, the flexible sheet 250 is almost entirely covered with a series of slats 251. Each of these slats is in two pieces 251A and 251B, the two pieces each being hollow metal and being riveted together through the flexible sheet. The edges of the pieces are cut back as at 252 to prevent them fouling each other during flexure of the sheet. The stiffening bar type 253 used at the quarter wavelength positions is different to the slats 251. To eliminate the need for bearings at these points, it is not allowed to rotate, and is, therefore, shaped to prevent excessive fiber bending in the sheet, the bar comprising two trough-shaped channels 254, 255 between which are sandwiched two layers of packing material 256, 257. Where the thrust rods 212 are fixed to the sheet, the bar is reinforced by a pair of plates 258, 259 and 260, 261 which are riveted to the bar. The thrust rods 208 pass through holes 262 in the bar 253. The belt is joined to the end thrust rods 215 by being passed around a rod 263, which is slotted into a hole 264 in a terminating block 265. Tension on the sheet results in the rod being pulled against the inner walls 266 of the block and being jammed into the block by a cleat action.

To transfer the tensions in the flexible sheet to the framework, a tie-link is used, as is shown most clearly in FIG. 26. An anchor block 267, is secured to the frame in any suitable manner, and holds one end of a flexible tie 268. The other end of the tie is secured to the terminating block. As can be seen from the drawing, the tie is made up of several layers of belt material wrapped around shaped ends 269, 270, the ends being trapped in the blocks by a wedging cleat action. The mouth 271 of the block 265 and the mouth 272 of the block 267 is shaped so as to keep the radius of bending of the tie at the point of contact with the blocks high.

The termination of the sides of the sheets at the side of the duct is shown most clearly in FIGS. 17 and 18. The sheets 200A ... 200H are trapped along their length between truncated triangular prisms 275, and can move between the sloping faces of the two adjacent prisms. For example, the sheet 200G can move between the faces 276 and 277. The sheets are thus held along their length, and are able to form a seal at the edges when two sheets are adjacent to each other at any point, as for example, the sheets 200E and 200F.

A form of control of the fan is illustrated in FIG. 17. Between the sidewalls 204 and 205 of the duct and the rows of truncated prisms 275 are a pair of channels 280, 281 which extend from the exit 282 to the inlet 283 to the fan. At one end of each of the channels there is a valve plate 284, which can be moved from a shut position, as shown in the drawing, to an open position by rotating the handle 285. The handle rotates a screw-threaded spindle 286, which in turn moves bosses 287, the latter pull moving arms 288 inwards, and thus pivot the plates 284 open about the pivot points 289. A deflector plate 290 is provided at the one end of each of the channels, and a deflector plate 291 is provided at the other end of each of the channels. Streamlined fairings 292, 293, 294 and 295 are provided to smooth the passage of fluid through the duct. If the fan is operated with the plate valves as shown in FIG. 17, the channels 280, 281 are inoperative, however, if the valves are then gradually opened, fluid flows back along the channels and is diverted back again into the duct and fed directly into the fan under pressure. This fluid operates the fan, so very little effective work is lost by the recirculation arrangement.

The materials from which the unit is made would depend upon the function, for example pumping cold air would not present many problems as to the erosion of the belt, and a simple Terylene belt which is similar in manufacture to a conveyor belt would suffice. Under higher temperature conditions a glass fiber belt is envisaged which could be impregnated with silicone rubber. Such a belt should enable operating temperatures of up to 230° C. to be considered. For still higher temperatures carbon fibers could be utilized. The self-lubricating properties of the fibers should enable a dense weave to be used, having a high resistance to gas leakage through the sheet so avoiding the problem of finding a flexible filler suitable for high temperatures. The other parts would be made from rigid materials such as metals or reinforced plastics, having a stiffness and corrosion resistance suitable for the environment being considered.

The theoretical analysis of the function and construction of the device which follows is believed to be correct in its entirety, and is thought to be useful in understanding the exact part played by individual integers of the belt.

The following nomenclature is used in the analysis: Symbol Definition Units A Amplitude of impeller wave ft. B Depth of recirculating channel ft. C _L Pressure loss coefficient for leakage flow - C _RB Pressure loss coefficient for re- circulating flow in the channel - C _RD Pressure loss coefficient for re- circulating flow in the diffusing jet - D Nozzle clearance ft. E Width of recirculating channel ft. F Thrust frame force lb. G Power consumption ft.-lb./sec. g Gravitational constant L Length of impeller wave ft. m Subscript representing maximum - N Frequency Hz. ΔP Fan pressure rise lb./ft. ² Δ P _RB Pressure loss in recirculation channel lb./ft. ² Δ P _RD Pressure loss in diffusing jet lb./ft. ² Q Fan volumetric discharge ft. ³ /sec. q _R Fan recirculation flow ft. ³ sec. q _L Fan leakage flow ft. ³ /sec. R Belt tension force lb. S Number of impellers per fan or module - T Time secs. t Belt clearance ft. U Weight of individual belt mass lb. V Impeller wave velocity ft./sec. V _Lt Leakage flow velocity in min. gap ft./sec. V _RB Recirculating flow velocity in channel ft./sec. V _RD Recirculating flow velocity at nozzle discharge ft./sec. W Width of impeller ft. w Weight of belt plus weights per unit area lb./ft. ² x Coordinate points defining the impeller shape ft. Z Nondimensional ratio defined by equation (31) - ρ _a Density of air at mean fan pressure lb./ft. ³ ρ _w Density of water lb./ft. ³ Overall fan efficiency - η _a Fan aerodynamic efficiency - η _m Fan mechanical efficiency - - Superscript used when a quantity is presented in alternative units - μ Viscosity of air at mean fan temper- ature and pressure lb./ft.-sec. ____________________________________________________________ _____________ _ Main Flow With Leakage

The forward velocity of the traveling wave is given as follows: V=LN (1)

When there is no pressure difference operating across the fan there is no back leakage, and the air is pushed forward at the velocity of the traveling wave. There will also be some forward flow in the leakage gap, Q _m L/LN× 2(A+ t/ 2) W.S. (2)

When a pressure difference is generated across the fan there will be a leakage flow superimposed on top of the forward flow, and this leakage will be limited only by the resistance of the flow channel formed by the sheets. The resistance of the channel will be the sum of contraction losses, expansion losses, and friction losses in varying amounts depending on the flow regime. It is reasonable to evaluate the total loss as a function of the leakage flow velocity head at the minimum cross section, ##SPC1##

It is to be expected that the loss coefficient C _L is a function of the Reynolds number of the leakage flow in the gap. Re=ρ _a V _Lt dh/μ (7) For a very wide narrow slot dh= 4× xt/ 2 x= 2 t (8) where x is slot width Re=(ρ _a q _L 2 t)/(2 tWS μ) or Re=(ρ _a q L)/WSμ) (9)

Thus from experimental data C L can be derived from equation (6) and plotted against the Reynolds number in equation (9).

Deriving the full flow equation for a fan. ##SPC2##

A special case that is worth evaluating is the maximum pressure rise at zero flow, i.e., ΔP _m occurs when Q= 0 notes: i. Using equation (11), if the relationship between C L and Re and the appropriate fan dimensions are known the characteristic relationship between Q and P can be computed. Experimental results can be plotted as loss coefficient as a function of Reynolds Number. ii. The scaling laws are quite precise, and can be best appreciated by examining equations (2) and (12). If the leakage gap is small with respect to wave amplitude then the maximum flow increases directly with increase in fan volume and with increase in fan speed. The maximum pressure rise increases directly as the pressure loss coefficient, as the square of the speed, amplitude and length, and inversely as the square of the leakage gap. Main Flow With Leakage and Recirculation

Flow that leaks back over the sheet, represents a complete loss of energy, and any method of flow control that involves leaking back unwanted flow is going to be very inefficient. Such methods include damper control and variation in amplitude to increase the leakage gap.

Variation of fan speed is a satisfactory method of obtaining control, and so is amplitude variation provided means are used to ensure that the leakage gap is kept constant. However, both would be relatively expensive and a cheap way can be obtained by allowing unwanted air to recirculate outside the main flow and to be returned into the stream through a variable nozzle, discharging in the flow direction. The upstream pressure energy is then converted into velocity energy at the nozzle and as the air jet is caused to diffuse by the resistance of the impellers it does work on the system. The only losses in the recirculating flow are frictional and form drag losses in the duct and nozzle and losses associated with the diffusion process. By proper attention to detail it is anticipated that these losses will be quite small.

The losses will be expressed as two components, one associated with the duct which will be a function of the duct velocity head, and the other associated with the nozzle flow which will be a function of the nozzle velocity head.

ΔP _RB =C _RB (ρ _a V _RB ² )/2 g (13)

ΔP _RD =C _RD (ρ _a V _RD ² )/2 g (14)

Applying the Bernolli equation to the recirculating flow at the point of entry and the point of nozzle discharge. ##SPC3## With recirculation

Q= Q _m -q _L -q _R (19) ##SPC4## Note: i. It will be seen that when D is zero the last term of equation (20) disappears and the equation reverts back to equation (11) as expected. ii. For different values of D a family of different fan characteristics is obtained. Flow control is therefore obtained by changing D, which gives a different fan characteristic crossing the system resistance line at a different flow condition. Efficiency

The system aerodynamic efficiency is defined as

The overall fan efficiency can then be determined by multiplying by the mechanical efficiency.

η=η _a . η _m (22)

The aerodynamic energy losses are in three parts: i. The loss caused by the leakage flow occurring across the full fan pressure rise. ii. The loss caused by the recirculation flow occurring across the pressure difference equal to the losses in the recirculating circuit. iii. The loss caused by the whole flow passing across a pressure difference equal to the friction losses in the sheets. Useful work on gas =Q×ΔP (23) Leakage loss =q _L ×ΔP (24) Recirculation loss =q _R ×(ΔP _RB +ΔP _RD ) (25) Frictional loss =Q _m ×ΔP _f (26)

Notes: i. Equation (27) could be broken down further, but it becomes ponderous and it is better to evaluate the components of the equation as they stand. ii. The frictional pressure loss can be determined by using the equation for the losses in pipes, using an equivalent hydraulic diameter for the sheets. iii. From equation (27) it is clear that if frictional losses are ignored and the recirculation flow is made zero, then the efficiency is equal to the ratio of the main flow divided by the main flow plus leakage. The smaller the leakage the greater the efficiency. Power Consumption and Rate of Working

Work is done on the gas by the impeller at a constant rate. This energy comes from the kinetic energy of the impeller weights, and the resulting deficit of energy is made up as work is done on the weights by the thrust frames. The sheet can therefore be regarded as an energy reservoir into which energy is fed by the thrust frames, and from which energy is extracted by the gas.

This concept can be used to establish a criterion for the belt mass, in that if the ratio of energy extracted by the gas to the ratio of energy present in the impeller is small, then sheet distortions will be minimized. Tests carried out at different energy ratios should indicate at what value the ratio becomes critical.

It is also likely that should the energy of the impeller decrease, there will be a tendancy for the impeller to extract further energy from the push rods. In this way the energy supplied by the push rods will tend to be constant with time. Using this as a basis it is possible to determine the force in each frame due to gas energy requirements.

The sheet equations assuming a sinusoidal shape are as follows: Y= Acos (2π NT+ 2πX/L ) (28) y= - a 2π nsin (2π NT+ 2π X/L ) (29) y= - a 4π ² n 2 cos (2π NT+ 2π X/L ) (30) Force on element dx= wWdx y/g Rate of energy supplied =wWdx y/g y to element dx,

This energy rate is zero as one half of the sheet is supplying work equal to that required by the other half. The rate of internal energy transfer will therefore be given by ##SPC5##

This expression is the parameter against which sheet stability can be judged, and experiment will determine the minimum value of Z that can be used in practice. The higher the value of Z the greater will the stability be. It will be noted that the stability can be improved by increasing the values of w, A, and N and reduced by increasing the gas pressure rise.

It will now be determined for the five thrust frame system how the energy is imparted to the impeller and what forces are involved. It will be assumed that for a high value of Z the energy input will be constant and equal to the energy supplied to the gas.

The energy will also be assumed to be equally supplied by four thrust frames separated by a quarter wavelength. The two end frames will each do one-half of the work of the center frames. It will be shown that a sinusoidally varying force 90° out of phase with the movement meets all the conditions.

F= F _m sin (2π NT+ 2π X/L ) (32) Rate of working =Fy= - F _m A 2π Nsin ² (2π NT+ 2π x/L) This applied for thrust frames at x= 0= L/ 4= L/ 2= 3 L/ 4 ##SPC6## This is the energy per sheet and this can be used to find the work force at any point in the system by considering the number of sheets that are in series beyond that point. It will be noted that this equation demonstrates that the energy requirement is constant with time. Note for one thrust frame

G= π F _m AN ft.-lb./sec. (34) Sheet Shape and Tension Forces

Up till now it has been assumed that the sheet shape is a sine wave. It is known that the coordinates of the sheet that are determined by the thrust frames are on a sine curve because this is arranged by having a large ratio of connecting rod length to crankshaft radius. However, it seems that theoretically the belt in between these fixed positions do not lie on a continuous sine curve. For practical purposes, for the ratio of length to amplitude in which the invention is at present concerned it will be demonstrated that a sine curve assumption is a good approximation. The expressions for the tensions that develop in the sheet will also be derived.

A quarter wavelength portion of belt at a fixed moment in time and having a ratio of wavelength to amplitude of 24:1 approximately will now be considered.

Assuming that the lumped impeller weights lie on a sine curve they have the coordinates as shown in FIG. 28.

For an identical weight U at each point on the sheet and neglecting the weight of the sheet itself,

F= Uy/g lb. from (28) and (30) F= U× 4π ² N 2 /g or

F= ky where k= U . 4π ² N 2 /g (35) therefore F ₁ =0.5× k F ₂ =0.433× k F ₃ =0.25× k Resolving for F ₁

2 . R ₁ ×0.067/1= 0.5 k

Resolving for F ₂ Vertically R ₂ ×0.183- R ₁ ×0.067= F ₂ =0.433 k R ₂ =(0.433+ 3.73× 0.067)k/ 0.183 R ₂ =0.683 k/ 0.183= 3.73 k Check horizontally R ₂ ×0.983 R ₁ ×0.998 Resolving for F ₃ Vertically R ₃ ×0.25- R ₂ ×0.183= F ₃ =0.25 k R ₃ =(0.25+ 3.73× 0.183)k/ 0.25 =0.933 k/ 0.25= 3.73 k horizontally

R ₃ ×0.968 R ₂ ×0.983

These results show that a sine curve is not the true shape of the vibrating belt. However, the horizontal force balances are only, at the most, 2 percent in error, so we can say that for practical purposes the sine wave is a good approximation to the actual curve.

In this case the belt tension is constant and is given by

Considering the sheet, in the case of a glass fiber reinforced sheet:

The sheet fibers are required to transmit tensile forces from one end to the other, and they must also be able to withstand the bending stresses that are set up due to flexing. When utilizing glass fiber, the following data is used as a basis for design: fiber diameter d = 0.0005 inch Young's Modulus E'=11× 10 ⁶ lb./in. ² Tensile strength of freshly drawn fiber =500,000 lb./in. ²

There does not appear to be any reliable fatigue data available for single glass fibers. For example, the design will be on a conservative basis; Assume therefore allowable bending stress f= 5,000 lb./in ² The bending stress for a fiber wrapped around a curved section of radius r. f= E' d/r 2 therefore r= E' d/f 2 r= 11× 10 ⁶ ×0.0005/5,000× 2= 0.55 inch.

Thus, provided the surfaces from which the sheet material unwraps is made 0.55 inch radius or greater, there should be no fatigue problems.

The purpose of the stiffening bar is to transmit gas and decelerating forces over the width of the sheet. The number of operating rods can be varied from one upwards. For two operating rods there is the choice of having them on the ends of the stiffening bar or in the center. By having them at the ends, penetrations through the impellers can be avoided, as also can obstructions in the airflow, but the bending movements are higher, and for a reasonable span the component's weight becomes high. If the operating rods are positioned within the span of the stiffening bars there is one position which gives the minimum bending moment and ensures that no bending forces are transmitted into the operating rods. This can be shown as follows:

At the point of support. ##SPC7##

The correct conditions are obtained if these bending moments are made equal.

Fl 2 /2 W= F(W- 2l) ² /Wl 2

W ² -2l 2 -4 Wl= 0

(W/l 1) ² -4(W/l )-2= 0

l= 0.224 W (39)

W-2l=0.552W (40)

BM= F 0.224 2 W ² /2 W

BM= 0.0252 F _m W (41)

It has been shown above that a sine wave shape for the belt satisfies the changing force requirements of individual mass on the sheet, and that this is done with a virtually constant value of tension forces. This condition will only hold if all the masses are identical. This means that for the operating rod inertia forces to be balanced out by sheet tension, then the mass of each free stiffening bar must be increased to equal the sum of the controlled stiffening bar mass and the associated portion of the attached thrust rod mass.

The conditions at the ends of the sheet are special ones. When the end stiffening bars are in midposition, the inertial force on the stiffening bar is zero, and the vertical component of sheet tension has to be balanced by a force in the operating rods. The force in the rods at one end of the sheet is equal and opposite to the force at the other end of the sheet, and therefore the net result is a balance of inertial forces in the linkage. The horizontal reactions are equal and opposite, and therefore, being interlinked, cancel. The vertical reactions are equal and opposite and produce a couple which is balanceable by an equal and opposite couple from a contraflexing sheet.

When the end stiffener bars are at the extremes of their travels, they develop an inertial force which is only partially balanced by the vertical component of sheet tension. However, it is possible to arrange the restraint link angle to ensure that the horizontal components of the restraint links and sheet tension forces cancel, and that the sums of their vertical components balances the stiffening bar inertia force. In this way the forces sustained by the operating rods is minimized.

When considering the linkages, four movements are required to be transmitted by them, and these are conveniently generated by four cranks at right angles. However, with such a system of cranks, although the forces balance out, a residual primary couple remains, the size of which is dependent on the particular arrangement used. To eliminate this couple, the arrangement shown in FIG. 20 was adopted. The cranks are divided into two groups, each group consisting of two cranks separated by a phase angle of 180°. One of the cranks is split in two and mounted either side of the other. In this way a complete balance of couple at the crankshaft, and also a complete balance of horizontal reactions at the bellcranks. The vertical reactions at the bellcranks cancel, but care has to be taken to provide a symmetrical coupling pattern so that no couple is left.

Although in principle all the primary forces and couples can be balanced out, certain secondary imbalances will remain, however, they are of higher frequency than the primary ones, and in small devices, can be handled by vibration isolation techniques.

It will be appreciated that although the description is in terms relating to a pump, the same unit would operate as a motor if fluid is forced through the unit, motion of the fluid past the flexible sheet would force down the thrust rods, causing the eccentric drive shaft to rotate and keeping the movement of the sheet in step so that it forms a traveling wave. Once such a traveling wave has been set up, it will be maintained by the fluid passing through the flow path, and will operate the unit as a motor.

Use of the fan as described above with reference to FIGS. 16 to 27 as a compressor involves passing fluid into a high-pressure region. Although the fan is capable of so doing, if the back pressure is very high it could give rise to a shock wave suddenly passing through the fluid being discharged as it is opened up to a higher pressure. Such an arrangement is inefficient, and what is required is a method of compressing the gas as it passes through the impeller, this can comprise reducing the wavelength of the sheet towards the exit, reducing the amplitude of the wave, or reducing the width of the sheet.

If compressed gas were to be fed into the exit of a compressor as mentioned immediately above, it would expand and in so doing create pressure differences which would cause work to be done on the sheets. In other words it would be working as a turbine. The turbine would be exactly the same shape as the compressor, but there would be differences in construction because of the higher turbine temperatures. It may be possible to form the sheets to withstand high temperatures without cooling, by constructing them with oxide fibers or carbon fibers, if nonoxidizing gas conditions are obtained. The latter condition should be possible in a gas turbine unit at the cost of some reduction in turbine efficiency if the combustion is arranged with a small oxygen deficiency and sufficient space is allowed for complete mixing to occur. Temperature control would be possible by recirculating spent gas. Turbine and compressor stages could be directly coupled, and the only shaft output required would be the final one to the power alternator. Even that shaft could be dispensed with if it were feasible to produce a special linear alternator to suit the linear action.

Using the fan as a pump for incompressible liquids is also feasible. However, it is thought that because of the size of most small pumps to advantages of the present fan would not be too apparent, and its main use would be for handling large volumes of sludges and slurries.

A further use of the fan would be in relation to vertical takeoff and landing (VTOL) aircraft. With its high power/volume and power/weight ratios the fan would appear to be very useful for such applications.

Although mechanical eccentrics have been described, it will be appreciated that other forms of eccentric may be used, for example a hydraulic coupling could be used based on a swash plate pump. Also an electrical system could be envisaged, in which the thrust rods were operated by solenoids.